求解功率追踪问题的图论方法

A method to solve power-tracing problem based on graph theory

提出了一种利用图论进行功率追踪的新方法。此方法以潮流结果有向图的关联矩阵和路径矩阵为基础 ,采用先序遍历图的方法搜寻被功率追踪的 2个节点间的所有路径 ,进而求得沿这些路径输送的功率值 ,在功率追踪时遵循功率“按比例分配”原则。此方法物理意义明确 ,且只需进行简单的四则运算 ,不必进行计算量较大的矩阵相乘和求逆等运算 ,易于编程实现 ,而且可以推广为对电力系统中某一割集进行功率追踪。利用本方法分析了粤港电力系统中广东电网向香港地区输电的算例 。

A new power tracing method using graph theory is introduced,which is based on the adjacency matrix and path matrix of the digraph of load flow solution.All the paths between two traced nodes are found out using the preorder traversal method and the electrical power transferred through these paths calculated.The proportional rule is abided during power tracing.This method has clear physical meaning and simple algorithm.Only the arithmetic operations are needed and the time consuming matrices multiply and inversion are avoided,so it is easy to be translated into real computer programs and extended to trace the power of a certain cut set in power system.The method is used to analyze the power transfer from Guangdong province to HKSAR,and the calculation results prove that it is fast and efficient.