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Edited* by Christopher J. R. Garrett, University of Victoria, Victoria, BC, Canada, and approved June 25, 2015 (received for review May 6, 2014)
Significance
Wind turbines generate electricity by removing kinetic energy from the atmosphere. We show that the limited replenishment of kinetic energy from aloft limits wind power generation rates at scales sufficiently large that horizontal fluxes of kinetic energy can be ignored. We evaluate these factors with regional atmospheric model simulations and find that generation limits can be estimated from the ‟preturbine” climatology by comparatively simple means, working best when the atmosphere between the surface and hub height is naturally well-mixed during the day. Our results show that the reduction of wind speeds and limited downward fluxes determine the limits in large-scale wind power generation to less than 1 W⋅m−2.
Abstract
Wind turbines remove kinetic energy from the atmospheric flow, which reduces wind speeds and limits generation rates of large wind farms. These interactions can be approximated using a vertical kinetic energy (VKE) flux method, which predicts that the maximum power generation potential is 26% of the instantaneous downward transport of kinetic energy using the preturbine climatology. We compare the energy flux method to the Weather Research and Forecasting (WRF) regional atmospheric model equipped with a wind turbine parameterization over a 105 km2 region in the central United States. The WRF simulations yield a maximum generation of 1.1 We⋅m−2, whereas the VKE method predicts the time series while underestimating the maximum generation rate by about 50%. Because VKE derives the generation limit from the preturbine climatology, potential changes in the vertical kinetic energy flux from the free atmosphere are not considered. Such changes are important at night when WRF estimates are about twice the VKE value because wind turbines interact with the decoupled nocturnal low-level jet in this region. Daytime estimates agree better to 20% because the wind turbines induce comparatively small changes to the downward kinetic energy flux. This combination of downward transport limits and wind speed reductions explains why large-scale wind power generation in windy regions is limited to about 1 We⋅m−2, with VKE capturing this combination in a comparatively simple way.
Footnotes
- ↵1To whom correspondence should be addressed. Email: lmiller{at}bgc-jena.mpg.de.
Author contributions: L.M.M., N.A.B., and A.K. designed research; L.M.M., N.A.B., D.B.M., F.G., A.J.M., R.V., D.W.K., and A.K. performed research; L.M.M., N.A.B., D.B.M., and A.K. analyzed data; and L.M.M., N.A.B., D.B.M., A.J.M., R.V., D.W.K., and A.K. wrote the paper.
The authors declare no conflict of interest.
↵*This Direct Submission article had a prearranged editor.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1408251112/-/DCSupplemental.
Freely available online through the PNAS open access option.
- Lee M. Millera,1,
- Nathaniel A. Brunsellb,
- David B. Mechemb,
- Fabian Gansa,
- Andrew J. Monaghanc,
- Robert Vautardd,
- David W. Keithe, and
- Axel Kleidona
- aMax Planck Institute for Biogeochemistry, 07701 Jena, Germany;
- bUniversity of Kansas, Lawrence, KS 66045;
- cNational Center for Atmospheric Research, Boulder, CO 80305;
- dLaboratoire des Sciences du Climat et de l’Environnement, Institut Pierre-Simon Laplace, Laboratoire Commissariat à l’Énergie Atomique, CNRS, Université de Versailles Saint-Quentin-en-Yvelines, Gif/Yvette Cedex, 78000 Versailles, France;
- eHarvard University, Cambridge, MA 02138
Edited* by Christopher J. R. Garrett, University of Victoria, Victoria, BC, Canada, and approved June 25, 2015 (received for review May 6, 2014)
Significance
Wind turbines generate electricity by removing kinetic energy from the atmosphere. We show that the limited replenishment of kinetic energy from aloft limits wind power generation rates at scales sufficiently large that horizontal fluxes of kinetic energy can be ignored. We evaluate these factors with regional atmospheric model simulations and find that generation limits can be estimated from the ‟preturbine” climatology by comparatively simple means, working best when the atmosphere between the surface and hub height is naturally well-mixed during the day. Our results show that the reduction of wind speeds and limited downward fluxes determine the limits in large-scale wind power generation to less than 1 W⋅m−2.
Abstract
Wind turbines remove kinetic energy from the atmospheric flow, which reduces wind speeds and limits generation rates of large wind farms. These interactions can be approximated using a vertical kinetic energy (VKE) flux method, which predicts that the maximum power generation potential is 26% of the instantaneous downward transport of kinetic energy using the preturbine climatology. We compare the energy flux method to the Weather Research and Forecasting (WRF) regional atmospheric model equipped with a wind turbine parameterization over a 105 km2 region in the central United States. The WRF simulations yield a maximum generation of 1.1 We⋅m−2, whereas the VKE method predicts the time series while underestimating the maximum generation rate by about 50%. Because VKE derives the generation limit from the preturbine climatology, potential changes in the vertical kinetic energy flux from the free atmosphere are not considered. Such changes are important at night when WRF estimates are about twice the VKE value because wind turbines interact with the decoupled nocturnal low-level jet in this region. Daytime estimates agree better to 20% because the wind turbines induce comparatively small changes to the downward kinetic energy flux. This combination of downward transport limits and wind speed reductions explains why large-scale wind power generation in windy regions is limited to about 1 We⋅m−2, with VKE capturing this combination in a comparatively simple way.
- generation limits
- turbine–atmosphere interactions
- wind resource
- kinetic energy flux
- extraction limits
Footnotes
- ↵1To whom correspondence should be addressed. Email: lmiller{at}bgc-jena.mpg.de.
Author contributions: L.M.M., N.A.B., and A.K. designed research; L.M.M., N.A.B., D.B.M., F.G., A.J.M., R.V., D.W.K., and A.K. performed research; L.M.M., N.A.B., D.B.M., and A.K. analyzed data; and L.M.M., N.A.B., D.B.M., A.J.M., R.V., D.W.K., and A.K. wrote the paper.
The authors declare no conflict of interest.
↵*This Direct Submission article had a prearranged editor.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1408251112/-/DCSupplemental.
Freely available online through the PNAS open access option.
Limits to wind power using two methods
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