基于矩阵摄动的谱聚类算法 确定电网最优分区数的研究

摘要

In order to solve the problem that the number of grid partitions is difficult to be determined and the partition is easy to be changed, a method of spectral clustering based on matrix perturbation is presented.In this paper, based on the spectral clustering algorithm, Lapiacian matrix of the network is constructed by the electric distance, and the number of partitions is determined according to the eigenvalue variation.Finally, the K-means clustering algorithm is used to partition the power grid.In the IEEE 14-node simulation system, the partition number and results from this method is the same as the previous partition number and results.The spatial distance of the IEEE39-node test system and the connecting tightness of the nodes are robust, Monte-Carlo stochastic simulation shows that in the case of smaller disturbances, the number of partitions of the method remains the same;while at larger disturbances, the number of partitions may be changed, but the probability of change is small.%针对电压控制的电网分区数量难以确定和分区易发生改变的问题,提出了一种基于矩阵摄动的谱聚类方法.该方法在谱聚类算法上,通过电气距离构造网络的Lapiacian矩阵,利用其特征根变化量确定分区数量,最后使用K-means聚类算法对电网进行分区.在IEEE14节点的仿真系统下,该方法与原有分区的分区数和分区结果相同.在IEEE39节点的测试系统下,该方法的空间电气距离和节点联系紧密度具有一定的鲁棒性;通过蒙特卡洛随机模拟,在扰动较小的情况下,该方法的分区数保持不变,而在较大扰动下,分区数可能会发生改变,但变化的概率很小.