  This paper applies a custom model order reduction technique to the
distribution grid state estimation problem. Specifically, the method targets
the situation where, due to pseudo-measurement uncertainty, it is advantageous
to run the state estimation solver potentially thousands of times over sampled
input perturbations in order to compute probabilistic bounds on the underlying
system state. This routine, termed the Accelerated Probabilistic State
Estimator (APSE), efficiently searches for the solutions of sequential state
estimation problems in a low dimensional subspace with a reduced order model
(ROM). When a sufficiently accurate solution is not found, the APSE reverts to
a conventional QR factorization-based Gauss-Newton solver. It then uses the
resulting solution to preform a simple basis expansion of the low-dimensional
subspace, thus improving the reduced model solver. Simulated test results,
collected from the unbalanced three-phase 8500-node distribution grid, show the
resulting algorithm to be almost an order of magnitude faster than a comparable
full-order Gauss-Newton solver and thus potentially fast enough for real-time
use.
