volume | PIER Journals

Abstract

Virtual synchronous generator (VSG) control is a representative grid-forming strategy for converter-interfaced renewable generation. In a conventional VSG, active-power feedback is calculated directly from terminal voltage and current, allowing voltage distortion and weak-grid-induced oscillatory components to enter the swing loop. This paper proposes a flux-linkage-based active-power calculation that reconstructs electromagnetic flux linkage from the measured converter voltage and evaluates active power through the flux-current relation. The calculation is integrated into a VSG controller with cascaded voltage and current inner loops. A small-signal impedance model and PSCAD/EMTDC simulations are combined to characterize the feedback-interaction mechanism and validate the method under grid-impedance, operating-point, disturbance, and filter-parameter variations. Compared with the conventional voltagebased VSG, the proposed method reduces steady-state active-power peak-to-peak ripple by 56.7-65.8% and frequency ripple by 42.6-66.7% in the grid-impedance sweep, and reduces the non-dc active-power component by 69.9-72.7% across the tested operating points, while maintaining comparable terminal current and voltage THD. Closed-loop active-power-command tests further quantify the associated reactive-power and local terminal-voltage responses under three converter-grid interface conditions. The impedance model identifies a 37.3% lower normalized resonance peak in the 40-250 Hz interaction band, while an electromagnetic transient (EMT) spectral study sampled at 50 kHz characterizes the adjacent 10-40 Hz and 500 Hz-10 kHz bands. These results demonstrate that flux-linkage-based power feedback improves the quality of the signal driving the virtual swing equation within a practical VSG architecture.

1. Rosso, Roberto, Xiongfei Wang, Marco Liserre, Xiaonan Lu, and Soenke Engelken, "Grid-forming converters: Control approaches, grid-synchronization, and future trends --- A review," IEEE Open Journal of Industry Applications, Vol. 2, 93-109, Apr. 2021.
doi:10.1109/ojia.2021.3074028 Google Scholar

2. Teng, Yuting, Wei Deng, Wei Pei, Yifeng Li, Li Dingv, and Hua Ye, "Review on grid-forming converter control methods in high-proportion renewable energy power systems," Global Energy Interconnection, Vol. 5, No. 3, 328-342, Jun. 2022.
doi:10.1016/j.gloei.2022.06.010 Google Scholar

3. Tarimer, I. and E. O. Yuzer, "Designing of a permanent magnet and directly driven synchronous generator for low speed turbines," Elektronika Ir Elektrotechnika, Vol. 112, No. 6, 15-18, 2011.
doi:10.5755/j01.eee.112.6.436 Google Scholar

4. Guerrero, Josep M., Jos Matas, Luis Garcia De Vicuna, Miguel Castilla, and Jaume Miret, "Decentralized control for parallel operation of distributed generation inverters using resistive output impedance," IEEE Transactions on Industrial Electronics, Vol. 54, No. 2, 994-1004, Apr. 2007.
doi:10.1109/tie.2007.892621 Google Scholar

5. Rocabert, Joan, Alvaro Luna, Frede Blaabjerg, and Pedro Rodríguez, "Control of power converters in AC microgrids," IEEE Transactions on Power Electronics, Vol. 27, No. 11, 4734-4749, Nov. 2012.
doi:10.1109/tpel.2012.2199334 Google Scholar

6. Zhang, Lidong, Lennart Harnefors, and Hans-Peter Nee, "Power-synchronization control of grid-connected voltage-source converters," IEEE Transactions on Power Systems, Vol. 25, No. 2, 809-820, May 2010.
doi:10.1109/tpwrs.2009.2032231 Google Scholar

7. Liu, Yang, Xinyuan Zhou, and Sen Ouyang, "Capacitor voltage synchronising control‐based VSG scheme for inertial and primary frequency responses of Type‐4 WTGs," IET Generation, Transmission & Distribution, Vol. 12, No. 14, 3461-3469, Aug. 2018.
doi:10.1049/iet-gtd.2017.1602 Google Scholar

8. Beck, Hans-Peter and Ralf Hesse, "Virtual synchronous machine," 2007 9th International Conference on Electrical Power Quality and Utilisation, 1-6, Barcelona, Spain, Oct. 2007.
doi:10.1109/EPQU.2007.4424220

9. Driesen, J. and K. Visscher, "Virtual synchronous generators," 2008 IEEE Power and Energy Society General Meeting --- Conversion and Delivery of Electrical Energy in the 21st Century, 1-3, Pittsburgh, PA, USA, Jul. 2008.
doi:10.1109/PES.2008.4596800

10. Zhong, Qing-Chang and George Weiss, "Synchronverters: Inverters that mimic synchronous generators," IEEE Transactions on Industrial Electronics, Vol. 58, No. 4, 1259-1267, Apr. 2011.
doi:10.1109/tie.2010.2048839 Google Scholar

11. D’Arco, Salvatore, Jon Are Suul, and Olav B. Fosso, "Small-signal modeling and parametric sensitivity of a virtual synchronous machine in islanded operation," International Journal of Electrical Power & Energy Systems, Vol. 72, 3-15, Nov. 2015.
doi:10.1016/j.ijepes.2015.02.005 Google Scholar

12. Zhou, Ziqi, Sante Pugliese, and Marco Liserre, "Stability comparison of grid-forming converters with different power calculation strategies," 2023 IEEE 14th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 800-805, Shanghai, China, Jun. 2023.
doi:10.1109/PEDG56097.2023.10215196

13. Leon, Jose David Vidal, Andres Tarraso, Jose Ignacio Candela, Joan Rocabert, and Pedro Rodriguez, "Grid-forming controller based on virtual admittance for power converters working in weak grids," IEEE Journal of Emerging and Selected Topics in Industrial Electronics, Vol. 4, No. 3, 791-801, Feb. 2023.
doi:10.1109/jestie.2023.3244744 Google Scholar

14. Johnson, Brian B., Mohit Sinha, Nathan G. Ainsworth, Florian Dörfler, and Sairaj V. Dhople, "Synthesizing virtual oscillators to control islanded inverters," IEEE Transactions on Power Electronics, Vol. 31, No. 8, 6002-6015, Aug. 2016.
doi:10.1109/tpel.2015.2497217 Google Scholar

15. Seo, Gab-Su, Marcello Colombino, Irina Subotic, Brian Johnson, Dominic Groß, and Florian Dörfler, "Dispatchable virtual oscillator control for decentralized inverter-dominated power systems: Analysis and experiments," 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), 561-566, Anaheim, CA, USA, Mar. 2019.
doi:10.1109/apec.2019.8722028

16. Kisinga, Daniel Angelo and Paul Trodden, "Virtual power circle based PQ decoupling technique for a virtual synchronous generator connected to a weak grid," 2023 IEEE Belgrade PowerTech, 1-6, Belgrade, Serbia, Jun. 2023.
doi:10.1109/PowerTech55446.2023.10202828

17. Gholami-Khesht, Hosein, Mohammad Monfared, and Saeed Golestan, "Low computational burden grid voltage estimation for grid connected voltage source converter-based power applications," IET Power Electronics, Vol. 8, No. 5, 656-664, May 2015.
doi:10.1049/iet-pel.2014.0466 Google Scholar

18. Sun, Jian, "Impedance-based stability criterion for grid-connected inverters," IEEE Transactions on Power Electronics, Vol. 26, No. 11, 3075-3078, Nov. 2011.
doi:10.1109/tpel.2011.2136439 Google Scholar

19. Harnefors, Lennart, Massimo Bongiorno, and Stefan Lundberg, "Input-admittance calculation and shaping for controlled voltage-source converters," IEEE Transactions on Industrial Electronics, Vol. 54, No. 6, 3323-3334, Dec. 2007.
doi:10.1109/tie.2007.904022 Google Scholar

20. Wen, Bo, Dushan Boroyevich, Rolando Burgos, Paolo Mattavelli, and Zhiyu Shen, "Analysis of D-Q small-signal impedance of grid-tied inverters," IEEE Transactions on Power Electronics, Vol. 31, No. 1, 675-687, Jan. 2016.
doi:10.1109/tpel.2015.2398192 Google Scholar

21. Chen, Jinlei, Qingyuan Gong, Yawen Zhang, Muhammad Fawad, Sheng Wang, Chuanyue Li, and Jun Liang, "Comprehensive assessment of transient stability for grid-forming converters considering current limitations, inertia and damping effects," CSEE Journal of Power and Energy Systems, Vol. 11, No. 1, 1-12, Jan. 2025.
doi:10.17775/CSEEJPES.2024.03160 Google Scholar

22. Wang, Jiashi and Ke Ma, "Inertia and grid impedance emulation of power grid for stability test of grid-forming converter," IEEE Transactions on Power Electronics, Vol. 38, No. 2, 2469-2480, Feb. 2023.
doi:10.1109/tpel.2022.3210926 Google Scholar

23. Elshenawy, Mahmoud Awad, Amr Ahmed A. Radwan, and Yasser Abdel-Rady I. Mohamed, "Analysis and weakening of sequence impedance coupling in grid-forming converters," IEEE Transactions on Power Delivery, Vol. 39, No. 6, 3292-3304, Dec. 2024.
doi:10.1109/tpwrd.2024.3461448 Google Scholar

24. Wang, Kailun, Qiang Song, Wenhua Liu, Biao Zhao, and Pinjia Zhang, "Reactive power characteristics and FRT strategy for grid-forming converters with virtual impedance-based current limiting," IEEE Transactions on Energy Conversion, Vol. 40, No. 2, 1165-1177, Jun. 2025.
doi:10.1109/tec.2024.3479726 Google Scholar

Dr. Yuexi Yang

Dr. Ziwei Zhao

Dr. Sichao Wang

Dr. Fangyuan Li

Dr. Liwen Zheng

Dr. Yang Liu