Distribution-Matching Likelihood-Free Importance 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. Probabilistic power flow (PPF) methods based on Monte Carlo simulation provide accurate uncertainty propagation but remain computationally demanding, while many analytical and approximation-based approaches rely on restrictive distributional assumptions. This letter proposes a Distribution-Matching Likelihood-Free Importance Sampling (DM-LFIS) framework for PPF. The method avoids explicit likelihood construction and posterior sampling, and instead propagates uncertainty by reweighting candidate operating states according to a discrepancy between simulated and observed power injection distributions. Data-driven and physics-informed proposals guided by DC and Newton--Raphson power flow solutions are used to improve sampling efficiency. Numerical results on standard IEEE test systems show that DM-LFIS accurately captures voltage and angle uncertainty with reduced computational cost compared to conventional Monte Carlo-based PPF methods.