Optimal sensor placement for parametric identification of electrical networks using mixed phasor measurements

In this paper we present an algorithm for placing sensors optimally along the edges of a large network of electrical oscillators to identify a parametric model for the network using a linear combination of three fundamental electrical signals- namely, the magnitude, the phase angle and the frequency of the voltage phasor along each edge, corrupted with Gaussian noise. We pose the identification problem as estimation of four essential parameters for each edge, namely the real and imaginary components of the edge-weight (or, equivalently the resistance and reactance along the transmission line), and the inertias of the two machines connected by this edge. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters, and show that the bounds are functions of the sensor locations and of the contribution of each variable in the combined output. We Anally state the condition for finding the optimal sensor location and the optimal signal combination to achieve the tightest Cramer-Rao bound.