Hierarchical Agglomerative Clustering of Selected Hungarian Medium Voltage Distribution Networks

Abstract

Nowadays the increase of photovoltaic penetration and simultaneously, the decentralization of electricity system, poses a number of challenges for distribution system developers and operators. The spread of high output power photovoltaic power plant connections demands the development of a network infrastructure. The analysis of development directions can be done with software simulation, for which network models are needed, which can characterize real networks well. To create such reference networks, knowing existing topologies, hierarchical agglomerative clustering can be a solution. When the parameters of the clusters are specified well, their software implementation can be done. In this study, a possible clustering process of selected Hungarian medium voltage overhead networks (including the determination of the optimal cluster number too), and the formulated network clusters are presented. The clustering of twenty selected 22 kV medium voltage networks was done using hierarchical agglomerative clustering. Then the optimal cluster number was determined. Based on Davis-Bouldin and Silhouette criterions, this cluster number was four. Two of the four generated clusters are single clusters, containing only one feeder. The size and looping of the characterized sample networks are well observable. In this paper a method has been created to generate medium voltage distribution network models, which can be used to simulate the effects of the growing photovoltaic penetration in the Hungarian distribution network.

Methodology for the formulation of medium voltage representative networks in three DSO areas

“…One of the biggest questions of data mining is which methods can be used on large data sets and how these tools are used. After reviewing studies in which electricity network topologies are grouped, it can be stated that for classification, k-means (and k-medoids) clustering and hierarchical clustering are the most frequently used techniques [2][3][4]. In this study, hierarchical agglomerative clustering is used for the formulation of medium voltage representative networks.…”

“…The name of the clustering method refers to the process of data processing. Within the group of hierarchical clustering algorithms, depending on the direction of the clustering process, two different algorithms can be identified: (i) agglomerative clustering and (ii) divisive clustering [2][3][4]. Hierarchical agglomerative clustering is a federation-based algorithm.…”

“…The step number of clustering algorithms is relatively high; it is around the size of the input data array to the third power (~n 3 ). In the case of large input data sets, this algorithm may be slow [2][3][4]. The advantage of this algorithm is that it corrects the distance errors between the local minimum and the centre of the clusters.…”

“…If two clusters are merged in one step, they cannot be divided again later, since the new cluster is used in the next step of the algorithm. The merging steps are considered critical, because incomplete mergers result in incorrect clustering [2][3][4]. In this paper, 1769 selected Hungarian medium voltage distribution feeders are examined and clustered with hierarchical agglomerative clustering (one of the most frequently used).…”

“…To perform simulation, the software implementation of networks is recommended. [2][3][4]. Since there is a significant number of various topology medium voltage networks in Hungary, their software implementation and a large range of simulations is a powerful time and resource absorbing exercise.…”