Abstract. Space–time correlations of power output fluctuations of wind turbine pairs provide information on the flow conditions within a wind farm and the interactions of wind turbines. Such information can play an essential role in controlling wind turbines and short-term load or power forecasting. However, the challenges of analysing correlations of power output fluctuations in a wind farm are the highly varying flow conditions. Here, we present an approach to investigate space–time correlations of power output fluctuations of streamwise-aligned wind turbine pairs based on high-resolution supervisory control and data acquisition (SCADA) data. The proposed approach overcomes the challenge of spatially variable and temporally variable flow conditions within the wind farm. We analyse the influences of the different statistics of the power output of wind turbines on the correlations of power output fluctuations based on 8 months of measurements from an offshore wind farm with 80 wind turbines. First, we assess the effect of the wind direction on the correlations of power output fluctuations of wind turbine pairs. We show that the correlations are highest for the streamwise-aligned wind turbine pairs and decrease when the mean wind direction changes its angle to be more perpendicular to the pair. Further, we show that the correlations for streamwise-aligned wind turbine pairs depend on the location of the wind turbines within the wind farm and on their inflow conditions (free stream or wake). Our primary result is that the standard deviations of the power output fluctuations and the normalised power difference of the wind turbines in a pair can characterise the correlations of power output fluctuations of streamwise-aligned wind turbine pairs. Further, we show that clustering can be used to identify different correlation curves. For this, we employ the data-driven k-means clustering algorithm to cluster the standard deviations of the power output fluctuations of the wind turbines and the normalised power difference of the wind turbines in a pair. Thereby, wind turbine pairs with similar power output fluctuation correlations are clustered independently from their location. With this, we account for the highly variable flow conditions inside a wind farm, which unpredictably influence the correlations.

Abstract. The optimisation of the power output of wind turbines requires the consideration of various aspects including turbine design, wind farm layout and more. An improved understanding of the interaction of wind turbines with the atmospheric boundary layer is an essential prerequisite for such optimisations. With numerical simulations, a variety of different situations and turbine designs can be compared and evaluated. For such a detailed analysis, the output of an extensive number of turbine and flow parameters is of great importance. In this paper a coupling of the aeroelastic code FAST (fatigue, aerodynamics, structures, and turbulence) and the large-eddy simulation tool PALM (parallelised large-eddy simulation model) is presented. The advantage of the coupling of these models is that it enables the analysis of the turbine behaviour, among others turbine power, blade and tower loads, under different atmospheric conditions. The proposed coupling is tested with the generic National Renewable Energy Laboratory (NREL) 5 MW turbine and the operational eno114 3.5 MW turbine. Simulating the NREL 5 MW turbine allows for a first evaluation of our PALM–FAST coupling approach based on characteristics of the NREL turbine reported in the literature. The basic test of the coupling with the NREL 5 MW turbine shows that the power curve obtained is very close to the one when using FAST alone. Furthermore, a validation with free-field measurement data for the eno114 3.5 MW turbine for a site in northern Germany is performed. The results show a good agreement with the free-field measurement data. Additionally, our coupling offers an enormous reduction of the computing time in comparison to an actuator line model, in one of our cases by 89 %, and at the same time an extensive output of turbine data.

Abstract. The optimisation of the power output of wind turbines requires the consideration of various aspects including turbine design, wind farm layout and more. An improved understanding of the interaction of wind turbines with the atmospheric boundary layer is an essential prerequisite for such optimisations. Using numerical simulations, a variety of different situations and turbine designs can be compared and evaluated. For such a detailed analysis, the output of an extensive number of turbine and flow parameters is of great importance. Usually simulations are either specified to the output of turbine parameters or the detailed simulation of the flow. In this paper a coupling of the aeroelastic code FAST and the Large-Eddy Simulation tool PALM is presented. The advantage of the coupling of these models is that it enables the analysis of the turbine behaviour, i.a. turbine power, blade and tower loads, under different atmospheric conditions. The proposed coupling is tested with the generic NREL 5 MW turbine and the operational eno114 3.5 MW turbine. Simulating the NREL 5 MW turbine allows for a first evaluation of our PALM-FAST-coupling approach based on characteristics of the NREL turbine reported in the literature. The comparisons of the simulations to the NREL literature values show very promising results. Furthermore, a validation with free-field measurement data for the eno114 3.5 MW turbine for a site in Northern Germany is performed. The results show a good agreement with the free field measurement data. Additionally, our coupling offers an enormous reduction of the computing time, in comparison to similar methods with the same detail, and at the same time an extensive output of the turbine data.

Abstract. The correlation of power output fluctuations of wind turbines in free field are investigated, taking into account the challenge of varying correlation states due to variable flow and wind turbine conditions within the wind farm. Based on eight months of 1 Hz SCADA data, measured at an offshore wind farm with 80 wind turbines, the influence of different parameters on the correlation of power output fluctuations is analysed. It is found that the correlation of power output fluctuations of wind turbines depends on the location of the wind turbines within the wind farm as well as the inflow conditions (free-stream or wake). Wind direction investigations show that the correlation is highest for streamwise aligned pairs and decreases towards spanwise pairs. Most importantly, the highly variable measurement data in a free-field wind farm has considerable influence on the identification of different correlation states. To account for that, the clustering algorithm k-means is used to group wind turbine pairs with similar correlations. The main outcome is that next to the location of a wind turbine pair in the wind farm the standard deviation in their power output and their power differences are suitable parameters to describe the correlation of power output fluctuations.