Advancing performance guarantees for DNN-based OPF in topology-flexible distribution networks

We tackled the lack of solution-quality guarantees for deep neural network (DNN)-based optimal power flow (OPF) in topology-flexible distribution networks (TFDNs), despited the black-box nature of DNN predictors. We formulated a bi-level min-max (BLMM) problem, whose inner level certifies the performance of a fixed DNN-based OPF solution and whose outer level updates the DNN to improve the certified bound. To solve the BLMM problem, we developed an iterative scheme grounded in Danskin’s theorem. In particular, we attained the exact solution by explicitly reformulating the BLMM problem through binary variables. To alleviate the computational burden from binary variables, we combined convex relaxation with pattern recognition, thereby reducing the required number of binary variables. The effectiveness of the proposed method is demonstrated on a 4-bus system and the IEEE 136-bus test system.