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A Distributionally Robust Model Predictive Control for Static and Dynamic Uncertainties in Smart Grids (2403.16402v1)

Published 25 Mar 2024 in eess.SY and cs.SY

Abstract: The integration of various power sources, including renewables and electric vehicles, into smart grids is expanding, introducing uncertainties that can result in issues like voltage imbalances, load fluctuations, and power losses. These challenges negatively impact the reliability and stability of online scheduling in smart grids. Existing research often addresses uncertainties affecting current states but overlooks those that impact future states, such as the unpredictable charging patterns of electric vehicles. To distinguish between these, we term them static uncertainties and dynamic uncertainties, respectively. This paper introduces WDR-MPC, a novel approach that stands for two-stage Wasserstein-based Distributionally Robust (WDR) optimization within a Model Predictive Control (MPC) framework, aimed at effectively managing both types of uncertainties in smart grids. The dynamic uncertainties are first reformulated into ambiguity tubes and then the distributionally robust bounds of both dynamic and static uncertainties can be established using WDR optimization. By employing ambiguity tubes and WDR optimization, the stochastic MPC system is converted into a nominal one. Moreover, we develop a convex reformulation method to speed up WDR computation during the two-stage optimization. The distinctive contribution of this paper lies in its holistic approach to both static and dynamic uncertainties in smart grids. Comprehensive experiment results on IEEE 38-bus and 94-bus systems reveal the method's superior performance and the potential to enhance grid stability and reliability.

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References (37)
  1. X. Fang, S. Misra, G. Xue, and D. Yang, “Smart grid — the new and improved power grid: A survey,” IEEE Communications Surveys and Tutorials, vol. 14, no. 4, pp. 944–980, 2012.
  2. D. Bienstock, M. Chertkov, and S. Harnett, “Chance-constrained optimal power flow: Risk-aware network control under uncertainty,” SIAM Review, vol. 56, no. 3, pp. 461–495, 2014.
  3. M. Lubin, Y. Dvorkin, and S. Backhaus, “A robust approach to chance constrained optimal power flow with renewable generation,” IEEE Transactions on Power Systems, vol. 31, no. 5, pp. 3840–3849, 2015.
  4. T. Summers, J. Warrington, M. Morari, and J. Lygeros, “Stochastic optimal power flow based on conditional value at risk and distributional robustness,” International Journal of Electrical Power & Energy Systems, vol. 72, pp. 116–125, 2015.
  5. W. Xie and S. Ahmed, “Distributionally robust chance constrained optimal power flow with renewables: A conic reformulation,” IEEE Transactions on Power Systems, vol. 33, no. 2, pp. 1860–1867, 2017.
  6. Y. Guo, K. Baker, E. Dall’Anese, Z. Hu, and T. H. Summers, “Data-based distributionally robust stochastic optimal power flow—Part i: Methodologies,” IEEE Transactions on Power Systems, vol. 34, no. 2, pp. 1483–1492, 2018.
  7. Y. Guo, K. Baker, E. Dall’Anese, Z. Hu, and T. H. Summers, “Data-based distributionally robust stochastic optimal power flow—Part ii: Case studies,” IEEE Transactions on Power Systems, vol. 34, no. 2, pp. 1493–1503, 2018.
  8. J. Zhai, Y. Jiang, Y. Shi, C. N. Jones, and X.-P. Zhang, “Distributionally robust joint chance-constrained dispatch for integrated transmission-distribution systems via distributed optimization,” IEEE Transactions on Smart Grid, vol. 13, no. 3, pp. 2132–2147, 2022.
  9. S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning, vol. 3, no. 1, pp. 1–122, 2011.
  10. C. Duan, W. Fang, L. Jiang, L. Yao, and J. Liu, “Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric,” IEEE Transactions on Power Systems, vol. 33, no. 5, pp. 4924–4936, 2018.
  11. Y. Cao and Y. Wang, “Robust charging schedule for autonomous electric vehicles with uncertain covariates,” IEEE Access, vol. 9, pp. 161565–161575, 2021.
  12. J. Feng, Z. Hu, and X. Duan, “Multi-agent based stochastic programming for planning of fast charging station integrated with photovoltaic and energy storage system,” in Proceedings of the 2021 IEEE/IAS Industrial and Commercial Power System Asia (ICPS Asia), pp. 425–430, 2021.
  13. S. Zeynali, N. Rostami, and M. Feyzi, “Multi-objective optimal short-term planning of renewable distributed generations and capacitor banks in power system considering different uncertainties including plug-in electric vehicles,” International Journal of Electrical Power & Energy Systems, vol. 119, p. 105885, 2020.
  14. S. Wang, F. Luo, Z. Y. Dong, and G. Ranzi, “Joint planning of active distribution networks considering renewable power uncertainty,” International Journal of Electrical Power & Energy Systems, vol. 110, pp. 696–704, 2019.
  15. Y. Wang, Y. Yang, L. Tang, W. Sun, and B. Li, “A Wasserstein based two-stage distributionally robust optimization model for optimal operation of cchp micro-grid under uncertainties,” International Journal of Electrical Power & Energy Systems, vol. 119, p. 105941, 2020.
  16. Y. Shi, H. D. Tuan, A. V. Savkin, T. Q. Duong, and H. V. Poor, “Model predictive control for smart grids with multiple electric-vehicle charging stations,” IEEE Transactions on Smart Grid, vol. 10, no. 2, pp. 2127–2136, 2019.
  17. Y. Shi, T. Hoang, A. Savkin, and H. V. Poor, “Model predictive control for on–off charging of electrical vehicles in smart grids,” IET Electrical Systems in Transportation, vol. 11, 06 2021.
  18. Y. Shi, H. D. Tuan, and A. V. Savkin, “Mixed integer nonlinear programming for joint coordination of plug-in electrical vehicles charging and smart grid operations,” in Proceedings of the 2019 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), pp. 1–6, 2019.
  19. Q. Li, P. Tian, Y. Shi, Y. Shi, and H. D. Tuan, “Distributionally robust optimization for vehicle-to-grid with uncertain renewable energy,” in Proceedings of the 2022 11th International Conference on Control, Automation and Information Sciences (ICCAIS), pp. 462–467, IEEE, 2022.
  20. Y. Shi, H. D. Tuan, A. V. Savkin, C.-T. Lin, J. G. Zhu, and H. V. Poor, “Distributed model predictive control for joint coordination of demand response and optimal power flow with renewables in smart grid,” Applied Energy, vol. 290, p. 116701, 2021.
  21. H. T. Nguyen and D.-H. Choi, “Distributionally robust model predictive control for smart electric vehicle charging station with V2G/V2V capability,” IEEE Transactions on Smart Grid, 2023.
  22. P. Mohajerin Esfahani and D. Kuhn, “Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations,” Mathematical Programming, vol. 171, no. 1, pp. 115–166, 2018.
  23. M. Fochesato and J. Lygeros, “Data-driven distributionally robust bounds for stochastic model predictive control,” in Proceedings of the 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 3611–3616, IEEE, 2022.
  24. A. Hakobyan and I. Yang, “Wasserstein distributionally robust control of partially observable linear systems: Tractable approximation and performance guarantee,” in Proceedings of the 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 4800–4807, IEEE, 2022.
  25. R. T. Rockafellar, S. Uryasev, et al., “Optimization of conditional value-at-risk,” Journal of Risk, vol. 2, pp. 21–42, 2000.
  26. D. Q. Mayne, M. M. Seron, and S. Raković, “Robust model predictive control of constrained linear systems with bounded disturbances,” Automatica, vol. 41, no. 2, pp. 219–224, 2005.
  27. D. Limón, I. Alvarado, T. Alamo, and E. F. Camacho, “Robust tube-based MPC for tracking of constrained linear systems with additive disturbances,” Journal of Process Control, vol. 20, no. 3, pp. 248–260, 2010.
  28. H.-G. Yeh, D. F. Gayme, and S. H. Low, “Adaptive VAR control for distribution circuits with photovoltaic generators,” IEEE Transactions on Power Systems, vol. 27, no. 3, pp. 1656–1663, 2012.
  29. J. Wang, J. Purewal, P. Liu, J. Hicks-Garner, S. Soukazian, E. Sherman, A. Sorenson, L. Vu, H. Tataria, and M. W. Verbrugge, “Degradation of lithium ion batteries employing graphite negatives and nickel–cobalt–manganese oxide+ spinel manganese oxide positives: Part 1, aging mechanisms and life estimation,” Journal of Power Sources, vol. 269, pp. 937–948, 2014.
  30. K. Antoniadou-Plytaria, D. Steen, O. Carlson, M. A. F. Ghazvini, et al., “Market-based energy management model of a building microgrid considering battery degradation,” IEEE Transactions on Smart Grid, vol. 12, no. 2, pp. 1794–1804, 2020.
  31. M. Farina, L. Giulioni, and R. Scattolini, “Stochastic linear model predictive control with chance constraints–a review,” Journal of Process Control, vol. 44, pp. 53–67, 2016.
  32. M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1,” 2014.
  33. T. H. Ruggles, D. J. Farnham, D. Tong, and K. Caldeira, “Developing reliable hourly electricity demand data through screening and imputation,” Scientific Data, vol. 7, no. 1, pp. 1–14, 2020.
  34. “See what Nord Pool can offer you..” https://www.nordpoolgroup.com/, 2022. [Online; accessed 2022-08-19].
  35. G. Pulazza, N. Zhang, C. Kang, and C. A. Nucci, “Transmission planning with battery-based energy storage transportation for power systems with high penetration of renewable energy,” IEEE Transactions on Power Systems, vol. 36, no. 6, pp. 4928–4940, 2021.
  36. R. D. Zimmerman, C. E. Murillo-Sánchez, and R. J. Thomas, “Matpower: Steady-state operations, planning, and analysis tools for power systems research and education,” IEEE Transactions on power systems, vol. 26, no. 1, pp. 12–19, 2010.
  37. M. Lee, M. Yoon, J. Cho, and S. Choi, “Probabilistic stability evaluation based on confidence interval in distribution systems with inverter-based distributed generations,” Sustainability, vol. 14, no. 7, p. 3806, 2022.
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