Robust Power System State Estimation From Rank-One Measurements

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 <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-based misfit is minimized. To uniquely cope with the nonconvexity and nonsmoothness of <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-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 <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-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.