Topology error detection and robust state estimation using nonlinear least absolute value

This paper proposes a new technique for robust state estimation in the presence of a small number of topological errors for power systems modeled by AC power flow equations. The developed method leverages the availability of a large volume of SCADA measurements and minimizes the \ell-{1} norm of nonconvex residuals augmented by a nonlinear, but convex, regularizer. Noting that a power network can be represented by a graph, we first study the properties of the solution obtained by the proposed estimator and argue that, under mild conditions, this solution identifies (small) subgraphs of the network that contain the topological errors in the model used for the state estimation problem. Then, we propose a method that can efficiently detect the topological errors by searching over the identified subgraphs. Furthermore, we develop a theoretical upper bound on the state estimation error to guarantee the accuracy of the proposed state estimation technique. The efficacy of the developed framework is demonstrated through numerical simulations on an IEEE benchmark system.