A Reproducible and Correlation-Aware Polynomial Chaos Framework for Probabilistic AC Power Flow in Renewable-Rich Distribution Networks

High renewable penetration introduces stochastic variability in distribution-network operation, requiring probabilistic AC power-flow tools that remain accurate in the tails while avoiding the computational burden of large Monte Carlo simulation. This paper presents a fully reproducible non-intrusive polynomial chaos expansion (PCE) framework for uncertainty propagation through nonlinear Newton–Raphson AC power flow. The method uses sparse-grid quadrature to train PCE surrogates from deterministic power-flow evaluations and is benchmarked against high-fidelity Monte Carlo simulations. In the validation, the IEEE 33-bus feeder is evaluated using up to 50,000 Monte Carlo samples, 95% bootstrap confidence intervals, PCE orders 2–5, correlated uncertainty scenarios, realistic thermal-loading recalibration, reactive-power sensitivity of renewable injections, multi-feeder testing on IEEE 33-bus, CIGRE MV, CIGRE LV, and IEEE 118-bus networks, and a 365-snapshot full-year daily screening. For the base IEEE 33-bus case, third-order PCE required only 494 deterministic power-flow evaluations and reproduced the 50,000-sample Monte Carlo benchmark with relative mean errors of 0.014% for minimum voltage, 0.119% for active losses, and 0.113% for substation import. The corresponding wall-clock speed-up was 13.29×, while reducing deterministic evaluations by approximately 101×. Correlated load–PV uncertainty increased the upper tail of substation import from 6.06 MW to 6.30 MW, and realistic thermal recalibration revealed line-loading p99 values above 100% for the 60% target case, demonstrating the operational value of physically meaningful ampacity settings. The proposed workflow provides an open, scalable, and tail-aware basis for uncertainty-informed distribution-network planning under renewable variability.