用扩散模型解决电力系统最优潮流的多解问题
DiffOPF: Diffusion Solver for Optimal Power Flow
- 将最优潮流建模为条件采样问题，学习负载与调度点的联合分布
- 可生成统计可信的热启动解，成本与约束满足性平衡更好
- 适用于需要应对参数多变的复杂电网场景
最优潮流（OPF）是从负荷到调度点的多值非凸映射。系统参数（如导纳、拓扑）的变动进一步导致相同负荷下存在多种调度点。现有深度学习OPF求解器为单值输出，无法捕捉参数变化带来的多样性，除非在特征空间中完全表示这些参数，而这代价过高。为此，我们提出基于扩散模型的OPF求解器——DiffOPF，将OPF视为条件采样问题。该方法从运行历史中学习负载与调度点的联合分布，并在给定负载条件下返回调度点的边缘分布。与单值求解器不同，DiffOPF能生成统计可信的热启动解，具备良好的成本与约束满足性权衡。我们研究了DiffOPF的样本复杂度，确保其解与优化基准解之间的距离在预设范围内，并在典型电力系统基准上进行了实验验证。
原文摘要 · Abstract (English)
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.
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