Eigen Characteristic of Sample Covariance Matrix Based Multi-Disturbance Positioning Method of Power System
Li Hongqian1, Han Song1, Zhou Zhongqiang2
1. Department of Electrical Engineering Guizhou University Guiyang 550025 China; 2. Guizhou Power Grid Dispatching and Control Centers Guiyang 550002 China
Abstract A random matrix theory based multiple disturbance positioning method employing maximum eigenvalue of sample covariance matrix (Max-ESCM) and its corresponding Minimum Eigenvector (Min-ESCM) is proposed for improving the efficiency of disturbance positioning and the adaptability in multi-disturbance condition. A group of data source matrices should be firstly constructed considering random load fluctuation and noise interference for simulating the working conditions in the real world. Then the standard matrices can be obtained using a moving window matrix. The sample covariance matrices would be formed as a consequence. Furthermore, the Max-ESCM may be acquired. Meanwhile, the Spiked model based dynamic threshold for Max-ESCM might be used for detecting the abnormal disturbance in power system. Consequently, the abnormal elements involving the Min-ESCM will be found according to the phase-transition phenomenon if the dynamic threshold for Max-ESCM is violated, which might be helpful for identifying the disturbed buses with anomalous variation. The case studies have been carried on an IEEE 118-bus system utilizing DIgSILENT and Matlab® software, involving three kinds of working conditions such as simultaneous disturbance events, successive disturbance events and simultaneous fault events. The results show that the proposed methodology is valid and efficient.
Li Hongqian,Han Song,Zhou Zhongqiang. Eigen Characteristic of Sample Covariance Matrix Based Multi-Disturbance Positioning Method of Power System[J]. Transactions of China Electrotechnical Society, 2021, 36(3): 646-655.
[1] 茆美琴, 陈强, 丁勇, 等. 基于模块化多电平换流器的电动汽车集群与智能电网集成系统参数优化设计[J]. 电工技术学报, 2018, 33(16): 146-154. Mao Meiqin, Chen Qiang, Ding Yong, et al.Parameters optimization design for MMC-based EV fleet integrated into smart grid[J]. Transactions of China Electrotechnical Society, 2018, 33(16): 146-154. [2] 罗深增, 李银红, 石东源. 广域测量系统可观性概率评估及其在PMU优化配置中的应用[J]. 电工技术学报, 2018, 33(8): 1844-1853. Luo Shenzeng, Li Yinhong, Shi Dongyuan.Wide Area monitoring system observability probabilistic evaluation and it’s application in optimal PMU placement[J]. Transactions of China Electrotechnical Society, 2018, 33(8): 1844-1853. [3] Yan Rong, Geng Guangchao, Jiang Quanyuan, et al.Fast transient stability batch assessment using cascaded convolutional neural networks[J]. IEEE Transactions on Power Systems, 2019, 34(4): 2802-2813. [4] 王毅, 张宁, 康重庆, 等. 电力用户行为模型:基本概念与研究框架[J]. 电工技术学报, 2019, 34(10): 2056-2068. Wang Yi, Zhang Ning, Kang Chongqing, et al.Electrical consumer behavior model: basic concept and research framework[J]. Transactions of China Electrotechnical Society, 2019, 34(10): 2056-2068. [5] Marchenko V A, Pastur L A.Distribution of eigenvalues for some sets of random matrices[J]. Sbornik Mathematics, 1967, 1(4): 507-536. [6] He Xing, Ai Qian, Qiu Caiming, et al.A big data architecture design for smart grids based on random matrix theory[J]. IEEE Transactions on Smart Grid, 2017, 8(2): 674-686. [7] Xiao Fei, Ai Qian.Electricity theft detection in smart grid using random matrix theory[J]. IET Generation, Transmission & Distribution, 2017, 12(2): 371-378. [8] 吴茜, 张东霞, 凌雪峰, 等. 基于传染病模型的电网扰动传播动力学分析[J]. 中国电机工程学报, 2019, 39(14): 4061-4069. Wu Qian, Zhang Dongxia, Ling Xuefeng, et al.Dynamic analysis of disturbance propagation in power grid based on an epidemic model[J]. Proceedings of the CSEE, 2019, 39(14): 4061-4069. [9] Han Song, Zhou Zhongqiang, Li Hongqian.Spiked population model based abnormal state detection of power system in low SNR environment[C]//2018 International Conference on Power System Technology, Guangzhou, 2018: 4405-4410. [10] 周忠强, 韩松. 基于样本协方差矩阵最大特征值的低信噪比环境电网异常状态检测[J]. 电力系统保护与控制, 2019, 47(8): 113-119. Zhou Zhongqiang, Han Song.Maximum eigenvalue based abnormal state detection of power system in low SNR environment[J]. Power System Protection and Control, 2019, 47(8): 113-119. [11] 李洪乾, 韩松, 周忠强. 利用Rayleigh熵和并行计算的大规模电网异常负荷快速识别[J]. 电力系统保护与控制, 2019, 47(23): 37-43. Li Hongqian, Han Song, Zhou Zhongqiang.Efficient abnormal load identification in large-scale power system employing Rayleigh quotient and parallel computing technology[J]. Power System Protection and Control, 2019, 47(23): 37-43. [12] Paul D.Asymptotics of sample eigenstructure for a large dimensional spiked covariance model[J]. Statistica Sinica, 2007, 17: 1617-1642. [13] 陈伟彪, 陈亦平, 姚伟, 等. 基于随机矩阵理论的故障时刻确定和故障区域定位方法[J]. 中国电机工程学报, 2018, 38(6): 1644-1655. Chen Weibiao, Chen Yiping, Yao Wei, et al.A random matrix theory-based approach to fault time determination and fault area location[J]. Proceedings of the CSEE, 2018, 38(6): 1644-1655. [14] 童晓阳, 余森林. 基于随机矩阵谱分析的输电线路故障检测算法[J]. 电力系统自动化, 2019, 43(10): 155-169. Tong Xiaoyang, Yu Senlin.Fault detection algorithm for transmission lines based on random matrix spectrum analysis[J]. Automation of Electric Power Systems, 2019, 43(10): 155-169. [15] 张力, 张子仲, 顾建炜. 基于随机矩阵理论的电网状态分析与扰动定位方法[J]. 电力系统自动化, 2018, 42(12): 99-105, 132. Zhang Li, Zhang Zizhong, Gu Jianwei.State analysis and disturbance positioning method of power grid based on random matrix theory[J]. Automation of Electric Power Systems, 2018, 42(12): 99-105, 132. [16] 陈恩泽, 刘涤尘, 廖清芬, 等. 多重扰动下的跨区电网低频振荡研究[J]. 电工技术学报, 2014, 29(2): 290-296. Chen Enze, Liu Dichen, Liao Qingfen, et al.Research on low frequency oscillation of interconnected power grid based on multiple disturbances[J]. Transactions of China Electrotechnical Society, 2014, 29(2): 290-296. [17] O’Rourke S. A note on the Marchenko-Pastur law for a class of random matrices with dependent entries[J]. Electronic Communications in Probability, 2012, 17(16): 1-13. [18] Han Song, Xu Zheng, Sun Bin, et al.Dynamic characteristic analysis of power system interarea oscillations using HHT[J]. International Journal of Electrical Power and Energy Systems, 2010, 32(10): 1085-1090. [19] 黄德所. 特征向量法建模机理[J]. 数学的实践与认识, 2016, 31(3): 268-272. Huang Desuo.The theory and modeling with EGM[J]. Mathematics in Practice and Theory, 2016, 31(3): 268-272. [20] 林超, 郑霖, 张文辉, 等. 基于RMT的无线传感网异常节点定位算法[J/OL]. 计算机工程, 2019, https://doi.org/10.19678/j.issn.1000-3428.0054163. Lin Chao, Zheng Lin, Zhang Wenhui, et al. RTM-based outlier node localization algorithm for wireless sensor networks[J/OL]. Computer Engineering, https://doi.org/10.19678/j.issn.1000-3428.0054163. [21] Silverstein J.Some limit theorems on the eigenvectors of large dimensional sample covariance matrices[J]. Journal of Multivariate Analysis, 1984, 15(3): 295-324. [22] Silverstein J.Weak convergence of random functions defined by the eigenvectors of sample covariance matrices[J]. The Annals of Probability, 1990, 18(3): 1174-1194. [23] Benaych-Georges F, Nadakuditi R R.The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices[J]. Advances in Mathematics, 2011, 227(1): 494-521. [24] 张佳楠, 袁启海, 余建明, 等. 基于联络线扩展区域分解协调的分布式并行状态估计[J]. 电力系统自动化, 2019, 43(4): 244-256. Zhang Jianan, Yuan Qihai, Yu Jianming, et al.Distributed parallel state estimation based on decomposition and coordination of tie-line extended area[J]. Automation of Electric Power Systems, 2019, 43(4): 244-256. [25] 刘运花, 黎雄, 刘志雄, 等. 基于灰色预测的广域电力系统稳定器分布延时补偿设计[J]. 电力系统自动化, 2015, 39(12): 44-49. Liu Yunhua, Li Xiong, Liu Zhixiong, et al.A compensation design for wide-area power system stabilizer distributed time delay based on grey prediction[J]. Automation of Electric Power Systems, 2015, 39(12): 44-49. [26] 吴茜, 张东霞, 刘道伟, 等. 基于随机矩阵理论的电网静态稳定态势评估方法[J]. 中国电机工程学报, 2016, 36(20): 5414-5420. Wu Qian, Zhang Dongxia, Liu Daowei, et al.A method for power system steady stability situation assessment based on random matrix theory[J]. Proceedings of the CSEE, 2016, 36(20): 5414-5420. [27] 毛钧毅, 韩松, 李洪乾. 适用于电网异常负荷动态判别的CNN阈值模型[J]. 计算机工程, 2020, 46(6): 308-313. Mao Junyi, Han Song, Li Hongqian.Threshold model with CNN applicable to abnormal load dynamic examination of power system[J]. Computer Engineering, 2020, 46(6): 308-313. [28] 许洪强, 孙世明, 葛朝强, 等. 电网调控实时数据平台体系架构及关键技术研究与应用[J]. 电力系统自动化, 2019, 43(22): 157-164. Xu Hongqiang, Sun Shiming, Ge Zhaoqiang, et al.Research and application of architecture and key technologies for power grid real-time dispatching and control data platform[J]. Automation of Electric Power Systems, 2019, 43(22): 157-164. [29] 莫文雄, 许中, 肖斐, 等. 基于随机矩阵理论的电力扰动事件时空关联[J]. 高电压技术, 2017, 43(7): 2386-2393. Mo Wenxiong, Xu Zhong, Xiao Fei, et al.Research on temporal-spatial correlation of power disturbance events based on random matrix theory[J]. High Voltage Engineering, 2017, 43(7): 2386-2393.
2021, Vol. 36 
