Topology-Based Clustering Techniques for Graph Partitioning Applied to the Italian Transmission Network

Abstract

As renewable energy sources are integrated into power systems, the complexity of their management increases. For the analysis of modern power systems, clustering algorithms have become indispensable tools. The representation of an electric power transmission system involves conceptualizing it as a graph—a mathematical structure depicting a set of nodes and edges. In the context of power systems, these nodes correspond to buses, and the edges represent branches. Weighting may be assigned to the edges to denote the strength of their connections. In this paper, spectral clustering and hierarchical agglomerative clustering have been employed to analyze the Italian transmission network. Spectral clustering relies on the eigenvalues and eigenvectors derived from the Laplacian matrix associated with the network. The hierarchical agglomerative clustering, based on Thévenin impedance to define the distances, merges the two closest clusters at each step. The primary objective of this research is to identify distinct areas within the network based solely on its topology. In pursuit of this goal, admittances and Thévenin impedances have been employed as weights in the graph representation. By utilizing these approaches, the research aims at uncovering meaningful structures and patterns within the power transmission system based on the inherent connectivity and strength of the network elements. The techniques have been used on two real network models to demonstrate the performance of the algorithms with different grid configurations.

Keywords

• Clustering techniques
• spectral clustering
• hierarchical clustering
• power grids