Fast Probabilistic Power Flow via DeepONet-GPR Surrogates

Modern power grids increasingly incorporate variable renewable energy sources (RES) such as wind and solar, introducing significant uncertainty into power flow studies. Traditional deterministic approaches cannot adequately capture these uncertainties, while Monte Carlo methods, though accurate, are computationally expensive. This paper proposes a novel operator-learning-based probabilistic power flow (PPF) framework that combines Deep Operator Networks (DeepONet) and Gaussian Process Regression (GPR) to achieve both speed and uncertainty quantification. DeepONet approximates the nonlinear power flow operator, swiftly mapping stochastic inputs (e.g., wind, solar, load uncertainties) to bus voltages and phase angles. GPR subsequently models the residual error to yield predictive intervals for robust uncertainty estimates. Numerical results on the IEEE 14-bus test system show that our approach achieves a 150×speed-up relative to brute-force Monte Carlo simulation, while maintaining high accuracy (voltage magnitude RMSE under 0.004 p.u.) and delivering well-calibrated confidence intervals (PICP ≈ 95%). This synergy between operator learning and probabilistic regression offers a scalable, real-time compatible solution for datadriven, risk-aware power system operations.