NODAL INERTIA ASSESSMENT FOR RENEWABLE ENERGY POWER SYSTEMS BASED ON VECTOR FITTING METHOD

Sun Mingrui, Wen Yunfeng, Liao Bangkun, Wang Jingwen, Fu Guobin, Wang Xuebin

Acta Energiae Solaris Sinica ›› 2026, Vol. 47 ›› Issue (8) : 381-394.

PDF(1731 KB)
Welcome to visit Acta Energiae Solaris Sinica, Today is
PDF(1731 KB)
Acta Energiae Solaris Sinica ›› 2026, Vol. 47 ›› Issue (8) : 381-394. DOI: 10.19912/j.0254-0096.tynxb.2025-0518

NODAL INERTIA ASSESSMENT FOR RENEWABLE ENERGY POWER SYSTEMS BASED ON VECTOR FITTING METHOD

  • Sun Mingrui1, Wen Yunfeng1, Liao Bangkun1, Wang Jingwen1, Fu Guobin2, Wang Xuebin2
Author information +
History +

Abstract

To address the critical issue of the lack of online assessment methods for nodal inertia in practical power grid dispatching and control, this paper proposes a nodal inertia assessment method in renewable energy power systems based on the vector fitting method. By analyzing the frequency response mechanisms of various inertia resources, a unified assessment framework for nodal inertia is established, covering both synchronous generators and renewable energy units. A transfer function parameter identification model is then developed based on the vector fitting method, and inertia levels are inverted by measuring the dynamic characteristics of nodal active power-frequency transfer function. To overcome the sensitivity of the traditional vector fitting method to initial pole configuration, particle swarm optimization is introduced to optimize the initial pole configuration, using frequency fitting mean square error as the fitness function. Finally, multiple operating condition simulations on an improved IEEE-39 node system demonstrate that the proposed method has significant advantages in assessment accuracy and applicability.

Key words

inertia / renewable energy / frequency response / nodal inertia assessment / vector fitting method / particle swarm optimization

Cite this article

Download Citations
Sun Mingrui, Wen Yunfeng, Liao Bangkun, Wang Jingwen, Fu Guobin, Wang Xuebin. NODAL INERTIA ASSESSMENT FOR RENEWABLE ENERGY POWER SYSTEMS BASED ON VECTOR FITTING METHOD[J]. Acta Energiae Solaris Sinica. 2026, 47(8): 381-394 https://doi.org/10.19912/j.0254-0096.tynxb.2025-0518

References

[1] 王博, 杨德友, 蔡国伟. 高比例新能源接入下电力系统惯量相关问题研究综述[J]. 电网技术, 2020, 44(8): 2998-3007.
Wang B, Yang D Y, Cai G W.Review of research on power system inertia related issues in the context of high penetration of renewable power generation[J]. Power System Technology, 2020, 44(8): 2998-3007.
[2] 李元臣, 文云峰, 叶希, 等. 基于多新息辨识的电力系统节点惯量估计方法[J]. 电力自动化设备, 2022(8): 89-95.
Li Y C, Wen Y F, Ye X, et al.Estimation method of power system nodal inertia based on multi-innovation identification[J]. Electric Power Automation Equipment, 2022(8): 89-95.
[3] 王振浩, 陈诗伦, 葛津铭, 等. 计及新能源场站调频能力的电力系统最小惯量评估方法[J]. 太阳能学报, 2024, 45(8): 494-502.
Wang Z H, Chen S L, Ge J M, et al.Minimum inertia evaluation method of power system considering frequency modulation capability of new energy stations[J]. Acta Energiae Solaris Sinica, 2024, 45(8): 494-502.
[4] 张超, 文云峰, 黎婧娴, 等. 考虑抑制二次跌落的风电自适应频率支撑控制策略及其参数整定[J]. 电工技术学报, 2026, 41(5): 1510-1525.
Zhang C, Wen Y F, Li J X, et al.An adaptive frequency support control strategy and parameter configuration method of wind power considering the mitigation secondary drop[J]. Transactions of China Electrotechnical Society, 2026, 41(5): 1510-1525.
[5] 张武其, 文云峰, 迟方德, 等. 电力系统惯量评估研究框架与展望[J]. 中国电机工程学报, 2021, 41(20): 6842-6855.
Zhang W Q, Wen Y F, Chi F D, et al.Research framework and prospect on power system inertia estimation[J]. Proceedings of the CSEE, 2021, 41(20): 6842-6855.
[6] Dulal S, Zhang C W, Olama M, et al.Inertia estimation and trend analysis of the United States power grid interconnections[J]. IEEE Access, 2024, 12: 194436-194448.
[7] 李勇, 常樊睿, 彭衍建, 等. 基于小扰动频率量测数据的电网节点惯量分布评估方法[J]. 电力系统自动化, 2024, 48(13): 50-59.
Li Y, Chang F R, Peng Y J, et al.Evaluation method for node inertia distribution of power grids based on small disturbance frequency measurement data[J]. Automation of Electric Power Systems, 2024, 48(13): 50-59.
[8] 朱介北, 郭力源, 王伟, 等. 基于二阶罚函数自适应变阶拟合的全局电网惯量时空感知[J]. 电力系统自动化, 2024, 48(19): 69-79.
Zhu J B, Guo L Y, Wang W, et al.Temporal-spatio inertia perception of global power grid based on adaptive variable-order fitting of second-order penalty function[J]. Automation of Electric Power Systems, 2024, 48(19): 69-79.
[9] Cai G W, Wang B, Yang D Y, et al.Inertia estimation based on observed electromechanical oscillation response for power systems[J]. IEEE Transactions on Power Systems, 2019, 34(6): 4291-4299.
[10] 杨德友, 邵致远, 王博. 基于动态模式分解的发电机惯量及阻尼系数评估方法[J]. 电网技术, 2022, 46(1): 311-321.
Yang D Y, Shao Z Y, Wang B.Evaluation of generator inertia and damping coefficient based on dynamic mode decomposition[J]. Power System Technology, 2022, 46(1): 311-321.
[11] 王博, 王宇, 张颂, 等. 基于随机数据驱动SDMD的电力系统区域惯量评估方法[J]. 电力系统自动化, 2024, 48(10): 78-86.
Wang B, Wang Y, Zhang S, et al.Regional inertia estimation method for power system based on random data-driven subspace dynamic mode decomposition[J]. Automation of Electric Power Systems, 2024, 48(10): 78-86.
[12] 任智强, 田铭兴, 姜宇, 等. 基于电力系统机电振荡的发电侧惯量评估[J]. 浙江大学学报(工学版), 2025, 59(4): 870-878.
Ren Z Q, Tian M X, Jiang Y, et al.Evaluation of generator side inertia based on electromechanical oscillation of power system[J]. Journal of Zhejiang University (Engineering Science), 2025, 59(4): 870-878.
[13] Kerdphol T, Watanabe M, Nishikawa R, et al.Inertia estimation of the 60 Hz Japanese power system from synchrophasor measurements[J]. IEEE Transactions on Power Systems, 2023, 38(1): 753-766.
[14] Linaro D, Bizzarri F, del Giudice D, et al. Continuous estimation of power system inertia using convolutional neural networks[J]. Nature Communications, 2023, 14: 4440.
[15] Tuttelberg K, Kilter J, Wilson D, et al.Estimation of power system inertia from ambient wide area measurements[J]. IEEE Transactions on Power Systems, 2018, 33(6): 7249-7257.
[16] Tuo M J, Li X P.Machine learning assisted inertia estimation using ambient measurements[J]. IEEE Transactions on Industry Applications, 2023, 59(4): 4893-4903.
[17] 李玉京, 胡鹏飞, 曹宇, 等. 计及频率响应延时的构网型变流器惯量参数数据驱动估计方法[J]. 电力系统自动化, 2024, 48(19): 80-88.
Li Y J, Hu P F, Cao Y, et al.Data-driven estimation method for inertia parameters of grid-forming converter considering frequency response delay[J]. Automation of Electric Power Systems, 2024, 48(19): 80-88.
[18] Muhammed A O, Isbeih Y J, El Moursi M S, et al. Artificial intelligence (AI) advanced techniques for real-time inertia estimation in renewable-based power systems[J]. IEEE Transactions on Industry Applications, 2025, 61(2): 2604-2619.
[19] Ghosh S, Isbeih Y J, Shawky El Moursi M, et al. An efficient method for estimating inertia of a PV-integrated power grid for enhanced security[J]. IEEE Transactions on Smart Grid, 2024, 15(6): 5885-5898.
[20] Gotti D, Bizzarri F, Brambilla A, et al.Inertia estimation of a power system area based on iterative equation error system identification[J]. IEEE Transactions on Power Systems, 2024, 39(5): 6469-6481.
[21] 张波, 张成健, 张经, 等. 基于系统辨识的新能源电力系统惯性常数快速追踪方法[J]. 电力自动化设备, 2025, 45(3): 163-170.
Zhang B, Zhang C J, Zhang J, et al.Fast tracking method of inertia constant of new energy power system based on system identification[J]. Electric Power Automation Equipment, 2025, 45(3): 163-170.
[22] 裴铭, 叶林, 罗雅迪, 等. 计及频率响应时空相关性的新能源电力系统惯量估计方法[J]. 电力系统自动化, 2024, 48(8): 53-66.
Pei M, Ye L, Luo Y D, et al.Inertia estimation method for power system with renewable energy considering spatio-temporal correlation of frequency response[J]. Automation of Electric Power Systems, 2024, 48(8): 53-66.
[23] Bizzarri F, del Giudice D, Grillo S, et al. Inertia estimation through covariance matrix[J]. IEEE Transactions on Power Systems, 2024, 39(1): 947-956.
[24] Mazidi M, McKelvey T, Chen P Y. A pure data-driven method for online inertia estimation in power systems using local rational model approach[J]. IEEE Transactions on Industry Applications, 2023, 59(5): 5506-5516.
[25] Liu K, Xu Y J, Gu W, et al.A Bayesian approach for online inertia estimation of synchronous and nonsynchronous generators[J]. IEEE Transactions on Instrumentation and Measurement, 2024, 73: 1006012.
[26] 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 J L, Xu Z.Regional inertia configuration method of renewable energy power system considering RoCoF constraint[J]. Acta Energiae Solaris Sinica, 2023, 44(9): 18-28.
[27] 李世春, 夏智雄, 程绪长, 等. 基于类噪声扰动的电网惯量常态化连续估计方法[J]. 中国电机工程学报, 2020, 40(14): 4430-4439, 4723.
Li S C, Xia Z X, Cheng X C, et al.Continuous estimation method of power system inertia based on ambient disturbance[J]. Proceedings of the CSEE, 2020, 40(14): 4430-4439, 4723.
[28] 刘旭, 张国驹, 裴玮, 等. 构网型变流器的现状与发展趋势[J]. 太阳能学报, 2024, 45(9): 101-111.
Liu X, Zhang G J, Pei W, et al.Current status and development trends of grid type converters[J]. Acta Energiae Solaris Sinica, 2024, 45(9): 101-111.
[29] 孙正龙, 李明达, 郝舒宇, 等. 基于能量耗散的电压源型双馈风电机组轴系扭振阻尼特性分析[J]. 电网技术, 2024, 48(12): 4855-4864.
Sun Z L, Li M D, Hao S Y, et al.Analysis of torsional vibration damping characteristics of voltage source doubly fed wind turbine shaft system based on energy dissipation[J]. Power System Technology, 2024, 48(12): 4855-4864.
[30] 李群, 殷明慧, 刘昆龙, 等. 面向构网永磁风电机组惯量支撑的物理转子绑定方法[J]. 电力系统自动化, 2025, 49(11): 91-101.
Li Q, Yin M H, Liu K L, et al.Physical rotor binding method for inertia support of grid-forming permanent magnet wind turbines[J]. Automation of Electric Power Systems, 2025, 49(11): 91-101.
[31] 孙正龙, 郝舒宇, 李明达, 等. 含构网型双馈风电的电力系统低频振荡能量结构分析方法[J]. 电工技术学报, 2025, 40(5): 1411-1426.
Sun Z L, Hao S Y, Li M D, et al.Low frequency oscillation analysis method for grid-forming doubly-fed wind power systems based on energy structures[J]. Transactions of China Electrotechnical Society, 2025, 40(5): 1411-1426.
[32] 黄俊凯, 杨知方, 余娟, 等. 面向频率稳定校核的风机快速频率响应低阶建模方法及其误差分析[J]. 中国电机工程学报, 2022, 42(18): 6752-6766.
Huang J K, Yang Z F, Yu J, et al.Low-order modeling of wind turbine-based fast frequency response and its error analysis for frequency stability assessment[J]. Proceedings of the CSEE, 2022, 42(18): 6752-6766.
[33] 马宁嘉, 谢小荣, 李浩志, 等. 计及频率动态分布性的新能源机组惯量需求分析[J]. 中国电机工程学报, 2024, 44(9): 3500-3507.
Ma N J, Xie X R, Li H Z, et al.Inertial requirements for renewable energy units considering the space-time distribution characteristics of frequency[J]. Proceedings of the CSEE, 2024, 44(9): 3500-3507.
[34] 刘可真, 谭化平, 杨春昊, 等. 考虑系统分区与节点频率动态响应的电力系统区域惯量估计方法[J]. 电力自动化设备, 2025, 45(5): 200-208.
Liu K Z, Tan H P, Yang C H, et al.Power system regional inertia estimation method considering system partitioning and dynamic response of node frequency[J]. Electric Power Automation Equipment, 2025, 45(5): 200-208.
[35] Skopetou N E, Sfetkos A I, Kontis E O, et al.Identification of inertia constants using time-domain vector fitting[J]. Electric Power Systems Research, 2024, 236: 110924.
PDF(1731 KB)

Accesses

Citation

Detail

Sections
Recommended

/