Estimating Dominant Oscillation Characteristics from Measurement Responses in Power Systems Utilizing Optimized Variable Projection
Li Xue, Yu Yang, Jiang Tao, Chen Houhe, Li Guoqing
Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology Ministry of Education Northeast Electric Power University Jilin 132012 China
Abstract:Estimating the accurate dynamic feature parameters of electromechanical oscillation, which include the dominant modes, mode shapes and participation factors, are very important for analyzing and damping the electromechanical oscillation in the bulk power grids. This paper develops a holistic assessment framework to estimate the dominant modes, mode shapes and participation factors from the synchrophasor measurements by using the optimized variable projection (OVP) in the power system. The synchrophasor measurements gathered from the PMUs is firstly preprocessed by finite difference method (FDM). Then, the preprocessed measurements are used to construct the low-order state matrix which contains the critical dynamic oscillation features of power systems. According to the constructed the low-order state matrix, the variable projection model is formulated, and the modes and mode shapes can be solved by optimized variable projection (OVP). For the estimated modes and mode shapes, cumulative energy weight of modes is developed to separate the dominant modes and their mode shapes of power systems from the estimated results. Further, the participation factors are estimated by using the separated dominant mode shapes. Finally, the proposed method is evaluated by the IEEE 68-bus test system as well as China Southern Power Grid. The results confirm that the proposed OVP based dynamic assessment approach performs great accuracy and effectiveness to estimate dominant modes and mode shapes from the synchrophasor measurements in bulk power grids.
[1] 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. [2] 张民谣, 高云鹏, 吴聪, 等. 基于自适应变分模式分解的非稳态电压闪变包络参数检测[J]. 电工技术学报, 2021, 36(3): 599-608. Zhang Minyao, Gao Yunpeng, Wu Cong, et al. Non-stationary voltage flicker envelope parameters detection based on adaptive variational mode decomposition[J]. Transactions of China Electrotechnical Society, 2021, 36(3): 599-608. [3] 刘一锋, 周小平, 洪乐荣, 等. 虚拟惯性控制的负荷变换器接入弱电网的序阻抗建模与稳定性分析[J]. 电工技术学报, 2021, 36(4): 843-856. Liu Yifeng,Zhou Xiaoping,Hong Lerong,et al. Sequence impedance modeling and stability analysis of load converter with virtual inertia control connected to weak grid[J]. Transactions of China Electrotechnical Society, 2021, 36(4): 843-856. [4] 胡鹏, 艾欣, 肖仕武, 等. 静止无功发生器序阻抗建模及对次同步振荡影响因素的分析[J]. 电工技术学报, 2020, 35(17): 3703-3713. Hu Peng, Ai Xin, Xiao Shiwu, et al. Sequence impedance of static var generator and analysis of influencing factors on subsynchronous oscillation[J]. Transactions of China Electrotechnical Society, 2020, 35(17): 3703-3713. [5] 王迎晨, 杨少兵, 宋可荐, 等. 基于滑模结构无源控制的车网耦合系统低频振荡抑制方法[J]. 电工技术学报, 2020, 35(3): 553-563. Wang Yingchen, Yang Shaobing, Song Kejian, et al. An approach based on SMS to suppress low-frequency oscillation in the EMUs and traction network coupling system using PBC[J]. Transactions of China Electrotechnical Society, 2020, 35(3): 553-563. [6] 崔屹峰, 李珍国, 贾清泉, 等. 基于参数辨识与状态估计的温控负荷响应能力动态评估[J]. 电力系统自动化, 2021, 45(1): 150-158. Cui Yifeng, Li Zhenguo, Jia Qingquan, et al. Dynamic evaluation of response potential of thermostatically controlled load based on parameter identification and state estimation[J]. Automation of Electric Power Systems, 2021, 45(1): 150-158. [7] Hauer J F, Demeure C J, Scharf L L.Initial results in Prony analysis of power system response signals[J]. IEEE Transactions on Power Systems, 1990, 5(1): 80-89. [8] 孙英云, 游亚雄, 侯建兰, 等. 基于差分正交匹配追踪和Prony算法的低频振荡模态辨识[J]. 电力系统自动化, 2015, 39(10): 69-74, 167. Sun Yingyun, You Yaxiong, Hou Jianlan, et al. Identification of low-frequency oscillation mode based on difference orthogonal matching pursuit and Prony algorithm[J]. Automation Electric Power Systems, 2015, 39(10): 69-74, 167. [9] 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. [10] 李国庆, 王丹, 姜涛, 等. 基于递归连续小波变换的电力系统振荡模式辨识[J]. 电力自动化设备, 2016, 36(9): 8-16. Li Guoqing, Wang Dan, Jiang Tao, et al. Power system oscillation mode identification based on recursive continuous wavelet transform[J]. Electric Power Automation Equipment, 2016, 36(9): 8-16. [11] Liu Hesen, Zhu Lin, Pan Zhuohong, et al. ARMAX-based transfer function model identification using wide-area measurement for adaptive and coordinated damping control[J]. IEEE Transactions on Smart Grid, 2017, 8(3): 1105-1115. [12] Jiang Tao, Li Xue, Yuan Haoyu, et al. Estimating electromechanical oscillation modes from synchrophasor measurements in bulk power grids using FSSI[J]. IET Generation, Transmission &Distribution, 2018, 12(10): 2347-2358. [13] 张程, 金涛.基于ISPM和SDM-Prony算法的电力系统低频振荡模式辨识[J]. 电网技术, 2016, 40(4): 1209-1216. Zhang Cheng, Jin Tao.Identification of power system low frequency oscillations with ISPM and SDM-Prony[J]. Power System Technology, 2016, 40(4): 1209-1216. [14] 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. [15] Dosiek L, Pierre J W.Estimating electromechanical modes and mode shapes using the multichannel ARMAX model[J]. IEEE Transactions on Power Systems, 2013, 28(2): 1950-1959. [16] Yang Deyou, Cai Guowei, Chan K.Extracting inter-area oscillation modes using local measurements and data-driven stochastic subspace technique[J]. Journal of Modern Power Systems and Clean Energy, 2017, 5(5): 704-712. [17] 谢剑, 王晓茹, 张鹏.基于PRCE方法的低频振荡模式识别[J]. 中国电机工程学报, 2017, 37(11): 3129-3138. Xie Jian, Wang Xiaoru, Zhang Peng.Identification of low-frequency oscillations based on PRCE algorithm[J]. Proceedings of the CSEE, 2017, 37(11): 3129-3138. [18] 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. [19] Netto M, Susuko Y, Mili L.Date-driven participation factors for nonlinear systems based on Koopman mode decomposition[J]. IEEE Control Systems Letters, 2019, 3(1): 198-203. [20] Golub G H, Pereyra V.Separable nonlinear least squares: the variable projection method and its applications[J]. Speech Communication, 2003, 45(1): 63-87. [21] Borden A R, Lesieutre B C.Variable projection method for power system modal identification[J]. IEEE Transactions on Power Systems, 2014, 29(6): 2613-2620. [22] Askham T, Kutz J N.Variable projection methods for an optimized dynamic mode decomposition[J]. SIAM Journal on Applied Dynamical Systems, 2018, 17(1): 380-416. [23] Li Xue, Jiang Tao, Yuan Haoyu, et al. An eigensystem realization algorithm based data-driven approach for extracting electromechanical oscillation dynamic patterns from synchrophasor measurements in bulk power grids[J]. International Journal of Electrical Power & Energy Systems, 2020, 116: 105549. [24] Rogers G.Power Systems Oscillations[M]. Norwell, MA: Kluwer, 2000. [25] Jiang Tao, Yuan Haoyu, Li Guoqing, et al. Spatial-temporal decomposition approach for systematically tracking dominant modes, mode shapes and coherent groups in power systems[J]. IET Generation, Transmission & Distribution, 2017, 11(8): 1889-1900.