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Nonlinear Dynamical Analysis of Hydraulic Turbine Governing Systems with Nonelastic Water Hammer Effect

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  • Junyi Li
  • Qijuan Chen

Abstract

A nonlinear mathematical model for hydroturbine governing system (HTGS) has been proposed. All essential components of HTGS, that is, conduit system, turbine, generator, and hydraulic servo system, are considered in the model. Using the proposed model, the existence and stability of Hopf bifurcation of an example HTGS are investigated. In addition, chaotic characteristics of the system with different system parameters are studied extensively and presented in the form of bifurcation diagrams, time waveforms, phase space trajectories, Lyapunov exponent, chaotic attractors, and Poincare maps. Good correlation can be found between the model predictions and theoretical analysis. The simulation results provide a reasonable explanation for the sustained oscillation phenomenon commonly seen in operation of hydroelectric generating set.

Suggested Citation

  • Junyi Li & Qijuan Chen, 2014. "Nonlinear Dynamical Analysis of Hydraulic Turbine Governing Systems with Nonelastic Water Hammer Effect," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, June.
    • Handle: RePEc:hin:jnljam:412578
    DOI: 10.1155/2014/412578
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    Cited by:

    1. Liu, Dong & Wang, Xin & Peng, Yunshui & Zhang, Hui & Xiao, Zhihuai & Han, Xiangdong & Malik, O.P., 2020. "Stability analysis of hydropower units under full operating conditions considering turbine nonlinearity," Renewable Energy, Elsevier, vol. 154(C), pages 723-742.
    2. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
    3. Qi Yang & Jing Qian & Jia Li & Yidong Zou & Danning Tian & Yun Zeng & Yan Long & Ganyuan Zhang, 2023. "A New Integral Sliding Mode Control for Hydraulic Turbine Governing Systems Based on Nonlinear Disturbance Observer Compensation," Sustainability, MDPI, vol. 15(17), pages 1-21, August.
    4. Gao, Chunyang & Yu, Xiangyang & Nan, Haipeng & Men, Chuangshe & Zhao, Peiyu & Cai, Qingsen & Fu, Jianing, 2021. "Stability and dynamic analysis of doubly-fed variable speed pump turbine governing system based on Hopf bifurcation theory," Renewable Energy, Elsevier, vol. 175(C), pages 568-579.

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