Abstract.
The North American power grid is one of the most complex technological networks, and its interconnectivity allows both for long-distance power transmission and for the propagation of disturbances. We model the power grid using its actual topology and plausible assumptions about the load and overload of transmission substations. Our results indicate that the loss of a single substation can result in up to \(25\%\) loss of transmission efficiency by triggering an overload cascade in the network. The actual transmission loss depends on the overload tolerance of the network and the connectivity of the failed substation. We systematically study the damage inflicted by the loss of single nodes, and find three universal behaviors, suggesting that \(40\%\) of the transmission substations lead to cascading failures when disrupted. While the loss of a single node can inflict substantial damage, subsequent removals have only incremental effects, in agreement with the topological resilience to less than \(1\%\) node loss.
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References
National Transmission Grid Study, Department of Energy, 2002, http:// www.eh.doe.gov/ntgs/reports.html
Electricity Technology Roadmap, 1999 Summary and Synthesis, by the Electric Power Research Institute, http://www.epri.com/corporate/discover_epri/ roadmap/
A.-L. Barabási, The New York Times, August 16 (2003)
R. Albert, A.-L. Barabási, Rev. of Mod. Phys. 74, 44 (2002); A.-L. Barabási, Linked: The New Science of Networks (Perseus Publishing, Cambridge, 2002); D.J. Watts, Six Degrees: The Science of a Connected Age (W.W. Norton & Co., New York, 2003); S.N. Dorogovtsev and J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003); M.E.J. Newman, SIAM Review 45, 167 (2003)
R. Albert, H. Jeong, A.-L. Barabási, Nature 406, 378 (2000)
R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000)
D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000)
R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 86, 3682 (2001)
A.E. Motter, T. Nishikawa, Y. Lai, Phys. Rev. E 66, 065103 (2002)
P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 320, 622 (2003)
R. Albert, I. Albert, G.L. Nakarado, Phys. Rev. E 69, 025103(R) (2004)
Y. Moreno, J.B. Gomez, A.F. Pacheco, Europhys. Lett. 58, 630 (2002)
P. Holme, B.J. Kim, Phys. Rev. E 65, 066109 (2002)
A.E. Motter, Y. Lai, Phys. Rev. E 66, 065102(R) (2002)
Y. Moreno, R. Pastor-Satorras, A. Vásquez, A. Vespignani, Europhys. Lett. 62, 292 (2003)
P. Crucitti, V. Latora, M. Marchiori, Phys. Rev. E 69, 045104(R) (2004)
P. Crucitti, V. Latora, M. Marchiori, Physica A 338, 92 (2004)
I. Dobson, B.A. Carreras, D.E. Newman, in Proceedings of Hawaii International Conference on System Sciences, January 2003, Hawaii
P. Echenique, J. Gómez-Gardeñes, Y. Moreno, cond-mat/0412053
Our access to this data was made possible by the National Renewable Energy Laboratory at Golden, Colorado
S. Wasserman, K. Faust, Social Networks Analysis (Cambridge University Press, Cambridge, 1994)
V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001)
J. Smith, Commun. ACM 31, 1202 (1988)
M.L. Van Name, B. Catchings, PC Magazine 1421, 13 (1996)
K. Hwang, F.A. Briggs, Computer Architecture and Parallel Processing (McGraw-Hill, 1988)
R. Jain, The Art of Computer Systems Performance Analysis (Wiley, New York, 1991)
W. Sweet, IEEE Spectrum 37, 43 (2000)
T.J. Overbay, American Scientist 88, (2000) 220..
Dromey Design electrical distribution analysis software, http://www.dromeydesign.com/dess/lfa.htm
T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms (MIT Press, 1990)
V. Latora, M. Marchiori, Phys. Rev. E 71, 015103(R) (2005)
K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001)
M.E.J. Newman, Phys. Rev. E 64, 016132 (2001)
L.C. Freeman, Sociometry 40, 35 (1977)
There are several alternative possibilities to the node load we are using in this paper for the cases in which the quantity of interest (information, bits, electric power) does not travel through geodesic paths only. Among such extensions we mention the flow betweenness and the random path betweenness [43] which include non-geodesic as well as geodesic paths. Nevertheless, both these betweennesses are more computationally demanding than the shortest path betweenness [43].
M.L. Wald, R. Perez-Pena, N. Banerjee, The New York Times, Aug. 16 (2003)
L.A.N. Amaral, A. Scala, M. Barthélémy, E.H. Stanley, Proc. Natl. Acad. Sci. USA 97, 11 (2000)
Note that the threshold of tolerance, below which efficiency loss due to cascading failures are observed, depends on the parameters of the degree and load distributions
B.A. Carreras, D.E. Newman, I. Dolrou, A.B. Poole, in Proceedings of Hawaii International Conference on System Sciences, January 2000, Maui, Hawaii
B.A. Carreras, V.E. Lynch, D.E. Newman, I. Dobson, in Proceedings of Hawaii International Conference on System Science, January 2003, Hawaii
A.E. Motter, Phys. Rev. Lett. 93, 098701 (2004)
Note that it is not possible to reduce the load of transmission substations by eliminating low-load leaf nodes. These nodes correspond to generators with one outgoing power line or distribution substations that have one incoming high-voltage power line. Consequently eliminating these nodes would diminish power generation or disconnect it from power consumption.
M.E.J. Newman, preprint cond-mat/0309045 (2003); M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004)
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Kinney, R., Crucitti, P., Albert, R. et al. Modeling cascading failures in the North American power grid. Eur. Phys. J. B 46, 101–107 (2005). https://doi.org/10.1140/epjb/e2005-00237-9
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DOI: https://doi.org/10.1140/epjb/e2005-00237-9