A Convex Neural Network Solver for DCOPF With Generalization Guarantees

Ling Zhang, Yize Chen, Baosen Zhang

Abstract: 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 the DCOPF problem, we train an input convex neural network. Second, we construct the training loss based on Karush–Kuhn–Tucker 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 significantly outperforms other machine learning methods.