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.
刘欣, 邓昊, 贾焦心, 王利桐, 孙海峰. 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[J]. 电工技术学报, 2025, 40(15): 4722-4739.
Liu Xin, Deng Hao, Jia Jiaoxin, Wang Litong, Sun Haifeng. Small-Signal Stability Analysis Method for Multi-Converter System with Grid-Forming and Grid-Following Inverters. Transactions of China Electrotechnical Society, 2025, 40(15): 4722-4739.
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