Robust power system state estimation from rank-one measurements

Gang Wang, Hao Zhu, Georgios B. Giannakis, Jian Sun

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The unique features of current and upcoming energy systems, namely, high penetration of uncertain renewables, unpredictable customer participation, and purposeful manipulation of meter readings, all highlight the need for fast and robust power system state estimation (PSSE). In the absence of noise, PSSE is equivalent to solving a system of quadratic equations, which, also related to power flow analysis, is NP-hard in general. Assuming the availability of all power flow and voltage magnitude measurements, this paper first suggests a simple algebraic technique to transform the power flows into rank-one measurements, for which the ℓ1-based misfit is minimized. To uniquely cope with the nonconvexity and nonsmoothness of ℓ1-based PSSE, a deterministic proximal-linear solver is developed based on composite optimization, whose generalization using stochastic gradients is discussed too. This paper also develops conditions on the ℓ1-based loss function such that exact recovery and quadratic convergence of the proposed scheme are guaranteed. Simulated tests using several IEEE benchmark test systems under different settings corroborate our theoretical findings, as well as the fast convergence and robustness of the proposed approaches.

Original languageEnglish (US)
Article number8601367
Pages (from-to)1391-1403
Number of pages13
JournalIEEE Transactions on Control of Network Systems
Issue number4
StatePublished - Dec 2019

Bibliographical note

Funding Information:
Manuscript received September 17, 2018; revised September 18, 2018, November 10, 2018, and November 30, 2018; accepted December 5, 2018. Date of publication January 4, 2019; date of current version December 17, 2019. The work of G. Wang and G. B. Giannakis was supported by the NSF under Grant 1514056, Grant 1505970, and Grant 1711471. The work of H. Zhu was supported by the NSF under Grant 1802319. The work of J. Sun was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 61621063, 61522303, 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 (IRT1208). Recommended by Associate Editor Y. Hong. (Corresponding author: Jian Sun.) G. Wang and G. B. Giannakis are with the Digital Technology Center and the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:, gangwang@;

Publisher Copyright:
© 2014 IEEE.


  • Bad data analysis
  • composite optimization
  • least-absolute-value estimator
  • proximal-linear algorithm
  • supervisory control and data acquisition measurement


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