DISTRIBUTIONS OF LARGE-SCALE POWER OUTAGES: EXTREME VALUES AND THE EFFECT OF TRUNCATION

R.L. Zaretzki,∗ W.M. Briggs,∗∗ M. Sterling,∗∗∗ and M. Shankar∗∗∗∗

References

  1. [1] B. Carreras, D. Newman, I. Dobson, & A. Poole, Evidencefor self organized criticality in a time series of electric powersystem blackouts, IEEE Transactions on Circuits and SystemsI, 51(9), 2004, 1733–1740.
  2. [2] I. Dobson, B. Carreras, V. Lynch, & D. Newman, Complexsystems analysis of series of blackouts: Cascading failure, crit-icality, and self-organization, IREP Conference: Bulk PowerSystem Dynamics and Control – VI, Cortina d’Ampezzo, Italy –IREP2004, vol. 1, 22–27 August 2004, 438–451.
  3. [3] I. Dobson, B.A. Carreras, & V.E. Lynch, Complex systemsanalyses of series of blackouts: Cascading failure, criticalpoints, and self-organization, Chaos, 17(2), 2007, 026103.
  4. [4] P. Bak, How nature works (New York: Copernicus, 1996).
  5. [5] M. Stubna & J. Folwer, An application of the highly optimizedtolerance model to electrical blackouts, International Journalof Bifurcation and Chaos, 1(13), 2003, 237–242.
  6. [6] B. Carreras, D. Newman, I. Dobson, & A. Poole, Initialevidence for self organized criticality in electric power systemblackouts, Thirty-third Hawaii International Conference onSystem Sciences, San Francisco, CA, 2000.
  7. [7] J. Chen, J.S. Thorp, & M. Parashar, Analysis of electric powersystem disturbance data, Thirty-Fourth Hawaii InternationalConference on System Sciences, Maui, Hawaii, 2001.
  8. [8] G.K. Zipf, Human behavior and the principle of least effort(Cambridge, MA: Addison-Wesley, 1949).
  9. [9] H.A. Simon, On a class of skew distribution functions,Biometrika, 52(4), 1955, 425–440.
  10. [10] R. Perline, Strong, weak, and false inverse power laws, Statis-tical Science, 20(1), 2005, 68–88.
  11. [11] S. Coles, An introduction to statistical modeling of extremevalues (New York: Springer, 2001).
  12. [12] P. Embrechts, C. Kluppelberg, & T. Mikosch, Modelling ex-tremal events (New York: Springer, 1997).
  13. [13] A. Azzalini & A. Capitano, Distributions generated by per-turbation of symmetry with emphasis on a multivariate skewt distribution, Journal of the Royal Statistical Society, SeriesB, 65(2), 2003, 367–389.
  14. [14] H. David & H. Nagaraja, Order statistics (New York: JohnWiley, 2003).
  15. [15] V.F. Pisarenko & D. Sornette, Characterization of the frequencyof extreme events by the Generalized Pareto Distribution, Pureand Applied Geophysics, 160(12), 2003, 2343–2364.
  16. [16] S. Resnick, Heavy-tail phenomena (New York: Springer, 2007).
  17. [17] N.L. Johnson, S. Kotz, & N. Balakrishnan, Continuous uni-variate distributions (New York: John Wiley, 1995).
  18. [18] A. Azzalini, The SN package, 2006.
  19. [19] H. Akaike, A new look at the statistical model identification,IEEE Transactions on Automatic Control, 19(6), 1974, 716–723.
  20. [20] G. Cassella & R. Berger, Statistical inference (Pacific Grove,CA: Duxbury Press, 2001).
  21. [21] H. Bozdogan, Model selection and Akaike’s information crite-rion (aic): The general theory and its analytical extensions,Psychometrika, 52(3), 1987, 345–370.
  22. [22] R. Billinton & R.N. Allan, Reliability evaluation of powersystems (New York: Plenum Press, 1996).
  23. [23] M. Mitzenmacher, A brief history of generative models forpower law and lognormal distributions, Internet Mathematics,1(2), 2004, 226–251.
  24. [24] I. Dobson, D. Newman, B. Carreras, & V. Lynch, An ini-tial complex systems analysis of the risks of blackouts inpower transmission systems, CRIS International Conferenceon Power Systems and Communications Infrastructures forthe Future, Beijing, 23–27 September 2002.71

Important Links:

Go Back