To shift the computational burden from real-time to offline in delay-critical power systems applications, recent works entertain the idea of using a deep neural network (DNN) to predict the solutions of the AC optimal power flow (AC-OPF) once presented load demands. As network topologies may change, training this DNN in a sample-efficient manner becomes a necessity. To improve data efficiency, this work utilizes the fact OPF data are not simple training labels, but constitute the solutions of a parametric optimization problem. We thus advocate training a sensitivity-informed DNN (SI-DNN) to match not only the OPF optimizers, but also their partial derivatives with respect to the OPF parameters (loads). It is shown that the required Jacobian matrices do exist under mild conditions, and can be readily computed from the related primal/dual solutions. The proposed SI-DNN is compatible with a broad range of OPF solvers, including a non-convex quadratically constrained quadratic program (QCQP), its semidefinite program (SDP) relaxation, and MATPOWER; while SI-DNN can be seamlessly integrated in other learning-to-OPF schemes. Numerical tests on three benchmark power systems corroborate the advanced generalization and constraint satisfaction capabilities for the OPF solutions predicted by an SI-DNN over a conventionally trained DNN, especially in low-data setups.
The Optimal Power Flow Operator: Theory and Computation
最优潮流问题（optimal power flow problem，OPF）是一种数学规划，用于确定如何在网络运行约束和潮流物理条件下分配功率。在这项工作中，我们把OPF问题视为一个运营商的映射用户需求产生的功率，并允许网络参数（如发电机和潮流限制）采取一些容许集的值。本文的贡献是形式化这一算子理论的方法，定义和表征限制参数集下的映射有一个单例输出，独立的绑定约束，是可微的。与优化文献中的相关结果相比，我们不依赖于引入辅助松弛变量。事实上，我们的方法提供的结果，有一个明确的解释，关于所研究的电力网络。我们进一步提供了一个封闭形式的表达式的OPF算子的雅可比矩阵，并描述了如何使用最近提出的计划，基于同质自对偶嵌入计算各种衍生物。我们的框架，把一个数学程序作为一个运营商，使我们能够从一个完全不同的数学角度提出灵敏度和鲁棒性问题，并提供新的见解研究问题。
