  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.
