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<p>To study the stochastic bifurcation of a permanent magnet synchronous wind turbine (PMSWT) under stochastic wind disturbances, a nonlinear stochastic mathematical model of a PMSWT was developed in Yang et al. (Acta Phys Sin 44:884–894, 2017), and a method based on the three-dimensional Gauss–Legendre integral was used to numerically analyze the stochastic P-bifurcation problem of a PMSWT system under stochastic disturbances. Reference to the derived three-dimensional path integration method based on the Gauss–Legendre integration formula, the smoothing probability density of the disturbed permanent magnet wind turbine system was computed, and a numerical simulation validated the theoretical analysis. According to the results, there were two P-bifurcations in the system because the joint PDFs of the system appeared to change twice with increasing intensity of the random disturbance. In particular, the joint probability density undergoes a transformation, transitioning from the shape of a crater to the shape of a single peak and then back again. The results reveal the mechanism of the influence of random disturbances of different intensities on a PMSWT and provide a reference basis for the safe and stable operation and control of the PMSWT.</p>

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Stochastic P-bifurcation analysis of a permanent magnet synchronous wind turbine based on the three-dimensional path integral method

  • 期刊论文

  • 发表日期：

    2026年2月20日

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  • Wei Chen,
  • Tiedong Shang,
  • Zhanhong Wei,
  • Qiangqiang Li,
  • Bo Wang

摘要

To study the stochastic bifurcation of a permanent magnet synchronous wind turbine (PMSWT) under stochastic wind disturbances, a nonlinear stochastic mathematical model of a PMSWT was developed in Yang et al. (Acta Phys Sin 44:884–894, 2017), and a method based on the three-dimensional Gauss–Legendre integral was used to numerically analyze the stochastic P-bifurcation problem of a PMSWT system under stochastic disturbances. Reference to the derived three-dimensional path integration method based on the Gauss–Legendre integration formula, the smoothing probability density of the disturbed permanent magnet wind turbine system was computed, and a numerical simulation validated the theoretical analysis. According to the results, there were two P-bifurcations in the system because the joint PDFs of the system appeared to change twice with increasing intensity of the random disturbance. In particular, the joint probability density undergoes a transformation, transitioning from the shape of a crater to the shape of a single peak and then back again. The results reveal the mechanism of the influence of random disturbances of different intensities on a PMSWT and provide a reference basis for the safe and stable operation and control of the PMSWT.