Distribution System Topology Detection Using Consumer Load and Line Flow Measurements

This work presents a topology detection method combining home smart meter information and sparse line flow measurements. The problem is formulated as a spanning tree detection problem over a graph given partial nodal and edge flow information in a deterministic and stochastic setting. In the deterministic case of known nodal power consumption and edge flows we provide sensor placement criterion which guarantees correct identification of all spanning trees. We then present a detection method which is polynomial in complexity to the size of the graph. In the stochastic case where loads are given by forecasts derived from delayed smart meter data, we provide a combinatorial Maximum a Posteriori (MAP) detector and a polynomial complexity approximate MAP detector which is shown to work near optimum in low noise regime numerical cases and moderately well in higher noise regime.