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Turbulence coherence and its impact on wind-farm power fluctuations. (English) Zbl 1415.76365

Summary: Using a physics-based approach, we infer the impact of the coherence of atmospheric turbulence on the power fluctuations of wind farms. Application of the random-sweeping hypothesis reveals correlations characterized by advection and turbulent diffusion of coherent motions. Those contribute to local peaks and troughs in the power spectrum of the combined units at frequencies corresponding to the advection time between turbines, which diminish in magnitude at high frequencies. Experimental inspection supports the results from the random-sweeping hypothesis in predicting spectral characteristics, although the magnitude of the coherence spectrum appears to be over-predicted. This deviation is attributed to the presence of turbine wakes, and appears to be a function of the turbulence approaching the first turbine in a pair.

MSC:

76F40 Turbulent boundary layers
76F05 Isotropic turbulence; homogeneous turbulence
Full Text: DOI

References:

[1] Abkar, M.; Dabiri, J. O., Self-similarity and flow characteristics of vertical-axis wind turbine wakes: an les study, J. Turbul., 18, 4, 373-389, (2017) · doi:10.1080/14685248.2017.1284327
[2] Abkar, M.; Porté-Agel, F., Influence of atmospheric stability on wind-turbine wakes: a large-eddy simulation study, Phys. Fluids, 27, 3, (2015) · doi:10.1063/1.4913695
[3] Adrian, R. J.; Meinhart, C. D.; Tomkins, C. D., Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech., 422, 1-54, (2000) · Zbl 0959.76503 · doi:10.1017/S0022112000001580
[4] Anvari, M.; Lohmann, G.; Wächter, M.; Milan, P.; Lorenz, E.; Heinemann, D.; Tabar, M. R. R.; Peinke, J., Short term fluctuations of wind and solar power systems, New J. Phys., 18, 6, (2016) · doi:10.1088/1367-2630/18/6/063027
[5] Anvari, M.; Wächter, M.; Peinke, J., Phase locking of wind turbines leads to intermittent power production, Europhys. Lett., 116, 6, (2017)
[6] Apt, J., The spectrum of power from wind turbines, J. Power Sources, 169, 2, 369-374, (2007) · doi:10.1016/j.jpowsour.2007.02.077
[7] Bandi, M. M., Spectrum of wind power fluctuations, Phys. Rev. Lett., 118, 2, (2017) · doi:10.1103/PhysRevLett.118.028301
[8] Bossuyt, J.; Meneveau, C.; Meyers, J., Wind farm power fluctuations and spatial sampling of turbulent boundary layers, J. Fluid Mech., 823, 329-344, (2017) · Zbl 1374.76089 · doi:10.1017/jfm.2017.328
[9] Chamorro, L. P.; Guala, M.; Arndt, R. E. A.; Sotiropoulos, F., On the evolution of turbulent scales in the wake of a wind turbine model, J. Turbul., 13, (2012) · doi:10.1080/14685248.2012.697169
[10] Chamorro, L. P.; Lee, S.-J.; Olsen, D.; Milliren, C.; Marr, J.; Arndt, R. E. A.; Sotiropoulos, F., Turbulence effects on a full-scale 2.5 mw horizontal-axis wind turbine under neutrally stratified conditions, Wind Energy, 18, 2, 339-349, (2015) · doi:10.1002/we.1700
[11] Cortina, G.; Calaf, M.; Cal, R. B., Distribution of mean kinetic energy around an isolated wind turbine and a characteristic wind turbine of a very large wind farm, Phys. Rev. F, 1, 7, (2016)
[12] Davenport, A. G., The spectrum of horizontal gustiness near the ground in high winds, Q. J. R. Meteorol. Soc., 87, 372, 194-211, (1961) · doi:10.1002/qj.49708737208
[13] Espana, G.; Aubrun, S.; Loyer, S.; Devinant, P., Wind tunnel study of the wake meandering downstream of a modelled wind turbine as an effect of large scale turbulent eddies, J. Wind Engng Ind. Aerodyn., 101, 24-33, (2012) · doi:10.1016/j.jweia.2011.10.011
[14] Jimenez, A.; Crespo, A.; Migoya, E.; García, J., Large-eddy simulation of spectral coherence in a wind turbine wake, Environ. Res. Lett., 3, 1, (2008) · doi:10.1088/1748-9326/3/1/015004
[15] Johnson, E.; Fontaine, A. A.; Jonson, M. L.; Meyer, R. S.; Straka, W. A.; Young, S.; Van Dam, C. P.; Shiu, H.; Barone, M., A 1:8.7 scale water tunnel test of an axial flow water turbine, Proceedings of the 1st Marine Energy Technology Symposium, (2013), Washington, DC
[16] Katzenstein, W.; Fertig, E.; Apt, J., The variability of interconnected wind plants, Energy Policy, 38, 8, 4400-4410, (2010) · doi:10.1016/j.enpol.2010.03.069
[17] Kinzel, M.; Araya, D. B.; Dabiri, J. O., Turbulence in vertical axis wind turbine canopies, Phys. Fluids, 27, 11, (2015) · doi:10.1063/1.4935111
[18] Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR, 30, 299-303, (1941)
[19] Kraichnan, R. H., Kolmogorov’s hypotheses and Eulerian turbulence theory, Phys. Fluids, 7, 11, 1723-1734, (1964) · Zbl 0151.41701 · doi:10.1063/1.2746572
[20] Lignarolo, L. E. M.; Ragni, D.; Scarano, F.; Ferreira, C. J. S.; Van Bussel, G. J. W., Tip-vortex instability and turbulent mixing in wind-turbine wakes, J. Fluid Mech., 781, 467-493, (2015) · Zbl 1359.76132 · doi:10.1017/jfm.2015.470
[21] Liu, H.; Jin, Y.; Tobin, N.; Chamorro, L. P., Towards uncovering the structure of power fluctuations of wind farms, Phys. Rev. E, 96, 6, (2017)
[22] Lu, H.; Porté-Agel, F., Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer, Phys. Fluids, 23, 6, (2011)
[23] Lukassen, L. J.; Stevens, R. J. A. M.; Meneveau, C.; Wilczek, M., Modeling space-time correlations of velocity fluctuations in wind farms, Wind Energy, 21, 7, 474-487, (2018) · doi:10.1002/we.2172
[24] Milan, P.; Wächter, M.; Peinke, J., Turbulent character of wind energy, Phys. Rev. Lett., 110, 13, (2013) · doi:10.1103/PhysRevLett.110.138701
[25] Panofsky, H. A.; Dutton, J. A., Atmospheric Turbulence: Models and Methods for Engineering Aplications, (1984), Wiley
[26] Schlez, W.; Infield, D., Horizontal, two point coherence for separations greater than the measurement height, Boundary-Layer Meteorol., 87, 3, 459-480, (1998) · doi:10.1023/A:1000997610233
[27] Shiu, H.; Van Dam, C. P.; Johnson, E.; Barone, M.; Phillips, R.; Straka, W.; Fontaine, A.; Jonson, M., A design of a hydrofoil family for current-driven marine-hydrokinetic turbines, Proceedings of the 2012 20th International Conference on Nuclear Engineering Collocated with the ASME 2012 Power Conference ICONE20-POWER2012, (2012), American Society of Mechanical Engineers
[28] Sørensen, P.; Cutululis, N. A.; Vigueras-Rodríguez, A.; Madsen, H.; Pinson, P.; Jensen, L. E.; Hjerrild, J.; Donovan, M., Modelling of power fluctuations from large offshore wind farms, Wind Energy, 11, 1, 29-43, (2008) · doi:10.1002/we.246
[29] Stevens, R. J. A. M.; Meneveau, C., Temporal structure of aggregate power fluctuations in large-eddy simulations of extended wind-farms, J. Renew. Energy, 6, 4, (2014)
[30] Tabar, M. R.; Anvari, M.; Lohmann, G.; Heinemann, D.; Wächter, M.; Milan, P.; Lorenz, E.; Peinke, J., Kolmogorov spectrum of renewable wind and solar power fluctuations, Eur. Phys. J.-Spec. Top., 223, 12, 2637-2644, (2014) · doi:10.1140/epjst/e2014-02217-8
[31] Tennekes, H., Eulerian and Lagrangian time microscales in isotropic turbulence, J. Fluid Mech., 67, 3, 561-567, (1975) · Zbl 0302.76033 · doi:10.1017/S0022112075000468
[32] Tian, W.; Ozbay, A.; Hu, H., Effects of incoming surface wind conditions on the wake characteristics and dynamic wind loads acting on a wind turbine model, Phys. Fluids, 26, 12, (2014) · doi:10.1063/1.4904375
[33] Tian, W.; Ozbay, A.; Hu, H., An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms, Wind Energy, 21, 2, 100-114, (2018) · doi:10.1002/we.2147
[34] Tobin, N.; Hamed, A. M.; Chamorro, L. P., Fractional flow speed-up from porous windbreaks for enhanced wind-turbine power, Boundary-Layer Meteorol., 163, 2, 253-271, (2017) · doi:10.1007/s10546-016-0228-8
[35] Tobin, N.; Zhu, H.; Chamorro, L. P., Spectral behaviour of the turbulence-driven power fluctuations of wind turbines, J. Turbul., 16, 9, 832-846, (2015) · doi:10.1080/14685248.2015.1031242
[36] Vigueras-Rodríguez, A.; Sørensen, P.; Cutululis, N. A.; Viedma, A.; Donovan, M. H., Wind model for low frequency power fluctuations in offshore wind farms, Wind Energy, 13, 5, 471-482, (2010) · doi:10.1002/we.368
[37] Wilczek, M.; Stevens, R. J. A. M.; Meneveau, C., Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models, J. Fluid Mech., 769, R1, (2015) · doi:10.1017/jfm.2015.116
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