Vulnerability Analysis of Power Grids Using Modified Centrality Measures

The aim of this paper is to propose modified centrality measures as a tool to identify critical nodes before a vulnerability analysis is performed in an electrical power grid. Pair dependency centrality is weighted using the grid active power flow, and this becomes the basis to define closeness and betweenness of its nodes, and hence to identify the most critical ones. To support the idea of using modified centralities, four power grids are tested to be either exponential or scale-free. To evaluate the proposal, information obtained via modified centrality measures is used to calculate global efficiency of the power grids.

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

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

[3]  Stephen P. Borgatti,et al.  Network Theory , 2013 .

[4]  L. Freeman Centrality in social networks conceptual clarification , 1978 .

[5]  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.

[6]  Charles Kim,et al.  Vulnerability Assessment of Power Grid Using Graph Topological Indices , 2007 .

[7]  Kwan-Liu Ma,et al.  The Derivatives of Centrality and their Applications in Visualizing Social Networks , 2009 .

[8]  Robin Roy Physical vulnerability of electric systems to sabotage , 1990 .

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

[10]  Jilai Yu,et al.  Priority evaluation of transmission lines based on vulnerability assemment , 2009, 2009 International Conference on Sustainable Power Generation and Supply.

[11]  Agata Fronczak,et al.  Average path length in random networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Bennouas Toufik Modélisation de parcours du Web et calcul de communautés par émergence , 2005 .

[13]  Linton C. Freeman,et al.  The gatekeeper, pair-dependency and structural centrality , 1980 .

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

[15]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[16]  H. R. Pota,et al.  Complex network framework based dependency matrix of electric power grid , 2011, AUPEC 2011.

[17]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

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

[19]  P. Gomes,et al.  New strategies to improve bulk power system security: lessons learned from large blackouts , 2004, IEEE Power Engineering Society General Meeting, 2004..

[20]  Martin Suter,et al.  Small World , 2002 .

[21]  Daehyun Ban A Flow-Based Centrality Measure through Resistance Distances in Smart-Grid Networks , 2011, 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011.

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

[23]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[24]  Alex Bavelas A Mathematical Model for Group Structures , 1948 .

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

[26]  Fei Xue,et al.  Extended topological approach for the assessment of structural vulnerability in transmission networks , 2010 .

[27]  C. W. Taylor,et al.  Model validation for the August 10, 1996 WSCC system outage , 1999 .

[28]  Huan Zhou,et al.  Vulnerability Assessment of Power Grid Based on Complex Network Theory , 2009, 2009 Asia-Pacific Power and Energy Engineering Conference.

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

[30]  Pierluigi Siano,et al.  Distributed Generation Capacity Evaluation Using Combined Genetic Algorithm and OPF , 2007 .