Learning Optimal Power Flow with Pointwise Constraints

Training learning parameterizations to solve optimal power flow (OPF) with pointwise constraints is proposed. In this novel training approach, a learning parameterization is substituted directly into an OPF problem with constraints required to hold over all problem instances. This is different from existing supervised learning methods in which constraints are required to hold across the average of problem instances. Training with pointwise constraints is undertaken in the dual domain with the use of augmented Lagrangian and dual gradient ascent algorithm. Numerical experiments demonstrate that training with pointwise constraints produces solutions with smaller constraint violations. Experiments further demonstrated that pointwise constraints are most effective at reducing constraint violations in corner cases - defined as those realizations in which constraints are most difficult to satisfy. Gains are most pronounced in power systems with large numbers of buses.