全纯嵌入微分法求解AC最优潮流
Learning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings
摘要：
交流最优潮流（AC-OPF）是电力系统运行的基本问题之一。AC-OPF传统上被视为一个约束优化问题，该问题在满足一组非线性等式约束（潮流方程）的同时寻求最优发电设定点。随着可再生能源发电的普及，电网运营商需要以更短的时间间隔解决更大的问题。这激发了研究兴趣，学习OPF解决方案与神经网络，具有快速的推理时间，并有可能扩展到大型网络。解决AC-OPF问题的主要困难在于处理具有伪根的等式约束，即存在满足功率流方程的电压分配，然而这些电压分配在物理上是不可实现的。这个属性使得任何依赖于投影梯度的方法都很脆弱，因为这些非物理根可以充当吸引子。在本文中，我们展示了有效的策略，绕过这个问题，通过一个潮流求解器，嵌入到一个全纯函数的潮流方程的操作区分。由此产生的基于学习的方法在200总线系统上进行了实验验证，我们表明，经过训练，学习代理可靠，快速地产生优化的潮流解决方案。具体来说，我们报告了12倍的速度和40%的鲁棒性增加相比，传统的求解器。据我们所知，这种方法构成了第一个基于学习的方法，成功地尊重完整的非线性AC-OPF方程。
英文摘要：
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 learning-based 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.
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