Joint Research Conference

June 24-26, 2014

Phasor measurement units (PMUs) are increasingly important for monitoring the state of an electrical power grid. PMUs measure voltage magnitude and phase at various points of generation and consumption. If a line goes down, power flows change throughout the grid according to known physical laws and the probability distribution of PMU measurements changes accordingly. This paper develops a method to compute the posterior distribution of the current topological state of a power grid from PMU measurements and considers the design goal of placing PMUs at strategic points in a distribution system to achieve good sensitivity to single-line outages. From a vector of PMU measurements probabilities are computed corresponding to the scenario that all power lines are operational and to scenarios that each given line is out. These probabilities are functions of the joint distributions of PMU measurements under each possible scenario, obtained through Monte Carlo simulations with random load profiles. We use log-spline densities to estimate marginal distributions of PMU measurements and fold these into a multivariate Gaussian copula to capture important correlations. Sensitivity to outages varies according to which line goes down and where PMUs are placed on the grid. A greedy search algorithm is demonstrated for placing PMUs at locations that provide good sensi- tivity to single-line outages.