DeepOPF-AL: Augmented Learning for Solving AC-OPF Problems with a Multi-Valued Load-Solution Mapping

The existence of multi-valued load-solution mapping in general non-convex problems poses a fundamental challenge to deep neural network (DNN) schemes. A well-trained DNN in the existing supervised learning framework fails to learn the multi-valued mapping accurately and generates inferior solutions. We propose augmented learning as a methodological framework to tackle this challenge. We focus on AC-OPF as an important example and develop DeepOPF-AL to solve it. The main idea is to train a DNN to learn a single-valued mapping from an augmented input, i.e., (load, initial point), to the solution generated by an iterative OPF solver with the load and initial point as intake. We then apply the learned augmented mapping to solve AC-OPF problems much faster than conventional solvers. Simulation results over IEEE test cases show that DeepOPF-AL achieves noticeably better optimality and similar feasibility and speedup performance as compared to a recent DNN scheme, with the same DNN size yet larger training-data size. We believe the augmented-learning approach will find applications in various problems with a multi-valued input-solution mapping.