Under the term global blockage, the cumulative induction of wind turbines in a wind farm has been recently suspected to be responsible for observed overestimations of the energy yield in large-size wind farms. In this paper, the practice of modeling this effect after linear superposition of single turbine inductions, calculated with three of the most recent analytic models, is compared to Large-Eddy-Simulations of idealized wind farms. We compare the models across two different farms, composed of 9 and 49 turbines, with two different heights of the atmospheric boundary layer, 300 and 500 m. The results show that the differences between the analytical models are negligible while they substantially differ from the LES results. The linear superposition of induction consistently underestimates the upstream velocity deficit with an error that increases as the wind farm size grows and the ABL height decreases. Also when calculating the power output at the turbines of the farm, the analytical models considered do not agree well with the LES. These comparisons reveal that the farm interactions with the atmospheric boundary layer may highly outclass the turbine induction in determining the extent of the global blockage effect. Therefore, we present a first dimensional approach to the problem based on LES, aimed at simplifying its characterization.

Abstract. We propose that considering mesoscale wind direction changes in the computation of wind farm cluster wakes could reduce the uncertainty of engineering wake modelling tools. The relevance of mesoscale wind direction changes is investigated using a wind climatology of the German Bight area covering 30 years, derived from the New European Wind Atlas (NEWA). Furthermore, we present a new solution for engineering modelling tools that accounts for the effect of such changes on the propagation of cluster wakes. Mesoscale wind direction changes are found to exceed 7° per 100 km in 50 % of all cases and are particularly large in the lower partial load range, which is associated with strong wake formation. Here, the quartiles reach up to 20° per 100 km. Especially on a horizontal scale of several tens to a hundred kilometers, wind direction changes are relevant. Both the temporal and spatial scale at which large wind direction changes occur depend on the presence of pressure systems. Furthermore, atmospheric conditions which promote far-reaching wakes were found to align with a strong turning in 14.6 % of the cases. In order to capture these mesoscale wind direction changes in engineering model tools, a wake propagation model was implemented into the Fraunhofer IWES wind farm and wake modelling software flappy. The propagation model derives streamlines from the horizontal velocity field and forces the single turbine wakes along these streamlines. This model has been qualitatively evaluated by simulating the flow around wind farm clusters in the German Bight with data from the mesoscale atlas of NEWA and comparing the results to Synthetic Aperture Radar (SAR) measurements for selected situations. The comparison reveals that the flow patterns are in good agreement if the underlying mesoscale data capture the velocity field well. For such cases, the new model provides an improvement compared to the baseline approach of engineering models, which assumes a straight-line propagation of wakes. The streamline and the baseline model have been further compared in terms of their quantitative effect on the energy yield. Simulating two neighbouring wind farm clusters over a time period of 10 years, it is found that there are no significant differences across the models when computing the total energy yield of both clusters. However, extracting the wake effect of one cluster on the other, the two models show a difference of about 1 %. Even greater differences are commonly observed when comparing single situations. Therefore, we claim that the model has the potential to reduce uncertainty in applications such as site assessment and short-term power forecasting.

The presence of offshore wind farms causes downstream regions of reduced wind velocity, i.e. wind farm (cluster) wakes, which can affect the power of wind farms downstream. Engineering models are now being used to simulate the effects of these wakes, and an important requirement for model validation is a comparison with full-field measurements. Our objective in this paper is to parametrize and validate two engineering wake models with long-range lidar measurements. We use a long-range scanning Doppler lidar to scan the near wake region of a 400 MW offshore wind farm and compare the wind velocities in the wake to the outputs of two engineering models: FarmFlow and flappy. We adapt FarmFlow to solve the flow in highly unstable atmospheres by modifying the boundary conditions, which enables the comparison of velocity profiles behind the farm. The models perform qualitatively well in predicting the wake deficit and shape close to the farm and at lower heights. They predict higher wake losses within the farm when compared to production power data in a strongly unstable atmospheric case. However, the current analysis is limited due to the lack of inflow measurements for model initialization, compounded by limited data availability. We discuss the possibilities and limitations of long-range scanning lidar data for cluster wake model validation and the need for inflow measurements for model initialization. We conclude that with detailed inflow measurements, scanning long-range lidars could serve as a good tool for the validation of wind farm wake models.

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Abstract. We propose that considering mesoscale wind direction changes in the computation of wind farm cluster wakes could reduce the uncertainty of engineering wake modeling tools. The relevance of mesoscale wind direction changes is investigated using a wind climatology of the German Bight area covering 30 years, derived from the New European Wind Atlas (NEWA). Furthermore, we present a new solution for engineering modeling tools that accounts for the effect of such changes on the propagation of cluster wakes. The mesoscale wind direction changes relevant to the operation of wind farm clusters in the German Bight are found to exceed 11∘ in 50 % of all cases. Particularly in the lower partial load range, which is associated with strong wake formation, the wind direction changes are the most pronounced, with quartiles reaching up to 20∘. Especially on a horizontal scale of several tens of kilometers to 100 km, wind direction changes are relevant. Both the temporal and spatial scales at which large wind direction changes occur depend on the presence of synoptic pressure systems. Furthermore, atmospheric conditions which promote far-reaching wakes were found to align with a strong turning in 14.6 % of the cases. In order to capture these mesoscale wind direction changes in engineering model tools, a wake propagation model was implemented in the Fraunhofer IWES wind farm and wake modeling software flappy (Farm Layout Program in Python). The propagation model derives streamlines from the horizontal velocity field and forces the single turbine wakes along these streamlines. This model has been qualitatively evaluated by simulating the flow around wind farm clusters in the German Bight with data from the mesoscale atlas of the NEWA and comparing the results to synthetic aperture radar (SAR) measurements for selected situations. The comparison reveals that the flow patterns are in good agreement if the underlying mesoscale data capture the velocity field well. For such cases, the new model provides an improvement compared to the baseline approach of engineering models, which assumes a straight-line propagation of wakes. The streamline and the baseline models have been further compared in terms of their quantitative effect on the energy yield. Simulating two neighboring wind farm clusters over a time period of 10 years, it is found that there are no significant differences across the models when computing the total energy yield of both clusters. However, extracting the wake effect of one cluster on the other, the two models show a difference of about 1 %. Even greater differences are commonly observed when comparing single situations. Therefore, we claim that the model has the potential to reduce uncertainty in applications such as site assessment and short-term power forecasting.