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Nonlinear analysis of a simple amplitude–phase motion equation for power-electronics-based power system

  • Miaozhuang He
  • Wei He
  • Jiabing Hu
  • Xiaoming Yuan
  • Meng Zhan
Original Paper
  • 70 Downloads

Abstract

With large-scale application of a large number of renewable energy sources, such as wind turbines, photovoltaics, and various power electronic equipment, the power electric system is becoming gradually more power-electronics-based, whose dynamical behavior becomes much complicated, compared to that of traditional power system. The recent developed theory of amplitude–phase motion equation provides a new framework for the general dynamic analysis of such a system. Based on this theory, we study a simple amplitude–phase motion equation, i.e., a single power-electronics device connected to an infinite-large system, but consider its nonlinear effect. With extensive and intensive theoretical analysis and numerical simulation, we find that basically the system shows some similarity with the classical second-order swing equation for a synchronous generator connected to an infinite bus, such as the two types of bifurcation including the saddle-node bifurcation and homoclinic bifurcation, and the dynamical behavior of stable fixed point, stable limit cycle, and their coexistence. In addition, we find that the Hopf bifurcation is possible, but for negative damping only. All these findings are expected to be helpful for further study of power-electronics-based power system, featured with nonlinearity of high-dimensional dynamic systems involved with not only a large timescale but also large space scale.

Keywords

Amplitude–phase motion equation Nonlinear dynamics Synchronous generator Bifurcation and basin stability Swing equation 

Notes

Acknowledgements

The authors thank the editor and reviewers very much for their comments and suggestions, and we also thank Mr. Jing Huang very much for his help of the manuscript. This study was funded by the National Key Research and Development Program of China (Grant number 2017YFB0902000), the Science and Technology Project of State Grid (Grant number SGXJ0000KXJS700841), and the National Nature Science Foundation of China (NSFC) (Grant number 11475253).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Wang, X., Blaabjerg, F., Wu, W.: Modeling and analysis of harmonic stability in an AC power-electronics-based power system. IEEE Trans. Power Electron. 29(12), 6421–6432 (2014)CrossRefGoogle Scholar
  2. 2.
    Yuan, X., Cheng, S., Hu, J.: Multi-time scale dynamics in power electronics-dominated power systems. Front. Mech. Eng. 12(3), 303–311 (2017)CrossRefGoogle Scholar
  3. 3.
    Boroyevich, D., Cvetkovic, I., Dong, D., Burgos, R., Wang, F., Lee, F.: Future electronic power distribution systems: a contemplative view. In: 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM, pp. 1369–1380 (2010)Google Scholar
  4. 4.
    Blaabjerg, F., Yang, Y., Yang, D., Wang, X.: Distributed power-generation systems and protection. Proc. IEEE 99, 1–21 (2017)Google Scholar
  5. 5.
    Wang, X., Blaabjerg, F.: Harmonic stability in power electronic based power systems: concept, modeling, and analysis. IEEE Trans. Smart Grid 99, 1–1 (2018)Google Scholar
  6. 6.
    Ni, Y., Chen, S., Zhang, B.: Dynamic Theory and Analysis of Power System. Tsinghua University Press, Beijing (2002). (In Chinese)Google Scholar
  7. 7.
    Zhao, M., Yuan, X., Hu, J., Yan, Y.: Voltage dynamics of current control time-scale in a VSC-connected weak grid. IEEE Trans. Power Syst. 31(4), 2925–2937 (2016)CrossRefGoogle Scholar
  8. 8.
    Yuan, H., Yuan, X., Hu, J.: Modeling of grid-connected VSCs for power system small-signal stability analysis in DC-link voltage control timescale. IEEE Trans. Power Syst. 32, 3981–3991 (2017)CrossRefGoogle Scholar
  9. 9.
    Ying, J., Yuan, X., Hu, J.: Inertia characteristic of DFIG-based WT under transient control and its impact on the first-swing stability of SGs. IEEE Trans. Energy Convers. 32(4), 1502–1511 (2017)CrossRefGoogle Scholar
  10. 10.
    Menck, P.J., Heitzig, J., Marwan, N., Kurths, J.: How basin stability complements the linear-stability paradigm. Nat. Phys. 9, 89–92 (2013)CrossRefGoogle Scholar
  11. 11.
    Menck, P.J., Heitzig, J., Kurths, J., Schellnhuber, H.J.: How dead ends undermine power grid stability. Nat. Commun. 5, 3969 (2014)CrossRefGoogle Scholar
  12. 12.
    Ji, P., Kurths, J.: Basin stability of the Kuramoto-like model in small networks. Eur. Phys. J. Spec. Top. 223(12), 2483–2491 (2014)CrossRefGoogle Scholar
  13. 13.
    Dobson, I., Chiang, H.D.: Towards a theory of voltage collapse in electric power system. Syst. Control Lett. 13(3), 253–262 (1989)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Chiang, H.D., Dobson, I., Thomas, R.J., Thorp, J.S., Fekih-Ahmed, L.: On voltage collapse in electric power systems. IEEE Trans. Power Syst. 5, 601–611 (1990)CrossRefGoogle Scholar
  15. 15.
    Vu, K.T., Liu, C.-C.: Shrinking stability regions and voltage collapse in power system. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 39(4), 271–289 (1992)CrossRefGoogle Scholar
  16. 16.
    Lu, Q., Wang, Z.H., Han, Y.D.: The Optimal Control of Transmission System. Beijing Science Press, Beijing (1982). (In Chinese)Google Scholar
  17. 17.
    Backhaus, S., Chertkov, M.: Getting a grip on the electrical grid. Phys. Today 66(5), 42–48 (2013)CrossRefGoogle Scholar
  18. 18.
    Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Books Publishing, Massachusetts (1994)zbMATHGoogle Scholar
  19. 19.
    Ji, W., Venkatasubramanian, V.: Hard-limit induced Chaos in a single-machine infinite-bus power system. IEEE Trans. Power Syst. 4, 3465–3470 (1995)Google Scholar
  20. 20.
    Ji, W., Venkatasubramanian, V.: Dynamics of a minimal power system model-invariant tori and quasi-periodic motions. IEEE Int. Symp. Circuits Syst. 2(5), 1131–1135 (2002)Google Scholar
  21. 21.
    Ma, J., Sun, Y., Yuan, X., Kurths, J., Zhan, M.: Dynamics and collapse in a power system model with voltage variation: the damping effect. Plos One 11(11), e0165943 (2016)CrossRefGoogle Scholar
  22. 22.
    Sharafutdinov, K., Rydin Gorjão, L., Matthiae, M., Faulwasser, T., Witthaut, D.: Rotor-angle versus voltage instability in the third-order model for synchronous generators. Chaos 28, 033117 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Gantmacher, F.: The Theory of Matrices, pp. 221–225. American Mathematical Society, Providence (2000)Google Scholar
  24. 24.
    Skubov, D., Lukin, A., Popov, L.: Bifurcation curves for synchronous electrical machine. Nonlinear Dyn. 83(4), 2323–2329 (2016)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Fell, J., Axmacher, N.: The role of phase synchronization in memory processes. Nat. Rev. Neurosci. 12(2), 105–118 (2011)CrossRefGoogle Scholar
  26. 26.
    Agrawal, G.P., Olsson, N.A.: Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers. IEEE J. Quantum Electron. 25, 2297–2306 (1989)CrossRefGoogle Scholar
  27. 27.
    Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76(11), 1804 (1996)CrossRefGoogle Scholar
  28. 28.
    Laurat, J., Longchambon, L., Fabre, C., Coudreau, T.: Experimental investigation of amplitude and phase quantum correlations in a type II optical parametric oscillator above threshold: from nondegenerate to degenerate operation. Opt. Lett. 30(10), 1177–1179 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Miaozhuang He
    • 1
  • Wei He
    • 1
  • Jiabing Hu
    • 1
  • Xiaoming Yuan
    • 1
  • Meng Zhan
    • 1
  1. 1.State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic EngineeringHuazhong University of Science and TechnologyWuhanChina

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