On the Distribution of Real-Valued Solutions to the Power Flow Equations
On the Distribution of Real-Valued Solutions to the Power Flow Equations
复制标题
潮流方程实值解的分布
DOI：
10.1109/allerton.2019.8919943
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
N. Boston
中科院分区：
文献类型：
--
作者：
B. Lesieutre;J. Lindberg;Alisha Zachariah;N. Boston
非线性潮流方程实值解的数量和性质尚未完全了解，也没有经过验证的简单方法来计算所有解。已经注意到，在实践中，方程倾向于允许比使用传统界限估计的更少的实值解。在本文中，我们研究了一种方法来计算作为多个参数的函数的解决方案的数量的分布。这种方法依赖于一种简化技术，该技术解决了一个变量的方程，其实值解的计算是简单的。重要的是，我们研究的基本问题，是否一个变量的实值解决方案必然意味着所有的变量将同时realvalued。我们目前的拓扑结构，这有利的属性被保留和拓扑结构，它失败。
The number and nature of real-valued solutions to the nonlinear power flow equations are not completely understood and there are no proven simple methods for computing all solutions. It has been noted that in practice the equations tend to admit many fewer real-valued solutions than what might be estimated using traditional bounds. In this paper we examine a means to calculate the distribution of number of solutions as a function of multiple parameters. This method relies on a reduction technique that resolves to an equation in one variable for which the calculation of real-valued solutions is straightforward. Importantly we examine the fundamental question of whether a real-valued solution in one variable necessarily implies all variables will be simultaneously realvalued. We present topologies for which this favorable property is retained and topologies for which it fails.