A minimum cover algorithm for PMU placement in power system networks under line observability constraints

In this paper we develop a graph-theoretic PMU placement algorithm for multi-area power system networks with the objective of identifying a dynamic equivalent model for the system. The system is considered to be divided into clusters or areas of synchronous generators, with each area connected to other sets of areas through designated transmission networks. The buses in the system are accordingly divided into two types, namely - boundary buses of the areas and boundary buses of the transmission networks. We first show that in order to derive the equivalent line parameters connecting the different areas we must have PMUs placed at the minimum vertex cover of the bipartite graphs formed between every pair of node-sets arising out of the boundary buses of the areas and those of the corresponding transmission networks they are connected to. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive an algorithm to compute the sub-optimal minimum cover for the multi-area system. The method is illustrated via a 4-6 bipartite network, as well as with two small examples from the WECC system. Statistical analyses of the algorithm are also presented describing how the final set of chosen PMU locations as well as the computational time needed to run the algorithm are dependent on the size, complexity and measurement constraints of the network.