Quantitative Evaluation Method of Multi-Region Frequency Support Strength Based on Eigen-Decomposition
Cao Hui1, Zhu Jizhong1, Song Xiaozhe2, Pan Jianhong2, Zhao Lianfei2, Liu Yun1
1. School of Electric Power Engineering South China University of Technology Guangzhou 510641 China; 2. State Grid Jilin Electric Power Company Limited Changchun 130021 China
Abstract：With the increasing penetration of renewable energy sources in power systems, the spatial heterogeneity of frequency regulation resources is becoming increasingly pronounced, while the inter-regional electrical coupling strength is gradually diminishing. Consequently, these factors lead to the increasingly significant frequency differences between different regions of the power grid. The estimation errors for quantitative metrics of system frequency support strength are significantly amplified under the traditional global frequency response model. Therefore, this paper proposes a quantitative evaluation method for multi-region frequency support strength considering the characteristics of spatial distribution differences. First, this paper derives an analytical model of regional frequency responses utilizing the eigen-decomposition of frequency modes. Furthermore, based on the multi-region frequency response analytical model, a quantitative metric for evaluating multi-region frequency support strength is established. This strength is characterized by the frequency nadir (Δfnadir) and the maximum rate of change of frequency (RoCoFmax) in homogeneous power systems where the parameters of the equipment across regions maintain identical ratios. During the model derivation process, a reasonable conservative design principle is introduced to preserve accuracy while ensuring a sufficient safety margin, thereby facilitating practical engineering applications. Subsequently, in contrast to homogeneous cases, heterogeneous systems are characterized by disproportional equipment parameters across different regions. To analyze such systems, this paper employs a parameter transfer methodology that converts heterogeneous system parameters into homogeneous equivalents. Building on this foundation, the paper develops a quantitative analytical model for evaluating multi-region frequency support strength, incorporating the coordinated participation of multiple types of frequency support equipment in heterogeneous power systems. The simulation results reveal that regional frequency can be decomposed into the common mode frequency (CMF), which represents the global system frequency dynamics, and the differential mode frequency (DMF), which captures inter-regional frequency deviations. With the non-uniform distribution of frequency regulation resources, a significant divergence occurs between the CMF and individual regional frequencies. Validation across multiple scenarios reveals that the proposed multi-region frequency support strength evaluation model demonstrates strong performance in homogeneous systems, with relative errors remaining within 5% while maintaining conservative characteristics. The relative errors of the heterogeneous-to-homogeneous parameter conversion method exhibit a positive correlation with the degree of system heterogeneity. Subsequent comprehensive validation in diverse heterogeneous systems confirms that the proposed analytical model consistently yields high numerical fidelity, maintaining relative errors well within 5% across a wide spectrum of operational scenarios. Finally, to further validate the proposed method, the proposed model is applied to the actual two-region England-Scotland power system. It demonstrates high accuracy and a desirable degree of conservatism, highlighting its practical engineering value. The main conclusions are as follows: (1) The proposed multi-region frequency response model, incorporating coordinated operation of diverse frequency regulation resources, accurately captures the dynamic characteristics of regional frequency. (2) The frequency support strength evaluation model for homogeneous systems exhibits both highly accurate and conservative performance across diverse operating conditions. (3) This study validates the feasibility of heterogeneous-to-homogeneous parameter conversion methodology. Furthermore, the validation results confirm that the multi-region frequency support strength evaluation model maintains acceptable accuracy in heterogeneous systems, thereby verifying its practical effectiveness in power systems.
曹徽, 朱继忠, 宋晓喆, 潘建宏, 赵连飞, 刘云. 基于特征模态分解的多区域频率支撑强度量化评估[J]. 电工技术学报, 2026, 41(15): 5058-5071.
Cao Hui, Zhu Jizhong, Song Xiaozhe, Pan Jianhong, Zhao Lianfei, Liu Yun. Quantitative Evaluation Method of Multi-Region Frequency Support Strength Based on Eigen-Decomposition. Transactions of China Electrotechnical Society, 2026, 41(15): 5058-5071.
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