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We present a detailed study on application of factor graphs and the beliefpropagation (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 adetailed convergence analysis. Using BP-based DC model we propose a fastreal-time state estimator for the power system SE. The proposed estimator iseasy to distribute and parallelize, thus alleviating computational limitationsand allowing for processing measurements in real time. The presented algorithmmay run as a continuous process.  Using insights from the DC model, we use two different approaches to derivethe BP algorithm for the non-linear model. The first method directly applies BPmethodology, however, providing only approximate BP solution for the non-linearmodel. In the second approach, we make a key further step by providing thesolution in which the BP is applied sequentially over the non-linear model,akin to what is done by the Gauss-Newton method. The resulting iterativeGauss-Newton belief propagation (GN-BP) algorithm can be interpreted as adistributed Gauss-Newton method with the same accuracy as the centralized SE.

Design and Analysis of Distributed State Estimation Algorithms Based on Belief Propagation and Applications in Smart Grids