Validation of a coupled atmospheric-aeroelastic model system for wind turbine power and load calculations

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 5 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. 10 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. 15

We make use of an Actuator Sector Method (ASM), where the blade movement is described as a segment of a circle. This allows for a larger time step in PALM than in FAST as the movement of the blade during that time step is captured in the area of the sector. A similar method is suggested in (Storey et al., 2015), where an ASM is tested in simulations. In (Storey et al., 2013) a coupling of FAST and an LES solver was described and investigated. In FAST itself an ALM is implemented, which in the case of (Storey et al., 2013) communicated with an ADM in the LES solver. (Storey et al., 2013) focused on the wake development, but not on the turbine parameters. In  a non-transient connection (meaning no continuous exchange of information) between an LES tool and the aeroelastic turbine model FAST was used for investigating the influence of wakes and atmospheric stability on turbine behaviour.
In this paper the enhanced coupling is presented. Furthermore, a systematic validation with measurement data for different 70 atmospheric conditions with respect to a detailed set of variables is shown. A first comparison to other codes with a limited number of selected test cases, and without describing the coupling in detail, has been performed in the context of a joint study (Doubrawa et al., 2020).
In section 2 the enhanced coupling method is introduced and described, followed by simulations of the generic NREL 5 MW turbine in section 3.1 and the comparison to measurement data in section 3.2. The use of the generic NREL 5 MW turbine 75 offers the opportunity to compare different models to each other with respect to the turbine output and computing times. To validate the proposed coupling and to assess the quality of the results, a non-generic turbine is simulated as well and compared to measurement data of a turbine situated in the north east of Germany.
With these comparisons, we show that the PALM-FAST coupling calculates realistic turbine output parameters, that this is not only valid for the global turbine parameters like power output, but also for individual component parameters like blade 80 and tower loads and that the differences in the turbine behaviour due to different atmospheric conditions can be seen in the simulations as well. The final section 4 contains the conclusions and an outlook to subsequent work.

Methodology: The PALM-FAST coupling
In the present work, the aeroelastic turbine code FAST (Jonkman and Buhl Jr., 2005), developed at the National Renewable Energy Laboratory (NREL), USA, and the Large-Eddy simulation (LES) tool PALM (Maronga et al., 2015), developed at In an ALM the rotor blades are simulated as moving lines in the model domain and require a small computational time step in order to calculate the movement andin order not to miss information at the fast moving blade tips. As the movement 95 of the blades is reproduced, an ALM can give information on the turbine in general, but also on separate blade data like blade loads. A more computational time saving option is to simulate the turbine rotor as a disk, which is done in ADM simulations. Additionally to the obstruction the rotor causes for the flow, a rotation can be added to the simulation (ADMR) which increases the quality of the wake simulation. However, no information about individual blade parameters can be gained in such a simulation. 100 To combine the advantages of both kinds of turbine models, i.e. the detailed output of the ALM and the low computational costs of the ADMR, a so-called Actuator Sector Method (ASM) is used in this work.
PALM, when run in a normal set-up without FAST, uses either the Courant Friedrichs Levy (CFL) criteria or the diffusion criteria to determine the largest possible time step, which in general is larger than a time step needed for a proper ALM simulation. Therefore, using the same time step in both, FAST and PALM, affects the computational time required for the LES. 105 In the present work, we decouple the time step and allow the pure LES time step criteria (CFL and diffusion criteria), which were mentioned above, to determine the time step in PALM and with this reduce the total computational time significantly.
In more detail, we use an ASM model for the projection of forces in PALM, whereas in FAST we still use the ALM model.
Through this set-up, the computing time can be reduced tremendously, since the more time consuming operations take place in PALM and not in FAST. However, for simplicity, our whole coupling routine described in this work is simply abbreviated 110 as ASM hereafter.
Our ASM works as follows (see figure 1a): While FAST carries out small time steps ∆t F as is necessary in an ALM, PALM uses its own time step ∆t P > ∆t F determined by the atmospheric model time step criteria. The simulation starts with FAST communicating the initial blade positions. The wind speeds at these positions are determined from the wind fields simulated by PALM and sent back to FAST. PALM then carries out one time step and is ahead in the simulation. Once PALM has calculated 115 its time step, the windfield is "frozen" and provides FAST with the wind speeds that are needed while FAST catches up and calculates up to the current simulation time in PALM.
FAST therefore receives wind speeds of this frozen windfield and calculates the responding forces for the blades. During the larger PALM time step, the rotor blades cover a segment of the rotor area, a sector. The width of the sector α is calculated by the PALM time step ∆t P and the rotor speed Ω, which the FAST model communicates to PALM at the beginning of the This smearing of the forces is realised by a polynomial resulting in a Gaussian shape that distributes the forces over the area 125 surrounding the rotor blade in all three direction of space, c.f. (Sørensen et al., 1998):  where η is the so-called regularisation function which is applied at the nodes of the grid within a certain vicinity of the turbine, r is the distance between the respective node and the blade element from which the respective force stems and ε is a factor of the grid size that is typically set to ε = 2 · ∆ (Troldborg, 2008), with ∆ being the grid size.

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In general, the forces that occur at the blades are calculated based on the wind speed that is present at the blade position, i.e.
the positions in the rotor plane. However, this wind speed does not represent the actual wind speed entirely as it depends on the grid resolution and has to be interpolated to the desired positions. Close to the last known blade positions this interpolation leads to errors and higher wind speeds than in reality, which leads to an overestimation of the power output. Additionally, the projection width of the forces, i.e. the width defined by the regularisation function, influences the wind speed close to the blade 135 immensely. To circumvent these issues, we take the wind speeds for the ASM in positions upstream of the turbine.
Far enough upstream of the rotor, the flow can be assumed to be almost undisturbed by the rotor. The wind speeds at the rotor area are then estimated using the induction model SWIRL of FAST. SWIRL uses the so-called Taylor's frozen turbulence hypothesis (Taylor, 1938) and calculates the induced velocity in axial and tangential direction. For further information see (Moriarty and Hansen, 2005) and (Harman, 1994). In the current coupling a temporal change of the wind field as it approaches 140 the rotor is not included. For the statistics of the turbine parameters this is not necessary, however, when the temporal sequence becomes relevant this can be resolved in the postprocessing of the results by shifting the results in time.
A comparison of different approaches, including the enhanced coupling described here, was done in (Doubrawa et al., 2020) to simulate site specific behaviour of a turbine. Besides LES, the discussed models also included Reynolds-Averaged Navier Stokes (RANS) simulations and were compared with respect to turbine output and wake data in different atmospheric stabilities.

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The models performed differently depending on the simulation of the inflow conditions and the used resolution. Especially for the neutral case our coupling showed very good results.

Validation
The validation of the coupling is divided into two parts. The first part is the evaluation of results using the generic NREL 5 MW turbine. The second part is the comparison to measurement data for a more extended analysis, for which a non-generic turbine 150 is simulated.
3.1 Validation of the coupling on the basis of the generic NREL 5 MW turbine The NREL 5 MW turbine (Jonkman et al., 2009b) is a generic turbine which has been used extensively in simulations , (Storey et al., 2013), (Storey et al., 2015), (Vollmer et al., 2016), (Sathe et al., 2013), . The NREL 5 MW turbine was developed by the National Renewable Energy Laboratory (NREL) and a FAST model of the turbine 155 is included in the FAST repository.
A comparison of four different methods is made. This includes a transient coupling between FAST and an ALM in PALM, meaning the same time step size in FAST and PALM, (abbreviated as ALM). Furthermore, the ASM with two different modes of retrieving the wind speed is used, namely the ASM with the described method of reading out wind speeds in front of the turbine in combination with the induction model SWIRL (denoted as ASM), and also taking the wind speeds at the rotor area 160 without any induction model (denoted as ASM w/o SWIRL). As fourth method FAST on its own is used (denoted as FAST).
For FAST on its own, the inflow wind option "steady wind conditions" is used. To evaluate the different methods, at first, a laminar case with the same wind speed over height is considered. where the wake does not affect the inflow yet was evaluated. Additionally, the surface condition is set to a free slip condition.
The wind speed in the flow is set to 8 m s −1 . The inflow conditions for FAST are set accordingly.

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In figure 2, a comparison of the generator power for the generic 5 MW NREL turbine is shown. The result calculated by FAST coincides with the expected value, as published by NREL (Jonkman et al., 2009b). The ALM and ASM w/o SWIRL result in a too high power output, which is assumed to be, most importantly, due to the wind speeds used to calculate the blade response which is taken in the rotor plane. A further difference can be seen in the projection of the forces, which leads to different shapes of the simulated rotor. As described above, in the rotor area there is the danger of reading out too large velocity values. The

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ASM bypasses this issue by using the SWIRL induction method and results in a generator power which corresponds well with the expected one. The ASM w/o SWIRL shows an even higher power output than the ALM. The reason for that may be that, in the ASM w/o SWIRL the area that is blocked in the rotor area is larger than for ALM which might result in higher wind speeds in between the sectors, like a nozzle. As the wind speeds next to the projected forces are used to calculate the turbine response, these higher wind speeds would lead to a higher power output.
A turbulent case is calculated as well. However, no comparison to FAST alone is done here since there is no literature value available to compare the results with. For the turbulent case, a neutral flow is simulated with neither heating nor cooling of the surface. A resolution of 4 m is used with 1200 × 480 grid points in flow direction and perpendicular to flow direction, respectively. In vertical direction 192 grid points and a vertical stretching are used again, resulting in a vertical height of 1728 m.
The roughness length is set to 0.05 m, the wind speed at hub height is about 7.4 m s −1 . In this simulation non-cyclic boundary 185 conditions are used. If cyclic boundary conditions were used, the wake of the turbine would be fed into the inflow again and would, therefore, distort the flow in front of the turbine. In order to avoid this, PALM offers the opportunity of non-cyclic boundary conditions and a turbulence recycling method, for more information see (Maronga et al., 2015). As for the laminar case, the ASM leads to a lower power output than the other models, whereas the differences are comparable to the laminar case in 2. Also, roughly the same peaks and therefore structures of the flow are present in the ASM results. This implies, that the coupling works in a turbulent environment as well.
Furthermore, these simulations are used to compare the computational times of the ALM and ASM. In the laminar case the 195 ASM is nine times faster than the ALM while using the same amount of cores, i.e. the computational time is reduced by up to 89%. The turbulent case is calculated with a difference in the allocated cores: the ALM uses four times more cores than the ASM, however the ASM is still about 3.5 times faster than the ALM. Consequently, the ASM provides the same set of output parameters as the ALM, but is significantly faster.    The onshore measurement site, from which data was available, is situated in Northern Germany close to the village of Brusow.
At the measurement site two eno114 3.5 MW turbines are present. For one turbine (turbine 1 in figure 5) measurement data was available, consisting i.a. of the power output, rotor speed, generator speed and tower, main shaft and blade root bending moments.
Apart from the two eno turbines the measurement site was also equipped with a met mast. Figure  From the 20 Hz data provided by the eddy-covariance stations, turbulence statistics with a resolution of 30 minutes are obtained 220 by applying the eddy-covariance Software TK3 (Mauder and Foken, 2015). The planar fit method (Wilczak et al., 2001) is used for correcting impacts of a tilted device on the turbulence statistics. For calculating the planar coefficients the whole available data set is taken into account. As the IRGASON is not an omni-directional device, planar fit coefficients are calculated for four different wind direction sectors as suggested by the manufacturer of the IRGASON. The distance of the met mast to the turbine, for which measurement data is available, was 280 m (≈ 2.5D) in direction 190 • referring to the wind turbine. Data of all sensors is available from 10. May until 30. June in 2017. To the east of the site of the turbines and met mast a forest is located which influences the measurements greatly. Therefore, the measurement data is filtered for the westerly wind directions, where mostly grainfields are situated.
We estimate the roughness length of the surrounding area using the wind speed u ec and the friction velocity u * , both provided by the lower eddy-covariance station, with equation 2 for data of neutral stratification, where k is the von Kármán constant, z ec 230 the height of the respective eddy-covariance station and z 0 the desired roughness length: The plot of the roughness length distribution (figure 6) shows an approximate roughness length of z 0 = 0.1 m for the westerly region. This value corresponds to farmland and hedges in the summer time according to Stull (2003), which is in agreement with the plants on site and therefore z 0 = 0.1 m is a reasonable value for the roughness length. From the data of the eddy-covariance

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stations the stability parameter z L , with z as the measurement height, here z ec , and L the Obukhov length, are obtained from the application of the software TK3 to it. In the following, the power that was produced during the respective times is plotted with respect to the wind speeds filtered by the stability, calculated from the data collected by the eddy-covariance stations. For that, the 50 Hz measurement data of the power is averaged over 10 min intervals, denoted as P 10 . These 10 min power values are sorted according to stability and wind speed and averaged according to the wind speed within the respective stability, resulting 240 inP 10 . For normalisation the maximum 10 min power value P 10 max is used. Accordingly, the standard deviation is calculated, i.e. the standard deviation is calculated for 10 min intervals σ P 10 , then these 10 min values are averaged according to their stability and wind speedσ P 10 and normalised with the maximum 10 min standard deviation value σ P 10 max . Figure 7 shows the resulting power curve, which is analysed with respect to the stability. Due to the relatively low number of measurements, the stabilities, based on the data of the lower eddy-covariance station of z ec = 2.3 m, are sorted for stable 245 ( z L > 0.0115), neutral (−0.0115 < z L < 0.0115) and unstable ( z L < −0.0115), but not for further classification in very stable and very unstable , c.f. table 1.
It can be seen that the measurement data coincides very well with the power curve provided by eno for the 3.5 MW turbine (c.f. (eno energy, 2019)). Also, no significant differences between the different stratifications can be observed. However, differences have a higher turbulence intensity (TI) than the stable cases. This is also visible in the standard deviation of the power (c.f. figure 8), as the higher TI in the neutral and unstable case leads to a higher standard deviation of the power than in the stable situations with lower TI.

Simulation set-up for Brusow
In the following, the simulation set-ups for PALM and FAST that are used for the comparison to the measurement data are 255 described.

PALM
In order to compare simulation results to the measurement data, simulations are computed that result in flow conditions similar to those observed under neutral boundary layer (NBL) and stable boundary layer (SBL) flow at Brusow. As can be seen in figures 9 and 10 most data is available for the NBL and slightly SBL.   To reduce local effects caused by possible persistent structures in the flow, the main run is simulated three times with three different turbine positions in y direction, respectively. Table 4 shows the differences of the flow between the turbine positions.
The power output resulting from the simulations at the different positions are used to be compared to the measured data, 275 yielding three results for both stabilities, respectively, as can be seen in figures 11 to 16. Table 4. Turbine positions along the y-axis (keeping the same x position), with the y-direction spanning from 0 m to 2595 m for the NBL and from 0 m to 2304 m for the SBL, in the model domain of the main run, additionally, the local wind speed U92m and turbulence intensity T I92m at hub height at these y-coordinates, taken 2.5D in front of the turbine averaged over the last 10 min of a 650 s simulation. subgrid scale one, hence it is likely that the TI in the simulations is slightly higher than seen here. Therefore, the simulation set-up seems to resemble the inflow conditions at Brusow reasonably well. Since the flow conditions in the simulations match the measurements, the turbine output is compared in the following.

FAST
The turbine model of the eno114 3.5 MW turbine for FAST was provided by eno, including structural information and a pitch, 285 a speed and a yaw control in the format of a Bladed .dll file. However, the yaw of the turbine is neglected, as the flow in PALM was directed in such a way that the turbine is aligned with the wind. In FAST the modules ElastoDyn, AeroDyn and ServoDyn were used, the degrees of freedom for the blade and tower were set to true except the rotor-teeter and yaw flag. All the platform degrees of freedom were neglected, i.e. set to false. The time step throughout all modules was set to ∆t = 0.01 s.
In the following plots the output data of the turbine in the simulations is compared to the measurement data. The main runs of the simulations are run for a simulation time of 650 s respectively, the results are averaged over 600 s, discarding the first 50 s as a spin-up of the turbine simulation, this time frame is derived from the laminar case, c.f. figure 4. To compare the power output of the simulations to the measurement data, the power needs to be set into relation with the correct corresponding inflow wind speed. As the wind speed in Brusow is determined from a cup anemometer on a met mast in a distance of 2.5D from the 295 turbine at hub height, in the simulation the wind speed is taken as well in a single point in a distance of 2.5D in front of the turbine position at hub height and averaged over time.
In figure 11 the simulation results are shown in comparison to the power curve determined by the measurement data at hub height. The error bars show the standard deviation of 10 min means. Figure 12 shows the same plot enlarged at the wind speeds of the simulation. According to (Dörenkämper et al., 2014), using offshore data, and (Wharton and Lundquist, 2012), 300 using onshore data, slight differences of the power output depending on the atmospheric stabilities can be seen. However, both publications together do not show a clear trend which stability generally leads to the higher power output. In an offshore environment, as in (Dörenkämper et al., 2014), unstable conditions lead to a higher power output below rated wind speed and at an onshore site, c.f. (Wharton and Lundquist, 2012), the stably stratified atmospheric boundary layer (ABL) yields the higher power output. However, different wind speeds were used as a reference, which makes a comparison of the results The measurement data of Brusow, with the wind speed at hub height as reference, does not show any clear tendency for the dependency of the wind turbine power on atmospheric stability, c.f. figures 7 and 11. A power curve depending on the rotor equivalent wind speed was calculated from the measured data as well, but does not conclude in a clear trend either. The rotor 310 equivalent wind speed was computed according to (Wagner et al., 2014), but due to the limited number of measurement heights and their irregular distribution over the height, the results could be prone to errors. Therefore, for further analysis the hub height wind speed is used. The apparent independence of the wind turbine power on atmospheric stability might be due to the limited amount of only two months of data that was available or might be depending on the measuring and classification of the stability.
As shown in (Wharton and Lundquist, 2012) the stability filtered power curve greatly depends on the measurement heights 315 used for determining the shear. However, this behaviour is also not present in the simulations. Therefore, in our case, the power output is not the proper parameter to show different turbine responses depending on the atmospheric stability.   Figure 13 shows the standard deviation of the power with respect to the wind speed. Higher fluctuations of the power in the neutral cases can be observed, corresponding to the higher TI that is present in the neutral stratification, c.f. (Mittelmeier et al., 2017). The simulation data shows a comparable behaviour with lower fluctuating power in the stable cases than in the neutral 320 ones. In the three neutral simulations the distribution of the standard deviation is spread relatively wide compared to the stable cases. The three different positions that were used for the neutral simulations differ slightly in wind speed and TI, which is not the case for the stable cases (c.f. table 4).
To check whether this distribution is comparable to the measurement data, a plot of the standard deviation of the power with respect to the TI is made ( figure 14). It shows the relation between the power fluctuations to the TI for all measured values 325 (green dots) and specifically the measured stable and neutral cases (blue and red asterisks) and in comparison the respective values of the simulations (blue and red crosses). The results of the simulations correspond well with the measurement data, therefore other turbine parameters available are compared. In specific, the blade and tower loads are investigated below.
16 https://doi.org/10.5194/wes-2020-114 Preprint. Discussion started: 8 December 2020 c Author(s) 2020. CC BY 4.0 License.  The flap-and edgewise blade root bending moments respectively are evaluated, but also data for the tower top and base loads is available and examined. Figures 15 and 16 show the measured blade root bending moments with respect to the wind speed, 330 the results of the simulations are indicated by crosses. The out-of-plane blade root bending shows a good agreement, the inplane blade root bending moment differs a bit more. However, a more suitable way to compare the loads is to look at the spectra.  x with respect to wind speed in comparison to the simulation results, averaged 10 min values sorted into stability and averaged according to wind speed, normalised with the maximum measured moment.
We filtered the data with respect to westerly winds, stability and rotor speed. The analysis of the rotor speed showed a difference in the controller behaviour of the real system to the modelled one. This can be seen in figures 26 and 27. Apparently, the rotor 335 speed curve at the start of the peak shaver region is slightly different (c.f. figure 27). Therefore, it is only possible to compare loads at either the same rotor speed or the same wind speed.
For the stable case some of the time intervals have to be discarded due to a varying quality of the load sensors, leaving one interval for the stable case where data is continuous for the blade and tower moments. For the neutral case the longest remaining interval covers a span of 165 s long. The conditions of the chosen intervals are shown in table 5. Ideally the chosen intervals 340 should match the simulation parameters, but due to the described limitations in the measurement data, the remaining intervals can be seen as the best fit. These available cases suffice for the validation of our code. For an even more detailed load analysis, better fits might be necessary. Table 5. Summary of the parameters of the measurement interval data used for the spectra of the blade and turbine loads: wind speed at hub height U92m, turbulence intensity at hub height T I92m, shear parameter α and the length of the available time interval t interval . In the following the stable case will be discussed in detail. The neutral case also shows a good agreement between simulation and measurement data, but covers only a short time interval of only 165 s, the corresponding spectra can be found in the It can also be seen, that the 1P peak is of different height in the tower load spectra. The peak of the simulation data reaches higher, than the one of the measurement data. This is probably due to an overestimated blade imbalance in the simulation which has been used to respect weight and pitch differences between the blades, c.f. (Zhang et al., 2015). In the FAST turbine model 360 one of the blades has a 1% higher mass density than the others and also a pitch offset of 0.3 • is set between all three blades.
This results in a very pronounced 1P peak that is not existing in the measurement data.
Notable is also that there seems to be a discrepancy between the simulation and measurement data in the tower top side-toside bending moment in stable and neutral conditions. This might be caused by the difference in the tower model to the real behaviour of the turbine tower. It can be seen that the first tower eigenfrequency is slightly lower on the real turbine and 365 therefore more prone to the rotational excitation. In the measurement data the first tower eigenfrequency is closer to the 1P peak and therefore the vibrations less damped.
Differences can also be observed in the 6P peak, especially in figures 19 and 20. The 6P peak is greatly influenced by the shear and the wind speed differences across the rotor area. A plot of the wind speed profiles can be found in the Appendix B, even though the shear is similar, the difference in the wind speeds, which are caused by the above described limitations in the 370 measurement data, led to diverging wind speed profiles.
In figures 24 and 25 a comparison between the neutral and stable simulation results for a blade root bending and tower bending moment, respectively, is shown. The bending moments that are mostly affected directly by the flow, i.e. by the thrust, are chosen. It can be observed that the neutral simulation leads to wider peaks due to the higher TI and the resulting varying rotor speed. Also, a difference in the height and depth of some peaks can be seen. Namely for the blade root bending out-of-plane 375 moment the 2P and for the tower fore-aft bending moments the 3P and 6P peaks are higher and reach further down for the stable case than the neutral case. These multiples of the rotor speed are influenced by the shear of the flow which also indicates a difference in the inflow of the turbines.       To investigate the loads further, rainflow counts and the value of the equivalent load range ∆ eq (non-normalised damaged equivalent loads (DEL)) were calculated. Equation 3 shows the used Palmgren-Miner rule, taken from (Vera-Tudela and Kühn, 380 2017): where n is the number of different loading amplitudes, N the number of cycles and ∆S the loading amplitude. Further, a Wöhler exponent of m = 10 for the blades, m = 4 for the tower and a reference number of cycles N ref = 10 7 is assumed.
A comparison between the measurement data and the simulation results is not useful in this case as the available intervals 385 vary in their inflow parameters and therefore the rotor speed. However, a comparison between the results of the simulation of the neutral and stable boundary layer flow, respectively, show the influence of the stability on the load outputs of the LES coupling. Table 6 shows the comparison of the equivalent load range for the stable and neutral simulations, calculated for a 10 min interval respectively. It can be observed that almost all the neutral values are higher than the ones from the simulation of the stable case. The only exception is the blade root bending in-plane load, which shows approximately the same value for 390 both cases. As this load is not that dependent on the flow, but rather influenced by gravity and rotor speed, the result still seems conclusive.
The values can be linked to the power spectra shown in figures 24 and 25. Particularly in the range of the lower frequencies larger PSD values are obtained for the neutral case in comparison with the stable case. To investigate the influence of the lower frequencies on the equivalent load range, the equivalent load range for the tower top fore-aft bending moment is calculated 395 with a high pass filter as an example. The following values result for the equivalent load range when the frequencies below 0.1 are disregarded: stable: ∆ eq = 81.8·10 5 kNm and neutral: ∆ eq = 98.7·10 5 kNm, which clearly shows that the lower frequency range has a great influence on the equivalent load range. A higher value for the neutral case is expected as the flow contains larger eddies than the stable case.
This should be considered as a qualitative result. For a final quantitative analysis simulations with considerably larger run times 400 or a number of simulations with different seeding would be required. Also, in the papers  and (Holtslag et al., 2016) no clear results are visible, in  it is stated that mainly the roughness has an influence on the loads, while the stability has only a small effect. In (Holtslag et al., 2016), on the other hand, a clear influence of stability on the loads is observed. Tower base side-to-side bending 373.6 963.7 Figure 24. Comparison of the blade root bending moments out-of-plane M b y for the stable and neutral simulation. The data is normalised by the maximum value of the blade root bending moments and the frequency is normalised by the rotor speed. Figure 25. Comparison of the tower top fore-aft bending moment M tt y for the stable and neutral simulation. The data is normalised by the maximum value of the tower top bending moments and the frequency is normalised by the rotor speed.
As can be found in figure 26 the measurement data shows a dependency on the atmospheric stability. Neutral conditions 405 lead to higher power output for the same rotor speed than stable conditions. This behaviour might be explained due to the higher fluctuations caused by higher TI and the therefore higher energy content in the wind. However, the simulations did not reproduce the same dependency, which might be explained by the difference in the turbine control. Figure 26. Power output, normalised by the maximum measured power, plotted with respect to the rotor speed, normalised with the maximum measured rotor speed with an added offset, for the measurement data in comparison to the simulation data. Figure 27. Relation between the rotor speed Ω, normalised with the maximum measured rotor speed with an added offset, with respect to the wind speed determined using the measurement data in comparison to the simulation data (×).

Conclusions
In this paper we presented a new computing routine which combines the advantages of an atmospheric flow simulation using the 410 LES tool PALM and the detailed calculation of the turbine answer by FAST. To quantify the output of the results a comparison to the generic NREL 5 MW turbine and a more extensive comparison to measurement data of a real turbine is shown.
The comparison of the turbine models for the NREL 5 MW turbine showed promising results concerning the quality of the turbine output. Most importantly, it also enabled to make a statement about the computational time of the enhanced coupling.
In the considered cases a saving of computational time of up to 89% could be observed in relation to the equally detailed ALM 415 coupling.
Furthermore, the results for the turbine parameters that are calculated by the new coupling resemble the measured data of the eno114 3.5 MW turbine well. For example the power output is reproduced very well, which is mostly due to the method of taking the wind speed in front of the turbine instead of directly at the rotor area to avoid an overestimation of the power. Also, the standard variation of the power shows a good resemblance to the measurement data. The parameter reflects the influence 420 of the turbulence in the flow and therefore the stability, which is also present in the simulated results. Keeping in mind, that the simulations were still idealised, i.e. only one homogeneous roughness length and no topography, there is good agreement between the simulated and the measured data.
The blade and tower loads are representative of the measurements in general. Deviations in the aeroelastic simulation model, especially the tower eigenfrequency, the selected rotor imbalance, the used controller and windspeeds led to slightly different 425 resulting loads compared to the measurements. However, the load spectra still show a very good agreement. Variations due to the atmospheric stability are clearly found. This indicates that the PALM-FAST coupling is suitable to investigate the effects of different atmospheric flows on turbine behaviour.
For future work, a further comparison to measurement data of different situations, such as unstable stratification or in a turbine wake, is worth considering to further substantiate the results. Examining the performance of the simulations for a turbine in a 430 wake would be a valuable continuation of the current results, as it is not clear how the induction model in particular behaves in a wake. However, due to the reduced computing time, the coupling is basically well suited for carrying out load analyses of a single turbine in a wind farm. As up to now ADM or ADMR has mostly been used in wind farms, since the use of ALM is too computationally intensive due to the required large model domains.
In addition, thanks to the time-saving detailed simulations, there is a multitude of possible applications. Apart from calculating 435 load analyses for wind farms, another possible application is to investigate the relationship between environment and turbine performance in footprint analyses. Furthermore, phenomena in atmospheric flows and their impact on turbine loads can be investigated, such as low level jets. Figure A2. Spectrum of the blade root bending in plane moment M b x in comparison to the simulation results (neutral). The data is normalised by the maximum value of the blade root bending moments and the frequency is normalised by the rotor speed.
29 https://doi.org/10.5194/wes-2020-114 Preprint. Discussion started: 8 December 2020 c Author(s) 2020. CC BY 4.0 License. Figure A3. Spectrum of the tower top bending moment in fore-to-aft direction M tt y : Comparison of the measurement data to the simulation results (neutral). The data is normalised by the maximum value of the tower top bending moments and the frequency is normalised by the rotor speed. Figure A4. Spectrum of the tower top bending moment in side-to-side direction M tt x : Comparison of the measurement data to the simulation results (neutral). The data is normalised by the maximum value of the tower base bending moments and the frequency is normalised by the rotor speed. Figure A5. Spectrum of the tower base bending moment in fore-to-aft direction M tb y : Comparison of the measurement data to the simulation results (neutral). The data is normalised by the maximum value of the tower top bending moments and the frequency is normalised by the rotor speed. Figure A6. Spectrum of the tower base bending moment in side-to-side direction M tb x : Comparison of the measurement data to the simulation results (neutral). The data is normalised by the maximum value of the tower base bending moments and the frequency is normalised by the rotor speed. Figure A7. Spectrum of the tower top torsion moment M tt z : Comparison of the measurement data to the simulation results (neutral). The data is normalised by the maximum value of the tower top torsion moment and the frequency is normalised by the rotor speed. the development of the method and the scientific analyses. MK provided intensive reviews on the load analyses. LJL provided intensive consultation on the scientific analyses and had a supervising function.
Competing interests. The authors declare that they have no conflict of interest. German Bundestag. "Ventus efficiens" (ZN3024) was funded by the Lower Saxony Ministry for Science and Culture. The computations were performed on the high performance computing system EDDY of the University of Oldenburg funded by the Federal Ministry of Economic Affairs and Energy. We acknowledge the wind turbine manufacturer eno energy for providing SCADA data, the FAST turbine model and their support of the work.