基于随机矩阵理论与熵理论的电网薄弱环节辨识方法
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摘要
电网薄弱环节辨识对保证电力系统的安全性有重要的意义。为了分析辨识电网薄弱环节,提出一种随机矩阵理论与熵理论相结合的辨识方法。首先介绍随机矩阵理论基本原理和薄弱环节特征。然后利用电压数据和相角数据构建矩阵,结合随机矩阵理论分析矩阵的统计特性,并将统计特性与电网物理特性对比分析。再结合熵理论建立薄弱节点辨识模型,利用变异系数量化分析数据波动特征,构建薄弱支路辨识模型。最后,利用IEEE39节点系统模型验证方法的正确性。
Power grid vulnerability identification is great significance for guaranteeing power system security. The method of combining the random matrix theory with entropy theory was put forward to identify weak links which endanger power system security. Firstly, the fundamental principles of the random matrix theory and the characteristics of power system security weak link were introduced. Secondly, random matrix based on voltage and phase angle data was constructed and its statistical properties was analyzed and compared with physical properties. Thirdly, based on entropy theory, weak node and branch identification model was established. Data fluctuation characteristics can be quantitatively estimated according to variation coefficient. Finally, case study based on IEEE 39 node system validates the proposed approach.
Power grid vulnerability identification is great significance for guaranteeing power system security. The method of combining the random matrix theory with entropy theory was put forward to identify weak links which endanger power system security. Firstly, the fundamental principles of the random matrix theory and the characteristics of power system security weak link were introduced. Secondly, random matrix based on voltage and phase angle data was constructed and its statistical properties was analyzed and compared with physical properties. Thirdly, based on entropy theory, weak node and branch identification model was established. Data fluctuation characteristics can be quantitatively estimated according to variation coefficient. Finally, case study based on IEEE 39 node system validates the proposed approach.
引文
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[14]刘威,张东霞,王新迎,等.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,et al.Power system transient stability analysis based on random matrix theory[J].Proceedings of the CSEE,2016,36(18):4854-4863(in Chinese).
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[18]Lytova A,Pastur L.Central limit theorem for linear eigenvalue statistics of random matrices with independent entries[J].The Annals of Probability,2009,37(5):1778-1840.
[19]卢锦玲,姬群星,朱永利.基于能量函数法的电网脆弱性评估[J].电网技术,2008,32(7):30-33,45.Lu Jinling,Ji Qunxing,Zhu Yongli.Power grid vulnerability assessment based on energy function[J].Power System Technology,2008,32(7):30-33,45(in Chinese).
[20]He Xing,Qiu R C,Ai Qian,et al.Designing for situation awareness of future power grids:an indicator system based on linear eigenvalue statistics of large random matrices[J].IEEE Access,2016,4:3557-3568.
[21]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):152-156.Feng Zhihong,Zhou Shuangxi.Determination of voltage collapse areas in large scale power system[J].Proceedings of the CSEE,1997,17(3):152-156(in Chinese).
[22]陈得治,张伯明,方兴.节点注入功率模式对电压稳定裕度的影响[J].电网技术,2009,33(2):62-67,72.Chen Dezhi,Zhang Boming,Fang Xing.Effect of nodal injection power mode on voltage stability margin[J].Power System Technology,2009,33(2):62-67,72(in Chinese).
[23]曹一家,陈晓刚,孙可.基于复杂网络理论的大型电力系统脆弱线路辨识[J].电力自动化设备,2006,26(12):1-5,31.Cao Yijia,Chen Xiaogang,Sun Ke.Identification of vulnerable lines in power grid based on complex network theory[J].Electric Power Automation Equipment,2006,26(12):1-5,31(in Chinese).
[2]李玲玲,鲁修学,孙东旺,等.基于元件功率的区域电力系统薄弱环节辨识算法[J].电力系统保护与控制,2014,42(4):77-83.Li Lingling,Lu Xiuxue,Sun Dongwang,et al.An identification algorithm of the weak links for regional power system based on element power[J].Power System Protection and Control,2014,42(4):77-83(in Chinese).
[3]苟竞,刘俊勇,刘友波,等.基于能量熵测度的电力系统连锁故障风险辨识[J].电网技术,2013,37(10):2754-2761.Gou Jing,Liu Junyong,Liu Youbo,et al.Energy entropy measure based risk identification of power grid cascading failures[J].Power System Technology,2013,37(10):2754-2761(in Chinese).
[4]靳冰洁,张步涵,姚建国,等.基于信息熵的大型电力系统元件脆弱性评估[J].电力系统自动化,2015,39(5):61-68.Jin Bingjie,Zhang Buhan,Yao Jianguo,et al.Large-scale power system components vulnerability assessment based on entropy[J].Automation of Electric Power Systems,2015,39(5):61-68(in Chinese).
[5]孙元章,程林,刘海涛.基于实时运行状态的电力系统运行可靠性评估[J].电网技术,2005,29(15):6-12.Sun Yuanzhang,Cheng Lin,Liu Haitao.Power system operating reliability evaluation based on real-time operating state[J].Power System Technology,2005,29(15):6-12(in Chinese).
[6]李勇,刘俊勇,刘晓宇,等.基于潮流熵的电网连锁故障传播元件的脆弱性评估[J].电力系统自动化,2012,36(19):11-16.Li Yong,Liu Junyong,Liu Xiaoyu,et al.Vulnerability assessment in power grid cascading failures based on entropy of power flow[J].Automation of Electric Power Systems,2012,36(19):11-16(in Chinese).
[7]王涛,岳贤龙,顾雪平,等.基于奇异值熵和潮流分布熵的电网关键节点辨识[J].电力自动化设备,2016,36(4):46-53.Wang Tao,Yue Xianlong,Gu Xueping,et al.Power grid critical node identification based on singular value entropy and power grid flow distribution entropy[J].Electric Power Automation Equipment,2016,36(4):46-53(in Chinese).
[8]刘文颖,王佳明,谢昶,等.基于脆性风险熵的复杂电网连锁故障脆性源辨识模型[J].中国电机工程学报,2012,32(31):142-149.Liu Wenying,Wang Jiaming,Xie Chang,et al.Brittleness source identification model for cascading failure of complex power grid based on brittle risk entropy[J].Proceedings of the CSEE,2012,32(31):142-149(in Chinese).
[9]张东霞,苗新,刘丽平,等.智能电网大数据技术发展研究[J].中国电机工程学报,2015,35(1):2-12.Zhang Dongxia,Miao Xin,Liu Liping,et al.Research on development strategy for smart grid big data[J].Proceedings of the CSEE,2015,35(1):2-12(in Chinese).
[10]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).
[11]Xu Xinyi,He Xing,Ai Qian,et al.A correlation analysis method for power systems based on random matrix theory[J].IEEE Transactions on Smart Grid,2015,doi:10.1109/TSG.2015.2508506.
[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]徐心怡,贺兴,艾芊,等.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,et al.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).
[14]刘威,张东霞,王新迎,等.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,et al.Power system transient stability analysis based on random matrix theory[J].Proceedings of the CSEE,2016,36(18):4854-4863(in Chinese).
[15]He Xing,Qiu R C,Ai Qian,et al.Linear eigenvalue statistics:an indicator ensemble design for situation awareness of power systems[J].ar Xiv:1512.07082,2015.
[16]Mar?enko V A,Pastur L A.Distribution of eigenvalues for some sets of random matrices[J].Mathematics of the USSR-Sbornik,1967,1(4):457-483.
[17]Qiu R C,Antonik P.Big data for smart grid[M]//Qiu R C,Antonik P.Smart Grid using Big Data Analytics:A Random Matrix Theory Approach.[S.l.]:John Wiley&Sons Ltd.,2017.
[18]Lytova A,Pastur L.Central limit theorem for linear eigenvalue statistics of random matrices with independent entries[J].The Annals of Probability,2009,37(5):1778-1840.
[19]卢锦玲,姬群星,朱永利.基于能量函数法的电网脆弱性评估[J].电网技术,2008,32(7):30-33,45.Lu Jinling,Ji Qunxing,Zhu Yongli.Power grid vulnerability assessment based on energy function[J].Power System Technology,2008,32(7):30-33,45(in Chinese).
[20]He Xing,Qiu R C,Ai Qian,et al.Designing for situation awareness of future power grids:an indicator system based on linear eigenvalue statistics of large random matrices[J].IEEE Access,2016,4:3557-3568.
[21]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):152-156.Feng Zhihong,Zhou Shuangxi.Determination of voltage collapse areas in large scale power system[J].Proceedings of the CSEE,1997,17(3):152-156(in Chinese).
[22]陈得治,张伯明,方兴.节点注入功率模式对电压稳定裕度的影响[J].电网技术,2009,33(2):62-67,72.Chen Dezhi,Zhang Boming,Fang Xing.Effect of nodal injection power mode on voltage stability margin[J].Power System Technology,2009,33(2):62-67,72(in Chinese).
[23]曹一家,陈晓刚,孙可.基于复杂网络理论的大型电力系统脆弱线路辨识[J].电力自动化设备,2006,26(12):1-5,31.Cao Yijia,Chen Xiaogang,Sun Ke.Identification of vulnerable lines in power grid based on complex network theory[J].Electric Power Automation Equipment,2006,26(12):1-5,31(in Chinese).