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Nonlinear Dynamics

, Volume 61, Issue 3, pp 477–482 | Cite as

Effect of noise on erosion of safe basin in power system

  • Du Qu Wei
  • Bo Zhang
  • Dong Yuan Qiu
  • Xiao Shu Luo
Original Paper

Abstract

We study the effect of Gaussian white noise on erosion of safe basin in a simple model of power system whose safe basin is integral in the absence of noise. The stochastic Melnikov method is first applied to predict the onset of basin erosion when the noise excitation is present in system. And then the eroded basins are simulated according to the necessary restrictions for the system’s parameters. It is found that for the noisy power system when the noise intensity σ is greater than a threshold, basin erosion occurs and as σ is further increased basin erosion is aggravated. These studies imply that random noise excitation can induce and enhance the basin erosion in the power system.

Keywords

Gaussian white noise Erosion of safe basin Stochastic Melnikov method Power system 

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References

  1. 1.
    Soliman, M.S., Thompson, J.M.T.: Integrity measures quantifying the erosion of smooth and fractal basins of attraction. J. Sound Vib. 135, 453–475 (1989) CrossRefMathSciNetGoogle Scholar
  2. 2.
    Soliman, M.S., Thompson, J.M.T.: Global dynamics underlying sharp basin erosion in nonlinear driven oscillators. Phys. Rev. A 45, 3425–3431 (1992) CrossRefGoogle Scholar
  3. 3.
    Thompson, J.M.T., Stewart, H.B.: Nonlinear Dynamics and Chaos, Geometrical Methods for Engineers and Scientists, 2nd edn. Wiley, Chichester (2002) Google Scholar
  4. 4.
    Santee, D.M., Gonçalves Paulo, B.: Oscillations of a beam on a non-linear elastic foundation under periodic loads. Shock Vib. 13, 273–284 (2006) Google Scholar
  5. 5.
    Aguirre, J., Viana Ricardo, L., Sanjuán, M.A.F.: Fractal structures in nonlinear dynamics. Rev. Mod. Phys. 81, 333–387 (2009) CrossRefGoogle Scholar
  6. 6.
    Nayfeh, A.H., Sanchez, N.E.: Bifurcations in a softening Duffing oscillator. Int. J. Non-Linear Mech. 24, 483–497 (1989) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Sanjuán, M.A.F.: The effect of nonlinear damping on the universal escape oscillator. Int. J. Bifurc. Chaos 9, 735–744 (1999) MATHCrossRefGoogle Scholar
  8. 8.
    Rega, G., Lenci, S.: Identifying, evaluating, and controlling dynamical integrity measures in non-linear mechanical oscillators. Nonlinear Anal. 63, 902–914 (2005) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Tchawoua, C., Siewe Siewe, M., Tchatchueng, S., Moukam Kakmeni, F.M.: Nonlinear dynamics of parametrically driven particles in a Φ 6 potential. Nonlinearity 21, 1041–1055 (2008) MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gan, C.B.: Noise-Induced chaos and basin erosion in softening Duffing oscillator. Chaos Solutions Fractals 25, 1069–1081 (2005) MATHCrossRefGoogle Scholar
  11. 11.
    Gan, C.B.: Noise-induced chaos in Duffing oscillator with double wells. Nonlinear Dyn. 45, 305–317 (2006) MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Rong, H., Wang, X., Xu, W., Fang, T.: Erosion of safe basins in a nonlinear oscillator under bounded noise excitation. J. Sound Vib. 313, 46–56 (2008) CrossRefGoogle Scholar
  13. 13.
    Kopell, N., Washburn, R.B.: Chaotic motions in the two-degree-of-freedom swing equations. IEEE Trans. Circuits Syst. 29, 738–746 (1982) MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Venkatasubramanian, V., Ji, W.: Coexistence of four different attractors in a fundamental powersystem model. IEEE Trans. Circuits Syst. I 46, 405–409 (1999) CrossRefGoogle Scholar
  15. 15.
    Carreras, B.A., Lynch, V.E., Dobson, I.: Critical points and transitions in an electric power transmission model for cascading failure blackouts. Chaos 12, 985–994 (2002) MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Nayfeh, M.A., Hamdan, A.M.A., Nayfeh, A.H.: Chaos and instability in a power system: subharmonic-resonant case. Nonlinear Dyn. 2, 53–72 (1991) CrossRefGoogle Scholar
  17. 17.
    Dhamala, M., Lai, Y.-C.: Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology. Phys. Rev. E 59, 1646–1655 (1999) CrossRefGoogle Scholar
  18. 18.
    Marcos, S.H.C., Lopes, S.R., Viana, R.L.: Boundary crises, fractal basin boundaries and electric power collapses. Chaos Solitons Fractals 15, 417–424 (2003) CrossRefGoogle Scholar
  19. 19.
    Zhang, Q., Wang, B.H., Yang, C.W.: Fractal erosion of safe basins in power system and its control. Power Syst. Technol. 29, 63–67 (2005) (in Chinese) Google Scholar
  20. 20.
    Lu, Q., Sun, Y.Z.: Nonlinear Control of Power System. China Science Press, Beijing (1993) Google Scholar
  21. 21.
    Chen, X., Zhang, W., Zhang, W.: Chaotic and subharmonic oscillations of a nonlinear power system. IEEE Trans. Circuits Syst. II 52, 811–815 (2005) CrossRefGoogle Scholar
  22. 22.
    Wei, D.Q., Luo, X.S.: Passivity-based adaptive control of chaotic oscillations in power system. Chaos Solitons Fractals 31, 665–671 (2007) MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Lin, H., Yim, S.C.S.: Analysis of a nonlinear system exhibiting chaotic, noisy chaotic, and random behaviors. ASME J. Appl. Mech. 63, 509–516 (1996) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Du Qu Wei
    • 1
    • 2
  • Bo Zhang
    • 1
  • Dong Yuan Qiu
    • 1
  • Xiao Shu Luo
    • 2
  1. 1.College of Electric PowerSouth China University of TechnologyGuangzhouChina
  2. 2.College of Electronic EngineeringGuangxi Normal UniversityGuilinChina

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