基于宏微观特征分层聚类的配电网拓扑相似性分析方法
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摘要
提出一种基于宏观与微观拓扑特征分层聚类的配电网拓扑相似性分析方法。首先,构建涵盖宏微观拓扑特征的指标集作为拓扑相似性分析的依据,包括宏观层面的网络社团特性和节点度相关性指标以及微观层面的线路功率传输性能和负荷分布密度指标;针对传统拓扑相似性分析方法难以对变量数不同的微观拓扑特征进行细粒度分析的问题,提出基于核密度估计的微观拓扑特征描述方法和基于Kullback-Leibler散度的微观特征相似性量度方法;再以基于标准离差率改进的谱聚类算法对宏微观拓扑特征集进行分层聚类,实现配电网拓扑相似性分析。算例分析表明,所提出的配电网拓扑相似性分析方法在表征配电网结构特性的能力及相似性分析效果方面相对于传统方法更优。
A topology similarity analysis method for distribution network based on hierarchical clustering of macroscopic and microscopic topology features is proposed. Firstly, the index set covering macroscopic and microscopic topology features is constructed as a basis for topology similarity analysis, including network community characteristics and node degree correlation indices at the macroscopic level, and line power transmission performance and load distribution density indices at the microscopic level. Since it is difficult for traditional topology similarity methods to make fine-grained analysis on microscopic topology features with different numbers of variables, a microscopic topology feature description method based on kernel density estimation and a microscopic feature similarity measurement method based on Kullback-Leibler divergence is proposed. The improved spectral clustering algorithm based on coefficient of variation is used for hierarchical clustering of macroscopic and microscopic topology feature sets, to realize topology similarity analysis for distribution network. Case study shows that the proposed topology similarity analysis method of distribution network is superior to the traditional method in the ability of representing structural characteristics of distribution networks and the effect of similarity analysis.
A topology similarity analysis method for distribution network based on hierarchical clustering of macroscopic and microscopic topology features is proposed. Firstly, the index set covering macroscopic and microscopic topology features is constructed as a basis for topology similarity analysis, including network community characteristics and node degree correlation indices at the macroscopic level, and line power transmission performance and load distribution density indices at the microscopic level. Since it is difficult for traditional topology similarity methods to make fine-grained analysis on microscopic topology features with different numbers of variables, a microscopic topology feature description method based on kernel density estimation and a microscopic feature similarity measurement method based on Kullback-Leibler divergence is proposed. The improved spectral clustering algorithm based on coefficient of variation is used for hierarchical clustering of macroscopic and microscopic topology feature sets, to realize topology similarity analysis for distribution network. Case study shows that the proposed topology similarity analysis method of distribution network is superior to the traditional method in the ability of representing structural characteristics of distribution networks and the effect of similarity analysis.
引文
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[15] MEHRLE D,STROSSER A,HARKIN A.Walk-modularity and community structure in networks[J].Network Science,2015,3(3):348-360.
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[18] 段凡丁.关于最短路径的SPFA快速算法[J].西南交通大学学报,1994,29(2):207-212.DUAN Fanding.A faster algorithm for shortest-path-SPFA[J].Journal of Southwest Jiaotong University,1994,29(2):207-212.
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[20] 郭艳平,颜文俊,包哲静,等.基于经验模态分解和散度指标的风力发电机滚动轴承故障诊断方法[J].电力系统保护与控制,2012,40(17):83-87.GUO Yanping,YAN Wenjun,BAO Zhejing,et al.Fault diagnosis of bearing in wind turbine based on empirical mode decomposition and divergence index[J].Power System Protection and Control,2012,40(17):83-87.
[21] 王兴良,王立宏,武栓虎.谱聚类中选取特征向量的动态选择性集成方法[J].模式识别与人工智能,2014,27(5):452-462.WANG Xingliang,WANG Lihong,WU Shuanhu.Eigen-vector selection algorithm for spectral clustering based on dynamic selective ensemble[J].Pattern Recognition and Artificial Intelligence,2014,27(5):452-462.
[22] 朱连江,马炳先,赵学泉.基于轮廓系数的聚类有效性分析[J].计算机应用,2010,30(增刊2):139-141.ZHU Lianjiang,MA Bingxian,ZHAO Xuequan.Clustering validity analysis based on silhouette coefficient[J].Journal of Computer Applications,2010,30(Supplement 2):139-141.
[23] 毛凯.复杂网络结构的稳定性与鲁棒性研究[J].计算机科学,2015,42(4):85-88.MAO Kai.Research on stability and robustness of complex network structure[J].Computer Science,2015,42(4):85-88.
[24] BILLINTON R,WANGDEE W.Delivery point reliability indices of a bulk electric system using sequential Monte Carlo simulation[J].IEEE Transactions on Power Delivery,2006,21(1):345-352.
[2] 郭晓斌,许悦,程乐峰,等.基于拓扑相似性分析的配电网网架可靠性评估[J].高电压技术,2018,44(11):3760-3769.GUO Xiaobin,XU Yue,CHENG Lefeng,et al.Reliability assessment of a distribution network architecture based on topological similarity analysis[J].High Voltage Engineering,2018,44(11):3760-3769.
[3] 苏韵掣,刘俊勇,刘友波,等.适用于配电网规划的可靠性指标改进显式估算算法[J].电力系统自动化,2017,41(1):79-87.DOI:10.7500/AEPS20160309004.SU Yunche,LIU Junyong,LIU Youbo,et al.Improved explicit analytical evaluation algorithm of reliability indices for distribution network[J].Automation of Electric Power Systems,2017,41(1):79-87.DOI:10.7500/AEPS 20160309004.
[4] 张弘鹏,余贻鑫.配电网拓扑结构概念聚类及其在优化规划中的应用[J].电力系统自动化,2003,27(22):31-35.ZHANG Hongpeng,YU Yixin.Conceptual clustering of distribution network topology and its application to optimal planning[J].Automation of Electric Power Systems,2003,27(22):31-35.
[5] 李姝润,王承民,谢宁.基于模式的配电网规划方法研究[J].现代电力,2018,35(1):33-38.LI Shurun,WANG Chengmin,XIE Ning.Research on distribution network planning method based on pattern[J].Modern Electric Power,2018,35(1):33-38.
[6] 张竣淇.配电网拓扑结构模式分析与自动化规划模型研究[D].广州:华南理工大学,2015.ZHANG Junqi.Distribution network topology pattern analysis and automation model research[D].Guangzhou:South China University of Technology,2015.
[7] 郭庆来,孙宏斌,张伯明,等.基于无功源控制空间聚类分析的无功电压分区[J].电力系统自动化,2005,29(10):36-40.GUO Qinglai,SUN Hongbin,ZHANG Boming,et al.Power network partitioning based on clustering analysis in Mvar control space[J].Automation of Electric Power Systems,2005,29(10):36-40.
[8] 梁海平,顾雪平.基于谱聚类的黑启动子系统划分[J].电网技术,2013,37(2):372-377.LIANG Haiping,GU Xueping.Black-start network partitioning based on spectral clustering[J].Power System Technology,2013,37(2):372-377.
[9] 宋婷,刘文予,刘俊涛.基于骨架树的线性骨架拓扑相似性度量算法[J].红外与激光工程,2005,34(1):74-79.SONG Ting,LIU Wenyu,LIU Juntao.Method of linear skeleton topological similarity measurement based on skeleton tree[J].Infrared and Laser Engineering,2005,34(1):74-79.
[10] KOUTRA D,VOGELSTEIN J T,FALOUTSOS C.Deltacon:a principled massive-graph similarity function[J].ACM Transactions on Knowledge Discovery from Data,2013,10(3):1-17.
[11] 于琳,孙莹,徐然,等.改进粒子群优化算法及其在电网无功分区中的应用[J].电力系统自动化,2017,41(3):89-95.DOI:10.7500/AEPS20160321004.YU Lin,SUN Ying,XU Ran,et al.Improved particle swarm optimization algorithm and its application in reactive power partitioning of power grid[J].Automation of Electric Power Systems,2017,41(3):89-95.DOI:10.7500/AEPS 20160321004.
[12] 肖传亮,赵波,周金辉,等.配电网中基于网络分区的高比例分布式光伏集群电压控制[J].电力系统自动化,2017,41(21):147-155.DOI:10.7500/AEPS20170101002.XIAO Chuanliang,ZHAO Bo,ZHOU Jinhui,et al.Network partition based cluster voltage control of high penetration distributed photovoltaic system in distribution networks[J].Automation of Electric Power Systems,2017,41(21):147-155.DOI:10.7500/AEPS20170101002.
[13] NIU Shuzi,WANG Daling,FENG Shi,et al.An improved spectral clustering algorithm for community discovery[C]// Ninth International Conference on Hybrid Intelligent Systems,August 12-14,2009,Shenyang,China:262-267.
[14] 李晓佳,张鹏,狄增如,等.复杂网络中的社团结构[J].复杂系统与复杂性科学,2008,5(3):19-42.LI Xiaojia,ZHANG Peng,DI Zengru,et al.Community structure in complex networks[J].Complex Systems and Complexity Science,2008,5(3):19-42.
[15] MEHRLE D,STROSSER A,HARKIN A.Walk-modularity and community structure in networks[J].Network Science,2015,3(3):348-360.
[16] 汪小帆,李翔,陈关荣.网络科学导论[M].北京:高等教育出版社,2012.WANG Xiaofan,LI Xiang,CHEN Guanrong.Network science:an introduction [M].Beijing:Higher Education Press,2012.
[17] NEWMAN M E J.Assortative mixing in networks[J].Physical Review Letters,2002,89(20):208701.
[18] 段凡丁.关于最短路径的SPFA快速算法[J].西南交通大学学报,1994,29(2):207-212.DUAN Fanding.A faster algorithm for shortest-path-SPFA[J].Journal of Southwest Jiaotong University,1994,29(2):207-212.
[19] 洪绍云,程浩忠,黄丽娜,等.有功潮流追踪优化建模及其应用[J].中国电力,2017,50(4):81-86.HONG Shaoyun,CHENG Haozhong,HUANG Lina,et al.Real power flow tracing optimal modeling and its application[J].Electric Power,2017,50(4):81-86.
[20] 郭艳平,颜文俊,包哲静,等.基于经验模态分解和散度指标的风力发电机滚动轴承故障诊断方法[J].电力系统保护与控制,2012,40(17):83-87.GUO Yanping,YAN Wenjun,BAO Zhejing,et al.Fault diagnosis of bearing in wind turbine based on empirical mode decomposition and divergence index[J].Power System Protection and Control,2012,40(17):83-87.
[21] 王兴良,王立宏,武栓虎.谱聚类中选取特征向量的动态选择性集成方法[J].模式识别与人工智能,2014,27(5):452-462.WANG Xingliang,WANG Lihong,WU Shuanhu.Eigen-vector selection algorithm for spectral clustering based on dynamic selective ensemble[J].Pattern Recognition and Artificial Intelligence,2014,27(5):452-462.
[22] 朱连江,马炳先,赵学泉.基于轮廓系数的聚类有效性分析[J].计算机应用,2010,30(增刊2):139-141.ZHU Lianjiang,MA Bingxian,ZHAO Xuequan.Clustering validity analysis based on silhouette coefficient[J].Journal of Computer Applications,2010,30(Supplement 2):139-141.
[23] 毛凯.复杂网络结构的稳定性与鲁棒性研究[J].计算机科学,2015,42(4):85-88.MAO Kai.Research on stability and robustness of complex network structure[J].Computer Science,2015,42(4):85-88.
[24] BILLINTON R,WANGDEE W.Delivery point reliability indices of a bulk electric system using sequential Monte Carlo simulation[J].IEEE Transactions on Power Delivery,2006,21(1):345-352.