Hierarchical Spectral Clustering of Power Grids

Ruben J. Sanchez-Garcia, Max Fennelly, Sean Norris, Nick Wright, Graham Niblo, Jacek Brodzki, Janusz W. Bialek
2014 IEEE Transactions on Power Systems  
Citation for published item: ¡ nhezEqr¡ %D u¡ en tF nd pennelyD wx nd xorrisD e¡ n nd rightD xik nd xiloD qrhm nd frodzkiD tek nd filekD tnusz F @PHIRA 9rierrhil spetrl lustering of power gridsF9D siii trnstions on power systemsFD PW @SAF ppF PPPWEPPQUF Further information on publisher's website: httpXGGdxFdoiForgGIHFIIHWGFPHIRFPQHTUST Publisher's copyright statement: This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see
more » ... nses/by/3.0/ Additional information: Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. Abstract-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 -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.
doi:10.1109/tpwrs.2014.2306756 fatcat:33x6h5iomrd6lp6gut3aurpnwe