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The Optimal Power Flow (OPF) problem is a fundamental building block for theoptimization of electrical power systems. It is nonlinear and nonconvex andcomputes the generator setpoints for power and voltage, given a set of loaddemands. It is often needed to be solved repeatedly under various conditions,either in real-time or in large-scale studies. This need is further exacerbatedby the increasing stochasticity of power systems due to renewable energysources in front and behind the meter. To address these challenges, this paperpresents a deep learning approach to the OPF. The learning model exploits theinformation available in the prior states of the system (which is commonlyavailable in practical applications), as well as a dual Lagrangian method tosatisfy the physical and engineering constraints present in the OPF. Theproposed model is evaluated on a large collection of realistic power systems.The experimental results show that its predictions are highly accurate withaverage errors as low as 0.2%. Additionally, the proposed approach is shown toimprove the accuracy of widely adopted OPF linear DC approximation by at leasttwo orders of magnitude.

Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods