基于高维随机矩阵理论的电网薄弱点评估方法
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摘要
电网薄弱节点的识别是电力系统安全稳定分析领域的重要内容之一。为了准确辨识电网薄弱环节,从数据驱动的角度出发,提出一种综合高维随机矩阵理论及熵理论的评估方法。分析利用电网实时数据构成高维随机矩阵的处理方法,将随机矩阵理论的统计规律映射到电网实际的运行状态,最后综合随机矩阵理论中M-P定理(TheMarcenkoPastur Law)、圆环率、线性特征值统计量及熵理论评估电网受扰后的脆弱性,构造了电网薄弱点判断指标。该方法不需要识别系统结构,避免了对系统的建模过程,且准确性较现有文献有所提升。通过IEEE39节点系统的仿真结果,验证了所提识别方法的有效性。
Identification of weak nodes in power grids is one of the important contents in the field of power system security and stability analysis. In order to accurately identify the weak nodes, an integrated identification method of high-dimensional matrix theory and the entropy theory was proposed from the data-driven point of view. In this paper, the processing method of using big data to construct real-time high-dimensional random matrices was proposed, and the statistical laws of random matrices were mapped to the actual operating states of the power grid. Based on the MarcenkoPastur law, linear eigenvalue statistics and entropy theory, the vulnerability of the power grid was evaluated. This method does not need to identify the system structure and can avoid the modeling process of the system, and the accuracy is higher. The simulation of IEEE39 nodes system verifies the effectiveness of this method.
Identification of weak nodes in power grids is one of the important contents in the field of power system security and stability analysis. In order to accurately identify the weak nodes, an integrated identification method of high-dimensional matrix theory and the entropy theory was proposed from the data-driven point of view. In this paper, the processing method of using big data to construct real-time high-dimensional random matrices was proposed, and the statistical laws of random matrices were mapped to the actual operating states of the power grid. Based on the MarcenkoPastur law, linear eigenvalue statistics and entropy theory, the vulnerability of the power grid was evaluated. This method does not need to identify the system structure and can avoid the modeling process of the system, and the accuracy is higher. The simulation of IEEE39 nodes system verifies the effectiveness of this method.
引文
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[14]魏大千,王波,刘涤尘.高维随机矩阵描述下的量测大数据建模与异常数据检测方法[J].中国电机工程学报,2015,35(S1):59-66.Wei Daqian,Wang Bo,Liu Dichen.A method for WAMSbig data modeling and abnormal data detection with large random matrices[J].Proceedings of the CSEE,2015,35(S1):59-66(in Chinese).
[15]刘威,张东霞,王新迎.基于随机矩阵理论的电力系统暂态稳定性分析[J].中国电机工程学报,2016,36(18):4854-4863.Liu Wei,Zhang Dongxia,Wang Xinying.Power system transient stability analysis based on random matrix theory[J].Proceedings of the CSEE,2016,36(18):4854-4863(in Chinese).
[16]王春义,牟宏,顾洁.基于大数据高维分析理论的用户用电模式分析[J].水电能源科学,2017,35(10):203-206.Wang Chunyi,Mou Hong,Gu Jie.Analysis of electric power user consumption pattern based on big data[J].Water Resources and Power,2017,35(10):203-206(in Chinese).
[17]严英杰,盛戈皞,王辉,等.基于高维随机矩阵大数据分析模型的输变电设备关键性能评估方法[J].中国电机工程学报,2016,36(2):435-445.Yan Yingjie,Sheng Gehao,Wang Hui,et al.The key state assessment method of power transmission equipment using big data analyzing model based on large dimensional random matrix[J].Proceedings of the CSEE,2016,36(2):435-445(in Chinese).
[18]吴茜,张东霞,刘道伟.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.A method for power system steady stability situation assessment based on random matrix theory[J].Proceedings of the CSEE,2016,36(20):5414-5420(in Chinese).
[19]徐心怡,贺兴,艾芊.基于随机矩阵理论的配电网运行状态相关性分析方法[J].电网技术,2016,40(3):781-790.Xu Xinyi,He Xing,Ai Qian.A correlation analysis method for operation status of distribution network based on random matrix theory[J].Power System Technology,2016,40(3):781-790(in Chinese).
[20]刘威,张东霞,丁玉成.基于随机矩阵理论与熵理论的电网薄弱环节辨识方法[J].中国电机工程学报,2017,37(20):5893-5901.Liu Wei,Zhang Dongxia,Ding Yucheng.Power grid vulnerability identification methods based on random matrix theory and entropy theory[J].Proceedings of the CSEE,2017,37(20):5893-5901(in Chinese).
[21]Wu J,Ota K,Dong M,et al.Big data analysis based security situational awareness for smart grid[J].IEEETransactions on Big Data,2018,4(3):408-417.
[22]梁越明,解紫城.基于信息熵和层次分析法的电网节点脆弱度评估[J].电力学报,2013,28(3):196-200.Liang Yueming,Xie Zicheng.Node vulnerability assessment on power grid based on information entropy and hierarchy process[J].Journal of Power System,2013,28(3):196-200(in Chinese).
[23]于群,冯安强,贺庆,等.基于综合薄弱度的电网节点脆弱性评估[J].现代电力,2017,34(2):36-42.Yu Qun,Feng Anqiang,He Xing,et al.Node vulnerability assessment of power gird based on comprehensive weak degree[J].Modern Electric Power,2017,34(2):36-42(in Chinese).
[24]刘小丽.基于复杂网络理论的电网脆弱线路和脆弱节点辨识[D].长沙:湖南大学,2016.Liu Xiaoli.Identification of vulnerable lines in power grid based on complex network theory[D].Changsha:Hunan University,2016(in Chinese).
[25]冯治鸿,周双喜.大规模电力系统电压失稳区的确定方法[J].中国电机工程学报,1997,17(3):9-13.Feng Zhihong,Zhou Shuangxi.Determination of voltage collapse areas in large scale power system[J].Proceedings of the CSEE,1997,17(3):9-13(in Chinese).
[2]王涛,岳贤龙,顾雪平.基于犹豫模糊决策法的电网脆弱性综合评估[J].电网技术,2017,41(7):2272-2281.Wang Tao,Yue Xianlong,Gu Xueping.Comprehensive evaluation of power grid vulnerability based on hesitant fuzzy decision making method[J].Power System Technology,2017,41(7):2272-2281(in Chinese).
[3]刘友波,刘俊勇,王民昆.计及动能注入介数的线路暂态脆弱性快速评估[J].中国电机工程学报,2011,31(13):40-47.Liu Youbo,Liu Junyong,Wang Minkun.Fast assessment method for transient vulnerability of transmission lines based on kinetic energy injection betweenness[J].Proceedings of the CSEE,2011,31(13):40-47(in Chinese).
[4]陈恩泽,刘涤尘,廖清芬,等.基于事故链的电网低频振荡及脆弱性分析[J].中国电机工程学报,2011,31(28):42-48.Chen Enze,Liu Dichen,Liao Qingfen,et al.Low frequency oscillation and vulnerability analysis of power grid based on the fault chains[J].Proceedings of the CSEE,2011,31(28):42-48(in Chinese).
[5]陈为化,江全元,曹一家.基于风险理论和模糊推理的电压脆弱性评估[J].中国电机工程学报,2005,25(24):20-25.Chen Weihua,Jiang Quanyuan,Cao Yijia.Voltage vulnerability assessment based on risk theory and fuzzy reasoning[J].Proceedings of the CSEE,2005,25(24):20-25(in Chinese).
[6]李勇,刘俊勇,刘晓宇.基于广义支路能量时空分布熵测度的线路脆弱度评估[J].中国电机工程学报,2013,33(34):187-196.Li Yong,Liu Junyong,Liu Xiaoyu.Assessment of vulnerable lines in power grid based on entropy of generalized branch energy[J].Proceedings of the CSEE,2013,33(34):187-196(in Chinese).
[7]彭小圣,邓迪元,程时杰.面向智能电网应用的电力大数据关键技术[J].中国电机工程学报,2015,35(3):503-511.Peng Xiaosheng,Deng Diyuan,Cheng Shijie.Key technologies of electric power big data and its application prospects in smart grid[J].Proceedings of the CSEE,2015,35(3):503-511(in Chinese).
[8]黄彦浩,于之虹,谢昶.电力大数据技术与电力系统仿真计算结合问题研究[J].中国电机工程学报,2015,35(1):13-22.Huang Yanhao,Yu Zhihong,Xie Chang.Study on the application of electric power big data technology in power system simulation[J].Proceedings of the CSEE,2015,35(1):13-22(in Chinese).
[9]陈伟彪,陈亦平,姚伟.采用WAMS时序信息的故障诊断方法及应用[J].电网技术,2017,41(6):1956-1963.Chen Weibiao,Chen Yiping,Yao Wei.A fault diagnosis method using WAMS time series information and its application[J].Power System Technology,2017,41(6):1956-1963(in Chinese).
[10]Brody T A,Flores J,French J B,et al.Random-matrix physics:spectrum and strength fluctuations[J].Reviews of Modern Physics,1981,53(3):385-479.
[11]Laloux L,Cizeau P,Potters M,et al.Random matrix theory and financial correlations[J].International Journal of Theoretical and Applied Finance,2000,3(3):391-397.
[12]He Xing,Ai Qian,Qiu R C,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.
[13]贺兴,艾芊,邱才明,等.随机矩阵理论在电力系统认知中的应用初探[J].电网技术,2017,41(4):1165-1173.He Xing,Ai Qian,Qiu Caiming,et al.A primary study on the situation awareness of power systems using random matrix theory[J].Power System Technology,2017,41(4):1165-1173(in Chinese).
[14]魏大千,王波,刘涤尘.高维随机矩阵描述下的量测大数据建模与异常数据检测方法[J].中国电机工程学报,2015,35(S1):59-66.Wei Daqian,Wang Bo,Liu Dichen.A method for WAMSbig data modeling and abnormal data detection with large random matrices[J].Proceedings of the CSEE,2015,35(S1):59-66(in Chinese).
[15]刘威,张东霞,王新迎.基于随机矩阵理论的电力系统暂态稳定性分析[J].中国电机工程学报,2016,36(18):4854-4863.Liu Wei,Zhang Dongxia,Wang Xinying.Power system transient stability analysis based on random matrix theory[J].Proceedings of the CSEE,2016,36(18):4854-4863(in Chinese).
[16]王春义,牟宏,顾洁.基于大数据高维分析理论的用户用电模式分析[J].水电能源科学,2017,35(10):203-206.Wang Chunyi,Mou Hong,Gu Jie.Analysis of electric power user consumption pattern based on big data[J].Water Resources and Power,2017,35(10):203-206(in Chinese).
[17]严英杰,盛戈皞,王辉,等.基于高维随机矩阵大数据分析模型的输变电设备关键性能评估方法[J].中国电机工程学报,2016,36(2):435-445.Yan Yingjie,Sheng Gehao,Wang Hui,et al.The key state assessment method of power transmission equipment using big data analyzing model based on large dimensional random matrix[J].Proceedings of the CSEE,2016,36(2):435-445(in Chinese).
[18]吴茜,张东霞,刘道伟.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.A method for power system steady stability situation assessment based on random matrix theory[J].Proceedings of the CSEE,2016,36(20):5414-5420(in Chinese).
[19]徐心怡,贺兴,艾芊.基于随机矩阵理论的配电网运行状态相关性分析方法[J].电网技术,2016,40(3):781-790.Xu Xinyi,He Xing,Ai Qian.A correlation analysis method for operation status of distribution network based on random matrix theory[J].Power System Technology,2016,40(3):781-790(in Chinese).
[20]刘威,张东霞,丁玉成.基于随机矩阵理论与熵理论的电网薄弱环节辨识方法[J].中国电机工程学报,2017,37(20):5893-5901.Liu Wei,Zhang Dongxia,Ding Yucheng.Power grid vulnerability identification methods based on random matrix theory and entropy theory[J].Proceedings of the CSEE,2017,37(20):5893-5901(in Chinese).
[21]Wu J,Ota K,Dong M,et al.Big data analysis based security situational awareness for smart grid[J].IEEETransactions on Big Data,2018,4(3):408-417.
[22]梁越明,解紫城.基于信息熵和层次分析法的电网节点脆弱度评估[J].电力学报,2013,28(3):196-200.Liang Yueming,Xie Zicheng.Node vulnerability assessment on power grid based on information entropy and hierarchy process[J].Journal of Power System,2013,28(3):196-200(in Chinese).
[23]于群,冯安强,贺庆,等.基于综合薄弱度的电网节点脆弱性评估[J].现代电力,2017,34(2):36-42.Yu Qun,Feng Anqiang,He Xing,et al.Node vulnerability assessment of power gird based on comprehensive weak degree[J].Modern Electric Power,2017,34(2):36-42(in Chinese).
[24]刘小丽.基于复杂网络理论的电网脆弱线路和脆弱节点辨识[D].长沙:湖南大学,2016.Liu Xiaoli.Identification of vulnerable lines in power grid based on complex network theory[D].Changsha:Hunan University,2016(in Chinese).
[25]冯治鸿,周双喜.大规模电力系统电压失稳区的确定方法[J].中国电机工程学报,1997,17(3):9-13.Feng Zhihong,Zhou Shuangxi.Determination of voltage collapse areas in large scale power system[J].Proceedings of the CSEE,1997,17(3):9-13(in Chinese).