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Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay

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

Abstract

This paper focuses on the stability of a hydropower station. First, we established a novel nonlinear mathematical model of a Francis hydro-turbine governing system considering both fractional-order derivative and time delay. The fractional-order α, which is introduced into the penstock system, in the range from 0.82 to 1.00 is on the left side of the model in a incommensurate manner in increment of 0.03 to provide an adjustable degree of system memory. The time delay τ, which exists between the signal and response in the hydraulic servo system, in the range from 0s to 0.26s is inserted on the right side of the model in increment of 0.04s. Utilizing the principle of statistical physics, we respectively explored the effects of the fractional-order α and the time delay τ on the stable region of the system. Furthermore, we exhaustively investigated the nonlinear dynamic behaviors of the system with different governor parameters by using bifurcation diagrams, time waveforms and power spectrums, finding that only under the condition of reasonable collocation of governor parameters the system can maintain stable operation. Finally, all of the above numerical experiments supply new methods for studying the stability of a hydropower station.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:329-338
    DOI: 10.1016/j.chaos.2016.06.018
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    Cited by:

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    2. Tianyao Zhang & Diyi Chen & Jing Liu & Beibei Xu & Venkateshkumar M, 2020. "A Feasibility Analysis of Controlling a Hybrid Power System over Short Time Intervals," Energies, MDPI, vol. 13(21), pages 1-21, October.
    3. Huang, Sunhua & Zhou, Bin & Bu, Siqi & Li, Canbing & Zhang, Cong & Wang, Huaizhi & Wang, Tao, 2019. "Robust fixed-time sliding mode control for fractional-order nonlinear hydro-turbine governing system," Renewable Energy, Elsevier, vol. 139(C), pages 447-458.
    4. Tianyao Zhang & Weibin Huang & Shijun Chen & Yanmei Zhu & Fuxing Kang & Yerong Zhou & Guangwen Ma, 2023. "The Scheduling Research of a Wind-Solar-Hydro Hybrid System Based on a Sand-Table Deduction Model at Ultra-Short-Term Scales," Energies, MDPI, vol. 16(7), pages 1-18, April.
    5. Yuqiang Tian & Bin Wang & Diyi Chen & Shaokun Wang & Peng Chen & Ying Yang, 2019. "Design of a Nonlinear Predictive Controller for a Fractional-Order Hydraulic Turbine Governing System with Mechanical Time Delay," Energies, MDPI, vol. 12(24), pages 1-16, December.
    6. Yu, Xiaodong & Yang, Xiuwei & Yu, Chao & Zhang, Jian & Tian, Yuan, 2021. "Direct approach to optimize PID controller parameters of hydropower plants," Renewable Energy, Elsevier, vol. 173(C), pages 342-350.
    7. 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.
    8. Ying Yang & Bin Wang & Yuqiang Tian & Peng Chen, 2020. "Fractional-Order Finite-Time, Fault-Tolerant Control of Nonlinear Hydraulic-Turbine-Governing Systems with an Actuator Fault," Energies, MDPI, vol. 13(15), pages 1-20, July.
    9. Dai, Hongzhe & Zheng, Zhibao & Wang, Wei, 2017. "On generalized fractional vibration equation," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 48-51.
    10. Tian, Yuqiang & Wang, Bin & Chen, Peng & Yang, Ying, 2021. "Finite-time Takagi–Sugeno fuzzy controller design for hydraulic turbine governing systems with mechanical time delays," Renewable Energy, Elsevier, vol. 173(C), pages 614-624.
    11. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    12. Zhang, Nan & Feng, Chen & Shan, Yahui & Sun, Na & Xue, Xiaoming & Shi, Liping, 2023. "A universal stability quantification method for grid-connected hydropower plant considering FOPI controller and complex nonlinear characteristics based on improved GWO," Renewable Energy, Elsevier, vol. 211(C), pages 874-894.
    13. Lisheng Li & Jing Qian & Yidong Zou & Danning Tian & Yun Zeng & Fei Cao & Xiang Li, 2022. "Optimized Takagi–Sugeno Fuzzy Mixed H 2 / H ∞ Robust Controller Design Based on CPSOGSA Optimization Algorithm for Hydraulic Turbine Governing System," Energies, MDPI, vol. 15(13), pages 1-31, June.

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