Distribution-Matching Likelihood-Free Sampling for Probabilistic Power Flow

The increasing penetration of renewable generation and electrified loads introduces non-Gaussian and strongly nonlinear uncertainty in power system operation. While Monte Carlo-based probabilistic power flow (PPF) methods provide accurate uncertainty propagation, they are computationally intensive, and many analytical or approximation approaches rely on restrictive distributional assumptions. This paper proposes a Distribution-Matching Likelihood-Free Sampling (DM-LFS) framework for PPF. Instead of constructing explicit likelihoods or posterior distributions, the method propagates uncertainty by reweighting candidate operating states based on discrepancies between simulated and observed power injection distributions. Sampling efficiency is enhanced through data-driven and physics-informed proposals guided by DC and Newton–Raphson power flow solutions. Results on standard IEEE test systems show that DM-LFS accurately captures voltage and angle uncertainty, achieving competitive computational performance relative to Monte Carlo methods while improving distributional consistency. Additionally, the approach reduces dependence on repeated full nonlinear power flow evaluations through proposal-guided sampling.