Analytical Modeling for Prediction of Horizontal-Axis Wind Turbines Power Generation in Wind Farms Based on an Analytical Wake Model

Document Type : Original Article


1 Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mechanical Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran


The development of models that predict power production of wind farms (WFs) by considering the interacting wakes is important; because wakes of the turbines exert a significant influence on power production of turbines, and hence on the layout of wind turbines in WFs. Thus, the purpose of present study was to provide an innovative analytical method for the prediction of power generation of the WFs that have a flat terrain and are consisted of horizontal-axis wind turbines (HAWTs) with the same hub height. The methodology employed utilized an analytical Gaussian model of HAWT wake to develop an analytical model that calculates the effective wind velocity acting on the downstream HAWT(s), which is further used for reading its generated power from the turbine’s catalog; thus, providing the generated power of the WF as the output. The results of presented model were validated by the field measurements data of Horns Rev WF and also were compared to two analytical models for predicting the generated power. The results were compared with two numerical simulations of the literature, and the output data of three commercial software. Moreover, the error analysis revealed that the presented model mostly showed superior accuracy in predicting the field measurements data.


Main Subjects

  1. Kazemian, M.E., S.A. Gandjalikhan Nassab and E. Jahanshahi Javarana, 2021. Techno-Economic Optimization of Combined Cooling, Heat and Power System Based on Response Surface Methodology. Iranian (Iranica) Journal of Energy & Environment, 12(4), pp: 285-296. Doi: 10.5829/IJEE.2021.12.04.02
  2. Norouzi, N., 2021. Assessment of Technological Path of Hydrogen Energy Industry Development: A Review. Iranian (Iranica) Journal of Energy & Environment, 12(4), pp: 273-284. Doi: 10.5829/IJEE.2021.12.04.01
  3. IEA. Renewable Electricity Generation by Source (Non-Combustible), World 1990-2018. 2018 [cited 2021; Available from:
  4. Manwell, J.F., J.G. McGowan and A.L. Rogers, 2010. Wind Energy Explained: Theory, Design and Application. John Wiley & Sons. Doi: 10.1002/9781119994367
  5. Archer, C.L., A. Vasel-Be-Hagh, C. Yan, S. Wu, Y. Pan, J.F. Brodie and A.E. Maguire, 2018. Review and Evaluation of Wake Loss Models for Wind Energy Applications. Applied Energy, 226, pp: 1187-1207. Doi: 10.1016/j.apenergy.2018.05.085
  6. Chanprasert, W., R. Sharma, J.E. Cater and S. Norris, 2022. Large Eddy Simulation of Wind Turbine Fatigue Loading and Yaw Dynamics Induced by Wake Turbulence. Renewable Energy, 190, pp: 208-222. Doi: 10.1016/j.renene.2022.03.097
  7. Porté-Agel, F., M. Bastankhah and S. Shamsoddin, 2020. Wind-Turbine and Wind-Farm Flows: A Review. Boundary-Layer Meteorology, 174(1), pp: 1-59. Doi: 10.1007/s10546-019-00473-0
  8. Cheng, Y., M. Zhang, Z. Zhang and J. Xu, 2019. A New Analytical Model for Wind Turbine Wakes Based on Monin-Obukhov Similarity Theory. Applied Energy, 239, pp: 96-106. Doi: 10.1016/j.apenergy.2019.01.225
  9. Kaldellis, J.K., P. Triantafyllou and P. Stinis, 2021. Critical Evaluation of Wind Turbines’ Analytical Wake Models. Renewable and Sustainable Energy Reviews, 144(4), pp: 110991. Doi: 10.1016/j.rser.2021.110991
  10. Naderi, S. and F. Torabi, 2017. Numerical Investigation of Wake Behind a Hawt Using Modified Actuator Disc Method. Energy Conversion and Management, 148, pp:1346-1357. Doi: 10.1016/j.enconman.2017.07.003
  11. Tian, L., Y. Song, P. Xiao, N. Zhao, W. Shen and C. Zhu, 2022. A New Three-Dimensional Analytical Model for Wind Turbine Wake Turbulence Intensity Predictions. Renewable Energy, 189, pp: 762-776. Doi: 10.1016/j.renene.2022.02.115
  12. Li, L., Z. Huang, M. Ge and Q. Zhang, 2022. A Novel Three-Dimensional Analytical Model of the Added Streamwise Turbulence Intensity for Wind-Turbine Wakes. Energy, 238, pp: 121806. Doi: 10.1016/
  13. Asad Ayoubi, P., M. Eftekhari Yazdi and I. Harsini, 2022. A 3D Analytical Model for Predicting Horizontal-Axis Wind Turbines Wake Based on a 2D Analytical Wake Model. Environmental Progress & Sustainable Energy. (Published Online) Doi:10.1002/ep.13856
  14. Ge, M., Y. Wu, Y. Liu and X.I. Yang, 2019. A Two-Dimensional Jensen Model with a Gaussian-Shaped Velocity Deficit. Renewable Energy, 141, pp: 46-56. Doi: 10.1016/j.renene.2019.03.127
  15. Bastankhah, M. and F. Porté-Agel, 2014. A New Analytical Model for Wind-Turbine Wakes. Renewable Energy, 70, pp: 116-123. Doi: 10.1016/j.renene.2014.01.002
  16. Gao, X., H. Yang and L. Lu, 2016. Optimization of Wind Turbine Layout Position in a Wind Farm Using a Newly-Developed Two-Dimensional Wake Model. Applied Energy, 174, pp: 192-200. Doi: 10.1016/j.apenergy.2016.04.098
  17. Ishihara, T. and G.-W. Qian, 2018. A New Gaussian-Based Analytical Wake Model for Wind Turbines Considering Ambient Turbulence Intensities and Thrust Coefficient Effects. Journal of Wind Engineering and Industrial Aerodynamics, 177, pp: 275-292. Doi: 10.1016/j.jweia.2018.04.010
  18. Zhang, W., Z. Lin and X. Liu, 2022. Short-Term Offshore Wind Power Forecasting-a Hybrid Model Based on Discrete Wavelet Transform (Dwt), Seasonal Autoregressive Integrated Moving Average (Sarima), and Deep-Learning-Based Long Short-Term Memory (Lstm). Renewable Energy, 185, pp: 611-628. Doi: 10.1016/j.renene.2021.12.100
  19. Rayi, V.K., S. Mishra, J. Naik and P. Dash, 2022. Adaptive Vmd Based Optimized Deep Learning Mixed Kernel Elm Autoencoder for Single and Multistep Wind Power Forecasting. Energy, 244, pp: 122585. Doi: 10.1016/
  20. Sasser, C., M. Yu and R. Delgado, 2022. Improvement of Wind Power Prediction from Meteorological Characterization with Machine Learning Models. Renewable Energy, 183, pp: 491-501. Doi: 10.1016/j.renene.2021.10.034
  21. Tian, L., W. Zhu, W. Shen, Y. Song and N. Zhao, 2017. Prediction of Multi-Wake Problems Using an Improved Jensen Wake Model. Renewable Energy, 102, pp: 457-469. Doi: 10.1016/j.renene.2016.10.065
  22. Wang, L., A.C. Tan, M. Cholette and Y. Gu, 2016. Comparison of the Effectiveness of Analytical Wake Models for Wind Farm with Constant and Variable Hub Heights. Energy Conversion and Management, 124, pp: 189-202. Doi: 10.1016/j.enconman.2016.07.017
  23. Niayifar, A. and F. Porté-Agel, 2016. Analytical Modeling of Wind Farms: A New Approach for Power Prediction. Energies, 9(9), pp: 741. Doi: 10.3390/en9090741
  24. Naderi, S., S. Parvanehmasiha and F. Torabi, 2018. Modeling of Horizontal Axis Wind Turbine Wakes in Horns Rev Offshore Wind Farm Using an Improved Actuator Disc Model Coupled with Computational Fluid Dynamic. Energy Conversion and Management, 171, pp: 953-968. Doi: 10.1016/j.enconman.2018.06.043
  25. Wu, Y.-T. and F. Porté-Agel, 2015. Modeling Turbine Wakes and Power Losses within a Wind Farm Using LES: An Application to the Horns Rev Offshore Wind Farm. Renewable Energy, 75, pp: 945-955. Doi: 10.1016/j.renene.2014.06.019
  26. Katic, I., J. Højstrup and N.O. Jensen, 1987. A Simple Model for Cluster Efficiency. European wind energy association conference and exhibition, 1, pp: 407-410.
  27. Kim, H., C. Singh and A. Sprintson, 2012. Simulation and Estimation of Reliability in a Wind Farm Considering the Wake Effect. IEEE Transactions on Sustainable Energy, 3(2), pp: 274-282. Doi: 10.1109/TSTE.2011.2174260
  28. Gao, X., B. Li, T. Wang, H. Sun, H. Yang, Y. Li, Y. Wang and F. Zhao, 2020. Investigation and Validation of 3D Wake Model for Horizontal-Axis Wind Turbines Based on Filed Measurements. Applied Energy, 260, pp: 114272. Doi: 10.1016/j.apenergy.2019.114272
  29. Renkema, D.J., 2007. Validation of Wind Turbine Wake Models, Master of Science Thesis. Delft University of Technology, 19, Pages: 590.