Impedance Characteristics and Oscillation Stability Mechanism in Grid-Forming Converters Based on Multi-Loop Decoupling
Yan Zihan1, Ai Xin1, Yu Siqi2, Liu Hui2, Li Yunhong2
1. State Key Lab of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China 2. Electric Power Research Institute of State Grid Jibei Electric Power Co. Ltd Beijing 100045 China
Abstract：The multi-loop control architecture of grid-forming converters (GFMs)—comprising outer power synchronization loops and inner voltage-current regulation loops—introduces complex coupling across multiple timescales, complicating the characterization of impedance properties and the analysis of oscillation mechanisms, particularly under diverse grid conditions such as weak/strong grids and series-compensated lines. Although substantial research has been conducted on GFM oscillation stability, two major challenges remain: the complexity of control topologies and difficulties in decoupling, and the lack of adaptability analysis under multi-scenario interactions. To address these issues, this paper proposes a novel modulation signal-based control loop decoupling method that quantitatively isolates the individual contributions of the frequency loop, voltage loop, and dual inner loops to the impedance characteristics. Firstly, the impedance expression of the GFM grid-connected system is shown to be determined by the transfer functions of modulated small signals with respect to voltage and current. Using harmonic linearization, these transfer functions were further decoupled to distinguish the effects of the frequency and voltage loops. The decoupled transfer functions were then incorporated into the impedance model to isolate the influence of each loop. This impedance decomposition method was also applied to GFMs with inner loops. By comparing the decomposition results of dual inner-loop control structures with those without inner loops, the interaction between the dual inner loops and the frequency/voltage loops can be analyzed separately. The study further revealed that the dual inner loops introduce an equivalent negative inductance, which counteracts the physical filter inductance and leads to capacitive impedance phase characteristics—a key factor affecting grid-connected stability. This mechanism was derived analytically through control path simplification and matrix operations. Frequency scanning in MATLAB/Simulink demonstrated strong agreement between the theoretical and simulated impedance across a wide frequency range, validating the proposed model. Impedance comparison and decomposition results indicate that the dual inner-loop structure decisively influences low-frequency capacitive behavior and high-frequency resonance peaks. By effectively controlling the voltage outside the filter, the dual inner loops counteract part of the filter impedance under steady control conditions, resulting in two major effects: (1) the phase-frequency characteristics of the GFM approach the negative damping region over a wider frequency range, shifting the high-frequency resonance backward; and (2) the risk of high-frequency oscillation in GFMs connected via LC filters is reduced. The outer loops primarily affect impedance characteristics near the fundamental frequency. The power-frequency resonance peak is dominated by the frequency loop. Compared to virtual synchronous generator (VSG) control, active power droop control significantly reduces the impedance magnitude at fundamental frequency and narrows the negative damping region. Similarly, reactive power droop control reduces the negative damping region more effectively than integral droop control. Thus, first-order control structures outperform second-order ones in terms of small-signal stability near fundamental frequency. Stability comparisons under different grid conditions yield the following conclusions: (1) The oscillation risk of GFMs without inner loops in strong grids can be mitigated by adopting first-order control structures or adjusting control parameters, such as reducing the voltage deviation feedback coefficient in the voltage loop and increasing the damping coefficient in the frequency loop; (2) The introduction of dual voltage-current inner loops increases oscillation risks in strong grids but enhances stability in series-compensated transmission scenarios. These findings are corroborated by time-domain simulations.
闫子晗, 艾欣, 于思奇, 刘辉, 李蕴红. 基于多环控制解耦的构网型变流器阻抗特性与振荡稳定机理研究[J]. 电工技术学报, 0, (): 250458-.
Yan Zihan, Ai Xin, Yu Siqi, Liu Hui, Li Yunhong. Impedance Characteristics and Oscillation Stability Mechanism in Grid-Forming Converters Based on Multi-Loop Decoupling. Transactions of China Electrotechnical Society, 0, (): 250458-.
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