Distributed State Estimation for Bilinear Power System Models Based on Weighted Least Absolute Value

Accurate, scalable, and outlier-robust state estimation (SE) is critical for large AC power systems with mixed SCADA and PMU measurements. This paper proposes D-BSE-L1, a distributed robust state estimator for the bilinear AC model. The method combines the bilinear state estimation framework with a convex weighted least absolute value (WLAV) loss so that all area subproblems become convex linear or quadratic programs coordinated by ADMM, and a cache-enabled Cholesky factorization is used to accelerate the third-stage linear solves. Simulations on the IEEE 14-, 118-, and 1062-bus systems show that D-BSE-L1 achieves estimation accuracy comparable to its centralized bilinear counterpart. Under severe bad-data conditions, its advantage over weighted least squares with the largest normalized residual test (WLS + LNRT) is pronounced: with 10% 1.5× bad data, the voltage magnitude and angle MAEs are about 62% and 54% of those of WLS + LNRT, and with 5% 5× bad data, they further drop to roughly 43% and 51%, while requiring only about one-tenth of the CPU time. On the 1062-bus system, D-BSE-L1 maintains the MAE of the centralized estimator but reduces runtime from 2.46 s to 0.72 s, providing a scalable, hyperparameter-free, and robust solution for partitioned state estimation in large-scale power grids.