Robust Optimal Operation of Smart Microgrid Considering Source–Load Uncertainty

The uncertainties arising from high renewable energy penetration on both the generation and demand sides pose significant challenges to distribution network security. Smart microgrids are considered an effective way to solve this problem. Existing studies exhibit limitations in prediction accuracy, Alternating Current (AC) power flow modeling, and integration with optimization frameworks. This paper proposes a closed-loop technical framework combining high-confidence interval prediction, second-order cone convex relaxation, and robust optimization to facilitate renewable energy integration in distribution networks via smart microgrid technology. First, a hybrid prediction model integrating Variational Mode Decomposition (VMD), Long Short-Term Memory (LSTM), and Quantile Regression (QR) is designed to extract multi-frequency characteristics of time-series data, generating adaptive prediction intervals that accommodate individualized decision-making preferences. Second, a second-order cone relaxation method transforms the AC power flow optimization problem into a mixed-integer second-order cone programming (MISOCP) model. Finally, a robust optimization method considering source–load uncertainties is developed. Case studies demonstrate that the proposed approach reduces prediction errors by 21.15%, decreases node voltage fluctuations by 16.71%, and reduces voltage deviation at maximum offset nodes by 17.36%. This framework significantly mitigates voltage violation risks in distribution networks with large-scale grid-connected photovoltaic systems.