The structure of electrical networks: a graph theory based analysis

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.

[1]  James H. Lambert,et al.  Inoperability Input-Output Model for Interdependent Infrastructure Sectors. I: Theory and Methodology , 2005 .

[2]  Jan Arne Telle,et al.  Algorithms for Vertex Partitioning Problems on Partial k-Trees , 1997, SIAM J. Discret. Math..

[3]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[4]  Edith Cohen.  Efficient parallel shortest-paths in digraphs with a separator decomposition , 1993, SPAA '93.

[5]  Hans L. Bodlaender,et al.  A Tourist Guide through Treewidth , 1993, Acta Cybern..

[6]  James H. Lambert,et al.  Inoperability Input-Output Model for Interdependent Infrastructure Sectors. II: Case Studies , 2005 .

[7]  Richard G. Little,et al.  Controlling Cascading Failure: Understanding the Vulnerabilities of Interconnected Infrastructures , 2002 .

[8]  Réka Albert,et al.  Structural vulnerability of the North American power grid. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Hans L. Bodlaender,et al.  Only few graphs have bounded treewidth , 1992 .

[10]  M. Amin,et al.  Modeling and control of complex interactive networks [Guest Editorial] , 2002 .

[11]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[12]  Joseph Naor,et al.  Fast approximate graph partitioning algorithms , 1997, SODA '97.

[13]  Harry B. Hunt,et al.  Efficient Algorithms for Solving Systems of Linear Equations and Path Problems , 1992, STACS.

[14]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[15]  Massoud Amin.  North America's Electricity Infrastructure: Are We Ready for More Perfect Storms? , 2003, IEEE Secur. Priv..

[16]  Ian Dobson,et al.  Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model , 2005 .

[17]  James S. Thorp,et al.  Expose hidden failures to prevent cascading outages [in power systems] , 1996 .

[18]  V. E. Lynch,et al.  Critical points and transitions in an electric power transmission model for cascading failure blackouts. , 2002, Chaos.

[19]  Lamine Mili,et al.  Risk assessment of catastrophic failures in electric power systems , 2004, Int. J. Crit. Infrastructures.

[20]  Madhav V. Marathe,et al.  Modeling and simulation of large biological, information and socio-technical systems: an interaction based approach , 2006 .

[21]  Vibhav Gogate,et al.  A Complete Anytime Algorithm for Treewidth , 2004, UAI.

[22]  By Massoud Amin.  Modeling and Control of Complex Interactive Networks , 2001 .

[23]  Edith Cohen.  Efficient Parallel Shortest-Paths in Digraphs with a Separator Decomposition , 1996, J. Algorithms.

[24]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.