{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:26:39Z","timestamp":1787325999225,"version":"3.56.0"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:p>The PMU 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.<\/jats:p>","DOI":"10.1137\/s0895480103432556","type":"journal-article","created":{"date-parts":[[2005,12,26]],"date-time":"2005-12-26T21:00:19Z","timestamp":1135630819000},"page":"744-761","source":"Crossref","is-referenced-by-count":109,"title":["The PMU Placement Problem"],"prefix":"10.1137","volume":"19","author":[{"given":"Dennis J.","family":"Brueni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lenwood S.","family":"Heath","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/59.260810"},{"key":"R2","unstructured":"D. J. Brueni,\n                      Minimal PMU Placement for Graph Observability: A Decomposition Approach\n                      , M. 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