The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of scenarios, which can be computationally challenging. As an alternative to iterative solvers, neural networks are often trained and used to solve DCOPF. These approaches can offer orders of magnitude reduction in computational time, but they cannot guarantee generalization, and small training error does not imply small testing errors. In this work, we propose a novel algorithm for solving DCOPF that guarantees the generalization performance. First, by utilizing the convexity of DCOPF problem, we train an input convex neural network. Second, we construct the training loss based on KKT optimality conditions. By combining these two techniques, the trained model has provable generalization properties, where small training error implies small testing errors. In experiments, our algorithm improves the optimality ratio of the solutions by a factor of five in comparison to end-to-end models.

中文翻译：

---

具有泛化保证的 DCOPF 凸神经网络求解器

直流最优潮流 (DCOPF) 问题是电力系统运行和规划中的一个基本问题。由于不确定性可再生资源在电力系统中的渗透率很高，因此需要针对大量场景重复求解 DCOPF，这在计算上具有挑战性。作为迭代求解器的替代方案，神经网络通常经过训练并用于求解 DCOPF。这些方法可以将计算时间减少几个数量级，但它们不能保证泛化，并且小的训练误差并不意味着小的测试误差。在这项工作中，我们提出了一种解决 DCOPF 的新算法，该算法保证了泛化性能。首先，利用 DCOPF 问题的凸性，我们训练一个输入凸神经网络。其次，我们基于 KKT 最优性条件构建训练损失。通过结合这两种技术，经过训练的模型具有可证明的泛化特性，其中小的训练误差意味着小的测试误差。在实验中，与端到端模型相比，我们的算法将解决方案的最优比提高了五倍。