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Higher-order Motif-based Time Series Classification for Forced Oscillation Source Location in Power Grids
Published 23 Jun 2023 in cs.LG and stat.ME | (2306.13397v1)
Abstract: Time series motifs are used for discovering higher-order structures of time series data. Based on time series motifs, the motif embedding correlation field (MECF) is proposed to characterize higher-order temporal structures of dynamical system time series. A MECF-based unsupervised learning approach is applied in locating the source of the forced oscillation (FO), a periodic disturbance that detrimentally impacts power grids. Locating the FO source is imperative for system stability. Compared with the Fourier analysis, the MECF-based unsupervised learning is applicable under various FO situations, including the single FO, FO with resonance, and multiple sources FOs. The MECF-based unsupervised learning is a data-driven approach without any prior knowledge requirement of system models or typologies. Tests on the UK high-voltage transmission grid illustrate the effectiveness of MECF-based unsupervised learning. In addition, the impacts of coupling strength and measurement noise on locating the FO source by the MECF-based unsupervised learning are investigated.
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[2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zeyringer, M., Price, J., Fais, B., Li, P.-H., Sharp, E.: Designing low-carbon power systems for great britain in 2050 that are robust to the spatiotemporal and inter-annual variability of weather. Nature Energy 3(5), 395–403 (2018) Fadlallah et al. [2013] Fadlallah, B., Chen, B., Keil, A., PrÃncipe, J.: Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Phys. Rev. E 87, 022911 (2013) Zhang et al. [2020] Zhang, Y., Gan, F., Chen, X.: Motif difference field: An effective image-based time series classification and applications in machine malfunction detection. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 3079–3083 (2020) Orazov et al. [2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Fadlallah, B., Chen, B., Keil, A., PrÃncipe, J.: Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Phys. Rev. E 87, 022911 (2013) Zhang et al. [2020] Zhang, Y., Gan, F., Chen, X.: Motif difference field: An effective image-based time series classification and applications in machine malfunction detection. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 3079–3083 (2020) Orazov et al. [2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, Y., Gan, F., Chen, X.: Motif difference field: An effective image-based time series classification and applications in machine malfunction detection. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 3079–3083 (2020) Orazov et al. [2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. 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[2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Fadlallah, B., Chen, B., Keil, A., PrÃncipe, J.: Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Phys. Rev. E 87, 022911 (2013) Zhang et al. [2020] Zhang, Y., Gan, F., Chen, X.: Motif difference field: An effective image-based time series classification and applications in machine malfunction detection. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 3079–3083 (2020) Orazov et al. [2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, Y., Gan, F., Chen, X.: Motif difference field: An effective image-based time series classification and applications in machine malfunction detection. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 3079–3083 (2020) Orazov et al. [2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). 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[2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, Y., Gan, F., Chen, X.: Motif difference field: An effective image-based time series classification and applications in machine malfunction detection. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 3079–3083 (2020) Orazov et al. [2012] Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. 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Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. 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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. 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[2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. 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In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Orazov, B., O’Reilly, O.M., Zhou, X.: On forced oscillations of a simple model for a novel wave energy converter: non-resonant instability, limit cycles, and bounded oscillations. Nonlinear Dynamics 67, 1135–1146 (2012) Inoue and Ishida [2008] Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. 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[2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. 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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Inoue, T., Ishida, Y.: Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force. Nonlinear Dynamics 52, 103–113 (2008) Han and Bi [2023] Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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[2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Han, X., Bi, Q.: Effects of amplitude modulation on mixed-mode oscillations in the forced van der pol equation. Nonlinear Dynamics, 1–10 (2023) Ghorbaniparvar [2017] Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. 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Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. 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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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[2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Ghorbaniparvar, M.: Survey on forced oscillations in power system. Journal of Modern Power Systems and Clean Energy 5(5), 671–682 (2017) Ye et al. [2016] Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Ye, H., Liu, Y., Zhang, P., Du, Z.: Analysis and detection of forced oscillation in power system. IEEE Transactions on Power Systems 32(2), 1149–1160 (2016) Follum et al. [2016] Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. 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Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Follum, J., Pierre, J.W., Martin, R.: Simultaneous estimation of electromechanical modes and forced oscillations. IEEE Transactions on Power Systems 32(5), 3958–3967 (2016) Mondal et al. [2019] Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. 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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Mondal, B., Choudhury, A.K., Viswanadh, M., Barnwal, S., Jain, D.: Application of pmu and scada data for estimation of source of forced oscillation. In: 2019 International Conference on Smart Grid Synchronized Measurements and Analytics (SGSMA), pp. 1–7 (2019). IEEE Wang and Sun [2017] Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. 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[2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. 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Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. 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[2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. 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[2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. 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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Wang, B., Sun, K.: Location methods of oscillation sources in power systems: a survey. Journal of modern power systems and clean energy 5(2), 151–159 (2017) Tang et al. [2016] Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. 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[2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. 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[1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Tang, F., Wang, B., Liao, Q., Pisani, C., Dong, C., Jia, J., Guo, K.: Research on forced oscillations disturbance source locating through an energy approach. International Transactions on Electrical Energy Systems 26(1), 192–207 (2016) Maslennikov and Litvinov [2020] Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. 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IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maslennikov, S., Litvinov, E.: Iso new england experience in locating the source of oscillations online. IEEE Transactions on Power Systems 36(1), 495–503 (2020) Li et al. [2018] Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. 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[2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). 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Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Li, S., Luan, M., Gan, D., Wu, D.: A model-based decoupling observer to locate forced oscillation sources in mechanical power. International Journal of Electrical Power & Energy Systems 103, 127–135 (2018) Zhou et al. [2017] Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. 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Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhou, N., Ghorbaniparvar, M., Akhlaghi, S.: Locating sources of forced oscillations using transfer functions. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–8 (2017). IEEE Nudell and Chakrabortty [2015] Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). 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[2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Nudell, T.R., Chakrabortty, A.: Graph-theoretic methods for measurement-based input localization in large networked dynamic systems. IEEE Transactions on Automatic Control 60(8), 2114–2128 (2015) Huang et al. [2018] Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). 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IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: Localization of forced oscillations in the power grid under resonance conditions. In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–5 (2018). IEEE Usman and Faruque [2019] Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. 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[2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Usman, M.U., Faruque, M.O.: Applications of synchrophasor technologies in power systems. Journal of Modern Power Systems and Clean Energy 7(2), 211–226 (2019) Meng et al. [2020] Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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[2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Meng, Y., Yu, Z., Lu, N., Shi, D.: Time series classification for locating forced oscillation sources. IEEE Transactions on Smart Grid 12(2), 1712–1721 (2020) Chevalier et al. [2018] Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. [2022] Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Chevalier, S., Vorobev, P., Turitsyn, K.: A bayesian approach to forced oscillation source location given uncertain generator parameters. IEEE Transactions on Power Systems 34(2), 1641–1649 (2018) Feng et al. 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IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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[2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Feng, S., Chen, J., Ye, Y., Wu, X., Cui, H., Tang, Y., Lei, J.: A two-stage deep transfer learning for localisation of forced oscillations disturbance source. International Journal of Electrical Power & Energy Systems 135, 107577 (2022) Talukder et al. [2021] Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. 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[2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Talukder, S., Liu, S., Wang, H., Zheng, G.: Low-frequency forced oscillation source location for bulk power systems: A deep learning approach. In: 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3499–3404 (2021). IEEE Matar et al. [2023] Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. 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[2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. 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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. 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Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Matar, M., Estevez, P.G., Marchi, P., Messina, F., Elmoudi, R., Wshah, S.: Transformer-based deep learning model for forced oscillation localization. International Journal of Electrical Power & Energy Systems 146, 108805 (2023) Huang et al. [2020] Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. [2020] Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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[2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Huang, T., Freris, N.M., Kumar, P., Xie, L.: A synchrophasor data-driven method for forced oscillation localization under resonance conditions. IEEE Transactions on Power Systems 35(5), 3927–3939 (2020) Anvari et al. 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[2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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[2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Anvari, M., Hellmann, F., Zhang, X.: Introduction to focus issue: Dynamics of modern power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 30(6), 063140 (2020) Dörfler et al. [2013] Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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[2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Dörfler, F., Chertkov, M., Bullo, F.: Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences 110(6), 2005–2010 (2013) Choi and Li [2019] Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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[2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Choi, Y.-P., Li, Z.: Synchronization of nonuniform kuramoto oscillators for power grids with general connectivity and dampings. Nonlinearity 32(2), 559 (2019) Filatrella et al. [2008] Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Filatrella, G., Nielsen, A.H., Pedersen, N.F.: Analysis of a power grid using a kuramoto-like model. The European Physical Journal B 61(4), 485–491 (2008) Kosterev et al. [1999] Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Kosterev, D.N., Taylor, C.W., Mittelstadt, W.A.: Model validation for the august 10, 1996 wscc system outage. IEEE transactions on power systems 14(3), 967–979 (1999) Thiel et al. [2006] Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Thiel, M., Romano, M.C., Kurths, J.: Spurious structures in recurrence plots induced by embedding. Nonlinear Dynamics 44, 299–305 (2006) Van der Maaten and Hinton [2008] Maaten, L., Hinton, G.: Visualizing data using t-sne. Journal of machine learning research 9(11) (2008) Feller [1967] Feller, W.: An introduction to probability theory and its applications. Technical report, Wiley series in probability and mathematical statistics, 3rd edn.(Wiley, New York, 1968 (1967) Manik et al. [2014] Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. 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[2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. 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IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. 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Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Manik, D., Witthaut, D., Schäfer, B., Matthiae, M., Sorge, A., Rohden, M., Katifori, E., Timme, M.: Supply networks: Instabilities without overload. The European Physical Journal Special Topics 223(12), 2527–2547 (2014) Simonsen et al. [2008] Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Simonsen, I., Buzna, L., Peters, K., Bornholdt, S., Helbing, D.: Transient dynamics increasing network vulnerability to cascading failures. Physical review letters 100(21), 218701 (2008) Hens et al. [2019] Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Hens, C., Harush, U., Haber, S., Cohen, R., Barzel, B.: Spatiotemporal signal propagation in complex networks. Nature Physics 15(4), 403–412 (2019) Khan and Pierre [2019] Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Khan, M.A., Pierre, J.W.: Separable estimation of ambient noise spectrum in synchrophasor measurements in the presence of forced oscillations. IEEE Transactions on Power Systems 35(1), 415–423 (2019) Rohden et al. [2014] Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Rohden, M., Sorge, A., Witthaut, D., Timme, M.: Impact of network topology on synchrony of oscillatory power grids. Chaos: An Interdisciplinary Journal of Nonlinear Science 24(1), 013123 (2014) Rohden et al. [2012] Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Rohden, M., Sorge, A., Timme, M., Witthaut, D.: Self-organized synchronization in decentralized power grids. Physical review letters 109(6), 064101 (2012) Brown et al. [2016] Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Brown, M., Biswal, M., Brahma, S., Ranade, S.J., Cao, H.: Characterizing and quantifying noise in pmu data. In: 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5 (2016). IEEE Zhang et al. [2020] Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020) Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
- Zhang, X., Lu, C., Lin, J., Wang, Y.: Experimental test of pmu measurement errors and the impact on load model parameter identification. IET Generation, Transmission & Distribution 14(20), 4593–4604 (2020)
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