Equality-embedded augmented Lagrangian neural network for DC optimal power flow

Direct current optimal power flow (DC-OPF) problems need to be solved more frequently to maintain safety and economic power system operation. Traditional solvers take too much time to get optimal results. To overcome it, a new self-supervised augmented Lagrangian neural network (ALNN) is proposed to solve DC-OPF problem. The proposed ALNN consists of two neural networks: the control net and the penalty net. The control net predicts active power of generators; the penalty net updates the Lagrangian multipliers. The equality constraints are embedded into the control net to guarantee no equality violations. The generalized reduced gradient method is used to reduce theviolations of inequality constraint. The effectiveness of the proposed model is demonstrated on IEEE 118-bus. The results show that with the help of equality embedding, the equality constraints are always satisfied, which in turn improves the feasibility of ALNN. Compared to the state-of-art models, the proposed model has higher feasibility and less constraint violations without comprising optimality. What is more, most of the inactive constraints can be found during the training process and then they are used to speed up the post-processing part.