Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality

TL;DR

This paper introduces an unsupervised deep learning framework for solving the non-convex AC optimal power flow problem efficiently, leveraging Lagrangian duality and power flow equations to reduce computational time and improve solution quality.

Contribution

It presents a novel unsupervised learning approach that does not require conventional solver-generated training data, using a modified augmented Lagrangian as the loss function.

Findings

Outperforms existing methods in computational speed.

Achieves solutions with small optimality gaps.

Demonstrates effectiveness on large-scale power networks.

Abstract

Non-convex AC optimal power flow (AC-OPF) is a fundamental optimization problem in power system analysis. The computational complexity of conventional solvers is typically high and not suitable for large-scale networks in real-time operation. Hence, deep learning based approaches have gained intensive attention to conduct the time-consuming training process offline. Supervised learning methods may yield a feasible AC-OPF solution with a small optimality gap. However, they often need conventional solvers to generate the training dataset. This paper proposes an end-to-end unsupervised learning based framework for AC-OPF. We develop a deep neural network to output a partial set of decision variables while the remaining variables are recovered by solving AC power flow equations. The fast decoupled power flow solver is adopted to further reduce the computational time. In addition, we propose using a modified augmented Lagrangian function as the training loss. The multipliers are adjusted dynamically based on the degree of constraint violation. Extensive numerical test results corroborate the advantages of our proposed approach over some existing methods.