DeepOPF: Deep Neural Networks for Optimal Power Flow

Note: 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 developed a preventive-learning approach to provably gaurantee DNN solution feasibility for DC-OPF problems and general optimization problems with linear constraints.

We also studied another fundamental problem of employing DNNs to solve non-convex AC-OPF problems admitting multiple load-solution mappings. We proposed an augmented learning approach,, named DeepOPF-AL, to address the issue and learn one unique augmented mapping that embeds all the different load-solution mappings. The learned augmented mapping can be used to generate solutions from the load input.

Tutorial

  • M. Chen and S. H. Low, “Machine Learning for Solving Optimal Power Flow Problems”, tutorial at ACM SIGMETRICS / IFIP Performance, Mumbai, India, June 6-10, 2022.

Publications

  • X. Pan, T. Zhao, and M. Chen, “DeepOPF: Deep Neural Network for DC Optimal Power Flow”, in Proceedings of the 10th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2019), Beijing, China, October 21 - 24, 2019. [PDF] Also available as technical report posted onto arXiv in May 2019. [PDF]

  • X. Pan, T. Zhao, M. Chen, and S. Zhang, “DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow”, IEEE Transactions on Power Systems, vol. 36, issue 3, pp. 1725 - 1735, May 2021. [PDF] Also available as technical report posted onto arXiv in Oct. 2019. [PDF]

  • X. Pan, M. Chen, T. Zhao, and S. H. Low “DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems”, IEEE Systems Journal, accepted, 2022. [PDF] Also available as a technical report on arXiv in July 2020. [PDF]

  • W. Huang, X. Pan, M. Chen, and S. H. Low, “DeepOPF-V: Solving AC-OPF Problems Efficiently”, IEEE Transactions on Power Systems, accepted, 2021. Technical report as arXiv preprint arXiv:2007.01002, 2021. [PDF]

  • T. Zhao, X. Pan, M. Chen, A. Venzke, and S. H. Low, “DeepOPF+: A Deep Neural Network Approach for DC Optimal Power Flow for Ensuring Feasibility”, in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2020), virtual conference, Nov. 11 - 13, 2020. [PDF]

  • T. Zhao, X. Pan, M. Chen, and S. H. Low, “Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems”, arXiv preprint arXiv:2112.08091, 2021. [PDF]

  • X. Pan, W. Huang, M. Chen and S. H. Low, “DeepOPF-AL: Augmented Learning for Solving AC-OPF Problems with Multiple Load-Solution Mappings”, arXiv preprint arXiv:2206.03365, 2022. [PDF]