Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-09-01T04:17:34.905Z Has data issue: false hasContentIssue false
  • English
  • Français

A momentum-conserving wake superposition method for wind farm power prediction

Published online by Cambridge University Press:  24 February 2020

Haohua Zong Open the ORCID record for Haohua Zong [Opens in a new window]  and
Fernando Porté-Agel Open the ORCID record for Fernando Porté-Agel [Opens in a new window]
Haohua Zong*
Affiliation:
Wind Engineering and Renewable Energy Laboratory (WIRE), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-ENAC-IIE-WIRE, 1015Lausanne, Switzerland
Fernando Porté-Agel
Affiliation:
Wind Engineering and Renewable Energy Laboratory (WIRE), École Polytechnique Fédérale de Lausanne (EPFL), EPFL-ENAC-IIE-WIRE, 1015Lausanne, Switzerland
*
†Email address for correspondence: haohua_zong@126.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Analytical wind turbine wake models and wake superposition methods are prevailing tools widely adopted by the wind energy community to predict the power production of wind farms. However, none of the existing wake superposition methods conserve the streamwise momentum. In this study, a novel wake superposition method capable of conserving the total momentum deficit in the streamwise direction is derived theoretically, and its performance is validated with both particle imaging velocimetry measurements and large-eddy simulation results. Detailed inter-method comparisons show that the novel wake superposition method outperforms all the existing methods by delivering an accurate prediction of the power production and the centreline wake velocity deficit, with a typical error of less than 5 % (excluding the near-wake region). Additionally, the momentum-conserving wake superposition method is extended to combine the transverse velocities induced by yawed wind turbines, and the secondary wake steering effect crucial to the power optimization in active wake control is well reproduced.

JFM classification

Wakes/Jets: Wakes

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A8
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Anderson, J. D. 2010 Fundamentals of Aerodynamics. Tata McGraw-Hill Education.Google Scholar
Barthelmie, R. J., Pryor, S. C., Frandsen, S. T., Hansen, K. S., Schepers, J. G., Rados, K., Schlez, W., Neubert, A., Jensen, L. E. & Neckelmann, S. 2010 Quantifying the impact of wind turbine wakes on power output at offshore wind farms. J. Atmos. Ocean. Technol. 27 (8), 1302–1317.CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2014 A new analytical model for wind-turbine wakes. J. Renew. Energy 70, 116–123.CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2016 Experimental and theoretical study of wind turbine wakes in yawed conditions. J. Fluid Mech. 806, 506–541.CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2017 A new miniature wind turbine for wind tunnel experiments. Part I: Design and performance. Energies 10 (7), 908.CrossRefGoogle Scholar
Bastankhah, M. & Porté-Agel, F. 2019 Wind farm power optimization via yaw angle control: a wind tunnel study. J. Renew. Sustain. Energy 11 (2), 023301.CrossRefGoogle Scholar
Bay, C., King, J., Fleming, P., Mudafort, R. & Martinez, L.2019 Unlocking the full potential of wake steering: implementation and assessment of a controls-oriented model. Tech. Rep. NREL/JA-5000-73777. National Renewable Energy Lab, USA.CrossRefGoogle Scholar
Chamorro, L. P. & Porté-Agel, F. 2010 Effects of thermal stability and incoming boundary-layer flow characteristics on wind-turbine wakes: a wind-tunnel study. Boundary-Layer Meteorol. 136 (3), 515–533.CrossRefGoogle Scholar
Frandsen, S., Barthelmie, R., Pryor, S., Rathmann, O., Larsen, S., Højstrup, J. & Thøgersen, M. 2006 Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energy 9 (1–2), 39–53.CrossRefGoogle Scholar
Jensen, N. O.1983 A note on wind turbine interaction. Tech. Rep. Ris-M-2411. Risoe National Laboratory.Google Scholar
Jiménez, Á., Crespo, A. & Migoya, E. 2010 Application of a LES technique to characterize the wake deflection of a wind turbine in yaw. Wind Energy 13 (6), 559–572.CrossRefGoogle Scholar
Katic, I., Højstrup, J. & Jensen, N. O. 1987 A simple model for cluster efficiency. In European Wind Energy Association Conference and Exhibition. A. Raguzzi.Google Scholar
Lissaman, P. B. S. 1979 Energy effectiveness of arbitrary arrays of wind turbines. J. Energy 3 (6), 323–328.CrossRefGoogle Scholar
Niayifar, A. & Porté-Agel, F. 2016 Analytical modeling of wind farms: a new approach for power prediction. Energies 9 (9), 741.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Porté-Agel, F., Bastankhah, M. & Shamsoddin, S. 2019 Wind-turbine and wind-farm flows: a review. Boundary-Layer Meteorol. 174 (1), 1–59.CrossRefGoogle ScholarPubMed
Porté-Agel, F., Wu, Y.-T. & Chen, C.-H. 2013 A numerical study of the effects of wind direction on turbine wakes and power losses in a large wind farm. Energies 6 (10), 5297–5313.CrossRefGoogle Scholar
Shapiro, C. R., Gayme, D. F. & Meneveau, C. 2018 Modelling yawed wind turbine wakes: a lifting line approach. J. Fluid Mech. 841, R1.CrossRefGoogle Scholar
Stevens, R. J. & Meneveau, C. 2017 Flow structure and turbulence in wind farms. Annu. Rev Fluid Mech. 49, 311–339.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Vermeulen, P. E. J.1980 An experimental analysis of wind turbine wakes. In 3rd International Symposium on Wind Energy Systems, Lyngby, Denmark, pp. 431–450.Google Scholar
Voutsinas, S., Rados, K. & Zervos, A. 1990 On the analysis of wake effects in wind parks. Wind Engng 204–219.Google Scholar