  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.
