Abstract. Our aim with this paper was the analysis of the influence of offshore cluster wakes on the power of a far-distant wind farm. We measured cluster wakes with long-range Doppler light detection and ranging (lidar) and satellite synthetic aperture radar (SAR) in different atmospheric stabilities and analysed their impact on the 400 MW offshore wind farm Global Tech I in the German North Sea using supervisory control and data acquisition (SCADA) power data. Our results showed clear wind speed deficits that can be related to the wakes of wind farm clusters up to 55 km upstream in stable and weakly unstable stratified boundary layers resulting in a clear reduction in power production. We discussed the influence of cluster wakes on the power production of a far-distant wind farm, cluster wake characteristics and methods for cluster wake monitoring. In conclusion, we proved the existence of wake shadowing effects with resulting power losses up to 55 km downstream and encouraged further investigations on far-reaching wake shadowing effects for optimized areal planning and reduced uncertainties in offshore wind power resource assessment.

Abstract. The objective of this paper was the experimental investigation of the accumulated induction effect of a large offshore wind farm as a whole, i.e. the global-blockage effect, in relation to atmospheric-stability estimates and wind farm operational states. We measured the inflow of a 400 MW offshore wind farm in the German North Sea with a scanning long-range Doppler wind lidar. A methodology to reduce the statistical variability of different lidar scans at comparable measurement conditions was introduced, and an extensive uncertainty assessment of the averaged wind fields was performed to be able to identify the global-blockage effect, which is small compared to e.g. wind turbine wake effects and ambient variations in the inflow. Our results showed a 4 % decrease in wind speed (accuracy range of 2 % to 6 %) at transition piece height (24.6 m) upwind of the wind farm with the turbines operating at high thrust coefficients above 0.8 in a stably stratified atmosphere, which we interpreted as global blockage. In contrast, at unstable stratification and similar operating conditions and for situations with low thrust coefficients (i.e. approx. 0 for not operating turbines and ≤ 0.3 for turbines operating far above rated wind speed) we identified no wind speed deficit. We discussed the significance of our measurements and possible sources of error in long-range scanning lidar campaigns and give recommendations on how to measure small flow effects like global blockage with scanning Doppler lidar. In conclusion, we provide strong evidence for the existence of global blockage in large offshore wind farms in stable stratification and the turbines operating at a high thrust coefficient by planar lidar wind field measurements. We further conclude that global blockage is dependent on atmospheric stratification.

Abstract. Our aim with this paper was the analysis of the influence of offshore cluster wakes on the power of a far distant wind farm. We measured cluster wakes with long range Doppler light detection and ranging (lidar) and satellite synthetic aperture radar (SAR) in different atmospheric stabilities and analysed their impact on the 400 MW offshore wind farm "Global Tech I" in the German North Sea using supervisory control and data acquisition (SCADA) power data. Our results showed clear wind speed deficits that can be related to the wakes of wind farm clusters up to 55 km upstream in stable and weakly unstable stratified boundary layers resulting in a clear reduction in power production. We discussed the influence of cluster wakes on the power production of a far distant wind farm, cluster wake characteristics and methods for cluster wake monitoring. In conclusion, we proved the existence of wake shadowing effects with resulting power losses up to 55 km downstream and encouraged further investigations on far reaching wake shadowing effects for optimized areal planning and reduced uncertainties in offshore wind power resource assessment.

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We present a new approach to model the complex dynamics of aerodynamic forces on an airfoil in turbulent inflow conditions. Our ansatz is based on stochastic differential equations and aims at replacing traditional look-up table methods used in wind turbine simulation systems by the effective response dynamics of lift and drag forces. The parameters of the model are derived directly from empirical data. Measurements were taken in the closed loop wind tunnel of the University of Oldenburg for an airfoil FX 79-W-151A. The turbulent inflow was generated using a fractal square grid as it is possible to generate in this way wind speed fluctuations with similar statistics as observed in nature. Forces were measured using two strain gauge force sensors at two end points of the vertically installed airfoil. The modeling is performed by applying a stochastic approach on the measured data. By estimating the first two Kramers-Moyal coefficients, a first-order stochastic differential equation called the Langevin equation is obtained. The stochastic model achieved through this approach is extended to account for oscillation effects contained in lift and drag dynamics that probably stem from unsteady aerodynamic effects. The results are optimized by applying a 2 test on the probability density functions (PDFs) of model and measurements. With the knowledge of the Langevin equation, synthetic time series are generated. Their stationary PDFs as well as conditional PDFs show good agreement with the actual measurements. A comparison of classical averaging and the stochastic approach shows that stochastic analysis achieves additional insight into the local dynamics of lift and drag forces.