基于无向图所有生成树的网络重构遗传算法

Genetic algorithm based on all spanning trees of undirected graph for distribution network reconfiguration

提出一种基于配电网简化图所有生成树的网络重构遗传算法。搜索出配电网简化图的所有生成树,简化图减去生成树得到连支,连支的每条边上有且仅有一个开关打开;提出以连支每条边的开关数量为基向量、打开开关在边上的编号为优化变量的十进制编码方法,大幅缩短了编码长度;每棵生成树对应一个子种群,并行计算子种群中的遗传操作,得到的子代个体自动满足配电网辐射状、无孤岛运行的约束条件,避免了传统网络重构遗传算法产生大量不可行解、搜索效率低的弊端。算例表明所提方法具有计算速度快、性能好的特点。

A genetic algorithm based on all spanning trees of the simplified graph of distribution network is proposed for its reconfiguration. The simplified graph of distribution network is searched to find all its spanning trees,which are subtracted from the simplified graph to obtain the connecting branches. Since only one of the switches in each connecting edge of a connecting branch could be open,a decimal coding method is proposed, which takes the switch quantity of each edge of a connecting branch as the base vector and the identification number of its opened switch as the optimization variable to significantly shorten the code length. With each spanning tree as a subpopulation, genetic operation is executed in parallel for each subpopulation and the obtained individuals satisfy the operational constraints of radial distribution network without islands automatically to avoid the numerous unfeasible solutions and low searching efficiency of conventional genetic algorithms. Case study shows that,the proposed method has high calculation speed and good performance.