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

## TL;DR

This paper introduces feasible point pursuit algorithms for power system state estimation, providing improved solutions for nonconvex problems and establishing a Cramér-Rao bound as a performance benchmark.

## Contribution

The paper proposes novel FPP-based solvers for power flow and PSSE, outperforming existing methods and converging to stationary points, with a new CRLB derivation for PSSE.

## Key findings

- FPP-based solvers outperform traditional methods in accuracy.
- The algorithms converge to stationary points of the WLS problem.
- Numerical tests show superior performance on IEEE systems.

## Abstract

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