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 graph theory. A set S of vertices is defined to be a power dominating set of a graphs 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. In this thesis, we investigate the power domination number of a block graph.

The PMU has been found to carry great deal of value for applications in the wide area monitoring of power systems. Historically, deployment of these devices has been limited by the prohibitive cost of the device itself. Therefore, the objective of the conventional optimal PMU placement problem is to find the minimum number devices, which if carefully placed throughout the network, either maximize observability or completely observe subject to different constraints. Now due to improved technology and digital relays serving a dual use as relay & PMU, the cost of the PMU device itself is not the largest portion of the deployment cost, but rather the substation installation. In a recently completed large-scale deployment of PMUs on the EHV network, Virginia Electric & Power Company (VEPCO) has found this to be so. The assumption then becomes that if construction work is done in a substation, enough PMU devices will be placed such that everything at that substation is measured. This thesis presents a technique proposed to minimize the number of substation installations thus indirectly minimizing the synchrophasor deployment costs. Also presented is a brief history of the PMU and its applications along with the conventional Optimal PMU placement problem and the scope for expanding this work. / Master of Science

In recent years, the placement of phasor measurement units (PMUs) in electric transmission systems has gained much attention. Engineers and mathematicians have developed a variety of algorithms to determine the best locations for PMU installation. But often these placement algorithms are not practical for real systems and do not cover the whole process. This thesis presents a strategy that is practical and addresses three important topics: system preparation, placement algorithm, and installation scheduling. To be practical, a PMU strategy should strive for full observability, work well within the heterogeneous nature of power system topology, and enable system planners to adapt the strategy to meet their unique needs and system configuration. Practical considerations for the three placement topics are discussed, and a specific strategy based on these considerations is developed and demonstrated on real transmission system models. / Master of Science