Distributed Gauss-Newton Method for AC State Estimation Using Belief Propagation

We present a detailed study on application of factor graphs and the belief propagation (BP) algorithm to the power system state estimation (SE) problem. We start from the BP solution for the linear DC model, for which we provide a detailed convergence analysis. Using insights from the DC model, we use two different approaches to derive the BP algorithm for the non-linear AC model. The first method directly applies BP methodology, however, providing only approximate BP solution for the AC model. In the second approach, we make a key further step by providing the solution in which the BP is applied sequentially over the AC model, akin to what is done by the Gauss-Newton method. The resulting BP-based Gauss-Newton algorithm has the interpretation of a fully distributed Gauss-Newton method with the same accuracy as the centralized SE, preserving a number of advantages of the BP framework. The paper provides extensive numerical study of the proposed algorithms, provides details on their convergence properties, and gives a number of useful insights for their implementation.