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A criterion for the Hopf bifurcation and the pathway to chaos of doubly fed induction generators

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Abstract

Aiming at the cause of limit cycles and the pathway of chaotic oscillation by doubly fed induction generator (DFIG) as its internal parameters change, this paper proposed a method to identify limit cycles and a numerical method to identify chaotic pathways. First, a simplified four-dimensional nonlinear dynamic model of the DFIG is developed. A simple criterion for the Hopf bifurcation parameter of the DFIG is given: the Routh–Hurwitz stability criterion. In addition, the relationship between the system at critical damping and the Hopf bifurcation is obtained. Second, the stability interval of the DFIG linearized system is verified using a time-domain approach when the system has recovered from a slight disturbance. Finally, periodic, quasi-periodic, and chaotic oscillations are predicted to occur based on the largest Lyapunov exponent and power spectrum to further determine the system’s parameters. The path and threshold of the tuning parameter inducing the DFIG into chaos are obtained to provide a theoretical basis for revealing the mechanism inducing chaotic oscillations. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed method.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 51767017 and 51867015), the Basic Research and Innovation Group Project of Gansu (No. 18JR3RA13), and the Major Science and Technology Project of Gansu (No. 19ZD2GA003).

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, 730050, Gansu Province, China

    Wei Chen, Qiangqiang Li, Zhanhong Wei, Jiangtao Li & Kun Wang

Authors
  1. Wei Chen
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  2. Qiangqiang Li
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  3. Zhanhong Wei
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  4. Jiangtao Li
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  5. Kun Wang
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Contributions

Prof. Chen provides funding and technical guidance; Mr. Li conducted theoretical derivation and experimental simulation; Other personnel checked and modified.

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Correspondence to Qiangqiang Li.

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Appendix

Appendix

See Table 4.

Table 4 Dimensionless simulation parameters of DFIG mathematical model
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Chen, W., Li, Q., Wei, Z. et al. A criterion for the Hopf bifurcation and the pathway to chaos of doubly fed induction generators. Electr Eng 105, 2595–2605 (2023). https://doi.org/10.1007/s00202-023-01819-1

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