Robust and scalable power system state estimation via composite optimization

Gang Wang, Georgios B. Giannakis, Jie Chen

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


In today's cyber-enabled smart grids, high penetration of uncertain renewables, purposeful manipulation of meter readings, and the need for wide-area situational awareness, call for fast, accurate, and robust power system state estimation. The least-absolute-value (LAV) estimator is known for its robustness relative to the weighted least-squares one. However, due to nonconvexity and nonsmoothness, existing LAV solvers based on linear programming are typically slow and, hence, inadequate for real-time system monitoring. This paper, develops two novel algorithms for efficient LAV estimation, which draw from recent advances in composite optimization. The first is a deterministic linear proximal scheme that handles a sequence of (5 10 in general) convex quadratic problems, each efficiently solvable either via off-the-shelf toolboxes or through the alternating direction method of multipliers. Leveraging the sparse connectivity inherent to power networks, the second scheme is stochastic and updates only a few entries of the complex voltage state vector per iteration. In particular, when voltage magnitude and (re)active power flow measurements are used only, this number reduces to one or two regardless of the number of buses in the network. This computational complexity evidently scales well to large-size power systems. Furthermore, by carefully mini-batching the voltage and power flow measurements, accelerated implementation of the stochastic iterations becomes possible. The developed algorithms are numerically evaluated using a variety of benchmark power networks. Simulated tests corroborate that improved robustness can be attained at comparable or markedly reduced computation times for medium- or large-size networks relative to existing alternatives.

Original languageEnglish (US)
Article number8632764
Pages (from-to)6137-6147
Number of pages11
JournalIEEE Transactions on Smart Grid
Issue number6
StatePublished - Nov 2019

Bibliographical note

Funding Information:
Manuscript received August 14, 2017; revised November 2, 2017, March 10, 2018, and October 7, 2018; accepted January 29, 2019. Date of publication February 1, 2019; date of current version October 30, 2019. The work of G. Wang and G. B. Giannakis was supported in part by the National Science Foundation under Grant 1514056, Grant 1505970, and Grant 1711471. The work of J. Chen was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61621063 and Grant 61522303, in part by the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization under Grant 61720106011, in part by the Projects of Major International (Regional) Joint Research Program NSFC under Grant 61720106011, and in part by the Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT1208. Paper no. TSG-01182-2017. (Corresponding author: Georgios B. Giannakis.) G. Wang and G. B. Giannakis are with the Digital Technology Center, University of Minnesota, Minneapolis, MN 55455 USA, and also with the Electrical and Computer Engineering Department, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:;

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  • SCADA measurements
  • alternating direction method of multipliers
  • cyberattacks
  • nonlinear AC estimation
  • prox-linear algorithms


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