The Topological and Electrical Structure of Power Grids

Numerous recent papers have found important relationships between network structure and risks within networks. These results indicate that network structure can dramatically affect the relative effectiveness of risk identification and mitigation methods. With this in mind this paper provides a comparative analysis of the topological and electrical structure of the IEEE 300 bus and the Eastern United States power grids. Specifically we compare the topology of these grids with that of random [1], preferential-attachment [2] and small-world [3] networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these abstract models do not provide substantial utility for modeling power grids. To better represent the topological properties of power grids we introduce a new graph generating algorithm, the minimum distance graph, that produces networks with properties that more nearly match those of known power grids. While these topological comparisons are useful, they do not account for the physical laws that govern flows in electricity networks. To elucidate the electrical structure of power grids, we propose a new method for representing electrical structure as a weighted graph. This analogous representation is based on electrical distance rather than topological connections. A comparison of these two representations of the test power grids reveals dramatic differences between the electrical and topological structure of electrical power systems.

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

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

[3]  Ian Dobson,et al.  Evidence for self-organized criticality in a time series of electric power system blackouts , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Ian Dobson,et al.  The Impact of Various Upgrade Strategies on the Long-Term Dynamics and Robustness of the Transmission Grid , 2004 .

[5]  Anna Scaglione,et al.  Generating Random Topology Power Grids , 2008, Proceedings of the 41st Annual Hawaii International Conference on System Sciences (HICSS 2008).

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

[7]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[8]  Stanley Milgram,et al.  An Experimental Study of the Small World Problem , 1969 .

[9]  Åke J. Holmgren,et al.  Using Disturbance Data to Assess Vulnerability of Electric Power Delivery Systems , 2006 .

[10]  A. Bose,et al.  Localized reactive power markets using the concept of voltage control areas , 2004, 2006 IEEE Power Engineering Society General Meeting.

[11]  M. E. J. Newman,et al.  Mixing patterns in networks: Empirical results and models , 2002 .

[12]  P. Hines,et al.  Reciprocally altruistic agents for the mitigation of cascading failures in electrical power networks , 2008, 2008 First International Conference on Infrastructure Systems and Services: Building Networks for a Brighter Future (INFRA).

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

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

[15]  P. Hines,et al.  Large blackouts in North America: Historical trends and policy implications , 2009 .

[16]  Rae Zimmerman,et al.  Risk-management and risk-analysis-based decision tools for attacks on electric power. , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[17]  M. Ilić,et al.  A Quantitative Analysis of the Relationship Between Congestion and Reliability in Electric Power Networks , 2007 .

[18]  Kathleen M. Carley,et al.  Modeling the Structure and Effectiveness of Intelligence Organizations: Dynamic Information Flow Simulation , 2003 .

[19]  Å. Holmgren.  A Framework for Vulnerability Assessment of Electric Power Systems , 2007 .

[20]  Mohamed A. El-Sharkawi,et al.  Modern Heuristic Optimization Techniques , 2008 .

[21]  A. Bose,et al.  A fast voltage security assessment method using adaptive bounding , 1999, Proceedings of the 21st International Conference on Power Industry Computer Applications. Connecting Utilities. PICA 99. To the Millennium and Beyond (Cat. No.99CH36351).

[22]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  D. Watts,et al.  A generalized model of social and biological contagion. , 2005, Journal of theoretical biology.

[24]  J. C. Sabonnadiere,et al.  Structural analysis of the electrical system , 1989 .

[25]  Paul Erdös,et al.  On random graphs, I , 1959 .

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

[27]  Mohamed A. El-Sharkawi,et al.  Modern heuristic optimization techniques :: theory and applications to power systems , 2008 .

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

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

[30]  Lee Garber,et al.  Denial-of-Service Attacks Rip the Internet , 2000, Computer.

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

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

[33]  D. Watts,et al.  Multiscale, resurgent epidemics in a hierarchical metapopulation model. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[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]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

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

[37]  Joel C. Miller,et al.  Effective vaccination strategies for realistic social networks , 2007 .

[38]  A. Sasson,et al.  Automatic Contingency Selection for On-Line Security Analysis - Real-Time Tests , 1979, IEEE Transactions on Power Apparatus and Systems.

[39]  Sandip Roy,et al.  Power System Extreme Event Detection: The Vulnerability Frontier , 2007, Proceedings of the 41st Annual Hawaii International Conference on System Sciences (HICSS 2008).

[40]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[41]  K.E. Holbert,et al.  PRA for vulnerability assessment of power system infrastructure security , 2005, Proceedings of the 37th Annual North American Power Symposium, 2005..

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

[43]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[44]  Paul S. Fischbeck,et al.  Estimating the Shape of Covert Networks , 2003 .

[45]  Liangzhong Yao,et al.  Vulnerability assessment for cascading failures in electric power systems , 2009, 2009 IEEE/PES Power Systems Conference and Exposition.

[46]  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.

[47]  J. C. Sabonnadiere,et al.  Structural Analysis of the Electrical System: Application to Secondary Voltage Control in France , 1989, IEEE Power Engineering Review.

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

[49]  Q. C. Lu,et al.  A new formulation of generator penalty factors , 1995 .