Unsupervised Deep Lagrange Dual With Equation Embedding for AC Optimal Power Flow

Conventional solvers are often computationally expensive for constrained optimization, particularly in large-scale and time-critical problems including AC optimal power flow (OPF) problems. While this leads to a growing interest in using neural networks (NNs) as fast optimal solution approximators, incorporating the constraints with NNs is challenging. In this regard, we propose deep Lagrange dual with equation embedding (DeepLDE), a framework that learns to find an optimal solution without using labels. To ensure feasible solutions, we embed equality constraints into the NNs and train the NNs using the primal-dual method to impose inequality constraints. The equality constraints correspond to power flow equations, and the inequality constraints include the operational limits of generators and transmission lines. We prove the convergence of DeepLDE and show that the previous primal-dual learning method cannot solely ensure equality constraints without the help of equation embedding. Simulation results on non-convex and AC-OPF problems show that the proposed DeepLDE achieves the smallest optimality gap among all the NN-based approaches while always ensuring feasible solutions. Furthermore, the computation time of the proposed method is up to 35 times faster than the baselines in solving constrained non-convex optimization, and/or AC-OPF.