Physics-Constrained Adversarial Training for Neural Networks in Stochastic Power Grids

The growth in distributed energy resources (DERs) is an important step toward solving the global climate crisis. However, many DERs, such as wind and solar power, are random and intermittent, causing the data in power grids to be perturbed with high uncertainty. Such perturbations degrade the performance of data-driven algorithms introduced in power grids for sensing and control. Existing approaches can strengthen machine learning models against well-designed malicious attacks. However, such physics-agnostic efforts fail to ensure the robustness to natural perturbations in power grids, that occur due to varying loads and changes in control inputs. This paper proposes a novel physics-constrained adversarial training method for robustifying neural networks for the crucial problem of locating edge-faults in power grids. Our approach relies on first deriving analytical physical laws that are satisfied by state perturbations in realistic grids, and then using the descriptive sets during adversarial training. Compared to state of the art methods, our perturbation-robust neural networks have higher robust accuracy as well as training efficiency. Also, we demonstrate that the proposed approach achieves a tighter upper bound of robust risks than traditional efforts. The numerical experimental results in the IEEE 68-bus benchmark system validate our adversarial training in two scenarios when loads and control inputs vary randomly. The proposed method shows superior performance in accuracy and efficiency for different perturbed datasets. In addition, we testify the influence of different inputs on the robustness.