Abstract：With the large-scale integration of high-proportion inverter-based resources (IBRs), the synchronous dynamic (SD) characteristics of modern power systems have undergone significant changes. The reduction in system equivalent inertia results in more severe frequency fluctuations, posing new challenges to frequency security and stability. Based on flexible control algorithms, these IBRs are mainly categorized into grid-forming inverters (GFMs) and grid-following inverters (GFLs). The distinct external characteristics of GFMs and GFLs further complicate the analysis of frequency stability in power systems. To quantitatively analyze the frequency support strength of IBRs, it is essential to consider the impact of various influencing factors on system stability. Modal Analysis based on the state-space model (MASS) quantifies the contribution of each state variable to a specific mode using the participation factor (PF). However, issues such as the black-box nature of the model and the curse of dimensionality limit its applicability in large-scale systems. Currently, impedance-based analysis methods have been widely discussed. Based on the whole-system dynamic admittance matrix and dynamic impedance matrix, the modal analysis based on impedance model (MAI) method introduces the impedance participation factor (IPF) and the admittance participation factor (APF). IPF and APF treat IBRs as a whole, considering their overall dynamic impact on system stability. As a result, MAI cannot provide detailed insights into the internal dynamics of IBRs. To address the control characteristics of GFMs, the impedance-based extended modal analysis (EMAI) method classifies the GFM dynamics into SD, dominated by the power frequency synchronization loop (PFL), and electromagnetic dynamics (ED), governed by the voltage control loop (VCL). For GFLs, the admittance- based EMAI method categorizes their dynamics into SD, dominated by the phase-locked loop (PLL), and ED, governed by the current control loop (CCL). However, the relationship between the impedance-based EMAI and the admittance-based EMAI remains unclear. Moreover, in large-scale systems, multiple oscillatory modes with weak damping may exist, and the SD of different IBRs may contribute to these modes. As a result, EMAI alone may not be sufficient for directly and equitably assessing the frequency support capability of different IBRs. This paper proposes an accurate evaluation method for IBR frequency support strength based on EMAI. First, the unification of the IPF and APF is demonstrated, thereby extending the applicability of the EMAI method to analyze the internal ED and SD of IBRs in hybrid power systems that contain GFMs and GFLs. Subsequently, based on EMAI, the maximum perturbation level of the dominant SD mode in IBRs is calculated to define the frequency support margin (FSM), which determines the frequency support strength of IBRs. Then, FSM is used to analyze the impact of different improvement measures on the frequency support strength of IBRs. Finally, simulations of a single GFM/GFL infinite system and a modified IEEE 14-bus system are conducted. Depending on data availability, the proposed method can adopt either a data-driven or model-driven approach, making it highly applicable in engineering practice. The unified EMAI enables the analysis of internal SD in different types of IBRs, without being restricted to specific frequency response ports, allowing for direct extraction from widely used impedance/admittance models. For GFMs, lower grid impedance, reduced proportional and integral gains of the VCL (narrower VCL bandwidth), and higher PFL droop gains lead to a decrease in frequency support strength. For GFLs, higher grid impedance, reduced proportional and integral gains of the CCL (resulting in a narrower CCL bandwidth), and increased proportional and integral gains of the PFL (resulting in a wider CCL bandwidth) contribute to a reduction in frequency support strength.
郑佳杰, 郑乐, 林家见, 徐辉, 刘崇茹. 基于扩展阻抗模态分析的逆变器频率支撑强度量化评估[J]. 电工技术学报, 2026, 41(8): 2788-2804.
Zheng Jiajie, Zheng Le, Lin Jiajian, Xu Hui, Liu Chongru. Quantitative Evaluation of Inverter Frequency Support Strength Based on Extended Impedance Modal Analysis. Transactions of China Electrotechnical Society, 2026, 41(8): 2788-2804.
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