Quantitative Vulnerability Analysis of Electric Power Networks

Holmgren, Å. J. 2006.Quantitative vulnerability analysis of electric power networks. Division of Safety Research, Department of Transport and Economics, KTH, Stockholm ISBN 10: 91-85539-01-5. 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.