arXiv Machine Learning By Nan Lin, Peter Palensky, Pedro Vergara Barrios

Bayesian Distribution System State Estimation with Flow Matching

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The paper introduces PoSE, a Bayesian posterior sampling method for distribution system state estimation that learns the distribution of substation injections via a neural network trained with flow matching. Unlike weighted least squares or supervised deep learning, PoSE preserves the full Bayesian structure and ensures every posterior sample satisfies the power flow equations. Experiments on IEEE 33‑bus and Iowa 240‑bus feeders show PoSE reduces injection error by up to 7.5% and provides more reliable uncertainty estimates than Gaussian priors or supervised estimators.

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