Machine learning can generate black-box surrogate models which are both extremely fast and highly accurate. Rigorously verifying the accuracy of these black-box models, however, is computationally challenging. When it comes to power systems, learning AC power flow is the cornerstone of any machine learning surrogate model wishing to drastically accelerate computations, whether it is for optimization, control, or dynamics. This paper develops for the first time, to our knowledge, a tractable neural network verification procedure which incorporates the ground truth of the non-linear AC power flow equations to determine worst-case neural network performance. Our approach, termed Sequential Targeted Tightening (STT), leverages a loosely convexified reformulation of the original verification problem, which is a mixed integer quadratic program (MIQP). Using the sequential addition of targeted cuts, we iteratively tighten our formulation until either the solution is sufficiently tight or a satisfactory performance guarantee has been generated. After learning neural network models of the 14, 57, 118, and 200-bus PGLib test cases, we compare the performance guarantees generated by our STT procedure with ones generated by a state-of-the-art MIQP solver, Gurobi 9.5. We show that STT often generates performance guarantees which are orders of magnitude tighter than the MIQP upper bound.

翻译：机器学习能够生成兼具极快速度与高精度的黑箱代理模型。然而，严格验证这些黑箱模型的准确性在计算上极具挑战性。在电力系统中，无论用于优化、控制还是动态分析，学习交流潮流计算都是任何希望大幅加速计算的机器学习代理模型的基石。据我们所知，本文首次提出一种可操作的神经网络验证程序，该程序结合非线性交流潮流方程的真实物理约束，以确定神经网络在最坏情况下的性能表现。我们的方法被称为“序列目标紧化（STT）”，它利用原始验证问题的松弛凸化重构形式——即混合整数二次规划（MIQP）问题。通过序列添加目标切割，我们迭代地收紧问题表述，直至解达到足够紧致或获得令人满意的性能保证。在学习14、57、118和200节点PGLib测试案例的神经网络模型后，我们将STT程序生成的性能保证与最先进的MIQP求解器Gurobi 9.5所生成的结果进行比较。结果表明，STT生成的性能保证通常比MIQP上界紧致数个数量级。