Power output and wake effects of very large wind farms investigated by large-eddy simulations

Abstract

Wind energy will be one of the most important energy sources in the carbon-neutral energy system of the future. A small but rapidly growing share of the installed wind capacity con- sists of offshore wind farms, which benefit from the high wind speeds and small turbulence intensities that prevail offshore. However, with the increasing expansion of offshore wind energy, these beneficial conditions are being affected by the wind farms themselves. Offshore wind farms can produce long wakes in which the wind speed is reduced and the turbulence intensity is enhanced. Additionally, the power output of the wind farm is reduced due to wake losses inside the wind farm. The aim of this thesis is to investigate the power output and wake effects of large (multi-gigawatt) wind farms with large-eddy simulations. Wind farms of this size have never been investigated before. The results show that the flow in large wind farms is more complex than in small (sub- gigawatt) wind farms. Large wind farms cause a counterclockwise flow deflection in the order of 10◦ due to a reduced Coriolis force inside the wind farm. The wind farm induced speed deficit spreads into the entire boundary layer and causes the flow to diverge in the vertical direction. This results in a vertical displacement of the inversion layer, which excites statio- nary gravity waves in the free atmosphere. The gravity waves affect the pressure distribution near the surface and cause a significant flow blockage resulting in speed deficits of approxi- mately 10% upstream of the wind farm. Smaller wind farms can also excite gravity waves, but their amplitude and blockage effect is much weaker. Simulations with wind farms that have a finite size in both lateral directions show that large wind farms cause a significant flow divergence in the crosswise direction. Large wind farms generate wakes with a length in the order of 100 km. Longer wakes (in terms of wind speed deficit) occur for shallower boundary layers and smaller turbine spacings. The effect of the atmospheric stability on the wake length could not clearly be stated because this parameter can not be changed without affecting others. The wake length in terms of turbulence intensity was found to be in the order of 10 km and to be independent of the wind farm size. In the simulated cases, large wind farms achieved wind farm efficiencies of only 41% − 64% in contrast to 66%−88% for small wind farms. The boundary layer height significantly affects the efficiency of large wind farms but not the efficiency of small wind farms. Energy budget analyses have shown that the advection of kinetic energy by the mean flow is the largest energy source for small wind farms. However, for large wind farms the largest energy source is the vertical turbulent flux of kinetic energy. For large wind farms the energy input by the geostrophic forcing becomes more dominant. This source is also enhanced by an increase in the ageostrophic wind speed component resulting from the counterclockwise flow deflection. A comparison with analytical wake models shows that their power output prediction deviates from the large-eddy simulation results by up to 40% and that they can not reproduce the flow complexity of large wind farms. The reason is that the wake models neglect relevant physical processes and energy sources and sinks. Further large-eddy simulation case studies with a systematic variation of the relevant parameters are needed to learn more about the flow behavior in large wind farms and to improve existing wake models.