  The Optimal Power Flow (OPF) problem is a fundamental building block for the
optimization of electrical power systems. It is nonlinear and nonconvex and
computes the generator setpoints for power and voltage, given a set of load
demands. It is often needed to be solved repeatedly under various conditions,
either in real-time or in large-scale studies. This need is further exacerbated
by the increasing stochasticity of power systems due to renewable energy
sources in front and behind the meter. To address these challenges, this paper
presents a deep learning approach to the OPF. The learning model exploits the
information available in the prior states of the system (which is commonly
available in practical applications), as well as a dual Lagrangian method to
satisfy the physical and engineering constraints present in the OPF. The
proposed model is evaluated on a large collection of realistic power systems.
The experimental results show that its predictions are highly accurate with
average errors as low as 0.2%. Additionally, the proposed approach is shown to
improve the accuracy of widely adopted OPF linear DC approximation by at least
two orders of magnitude.
