Hierarchical Spectral Clustering of Power Grids
Hierarchical Spectral Clustering of Power Grids
复制标题
DOI：
10.1109/tpwrs.2014.2306756
复制
发表时间：
2014-03
影响因子：
6.6
通讯作者：
Rubén J. Sánchez-García;Max Fennelly;S. Norris;N. Wright;Graham A. Niblo;J. Brodzki;J. Bialek
中科院分区：
文献类型：
--
作者：
Rubén J. Sánchez-García;Max Fennelly;S. Norris;N. Wright;Graham A. Niblo;J. Brodzki;J. Bialek
电力传输系统可以由具有节点和链路的网络来表示，所述节点和链路分别表示母线和输电线。每条线路都可以被赋予一个权重，代表线路的某些电气属性，例如给定时间的线路导纳或平均功率流。我们使用层次谱聚类方法来揭示这种网络的内部连通性结构。谱聚类使用与网络相关的矩阵的特征值和特征向量，它在计算上非常高效，并且适用于任何权重选择。当使用线路导纳时，它揭示了底层网络的静态内部连接结构，而使用潮流则突出显示了具有最小功率流干扰的孤岛，因此它自然与受控孤岛有关。我们的方法超越了标准的k-均值算法，而是将完整的网络子结构表示为树状图。我们提供了在电力系统中使用频谱聚类的完整的理论证明，并包括了我们的方法在几个小、中、大规模的测试系统上的结果，包括一个英国传输网络的模型。
A power transmission system can be represented by a network with nodes and links representing buses and electrical transmission lines, respectively. Each line can be given a weight, representing some electrical property of the line, such as line admittance or average power flow at a given time. We use a hierarchical spectral clustering methodology to reveal the internal connectivity structure of such a network. Spectral clustering uses the eigenvalues and eigenvectors of a matrix associated to the network, it is computationally very efficient, and it works for any choice of weights. When using line admittances, it reveals the static internal connectivity structure of the underlying network, while using power flows highlights islands with minimal power flow disruption, and thus it naturally relates to controlled islanding. Our methodology goes beyond the standard k-means algorithm by instead representing the complete network substructure as a dendrogram. We provide a thorough theoretical justification of the use of spectral clustering in power systems, and we include the results of our methodology for several test systems of small, medium and large size, including a model of the Great Britain transmission network.