Accelerated Probabilistic State Estimation in Distribution Grids via Model Order Reduction

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. The resulting solution is then used to preform a 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.