DeepOPF: Deep Neural Networks for Optimal Power FlowNote: We help to maintain a list of related papers on machine learning for optimal power flow. This is the first work in the literature applying neural networks to directly solve the optimal power flow (OPF) problem. Previous learning-based solutions employ machine learning techniques as a module to facilitate conventional OPF solvers. In the first paper listed below, we develop DeepOPF as a Deep Neural Network (DNN) based approach for solving direct current optimal power flow (DC-OPF) problems. DeepOPF is inspired by the observation that solving DC-OPF for a given power network is equivalent to characterizing a high-dimensional mapping between the load inputs and the dispatch and transmission decisions. We first train a DNN to learn the mapping and predict the generations from the load inputs. We then directly reconstruct the phase angles from the generations and loads by using the power flow equations. Such a predict-and-reconstruct approach reduces the dimension of the mapping to learn, subsequently cutting down the size of the DNN and the amount of training data needed. We further derive a condition for tuning the size of the DNN according to the desired approximation accuracy of the load-generation mapping. We develop a post-processing procedure based on l1-projection to ensure the feasibility of the obtained solution, which can be of independent interest. Simulation results for IEEE test cases show that DeepOPF generates feasible solutions with less than 0.2% optimality loss, while speeding up the computation time by up to two orders of magnitude as compared to a state-of-the-art solver. We have also extended the aobve approach to the non-convex AC-OPF settings and the most recent results show that DeepOPF can achieve 15,000x speedup for solving AC-OPF problems over a 2000-bus test case with minor optimality loss, and the obtained solutions are feasibile with or without simple postprocessing. Recently, we have developed a preventive-learning approach to provably gaurantee DNN solution feasibility for DC-OPF problems and general optimization problems with linear constraints. Publications
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