Training a Trustworthy DNN for Optimal Power Flow in Active Distribution Networks

With the fast development of distributed energy resources (DERs), optimal power flow (OPF) in an active distribution network (ADN) has drawn much attention. To deal with uncertainties of renewable DERs, it even requires tremendous computations of OPF in ADN (ADN-OPF) within a limited operational time. This motivates the application of a deep neural network (DNN) in ADN-OPF due to its end-to-end characteristic. However, the trustworthiness of a DNN is required to alleviate the worries of employing such DNN-based OPF methods, while the black-box nature of a DNN makes ADN operators hard to justify whether a DNN is trustworthy. To this end, this paper develops a novel framework that contains the learning and evaluation modules to train a trustworthy DNN for fast implementing ADN-OPF. In the learning module, a DNN is trained by minimizing a loss function over a training data set that is iteratively augmented for performance improvement. The evaluation module theoretically assesses the performance of the trained DNN by quantifying its trustworthiness, achieved by solving a series of mixed-integer problems (MIPs). Also, the evaluation module can augment samples added back to the training data set for performance improvement in the learning module. Finally, to alleviate the computational burden of the training process incurring from binary variables in MIPs, an acceleration strategy is developed based on convex relaxation and pattern recognition. The effectiveness of the proposed framework and strategy is verified in a 6-bus test system and the IEEE 136-bus test system.