Graph-theoretic algorithms for PMU placement in power systems under measurement observability constraints

In this paper we develop two graph-theoretic PMU placement algorithms for multi-area power system networks with the objective of identifying a dynamic equivalent model for the system. We first show that 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. 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, first for a bipartite graph and then for any general topology. We illustrate our results using a IEEE 34-bus model.