Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid

Xin Jin; Zhipeng Zhou; Ningyi Dai

doi:10.35833/MPCE.2025.000833

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Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid

Original Paper | 更新时间：2026-09-28

- Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid
- Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid
- MPCE 2026年14卷第5期页码：1672-1683
- 作者机构：
  
  State Key Laboratory of Internet of Things for Smart City and the Department of Electrical and Computer Engineering, University of Macau, Macao, China
- 作者简介：
  
  Xin Jin received the B.S. degree in automation from Northeastern University, Shenyang, China, in 2017, and the M.S. degree in electrical engineering from Chongqing University, Chongqing, China, in 2020. He is currently working toward the Ph.D. degree in electrical and computer engineering with University of Macau, Macao, China. In 2025, he was a Visiting Researcher with Auckland University of Technology, Auckland, New Zealand. His research interests include modeling, analysis, and design of power electronic system. Email:yc27997@um.edu.mo
  Zhipeng Zhou received the B.S. degree in electrical engineering and automation from Jilin University, Changchun, China, in 2019, and the M.S. degree in electrical and computer engineering from University of Macau, Macao, China, in 2022. He is currently working toward the Ph.D. degree in electrical and computer engineering with University of Macau, Macao, China. His research interests include power electronics, modular multilevel converter, harmonics suppression, and optimization algorithm. Email:yc37936@um.edu.mo
  Ningyi Dai received the B.Sc. degree in electrical engineering from Southeast University, Nanjing, China, in 2001, and the M.Sc. and Ph.D. degrees in electrical and electronics engineering from University of Macau, Macao, China, in 2004 and 2007, respectively. She is currently an Associate Professor in the Department of Electrical and Computer Engineering and the State Key Laboratory of Internet of Things for Smart City, University of Macau. She is also the Assistant Dean of the Faculty of Science and Technology, University of Macau. Her research interests include application of power electronics in power system, and design and control of multi-level power converter. Email:nydai@um.edu.mo
- 基金信息：
  
  This paper was supported by the Science and Technology Development Fund, Macau SAR(001/2024/SKL);FDCT-GDST(0038/2024/AGJ);the Guang Dong-Macau Joint Funding Scheme for Science and Technology Innovation(2024A0505090017)
- DOI：10.35833/MPCE.2025.000833
  中图分类号：
- 收稿：2025-09-05，
  
  修回：2025-12-04，
  
  录用：2026-03-16，
  
  网络首发：2026-04-01，
  
  纸质出版：2026-09-15
- 稿件说明：
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Xin Jin, Zhipeng Zhou, Ningyi Dai. Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid[J]. MPCE, 2026,14(5):1672-1683.

Jin Xin,Zhou Zhipeng,Dai Ningyi.Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1672-1683.
Xin Jin, Zhipeng Zhou, Ningyi Dai. Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid[J]. MPCE, 2026,14(5):1672-1683. DOI： 10.35833/MPCE.2025.000833.

Jin Xin,Zhou Zhipeng,Dai Ningyi.Robust Stability Analysis and Design of Parallel Grid-forming Converters in Islanded Microgrid[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1672-1683. DOI： 10.35833/MPCE.2025.000833.

摘要

Abstract

The stability of microgrid (MG) is affected by the interaction between parallel inverter-based resources (IBRs)

especially when grid-forming (GFM) control is implemented in islanded MG to provide voltage support. In this paper

the robust stability analysis using structured singular value (SSV) approach and design of parallel GFM converters in islanded MG by structured

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119205053&type=

2.03200006

2.96333337

synthesis are presented

catering to its multi-input multi-output (MIMO) nature. Specifically

a modular state-space model of parallel GFM converters in islanded MG is derived with component connection method (CCM). Model uncertainty is captured against the nominal model

delivering a certain degree of robustness for stability analysis

in the face of potential parametric uncertainty and resonance effects induced by parallel GFM converters. Moreover

the effects of system parameters on robust stability are comprehensively analyzed

and a robust design is proposed for virtual impedance (VI) tuning. The accuracy of modelling and robust stability analysis

as well as the effectiveness of the robust design is validated in MATLAB/Simulink/PLECS and real-time digital simulator (RTDS).

关键词

Keywords

references

M. Chen, D. Zhou, and F. Blaabjerg, “Modelling, implementation, and assessment of virtual synchronous generator in power systems,” Journal of Modern Power Systems and Clean Energy , vol. 8 , no. 3 , pp. 399 - 411 , May 2020.

J. Wang, Z. Liu, Y. Shi et al. , “A communication-less secondary control method for parallel grid-forming inverters in islanded microgrids based on mode switching,” IEEE Transactions on Power Electronics , vol. 39 , no. 3 , pp. 3683 - 3701 , Mar. 2024 .

A. González-Cajigas, J. Roldán-Pérez, and E. J. Bueno, “Design and analysis of parallel-connected grid-forming virtual synchronous machines for island and grid-connected applications,” IEEE Transactions on Power Electronics , vol. 37 , no. 5 , pp. 5107 - 5121 , May 2022.

S. Fu, Y. Sun, L. Li et al. , “Power oscillation suppression of multi-VSG grid via decentralized mutual damping control,” IEEE Transactions on Industrial Electronics , vol. 69 , no. 10 , pp. 10202 - 10214 , Oct. 2022 .

X. Wang, M. G. Taul, H. Wu et al. , “Grid-synchronization stability of converter-based resources – an overview,” IEEE Open Journal of Industry Applications , vol. 1 , pp. 115 - 134 , Aug. 2020 .

Q. Zhong and G. Weiss, “Synchronverters: inverters that mimic synchronous generators,” IEEE Transactions on Industrial Electronics , vol. 58 , no. 4 , pp. 1259 - 1267 , Apr. 2011 .

R. H. Lasseter, Z. Chen, and D. Pattabiraman, “Grid-forming inverters: a critical asset for the power grid,” IEEE Journal of Emerging and Selected Topics in Power Electronics , vol. 8 , no. 2 , pp. 925 - 935 , Jun. 2020 .

F. Zhao, T. Zhu, Z. Li et al. , “Low-frequency resonances in grid-forming converters: causes and damping control,” IEEE Transactions on Power Electronics , vol. 39 , no. 11 , pp. 14430 - 14447 , Nov. 2024 .

F. Zhao, T. Zhu, L. Harnefors et al. , “Closed-form solutions for grid-forming converters: a design-oriented study,” IEEE Open Journal of Power Electronics , vol. 5 , pp. 186 - 200 , Feb. 2024 .

R. Liu, H. Zhang, C. Xue et al. , “Distributed low-frequency oscillation damping in low-volta ge islanded multi-bus microgrids with virtual synchronous generators,” IEEE Transactions on Smart Grid , vol. 15 , no. 6 , pp. 5331 - 5345 , Nov. 2024 .

J. Liu, Y. Miura, and T. Ise, “Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter-based distributed generators,” IEEE Transactions on Power Electronics , vol. 31 , no. 5 , pp. 3600 - 3611 , May 2016.

Z. Shuai, W. Huang, Z. J. Shen et al. , “Active power oscillation and suppression techniques between two parallel synchronverters during load fluctuations,” IEEE Transactions on Power Electronics , vol. 35 , no. 4 , pp. 4127 - 4142 , Apr. 2020 .

M. Chen, D. Zhou, C. Wu et al. , “Characteristics of parallel inverters applying virtual synchronous generator control,” IEEE Transactions on Smart Grid , vol. 12 , no. 6 , pp. 4690 - 4701 , Nov. 2021 .

B. Yang, H. Li, S. Xu et al. , “Systematic methods to eliminate the transient circulating powers in the multi-VSGs system,” IEEE Transactions on Smart Grid , vol. 15 , no. 1 , pp. 179 - 190 , Jan. 2024 .

S. Chen, H. Han, Z. Wu et al. , “Distributed frequency interactive damping control for multiple VSGs in islanded microgrids,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 71 , no. 8 , pp. 3867 - 3879 , Aug. 2024 .

X. Li, S. Huang, Z. Wang et al. , “Decentralized frequency restoration and power oscillation damping control for islanded microgrids with multiple VSGs,” Journal of Modern Power Systems and Clean Energy , vol. 13 , no. 2 , pp. 564 - 573 , Mar. 2025 .

M. Yang, Y. Wang, and J. M. Guerrero, “Impact of reactive power control on low-frequency oscillation of virtual synchronous generators,” IEEE Transactions on Power Systems , vol. 40 , no. 4 , pp. 3604 - 3607 , Jul. 2025 .

N. Pogaku, M. Prodanovic, and T. C. Green, “Modeling, analysis and testing of autonomous operation of an inverter-based microgrid,” IEEE Transactions on Power Electronics , vol. 22 , no. 2 , pp. 613 - 625 , Mar. 2007 .

M. Li, Y. Wang, W. Hu et al. , “Unified modeling and analysis of dynamic power coupling for grid-forming converters,” IEEE Transactions on Power Electronics , vol. 37 , no. 2 , pp. 2321 - 2337 , Feb. 2022 .

S. Fu, Y. Sun, J. Lin et al. , “ P / Q-ω / V admittance modeling and oscillation analysis for multi-VSG grid-connected system,” IEEE Transactions on Power Systems , vol. 38 , no. 6 , pp. 5849 - 5859 , Nov. 2023 .

R. Wang, Y. Wang, P. Zhang et al. , “System modeling and robust stability region analysis for multi-inverters based on VSG,” IEEE Journal of Emerging and Selected Topics in Power Electronics , vol. 12 , no. 6 , pp. 6042 - 6052 , Dec. 2024 .

Z. Shuai, Y. Hu, Y. Peng et al. , “Dynamic stability analysis of synchronverter-dominated microgrid based on bifurcation theory,” IEEE Transactions on Industrial Electronics , vol. 64 , no. 9 , pp. 7467 - 7477 , Sept. 2017.

J. Yu, S. Wang, Z. Liu et al. , “Accurate small-signal terminal characteristic model and SISO stability analysis approach for parallel grid-forming inverters in islanded microgrids,” IEEE Transactions on Power Electronics , vol. 38 , no. 5 , pp. 6597 - 6612 , May 2023.

S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design . Hoboken: Wiley, 2001.

K. Zhou and J. C. Doyle, Essentials of Robust Control . Upper Saddle River: Prentice-Hall, 1998.

R. Rosso, S. Engelken, and M. Liserre, “Robust stability analysis of synchronverters operating in parallel,” IEEE Transactions on Power Electronics , vol. 34 , no. 11 , pp. 11309 - 11319 , Nov. 2019 .

D. B. Rathnayake, S. P. Me, R. Razzaghi et al. , “ H ∞ -based control design for grid-forming inverters with enhanced damping and virtual inertia,” IEEE Journal of Emerging and Selected Topics in Power Electronics , vol. 11 , no. 2 , pp. 2311 - 2325 , Apr. 2023 .

A. Singh, V. Debusschere, N. Hadjsaid et al. , “Slow-interaction converter-driven stability in the distribution grid: small-signal stability analysis with grid-following and grid-forming inverters,” IEEE Transactions on Power Systems , vol. 39 , no. 2 , pp. 4521 - 4536 , Mar. 2024 .

M. A. Guerrero, B. Lakshminarayanan, and C. R. Rojas, “Data-driven estimation of structured singular values,” IEEE Control Systems Letters , vol. 9 , pp. 1976 - 1981 , Jun. 2025 .

Y. Chen, S. Pan, M. Huang et al. , “Robust stability assessment of single-phase inverter with multiparameter distributions,” IEEE Transactions on Power Electronics , vol. 37 , no. 5 , pp. 6062 - 6073 , May 2022.

S. Sumsurooah, M. Odavic, and S. Bozhko, “

approach to robust stability domains in the space of parametric uncertainties for a power system with ideal CPL,” IEEE Transactions on Power Electronics , vol. 33 , no. 1 , pp. 833 - 844 , Jan. 2018 .

M. Naderi, Y. Khayat, Q. Shafiee et al. , “Robust synchronization of multiple converter-based weak microgrids for smooth interconnection,” IEEE Transactions on Power Systems , vol. 39 , no. 2 , pp. 2763 - 2774 , Mar. 2024 .

S. Chakraborty, M. T. Rana, and M. V. Salapaka, “A robust power hardware-in-the-loop interface under uncertain software and hardware system,” IEEE Transactions on Industrial Electronics , vol. 72 , no. 6 , pp. 6088 - 6102 , Jun. 2025 .

Mathworks Inc. (2025, Mar.). Matlab robust control toolbox user’s guide. [Online]. Available: http://www.mathworks.com/help/pdf_doc/robust/robust_ug.pdf

P. Gahinet and P. Apkarian, “Structured H ∞ synthesis in MATLAB,” in Proceedings of the 18th World Congress of the International Federation of Automatic Control , Milano, Italy, Aug.-Sept. 2011, pp. 1435 - 1440 .

J. Zhao, J. Dong, H. Cheng et al. , “Power oscillation analysis and suppression for paralleled system of diesel generator and virtual synchronous generator integrated with periodic pulsed load,” Journal of Modern Power Systems and Clean Energy , vol. 14 , no. 2 , pp. 416 - 429 , Mar. 2026 .

M. Ghafouri, U. Karaagac, H. Karimi et al. , “Robust subsynchronous interaction damping controller for DFIG-based wind farms,” Journal of Modern Power Systems and Clean Energy , vol. 7 , no. 6 , pp. 1663 - 1674 , Nov. 2019 .

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