Electrical Structure-Based PMU Placement in Electric Power Systems

Recent work on complex networks compared the topological and electrical structures of the power grid, taking into account the underlying physical laws that govern the electrical connectivity between various components in the network. A distance metric, namely, resistance distance was introduced to provide a more comprehensive description of interconnections in power systems compared with the topological structure, which is based only on geographic connections between network components. Motivated by these studies, in this paper we revisit the phasor measurement unit (PMU) placement problem by deriving the connectivity matrix of the network using resistance distances between buses in the grid, and use it in the integer program formulations for several standard IEEE bus systems. The main result of this paper is rather discouraging: more number of PMUs are required, compared with those obtained using the topological structure, to meet the desired objective of complete network observability without zero injection measurements. However, in light of recent advances in the electrical structure of the grid, our study provides a more realistic perspective of PMU placement in power systems. By further exploring the connectivity matrix derived using the electrical structure, we devise a procedure to solve the placement problem without resorting to linear programming.