Nonlinear Least Absolute Value Estimator for Topology Error Detection and Robust State Estimation

Topology error, a modeling misrepresentation of the power system network configuration, can undermine the quality of state estimation. In this paper, we propose a new methodology for robust power system state estimation (PSSE) modeled by AC power flow equations when there exists a small number of topological errors. The developed technique utilizes the availability of a large number of SCADA measurements and minimizes the $\ell _{1}$ norm of nonconvex residuals augmented by a nonlinear, but convex, regularizer. Representing the power network by a graph, we first study the properties of the solution obtained from the proposed NLAV estimator and demonstrate that, under mild conditions, this solution identifies a small subgraph of the network that contains the topological errors in the model used for the state estimation problem. Then, we introduce a method that can efficiently detect the topological errors by searching over the identified subgraph. In addition, 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 IEEE benchmark systems.