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Hopf bifurcation control of hydro-turbine governing system with sloping ceiling tailrace tunnel using nonlinear state feedback

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  • Guo, Wencheng
  • Yang, Jiandong

Abstract

Aiming at improving the regulation quality of a hydro-turbine governing system with sloping ceiling tailrace tunnel, Hopf bifurcation control using nonlinear state feedback is studied. Firstly, the nonlinear mathematical model of a hydro-turbine governing system with sloping ceiling tailrace tunnel is presented. Then, a novel control strategy using nonlinear state feedback with polynomial functions is proposed, and Hopf bifurcation control of a hydro-turbine governing system using the proposed control strategy is described. Finally, the application and functional mechanism of the proposed control strategy are analyzed by comparison with the PID strategy. The results indicate that: The proposed nonlinear state feedback control strategy is able to make the frequency of a hydro-turbine unit return to the initial value (i.e. rated frequency), and the regulation quality and the response speed are obviously better than those under the PID strategy. The effect of the linear term of nonlinear state feedback control strategy is to modify the system's linear stability, in order to eliminate or delay an existing bifurcation. Altering the nonlinear term can change the stability of bifurcation solutions, for example, converting a Hopf bifurcation from subcritical to supercritical.

Suggested Citation

  • Guo, Wencheng & Yang, Jiandong, 2017. "Hopf bifurcation control of hydro-turbine governing system with sloping ceiling tailrace tunnel using nonlinear state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 426-434.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:426-434
    DOI: 10.1016/j.chaos.2017.09.003
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    Cited by:

    1. Wang, Le & Guo, Wencheng, 2022. "Nonlinear hydraulic coupling characteristics and energy conversion mechanism of pipeline - surge tank system of hydropower station with super long headrace tunnel," Renewable Energy, Elsevier, vol. 199(C), pages 1345-1360.
    2. Xu, Pan & Fu, Wenlong & Lu, Qipeng & Zhang, Shihai & Wang, Renming & Meng, Jiaxin, 2023. "Stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel and upstream surge tank considering nonlinear hydro-turbine characteristics," Renewable Energy, Elsevier, vol. 210(C), pages 556-574.
    3. Guo, Wencheng & Zhu, Daoyi, 2020. "Setting condition of downstream surge tank of hydropower station with sloping ceiling tailrace tunnel," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Xu, Beibei & Zhang, Jingjing & Egusquiza, Mònica & Chen, Diyi & Li, Feng & Behrens, Paul & Egusquiza, Eduard, 2021. "A review of dynamic models and stability analysis for a hydro-turbine governing system," Renewable and Sustainable Energy Reviews, Elsevier, vol. 144(C).
    5. 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.
    6. Zhu, Daoyi & Guo, Wencheng, 2019. "Critical sectional area of surge chamber considering nonlinearity of head loss of diversion tunnel and steady output of turbine," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 165-172.
    7. Wencheng Guo, 2019. "A Review of the Hydraulic Transient and Dynamic Behavior of Hydropower Plants with Sloping Ceiling Tailrace Tunnels," Energies, MDPI, vol. 12(17), pages 1-28, August.
    8. Liu, Yang & Guo, Wencheng, 2021. "Multi-frequency dynamic performance of hydropower plant under coupling effect of power grid and turbine regulating system with surge tank," Renewable Energy, Elsevier, vol. 171(C), pages 557-581.
    9. Xu, Xinyu & Guo, Wencheng, 2020. "Stability of speed regulating system of hydropower station with surge tank considering nonlinear turbine characteristics," Renewable Energy, Elsevier, vol. 162(C), pages 960-972.
    10. Zhou, Jianxu & Mao, Yutong & Shen, Aili & Zhang, Jian, 2023. "Modeling and stability investigation on the governor-turbine-hydraulic system with a ceiling-sloping tail tunnel," Renewable Energy, Elsevier, vol. 204(C), pages 812-822.
    11. Chen, Zi & Guo, Wencheng, 2023. "Stability and dynamic response of two-stage hydropower stations cascaded by regulating reservoir," Renewable Energy, Elsevier, vol. 202(C), pages 651-666.

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