Robust power system state estimation from rank-one measurements

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

Research output: Contribution to journalArticle

5 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


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

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