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The electrical structure of the power grid is utilized to address the phasormeasurement unit (PMU) placement problem. First, we derive the connectivitymatrix of the network using the resistance distance metric and employ it in thelinear program formulation to obtain the optimal number of PMUs, for completenetwork observability without zero injection measurements. This approach wasdeveloped by the author in an earlier work, but the solution methodology toaddress the location problem did not fully utilize the electrical properties ofthe network, resulting in an ambiguity. In this paper, we settle this issue byexploiting the coupling structure of the grid derived using the singular valuedecomposition (SVD)-based analysis of the resistance distance matrix to solvethe location problem. Our study, which is based on recent advances in complexnetworks that promote the electrical structure of the grid over its topologicalstructure and the SVD analysis which throws light on the electrical coupling ofthe network, results in a unified framework for the electrical structure-basedPMU placement. The proposed method is tested on IEEE bus systems, and theresults uncover intriguing connections between the singular vectors and averageresistance distance between buses in the network.

A Unifying Framework for the Electrical Structure-Based Approach to PMU Placement in Electric Power Systems