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Alternating current optimal power flow (AC-OPF) is one of the fundamentalproblems in power systems operation. AC-OPF is traditionally cast as aconstrained optimization problem that seeks optimal generation set pointswhilst fulfilling a set of non-linear equality constraints -- the power flowequations. With increasing penetration of renewable generation, grid operatorsneed to solve larger problems at shorter intervals. This motivates the researchinterest in learning OPF solutions with neural networks, which have fastinference time and is potentially scalable to large networks. The maindifficulty in solving the AC-OPF problem lies in dealing with this equalityconstraint that has spurious roots, i.e. there are assignments of voltages thatfulfill the power flow equations that however are not physically realizable.This property renders any method relying on projected-gradients brittle becausethese non-physical roots can act as attractors. In this paper, we showefficient strategies that circumvent this problem by differentiating throughthe operations of a power flow solver that embeds the power flow equations intoa holomorphic function. The resulting learning-based approach is validatedexperimentally on a 200-bus system and we show that, after training, thelearned agent produces optimized power flow solutions reliably and fast.Specifically, we report a 12x increase in speed and a 40% increase inrobustness compared to a traditional solver. To the best of our knowledge, thisapproach constitutes the first learning-based approach that successfullyrespects the full non-linear AC-OPF equations.

Learning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings