Improving the Robustness of Data-Driven OPF by Nonlinearity-Focused Sampling

Data-driven optimal power flow (OPF) leverages neural networks (NNs) to learn the OPF maps from samples. However, the inherent intricate nonlinearity in the OPF problem poses significant challenges to learning different samples. It often results in unacceptable errors in highly nonlinear regions, such as localized areas with identical active constraints and global boundaries where active constraints vary. Therefore, this paper proposes a nonlinearity-focused sampling method to enrich the OPF samples with high nonlinearity. The proposed method forces the NNs to pay more attention to those nonlinear regions and further improves their robustness. Firstly, the local nonlinearity-focused sampling technique is established based on physics-informed adversarial searching. By merging the gradient of physics models and NNs, it can precisely search the local samples with intolerable errors caused by high nonlinearity. Additionally, a global nonlinearity-focused sampling algorithm is proposed to precisely locate the boundary where active constraints vary, representing an entirely different OPF solution pattern. An iterative strategy is presented to acquire the global samples exhibiting high nonlinearity and learning difficulty. Consequently, the constructed dataset could accurately capture the inherent intricate nonlinearity in OPF and emphasize what NN needs to learn. Extensive simulations on various systems demonstrate that the NNs trained using the OPF datasets constructed by the proposed method can achieve more robust performance.