Network equivalence is a technique useful for many areas including power systems. In many power system analyses, generation shift factor (GSF)-based bus clustering methods have been widely used to reduce the complexity of the equivalencing problem. GSF captures power flow on a line when power is injected at a node using bus to bus electrical distance. A more appropriate measure is the one which captures what may be called the electrical line distance with respect to a bus termed as relative bus to line distance. With increase in power transactions across different regions, the use of relative bus to line distance becomes appropriate for many analyses. Inspired by the recent trends in network science on the study of network dynamics based on the topological characteristics of a network, in this paper, we present a bus clustering method based on average electrical distance (AED). AED is independent of changes in location of slack bus and is based on the concept of electrical distance introduced in the context of molecular chemistry and pursued later for applications in social and complex networks. AED represents the AED from a bus to buses of the transmission line of interest. We first propose an AED-based method to group the buses into clusters for power systems network equivalence using k-means clustering algorithm integrated with silhouette analysis. One limitation of this method is that despite its speed, sometimes it may yield clusters of inferior quality compared to the optimal solution. To overcome this limitation, we next present our improved clustering method which incorporates a seeding technique that initializes centroids probabilistically. We also incorporate a technique in our method to find the number of clusters, k, to be given as input to our clustering algorithm. The resulting algorithm called AED-based k-means++ clustering method yields a clustering that is O(logk) competitive. Our network equivalence technique is next described. Finally, the efficacy of our new equivalencing technique is demonstrated by evaluating its performance on the IEEE 300-bus system and comparing that to the performance of our AED-based method (Sharma et al. in Power network equivalents: a network science-based k-means clustering method integrated with silhouette analysis. In: Complex networks and their application VI, Lyon, France. p. 78–89, 2017) and the existing GSF-based method.

中文翻译：

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基于网络科学的k -means ++聚类方法用于电力系统网络等效

网络等效是一种对许多领域（包括电力系统）有用的技术。在许多电力系统分析中，基于发电移位因子（GSF）的总线聚类方法已被广泛用于降低等价问题的复杂性。当使用总线到总线的电气距离在节点上注入功率时，GSF会捕获线路上的功率流。一种更合适的措施是捕获相对于称为相对母线到线路距离的母线的电气线路距离的方法。随着不同地区电力交易的增加，使用相对总线到线路的距离已适合许多分析。受到网络科学的最新趋势的启发，本文基于网络的拓扑特性研究网络动力学，我们提出一种基于平均电气距离（AED）的总线聚类方法。AED与松弛总线位置的变化无关，它基于在分子化学领域引入的电距离概念，后来在社会和复杂网络中得到应用。AED代表从总线到目标传输线的AED。我们首先提出一种基于AED的方法，使用结合了轮廓分析的k均值聚类算法，将总线分组为电力系统网络等效性的集群。这种方法的一个局限性是，尽管它的速度很快，但与最佳解决方案相比，有时仍会产生质量较差的簇。为了克服此限制，接下来，我们介绍我们的改进的聚类方法，该方法结合了可概率地初始化质心的播种技术。我们还将一种技术纳入我们的方法中，以找到要作为聚类算法输入输入的聚类数k。所得的算法称为基于AED的k-means ++聚类方法，产生的聚类具有O（logk）竞争性。接下来描述我们的网络等效技术。最后，通过评估其在IEEE 300总线系统上的性能并将其与基于AED的方法的性能进行比较，证明了我们新的等效技术的有效性（Sharma等人在《电力网络等效技术》中：基于网络科学的知识均值聚类方法与轮廓分析相结合。于：复杂网络及其应用VI，法国里昂，第78–89页，