Power grid operators typically solve large-scale, nonconvex optimal power
flow (OPF) problems throughout the day to determine optimal setpoints for
generators while adhering to physical constraints. Despite being at the heart
of many OPF solvers, Newton-Raphson can be slow and numerically unstable. To
reduce the computational burden associated with calculating the full Jacobian
and its inverse, many Quasi-Newton methods attempt to find a solution to the
optimality conditions by leveraging an approximate Jacobian matrix. In this
paper, a Quasi-Newton method based on machine learning is presented which
performs iterative updates for candidate optimal solutions without having to
calculate a Jacobian or approximate Jacobian matrix. The proposed
learning-based algorithm utilizes a deep neural network with feedback. With
proper choice of weights and activation functions, the model becomes a
contraction mapping and convergence can be guaranteed. Results shown for
networks up to 1,354 buses indicate the proposed method is capable of finding
approximate solutions to AC OPF very quickly.

本文提出了一种基于机器学习的拟牛顿方法，使用深度神经网络进行迭代更新，能够快速找到交流 OPF 近似解，并消除了计算雅各比矩阵或近似雅各比矩阵的必要性。

一种基于学习增强的拟牛顿法用于交流潮流最优功率流计算

A Learning-boosted Quasi-Newton Method for AC Optimal Power Flow

Estimators based on influence functions (IFs) have been shown to be effective
in many settings, especially when combined with machine learning techniques. By
focusing on estimating a specific target of interest (e.g., the average effect
of a treatment), rather than on estimating the full underlying data generating
distribution, IF-based estimators are often able to achieve asymptotically
optimal mean-squared error. Still, many researchers find IF-based estimators to
be opaque or overly technical, which makes their use less prevalent and their
benefits less available. To help foster understanding and trust in IF-based
estimators, we present tangible, visual illustrations of when and how IF-based
estimators can outperform standard ``plug-in'' estimators. The figures we show
are based on connections between IFs, gradients, linear approximations, and
Newton-Raphson.

通过与梯度、线性逼近和牛顿 - 拉弗森方法的连接，提供影响函数估计器何时如何优于标准 “插入式” 估计器的具体、视觉化示例。