Learning to Solve the AC Optimal Power Flow via a Lagrangian Approach

Using deep neural networks to predict the solutions to AC optimal power flow (ACOPF) problems has been an active direction of research. However, because the ACOPF is nonconvex, it is difficult to construct a good data set that contains mostly globally optimal solutions. To overcome the challenge that the training data may contain suboptimal solutions, we propose a Lagrangian-based approach. First, we use a neural network to learn the dual variables of the ACOPF problem. Then, from the predicted dual variables, we use a second neural network to predict solutions of the partial Lagrangian and use the predicted solutions as warm starts for the ACOPF problem. We test our approach on standard and modified IEEE networks and show that our approach can reach more globally optimal solutions with significant computational speedup even when the training data consists of mostly suboptimal solutions.