A hard-constrained NN learning framework for rapidly restoring AC-OPF from DC-OPF

TL;DR

The paper tackles real-time AC-OPF by introducing a hard-constrained, unsupervised learning framework that learns a residual correction to DC-OPF and uses a differentiable optimization layer to restore AC-feasibility, guided by a projection-based training loss. By embedding an optimization-based feasibility restoration and employing a replay buffer, it achieves feasible, near-optimal solutions with substantial speedups (up to about $40\times$) over traditional solvers, even on large-scale networks like PEGASE-9241. The approach does not rely on ground-truth AC-OPF targets and remains robust under topology changes, achieving high feasibility when combined with a PF solver for real-time operation. Overall, the method offers a practical path to rapid, reliable AC-OPF in dynamic power systems, balancing feasibility and optimality through a principled projection-based training regime.

Abstract

This paper proposes a hard-constrained unsupervised learning framework for rapidly solving the non-linear and non-convex AC optimal power flow (AC-OPF) problem in real-time operation. Without requiring ground-truth AC-OPF solutions, feasibility and optimality are ensured through a properly designed learning environment and training loss. Inspired by residual learning, the neural network (NN) learns the correction mapping from the DC-OPF solution to the active power setpoints of the generators through re-dispatch. A subsequent optimization model is utilized to restore the optimal AC-OPF solution, and the resulting projection difference is employed as the training loss. A replay buffer is utilized to enhance learning efficiency by fully leveraging past data pairs. The optimization model is cast as a differentiable optimization layer, where the gradient is derived by applying the implicit function theorem to the KKT conditions at the optimal solution. Tested on IEEE-118 and PEGASE-9241 bus systems, numerical results demonstrate that the proposed NN can obtain strictly feasible and near-optimal solutions with reduced computational time compared to conventional optimization solvers. In addition, aided by the updated DC-OPF solution under varying topologies, the trained NN, together with the PF solver, can rapidly find the corresponding AC solution. The proposed method achieves a $40\times$ time speedup, while maintaining an average constraint violation on the order of $10^{-4}$ and an optimization gap below $1\%$.

Figures (5)

• Figure 1: The proposed optimization-based end-to-end unsupervised learning framework for AC-OPF.
• Figure 2: The testing framework with a subsequent PF solver $M^\text{pf}_{\text{prop}}$.
• Figure 3: The evolution process of the training (projection) loss with the training epoch on the PEGASE-9241 bus system. The learning rate is reduced from $0.0005$ to $0.0001$ at epoch 50.
• Figure 4: The average absolute difference of the NN output and the closest strict feasible solution of the testing samples on the PEGASE-9241 bus system.
• Figure 5: The histogram of the average power generation output difference of the NN output and the DC-OPF solution of the testing samples on the PEGASE-9241 bus system.