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

Abstract

Alternating current optimal power flow (AC-OPF) is one of the fundamental problems in power systems operation. AC-OPF is traditionally cast as a constrained optimization problem that seeks optimal generation set points whilst fulfilling a set of non-linear equality constraints -the power flow equations. With increasing penetration of renewable generation, grid operators need to solve larger problems at shorter intervals. This motivates the research interest in learning OPF solutions with neural networks, which have fast inference time and is potentially scalable to large networks. The main difficulty in solving the AC-OPF problem lies in dealing with this equality constraint that has spurious roots, i.e. there are assignments of voltages that fulfill the power flow equations that however are not physically realizable. This property renders any method relying on projected-gradients brittle because these non-physical roots can act as attractors. In this paper, we show efficient strategies that circumvent this problem by differentiating through the operations of a power flow solver that embeds the power flow equations into a holomorphic function. The resulting learningbased approach is validated experimentally on a 200-bus system and we show that, after training, the learned agent produces optimized power flow solutions reliably and fast. Specifically, we report a 12x increase in speed and a 40% increase in robustness compared to a traditional solver. To the best of our knowledge, this approach constitutes the first learning-based approach that successfully respects the full non-linear AC-OPF equations.

Reinforcement Learning for Battery Energy Storage Dispatch augmented with Model-based Optimizer

“…To account for the impact of the current action on future rewards, the total discounted reward at time step t under a given policy π, denoted by R t , is defined as the sum of the instant reward at time step t and discounted rewards from the next time step, t + τ , given by (18).…”

“…Unfortunately, existing modelfree RL algorithms ignore the crucial information embedded in the physics-based model of the power distribution systems and may thus compromise the optimizer performance and pose scalability challenges. In more recent works, including power systems model information in neural networks has shown to improve the performance of the OPF problems [17], [18].…”