A Convex Neural Network Solver for DCOPF with Generalization Guarantees

TL;DR

This paper introduces a convex neural network approach for solving the DCOPF problem that guarantees generalization, ensuring small training errors lead to small testing errors, and significantly improves solution optimality.

Contribution

The paper presents a novel convex neural network method for DCOPF with provable generalization guarantees based on KKT conditions and convexity.

Findings

Improves optimality ratio by a factor of five over end-to-end models.

Guarantees small training error implies small testing error.

Utilizes convexity and KKT conditions for training loss design.

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 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.