Brueni, Dennis J.Heath, Lenwood S.2014-05-282014-05-282005Brueni, D. J.; Heath, L. S., "The PMU placement problem," SIAM J. Discrete Math., 19(3), 744-761, (2005). DOI: 10.1137/s08954801034325560895-4801http://hdl.handle.net/10919/48139PMU placement problem is an optimization problem abstracted from an approach to supervising an electrical power system. The power system is modeled as a graph, and adequate supervision of the system requires that the voltage at each node and the current through each edge be observable. A phasor measurement unit ( PMU) is a monitor that can be placed at a node to directly observe the voltage at that node, as well as the current and its phase through all incident edges. The PMU placement problem is to place PMUs at a minimum number of nodes so that the entire electric power system is observed. A new simpler definition of graph observability and several complexity results for the PMU placement problem are presented. The PMU placement problem is shown to be NP-complete even for planar bipartite graphs. Several fundamental properties of PMU placements are proven, including the property that a minimum PMU placement requires no more than 1/3 of the nodes in a connected graph of at least 3 nodes.en-USIn Copyrightphasor measurement unitpower system graph observabilitydominationelectric power monitoringnp-completenesssynchronized phasor measurementsfault detection/location techniquetransmission-linesstate estimationpower-systemslocation algorithmmeasurement unitsobservabilitypredictionprotectionmathematics, appliedArticle - Refereedhttp://epubs.siam.org/doi/abs/10.1137/S0895480103432556https://doi.org/10.1137/s0895480103432556