Optimal Placement of PMUs for Identification of Power System Models using Noisy Measurement Data

In this paper we address the problem of placing Phasor Measurement Units (PMUs) on a long transmission line connecting two areas of a power system network. Dynamic measurements of electrical signals such as magnitudes and phases of bus voltages and line currents, corrupted with Gaussian noise, are available from these PMUs. Our objective is to determine the best locations for their placement such that, given a particular measured noisy signal, the error in identifying a two-machine interarea equivalent model of the two-area power system is minimum. We first show that the identification problem is equivalent to estimating four essential model parameters, namely the two intra-area reactances, and the inertias of the two aggregated machines. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters, and show that the bounds are functions of the PMU location. We finally state the condition for finding the optimal PMU location to achieve the tightest Cramer-Rao bound.