Differentiable Optimization for Deep Learning-Enhanced DC Approximation of AC Optimal Power Flow

TL;DR

This work targets faster, more faithful approximations of AC-OPF by learning how to adjust DC-OPF parameters. It introduces DC2AC, a neural network that predicts adjusted nodal shunt conductances and branch susceptances, feeding into a differentiable DC-OPF layer trained end-to-end via the implicit function theorem to align with AC-OPF solutions. By leveraging offline AC-OPF data and KKT-based sensitivities, the method achieves superior accuracy for active and reactive power flows compared to standard proxies and unadjusted DC-OPF, particularly in typical operating regimes. The approach offers a scalable, interpretable route to AC-feasible grid optimization and highlights areas for improvement in reactive-power coupling and computational speed through advanced solvers and hardware acceleration.

Abstract

The growing scale of power systems and the increasing uncertainty introduced by renewable energy sources necessitates novel optimization techniques that are significantly faster and more accurate than existing methods. The AC Optimal Power Flow (AC-OPF) problem, a core component of power grid optimization, is often approximated using linearized DC Optimal Power Flow (DC-OPF) models for computational tractability, albeit at the cost of suboptimal and inefficient decisions. To address these limitations, we propose a novel deep learning-based framework for network equivalency that enhances DC-OPF to more closely mimic the behavior of AC-OPF. The approach utilizes recent advances in differentiable optimization, incorporating a neural network trained to predict adjusted nodal shunt conductances and branch susceptances in order to account for nonlinear power flow behavior. The model can be trained end-to-end using modern deep learning frameworks by leveraging the implicit function theorem. Results demonstrate the framework's ability to significantly improve prediction accuracy.

Figures (6)

• Figure 1: The proposed framework for deep learning-based DC-OPF adjustment.
• Figure 2: Accuracy vs. total demand across methods.
• Figure 3: DC Optimal Power Flow (DC-OPF)
• Figure 4: Dual of DC-OPF
• Figure 5: AC Optimal Power Flow (AC-OPF)