Distributed State Estimation in Power System Using Belief Propagation: Algorithms and Performance
We present a detailed study of the applications of factor graphs and the belief propagation (BP) algorithm to the state estimation (SE) problem. Our methodology starts with the BP solution for the linearized DC model, and use insights obtained therein to derive the BP algorithm for the non-linear AC model. Then, we make a key further step, where we present 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 brought in by the BP framework. The BP-based algorithms presented in this paper are fully distributed, however, they can be easily extended to the case of multi-area SE. Finally, the paper provides extensive numerical study of the proposed algorithms and gives a number of useful insights for their implementation.