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Spurious Critical Points in Power System State Estimation

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Title:Spurious Critical Points in Power System State Estimation
Authors:Zhang, Richard
Lavaei, Javad
Baldick, Ross
Keywords:Markets, Policy, and Computation
local minima, nonconvex optimization, power systems, state estimation
Date Issued:03 Jan 2018
Abstract:The power systems state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares (NLS). 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 quadratic 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 critical points of the nonconvex least squares objective become increasing rare and far-away from the true solution with the addition of redundant information.
Pages/Duration:10 pages
Rights:Attribution-NonCommercial-NoDerivatives 4.0 International
Appears in Collections: Markets, Policy, and Computation

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