A study of the impacts of flow direction and electrical constraints on vulnerability assessment of power grid using electrical betweenness measures

In this paper, we analyze the impacts of major electrical properties, including node constraints, line limits, and flow direction, on vulnerability assessment of power grid using several types of electrical betweenness measures. Specifically, we first propose a set of new electrical betweenness measures, which takes into account flow direction in power grids. Then, the impacts of major electrical properties on vulnerability assessment of power grid are analyzed by comparing the identification results of critical components based on the proposed electrical betweenness measures with those based on the other two types of electrical betweenness measures reported in the literature, which take into consideration node constraints and line limits, respectively. Analysis results show the important impact of flow direction on the identification of critical components. The results lead us to introduce a set of combined electrical betweenness measures that take into account node constraints, line limits, and flow direction together. Simulation results on the IEEE 300-bus system and the Italian power grid show that the combined electrical betweenness measures are superior in identifying critical components and more useful in assessing power grid vulnerability.

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

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

[3]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

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

[5]  Antonio Scala,et al.  Cascade failures and distributed generation in power grids , 2012, Int. J. Crit. Infrastructures.

[6]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[7]  Seth Blumsack,et al.  The Topological and Electrical Structure of Power Grids , 2010, 2010 43rd Hawaii International Conference on System Sciences.

[8]  Marco Aiello,et al.  Towards Decentralization: A Topological Investigation of the Medium and Low Voltage Grids , 2011, IEEE Transactions on Smart Grid.

[10]  A K M Zami-Ur Rahman,et al.  An Ex Ante Probabilistic Study of Market Power with Emphasis on the Transmission Constraints , 2011 .

[11]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Guido Caldarelli,et al.  Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science , 2007 .

[13]  Enrico Pons,et al.  A perspective overview of topological approaches for vulnerability analysis of power transmission grids , 2015, Int. J. Crit. Infrastructures.

[14]  Zhe Zhang,et al.  An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load , 2011 .

[15]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[16]  Y. Moreno,et al.  Instability of scale-free networks under node-breaking avalanches , 2001 .

[17]  Yang Jingyan,et al.  Vulnerability assessment of bulk power grid based on complex network theory , 2008, 2008 Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies.

[18]  Ake J Holmgren,et al.  Using Graph Models to Analyze the Vulnerability of Electric Power Networks , 2006, Risk analysis : an official publication of the Society for Risk Analysis.

[19]  S Arianos,et al.  Power grid vulnerability: a complex network approach. , 2008, Chaos.

[20]  Kai Sun,et al.  An Interaction Model for Simulation and Mitigation of Cascading Failures , 2014, IEEE Transactions on Power Systems.

[21]  Wolfgang Kröger,et al.  Performance of Electric Power Systems Under Physical Malicious Attacks , 2013, IEEE Systems Journal.

[22]  P. Hines,et al.  Do topological models provide good information about electricity infrastructure vulnerability? , 2010, Chaos.

[23]  Lu Zongxiang,et al.  Cascading failure analysis of bulk power system using small-world network model , 2005, 2004 International Conference on Probabilistic Methods Applied to Power Systems.

[24]  Benyun Shi,et al.  Decentralized control and fair load-shedding compensations to prevent cascading failures in a smart grid , 2015 .

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

[26]  Fei Xue,et al.  Analysis of structural vulnerabilities in power transmission grids , 2009, Int. J. Crit. Infrastructure Prot..

[27]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[28]  Di Wu,et al.  Extended Topological Metrics for the Analysis of Power Grid Vulnerability , 2012, IEEE Systems Journal.

[29]  Fei Xue,et al.  Structural vulnerability of power systems: A topological approach , 2011 .

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

[31]  Ming Ding,et al.  Reliability assessment to large-scale power grid based on small-world topological model , 2006, 2006 International Conference on Power System Technology.

[32]  Marco Aiello,et al.  The Power Grid as a Complex Network: a Survey , 2011, ArXiv.

[33]  Martí Rosas-Casals,et al.  Correlating empirical data and extended topological measures in power grid networks , 2015, Int. J. Crit. Infrastructures.

[34]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Wolfgang A. Halang,et al.  Understanding the cascading failures in Indian power grids with complex networks theory , 2013 .

[36]  L. Issacharoff,et al.  Influence of the topology on the power flux of the Italian high-voltage electrical network , 2009, 0909.1664.

[37]  Jun Yan,et al.  Cascading Failure Analysis With DC Power Flow Model and Transient Stability Analysis , 2015, IEEE Transactions on Power Systems.

[38]  Pierre Henneaux,et al.  Probability of failure of overloaded lines in cascading failures , 2015 .

[39]  Min Ouyang,et al.  Correlation analysis of different vulnerability metrics on power grids. , 2014 .

[40]  Anna Scaglione,et al.  The Node Degree Distribution in Power Grid and Its Topology Robustness under Random and Selective Node Removals , 2010, 2010 IEEE International Conference on Communications Workshops.

[41]  Anna Scaglione,et al.  Electrical centrality measures for electric power grid vulnerability analysis , 2010, 49th IEEE Conference on Decision and Control (CDC).

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

[43]  Seth Blumsack,et al.  A Centrality Measure for Electrical Networks , 2008, Proceedings of the 41st Annual Hawaii International Conference on System Sciences (HICSS 2008).

[44]  M. L. Sachtjen,et al.  Disturbances in a power transmission system , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

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

[48]  J. Ser,et al.  A Critical Review of Robustness in Power Grids Using Complex Networks Concepts , 2015 .

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

[50]  M. Ouyang.  Comparisons of purely topological model, betweenness based model and direct current power flow model to analyze power grid vulnerability. , 2013, Chaos.

[51]  Di Wu,et al.  The Concept of Betweenness in the Analysis of Power Grid Vulnerability , 2010, 2010 Complexity in Engineering.

[52]  Anna Filomena Carbone,et al.  Power Grid Complexity , 2011 .

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

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