The measurement database used in this study was recorded from April to July 2009 as part of the DAN-AERO project . It contains 9600 data files with 10 min measurements from a Siemens 3.6 MW wind turbine located at the Høvsøre test site for large wind turbines in Denmark, as well as measurements from the nearby met masts (see Fig. ). The rotor diameter is 107 m and the hub height is 89.5 m. The turbine was equipped with blade-root bending-moment sensors and a blade-mounted five-hole pitot tube.

As seen in Fig. , the turbine was located in the middle of a row of five megawatt-scale wind turbines. Mast3, which is located around 2.5 diameters west of the turbine, provides hub-height wind-speed observations, whereas the main met mast, 820 m south of the turbine, measures the wind speed at six different heights ranging from 10 to 116.5 m.

Five-hole pitot tubes have been used in several research experiments to measure the local inflow relative to the blades .

During the current measurement period, an Aeroprobe CPSPY5 five-hole pitot tube was mounted on one of the blades at a radius of 36 m, i.e. around one-third from the tip. A five-hole pitot tube measures the relative flow speed as well as the flow angle in two perpendicular planes. The pitot tube was calibrated by Aeroprobe, and the uncertainty of the measured relative flow speed and angles was determined to be less than 0.2 % and 0.2∘ respectively .

From the relative flow speed and two perpendicular angles, the relative 3-D flow velocity vector can be calculated , and subtracting the velocity due to sensor movement yields the flow velocity in the rotor plane; more details about this process, the measurement database and measurement-related issues are available in .

In this study, the velocity due to sensor movement is calculated based on the rotor rotation and the pitch motion. This means that movement due to dynamic tower and blade deflection is not included, and some discrepancy is consequently expected. In Pedersen et al. (2018), the error introduced by not taking the tower and blade deflection into account is investigated using HAWC2 simulations, and the root-mean-squared error of the instant axial wind speed is found to be around 2 %.

The flow velocity is mapped from the rotating blade section coordinate system to fixed global cartesian coordinates. During this process, additional uncertainty is introduced, as the exact orientation of the blade section is unknown due to the deflection and torsion of the structure.

Finally, the wind-turbine induction, i.e. the disturbance of the inflow field caused by the presence of the rotor, is estimated using a combination of aerodynamic models. In this study, the aerodynamic models comprise blade element momentum (BEM) based models for axial and tangential induction, a radial induction model and tip loss correction, as well as models for skew and dynamic inflow.

Subtracting the estimated induction from the measured flow velocity results in an estimate of the free-stream inflow velocity, which would have been observed at the same time and location without the presence of the turbine. In this step, uncertainty is also introduced due to the mismatch between the applied simple engineering models and the complex real world. The process and the introduced uncertainties are described in detail by . Furthermore, based on numerical simulations, found that the error of the estimated axial 10 min mean wind speed obtained from a BMFS is less than 0.25 m s-1 for all wind speeds, whereas the error of the standard deviation is less than 0.1 m s-1. Whether the introduced uncertainties outweigh the advantage of measuring at the blade will be investigated in this study.

The blade-root load sensors comprise flap-wise and edge-wise bending-moment sensors (see Fig. ) on all three blades. They are located 3.2 m from the hub centre.

Some of the sensors are found to drift considerably with temperature. Therefore, a linear temperature correction is applied before performing the calibration.

The edge-wise bending-moment sensors are calibrated using a set of time series measured at low wind speed and with pitch angles around 0∘. In these cases, the edge-wise loads are dominated by the gravity loading; therefore, the loads are fitted to a sinusoidal signal with a magnitude equal to the self-weight moment of the blade: 1Minimizea,b∑θrotoraMy(θrotor)+b-Mswsin⁡(θrotor), where a and b are calibration factors, My is the measured edge-wise bending moment, θrotor is the rotor position and Msw is the moment when the blade is in the horizontal position due to the weight of the blade from the load sensor to the tip.

Similarly, the flap-wise bending-moment sensors can be calibrated using time series measured at a low wind speed and a 90∘ pitch angle. However, the measurement database does not contain time series with a 90∘ pitch angle and low wind speed; it was, therefore, necessary to use time series with lower pitch angles for the calibration. Hence, the pitch angle must be included in the calibration formula: 2Minimizea,b∑θrotoraMx(θrotor)+b-Mswsin⁡(θpitch)sin⁡(θrotor), where Mx is the measured flap-wise bending moment, and θpitch is the pitch angle.

The mean flap-wise bending moments of the three blades are not equal after this calibration. This is, however, justified as the measured pitch angles of blades 2 and 3 are offset by around -0.4 and +1∘ respectively, compared with blade 1. These pitch offsets are included in the aeroelastic simulations (see Sect. ).

The current measurement database contains no tower-load sensors. The dynamic tower loads are, however, mainly induced by the aerodynamic blade loads; therefore, it is possible to derive tower-load estimations from the blade-root load sensors.

The tower-bottom fore–aft bending moment is dominated by the constant weight of the rotor and the dynamic thrust on the rotor. The thrust is related to the rotor-plane projection of the blade-root bending moments (i.e. mainly the flap-wise bending moments), and using a linear calibration a good approximation can be achieved for a given wind speed: 3MTBforeaft,est=atb∑i=1…3MBRi+btb, where MTBforeaft,est is the estimated tower-bottom fore–aft bending moment, MBRi is the rotor-plane projection of the blade-root bending moment of blade i (see Fig. ), and atb and btb are calibration constants.

Similarly, approximations of the tower-top tilt and yaw moments can be formulated as 4MTTtilt,est=atilt∑i=1…3MBRicos⁡θrotor-2i3π+btilt5MTTyaw,est=ayaw∑i=1…3MBRicos⁡θrotor-2i3π+π2+byaw

The derived tower-load sensors have been calibrated based on HAWC2 simulations. Applied to other HAWC2 simulations with comparable wind conditions, the tower loads derived from the blade-root sensors fit quite well with the actual simulated tower loads (see 8 m s-1 example in Fig. ).

The calibration constants are, however, dependent on the mean wind speed. Hence, the fine agreement seen in Fig.  is only obtainable when using the correct wind-speed-specific calibration constants.

The calibration constants are consequently determined for wind speeds ranging from 4 to 15 m s-1 and interpolated based on the revolution-averaged pitot-tube mean wind speed. To test the calibration, the equivalent fatigue load of the derived tower-load sensors have been calculated for five independent simulation sets. The estimated loads are then compared to the HAWC2-simulated “real” tower loads. The relative error is shown in Fig. .

At low wind speeds, the tower-bottom bending moment is dominated by structural loads, whereas the impact of the aerodynamic blade loads is limited. Hence, the derived tower-bottom sensor deviates considerably from the simulated tower-bottom signal, and the fatigue load error is relatively high (see Fig. ). Therefore, the derived tower-bottom fore–aft loads will be discarded for wind speeds below 6 m s-1. In all other cases, the mean error is less than 5 %. Note that this deviation will not affect the discrepancies between the measurements and simulations in the results section directly, as the presented tower loads in both cases will be derived from the blade-root loads even though the “real” tower loads are also simulated directly by HAWC2.

The simulations used in this study are performed using HAWC2 – a non-linear finite-element-based aeroelastic code intended for computing the wind-turbine response in the time domain .

The turbine model used for the simulations is based on the structural and aerodynamic data of the Siemens 3.6 MW turbine, which was tested at Høvsøre in 2009 during the DAN-AERO project (see Sect. ).

To match the pitch-angle offsets observed in the measurements (see Sect. ), the blades are modelled with slightly different pitch angles.

Within the HAWC2 framework, the turbine is controlled by the Basic DTU controller . This controller has been set up to match the behaviour of the Siemens controller, which was controlling the turbine during the measurement period, as well as possible. In some cases and regions, however, mismatch between the two controllers should be expected.

In this section, the inflow characteristics used for the different cases are described (see an overview of the five cases in Table ). Cases 1–3 are based on met-mast sensors, whereas cases 4 and 5 are based on the estimated free-stream pitot-tube wind speed (see Sect. ). Table  gives an overview of the actual inflow parameters extracted from the 20 periods.

In Case 1, only the wind speeds are different between the periods. Therefore, the load levels within the two wind-speed groups are very similar, as seen in Fig. . In this case, the simulated loads do not reflect the measured load variation; thus, the mean relative error seen in Fig.  is high, especially for the flap and tower-bottom loads at 8 m s-1  where the relative variation is huge, but also in the tilt and yaw moments at 14 m s-1  where the simulated loads are too high. It should also be noted that the variation of the simulations due to different turbulence realizations (seeds) does not reflect the measured variation, except for the yaw and tilt moments in the high-wind situations.

In Case 2, information about the wind-speed trend, the measured turbulence level and the shear profile is included in the simulations.

Including the wind-speed trend increases the loads considerably in some periods. In P7, for example, the mean wind speed decreases 2.9 m s-1 (linear fit) during the 10 min (see Table ). Including this trend increases the flap and tower-bottom fatigue loads by around 30 %. This indicates that wind-speed trends are important to include in simulations for load validations.

In the selected periods, the turbulence intensity varies from 3.1 to 9.2 %. Including this information makes the range of the simulated loads reflect the range of the measured loads. The turbulence scaling approach, which is used for Case 1, is found to introduce substantial variation due to different turbulence realizations (seeds). This variation is considerably reduced in this and the succeeding cases by fitting the αϵ2/3 turbulence parameter. All things being equal, the αϵ2/3-fitting method reduces the average seed-induced variation of yaw loads at 14 m s-1 from 450 to 90 kNm, while the maximum error of the tilt and yaw moments at 14 m s-1 is approximately reduced from 80 % to 40 %.

The terrain is rather flat towards the west; therefore, the power shear exponents are modest (0.06 to 0.21) and are generally similar to the site-average values (0.09 for 8 m s-1 and 0.13 for 14 m s-1). The largest difference is found in P1, where the shear coefficient is increased from 0.09 to 0.21, which seen in isolation increases the simulated flap loads of this period by 9 %–18 %. In general, however, the effect of including the measured shear profile is limited, but the situation may be different if periods with wind from other directions were also considered or for extreme atmospheric stability conditions.

Furthermore, the stability dependent L and Γ parameters are used for the turbulence generation. Using these non-standard parameters, affects the flap and tower-bottom loads significantly in some periods. In P1 (stable conditions), the tower-bottom load decreases by 22 %, whereas it increases by 20 % in P11 (very unstable conditions). In these periods, however, the error of the simulated loads is not reduced.

Figure  reveals that the mean error of all loads is significantly reduced by utilizing these inflow characteristics. However, the correlation between the measured and simulated load levels is still poor. The simulated tower-bottom load of P5, for instance, is up to 67 % too high, and the measured tilt-moment fatigue loads of P2 and P5 are almost equal, even though they account for the minimum and maximum simulated loads respectively (see Fig. ).

In Case 3, constraint turbulence simulation has been applied to constrain the turbulence to match the Mast3 wind-speed recordings at the position of Mast3, i.e. 250 m upstream. It has an effect on most of the simulated loads, but it slightly increases the mean error of all load sensors (see Fig. ).

The biggest error increase is seen for P5, which has a distinct drop in the wind speed measured by Mast3 in the middle of the period. In the simulations, a similar drop, introduced by the constraint turbulence simulator, is unaffectedly advected with the steady mean wind to the turbine in agreement with Taylor's frozen turbulence hypothesis . Around 30 s later, the same wind-speed drop subsequently hits the turbine and induces significant fatigue loads. In the real world, however, the turbulence structures change, the mean wind is not always steady and the wind-speed drop may even pass beside the turbine. In P5, a small drop is measured in the flap-wise bending moment, but it is only half the size of the simulated drop.

Case 4 uses inflow characteristics extracted from the estimated free-stream pitot-tube wind speed. As seen in Table , these characteristics are different from the met-mast characteristics: the mean wind speed deviates up to 0.77 m s-1, the wind-speed trend up to 1.45 m s-1, the turbulence intensity up to 2.3 % and the power shear coefficient up to 0.11.

These mismatches are caused by the spatial distance between the locations of measurements, fundamental differences in the sensor technology and measurement method, and the uncertainties introduced in the conversion from pitot-tube measurement to free-stream wind speed in the fixed global coordinates (see Sect. ).

Compared with Case 2 (the most equivalent met-mast case), all mean errors decrease by 5 % or more except the mean error of the tilt moment at 8 m s-1 (see Fig. ). The error ranges also decrease considerably for the flap and tower-bottom loads (see Fig. ), whereas they are similar for the tilt- and yaw-moment error.

In Case 5, the measured mean-wind-speed variations over the rotor area are modelled; furthermore, the instant measured pitot-tube wind speed is used to constrain the turbulence model.

Modelling the measured mean-wind-speed variations via the grid-based approach (exemplified in Fig. ) increases all loads, except the yaw moments. In some periods, the flap load increases up to 15 %, and seen in isolation, the use of this approach slightly decreases the error of most of the simulated loads. It may be that the mismatch introduced by extrapolating the wind speed measured on the pitot-tube path to the whole rotor area almost neutralizes the positive effects, in which case more pitot tubes would be beneficial.

In this case, the turbulence field is generated using standard Mann turbulence L and Γ parameters and constraint turbulence simulation. In theory, this approach is problematic as the statistics of the applied constraints may be different from the standard parameters, such that the constraint turbulence simulator needs to compensate in other parts of the turbulence field to obtain the requested statistics. Using the stability-dependent L and Γ parameters instead has been tried. It was found to have a small positive effect on the errors at 8 m s-1 and a similar small, but negative, effect on the errors at 14 m s-1. Therefore, we have chosen to use the standard parameters in this case, to avoid the need for met-mast measurements to determine the stability conditions.

In the selected periods, the use of constraint turbulence simulation reduces the mean error for all load sensors. Furthermore, the range of the simulated loads due to different turbulence realizations decreases considerably, such that the need for multiple simulations with different seeds is reduced (see Fig. ).

In Case 5, the range of the simulated loads reflects the range of the measured loads. Therefore, they are assumed to be much more suitable for load extrapolation than the loads of Case 1.

The derived tower loads are slightly underestimated at 8 m s-1 and overestimated at 14 m s-1. These deviations may be introduced by the derivation of the synthetic tower loads (see Sect. ), by the associated calibration of these uncertainties in the measured pitch-angle offsets, and by different control behaviour due to differences between the Siemens controller and the Basic DTU controller.

Only a few of the lines that connect the measured and simulated flap and tower-bottom observations intersect, meaning that the inflow conditions that result in high-load levels in the measurements also result in high-load levels in the simulations and vice versa. The same tendency is seen for the tilt and yaw moment at 14 m s-1.

At the beginning of this section, it was concluded that an advanced approach that considers combinations of inflow parameters would be required to predict the loads of specific periods. Aeroelastic simulations can be considered to be such an approach, and to compare these simulations to the single parameter approach in Figs. , and , two additional simulation sets were performed. Both sets comprise 970 simulations representing all suitable periods in the measurement database (one seed per period). In the first set, inflow information is extracted from the met masts (similar to Case 2), whereas the second set is based on information from the pitot tube (similar to Case 5). Figures  and  show the equivalent loads, coloured according to the HAWC2-simulated load relative to the wind-speed-dependent measured load range. This means that the red dots represent periods where the simulated load equals the maximum measured load at that wind speed, whereas the blue dots represent periods where the simulated load equals the minimum measured load. In other words, unmixed rainbow-coloured scatter means that the measured and simulated loads are similar and that the measured scatter can be predicted.

The most promising result is seen in the flap and tower-bottom loads coloured according to the pitot-tube-based simulations (top row of Fig. ) where the scatter is almost rainbow-coloured. This means that HAWC2 simulations with inflow characteristics extracted from the pitot tube are able to explain most of the measured flap and tower-bottom load scatter. The met-mast-based counterparts (top row of Fig. ) are more mixed, even though most of the red observations are in the upper part of the scatter, and most of the blue observations are in the lower part.

The tilt and yaw moment scatter, in comparison, cannot be explained using these approaches. In both cases, most high-load observations are underestimated from 4 to 8 m s-1 and from 10 to 12 m s-1, whereas low-load observations are overestimated from 8 to 10 m s-1 and above 12 m s-1.