A network science-based k-means++ clustering method for power systems network equivalence

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.