Power System State Estimation via Feasible Point Pursuit: Algorithms and Cramer-Rao Bound

摘要

Accurately monitoring the system's operating point is central to the reliableand economic operation of an electric power grid. Power system state estimation(PSSE) aims to obtain complete voltage magnitude and angle information at eachbus given a number of system variables at selected buses and lines. Power flowanalysis is a special case of PSSE, and amounts to solving a set of noise-freepower flow equations. Physical laws dictate quadratic relationships betweenavailable quantities and unknown voltages, rendering general instances of powerflow and PSSE nonconvex and NP-hard. Past approaches are largely based ongradient-type iterative procedures or semidefinite relaxation (SDR). Due tononconvexity, the solution obtained via gradient-type schemes depends oninitialization, while SDR methods do not perform as desired in challengingscenarios. This paper puts forth novel \emph{feasible point pursuit}(FPP)-based solvers for power flow and PSSE, which iteratively seek feasiblesolutions for a nonconvex quadratically constrained quadratic programming(QCQP) reformulation of the weighted least-squares (WLS) problem. Relative tothe prior art, the developed solvers offer superior performance at the cost ofhigher complexity. Furthermore, they converge to a stationary point of the WLSproblem. As a baseline for comparing different estimators, the Cram{\' e}r-Raolower bound (CRLB) is derived for the fundamental PSSE problem in this paper.Judicious numerical tests on several IEEE benchmark systems showcase markedlyimproved performance of our FPP-based solvers for both power flow and PSSEtasks over popular WLS-based Gauss-Newton iterations and SDR approaches.