含构网型与跟网型逆变器的多变流器系统小干扰稳定性分析方法

doi:10.19595/j.cnki.1000-6753.tces.241348

Abstract
Figure/Table
References
Related Citation (11)

Download: PDF (0 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract In recent years, small-signal stability analysis of multi-converter grid-tied systems has gained significant research attention. Existing methods in the literature often overlook three critical aspects: (1) calculating the number of right-half-plane (RHP) poles in the closed-loop transfer function, (2) addressing the singularities of the converter admittance matrix at 50 Hz, and (3) evaluating the impact of individual converters on system stability. To address these gaps, this study investigates small-signal stability analysis methods for multi-converter systems comprising grid-forming (GFM) and grid-following (GFL) inverters, with a focus on determining the number of RHP poles in the sequence admittance of GFM inverters.
First, a Norton-form mathematical model of the multi-converter system is established based on sequence admittance modeling. On the basis, the small signal stability analysis method of the multi-converter system is derived, and the step-by-step stability assessment procedures are presented. Secondly, due to the possibility of RHP poles in the sequence admittance matrix of the GFM converters, the frequency characteristic of the output sequence impedance matrix of the grid-forming converter, virtual synchronous generator (VSG), at 50 Hz is analyzed. A principled approach is proposed to construct the Nyquist curve at 50 Hz, enabling accurate calculation of the RHP poles in the VSG admittance matrix. Third, two case studies of multi-converter systems are analyzed to demonstrate how individual converters influence system stability. Finally, time-domain simulations and hardware-in-the-loop experiments validate the proposed method by comparing critical stability conditions with theoretical predictions.
Key findings include: (1) The proposed Norton-form model accommodates arbitrary network topologies and any number of GFM/GFL converters, enabling holistic stability analysis while quantifying the impact of individual converters. Stability margins are computed using Nyquist curves, with mirror-frequency effects accounted for to prevent misjudgment. (2) Analysis of VSG admittance RHP poles reveals that ignoring impedance matrix behavior at 50 Hz and ∞Hz leads to erroneous pole counts and stability assessments.
Three conclusions are drawn: (1) The recursive formulation of the proposed method supports systems with arbitrary converter counts, while the use of open-circuit impedance matrices generalizes the approach to any grid structure. (2) The method circumvents high-dimensional eigenvalue analysis of closed-loop transfer functions, relying instead on analytical eigenvalue formulas without numerical approximations. (3) By resolving the 50 Hz singularity in GFM admittance matrices, the correct count of RHP poles in the return ratio matrix is ensured, eliminating stability misclassification.

Key words： Multi-converter system grid-forming inverters grid-following inverters small-signal stability analysis hardware-in-the-loop experiment

Received: 28 July 2024

PACS:

TM712

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Liu Xin
	Deng Hao
	Jia Jiaoxin
	Wang Litong
	Sun Haifeng

Cite this article:

Liu Xin,Deng Hao,Jia Jiaoxin等. Small-Signal Stability Analysis Method for Multi-Converter System with Grid-Forming and Grid-Following Inverters[J]. Transactions of China Electrotechnical Society, 2025, 40(15): 4722-4739.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.241348 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I15/4722

[1] 雷雨, 李光辉, 王伟胜, 等. 跟网型和构网型新能源并网控制阻抗对比与振荡机理分析[J]. 中国电机工程学报, 2025, 45(1): 150-163.
Lei Yu, Li Guanghui, Wang Weisheng, et al.Com- parison of impedance characteristics and oscillation mechanism for grid following and grid forming renewable energy[J]. Proceedings of the CSEE, 2025, 45(1): 150-163.
[2] 黄萌, 凌扬坚, 耿华, 等. 功率同步控制的构网型变流器多机交互分析与稳定控制研究综述[J]. 高电压技术, 2023, 49(11): 4571-4583.
Huang Meng, Ling Yangjian, Geng Hua, et al.An overview on multi-VSCs interaction analysis and stability controls of grid-forming converters with power synchronization control[J]. High Voltage Engineering, 2023, 49(11): 4571-4583.
[3] Harnefors L, Hinkkanen M, Riaz U, et al.Robust analytic design of power-synchronization control[J]. IEEE Transactions on Industrial Electronics, 2019, 66(8): 5810-5819.
[4] Zhou Yuhan, Xin Huanhai, Wu Di, et al.Small-signal stability assessment of heterogeneous grid-following converter power systems based on grid strength analysis[J]. IEEE Transactions on Power Systems, 2023, 38(3): 2566-2579.
[5] Yang Dongsheng, Wang Xiongfei.Unified modular state-space modeling of grid-connected voltage- source converters[J]. IEEE Transactions on Power Electronics, 2020, 35(9): 9700-9715.
[6] Zhu Yue, Gu Yunjie, Li Yitong, et al.Impedance- based root-cause analysis: comparative study of impedance models and calculation of eigenvalue sensitivity[J]. IEEE Transactions on Power Systems, 2023, 38(2): 1642-1654.
[7] Liao Shuhan, Huang Meng, Zha Xiaoming, et al.Emulation of multi-inverter integrated weak grid via interaction-preserved aggregation[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(4): 4153-4164.
[8] Gao Xian, Zhou Dao, Anvari-Moghaddam A, et al.Stability analysis of grid-following and grid-forming converters based on state-space model[C]//2022 Inter- national Power Electronics Conference (IPEC-Himeji 2022-ECCE Asia), Himeji, Japan, 2022: 422-428.
[9] 陈新, 王赟程, 龚春英, 等. 采用阻抗分析方法的并网逆变器稳定性研究综述[J]. 中国电机工程学报, 2018, 38(7): 2082-2094, 2223.
Chen Xin, Wang Yuncheng, Gong Chunying, et al.Overview of stability research for grid-connected inverters based on impedance analysis method[J]. Proceedings of the CSEE, 2018, 38(7): 2082-2094, 2223.
[10] Sun Jian.Impedance-based stability criterion for grid- connected inverters[J]. IEEE Transactions on Power Electronics, 2011, 26(11): 3075-3078.
[11] Wu Heng, Wang Xiongfei, Kocewiak Ł H.Impedance- based stability analysis of voltage-controlled MMCs feeding linear AC systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(4): 4060-4074.
[12] Guo Jian, Chen Yandong, Wu Wenhua, et al.Wideband dq-frame impedance modeling of load-side virtual synchronous machine and its stability analysis in comparison with conventional PWM rectifier in weak grid[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(2): 2440-2451.
[13] 涂春鸣, 邹凯星, 高家元, 等. 基于不对称正负反馈效应的PQ功率控制并网逆变器稳定性分析[J]. 电工技术学报, 2023, 38(2): 496-509.
Tu Chunming, Zou Kaixing, Gao Jiayuan, et al.Stability analysis of grid-connected inverter under PQ power control based on asymmetric positive- negative-feedback effects[J]. Transactions of China Electrotechnical Society, 2023, 38(2): 496-509.
[14] 唐圣德, 胡海涛, 肖冬华, 等. 基于阻抗测量信息的电气化铁路“多车共网”系统稳定性分析[J]. 电工技术学报, 2024, 39(19): 6039-6053.
Tang Shengde, Hu Haitao, Xiao Donghua, et al.Stability analysis of electrified railway multiple train- network system based on impedance measurement information[J]. Transactions of China Electrotech- nical Society, 2024, 39(19): 6039-6053.
[15] Bode H W.Network Analysis and Feedback Amplifier Design[M]. New York: D. Van Nostrand Co. Inc, 1945.
[16] 郝艺, 周瑀涵, 刘晨曦, 等. 含跟网型储能的新能源多馈入系统小扰动电压支撑强度分析[J]. 电工技术学报, 2024, 39(11): 3569-3580.
Hao Yi, Zhou Yuhan, Liu Chenxi, et al.Small- disturbance voltage support strength analysis for renewable multi-infeed system with grid-following energy storage[J]. Transactions of China Electro- technical Society, 2023, 38(21): 5758-5770.
[17] Zhang Haitao, Wang Xiuli, Mehrabankhomartash M, et al.Harmonic stability assessment of multiterminal DC (MTDC) systems based on the hybrid AC/DC admittance model and determinant-based GNC[J]. IEEE Transactions on Power Electronics, 2022, 37(2): 1653-1665.
[18] Zhang Haitao, Mehrabankhomartash M, Saeedifard M, et al.Stability analysis of a grid-tied interlinking converter system with the hybrid AC/DC admittance model and determinant-based GNC[J]. IEEE Transa- ctions on Power Delivery, 2022, 37(2): 798-812.
[19] Wen Bo, Boroyevich D, Burgos R, et al.Inverse Nyquist stability criterion for grid-tied inverters[J]. IEEE Transactions on Power Electronics, 2017, 32(2): 1548-1556.
[20] 李信栋, 苟兴宇. 多输入多输出线性定常系统稳定裕度的分析与改进[J]. 控制理论与应用, 2014, 31(1): 105-111.
Li Xindong, Gou Xingyu.Analysis and improvement of stability margin for multi-input multi-output linear time-invariant systems[J]. Control Theory & Appli- cations, 2014, 31(1): 105-111.
[21] Liu Fangcheng, Liu Jinjun, Zhang Haodong, et al.Stability issues of Z+Z type cascade system in hybrid energy storage system (HESS)[J]. IEEE Transactions on Power Electronics, 2014, 29(11): 5846-5859.
[22] Xue Danhong, Liu Jinjun, Liu Zeng.Impedance-based stability analysis of two- terminal cascaded voltage source converter system[C]//2019 4th IEEE Work- shop on the Electronic Grid (eGRID), Xiamen, China, 2019: 1-5.
[23] 于彦雪, 马慧敏, 陈晓光, 等. 弱电网下基于准静态模型的混合控制微电网逆变器同步稳定性研究[J]. 电工技术学报, 2022, 37(1): 152-164.
Yu Yanxue, Ma Huimin, Chen Xiaoguang, et al.Synchronous stability research of inverters in hybrid microgrid based on the quasi-static models under weak grid[J]. Transactions of China Electrotechnical Society, 2022, 37(1): 152-164.
[24] Wang Xiongfei, Blaabjerg F, Loh P C.An impedance- based stability analysis method for paralleled voltage source converters[C]//2014 International Power Elec- tronics Conference (IPEC-Hiroshima 2014-ECCE ASIA), Hiroshima, Japan, 2014: 1529-1535.
[25] Cao Wenchao, Ma Yiwei, Wang F.Sequence- impedance-based harmonic stability analysis and controller parameter design of three-phase inverter- based multibus AC power systems[J]. IEEE Transa- ctions on Power Electronics, 2017, 32(10): 7674-7693.
[26] Guo Zixuan, Zhang Xing, Li Ming, et al.Stability analysis and capacity distribution of multi-paralleled current-controlled inverters and voltage-controlled VSGs grid-connected system[C]//2021 IEEE 12th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Chicago, IL, USA, 2021: 1-8.
[27] Jiang Shan, Zhu Ye, Konstantinou G.Settling angle- based stability criterion for power-electronics- dominated power systems[J]. IEEE Transactions on Power Electronics, 2023, 38(3): 2972-2984.
[28] Jiang Shan, Zhu Ye, Konstantinou G.Stability analysis of multi-bus power electronics defined power systems using phase information of nodal admittance matrix[J]. IEEE Transactions on Power Systems, 2024, 39(4): 6063-6075.
[29] Yang Dongsheng, Sun Yin.SISO impedance-based stability analysis for system-level small-signal stability assessment of large-scale power electronics- dominated power systems[J]. IEEE Transactions on Sustainable Energy, 2022, 13(1): 537-550.
[30] Zhang Chen, Cai Xu, Rygg A, et al.Sequence domain SISO equivalent models of a grid-tied voltage source converter system for small-signal stability analysis[J]. IEEE Transactions on Energy Conversion, 2018, 33(2): 741-749.
[31] 杜燕, 赵韩广, 杨向真, 等. 考虑频率耦合效应的虚拟同步发电机序阻抗建模[J]. 电源学报, 2020, 18(6): 42-49.
Du Yan, Zhao Hanguang, Yang Xiangzhen, et al.Sequence impedance modeling of virtual synchronous generator considering frequency coupling effect[J]. Journal of Power Supply, 2020, 18(6): 42-49.
[32] 徐少博, 徐永海, 陶顺, 等. 计及边带分量频率耦合的电压源型换流器输入导纳建模[J]. 电工技术学报, 2023, 38(11): 2883-2893.
Xu Shaobo, Xu Yonghai, Tao Shun, et al.Voltage source converter input admittance model considering frequency coupling of sideband components[J]. Transactions of China Electrotechnical Society, 2023, 38(11): 2883-2893.
[33] 刘欣, 郭志博, 贾焦心, 等. 基于序阻抗的虚拟同步发电机并网稳定性分析及虚拟阻抗设计[J]. 电工技术学报, 2023, 38(15): 4130-4146.
Liu Xin, Guo Zhibo, Jia Jiaoxin, et al.Stability analysis and virtual impedance design of virtual synchronous machine based on sequence impe- dance[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4130-4146.
[34] 李红, 梁军杨, 王振民, 等. 跟网型变换器的小扰动同步稳定机理分析与致稳控制[J]. 电工技术学报, 2024, 39(12): 3802-3815.
Li Hong, Liang Junyang, Wang Zhenmin, et al.Smallsignal synchronization stability analysis and improved control strategy for grid following con- verter[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3802-3815.
[35] Gu Yunjie, Li Yitong, Zhu Yue, et al.Impedance- based whole-system modeling for a composite grid via embedding of frame dynamics[J]. IEEE Transa- ctions on Power Systems, 2021, 36(1): 336-345.
[36] Cao Wenchao, Ma Yiwei, Wang F.Harmonic stability analysis and controller parameter design of three- phase inverter-based multi-bus AC systems based on sequence impedances[C]//2016 IEEE Energy Con- version Congress and Exposition (ECCE), Milwaukee, WI, USA, 2016: 1-8.
[37] Rygg A, Molinas M, Zhang Chen, et al.A modified sequence-domain impedance definition and its equivalence to the dq-domain impedance definition for the stability analysis of AC power electronic systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2016, 4(4): 1383-1396.
[38] Shah S, Parsa L.Impedance modeling of three-phase voltage source converters in DQ, sequence, and phasor domains[J]. IEEE Transactions on Energy Conversion, 2017, 32(3): 1139-1150.