Feeder Topology Identification

Advanced control of distributed energy resources at the consumer level requires full situational awareness of the the distribution system. One important problem is that of feeder topology identification, due to changing switch configurations, given a sparse number of measurements. We formulate the problem for residential feeders as a spanning tree identification problem over a general graph. Given a set of power flow measurements and load pseudo measurements, we show that the underlying graph structure is crucial in defining identifiability of the correct spanning tree on the graph. First we solve the deterministic case of known true loads and measured power flow. We show that the placement of sensors on the network alone determine whether the set of spanning trees can be correctly identified. In the stochastic case where loads are in the form of noisy forecasts, we present a locally optimal sensor placement algorithm.