Dynamic Complex-Frequency Control of Grid-Forming Converters
Abstract: Complex droop control, alternatively known as dispatchable virtual oscillator control (dVOC), stands out for its unique capabilities in synchronization and voltage stabilization among existing control strategies for grid-forming converters. Complex droop control leverages the novel concept of ``complex frequency'', thereby establishing a coupled connection between active and reactive power inputs and frequency and rate-of-change-of voltage outputs. However, its reliance on static droop gains limits its ability to exhibit crucial dynamic response behaviors required in future power systems. To address this limitation, this paper introduces dynamic complex-frequency control, upgrading static droop gains with dynamic transfer functions to enhance the richness and flexibility in dynamic responses for frequency and voltage control. Unlike existing approaches, the complex-frequency control framework treats frequency and voltage dynamics collectively, ensuring small-signal stability for frequency synchronization and voltage stabilization simultaneously. The control framework is validated through detailed numerical case studies on the IEEE nine-bus system, also showcasing its applicability in multi-converter setups.
- R. Musca, A. Vasile, and G. Zizzo, “Grid-forming converters. a critical review of pilot projects and demonstrators,” Renew. Sustain. Energy Rev., vol. 165, p. 112551, 2022.
- J. W. Simpson-Porco, F. Dörfler, and F. Bullo, “Synchronization and power sharing for droop-controlled inverters in islanded microgrids,” Automatica, vol. 49, no. 9, pp. 2603–2611, 2013.
- N. Ainsworth and S. Grijalva, “A structure-preserving model and sufficient condition for frequency synchronization of lossless droop inverter-based ac networks,” IEEE Trans. Power Syst., vol. 28, no. 4, pp. 4310–4319, 2013.
- Z. Shuai, C. Shen, X. Liu, Z. Li, and Z. J. Shen, “Transient angle stability of virtual synchronous generators using lyapunov’s direct method,” IEEE Trans. Smart Grid, vol. 10, no. 4, pp. 4648–4661, 2018.
- M. Colombino, D. Groß, J.-S. Brouillon, and F. Dörfler, “Global phase and magnitude synchronization of coupled oscillators with application to the control of grid-forming power inverters,” IEEE Trans. Autom. Control, vol. 64, no. 11, pp. 4496–4511, 2019.
- G.-S. Seo, M. Colombino, I. Subotic, B. Johnson, D. Groß, and F. Dörfler, “Dispatchable virtual oscillator control for decentralized inverter-dominated power systems: Analysis and experiments,” in 2019 IEEE Applied Power Electronics Conference and Exposition (APEC). IEEE, 2019, pp. 561–566.
- M. Lu, “Virtual oscillator grid-forming inverters: State of the art, modeling, and stability,” IEEE Trans. Power Electron., vol. 37, no. 10, pp. 11 579–11 591, 2022.
- C. Arghir and F. Dörfler, “The electronic realization of synchronous machines: Model matching, angle tracking, and energy shaping techniques,” IEEE Trans. Power Electron., vol. 35, no. 4, pp. 4398–4410, 2019.
- X. He, V. Häberle, I. Subotić, and F. Dörfler, “Nonlinear stability of complex droop control in converter-based power systems,” IEEE Control Syst. Lett., vol. 7, pp. 1327–1332, 2023.
- F. Milano, “Complex frequency,” IEEE Trans. Power Syst., vol. 37, no. 2, pp. 1230–1240, 2021.
- J. Björk, K. H. Johansson, and F. Dörfler, “Dynamic virtual power plant design for fast frequency reserves: Coordinating hydro and wind,” IEEE Trans. Control Netw. Syst., 2022.
- V. Häberle, M. W. Fisher, E. Prieto-Araujo, and F. Dörfler, “Control design of dynamic virtual power plants: An adaptive divide-and-conquer approach,” IEEE Trans. Power Syst., vol. 37, no. 5, pp. 4040–4053, 2021.
- V. Häberle, A. Tayyebi, X. He, E. Prieto-Araujo, and F. Dörfler, “Grid-forming and spatially distributed control design of dynamic virtual power plants,” IEEE Trans. Smart Grid, vol. 7, no. 2, pp. 1761 – 1777, 2023.
- Y. Jiang, A. Bernstein, P. Vorobev, and E. Mallada, “Grid-forming frequency shaping control for low-inertia power systems,” in 2021 American Control Conference (ACC). IEEE, 2021, pp. 4184–4189.
- F. Paganini and E. Mallada, “Global analysis of synchronization performance for power systems: Bridging the theory-practice gap,” IEEE Trans. Autom. Control, vol. 65, no. 7, pp. 3007–3022, 2020.
- X. He, V. Häberle, and F. Dörfler, “Complex-frequency synchronization of converter-based power systems,” arXiv:2208.13860, 2022.
- R. Domingo-Enrich, “Complex-frequency control of dynamic virtual power plants,” Master’s thesis, ETH Zurich, 2023.
- A. Tayyebi, D. Groß, A. Anta, F. Kupzog, and F. Dörfler, “Frequency stability of synchr. machines and grid-forming power conv.” IEEE Trans. Emerg. Sel. Topics Power Electron., vol. 8, no. 2, pp. 1004–1018, 2020.
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