Partially Permutation-Invariant Neural Network for Solving Two-Stage Stochastic AC-OPF Problem

We develop DeepOPF-Stoc as a neural network approach to efficiently solve the two-stage stochastic AC optimal power flow (AC-OPF) problem, which emphasizes reliable and cost-effective grid operation while accounting for uncertainties in renewable energy generation and load demand. We first identify a crucial partial permutation-invariance property of the mapping from load to first-stage solution. We then leverage this property in DeepOPF-Stoc to design (i) PPNN as a principled architectural framework that orchestrates standard neural network designs to learn such mappings, and (ii) a PPNN-aware sampling algorithm to prepare training data efficiently. DeepOPF-Stoc effectively addresses the dimensionality explosion issue inherent in vanilla designs, significantly reducing both the required number of neurons and the volume of training data. Our theoretical analysis confirms the universal approximation capability of PPNNs for our application. We further prove that the PPNN-aware sampling algorithm improves sampling efficiency by a factor of K! compared to uniform sampling, where K represents the number of second-stage scenarios. Simulation results on IEEE 118-bus and synthetic 793-bus test systems demonstrate the superiority of DeepOPF-Stoc over state-of-the-art alternatives. It achieves two orders of magnitude speedup compared to iterative solvers while generating feasible first-stage solutions with comparable second-stage out-of-sample feasibility and 0.95% cost difference.