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In this paper, we propose the application of the concept of power domination integrity to an electric power network. A phasor measurement unit (PMU) is used to analyze and control the power system by measuring voltage phase in electrical nodes and transmission lines. Due to the high cost of PMUs, it is necessary to minimize the number of PMUs such that the depth of observability is ensured. Placing PMUs in a network can be formulated as a graph theoretic problem of finding the minimum number of nodes (PMUs) in a graph that has a maximum number of links with other nodes. To achieve this, the concept of domination in graph theory is applied to power networks by redefining ``adjacency'' of a vertex as an ``observed'' vertex. The power domination number identifies the number of PMUs to be placed. The proposed concept of power domination integrity gives not only the minimum number of PMUs but also identifies the optimal locations for PMU placement in an electric power network.

Application of domination integrity of graphs in PMU placement in electric power networks