Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks

To shift the computational burden from real-time to offline in delay-critical power systems applications, recent works entertain the idea of using a deep neural network (DNN to predict the solutions of the AC optimal power flow (AC-OPF once presented load demands. As network topologies may change, training this DNN in a sample-efficient manner becomes a necessity. To improve data efficiency, this work utilizes the fact OPF data are not simple training labels, but constitute the solutions of a parametric optimization problem. We thus advocate training a sensitivity-informed DNN (SI-DNN to match not only the OPF optimizers, but also their partial derivatives with respect to the OPF parameters (loads . It is shown that the required Jacobian matrices do exist under mild conditions, and can be readily computed from the related primal/dual solutions. The proposed SI-DNN is compatible with a broad range of OPF solvers, including a non-convex quadratically constrained quadratic program (QCQP, its semidefinite program (SDP relaxation, and MATPOWER; while SI-DNN can be seamlessly integrated in other learning-to-OPF schemes. Numerical tests on three benchmark power systems corroborate the advanced generalization and constraint satisfaction capabilities for the OPF solutions predicted by an SI-DNN over a conventionally trained DNN, especially in low-data setups.