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Using graph models to analyze the vulnerability of electric power networks
KTH, School of Architecture and the Built Environment (ABE), Transport and Economics, Safety Research.
2006 (English)In: Risk Analysis, ISSN 0272-4332, E-ISSN 1539-6924, Vol. 26, no 4, 955-969 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we model electric power delivery networks as graphs, and conduct studies of two power transmission grids, i.e., the Nordic and the western states (U.S.) transmission grid. We calculate values of topological (structural) characteristics of the networks and compare their error and attack tolerance (structural vulnerability), i.e., their performance when vertices are removed, with two frequently used theoretical reference networks (the Erdos-Renyi random graph and the Barabasi-Albert scale-free network). Further, we perform a structural vulnerability analysis of a fictitious electric power network with simple structure. In this analysis, different strategies to decrease the vulnerability of the system are evaluated. Finally, we present a discussion on the practical applicability of graph modeling.

Place, publisher, year, edition, pages
2006. Vol. 26, no 4, 955-969 p.
Keyword [en]
electric power system; graph theory; intentional attack; network analysis; random failure; vulnerability
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-5740DOI: 10.1111/j.1539-6924.2006.00791.xISI: 000239897400009ScopusID: 2-s2.0-33748439665OAI: diva2:10211
QC 20100831Available from: 2006-05-17 Created: 2006-05-17 Last updated: 2010-12-06Bibliographically approved
In thesis
1. Quantitative vulnerability analysis of electric power networks
Open this publication in new window or tab >>Quantitative vulnerability analysis of electric power networks
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Disturbances in the supply of electric power can have serious implications for everyday life as well as for national (homeland) security. A power outage can be initiated by natural disasters, adverse weather, technical failures, human errors, sabotage, terrorism, and acts of war. The vulnerability of a system is described as a sensitivity to threats and hazards, and is measured by P (Q(t) > q), i.e. the probability of at least one disturbance with negative societal consequences Q larger than some critical value q, during a given period of time (0,t]. The aim of the thesis is to present methods for quantitative vulnerability analysis of electric power delivery networks to enable effective strategies for prevention, mitigation, response, and recovery to be developed.

Paper I provides a framework for vulnerability assessment of infrastructure systems. The paper discusses concepts and perspectives for developing a methodology for vulnerability analysis, and gives examples related to power systems.

Paper II analyzes the vulnerability of power delivery systems by means of statistical analysis of Swedish disturbance data. It is demonstrated that the size of large disturbances follows a power law, and that the occurrence of disturbances can be modeled as a Poisson process.

Paper III models electric power delivery systems as graphs. Statistical measures for characterizing the structure of two empirical transmission systems are calculated, and a structural vulnerability analysis is performed, i.e. a study of the connectivity of the graph when vertices and edges are disabled.

Paper IV discusses the origin of power laws in complex systems in terms of their structure and the dynamics of disturbance propagation. A branching process is used to model the structure of a power distribution system, and it is shown that the disturbance size in this analytical network model follows a power law.

Paper V shows how the interaction between an antagonist and the defender of a power system can be modeled as a game. A numerical example is presented, and it is studied if there exists a dominant defense strategy, and if there is an optimal allocation of resources between protection of components, and recovery.

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. x, 37 p.
Trita-TEC-PHD, ISSN 1653-4468 ; 06:001
Safety Analysis, vulnerability, homeland security, risk analysis, network, electric power system, blackout, power law, statistical analysis, graph theory, branching process, game theory, Säkerhetsanalys
National Category
Engineering and Technology
urn:nbn:se:kth:diva-3969 (URN)91-85539-01-5 (ISBN)
Public defence
2006-06-02, F2, KTH, Lindstedsvägen 28, Stockholm, 10:15
QC 20100831Available from: 2006-05-17 Created: 2006-05-17 Last updated: 2010-08-31Bibliographically approved

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