JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 94-99.doi: 10.6040/j.issn.1671-9352.0.2021.410

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Bifurcation of hydraulic turbine governing system under color noise excitation

ZHANG Mei-jiao, ZHANG Jian-gang*, NAN Meng-ran, WEI Li-xiang   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Online:2021-12-20 Published:2021-11-25

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Abstract: Based on the saturated nonlinear proportional-integral(PI)governing system of a hydraulic turbine, a hydraulic turbine governing system under the excitation of color noise is established, the stochastic bifurcation behavior of system is studied. The system is simplified to an equivalent nonlinear white noise model by using the uniform color noise approximation principle. The central manifold theorem is used to reduce the dimension of system, the Ito differential equations and FPK equations are obtained according to stochastic average method, the stochastic bifurcation condition of system is discussed. Through numerical simulation, the stochastic bifurcation behaviors of system under the influence of different autocorrelation time and noise intensity are discussed respectively, the validity of theory of stochastic averaging and the occurrence of bifurcation phenomenon are verified.

Key words: hydraulic turbine governing system, color noise, stochastic averaging, stochastic bifurcation

CLC Number: 

  • O324
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