Unsupervised Learning for Solving AC Optimal Power Flows: Design, Analysis, and Experiment

With the increasing penetration of renewables, AC optimal power flow (AC-OPF) problems need to be solved more frequently for reliable and economic power system operation. Supervised learning approaches have been developed to solve AC-OPF problems fast and accurately. However, due to the non-convexity of AC-OPF problems, it is non-trivial and computationally expensive to prepare a large training dataset, and multiple load-solution mappings may exist to impair learning even if the dataset is available. In this paper, we develop an unsupervised learning approach ($\mathsf{DeepOPF-NGT}$) that does not require ground truths. $\mathsf{DeepOPF-NGT}$ utilizes a properly designed loss function to guide neural networks in directly learning a legitimate load-solution mapping. Kron reduction is used to remove the zero-injection buses from the prediction. To tackle the unbalanced gradient pathologies known to deteriorate the learning performance, we develop an adaptive learning rate algorithm to dynamically balance the gradient contributions from different loss terms during training. Further, we derive conditions for unsupervised learning to learn a legitimate load-solution mapping and avoid the multiple mapping issue in supervised learning. Results of the 39/118/300 /1354-bus systems show that $\mathsf{DeepOPF-NGT}$ achieves optimality, feasibility, and speedup performance comparable to the state-of-the-art supervised approaches and better than the unsupervised ones, and a few ground truths can further improve its performance.