基于特征模态分解的多区域频率支撑强度量化评估

doi:10.19595/j.cnki.1000-6753.tces.251271

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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 (Δf_nadir) and the maximum rate of change of frequency (RoCoF_max) 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.

Key words： Regional frequency frequency support strength quantitative analysis rate of change of frequency frequency nadir

Received: 18 July 2025

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TM712

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	Articles by authors
	Cao Hui
	Zhu Jizhong
	Song Xiaozhe
	Pan Jianhong
	Zhao Lianfei
	Liu Yun

Cite this article:

Cao Hui,Zhu Jizhong,Song Xiaozhe等. Quantitative Evaluation Method of Multi-Region Frequency Support Strength Based on Eigen-Decomposition[J]. Transactions of China Electrotechnical Society, 2026, 41(15): 5058-5071.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251271 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I15/5058

[1] 张显, 王彩霞, 谢开, 等. “双碳”目标下中国绿色电力市场建设关键问题[J]. 电力系统自动化, 2024, 48(4): 25-33.
Zhang Xian, Wang Caixia, Xie Kai, et al.Key issues of green electricity market construction in China under goals of carbon emission peak and carbon neutrality[J]. Automation of Electric Power Systems, 2024, 48(4): 25-33.
[2] 丁俊, 王欣怡, 邵烨楠, 等. 新型电力系统的影响因素分析[J]. 电气技术, 2022(7): 42-45.
Ding Jun, Wang Xinyi, Shao Yenan, et al.Analysis on influencing factors of new power system[J]. Electrical Engineering, 2022(7): 42-45.
[3] 安军, 李可心, 周毅博, 等. 面向抑制频率波动的新型电力系统调频能力需求评估[J]. 电工技术学报, 2026, 41(5): 1495-1509.
An Jun, Li Kexin, Zhou Yibo, et al.Evaluation of frequency modulation capability demand for new power system oriented to suppressing frequency fluctuations[J]. Transactions of China Electrotechnical Society, 2026, 41(5): 1495-1509.
[4] Azizipanah-Abarghooee R, Malekpour M, Dragičević T, et al.A linear inertial response emulation for variable speed wind turbines[J]. IEEE Transactions on Power Systems, 2020, 35(2): 1198-1208.
[5] 马遥, 胥国毅, 旷世奇, 等. 计及响应差异的新能源场站调频能力评估方法[J]. 中国电机工程学报, 2026, 46(9): 3493-3503.
Ma Yao, Xu Guoyi, Kuang Shiqi, et al.Evaluation method for frequency-modulation capability of new-energy power plants considering response differences[J]. Proceedings of the CSEE, 2026, 46(9): 3493-3503.
[6] 张祥宇, 邵孜建, 付媛. 风储并网发电系统的虚拟多段协同调速与频率安全支撑技术[J]. 电工技术学报, 2025, 40(15): 4677-4693.
Zhang Xiangyu, Shao Zijian, Fu Yuan.Virtual multi-stage coordinated speed regulation and frequency safety support technology of wind-storage grid-connected power generation system[J]. Transactions of China Electrotechnical Society, 2025, 40(15): 4677-4693.
[7] 赵冬梅, 宋晨铭, 冯向阳, 等. 100%新能源场景下考虑频率稳定约束的源网荷储一体化系统储能优化配置[J]. 电工技术学报, 2025, 40(7): 2146-2161.
Zhao Dongmei, Song Chenming, Feng Xiangyang, et al.The optimal configuration of energy storage in the source-grid-load-storage integrated system considering frequency stability constraints in 100% new energy scenarios[J]. Transactions of China Electrotechnical Society, 2025, 40(7): 2146-2161.
[8] Li Xiangxin, Zhou Ming, Luo Yazhou.A disturbance source location method on the low frequency oscillation with time-varying steady-state points[J]. CES Transactions on Electrical Machines and Systems, 2018, 2(2): 226-231.
[9] 刘琦, 占萌, 李威, 等. 同步机和非同步机电源接入强弱网系统小扰动稳定特性比较与统一分析[J]. 电工技术学报, 2026, 41(1): 182-200.
Liu Qi, Zhan Meng, Li Wei, et al.Comparison and unified analysis of small-signal stability characteristics of systems with synchronous and asynchronous power sources connected to strong and weak grids[J]. Transactions of China Electrotechnical Society, 2026, 41(1): 182-200.
[10] 韩刚, 张琛, 蔡旭. 电网短路故障引发的全功率风电机组频率失稳机理与控制方法[J]. 电工技术学报, 2018, 33(10): 2167-2175.
Han Gang, Zhang Chen, Cai Xu.Mechanism of frequency instability of full-scale wind turbines caused by grid short circuit fault and its control method[J]. Transactions of China Electrotechnical Society, 2018, 33(10): 2167-2175.
[11] 贺海磊, 张彦涛, 孙骁强, 等. 考虑频率安全约束的西北电网新能源开发及直流外送规模评估方法[J]. 中国电机工程学报, 2021, 41(14): 4753-4762.
He Hailei, Zhang Yantao, Sun Xiaoqiang, et al.Evaluation method of renewable energy development scale and DC transmission scale of China northwest power grid by considering frequency security constraints[J]. Proceedings of the CSEE, 2021, 41(14): 4753-4762.
[12] Gu Huajie, Yan Ruifeng, Saha T.Review of system strength and inertia requirements for the national electricity market of Australia[J]. CSEE Journal of Power and Energy Systems, 2019, 5(3): 295-305.
[13] 李卫东, 王祥旭, 于瀚林, 等. 大扰动下电力系统频率安全概率指标初探[J]. 电力系统自动化, 2025, 49(10): 12-19.
Li Weidong, Wang Xiangxu, Yu Hanlin, et al.Preliminary study on probabilistic indicators for frequency security of power systems under large disturbances[J]. Automation of Electric Power Systems, 2025, 49(10): 12-19.
[14] Chan M L, Dunlop R D, Schweppe F. Dynamic equivalents for average system frequency behavior following major distribances[J]. IEEE Transactions on Power Apparatus and Systems, 1972, PAS-91(4): 1637-1642.
[15] Anderson P M, Mirheydar M.A low-order system frequency response model[J]. IEEE Transactions on Power Systems, 1990, 5(3): 720-729.
[16] Paganini F, Mallada E.Global analysis of synchronization performance for power systems: bridging the theory-practice gap[J]. IEEE Transactions on Automatic Control, 2020, 65(7): 3007-3022.
[17] Gao Huisheng, Xin Huanhai, Huang Linbin, et al.Common-mode frequency in converter-integrated power systems: definition, analysis, and quantitative evaluation[J]. IEEE Transactions on Power Systems, 2022, 37(6): 4846-4860.
[18] 高晖胜, 辛焕海, 黄林彬, 等. 新能源电力系统的共模频率分析及其特征量化[J]. 中国电机工程学报, 2021, 41(3): 890-899.
Gao Huisheng, Xin Huanhai, Huang Linbin, et al.Characteristic analysis and quantification of common mode frequency in power systems with high penetration of renewable resources[J]. Proceedings of the CSEE, 2021, 41(3): 890-899.
[19] 李智轩, 陈亦平, 雪映, 等. 多分区异步互联电力系统频率稳定分析与控制研究综述[J]. 电网技术, 2024, 48(12): 5003-5023.
Li Zhixuan, Chen Yiping, Xue Ying, et al.Frequency stability analysis and control of multi-area asynchronous interconnected systems: a review[J]. Power System Technology, 2024, 48(12): 5003-5023.
[20] Wall P, Shams N, Terzija V, et al.Smart frequency control for the future GB power system[C]//2016 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), Ljubljana, Slovenia, 2016: 1-6.
[21] 胡源, 薛松, 张寒, 等. 近30年全球大停电事故发生的深层次原因分析及启示[J]. 中国电力, 2021, 54(10): 204-210.
Hu Yuan, Xue Song, Zhang Han, et al.Cause analysis and enlightenment of global blackouts in the past 30 years[J]. Electric Power, 2021, 54(10): 204-210.
[22] 典焱. 英国大停电事故分析: 新能源大量替代传统火电将导致系统惯量水平下降[J]. 电力设备管理, 2019(9): 98.
Dian Yan.Analysis of the UK's blackouts: a large replacement of traditional thermal power by new energy sources will lead to a decline in system inertia levels[J]. Electric Power Equipment Management, 2019(9): 98.
[23] Bi Tianshu, Liu Jiahao, Wang Cheng.Online estimation of area-level inertia considering inter-area equivalent frequency dynamics[J]. IEEE Transactions on Power Systems, 2025, 40(1): 57-72.
[24] 马燕峰, 李金媛, 王子建, 等. 基于量测数据的新能源电力系统区域等效惯量评估方法[J]. 电工技术学报, 2024, 39(17): 5406-5421.
Ma Yanfeng, Li Jinyuan, Wang Zijian, et al.Assessment method of regional equivalent inertia of new energy power system based on measured data[J]. Transactions of China Electrotechnical Society, 2024, 39(17): 5406-5421.
[25] 赵强, 张玉琼, 陈紫薇, 等. 计及储能的低惯量电力系统频率特性分析[J]. 中国电机工程学报, 2023, 43(3): 904-914.
Zhao Qiang, Zhang Yuqiong, Chen Ziwei, et al.Frequency characteristic analysis of low-inertia power system considering energy storage[J]. Proceedings of the CSEE, 2023, 43(3): 904-914.
[26] Shen Jiakai, Li Weidong, Liu Liu, et al.Frequency response model and its closed-form solution of two-machine equivalent power system[J]. IEEE Transactions on Power Systems, 2021, 36(3): 2162-2173.
[27] Liu Jiahao, Wang Cheng, Zhao Junbo, et al.RoCoF constrained unit commitment considering spatial difference in frequency dynamics[J]. IEEE Transactions on Power Systems, 2024, 39(1): 1111-1125.
[28] Badesa L, Teng Fei, Strbac G.Conditions for regional frequency stability in power system scheduling: part I: theory[J]. IEEE Transactions on Power Systems, 2021, 36(6): 5558-5566.
[29] Badesa L, Teng Fei, Strbac G.Conditions for regional frequency stability in power system scheduling: part II: application to unit commitment[J]. IEEE Transactions on Power Systems, 2021, 36(6): 5567-5577.
[30] Kundur P.Power System Stability and Control[M]. New York: McGraw-Hill, 1994.
[31] Liao Huanxin, Yang Chao, Gao Huisheng, et al.Comprehensive-contribution-based primary frequency regulation market design for the converter-integrated power system[J]. IEEE Transactions on Power Systems, 2024, 39(2): 3825-3838.
[32] 胡光, 高晖胜, 辛焕海, 等. 考虑惯量模态特征的电力系统频率性能量化方法[J]. 中国电机工程学报, 2023, 43(22): 8559-8569.
Hu Guang, Gao Huisheng, Xin Huanhai, et al.A quantification method for frequency performance of power system considering modal feature of inertia[J]. Proceedings of the CSEE, 2023, 43(22): 8559-8569.
[33] 高丙团, 胡正阳, 王伟胜, 等. 新能源场站快速有功控制及频率支撑技术综述[J]. 中国电机工程学报, 2024, 44(11): 4335-4352.
Gao Bingtuan, Hu Zhengyang, Wang Weisheng, et al.Review on fast active power control and frequency support technologies of renewable energy stations[J]. Proceedings of the CSEE, 2024, 44(11): 4335-4352.
[34] 颜湘武, 张伟超, 崔森, 等. 基于虚拟同步机的电压源逆变器频率响应时域特性和自适应参数设计[J]. 电工技术学报, 2021, 36(增刊1): 241-254.
Yan Xiangwu, Zhang Weichao, Cui Sen, et al.Frequency response characteristics and adaptive parameter tuning of voltage-sourced converters under VSG control[J]. Transactions of China Electrotechnical Society, 2021, 36(S1): 241-254.
[35] Dorfler F, Bullo F.Kron reduction of graphs with applications to electrical networks[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2013, 60(1): 150-163.
[36] Gao Huisheng, Yuan Hui, Xin Huanhai, et al.Nodal frequency performance of power networks[C]//2019 IEEE 8th International Conference on Advanced Power System Automation and Protection (APAP), Xi'an, China, 2019: 1838-1842.
[37] Tuo Mingjian, Li Xingpeng.Security-constrained unit commitment considering locational frequency stability in low-inertia power grids[J]. IEEE Transactions on Power Systems, 2023, 38(5): 4134-4147.
[38] 谢小荣, 贺静波, 毛航银, 等. “双高”电力系统稳定性的新问题及分类探讨[J]. 中国电机工程学报, 2021, 41(2): 461-475.
Xie Xiaorong, He Jingbo, Mao Hangyin, et al.New issues and classification of power system stability with high shares of renewables and power electronics[J]. Proceedings of the CSEE, 2021, 41(2): 461-475.
[39] Hajiakbari Fini M, Hamedani Golshan M E, Martí J R, et al. Determining the required frequency control reserve and capacity and location of synchronous and virtual inertial resources[J]. IEEE Transactions on Sustainable Energy, 2023, 14(1): 27-38.
[40] 张君黎, 徐政. 考虑RoCoF约束的新能源电力系统惯量分区配置方法[J]. 太阳能学报, 2023, 44(9): 18-28.
Zhang Junli, Xu Zheng.Regional inertia configuration method of renewable energy power system considering RoCoF constraint[J]. Acta Energiae Solaris Sinica, 2023, 44(9): 18-28.