Annual wake impacts in and between wind farm clusters modelled by a mesoscale numerical weather prediction model and fast-running engineering models

Abstract. With the rapid increase in wind farm developments, it is essential to evaluate the impacts of newly constructed wind farms on adjacent existing and planned wind farms. Various numerical models have been used to study the interactions between adjacent farms, spanning from fast-running engineering models to numerical weather prediction models. These models are essential to anticipate and mitigate wake effects in future wind energy deployments. Since the atmospheric conditions are variable over the year, it is important to characterize the variation of the wake interactions over the year, important for wind farm operation and planning. Due to the higher computational cost of numerical weather prediction models compared to fast-running engineering models, they are limited in their capacity to evaluate a wide range of design scenarios or very long simulation periods. In this study, we investigate the annual variation of wake effects coming from a new wind farm cluster on adjacent, existing wind farms in the North Sea using a simulation of a representative year. We compare results from a numerical weather prediction model (the Weather and Research Forcasting model) and for multiple fast-running engineering wake models (Gauss-BPA, Jensen (k_w = 0.02), Jensen (k_w = 0.04), Cumulative curl, TurbOPark (A = 0.04), TurbOPark (A = 0.06)), providing insights into variations in wake loss predictions among the models. Indeed, both the numerical weather prediction model and the engineering models make different assumptions to predict wake interactions between wind farms. Throughout this study a distinction is made between external wake losses, caused by the newly built wind farm cluster only, and internal wake losses, which are generated by the individual wind farms of the existing cluster. Temporal variations in stability are the main driver of hourly and seasonal variations in external wake losses, while internal losses are also determined by seasonal variations in wind speed. While yearly averaged external wind farm losses from the numerical weather prediction model are limited to 4 %, the internal wake losses reach as high as 3 % for the closest adjacent, existing wind farm to the new wind farm cluster. Additionally, all engineering models considered predict lower wake losses compared to the numerical weather prediction model, but predictions exhibit a very large range of magnitudes, ranging from 98 % to 33 % difference for external wakes and 59 % to 14 % for internal wakes compared to the numerical weather prediction model. Not only do the results differ quantitatively but also qualitatively between model strategies, i.e. yearly spatial distributions, especially for the external wake predictions of the former fast-running engineering models (Gauss-BPA, Jensen (k_w = 0.02), Jensen (k_w = 0.04)) and the numerical weather prediction model. These engineering models do not capture the same qualitative trend as the numerical weather prediction model while the newly designed engineering models (Cumulative curl, TurbOPark (A = 0.04), TurbOPark (A = 0.06)) do. For the internal wake losses, qualitatively, both engineering models and the numerical weather prediction model show higher internal wake losses for turbines located in the center of the wind farm, with highest losses for densely spaced turbines, and lower losses at the edge of the wind farm, however all models show different magnitudes of losses.