Period-doubling route to chaos in an electrical power system
Period-doubling route to chaos in an electrical power system
- Author(s): B. Lee and V. Ajjarapu
- DOI: 10.1049/ip-c.1993.0071
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- Author(s): B. Lee 1 and V. Ajjarapu 1
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View affiliations
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Affiliations:
1: Department of Electrical Engineering and Computer Engineering, Iowa State University, Ames, USA
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Affiliations:
1: Department of Electrical Engineering and Computer Engineering, Iowa State University, Ames, USA
- Source:
Volume 140, Issue 6,
November 1993,
p.
490 – 496
DOI: 10.1049/ip-c.1993.0071 , Print ISSN 0143-7046, Online ISSN 2053-7921
This in-depth introduction to chaos in an electrical power system presents techniques for recognising and classifying chaotic behaviour. A cascade of period-doubling bifurcation, which leads to chaos, is observed. Results on a sample power system are presented. The practical significance of chaos for power system operation is also discussed.
Inspec keywords: bifurcation; chaos; power systems; power system stability
Other keywords:
Subjects: Power systems
References
-
-
1)
- B.Z. Kaplan , D. Yardeni . Possible chaotic phenomenon in a three-phase oscillator. IEEE Trans. , 8 , 1148 - 1151
-
2)
- : `Summary of interaction dynamics task force's survey on voltage collapse phenomenon, North American Electric Reliability Council', NERC Report, August 1991, Survey of the voltage collapse phenomenon.
-
3)
- Chiang, H.D., Dobson, I., Thomas, R.J., Thorp, J.S., Fekih-Ahmed, L.: `On voltage collapse in electric power systems', IEEE PICA conference, 1989, Seattle, WA, USA.
-
4)
- B.D. Hassard , N.D. Kazarinoff , Y.H. Wan . (1981) , Theory and applications of Hopf bifurcation.
-
5)
- R. Seydel . (1988) , From equilibrium to chaos.
-
6)
- Rajagopalan, C., Sauer, P.W., Pai, M.A.: `Analysis of voltage control system exhibiting Hopf bifurcation', Proceedings of 28th IEEE conference on Decision and control, December 1989, Tampa, FL, USA, p. 332–335.
-
7)
- Abed, E.H., Alexander, J.C., Wang, H., Hamdan, A.M.A., Lee, H.C.: `Dynamic bifurcations in a power system model exhibiting voltage collapse', Technical research report, 1992.
-
8)
- V.I. Arnold . (1983) , Geometrical methods in the theory of ordinary dif ferential equations.
-
9)
- E. Doedel . (1986) , AUTO, Software for continuation and bifurcation problems in ordinary differential equations.
-
10)
- Abed, E.H., Hamdan, A., Lee, H.C., Parlos, A.: `On bifurcations in power system models and voltage collapse', Proceedings of 27th IEEE conference on Decision and control, 1990, Honolulu, HI, USA, p. 3014, 3015.
-
11)
- M.A. Nayfeh , A.M.A. Hamdan , A.H. Nayfeh . Chaos and instability in a power system—primary resonant case. Nonlinear dynamics , 313 - 339
-
12)
- V. Ajjarapu , B. Lee . Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system. IEEE Trans. , 1 , 424 - 431
-
13)
- Chiang, H.D., Liu, C.W., Varaiya, P.P., Wu, F.F., Lauby, M.G.: `Chaos in a simple power system', paper 92WM151-1PWRS, IEEE PES winter meeting.
-
14)
- Tamura, Y.: `A scenario of voltage collapse In a power system with induction motor loads with a cascaded transition of bifurcation', Proceedings of workshop on bulk power system voltage phenomena, Voltage stability and security, August 1991, USA, Deck Creek Lake, MD, p. 332–335.
-
15)
- J. Sotomayor , P.M. Peixoto . (1973) Generic bifurcations of dynamical systems, Dynamical systems.
-
16)
- R.M. May . Simple mathematical models with very complicated dynamics. Nature , 459 - 467
-
17)
- B.-L. Hao . (1990) , Chaos II.
-
18)
- M.J. Feigenbaum . Quantitative universality for a class of non linear transformations. J. Stat. Phys. , 1 , 25 - 52
-
19)
- P. Varaiya , F.F. Wu , R.-L. Chen . Direct methods for transient stability analysis of power systems: recent results. Proc. IEEE , 1703 - 1715
-
20)
- V. Ajjarapu , B. Lee . Discussion of Reference 11 in. IEEE Trans.
-
21)
- Lai, L.L., Jaing, Z.Y., Jaing, R.H.: `Chaotic phenomena in power systems', Proceedings of international conference Control'91, 1991, UK, Edinburgh.
-
22)
- N. Koppel , R.B. Washburn . Chaotic motions in the two-degree-of-freedom swing equations. IEEE Trans. , 738 - 746
-
23)
- Walve, K.: `Modeling of power system components at severe disturbances', paper 38-18, CIGRE international conference on Large high-voltage electric systems, 1986, p. 38–18.
-
24)
- J.C. Alexander . Oscillatory solution of a model system of non linear swing equation. Int. J. Electr. Power Energy Syst. , 130 - 136
-
25)
- E.H. Abed . Nonlinear oscillations in power systems. Int. J. Electr. Power Energy Syst. , 37 - 43
-
26)
- J. Guckenheimer , P.J. Holmes . (1983) , Nonlinear oscillation, dynamical systems, and bifurcations of vector fields.
-
27)
- Ajjarapu, V., Lee, B.: `Nonlinear oscillations and voltage collapse phenomena in an electrical power system', Proceedings of 22nd North American Power Symposium, 1990, AL, USA, Auburn.
-
1)