Modeling cascading failures in the North American power grid

  • R. Kinney
  • P. Crucitti
  • R. AlbertEmail author
  • V. Latora
Statistical and Nonlinear Physics


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.


Neural Network Complex System Nonlinear Dynamics Power Transmission Single Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. National Transmission Grid Study, Department of Energy, 2002, http:// Google Scholar
  2. Electricity Technology Roadmap, 1999 Summary and Synthesis, by the Electric Power Research Institute, roadmap/ Google Scholar
  3. A.-L. Barabási, The New York Times, August 16 (2003) Google Scholar
  4. 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) Google Scholar
  5. R. Albert, H. Jeong, A.-L. Barabási, Nature 406, 378 (2000) CrossRefPubMedGoogle Scholar
  6. R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000) CrossRefPubMedGoogle Scholar
  7. D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000) CrossRefPubMedGoogle Scholar
  8. R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 86, 3682 (2001) CrossRefPubMedGoogle Scholar
  9. A.E. Motter, T. Nishikawa, Y. Lai, Phys. Rev. E 66, 065103 (2002) CrossRefGoogle Scholar
  10. P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 320, 622 (2003) Google Scholar
  11. R. Albert, I. Albert, G.L. Nakarado, Phys. Rev. E 69, 025103(R) (2004) CrossRefGoogle Scholar
  12. Y. Moreno, J.B. Gomez, A.F. Pacheco, Europhys. Lett. 58, 630 (2002) CrossRefGoogle Scholar
  13. P. Holme, B.J. Kim, Phys. Rev. E 65, 066109 (2002) CrossRefGoogle Scholar
  14. A.E. Motter, Y. Lai, Phys. Rev. E 66, 065102(R) (2002) CrossRefGoogle Scholar
  15. Y. Moreno, R. Pastor-Satorras, A. Vásquez, A. Vespignani, Europhys. Lett. 62, 292 (2003) CrossRefGoogle Scholar
  16. P. Crucitti, V. Latora, M. Marchiori, Phys. Rev. E 69, 045104(R) (2004) CrossRefGoogle Scholar
  17. P. Crucitti, V. Latora, M. Marchiori, Physica A 338, 92 (2004) Google Scholar
  18. I. Dobson, B.A. Carreras, D.E. Newman, in Proceedings of Hawaii International Conference on System Sciences, January 2003, Hawaii Google Scholar
  19. P. Echenique, J. Gómez-Gardeñes, Y. Moreno, cond-mat/0412053 Google Scholar
  20. Our access to this data was made possible by the National Renewable Energy Laboratory at Golden, Colorado Google Scholar
  21. S. Wasserman, K. Faust, Social Networks Analysis (Cambridge University Press, Cambridge, 1994) Google Scholar
  22. V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001) CrossRefPubMedGoogle Scholar
  23. J. Smith, Commun. ACM 31, 1202 (1988) CrossRefGoogle Scholar
  24. M.L. Van Name, B. Catchings, PC Magazine 1421, 13 (1996) Google Scholar
  25. K. Hwang, F.A. Briggs, Computer Architecture and Parallel Processing (McGraw-Hill, 1988) Google Scholar
  26. R. Jain, The Art of Computer Systems Performance Analysis (Wiley, New York, 1991) Google Scholar
  27. W. Sweet, IEEE Spectrum 37, 43 (2000) CrossRefGoogle Scholar
  28. T.J. Overbay, American Scientist 88, (2000) 220.. Google Scholar
  29. Dromey Design electrical distribution analysis software, Google Scholar
  30. T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms (MIT Press, 1990) Google Scholar
  31. V. Latora, M. Marchiori, Phys. Rev. E 71, 015103(R) (2005) CrossRefGoogle Scholar
  32. K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001) CrossRefPubMedGoogle Scholar
  33. M.E.J. Newman, Phys. Rev. E 64, 016132 (2001) CrossRefGoogle Scholar
  34. L.C. Freeman, Sociometry 40, 35 (1977) Google Scholar
  35. 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]. Google Scholar
  36. M.L. Wald, R. Perez-Pena, N. Banerjee, The New York Times, Aug. 16 (2003) Google Scholar
  37. L.A.N. Amaral, A. Scala, M. Barthélémy, E.H. Stanley, Proc. Natl. Acad. Sci. USA 97, 11 (2000) CrossRefGoogle Scholar
  38. 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 Google Scholar
  39. B.A. Carreras, D.E. Newman, I. Dolrou, A.B. Poole, in Proceedings of Hawaii International Conference on System Sciences, January 2000, Maui, Hawaii Google Scholar
  40. B.A. Carreras, V.E. Lynch, D.E. Newman, I. Dobson, in Proceedings of Hawaii International Conference on System Science, January 2003, Hawaii Google Scholar
  41. A.E. Motter, Phys. Rev. Lett. 93, 098701 (2004) CrossRefPubMedGoogle Scholar
  42. 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. Google Scholar
  43. M.E.J. Newman, preprint cond-mat/0309045 (2003); M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004) CrossRefGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of Missouri-RollaRollaUSA
  2. 2.Scuola Superiore di CataniaCataniaItaly
  3. 3.Department of Physics and Huck Institutes of Life Sciences, Pennsylvania State University, University ParkParkUSA
  4. 4.Dipartimento di Fisica ed AstronomiaUniversità di Catania and INFNCataniaItaly

Personalised recommendations