The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a given load. Existing deep learning OPF solvers are single-valued and thus fail to capture the variability of system parameters unless fully represented in the feature space, which is prohibitive. To solve this problem, we introduce a diffusion-based OPF solver, termed \textit{DiffOPF}, that treats OPF as a conditional sampling problem. The solver learns the joint distribution of loads and dispatch setpoints from operational history, and returns the marginal dispatch distributions conditioned on loads. Unlike single-valued solvers, DiffOPF enables sampling statistically credible warm starts with favorable cost and constraint satisfaction trade-offs. We explore the sample complexity of DiffOPF to ensure the OPF solution within a prescribed distance from the optimization-based solution, and verify this experimentally on power system benchmarks.

翻译：最优潮流（OPF）是一种从负荷到调度设定值的多值、非凸映射。系统参数（如导纳、拓扑结构）的变异性进一步导致给定负荷下调度设定值的多重性。现有的深度学习OPF求解器为单值映射，因此除非在特征空间中完整表示系统参数（这在实际中不可行），否则无法捕捉系统参数的变异性。为解决这一问题，我们提出一种基于扩散的OPF求解器，命名为\textit{DiffOPF}，将OPF视为条件采样问题。该求解器从运行历史中学习负荷与调度设定值的联合分布，并返回以负荷为条件的边际调度分布。与单值求解器不同，DiffOPF能够生成具备统计可信性的热启动方案，在成本与约束满足之间实现更优权衡。我们研究了DiffOPF的样本复杂度，以确保OPF解与基于优化的解保持在预设距离内，并在电力系统基准测试中通过实验验证了该性质。