Developing Neural Network Schemes for Solving Two-Stage Stochastic AC Optimal Power Flow Problems: Exploiting the Partial Permutation-Invariance Property

*Project Background*Optimal Power Flow (OPF) is a cornerstone of power system operations, essential for maintaining grid reliability and economic efficiency. It determines optimal power generation and transmission decisions to meet fixed, deterministic load while minimizingcosts and adhering to physical and operational constraints. However, the rapid integration of renewable generation and demand-side management has introduced significant uncertainties in supply and demand, with variations reaching 20% of installed capacity in the US grid. This uncertainty renders traditional deterministic OPF solutions increasingly inadequate, potentially leading to excessive reserve requirements, higher operational costs, and increased system risks.To address this challenge, grid operators are turning to advanced approach, particularly scenario-based two-stage stochastic AC-OPF. This approach explicitly accounts for future uncertainties by incorporating multiple scenarios of renewable generation andload demand. However, it faces a critical hurdle: *dimensionality explosion*. As the number of scenarios increases, the problem size grows linearly, making conventional iterative methods computationally prohibitive for real-time operations. Similarly, standard NN approaches, while effective for deterministic OPF, suffer from the same dimensionality issues when applied to stochastic problems.*Project Aim and Description*We will develop new NN schemes for solving scenario-based two-stage stochastic ACOPF problems orders of magnitude faster than iterative solvers, without suffering from the dimensionality explosion issue. Our approach is threefold: 1. We will exploit (i) the partial permutation-invariance property of two-stage stochastic AC-OPF problems and (ii) Kolmogorov-Arnold representation theorem to design a novel Partial Permutation-Invariance Neural Network (PPNN). This design can learn the load-to-solution mapping effectively without suffering from dimensionality explosion. 2. We will develop efficient training methodologies for PPNN, including data preparation techniques that leverage permutation invariance and training PPNN on smaller-scale problems to handle larger-scale problems effectively. 3. We will conduct extensive experiments using synthetic and real-world data on IEEE test cases and real-world power grid configurations. We will benchmark our PPNN scheme against state-of-the-art iterative solvers and alternative machine learning solutions. Our methodologies can provide generalizable insights and tools for using machine learning to solve a broad range of stochastic optimization problems. *Preliminary Result and Significance of Project*We have developed a preliminary PPNN scheme. The initial results show that it achieves up to 800x speed-up compared to latest iterative solvers with minor optimality loss and similar out-of-sample feasibility performance. The expected outcome helps enable realtime, reliable, and cost-effective grid operation while accounting for renewable/load uncertainties, supporting the integration of renewable generation to fight climate change.