Nonlinear Dynamics

, Volume 95, Issue 3, pp 1965–1976 | Cite as

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

  • Miaozhuang He
  • Wei He
  • Jiabing Hu
  • Xiaoming Yuan
  • Meng ZhanEmail author
Original Paper


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.


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



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.


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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
    Email author
  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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