Stability Region Boundary of Multi-Parallel Grid-Following Converter Systems Considering Nonlinear Coupling Interactions

Authors

Zhenglong Sun, Naiyuan Liu, Zhifeng He, Yidong Yang, Rui Zhang, Hao Yang, Juri Belikov, Yoash Levron, Guowei Cai

Abstract

In multi-parallel grid-following voltage source converters (MGFL-VSCs), the nonlinear dynamics of the control loops and their coupling interactions substantially affect the transient synchronization stability (TSS) of MGFL-VSCs. This study focuses on the effects of nonlinear coupling interactions on TSS of the MGFL-VSC systems. First, on the basis of differential–algebraic equation–stability region boundary (SRB) theory, the study analyzes the effects of nonlinear dynamics and coupling interactions and plots the SRB of MGFL-VSCs. Results show that the coupling interactions limit the maximum phase angle of the phase-locked loop. The SRB of MGFL-VSCs consists of a stable manifold of unstable equilibrium points, a stable manifold of semi-singular points, and certain singular surfaces. The composition of SRB is closely related to the coupling interactions of nonlinear control. Second, on the basis of the correlation between SRB and transient instability modes, the transient instability modes of MGFL-VSCs are divided into traditional and coupling interaction instability modes, and the evolution of instability modes is systematically studied in consideration of nonlinear coupling interactions. In addition, an online assessment method that is based on the Port–Hamiltonian energy function is proposed. This method can quantitatively estimate the effect of coupling interactions on TSS by using the nonlinear normalized energy index. Finally, experimental and simulation results are provided to compare the proposed approach with existing methods and verify its effectiveness.

Citation

• Journal: IEEE Transactions on Power Systems
• Year: 2026
• Volume: 41
• Issue: 5
• Pages: 3948–3964
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tpwrs.2026.3684552

BibTeX

@article{Sun_2026,
  title={{Stability Region Boundary of Multi-Parallel Grid-Following Converter Systems Considering Nonlinear Coupling Interactions}},
  volume={41},
  ISSN={1558-0679},
  DOI={10.1109/tpwrs.2026.3684552},
  number={5},
  journal={IEEE Transactions on Power Systems},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Sun, Zhenglong and Liu, Naiyuan and He, Zhifeng and Yang, Yidong and Zhang, Rui and Yang, Hao and Belikov, Juri and Levron, Yoash and Cai, Guowei},
  year={2026},
  pages={3948--3964}
}

Download the bib file

References

• Chen Y, Preece R, Barnes M (2024) A Framework for Analyzing System Loadability With Multiple VSCs Using a Hybrid Model. IEEE Trans Power Syst 39(1):1079–1094. https://doi.org/10.1109/tpwrs.2023.323966 – 10.1109/tpwrs.2023.3239663
• Grid incident in Spain and Portugal on 28 April 2025: Factual report. (2025)
• Wu C, Lyu Y, Wang Y, Blaabjerg F (2024) Transient Synchronization Stability Analysis of Grid-Following Converter Considering the Coupling Effect of Current Loop and Phase Locked Loop. IEEE Trans Energy Convers 39(1):544–554. https://doi.org/10.1109/tec.2023.331409 – 10.1109/tec.2023.3314095
• Ding W, Geng H, Ren B, Li Q, Sun R (2024) Analytical Switching Modelling Method of Grid-Connected Converters for Transient Stability Analysis. IEEE Trans on Ind Applicat 60(5):7511–7521. https://doi.org/10.1109/tia.2024.340397 – 10.1109/tia.2024.3403978
• Carreño M, Song J, Gomis-Bellmunt O, Griñó R (2025) Design-Oriented Large-Signal Stability Analysis of Synchronous Reference Frame Phase-Locked Loop. IEEE Trans Power Delivery 40(3):1235–1243. https://doi.org/10.1109/tpwrd.2024.345453 – 10.1109/tpwrd.2024.3454533
• Ma Y, Zhu D, Hu J, Liu D, Ji X, Zou X, Kang Y (2024) Reduced-Order Modeling and Transient Stability Analysis of Grid-Connected VSC in DC-Link Voltage Control Timescale. IEEE J Emerg Sel Topics Power Electron 12(3):2981–2993. https://doi.org/10.1109/jestpe.2024.337030 – 10.1109/jestpe.2024.3370306
• Huang S, Yao J, Luo Y, Lin Y, Gong S (2023) Coupling characteristic analysis and synchronization stability control for Multi-Paralleled VSCs system under symmetric faults. International Journal of Electrical Power & Energy Systems 151:109134. https://doi.org/10.1016/j.ijepes.2023.10913 – 10.1016/j.ijepes.2023.109134
• He X, Geng H (2022) PLL Synchronization Stability of Grid-Connected Multiconverter Systems. IEEE Trans on Ind Applicat 58(1):830–842. https://doi.org/10.1109/tia.2021.312126 – 10.1109/tia.2021.3121262
• Liu Y, Geng H, He C, Ding W, Shen C, Yang G (2024) Equivalent Aggregated Modeling of Multi-VSC System for Transient Synchronization Stability Analysis. IEEE Trans Power Syst 39(2):4296–4310. https://doi.org/10.1109/tpwrs.2023.331175 – 10.1109/tpwrs.2023.3311759
• Wang Z, Guo L, Li X, Zhou X, Zhu J, Wang C (2025) Multi-Swing PLL Synchronization Transient Stability of Grid-Connected Paralleled Converters. IEEE Trans Sustain Energy 16(1):716–729. https://doi.org/10.1109/tste.2024.348141 – 10.1109/tste.2024.3481417
• Lin Z, Liu R, Li YR (2025) Transient Stability Analysis and Coordinated Phase Control Method for Multiparallel PLL-Synchronized Inverters During Grid Fault. IEEE Trans Power Electron 40(8):11442–11451. https://doi.org/10.1109/tpel.2025.355414 – 10.1109/tpel.2025.3554146
• Xiong J, Pei W, Ye H, Kong L (2024) Transient Stability of Multiple Phase-Locked-Loop-Type Voltage Source Converters System Based on Amplitude Mapping Model. IEEE Trans Smart Grid 15(1):557–569. https://doi.org/10.1109/tsg.2023.327478 – 10.1109/tsg.2023.3274786
• Wang Z, Guo L, Li X, Wang Z, Zang X, Zhu J, Zhou X, Wang C (2024) Transient Synchronization Stability of Grid-Tied Multi-VSCs System Considering Nonlinear Damping and Transient Interactions. IEEE Trans Power Electron 39(12):16775–16791. https://doi.org/10.1109/tpel.2024.344535 – 10.1109/tpel.2024.3445352
• Yi X, Peng Y, Zhou Q, Huang W, Xu L, Shen ZJ, Shuai Z (2022) Transient Synchronization Stability Analysis and Enhancement of Paralleled Converters Considering Different Current Injection Strategies. IEEE Trans Sustain Energy 13(4):1957–1968. https://doi.org/10.1109/tste.2022.317691 – 10.1109/tste.2022.3176919
• Li X, Tian Z, Zha X, Sun P, Hu Y, Huang M, Sun J (2023) Nonlinear Modeling and Stability Analysis of Grid-Tied Paralleled-Converters Systems Based on the Proposed Dual-Iterative Equal Area Criterion. IEEE Trans Power Electron 38(6):7746–7759. https://doi.org/10.1109/tpel.2023.324676 – 10.1109/tpel.2023.3246763
• Fu X, Huang M, Tse CK, Yang J, Ling Y, Zha X (2023) Synchronization Stability of Grid-Following VSC Considering Interactions of Inner Current Loop and Parallel-Connected Converters. IEEE Trans Smart Grid 14(6):4230–4241. https://doi.org/10.1109/tsg.2023.326275 – 10.1109/tsg.2023.3262756
• Wang T, Ji T, Jiao D, Li Y, Wang Z (2022) Transient synchronization stability analysis of PLL-based VSC using Lyapunov’s direct method. International Journal of Electrical Power & Energy Systems 141:108135. https://doi.org/10.1016/j.ijepes.2022.10813 – 10.1016/j.ijepes.2022.108135
• Huang, Synchronization stability analysis of multi-VSC grid-connected system via multi-scale method. CSEE J. Power Energy Syst. (2023)
• Yang Z, Yu J, Kurths J, Zhan M (2021) Nonlinear Modeling of Multi-Converter Systems Within DC-Link Timescale. IEEE J Emerg Sel Topics Circuits Syst 11(1):5–16. https://doi.org/10.1109/jetcas.2020.304436 – 10.1109/jetcas.2020.3044361
• Chen L, Min Y, Hao L, Xing G, Li Y, Xu S (2024) Large-disturbance Stability Analysis of Power Systems with Synchronous Generator and Converter-interfaced Generation. Journal of Modern Power Systems and Clean Energy 12(3):997–1002. https://doi.org/10.35833/mpce.2023.00005 – 10.35833/mpce.2023.000051
• Tian Z, Tang Y, Zha X, Sun J, Huang M, Fu X, Liu F (2022) Hamilton-Based Stability Criterion and Attraction Region Estimation for Grid-Tied Inverters Under Large-Signal Disturbances. IEEE J Emerg Sel Topics Power Electron 10(1):413–423. https://doi.org/10.1109/jestpe.2021.307618 – 10.1109/jestpe.2021.3076189
• Tian Z, Li X, Zha X, Tang Y, Sun P, Huang M, Yu P (2023) Transient Synchronization Stability of an Islanded AC Microgrid Considering Interactions Between Grid-Forming and Grid-Following Converters. IEEE J Emerg Sel Topics Power Electron 11(4):4463–4476. https://doi.org/10.1109/jestpe.2023.327141 – 10.1109/jestpe.2023.3271418
• Nagam SS, Pal BC, Wu H, Blaabjerg F (2025) Synchronization Stability Analysis of SRF-PLL and DSOGI-PLL Using Port-Hamiltonian Framework. IEEE Trans Contr Syst Technol 33(3):952–962. https://doi.org/10.1109/tcst.2024.352371 – 10.1109/tcst.2024.3523711
• Liu N, Sun Z, He Z (2025) Stability Region Boundary of Multi-Paralleled Grid-Following Converter Systems Considering PLL Coupling Interactions. 2025 IEEE Power & Energy Society General Meeting (PESGM) 1– – 10.1109/pesgm52009.2025.11225651
• {“status”:”error” – 10.1109/tpel.2022.3153283
• Wang C, Jiang T, Chen H, Li X, Li G (2018) Transient Stability Assessment in Hybrid AC/DC Systems via Port Energy. 2018 IEEE Power & Energy Society General Meeting (PESGM) 1– – 10.1109/pesgm.2018.8586188
• Ghosh S, Isbeih YJ, Azman SK, Moursi MSE, El-Saadany E (2022) Optimal PMU Allocation Strategy for Completely Observable Networks With Enhanced Transient Stability Characteristics. IEEE Trans Power Delivery 37(5):4086–4102. https://doi.org/10.1109/tpwrd.2022.314446 – 10.1109/tpwrd.2022.3144462
• Fu X, Sun J, Huang M, Tian Z, Yan H, Iu HH-C, Hu P, Zha X (2021) Large-Signal Stability of Grid-Forming and Grid-Following Controls in Voltage Source Converter: A Comparative Study. IEEE Trans Power Electron 36(7):7832–7840. https://doi.org/10.1109/tpel.2020.304748 – 10.1109/tpel.2020.3047480
• Ding W, He C, Geng H, Liu Y (2025) A Novel Lyapunov Function for Transient Synchronization Stability Analysis of Grid-Following Converters. IEEE Trans Power Syst 40(4):3588–3591. https://doi.org/10.1109/tpwrs.2025.354534 – 10.1109/tpwrs.2025.3545348
• Zhang Y, Zhang C, Cai X (2022) Large-Signal Grid-Synchronization Stability Analysis of PLL-Based VSCs Using Lyapunov’s Direct Method. IEEE Trans Power Syst 37(1):788–791. https://doi.org/10.1109/tpwrs.2021.308902 – 10.1109/tpwrs.2021.3089025