Physics-Aware Deep Learning for Optimal Power Flow

Distribution grids are currently challenged by the rampant integration of distributed energy resources (DER). Scheduling DERs via an optimal power flow problem (OPF) in real time and at scale under uncertainty is a formidable task. Prompted by the success of deep neural networks (DNNs) in other fields, this talk presents two learning-based schemes for near-optimal DER operation. The first solution engages a DNN to predict the solutions of an OPF given the anticipated demands and renewable generation. Different from the generic learning setup, the training dataset here (namely past OPF solutions) features rich yet largely unexploited structure. To leverage prior information, we train a DNN to match not only the OPF solutions, but also their partial derivatives with respect to the input parameters of the OPF. Sensitivity analyses for non-convex and convexified renditions of the OPF show how such derivatives can be readily computed from the OPF solutions. The proposed sensitivity-informed DNN features sample efficiency improvements at a modest computational increase. Nonetheless, this two-stage OPF-then-learn approach may not be suitable for DER operation when the OPF input parameters are changing rapidly. To deal with such setups, we put forth an alternative OPF-and-learn scheme. Here the DNN is not trained to mimic the OPF minimizers but is rather organically integrated into a stochastic OPF formulation. A key advantage of this second DNN is that it can be driven by partial OPF inputs or proxies being the measurements the utility can collect from the grid in real time.