  Distribution grids represent the final tier in electric networks consisting
of medium and low voltage lines that connect the distribution substations to
the end-users. Traditionally, distribution networks have been operated in a
radial topology that may be changed from time to time. Due to absence of a
significant number of real-time line monitoring devices in the distribution
grid, estimation of the topology is a problem critical for its observability
and control. This paper develops a novel graphical learning based approach to
estimate the radial operational grid structure using voltage measurements
collected from the grid loads. The learning algorithm is based on conditional
independence tests for continuous variables over chordal graphs and has wide
applicability. It is proven that the scheme can be used for several power flow
laws (DC or AC approximations) and more importantly is independent of the
specific probability distribution controlling individual bus power usage. The
complexity of the algorithm is discussed and its performance is demonstrated by
simulations on distribution test cases.
