Sparsity Promoting Dynamic Mode Decomposition Based Dominant Modes and Mode Shapes Estimation in Bulk Power Grid
Li Xue1, Yu Yang1, Jiang Tao1, Li Guoqing1, Liu Chunxiao2
1. Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology Ministry of Education Northeast Electric Power University Jilin 132012 China; 2. Power Dispatching and Control Center China Southern Power Grid Guangzhou 510623 China
Abstract：This paper proposes a sparsity promoting dynamic mode decomposition (SPDMD) approach for dominant modes and mode shapes assessment in bulk power grid by using the wide area measurement. The SPDMD is first employed to estimate the low-order state matrix containing the critical dynamic oscillation features from the multichannel wide area measurements. Then, the alternating direction multiplier method (ADMM) and Lagrangian multiplier (LM) are used to estimate the optimized amplitude coefficients of the oscillation modes embedded in the low-order state matrix. Further, using the optimized amplitude coefficients, the dominant modes and mode shapes are separated. Finally, the proposed approach was evaluated by the 16-machine 68-bus test system as well as China Southern Power Grid, the results confirm the accuracy and effectively of the proposed SPDMD in dominant modes and mode shapes.
李雪, 于洋, 姜涛, 李国庆, 刘春晓. 基于稀疏增强动态解耦的电力系统振荡模式与模态辨识方法[J]. 电工技术学报, 2021, 36(13): 2832-2843.
Li Xue, Yu Yang, Jiang Tao, Li Guoqing, Liu Chunxiao. Sparsity Promoting Dynamic Mode Decomposition Based Dominant Modes and Mode Shapes Estimation in Bulk Power Grid. Transactions of China Electrotechnical Society, 2021, 36(13): 2832-2843.
[1] Jiang Tao, Jia Hongjie, Zhao Jinli, et al.Mode matching pursuit for estimating dominant modes in bulk power grid[J]. IET Generation, Transmission & Distribution, 2014, 8(10): 1677-1686. [2] 刘九良, 王彤, 朱劭璇, 等. 计及保护信息的电力系统暂态稳定裕度解析算法[J]. 电工技术学报, 2020, 35(3): 542-552. Liu Jiuliang, Wang Tong, Zhu Shaoxuan, et al.An analytic method for power system transient stability margin considering protection information[J]. Transactions of China Electrotechnical Society, 2020, 35(3): 542-552. [3] 马燕峰, 霍亚欣, 李鑫, 等. 考虑时滞影响的双馈风电场广域附加阻尼控制器设计[J]. 电工技术学报, 2020, 35(1): 158-166. Ma Yanfeng, Huo Yaxin, Li Xin, et al.Design of wide area additional damping controller for doubly fed wind farms considering time delays[J]. Transactions of China Electrotechnical Society, 2020, 35(1): 158-166. [4] 张小店, 王楷夫, 方连航, 等. 窄带模态分解算法在电力系统低频振荡特征参数辨识中的应用研究[J]. 电气技术, 2019, 20(4): 61-66, 71. Zhang Xiaodian, Wang Kaifu, Fang Lianhang, et al.Applied study of narrow-band mode decomposition for identifying the parameters of low frequency oscillations in power systems[J]. Electrical Engineering, 2019, 20(4): 61-66, 71. [5] 薛安成, 王嘉伟. 基于非光滑分岔的单机水电系统超低频频率振荡机理分析[J]. 电工技术学报, 2020, 35(7): 1489-1497. Xue Ancheng, Wang Jiawei.Mechanism analysis of ultra-low frequency oscillation of single hydropower system based on non-smooth bifurcation[J]. Transactions of China Electrotechnical Society, 2020, 35(7): 1489-1497. [6] 刘素贞, 魏建, 张闯, 等. 基于FPGA的超声信号自适应滤波与特征提取[J]. 电工技术学报, 2020, 35(13): 2870-2878. Liu Suzhen, Wei Jian, Zhang Chuang, et al.Adaptive filtering and feature extraction of ultrasonic signal based on FPGA[J]. Transactions of China Electrotechnical Society, 2020, 35(13): 2870-2878. [7] 姜涛. 基于广域量测信息的电力大系统安全性分析与协调控制[D]. 天津: 天津大学, 2015. [8] Jiang Tao, Mu Yunfei, Jia Hongjie, et al.A novel dominant mode estimation method for analyzing inter-area oscillation in China Southern Power Grid[J]. IEEE Transactions on Smart Grid, 2016, 7(5): 2549-2560. [9] Papadopoulos T A, Chrysochos A I, Kontis E O, et al.Measurement-based hybrid approach for ring-down analysis of power systems[J]. IEEE Transactions on Power Systems, 2016, 31(6): 4435-4446. [10] 陈刚, 段晓, 张继红. 基于ARMA模型的低频振荡模式在线辨识技术研究[J]. 电网技术, 2010, 34(11): 48-54. Chen Gang, Duan Xiao, Zhang Jihong.A new approach for online identification of low frequency oscillation modes based on auto-regressive moving-average model[J]. Power System Technology, 2010, 34(11): 48-54. [11] 竺炜, 唐颖杰, 周有庆, 等. 基于改进Prony算法的电力系统低频振荡模式识别[J]. 电网技术, 2009, 33(5): 44-53. Zhu Wei, Tang Yingjie, Zhou Youqing.Identification of power system low frequency oscillation mode based on improved Prony algorithm[J]. Power System Technology, 2009, 33(5): 44-53. [12] 张俊峰, 杨婷, 陈珉, 等. 基于Prony滑动平均窗算法的电力系统低频振荡特征分析[J]. 电力自动化设备, 2018, 38(10): 178-183. Zhang Junfeng, Yang Ting, Chen Min, et al.Power system low-frequency oscillation characteristic analysis based on Prony moving average window algorithm[J]. Electric Power Automation Equipment, 2018, 38(10): 178-183. [13] 葛维春, 殷翔祥, 葛延峰, 等. 基于MEMD和HHT的电力系统低频振荡模式识别方法研究[J]. 电力系统保护与控制, 2020, 48(6): 124-135. Ge Weichun, Yin Xiangxiang, Ge Yanfeng, et al.Estimating low frequency oscillation mode in power systems using multivariate empirical mode decomposition and Hilbert-Huang transform[J]. Power System Protection and Control, 2020, 48(6): 124-135. [14] 杨德昌, Rehtanz C, 李勇, 等. 基于改进希尔伯特-黄变换算法的电力系统低频振荡分析[J]. 中国电机工程学报, 2011, 31(10): 102-108. Yang Dechang, Rehtanz C, Li Yong, et al.Researching on low frequency oscillation in power system based on improved HHT algorithm[J]. Proceedings of the CSEE, 2011, 31(10): 102-108. [15] 姜涛, 刘方正, 陈厚合, 等. 基于多通道快速傅里叶小波变换的电力系统主导振荡模式及模态协同辨识方法研究[J]. 电力自动化设备, 2019, 39(7): 125-132. Jiang Tao, Liu Fangzheng, Chen Houhe, et al.Cooperated identification method of dominant oscillation modes and mode shapes for power system based on multi-channel fast Fourier transform based continuous wavelet transform[J]. Electric Power Automation Equipment, 2019, 39(7): 125-132. [16] 刘君, 肖辉, 曾林俊, 等. 基于RSSD和ICA算法的低频振荡模态参数辨识[J]. 电工技术学报, 2018, 33(21): 5051-5058. Liu Jun, Xiao Hui, Zeng Linjun, et al.Parameter identification of low frequency oscillation based on RSSD and ICA algorithm[J]. Transactions of China Electrotechnical Society, 2018, 33(21): 5051-5058. [17] Li Xue, Cui Hantao, Jiang Tao, et al.Multichannel continuous wavelet transform approach to estimate electromechanical oscillation modes,mode shapes and coherent groups from synchrophasors in bulk power grid[J]. International Journal of Electrical Power & Energy Systems, 2018, 96: 222-237. [18] Jiang Tao, Yuan Haoyu, Jia Hongjie, et al.Stochastic subspace identification-based approach for tracking inter-area oscillatory modes in bulk power system utilising synchrophasor measurements[J]. IET Generation, Transmission & Distribution, 2015, 9(15): 2409-2418. [19] Messina A R, Vittal V.Extraction of dynamic patterns from wide-area measurements using empirical orthogonal functions[J]. IEEE Transactions on Power Systems, 2007, 22(2): 682-692. [20] Susuki Y, Mezić I.Nonlinear Koopman modes and coherency identification of coupled swing dynamics[J]. IEEE Transactions on Power Systems, 2011, 26(4): 1894-1904. [21] Barocio E, Pal B C, Thornhill N F, et al.A dynamic mode decomposition framework for global power system oscillation analysis[J]. IEEE Transactions on Power Systems, 2015, 30(6): 2902-2912. [22] Schmid P J.Dynamic mode decomposition of numerical and experimental data[J]. Journal of Fluid Mechanic, 2010, 656: 5-28. [23] Mihailo R Jovanovi´c, Schmid P J, Nichols J W.Sparsity-promoting dynamic mode decomposition[J]. Physics of Fluids, 2014, 26(2): 024103-024124. [24] 苏安龙, 孙志鑫, 何晓洋, 等. 基于多元经验模式分解的电力系统低频振荡模式辨识[J]. 电力系统保护与控制, 2019, 47(22): 113-125. Su Anlong, Sun Zhixin, He Xiaoyang, et al.Identification of low-frequency oscillation modes in power systems based on multiple empirical mode decomposition[J]. Power System Protection and Control, 2019, 47(22): 113-125. [25] 李雪, 姜涛, 陈厚合, 等. 基于图分割的电力系统同调机群辨识新方法[J]. 中国电机工程学报, 2019, 39(23): 6815-6825. Li Xue, Jiang Tao, Chen Houhe, et al.A graph cut approach for separating coherent groups of generators in bulk power grid using synchrophasors[J]. Proceedings of the CSEE, 2019, 39(23): 6815-6825. [26] Rogers G.Power systems oscillations[M]. Norwell, MA: Kluwer, 2000.
2021, Vol. 36 
