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Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system

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  • Xu, Beibei
  • Chen, Diyi
  • Zhang, Hao
  • Wang, Feifei

Abstract

In this paper, a fractional order mathematical model of a hydro-turbine governing system is presented to analyze the dynamic stability of the hydro-turbine governing system in the process of operation. The fractional order hydro-turbine governing system is composed of a hydro-turbine and penstock system, a generator system and a hydraulic servo system. As a pioneering work, we proposed a universal solution about the relationship of two parameters in higher-degree equations according to the stability theorem of a fractional order system. Based on the above theorem, we presented a variable law of stable regions of the fractional-order hydro-turbine governing system and analyzed the effect of various degree of elastic water hammer on the stable regions of the parameters kd and kp with the increase of fractional order α. The nonlinear dynamic behaviors of the system are also studied in detail. Finally, all of these results supply some basic theories for the running of a hydropower plant.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:50-61
    DOI: 10.1016/j.chaos.2015.01.025
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    3. Wang, Feifei & Chen, Diyi & Xu, Beibei & Zhang, Hao, 2016. "Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 329-338.
    4. Deshpande, Amey S. & Daftardar-Gejji, Varsha, 2017. "On disappearance of chaos in fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 119-126.
    5. Sheng Chen & Gaohui Li & Delou Wang & Xingtao Wang & Jian Zhang & Xiaodong Yu, 2019. "Impact of Tail Water Fluctuation on Turbine Start-Up and Optimized Regulation," Energies, MDPI, vol. 12(15), pages 1-17, July.
    6. Wuyi Wan & Boran Zhang & Xiaoyi Chen, 2018. "Investigation on Water Hammer Control of Centrifugal Pumps in Water Supply Pipeline Systems," Energies, MDPI, vol. 12(1), pages 1-20, December.
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    8. Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    9. 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.
    10. 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).
    11. Yu, Xiaodong & Yang, Xiuwei & Zhang, Jian, 2019. "Stability analysis of hydro-turbine governing system including surge tanks under interconnected operation during small load disturbance," Renewable Energy, Elsevier, vol. 133(C), pages 1426-1435.
    12. Liu, Yi & Zhang, Jian & Liu, Zhe & Chen, Long & Yu, Xiaodong, 2022. "Surge wave characteristics for hydropower plant with upstream double surge tanks connected in series under small load disturbance," Renewable Energy, Elsevier, vol. 186(C), pages 667-676.
    13. Wang, Cong & Li, Dong-hang & Zhang, Hong-li & Ma, Ping & Li, Xin-kai & Zhang, Shao-hua & Dong, Ying-chao, 2024. "Prescribed performance sliding mode control for the bursting oscillation of a fractional-order hydro-turbine governing system based on time-varying tangent barrier Lyapunov function," Applied Energy, Elsevier, vol. 356(C).
    14. Tsapla Fotsa, R. & Woafo, P., 2016. "Chaos in a new bistable rotating electromechanical system," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 48-57.
    15. Yu, Xiaodong & Zhang, Jian & Fan, Chengyu & Chen, Sheng, 2016. "Stability analysis of governor-turbine-hydraulic system by state space method and graph theory," Energy, Elsevier, vol. 114(C), pages 613-622.
    16. Xu, Beibei & Chen, Diyi & Patelli, Edoardo & Shen, Haijun & Park, Jae-Hyun, 2019. "Mathematical model and parametric uncertainty analysis of a hydraulic generating system," Renewable Energy, Elsevier, vol. 136(C), pages 1217-1230.
    17. O. A. Rosas-Jaimes & G. A. Munoz-Hernandez & G. Mino-Aguilar & J. Castaneda-Camacho & C. A. Gracios-Marin, 2019. "Evaluating Fractional PID Control in a Nonlinear MIMO Model of a Hydroelectric Power Station," Complexity, Hindawi, vol. 2019, pages 1-15, January.
    18. Chen, Jinbao & Zheng, Yang & Liu, Dong & Du, Yang & Xiao, Zhihuai, 2023. "Quantitative stability analysis of complex nonlinear hydraulic turbine regulation system based on accurate calculation," Applied Energy, Elsevier, vol. 351(C).

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