TY - JOUR
T1 - Spurious local minima in power system state estimation
AU - Zhang, Richard Y.
AU - Lavaei, Javad
AU - Baldick, Ross
N1 - Funding Information:
Manuscript received December 5, 2018; revised May 16, 2019; accepted May 25, 2019. Date of publication June 3, 2019; date of current version September 17, 2019. This work was supported in part by the National Science Foundation under grants ECCS-1808859 and ECCS-1406894, in part by the Office of Naval Research under Grant N00014-17-1-2933, in part by the Defense Advanced Research Projects Agency Young Faculty Award, and in part by the Air Force Office of Scientific Research Young Investigator Research Program Award. This paper was presented in part at the Hawaii International Conference on System Sciences, 2018 [1]. Recommended by Associate Editor M. Chertkov. (Corresponding author: Richard Y. Zhang.) R. Y. Zhang was with the Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720 USA. He is now with the Department of Electrical and Computer Engineering, University of Illinois, Urbana–Champaign, Champaign, IL 61820 USA (e-mail:,[email protected]).
Publisher Copyright:
© 2014 IEEE.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2019/9
Y1 - 2019/9
N2 - 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.
AB - 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.
KW - Critical points
KW - local minima
KW - nonconvex optimization
KW - power systems
KW - state estimation
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U2 - 10.1109/TCNS.2019.2920586
DO - 10.1109/TCNS.2019.2920586
M3 - Article
SN - 2325-5870
VL - 6
SP - 1086
EP - 1096
JO - IEEE Transactions on Control of Network Systems
JF - IEEE Transactions on Control of Network Systems
IS - 3
M1 - 8728030
ER -