Power grid vulnerability: a complex network approach.

Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.

[1]  Sergi Valverde,et al.  Topology and evolution of technology innovation networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Guanrong Chen,et al.  Universal robustness characteristic of weighted networks against cascading failure. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Vittorio Rosato,et al.  Topological properties of high-voltage electrical transmission networks , 2007 .

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

[5]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[6]  Christian Posse,et al.  Evaluating North American Electric Grid Reliability Using the Barabasi-Albert Network Model , 2004, nlin/0408052.

[7]  B. M. Fulk MATH , 1992 .

[8]  G. Ejebe,et al.  Automatic Contingency Selection , 1979, IEEE Transactions on Power Apparatus and Systems.

[9]  IEEE Power Engineering Society General Meeting , 2007, 2007 IEEE Power Engineering Society General Meeting.

[10]  Anna T. Lawniczak,et al.  Network traffic behaviour near phase transition point , 2005, nlin/0510070.

[11]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[12]  V. Gol'dshtein,et al.  Vulnerability and Hierarchy of Complex Networks , 2004, cond-mat/0409298.

[13]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[14]  Feng Liu,et al.  Empirical analysis of the ship-transport network of China. , 2007, Chaos.

[15]  Adilson E Motter,et al.  Introduction: optimization in networks. , 2007, Chaos.

[16]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[17]  Xiaogang Jin,et al.  Optimal structure of complex networks for minimizing traffic congestion. , 2007, Chaos.

[18]  J. Rogers Chaos , 1876 .

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

[20]  Vito Latora,et al.  Modeling cascading failures in the North American power grid , 2005 .

[21]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[22]  V. Latora,et al.  Multiscale vulnerability of complex networks. , 2007, Chaos.

[23]  K. Goh,et al.  Load distribution in weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Benjamin A Carreras,et al.  Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization. , 2007, Chaos.

[25]  Yoshisuke Ueda,et al.  Attractor and Basin Portraits of a Double Swing Power System , 2004, Int. J. Bifurc. Chaos.

[26]  Massimo Marchiori,et al.  A topological analysis of the Italian electric power grid , 2004 .

[27]  Yong Yu,et al.  Transport optimization on complex networks , 2007, Chaos.

[28]  J Doyle,et al.  Highly optimized tolerance and power laws in dense and sparse resource regimes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Massimo Marchiori,et al.  Vulnerability and protection of infrastructure networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Martí Rosas-Casals,et al.  Robustness of the European power grids under intentional attack. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[32]  川村 修,et al.  海外諸国向け火力発電所の設計(英国)("IEEE Transactions on Power Apparatus and Systems"1968年5月号) , 1969 .

[33]  F. Sorrentino Effects of the network structural properties on its controllability. , 2007, Chaos.

[34]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[35]  A. Motter,et al.  Fluctuation-driven capacity distribution in complex networks , 2008, 0805.3725.

[36]  Gang Zhang,et al.  Synchronization of complex dynamical networks via impulsive control. , 2007, Chaos.

[37]  B A Carreras,et al.  Complex dynamics of blackouts in power transmission systems. , 2004, Chaos.

[38]  Massimo Marchiori,et al.  LOCATING CRITICAL LINES IN HIGH-VOLTAGE ELECTRICAL POWER GRIDS , 2005, The Random and Fluctuating World.

[39]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[40]  J. Gómez-Gardeñes,et al.  Scaling breakdown in flow fluctuations on complex networks. , 2008, Physical review letters.

[41]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[42]  Adilson E Motter Cascade control and defense in complex networks. , 2004, Physical review letters.

[43]  Yoshisuke Ueda,et al.  Basin Configuration of a Six-Dimensional Model of an Electric Power System , 2002, Int. J. Bifurc. Chaos.

[44]  Ricard V. Solé,et al.  Topological Vulnerability of the European Power Grid under Errors and Attacks , 2007, Int. J. Bifurc. Chaos.

[45]  Celso Grebogi,et al.  International Journal of Bifurcation and Chaos: Editorial , 2008 .

[46]  Massimo Marchiori,et al.  Model for cascading failures in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Henk Sol,et al.  Proceedings of the 54th Hawaii International Conference on System Sciences , 1997, HICSS 2015.

[49]  Massimo Marchiori,et al.  How the science of complex networks can help developing strategies against terrorism , 2004 .

[50]  Adilson E Motter,et al.  Range-based attack on links in scale-free networks: are long-range links responsible for the small-world phenomenon? , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Jiang Chuanwen,et al.  A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation , 2005, Math. Comput. Simul..