基于半监督谱聚类的黑启动分区策略

采用并行恢复策略可以有效加快电力系统发生大停电事故后的恢复进程,而合理的分区策略是并行恢复的基础。现有分区方法多数存在对算法初值依赖性强、难以获得全局最优解等缺点,而半监督谱聚类具有能够识别任意形状的样本空间并能够收敛于全局最优解,且适用于分区问题的特点。在此背景下,提出了基于半监督谱聚类的黑启动分区策略。首先,给定节点间电气距离的倒数为相关线路的权重,在此基础上建立电力系统无向加权图,进而依据比例割集准则建立黑启动分区策略。该策略由2步构成:第一步建立待恢复机组的分组模型,其以给定时间段内最大化系统发电量和最小化恢复线路总电容为优化目标,从而保证机组的安全快速启动;第二步以得到的机组分组信息为基础,利用半监督谱聚类算法求解黑启动分区模型。为了克服传统k-means算法对初始聚类中心敏感的缺点,在利用半监督谱聚类算法对特征向量进行聚类的最后一步采用了k-means++算法对特征向量进行聚类。最后,以新英格兰10机39节点系统和IEEE 30节点系统为例说明了所发展的模型和方法的基本特征。

Black-Start Zoning Strategy Based Semi-Supervised Spectral Clustering Algorithm

Power system restoration after a blackout can be speeded up by employing a parallel restoration strategy, while a reasonable zoning strategy is the basis of parallel restoration.The performances of most of the existing black-start zoning methods are highly dependent on the specified initial values, and it is hard to attain the global optimal solution by these methods.The semi-supervised spectral clustering algorithm is able to identify any shapes of sample spaces, and to attain the global optimal solution, which can be employed for black-start zoning.Given this background, this paper proposes the black-start zoning strategy based on the semi-supervised spectral clustering algorithm.Firstly, the reciprocal of electrical distance between nodes is used to determine the weight of the line, and then the undirected weighted graph of the power system concerned can be formed.On this basis, a black-start zoning strategy is presented based on the ratio cut set criterion.The proposed strategy consists of two steps.In the first step, a grouping optimization model of generators to be restored is presented for speeding the power system restoration, with both the maximization of the restored generation quantity in the given period and the minimization of the total capacitance of the restored transmission lines included in the objective function of the optimization problem.In the second step, the semi-supervised clustering algorithm is employed to solve the black-start zoning model based on the grouping information attained in the first step.In the the last step of semi-supervised spectral clustering algorithm, the k-means++ algorithm is employed to cluster the feature vectors, so as to avoid the drawback of the traditional k-means algorithm that the clustering result is sensitive to the specified initial cluster centers.Finally, the New England 10-unit 39-bus power system and IEEE 30-bus power system are employed to demonstrate the basic features of the developed model and method.