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Research Article

Wind speed reductions by large-scale wind turbine deployments lower turbine efficiencies and set low generation limits

Lee M. Miller and Axel Kleidon
  1. aBiospheric Theory and Modelling, Max Planck Institute for Biogeochemistry, D-07701 Jena, Germany

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PNAS November 29, 2016 113 (48) 13570-13575; first published November 14, 2016; https://doi.org/10.1073/pnas.1602253113
Lee M. Miller
aBiospheric Theory and Modelling, Max Planck Institute for Biogeochemistry, D-07701 Jena, Germany
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  • For correspondence: lmiller@seas.harvard.edu
Axel Kleidon
aBiospheric Theory and Modelling, Max Planck Institute for Biogeochemistry, D-07701 Jena, Germany
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  1. Edited by Kerry A. Emanuel, Massachusetts Institute of Technology, Cambridge, MA, and approved September 23, 2016 (received for review February 9, 2016)

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Significance

Understanding the limits of electricity generation from winds is a requirement for planning a renewable energy future. A difficulty in estimating such limits is that wind turbines remove kinetic energy from the atmosphere, so that many turbines should reduce wind speeds, ultimately setting a limit to how much kinetic energy can be taken out of the atmosphere. We show that this slowdown effect can be accounted for by detailed climate model simulations and a relatively simple method that does not directly simulate atmospheric dynamics. This slowdown effect is critical to consider, as it makes each turbine less productive and shows that few land areas can yield more than 1.0 We m−2 of electricity at large scales.

Abstract

Wind turbines generate electricity by removing kinetic energy from the atmosphere. Large numbers of wind turbines are likely to reduce wind speeds, which lowers estimates of electricity generation from what would be presumed from unaffected conditions. Here, we test how well wind power limits that account for this effect can be estimated without explicitly simulating atmospheric dynamics. We first use simulations with an atmospheric general circulation model (GCM) that explicitly simulates the effects of wind turbines to derive wind power limits (GCM estimate), and compare them to a simple approach derived from the climatological conditions without turbines [vertical kinetic energy (VKE) estimate]. On land, we find strong agreement between the VKE and GCM estimates with respect to electricity generation rates (0.32 and 0.37 We m−2) and wind speed reductions by 42 and 44%. Over ocean, the GCM estimate is about twice the VKE estimate (0.59 and 0.29 We m−2) and yet with comparable wind speed reductions (50 and 42%). We then show that this bias can be corrected by modifying the downward momentum flux to the surface. Thus, large-scale limits to wind power use can be derived from climatological conditions without explicitly simulating atmospheric dynamics. Consistent with the GCM simulations, the approach estimates that only comparatively few land areas are suitable to generate more than 1 We m−2 of electricity and that larger deployment scales are likely to reduce the expected electricity generation rate of each turbine. We conclude that these atmospheric effects are relevant for planning the future expansion of wind power.

  • momentum
  • natural limits
  • surface stress
  • wind energy
  • vertical transport

Footnotes

  • ↵1Present address: Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.

  • ↵2To whom correspondence should be addressed. Email: lmiller{at}seas.harvard.edu.
  • Author contributions: L.M.M. and A.K. designed research, performed research, analyzed data, and wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1602253113/-/DCSupplemental.

Freely available online through the PNAS open access option.

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Estimating wind power limits
Lee M. Miller, Axel Kleidon
Proceedings of the National Academy of Sciences Nov 2016, 113 (48) 13570-13575; DOI: 10.1073/pnas.1602253113

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Estimating wind power limits
Lee M. Miller, Axel Kleidon
Proceedings of the National Academy of Sciences Nov 2016, 113 (48) 13570-13575; DOI: 10.1073/pnas.1602253113
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