  Fast power system state estimation (SE) solution is of paramount importance
for achieving real-time decision making in power grid operations. Semidefinite
programming (SDP) reformulation has been shown effective to obtain the global
optimum for the nonlinear SE problem, while suffering from high computational
complexity. Thus, we leverage the recent advances in nonconvex SDP approach
that allows for the simple first-order gradient-descent (GD) updates. Using the
power system model, we can verify that the SE objective function enjoys nice
properties (strongly convex, smoothness) which in turn guarantee a linear
convergence rate of the proposed GD-based SE method. To further accelerate the
convergence speed, we consider the accelerated gradient descent (AGD)
extension, as well as their robust versions under outlier data and a hybrid
GD-based SE approach with additional synchrophasor measurements. Numerical
tests on the IEEE 118-bus, 300-bus and the synthetic ACTIVSg2000-bus systems
have demonstrated that FGD-SE and AGD-SE, can approach the near-optimal
performance of the SDP-SE solution at significantly improved computational
efficiency, especially so for AGD-SE.
