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Numerical investigation of the average wind speed of a single wind turbine and development of a novel three-dimensional multiple wind turbine wake model

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  • Sun, Haiying
  • Yang, Hongxing

Abstract

This paper reports the newly developed three-dimensional analytical wake models for single and multiple wind turbines. Firstly, the average wind speed of a single wind turbine is studied based on the single wake model. For a single wind turbine, assuming the incoming wind is distributed as power law in the vertical direction, the average wind speeds have a close relationship to the power exponent α, the hub height h0 and the rotor radius r0. When α=0.4, the average wind speed can decrease to 96% of the speed at the hub height. Secondly, the three-dimensional multiple wake model is developed based on the single wake model. The method of Sum of Squares is applied to solve the wake adding problem. The available wind tunnel experimental data of two different layouts are used to validate the wake model. At the three representative heights, the wake model predicts the distribution of wind speed accurately. For Layout 1, at the hub and the top heights, most of the relative errors between the wake model results and the experimental data are smaller than 6%. At the top height, all relative errors are smaller than 20%. For Layout 2, the largest errors of the wake model are 8.5% at the top height, 17.8% at the bottom height and 21.2% at the hub height. The results predicted by the multiple wake model are demonstrated as well. The presented wake model can be used to describe the wind distribution and optimize the layout of wind farm.

Suggested Citation

  • Sun, Haiying & Yang, Hongxing, 2020. "Numerical investigation of the average wind speed of a single wind turbine and development of a novel three-dimensional multiple wind turbine wake model," Renewable Energy, Elsevier, vol. 147(P1), pages 192-203.
    • Handle: RePEc:eee:renene:v:147:y:2020:i:p1:p:192-203
    DOI: 10.1016/j.renene.2019.08.122
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    Cited by:

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    8. Liu, Weiqi & Shi, Jian & Chen, Hailong & Liu, Hengxu & Lin, Zi & Wang, Lingling, 2021. "Lagrangian actuator model for wind turbine wake aerodynamics," Energy, Elsevier, vol. 232(C).
    9. Dou, Bingzheng & Qu, Timing & Lei, Liping & Zeng, Pan, 2020. "Optimization of wind turbine yaw angles in a wind farm using a three-dimensional yawed wake model," Energy, Elsevier, vol. 209(C).
    10. Gao, Xiaoxia & Chen, Yao & Xu, Shinai & Gao, Wei & Zhu, Xiaoxun & Sun, Haiying & Yang, Hongxing & Han, Zhonghe & Wang, Yu & Lu, Hao, 2022. "Comparative experimental investigation into wake characteristics of turbines in three wind farms areas with varying terrain complexity from LiDAR measurements," Applied Energy, Elsevier, vol. 307(C).
    11. Fei, Zhao & Tengyuan, Wang & Xiaoxia, Gao & Haiying, Sun & Hongxing, Yang & Zhonghe, Han & Yu, Wang & Xiaoxun, Zhu, 2020. "Experimental study on wake interactions and performance of the turbines with different rotor-diameters in adjacent area of large-scale wind farm," Energy, Elsevier, vol. 199(C).
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    13. Kaldellis, John K. & Triantafyllou, Panagiotis & Stinis, Panagiotis, 2021. "Critical evaluation of Wind Turbines’ analytical wake models," Renewable and Sustainable Energy Reviews, Elsevier, vol. 144(C).
    14. Sun, Haiying & Gao, Xiaoxia & Yang, Hongxing, 2020. "A review of full-scale wind-field measurements of the wind-turbine wake effect and a measurement of the wake-interaction effect," Renewable and Sustainable Energy Reviews, Elsevier, vol. 132(C).
    15. Sun, Haiying & Yang, Hongxing & Gao, Xiaoxia, 2023. "Investigation into wind turbine wake effect on complex terrain," Energy, Elsevier, vol. 269(C).
    16. Wang, Shuai & Li, Bin & Li, Guanzheng & Yao, Bin & Wu, Jianzhong, 2021. "Short-term wind power prediction based on multidimensional data cleaning and feature reconfiguration," Applied Energy, Elsevier, vol. 292(C).
    17. Lin, Jian Wei & Zhu, Wei Jun & Shen, Wen Zhong, 2022. "New engineering wake model for wind farm applications," Renewable Energy, Elsevier, vol. 198(C), pages 1354-1363.
    18. Ling, Ziyan & Zhao, Zhenzhou & Liu, Yige & Liu, Huiwen & Ali, Kashif & Liu, Yan & Wen, Yifan & Wang, Dingding & Li, Shijun & Su, Chunhao, 2024. "Multi-objective layout optimization for wind farms based on non-uniformly distributed turbulence and a new three-dimensional multiple wake model," Renewable Energy, Elsevier, vol. 227(C).
    19. Wang, Tengyuan & Cai, Chang & Wang, Xinbao & Wang, Zekun & Chen, Yewen & Song, Juanjuan & Xu, Jianzhong & Zhang, Yuning & Li, Qingan, 2023. "A new Gaussian analytical wake model validated by wind tunnel experiment and LiDAR field measurements under different turbulent flow," Energy, Elsevier, vol. 271(C).
    20. Tao, Siyu & Xu, Qingshan & Feijóo, Andrés & Zheng, Gang & Zhou, Jiemin, 2020. "Wind farm layout optimization with a three-dimensional Gaussian wake model," Renewable Energy, Elsevier, vol. 159(C), pages 553-569.
    21. Paxis Marques João Roque & Shyama Pada Chowdhury & Zhongjie Huan, 2021. "Performance Enhancement of Proposed Namaacha Wind Farm by Minimising Losses Due to the Wake Effect: A Mozambican Case Study," Energies, MDPI, vol. 14(14), pages 1-22, July.
    22. Zheng Yuan & Jin Jiang & Jun Zang & Qihu Sheng & Ke Sun & Xuewei Zhang & Renwei Ji, 2020. "A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine," Energies, MDPI, vol. 14(1), pages 1-21, December.
    23. Sun, Haiying & Qiu, Changyu & Lu, Lin & Gao, Xiaoxia & Chen, Jian & Yang, Hongxing, 2020. "Wind turbine power modelling and optimization using artificial neural network with wind field experimental data," Applied Energy, Elsevier, vol. 280(C).

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