论文标题
电源方程的真实解决方案数量的分布
The Distribution of the Number of Real Solutions to the Power Flow Equations
论文作者
论文摘要
在本文中，我们研究了在不同的电参数上，实际解决方案数量到功率流程方程的分布。我们介绍了一种新的单片和参数同拷贝延续方法，以快速找到对功率流程方程的所有解决方案。我们将此方法应用于对功率流程方程的分布，并将这些分布与随机多项式的分布进行比较。据观察，尽管功率流程方程倾向于接受相比的复杂溶液总数少得多的实值解决方案，但对于低水平的载荷，它们倾向于接受比相应的随机多项式所吸收的更多。我们表明，对于循环图，实际解决方案的数量可以实现特定参数值的最大界限，而对于具有四个或多个顶点的完整图，有一个可无限的真实解决方案的感应值。
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all solutions to the power flow equations. We apply this method to find distributions of the number of real solutions to the power flow equations and compare these distributions to those of random polynomials. It is observed that while the power flow equations tend to admit many fewer real-valued solutions than a bound on the total number of complex solutions, for low levels of load they tend to admit many more than a corresponding random polynomial. We show that for cycle graphs the number of real solutions can achieve the maximum bound for specific parameter values and for complete graphs with four or more vertices there are susceptance values that give infinitely many real solutions.
