基于可变数据窗口的电力系统惯量估计方法

doi:10.16183/j.cnki.jsjtu.2024.339

摘要/Abstract

摘要：

针对固定数据窗口难以适应时变频率波动的问题,提出一种基于可变数据窗口的电力系统惯量估计方法.首先,分析电力系统惯量响应过程,采用有源自回归模型表征频率动态特性,构建参数辨识模型.其次,利用自适应中值-均值组合滤波方法进行数据预处理,并通过模糊逻辑控制器设置带遗忘因子递推最小二乘方法的参数.然后,构建量化辨识误差及连续窗口间辨识结果差异程度的评估指标,根据不同场景在线调整数据窗口长度,以实现系统惯量的准确估计.最后,通过算例分析验证所提方法的有效性.算例结果表明:该方法能够适应惯量参数变化的场景,有效降低惯量估计误差.

关键词: 等效惯量, 频率动态, 参数辨识, 在线估计, 可变数据窗口

Abstract:

Due to the ineffectiveness of fixed data window caused by time-varying frequency dynamics, an estimation for inertia of power systems based on variable data window is proposed. First, the process of power system inertia response is analyzed, and the auto-regressive with extra inputs model is used to depict frequency dynamics, on which a parameter identification model is developed. Next, the frequency measurement data are preprocessed based on the adaptive median-mean combined filter, and the fuzzy logic controller is used to set the parameters of the forgetting factor recursive least square method. Then, indices measuring the identification error and the difference of the results of successive windows are developed to realize the online variation of data window length and calculate the system inertia. Finally, case studies are conducted to validate the effectiveness of the proposed approach. The results show that the proposed approach can adapt to the changing inertia and is effective in reducing the inertia estimation error.

Key words: equivalent inertia, frequency dynamic, parameter identification, online estimation, variable data window

中图分类号:

TM715

曹永吉, 李常刚. 基于可变数据窗口的电力系统惯量估计方法[J]. 上海交通大学学报, 2026, 60(4): 541-549.

CAO Yongji, LI Changgang. Estimation Approach for Inertia of Power System Based on Variable Data Window[J]. Journal of Shanghai Jiao Tong University, 2026, 60(4): 541-549.

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参考文献 26

[1]	曹永吉, 张恒旭, 施啸寒, 等. 规模化分布式能源参与大电网安全稳定控制的机制初探[J]. 电力系统自动化, 2021, 45(18): 1-8.
	CAO Yongji, ZHANG Hengxu, SHI Xiaohan, et al. Preliminary study on participation mechanism of large-scale distributed energy resource in security and stability control of large power grid[J]. Automation of Electric Power Systems, 2021, 45(18): 1-8.
[2]	王佳颖, 陆春光, 矫文书, 等. 考虑光伏不确定性的高耗能工业园区双时间尺度优化调度[J/OL]. 上海交通大学学报. https://link.cnki.net/doi/10.16183/j.cnki.jsjtu.2024.248.
	WANG Jiaying, LU Chunguang, JIAO Wenshu, et al. Dual-time-scale optimal scheduling for high energy-consuming industrial park considering uncertainty of photovoltaic[J/OL]. Journal of Shanghai Jiao Tong University. https://link.cnki.net/doi/10.16183/j.cnki.jsjtu.2024.248.
[3]	曹永吉, 张江丰, 王天宇, 等. 基于分布式模型预测控制的自适应二次调频策略[J]. 上海交通大学学报, 2025, 59(3): 333-341. doi: 10.16183/j.cnki.jsjtu.2023.352
	CAO Yongji, ZHANG Jiangfeng, WANG Tianyu, et al. Self-adaptive secondary frequency regulation strategy based on distributed model predictive control[J]. Journal of Shanghai Jiao Tong University, 2025, 59(3): 333-341.
[4]	曾国辉, 廖鸿飞, 赵晋斌, 等. 直流微网双向DC/DC变换器虚拟惯量和阻尼系数自适应控制策略[J]. 电力系统保护与控制, 2022, 50(6): 65-73.
	ZENG Guohui, LIAO Hongfei, ZHAO Jinbin, et al. A self-adaptive control strategy of virtual inertia and a damping coefficient for bidirectional DC-DC converters in a DC microgrid[J]. Power System Protection & Control, 2022, 50(6): 65-73.
[5]	张恒旭, 高志民, 曹永吉, 等. 高比例可再生能源接入下电力系统惯量研究综述及展望[J]. 山东大学学报(工学版), 2022, 52(5): 1-13.
	ZHANG Hengxu, GAO Zhimin, CAO Yongji, et al. Review and prospect of research on power system inertia with high penetration of renewable energy source[J]. Journal of Shandong University (Engineering Science), 2022, 52(5): 1-13.
[6]	LIANG Z R, MIETH R, DVORKIN Y. Inertia pricing in stochastic electricity markets[J]. IEEE Transactions on Power Systems, 2023, 38(3): 2071-2084. doi: 10.1109/TPWRS.2022.3189548 URL
[7]	李仪博, 周前, 朱丹丹, 等. 提高海上风电场主动频率支撑能力的控制策略[J]. 上海交通大学学报, 2025, 59(10): 1442-1450. doi: 10.16183/j.cnki.jsjtu.2023.581
	LI Yibo, ZHOU Qian, ZHU Dandan, et al. Control strategy for improving active frequency support capability of offshore wind farm[J]. Journal of Shanghai Jiao Tong University, 2025, 59(10): 1442-1450.
[8]	WALL P, TERZIJA V. Simultaneous estimation of the time of disturbance and inertia in power systems[J]. IEEE Transactions on Power Delivery, 2014, 29(4): 2018-2031. doi: 10.1109/TPWRD.2014.2306062 URL
[9]	ASHTON P M, SAUNDERS C S, TAYLOR G A, et al. Inertia estimation of the GB power system using synchrophasor measurements[J]. IEEE Transactions on Power Systems, 2015, 30(2): 701-709. doi: 10.1109/TPWRS.2014.2333776 URL
[10]	刘方蕾, 胥国毅, 王凡, 等. 基于差值计算法的系统分区惯量评估方法[J]. 电力系统自动化, 2020, 44(20): 46-53.
	LIU Fanglei, XU Guoyi, WANG Fan, et al. Assessment method of system partition inertia based on differential calculation method[J]. Automation of Electric Power Systems, 2020, 44(20): 46-53.
[11]	PHURAILATPAM C, RATHER Z H, BAHRANI B, et al. Measurement-based estimation of inertia in AC microgrids[J]. IEEE Transactions on Sustainable Energy, 2020, 11(3): 1975-1984. doi: 10.1109/TSTE.5165391 URL
[12]	李东东, 董楠, 姚寅, 等. 考虑频率响应分散性及系统分区的含风电系统等效惯量估计[J]. 电力系统保护与控制, 2023, 51(3): 36-45.
	LI Dongdong, DONG Nan, YAO Yin, et al. Equivalent inertia estimation of a power system containing wind power considering dispersion of frequency response and system partitioning[J]. Power System Protection & Control, 2023, 51(3): 36-45.
[13]	CAO X, STEPHEN B, ABDULHADI I F, et al. Switching Markov Gaussian models for dynamic power system inertia estimation[J]. IEEE Transactions on Power Systems, 2016, 31(5): 3394-3403. doi: 10.1109/TPWRS.2015.2501458 URL
[14]	李昭良, 胥国毅, 王程, 等. 计及功率响应延时补偿的换流器接口电源等效惯量估计方法[J]. 电力系统自动化, 2023, 47(1): 12-21.
	LI Zhaoliang, XU Guoyi, WANG Cheng, et al. Equivalent inertia estimation method for converter-interfaced generator considering power response delay compensation[J]. Automation of Electric Power Systems, 2023, 47(1): 12-21.
[15]	ZHANG J B, XU H C. Online identification of power system equivalent inertia constant[J]. IEEE Transactions on Industrial Electronics, 2017, 64(10): 8098-8107. doi: 10.1109/TIE.2017.2698414 URL
[16]	TUTTELBERG K, KILTER J, WILSON D, et al. Estimation of power system inertia from ambient wide area measurements[C]// 2019 IEEE Power & Energy Society General Meeting. Atlanta, USA: IEEE, 2020: 1.
[17]	程定一, 马欢, 秦昊, 等. 基于准稳态数据的电力系统等效惯量评估方法[J]. 现代电力, 2023, 40(4): 434-440.
	CHENG Dingyi, MA Huan, QIN Hao, et al. Estimation method for power system equivalent inertia based on quasi-steady-state data[J]. Modern Electric Power, 2023, 40(4): 434-440.
[18]	曹斌, 原帅, 刘家豪, 等. 考虑频率动态响应实时分区的电力系统惯量在线评估方法[J]. 电网技术, 2023, 47(3): 930-941.
	CAO Bin, YUAN Shuai, LIU Jiahao, et al. Power system online inertia estimation considering real-time clustering of frequency dynamic response[J]. Power System Technology, 2023, 47(3): 930-941.
[19]	孙华东, 王宝财, 李文锋, 等. 高比例电力电子电力系统频率响应的惯量体系研究[J]. 中国电机工程学报, 2020, 40(16): 5179-5192.
	SUN Huadong, WANG Baocai, LI Wenfeng, et al. Research on inertia system of frequency response for power system with high penetration electronics[J]. Proceedings of the CSEE, 2020, 40(16): 5179-5192.
[20]	张恒旭, 曹永吉, 张怡, 等. 电力系统频率动态行为衍变与分析方法需求综述[J]. 山东大学学报(工学版), 2021, 51(5): 42-52.
	ZHANG Hengxu, CAO Yongji, ZHANG Yi, et al. Review of frequency dynamic behavior evolution and analysis method requirements of power system[J]. Journal of Shandong University (Engineering Science), 2021, 51(5): 42-52.
[21]	唐震, 郝丽花, 冯静. 局部频率测量数据驱动的电力系统功率缺额在线评估方法[J]. 上海交通大学学报, 2023, 57(4): 403-411. doi: 10.16183/j.cnki.jsjtu.2021.401
	TANG Zhen, HAO Lihua, FENG Jing. Online estimation of power shortage in power systems driven by local frequency measurement data[J]. Journal of Shanghai Jiao Tong University, 2023, 57(4): 403-411.
[22]	CHEN X, ZHAO S Y, LIU F, et al. Laplace distribution based online identification of linear systems with robust recursive expectation-maximization algorithm[J]. IEEE Transactions on Industrial Informatics, 2023, 19(8): 9028-9036. doi: 10.1109/TII.2022.3225026 URL
[23]	DE ALBUQUERQUE J C, DE AQUINO R R B, NETO O N, et al. Power curve modelling for wind turbine using artificial intelligence tools and pre-established inference criteria[J]. Journal of Modern Power Systems & Clean Energy, 2021, 9(3): 526-533.
[24]	曹永吉, 张恒旭, 张怡, 等. 基于事件驱动的机组快速频率响应控制方法[J]. 电力系统自动化, 2021, 45(19): 148-154.
	CAO Yongji, ZHANG Hengxu, ZHANG Yi, et al. Event-driven fast frequency response control method for generator unit[J]. Automation of Electric Power Systems, 2021, 45(19): 148-154.
[25]	MAFI M, RAJAEI H, CABRERIZO M, et al. A robust edge detection approach in the presence of high impulse noise intensity through switching adaptive median and fixed weighted mean filtering[J]. IEEE Transactions on Image Processing, 2018, 27(11): 5475-5490. doi: 10.1109/TIP.83 URL
[26]	邓旭晖, 陈中, 杨凯, 等. 基于多任务学习卷积网络的非侵入式负荷监测方法[J]. 电力系统自动化, 2023, 47(8): 189-197.
	DENG Xuhui, CHEN Zhong, YANG Kai, et al. Non-intrusive load monitoring method based on multi-task learning convolutional network[J]. Automation of Electric Power Systems, 2023, 47(8): 189-197.

ΔE	E
ΔE	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PM	PM	PS	ZO	NS
NM	PB	PB	PM	PS	PS	NS	NS
NS	PB	PM	PM	PS	PS	NS	NS
ZO	PM	PM	PS	ZO	ZO	NM	NM
PS	PS	PS	ZO	NS	NM	NM	NB
PM	PS	PS	NS	NS	NM	NB	NB
PB	PS	PS	NS	NS	NM	NB	NB

方法	RMSE	MAE	NRP/%
方法1(中值-均值滤波方法)	5.0220	0.0290	87.35
方法2(带修正因子的中值- 均值滤波方法)	4.2632	0.0246	91.29
所提方法	2.9536	0.0171	95.13

方法	RMSE	MAE	ME
方法3(ARMAX模型方法)	0.0304	0.0242	0.1235
方法4(固定数据窗口方法)	0.0276	0.0220	0.1143
所提方法	0.0148	0.0118	0.0581

方法	时间区间 0~200 s		时间区间 200~300 s
方法	惯量估计值/s	惯量估计误差/%	惯量估计值/s	惯量估计误差/%
方法3(ARMAX模型方法)	7.11	11.31	8.12	14.33
方法4(固定数据窗口方法)	5.94	6.92	6.51	8.37
所提方法	6.23	2.47	6.92	2.53