首次揭示机器学习求解电力优化问题的规模规律,指导高效部署。
Scaling Laws of Machine Learning for Optimal Power Flow
- 系统研究数据量与计算量对模型性能的影响规律
- 发现精度随数据和算力提升呈幂律增长,约束违反率下降
- 给出最优算力配置边界,适合电力系统工程师参考
最优潮流(OPF)是电力系统运行的核心任务。尽管深度神经网络(DNN)等机器学习方法被广泛研究以提升求解速度与性能,其实际部署仍面临两大关键问题:可靠结果所需的最小训练数据量是多少?如何在精度与实时计算限制间平衡模型复杂度?现有研究多基于离散场景评估,缺乏对这些规模关系的量化分析,导致现实应用中依赖试错式开发。本文首次系统开展基于机器学习的OPF规模研究,覆盖两个维度:数据规模(0.1K–40K训练样本)与计算规模(多种具有不同浮点运算量的神经网络架构)。结果表明,无论DNN还是物理信息神经网络(PINN),其预测误差(MAE)、约束违反率与计算速度均与资源维度呈现一致的幂律关系。对于交流最优潮流(ACOPF),精度随数据量与训练算力增加而提升。这些规模定律使OPF的机器学习流程设计具备可预测性与原则性。进一步揭示了预测精度与约束可行性之间的偏差,并刻画了计算最优前沿。本工作为机器学习在最优潮流中的设计与部署提供了量化指导。
原文摘要 · Abstract (English)
Optimal power flow (OPF) is one of the fundamental tasks for power system operations. While machine learning (ML) approaches such as deep neural networks (DNNs) have been widely studied to enhance OPF solution speed and performance, their practical deployment faces two critical scaling questions: What is the minimum training data volume required for reliable results? How should ML models' complexity balance accuracy with real-time computational limits? Existing studies evaluate discrete scenarios without quantifying these scaling relationships, leading to trial-and-error-based ML development in real-world applications. This work presents the first systematic scaling study for ML-based OPF across two dimensions: data scale (0.1K-40K training samples) and compute scale (multiple NN architectures with varying FLOPs). Our results reveal consistent power-law relationships on both DNNs and physics-informed NNs (PINNs) between each resource dimension and three core performance metrics: prediction error (MAE), constraint violations and speed. We find that for ACOPF, the accuracy metric scales with dataset size and training compute. These scaling laws enable predictable and principled ML pipeline design for OPF. We further identify the divergence between prediction accuracy and constraint feasibility and characterize the compute-optimal frontier. This work provides quantitative guidance for ML-OPF design and deployments.
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