Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 77-79). Also available via the Internet.

This thesis explores the PMU placement problem, that is, the placement of a minimal number of Phase Measurement Units (PMUs) on the nodes of a power system graph such that the entire graph is observed. The NP-completeness of PMU placement for planar bipartite graphs is shown. PMU placement algorithms are developed for graphs of bounded tree width, such as trees and outer planar graphs. Graph decompositions are used to develop efficient algorithms that produce minimal PMU covers. These algorithms are developed, analyzed, and compared theoretically. Algorithm animations were used in the study to develop insight into the problem and to understand algorithm behavior. / Master of Science

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graphs (see SIAM J. Discrete Math. 15(4) (2002), 519-529). A set S of vertices is defined to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph is its power domination number. We investigate the power domination number of a block graph.