PMU placement for dynamic equivalencing of power systems under flow observability constraints

• We present graph-theoretic interpretations of model reduction in large power system networks.
• We develop two PMU placement algorithms to identify reduced-order power system models with channel observability constraints.
• We illustrate the two algorithms using examples from WECC and IEEE prototype models.
• We present statistical analyses of the algorithms to highlight their robustness against network size and meshness.

In this paper we develop two graph-theoretic algorithms for placing Phasor Measurement Units (PMUs) in a multi-area power system network with the objective of identifying its dynamic equivalent model. The system is considered to be divided into clusters of synchronous generators and loads, with each area connected to other sets of areas through designated 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 from the boundary buses of these areas. Considering further that the number of tie-lines observable from any given PMU is constrained by an upper limit, we derive two sets of algorithms to compute the sub-optimal minimum cover, first for a bipartite graph and then for any general topology. The respective algorithms are referred to as CONPLAC and CONITPLAC. Results are illustrated using a IEEE 34-bus system pointing to the robustness of the proposed algorithms against time-varying network topology. Finally, we present statistical analyses to describe how the final set of chosen PMU locations and the computational time of these algorithms depend on network size, complexity and measurement constraints.