Physics-Informed Gradient Estimation for Accelerating Deep Learning based AC-OPF

TL;DR

This work tackles real-time AC-OPF by marrying semi-supervised learning with data augmentation and physics-informed gradient estimation to reduce data preparation and training time. A FDPF-embedded learning framework constrains the optimization to the power-flow equations, while a ridge-regression-based pseudo-labeling scheme provides pseudo targets for extensive training data. To alleviate computational bottlenecks, the authors develop implicit-gradient backpropagation with batch-mean Jacobian estimates and a reduced branch set, including linearized and decoupled Jacobian variants, enabling scalable training. Empirical results on IEEE-118 and PEGASE-based grids show near-feasible, near-optimal solutions with substantial speedups (up to tens of times) and per-instance online solving times in seconds for large systems, suggesting practical viability for real-time ISO operations.

Abstract

The optimal power flow (OPF) problem can be rapidly and reliably solved by employing responsive online solvers based on neural networks. The dynamic nature of renewable energy generation and the variability of power grid conditions necessitate frequent neural network updates with new data instances. To address this need and reduce the time required for data preparation time, we propose a semi-supervised learning framework aided by data augmentation. In this context, ridge regression replaces the traditional solver, facilitating swift prediction of optimal solutions for the given input load demands. Additionally, to accelerate the backpropagation during training, we develop novel batch-mean gradient estimation approaches along with a reduced branch set to alleviate the complexity of gradient computation. Numerical simulations demonstrate that our neural network, equipped with the proposed gradient estimators, consistently achieves feasible and near-optimal solutions. These results underline the effectiveness of our approach for practical implementation in real-time OPF applications.

Figures (5)

• Figure 1: The proposed FCNN learning framework for the AC-OPF problem.
• Figure 3: The training loss trajectory of different gradient estimation methods. The learning rate is set to 0.0005 for the initial 90 epochs, then reduced to 0.0001 for the last 30 epochs.
• Figure 4: The total training loss trajectory of the proposed method $M_4$ over epochs on the IEEE-118 bus system. The learning rate is 0.0005 in the first 90 epochs and 0.0001 in the last 30 epochs.
• Figure 5: The total training loss evolution process of the proposed method $M_4$ over epochs on the PEGASE-1354 bus system. The learning rate is 0.0005 in the first 70 epochs and 0.0001 in the last 50 epochs.
• Figure 6: The total training loss trajectory of the proposed method $M_4$ over epochs using different learning rate schedules on the IEEE-118 bus system. The plot starts from the second epoch for better demonstration.

Theorems & Definitions (1)

• Remark 1: The role of weight $w_{v}$