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Optimal Measurement Allocation Algorithms for Parametric Model Identification of Power Systems

In this paper, we present an optimization algorithm that selects the optimal sets of points for placing phasor measurement units (PMUs) on the transmission lines of a multimachine power system for the purpose of identifying the best model fit for its wide-area swing dynamics. Alternatively, the method can also be viewed as a way to select the optimal set of points at which phasor values should be computed using measurements available from PMUs such that these computed values, also referred to here as pseudo-measurements, can generate the best estimate of the swing model, especially when the measurements are noisy. We pose the identification problem as an equivalent parameter estimation problem for the admittance of each tie-line and the inertia of each machine using phasor measurements of voltage magnitude, phase angle and frequency, corrupted with high-frequency measurement noise. We then formulate the Cramer-Rao bounds (CRBs) for the estimates of these unknown parameters, and show that the bounds are functions of the PMU locations and of the contribution of each measurement variable in the combined output. We finally state the condition for finding the optimal PMU location that guarantees the tightest CRB, and, therefore, the most accurate swing model for the system.