Spurious Local Minima in Power System State Estimation

Abstract

The power system state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares. This is a nonconvex optimization problem, so even in the absence of measurement errors, local search algorithms like Newton/Gauss–Newton can become “stuck” at local minima, which correspond to nonsensical estimations. In this paper, we observe that local minima cease to be an issue as redundant measurements are added. Posing state estimation as an instance of the low-rank matrix recovery problem, we derive a bound for the distance between the true solution and the nearest spurious local minimum. We use the bound to show that spurious local minima of the nonconvex least-squares objective become far-away from the true solution with the addition of redundant information.