The Shepherds Flat Wind Farm is an 845 MW wind farm in the U.S. state of Oregon. Credit: Steve Wilson / Wikipedia.

(Phys.org)—Wind turbine farms now account for an estimated 3.3 percent of electricity generation in the United States, and 2.9 percent of electricity generated globally. The wind turbine industry is growing along all vectors, with increasingly sprawling farms of ever-larger and more densely sited turbines producing growing amounts of power. But the laws of physics are stubborn—wind turbines remove kinetic energy from the atmospheric flow. So engineers and scientists have sought realistic estimates of the limits to large-scale wind generation. Such estimates could provide guidelines for the maximum size and density to which a wind turbine farm can increase before reaching a point of diminishing returns.

An international group of researchers recently collaborated on a comparison of two different methods of estimating the limits of power generation for wind farms, which has been reported in the Proceedings of the National Academy of Sciences. They approximated the dynamics by which wind turbines remove kinetic energy from the atmosphere using the vertical kinetic energy (VKE) flux method and compared the results to those from the Weather Research and Forecasting (WRF) regional atmospheric model. Their findings are complex, and while the two techniques produce results that diverge in many ways, together, they illuminate atmospheric variables that are not obviously revealed by the two methods in isolation.

To evaluate the limits to wind power generation, they used reference climatology of Central Kansas for the time period of May 15 to September 30, 2001. The simulation uses a horizontal farm grid spacing of 12 km with 31 vertical levels. Wind turbine characteristics were modeled on the technical specifications of existing models.

The WRF simulations include a realistic parameterization of wind turbines, and the results demonstrated that a greater installed capacity within a wind farm region increases the total rate of electricity generation. When the installed capacity of the wind farm is increased, the marginal return of electricity generation occurs during periods with higher wind speeds. The authors note that their results do not account for the effects of reduced wind speeds within wind farms, and that the numbers from WRF simulations are likely to be too high.

The VKE flux method captures the magnitude of wind power generation along with temporal variations, but does not account for atmospheric effects. While the daily mean estimates for electricity generation produced by the two methods are closely correlated, WRF is much better at capturing accurate estimates at night—VKE underestimates nighttime generation magnitudes by almost 45 percent. "We attribute this underestimation of wind power generation by VKE at night to its use of the preturbine downward kinetic flux of the control. The atmospheric flow in [Central Kansas] typically decouples from the stable surface conditions at night in the summer, which leads to the formation of the low-level jet near the surface," the authors write.

Nevertheless, VKE captures the temporal dynamics and the reduction in wind speed quite well, and the authors consider the two methods to be energetically consistent with one another. The study concludes that comparatively simple methods can be applied to estimates of large-scale wind power generation. The authors write, "Although many current wind farms are still comparatively small and can therefore sustain greater generation rates, an energetically consistent approach becomes relevant when the installed capacity of the wind farm approaches the kinetic energy flux into the wind farm region."

More information: "Two methods for estimating limits to large-scale wind power generation." PNAS 2015 ; published ahead of print August 24, 2015, "Two methods for estimating limits to large-scale wind power generation."2015 ; published ahead of print August 24, 2015, DOI: 10.1073/pnas.1408251112 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. Journal information: Proceedings of the National Academy of Sciences

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