Skip to main content

Main menu

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
    • Front Matter Portal
    • Journal Club
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Accessibility Statement
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian

User menu

  • Log in
  • My Cart

Search

  • Advanced search
Home
Home
  • Log in
  • My Cart

Advanced Search

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
    • Front Matter Portal
    • Journal Club
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
Research Article

Two methods for estimating limits to large-scale wind power generation

Lee M. Miller, Nathaniel A. Brunsell, David B. Mechem, Fabian Gans, Andrew J. Monaghan, Robert Vautard, David W. Keith, and Axel Kleidon
  1. aMax Planck Institute for Biogeochemistry, 07701 Jena, Germany;
  2. bUniversity of Kansas, Lawrence, KS 66045;
  3. cNational Center for Atmospheric Research, Boulder, CO 80305;
  4. 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;
  5. eHarvard University, Cambridge, MA 02138

See allHide authors and affiliations

PNAS first published August 24, 2015; https://doi.org/10.1073/pnas.1408251112
Lee M. Miller
aMax Planck Institute for Biogeochemistry, 07701 Jena, Germany;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: lmiller@bgc-jena.mpg.de
Nathaniel A. Brunsell
bUniversity of Kansas, Lawrence, KS 66045;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
David B. Mechem
bUniversity of Kansas, Lawrence, KS 66045;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Fabian Gans
aMax Planck Institute for Biogeochemistry, 07701 Jena, Germany;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Andrew J. Monaghan
cNational Center for Atmospheric Research, Boulder, CO 80305;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Robert Vautard
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;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
David W. Keith
eHarvard University, Cambridge, MA 02138
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Axel Kleidon
aMax Planck Institute for Biogeochemistry, 07701 Jena, Germany;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  1. Edited* by Christopher J. R. Garrett, University of Victoria, Victoria, BC, Canada, and approved June 25, 2015 (received for review May 6, 2014)

  • Article
  • Figures & SI
  • Info & Metrics
  • PDF
Loading

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.

Next
Back to top
Article Alerts
Email Article

Thank you for your interest in spreading the word on PNAS.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
Two methods for estimating limits to large-scale wind power generation
(Your Name) has sent you a message from PNAS
(Your Name) thought you would like to see the PNAS web site.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Citation Tools
Limits to wind power using two methods
Lee M. Miller, Nathaniel A. Brunsell, David B. Mechem, Fabian Gans, Andrew J. Monaghan, Robert Vautard, David W. Keith, Axel Kleidon
Proceedings of the National Academy of Sciences Aug 2015, 201408251; DOI: 10.1073/pnas.1408251112

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Request Permissions
Share
Limits to wind power using two methods
Lee M. Miller, Nathaniel A. Brunsell, David B. Mechem, Fabian Gans, Andrew J. Monaghan, Robert Vautard, David W. Keith, Axel Kleidon
Proceedings of the National Academy of Sciences Aug 2015, 201408251; DOI: 10.1073/pnas.1408251112
del.icio.us logo Digg logo Reddit logo Twitter logo CiteULike logo Facebook logo Google logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Mendeley logo Mendeley
Proceedings of the National Academy of Sciences: 118 (15)
Current Issue

Submit

Sign up for Article Alerts

Jump to section

  • Article
  • Figures & SI
  • Info & Metrics
  • PDF

You May Also be Interested in

Water from a faucet fills a glass.
News Feature: How “forever chemicals” might impair the immune system
Researchers are exploring whether these ubiquitous fluorinated molecules might worsen infections or hamper vaccine effectiveness.
Image credit: Shutterstock/Dmitry Naumov.
Reflection of clouds in the still waters of Mono Lake in California.
Inner Workings: Making headway with the mysteries of life’s origins
Recent experiments and simulations are starting to answer some fundamental questions about how life came to be.
Image credit: Shutterstock/Radoslaw Lecyk.
Cave in coastal Kenya with tree growing in the middle.
Journal Club: Small, sharp blades mark shift from Middle to Later Stone Age in coastal Kenya
Archaeologists have long tried to define the transition between the two time periods.
Image credit: Ceri Shipton.
Illustration of groups of people chatting
Exploring the length of human conversations
Adam Mastroianni and Daniel Gilbert explore why conversations almost never end when people want them to.
Listen
Past PodcastsSubscribe
Panda bear hanging in a tree
How horse manure helps giant pandas tolerate cold
A study finds that giant pandas roll in horse manure to increase their cold tolerance.
Image credit: Fuwen Wei.

Similar Articles

Site Logo
Powered by HighWire
  • Submit Manuscript
  • Twitter
  • Facebook
  • RSS Feeds
  • Email Alerts

Articles

  • Current Issue
  • Special Feature Articles – Most Recent
  • List of Issues

PNAS Portals

  • Anthropology
  • Chemistry
  • Classics
  • Front Matter
  • Physics
  • Sustainability Science
  • Teaching Resources

Information

  • Authors
  • Editorial Board
  • Reviewers
  • Subscribers
  • Librarians
  • Press
  • Cozzarelli Prize
  • Site Map
  • PNAS Updates
  • FAQs
  • Accessibility Statement
  • Rights & Permissions
  • About
  • Contact

Feedback    Privacy/Legal

Copyright © 2021 National Academy of Sciences. Online ISSN 1091-6490