Optimal sensor placement for parametric model identification of electrical networks, part I: Open loop estimation

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 dynamic measurements of electrical signals such as magnitudes and phase angles of voltages and currents, 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. We finally state the condition for finding the optimal sensor location to achieve the tightest Cramer-Rao bound.