Title: The structure of electrical networks: a graph theory based analysis

Authors: Karla Atkins, Jiangzhuo Chen, V.S. Anil Kumar, Achla Marathe

Addresses: Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061, USA. ' Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061, USA. ' Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061, USA. ' Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061, USA

Abstract: We study the vulnerability of electrical networks through structural analysis from a graph theory point of view. We measure and compare several important structural properties of different electrical networks, including a real power grid and several synthetic grids, as well as other infrastructural networks. The properties we consider include the minimum dominating set size, the degree distribution and the shortest path distribution. We also study the network vulnerability under attacks in terms of maximum component size, number of components and flow vulnerability. Our results suggest that all grids are more vulnerable to targeted attacks than to random attacks. We also observe that the electrical networks have low treewidth, which explains some of the vulnerability. We prove that with a small treewidth, a few important structural properties can be computed more efficiently.

Keywords: electricity infrastructure; critical infrastructures; vulnerability; graph theory; electrical networks; power supply; attacks.

DOI: 10.1504/IJCIS.2009.024874

International Journal of Critical Infrastructures, 2009 Vol.5 No.3, pp.265 - 284

Published online: 02 May 2009 *

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