The purpose of the measurement campaign was, among others, power curve verification and load validation of the Vestas V236 prototype wind turbine. The turbine has a rotor diameter of 236 m and a hub height of 163 m, with a rated power output of 15 MW. It is an offshore wind turbine, and several variants are currently under installation in wind farms in the North Sea and the Baltic Sea.

The campaign lasted for 2 years, from 2023 to 2025, and took place at the Test Center Østerild. It is located in north Jutland, Denmark, about 50 km from the coast. We refer the reader to for a detailed description of the site. The prototype turbine was equipped with many sensors that measured bending moments on various components, the power output of the turbine, pitch angle of all the blades and rotation speed, among other operational data. An overview of the data signals used in this study is shown in Table . An IEC-complaint meteorological mast was also present, about 660 m to the west of the prototype. Since the dominant wind direction was westerly, the mast was often present upstream of the turbine. It was equipped with a sonic anemometer at 155 m; cup anemometers at 45 m, 104 and 163 m; and wind vanes at 45 and 159 m above ground level.

The steps involved in the curation of the data are described below, with the data availability after each step shown in Table . Note that the goal of data curation was to obtain turbulence measurements appropriate for a one-to-one comparison.

The data were sampled at a frequency of 5 Hz and partitioned into periods of 10 min. This sampling frequency is chosen as turbulent fluctuations that are faster than the Nyquist frequency of 2.5 Hz are not deemed to be important from a fatigue loads perspective. Only those periods were selected for further analysis, where the 10 min mean wind direction θ‾ measured by the wind vane at 163 m was between 225° and 315°. Note that ⋅‾ refers to time averaging, and the wind directions are expressed in meteorological convention, with 0° being wind coming from the north. The westerly sector is selected because winds from this direction can be assumed to be homogenous and free from the wake of neighbouring turbines . Subsequently, the 10 min mean wind speed (u‾) and direction measured by the sonic anemometer at 155 m were compared to the cup and vane at 163 and 159 m, respectively. The purpose of this comparison was to identify inaccuracies in the instruments and remove the corresponding periods from the dataset. As seen in Fig. , the instruments agreed in the measurements of the mean wind speed and direction. Although biases of 0.3 ms-1 and 1° are detected in (a) and (b), respectively, this can be attributed to the sonic anemometer being placed 8 and 4 m lower than the cup and vane, respectively. Next, the 10 min periods where the mean wind speed was outside the turbine operating region were removed. This was followed by calculating the Monin–Obukhov length (Lmo) for each of the remaining 10 min periods: 1Lmo=-u*3θv‾κgw′θv′‾, where θv is the virtual potential temperature, κ is the von Kármán constant, w′ denotes the fluctuating vertical wind-velocity component and w′θv′‾ is the vertical flux of virtual potential temperature. Moreover, the friction velocity, u* is given by 2u*=-u′w′‾. Note that we used the sonic temperature (Ts) in Eq. (), as Ts‾ and w′Ts′‾ are considered to be acceptable approximations to θv‾ and w′θv′‾, respectively .

The 10 min data were subsequently binned according to the mean wind speed measured by the sonic anemometer at 155 m and the Monin–Obukhov length based on the stability classifications suggested by and shown in Table . The size of the mean wind speed bins was 2 ms-1, with the bin centres being odd numbers from 5–21. Table  is only applicable within the surface layer where the friction velocity and temperature flux do not change with height. While this assumption may not be strictly valid for the measurement height of 155 m, the reader is cautioned against using Table  outside the surface layer.

The probability distribution of Lmo conditioned on u‾ is shown in Fig. . We found stable conditions to be most frequent at low wind speeds, contrary to the observations of , wherein unstable conditions were dominant at wind speeds below 11 ms-1. This observation is likely a sampling bias. The instruments briefly stopped recording data in the summer of 2024 (as noted in row 2 of Table ) when unstable conditions are more frequent. Neutral and near-neutral conditions were dominant at mean wind speeds above 14 ms-1, which is likely a result of mechanically generated turbulence being relatively stronger than the effects of buoyancy.

In the subsequent processing step, we aimed to find the longest period of contiguous measurements within each bin. Table  shows the capture matrix indicating the number of contiguous 10 min periods (Nbin) found for each bin. The turbulence measurements (namely the auto-spectra) were averaged over Nbin periods and fitted to the Mann model. Thus, we used Bartlett's method to compute the auto-spectra. If Nbin<4, the uncertainties in the measurements were deemed to be too high and a fit with the Mann model could not be obtained. As a consequence, a one-to-one comparison could not be carried out in the corresponding bins. In other words, each bin required at least 40 min of continuous data. This condition was satisfied in 39 bins.

The choice to limit the analysis to periods with contiguous data was motivated by the observation that wind speed and stability did not fully describe turbulence at these heights. Indeed, when computing the spectra for all 10 min periods within a given bin, we found the spread to be large, encompassing 3 orders of magnitude, from 10-3 to 1m2s-2. Additionally, as described later, spectral fitting was the preferred method for inflow assimilation. Thus, by attempting to fit the Mann model to the bin-averaged spectra, we risked lumping together distinct atmospheric conditions which would add significant uncertainty to the comparisons of loads. On the other hand, by selecting a contiguous period of measurements with minimal spread in the individual spectra, the resultant uncertainty was lower and easier to quantify as it was purely statistical in nature.

The goal of inflow assimilation is to achieve a faithful representation of the measured inflow in the simulation environment. To replicate the turbulence in the simulations, we use spectral fitting. Herein, the Mann model is fitted to the auto-spectra of the along-wind u, cross-wind v and vertical w wind components as well as the real part of the uw cross-spectrum to obtain the three model parameters: L, αε2/3 and Γ for each stability and wind speed bin. These parameters are then used to generate a turbulence box which is provided as input to the aeroelastic solver .

Previous one-to-one comparisons have used different inflow assimilation methods such as scaling a turbulence box with the measured variances in the three components or by constraining a turbulence box on a set of measurements. However, the former has been shown to possess a high level of uncertainty , while the latter is more suitable for measurements from a nacelle lidar . Since measurements of the auto-spectra contain the length scale and variance, both of which have a significant influence on fatigue loads, fitting the turbulence model to the spectra can achieve accurate assimilation of the inflow for the purposes of load validation .

The fitting procedure is as follows. Measurements of auto-spectra are computed by 3Si(f)=2πNbinT∑k=1Nbinuik(f,T)2 where 4uik(f,T)=12π∫0Tuik(t)exp⁡(-2πift)dt, is the Fourier transform of the ith component such that (u1,u2,u3)=(u,v,w) and T=600s. Note that measurements of the three wind components at a sampling frequency of 5 Hz are obtained from the sonic anemometer. The spectra are further block-averaged over logarithmic bins Nl to reduce the level of noise at the high frequency end of the spectrum. The block-averaging is done such that there are 12 points per decade, which means that Nl increases with frequency. Hence, the statistical uncertainty in the measurements σ(〈Si〉) is quantified by 5σ(〈Si〉)=〈Si〉NbinNl.

Then, the model parameters that minimize the error ξ2 are obtained by an optimization algorithm. ξ2 is defined as 6ξ2L,Γ,αε23=∑i=13∑n=1Nlog⁡k1nFi-log⁡k1nFi,m2+∑n=1Nlog⁡k1nℜ(χuw)-log⁡k1nℜ(χuw,m)2, where the subscript m refers to the estimated spectra and χuw is the uw cross-spectrum. On the other hand, the modelled spectra are given by 7Fik1;L,Γ,αε23=∬-∞∞Φiik;L,Γ,αε23dk2dk3. Here, Φ(k) is the spectral tensor derived by defined over wave number space: k=(k1,k2,k3). Note that Taylor's hypothesis is used to move between frequency and wave number space. Moreover, the coherence, γuu2, is defined as 8γuu2(f,Δy,Δz)=|χuu(f,Δy,Δz)|2Su(f,0,0)Su(f,Δy,Δz), where Δy and Δz are the lateral and vertical separations, respectively, and χuu is the cross-spectrum between u(t,0,0) and u(t,Δy,Δz).

Figure  shows the estimated spectra under different stability conditions along with the fit derived from Eq. () at a mean wind speed of 9 ms-1. Note that the area under the spectra of a given component is equal to the variance of that component, while the location of the spectral peak is related to the length scale. As expected, unstable conditions show much more variance (or turbulence intensity) and larger length scales as compared to stable conditions, whereas neutral conditions are intermediate. The Mann model fits the spectra well in the given frequency range.

The model parameters obtained in each stability and wind speed bin are shown in Fig. . The parameter αε2/3 is proportional to the square of the mean wind speed and hence αε2/3 is observed to vary linearly with u‾. Furthermore, αε2/3 is also related to the variance in the wind speed . Thus, Fig. a shows that higher wind speeds are associated with more turbulence. Length scales as large as 180 m are observed in certain unstable conditions, while stable conditions usually show length scales lower than 50 m. The anisotropy parameter Γ appears to be lower for unstable conditions as compared to stable conditions at low wind speeds. Γ is related to the ratio of the variances in the three wind components, and Γ=0 when σu=σv=σw. Thus, convective conditions show lower values of Γ, as the fluctuations in v and w tend be to stronger than under stable conditions. The variation in Γ decreases with wind speed, probably due to the decrease in the data availability of non-neutral stabilities at higher wind speeds. Note that Γ might also depend on surface roughness and boundary layer depth, which are outside the scope of this study but can be investigated in the future.

Given the importance of vertical shear and veer on fatigue loads , we also attempted to replicate the measured variation of mean wind speed and direction with height in the simulation setup. Data from three cup anemometers present at heights 45, 105 and 163 m, and two wind vanes present at 45 and 159 m were used to obtain the mean vertical profiles of the along-wind component and the wind direction u‾(z) and θ‾(z). Next, the shear parameter αs was extracted by fitting the power law profile to the measurements: 9u‾(z)=u‾(zh)zzhαs, where zh is the hub height. Here, the shear above the rotor is assumed to follow the same power profile as measured below the rotor. Note that Eq. () provided a good fit to the measurements as the coefficient of determination (R2) was always greater than 0.92 in all 39 bins. The veer profile, on the other hand, is assumed to be a linear function of height: 10θ‾(z)=β(z-zh). β is obtained by fitting the measured profile of θ‾(z) to Eq. (). The values of αs and β for all stability and wind speed bins are shown in Fig. . A larger variation with height in the wind speed and direction is observed during stable conditions as compared to unstable conditions, as more turbulent mixing occurs in the latter, which leads to more uniformity in the mean wind speed and direction.

Thus, the wind box up provided to the aeroelastic solver is 11up(x,y,z)=um(x,y,z;αε2/3,L,Γ)+exu‾(zh)zzhαs+eyu‾(z)tan⁡(β(z-zh)). Here, um is the wind box of turbulent fluctuations with zero mean generated using the Hipersim library and ex, ey are the unit vectors in the along-wind and cross-wind directions.

The turbulence boxes had a temporal resolution of Δt=0.15s, hence the spatial resolution in the along-wind direction Δx was u‾(zh)Δt. Given a total simulation time of 600 s, the number of grid points in the x direction were 8094. On the other hand, the vertical and lateral grid resolution was 3.8 m, with 64 grid points in either direction. These values were recommended by for the convergence of fatigue load estimates. They also suggest using at least seven turbulence seeds to reach a standard error of less than 5 % in the damage equivalent moment on the blades and the tower. Thus, in this study, a total of 7×39=273 simulations were performed.

The dynamic response of the turbine to a given wind input is simulated in the Vestas turbine simulator (VTS). It is a state-of-the-art blade element and momentum theory (BEM) solver derived from Flex5 and based on the mode shape approach using generalized coordinates, masses, stiffnesses and forces. The solver is non-linear as mass, damping and stiffness matrices are recalculated at every time step. It includes tip loss correction and a dynamic stall model, and is linked to the controller via a dynamic-link library (DLL). Since the system of equations is not stiff, a very efficient equation solver may be used (Runge–Kutta–Nyström with Cholesky decomposition), with a relatively large constant time step.

Fatigue loads are often characterized by the 1 Hz damage equivalent moment DM, which is based on the Palmgren–Miner damage rule . Consider S(t) to be the time-dependent bending moment on a particular component. S(t) is first decomposed into a set of single amplitude load ranges Si, and the number of cycles for each load range ni are calculated using rain-flow counting . Moreover, the number of cycles to failure Ni at a certain load range are found using the Wöhler S–N curve: 12Ni=S0Sim, where m is the Wöhler exponent of the material and S0 is the y intercept of the S–N curve. Note that in this study, m is taken as 4 for steel and 10 for glass fibre composite . The fatigue damage suffered by the material at particular load range is given by 13Di=niNi. Thus, the total damage according to Palmgren–Miner's rule is 14D=∑Di=∑niNi. Finally, DM is defined as the single amplitude time-varying load applied on the component for neq cycles such that it results in the same level of accumulated damage as S(t): 15DM(S)=∑niSimneq1m, where neq is 600, which implies that DM(S) is applied at a frequency of 1 Hz for a duration of 10 min.

We inform the reader that all the results presented in the next section have been anonymized. This was achieved by scaling the absolute value of a given quantity (say X) as follows: 16X̃=XXmax-Xmin, where Xmin and Xmax are the minimum and maximum values of X, respectively. Note that the minimum and maximum are the same for a given load channel, and are computed over all stabilities and mean wind speeds. Thus, all loads from a particular channel, irrespective of whether they are obtained from measurements or simulations, are scaled with the same values of Xmin and Xmax. As a result, Eq. () is a rescaling operation that preserves all qualitative differences between the data points.

The difference between damage equivalent moments in the simulations and measurements are quantified using the z score Z defined as follows: 17Z=A‾-B‾σA‾2+σB‾2, where 18σA‾=σANA. A and B refer to the measured and simulated quantities respectively. NA is the number of 10 min samples whose values can be found in Table , while NB=7, which corresponds to the number of seeds used in each wind speed and stability bin. Note that when Z=1, A‾ and B‾ are 1σ apart, where 19σ=σA‾2+σB‾2. Furthermore, a positive value indicates that fatigue loads are overestimated in the simulation, while a negative value indicates an underestimation.

The mean damage equivalent moments are computed from the measurements of bending moments at the tower bottom and blade root, and are shown in Figs.  and  as functions of wind speed and atmospheric stability. Note that the fore-aft direction is parallel to the mean wind direction and side-side is perpendicular to it, when the yaw-misalignment is zero. Moreover, Fig.  shows the damage equivalent loads on one of the blades, although similar results were obtained for all three. Lastly, the error bar indicates the standard deviation of the damage equivalent moment, which is also scaled according to Eq. ().

Figure a shows that the damage equivalent moments at the tower bottom in the fore-aft direction are significantly influenced by atmospheric stability. For instance, in the 11 ms-1 wind speed bin, which is around the turbine's rated wind speed, the fatigue loads are twice as high under unstable and neutral conditions as compared to stable conditions. Averaging over the wind speed bins where data are simultaneously available for unstable, neutral and stable conditions, the damage equivalent moments are 98 % and 65 % higher under unstable and neutral conditions as compared to stable ones. Moreover, the standard deviation of the damage equivalent moment is also 1.5 times higher under unstable and neutral conditions. On the other hand, the fatigue loads in the side-side direction are not as strongly influenced by stability. The difference in damage equivalent loads in this direction between unstable and stable conditions is 17 %. Similar trends are observed in the damage equivalent moments at the tower top.

As seen in Figs. , and , unstable conditions are generally associated with higher turbulence intensities (TIu) and larger length scales but lower shear in the vertical wind profile. Thus, the results presented herewith show that tower loads are mainly driven by turbulence and not shear. Indeed, it is expected that a three-bladed rotor will average out the effects of load variation due to the wind profile. The TIu, on the other hand, quantifies the fluctuations of a given wind component around its mean, and consequently, a larger TIu of the along-wind component can lead to larger variations in tower loads. However, the TIu alone is not a sufficient proxy for fatigue loads. The length scale describes the size of the eddies, which drive the turbulent fluctuations. Eddies that are comparable to the rotor diameter cause variations in the dynamic loads, while eddies that are smaller in size are filtered out. Indeed, these results are not surprising given the insights from buffeting theory for bridges and towers. and showed that for a linear approximation, the buffeting response is proportional to the turbulence intensity. Hence, the TIu and length scale together are responsible for fatigue loads on the tower being 98 % higher under unstable conditions as compared to stable conditions. We also note that the damage equivalent moments under neutral conditions do not necessarily represent the mean loads at any given wind speed. They appear to be closer to unstable conditions than to stable ones. This is because the TI and length scale of the load-driving u component under neutral conditions was closer to the values under unstable conditions.

The damage equivalent loads on the blade in the flapwise direction are impacted to a lower degree by atmospheric stability. At wind speeds below rated (the rated wind speed is approximately 11 ms-1), unstable and neutral conditions cause approximately 20 % more fatigue damage as compared to stable conditions. However, at wind speeds above rated, the damage equivalent loads under neutral and stable conditions differ by -2%. These observations are caused by the opposing effects of turbulence and shear, both of which affect the fatigue loads on a wind turbine blade. While unstable conditions are more turbulent, the mean wind speed does not vary appreciably with height. Stable conditions show converse behaviour such that the two drivers of fatigue loads (turbulence and shear) tend to nullify each other in Fig. . Moreover, as pitch control is activated at wind speeds above rated, the blade pitches out of the mean wind. Hence, the flapwise loads become less sensitive to turbulence and shear becomes relatively dominant. This causes stable conditions to be slightly more detrimental at high wind speeds. In the case of the edgewise loads on the blade, as they are mainly driven by gravity, no significant dependence on stability or turbulence is observed. Thus, we exclude them from the one-to-one comparisons presented in the next section. The side-side loads on the tower bottom are also excluded as they are not only dependent on the inflow but also on a range of different factors such as mass and pitch imbalances on the blades. As it is difficult to accurately quantify these imbalances, they cannot be replicated in a simulation. Hence, attributing any disagreement between measured and simulated loads to differences in the inflow cannot be achieved with a sufficient degree of confidence. On the other hand, the tower fore-aft and blade flapwise loads are significantly more sensitive to the inflow. Thus, our one-to-one comparison is limited to these two load channels.

Figure  shows the one-to-one comparison of damage equivalent moments on the bottom on the tower in the fore-aft direction, while Table  presents the z scores. They indicate that the tower-bottom damage equivalent moments are overestimated when inflow turbulence is modelled with the Mann model, and the model parameters are derived by fitting the model to measurements of the auto-spectra. In most instances, the overestimation is fairly low and the loads differ by less than 3σ. However, at certain wind speeds under near-neutral stable, stable, very stable and unstable conditions, the loads are overestimated by more than 5σ. We found that in the bins with near-neutral, stable and very stable conditions, the vertical coherence in the u component predicted by the model was higher than the measurements. Using data from the sonic anemometer at 155 m, and the cup anemometer and wind vane at 45 m, we found measurements of γuu2(f,0,110), which were compared to the coherences from the turbulence model. In the frequencies between 10-3 and 10-2Hz, the model overestimated the coherence by up to 174 %. We suspect that the lateral coherence is also overestimated in these cases. Indeed, showed that coherence in the frequency range between 10-3 and 10-2Hz has a significant impact on the fatigue loads experienced by the towers of multi-megawatt turbines. Regarding the case with unstable conditions at 11 ms-1, the measurements of the auto-spectra show that the variance in the w component is higher than that in the u and v components at frequencies below 10-2Hz. Such observations have been made before under strongly convective conditions at an altitude of 200 m. However, the Mann model is based on the assumption that σu>σv>σw, which is true in the case of shear-driven turbulence but invalid for some unstable conditions, especially for altitudes above 100 m. Thus, fitting the model to the observations of the auto-spectra results in a relatively poor fit, which we believe causes the large mismatch between simulated and measured loads on the tower (and the blade). The one-to-one comparison of tower-top moments in the fore-aft direction were found to be identical to the tower bottom.

The one-to-one comparison of the damage equivalent moments on the blade in the flapwise direction is shown in Fig. , while the z scores are displayed in Table . In this case as well, the difference in loads is often less than 3σ. Although the measured loads in Fig. d appear to be higher than the simulated loads at 17 ms-1 and higher, the absolute difference being less than 3σ means that the discrepancy can be better explained as a statistical error. However, at mean wind speeds of 9, 11 and 13 ms-1, the damage equivalent moments under very stable and stable conditions are overestimated by more than 11σ. We find that the cause for this discrepancy is the method of assimilating the measured vertical shear into the simulation environment. The power law profile of Eq. () was fitted to measurements at and below hub height, and the shear coefficient was assumed to be independent of height. However, under stable conditions, the boundary layer height can be as low as 300 m. Thus, the vertical profile of wind speed between hub height (163 m) and rotor top (281 m) is not necessarily the same as between rotor bottom (45 m) and hub height. By analysing the vertical wind profile measured from a nacelle lidar, we found that the power law overestimates the mean wind speeds above hub height by 1–2 ms-1. Consequently, the blade root bending moment had a larger range in the simulations and the damage equivalent moments were overestimated.