Controlled test for predictive power of Lyapunov exponents: Their inability to predict epileptic seizures
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Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents co...
Bifurcation analysis of a model of the budding yeast cell cycle
We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeas...
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Complex dynamics of blackouts in power transmission systems
Chaos 14, 643 (2004); doi:10.1063/1.1781391
Published 1 September 2004
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In order to study the complex global dynamics of a series of blackouts in power transmission systems a dynamical model of such a system has been developed. This model includes a simple representation of the dynamical evolution by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of generator capacity. Two types of blackouts have been identified, each having different dynamical properties. One type of blackout involves the loss of load due to transmission lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackout over the other depends on operational conditions and the proximity of the system to one of its two critical points. The model displays characteristics such as a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America. ©2004 American Institute of Physics.
| History: | Received 27 August 2003; accepted 21 June 2004; published 1 September 2004 |
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http://link.aip.org/link/?CHAOEH/14/643/1 |
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REFERENCES (25)
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- D. N. Ewart,
IEEE Spectrum 15, 36 (1978) . - B. A. Carreras, D. E. Newman, I. Dobson, and A. B. Poole, "Evidence for self-organized criticality in electric power system blackouts" (to be published).
- J. Chen, J. S. Thorp, and M. Parashar, "Analysis of electric power disturbance data," 34th Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001.
- Information on electric systems disturbances in North America can be downloaded from the NERC website at http://www.nerc.com/dawg/database.html.
- B. A. Carreras, V. Lynch, I. Dobson, and D. E. Newman, "Blackout mitigation assessment in power transmission systems," 36th Hawaii International Conference on System Sciences, Hawaii, January 2003. Available from IEEE at http://ieeexplore.ieee.org.
- I. Dobson, B. A. Carreras, V. Lynch, and D. E. Newman, "An initial model for complex dynamics in electric power system blackouts," 34th Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001. Available from IEEE at http://ieeexplore.ieee.org.
- B. A. Carreras, D. E. Newman, I. Dobson, and A. B. Poole, "Modeling blackout dynamics in power transmission networks with simple structure," 34th Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001. Available from IEEE at http://ieeexplore.ieee.org.
- B. A. Carreras, V. Lynch, I. Dobson, and D. E. Newman, Chaos 12, 985 (2002).
- P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
- M. L. Sachtjen, B. A. Carreras, and V. E. Lynch, Phys. Rev. E 61, 4877 (2000).
- J. Chen and J. S. Thorp, "A reliability study of transmission system protection via a hidden failure DC load flow model," IEEE Fifth International Conference on Power System Management and Control, 17–19 April 2002, pp. 384–389.
- J. Chen, J. S. Thorp, and I. Dobson, "Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model," preprint (to be published).
- M. D. Stubna and J. Fowler,
Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, 237 (2003) . - S. Roy, C. Asavathiratham, B. C. Lesieutre, and G. C. Verghese, "Network models: Growth, dynamics, and failure," in Proceedings of the 34th Annual Hawaii International Conference on System Sciences, 3–6 January 2001, pp. 728–737.
- D. L. Pepyne, C. G. Panayiotou, C. G. Cassandras, and Y.-C. Ho, "Vulnerability assessment and allocation of protection resources in power systems," in Proceedings of the American Control Conference, Vol. 6, 25–27 June 2001, pp. 4705–4710.
- C. L. DeMarco, "A phase transition model for cascading network failure,"
IEEE Control Syst. Mag. 21, 40–51 (2001) . - P. A. Parrilo, S. Lall, F. Paganini, G. C. Verghese, B. C. Lesieutre, and J. E. Marsden, "Model reduction for analysis of cascading failures in power systems," in Proceedings of the 1999 American Control Conference, Vol. 6, 2–4 June 1999, pp. 4208–4212.
- B. Stott and E. Hobson,
IEEE Trans. Power Appar. Syst. PAS-97, 1713 (1978) . - B. Stott and E. Hobson,
IEEE Trans. Power Appar. Syst. PAS-97, 1721 (1978) . - B. Stott and J. L. Marinho, IEEE Trans. Power Appar. Syst. PAS-97, 837 (1979).
- The IEEE 118 bus network model is a standard test system; see http://www.ee.washington.edu/research/pstca/.
- Statistical Yearbook of the electric utility industry/1998, published by Edison Electric Institute (1998).
- H. E. Hurst,
Trans. Am. Soc. Civ. Eng. 116, 770 (1951) . - B. B. Mandelbrot and J. R. Wallis,
Water Resour. Res. 4, 909 (1969) . - W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1988).
