标题： 通过潮流解进行微分以实现导纳和拓扑控制 显示英文标题

标题： Differentiating Through Power Flow Solutions for Admittance and Topology Control

摘要： 电力潮流方程通过网络导纳矩阵将母线电压相量与功率注入相关联。 这些方程是电力系统关键运行和保护功能的核心（例如，最优潮流调度和控制、状态估计、保护和故障定位等）。 由于对网络导纳参数的控制、优化和估计是电力系统多个研究方向的核心，我们提出了一种通过对网络导纳参数进行隐式微分来获得的潮流解的线性化方法。 这是通过利用隐函数定理实现的，在此我们证明了在较弱条件下，这种微分必然存在，并且适用于一般的电力系统（辐射状或网状）。 所提出的理论用于推导复数电压、线路电流和功率流动的灵敏度。 围绕复数网络导纳参数变化对潮流方程进行线性化的理论具有广泛的应用。 我们展示了几种应用，例如在不求解潮流方程的情况下预测网络拓扑变化时的节点电压。 我们展示了连续导纳控制的应用，该控制用于提高给定配电网络的承载能力。 显示英文摘要

摘要： The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and control, state estimation, protection, and fault location, among others). As control, optimization, and estimation of network admittance parameters are central to multiple avenues of research in electric power systems, we propose a linearization of power flow solutions obtained by implicitly differentiating them with respect to the network admittance parameters. This is achieved by utilizing the implicit function theorem, in which we show that such a differentiation is guaranteed to exist under mild conditions and is applicable to generic power systems (radial or meshed). The proposed theory is applied to derive sensitivities of complex voltages, line currents, and power flows. The developed theory of linearizing the power flow equations around changes in the complex network admittance parameters has numerous applications. We demonstrate several of these applications, such as predicting the nodal voltages when the network topology changes without solving the power flow equations. We showcase the application for continuous admittance control, which is used to increase the hosting capacity of a given distribution network.