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In this paper, we propose a solution to an AC state estimation problem inelectric power systems using a fully distributed Gauss-Newton method. Theproposed method is placed within the context of factor graphs and beliefpropagation algorithms and closed-form expressions for belief propagationmessages exchanged along the factor graph are derived. The obtained algorithmprovides the same solution as the conventional weighted least-squares stateestimation. Using a simple example, we provide a step-by-step presentation ofthe proposed algorithm. Finally, we discuss the convergence behaviour using theIEEE 14 bus test case.

Distributed Gauss-Newton Method for AC State Estimation: A Belief Propagation Approach