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The European Physical Journal Special Topics

, Volume 228, Issue 9, pp 1793–1808 | Cite as

Periodic motions and chaos in power system including power disturbance

  • Jianzhe HuangEmail author
Regular Article Topical issue
  • 13 Downloads
Part of the following topical collections:
  1. Periodic Motions and Chaos in Nonlinear Dynamical Systems

Abstract

Single-machine infinite-bus power system is a nonlinear dynamic system with state variable in the sinusoidal function. With traditional analytical approaches, it is difficult to analyze such a nonlinear system since the rotor angle difference cannot always stay in an infinitesimal small value. In this paper, a single-machine infinite-bus power system with power disturbance will be discussed. The implicit discrete maps approach will be applied to solve the periodic motions for such a power system, and the stability condition will be discussed. The analytical expressions for periodic motions for such a single-machine infinite-bus power system can be recovered with a series of Fourier functions. The bifurcation diagram for such a system will be given to show the complexity of the motions when the frequency of the disturbance varies, and 2-D parameter map for chaotic motion will be obtained by calculating the Kolmogorov-Sinai entropy density. From analytical bifurcation for period-1 and period-2 motions, the evolution process of the periodic motion to chaos can be analytically explained.

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References

  1. 1.
    M.A. Nayfeh, A.M.A. Hamdan, A.H. Neyfeh, Nonlinear Dyn. 1, 313 (1990)CrossRefGoogle Scholar
  2. 2.
    W.N. Zhang, W.D. Zhang, Appl. Math. Mech. 20, 1175 (1999)CrossRefGoogle Scholar
  3. 3.
    L.F.C. Alberto, N.G. Bretas, IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 47, 1085 (2000)CrossRefGoogle Scholar
  4. 4.
    H.K. Chen, T.N. Lin, J.H. Chen, Chaos Solitons Fractals 24, 1307 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    X.W. Chen, W.N. Zhang, W.D. Zhang, IEEE Trans. Circuits Syst. II: Express Briefs, Briefs 52, 811 (2005)Google Scholar
  6. 6.
    X.Z. Duan, J.Y. Wen, S.J. Cheng, Sci. Chin. Ser. E: Technol. Sci. 52, 436 (2009)CrossRefGoogle Scholar
  7. 7.
    D.Q. Wei, X.S. Luo, Europhys. Lett. 86, 50008 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    N.S. Manjarekar, R.N. Banavar, R. Ortega, Int. J. Electr. Power Energy Syst. 32, 63 (2010)CrossRefGoogle Scholar
  9. 9.
    D.Q. Wei, B. Zhang, D.Y. Qiu, X.S. Luo, Nonlinear Dyn. 61, 477 (2010)CrossRefGoogle Scholar
  10. 10.
    R.C. Kumaran, T.G. Venkatesh, K.S. Swarup, Int. J. Electr. Power Energy Syst. 33, 1384 (2011)CrossRefGoogle Scholar
  11. 11.
    X.D. Wang, Y.S. Chen, G. Han, C.Q. Song, Appl. Math. Modell. 39, 2951 (2015)CrossRefGoogle Scholar
  12. 12.
    D.K. Sambariya, R. Prasad, Electr. Power Compon. Syst. 45, 34 (2017)CrossRefGoogle Scholar
  13. 13.
    B.C. Rout, D.K. Lal, A.K. Barisal, Cogent Eng. 4, 1362804 (2017)CrossRefGoogle Scholar
  14. 14.
    S. Keskes, N. Bouchiba, S. Sallem, L. ChrifiAlaoui, M. Kammoun, in Proceedings of the International Conference on Systems and Control, Batna, 2017Google Scholar
  15. 15.
    M.A. Hernandez, A.R. Messina, IEEE Trans. Power Syst. 33, 5124 (2018)ADSCrossRefGoogle Scholar
  16. 16.
    A.C.J. Luo, Memorized Discrete Systems and Time-delay (Springer, Cham, 2016)Google Scholar
  17. 17.
    D.H. Wang, J.Z. Huang, Chaos Solitons Fractals 95, 168 (2017)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Y. Guo, A.C.J. Luo, J. Vib. Testing Syst. Dyn. 1, 93 (2017)CrossRefGoogle Scholar
  19. 19.
    Y.Y. Xu, A.C.J. Luo, J. Vib. Testing Syst. Dyn. 2, 119 (2018)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aeronautics and Astronautics, Shanghai Jiao Tong UniversityShanghaiP.R. China

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