FAST.Farm load validation for single wake situations at alpha ventus

. The main objective of the presented work is the validation of the simulation tool FAST.Farm for the calculation of power and structural loads in single wake situations; the basis for the validation is the measurement data base of the op-erating offshore wind farm alpha ventus. The approach is described in detail and covers calibration of the aeroelastic turbine model, transfer of environmental conditions to simulations, (cid:58) and comparison between simulations and adequately ﬁltered measurements. It is shown that FAST.Farm accurately predicts power and structural load distributions over wind direction (cid:58)(cid:58)(cid:58)(cid:58) with discrepancies (cid:58)(cid:58) of (cid:58)(cid:58)(cid:58)(cid:58) less (cid:58)(cid:58)(cid:58)(cid:58) than (cid:58)(cid:58)(cid:58)(cid:58)(cid:58) 10 % (cid:58)(cid:58)(cid:58) for (cid:58)(cid:58)(cid:58)(cid:58) most (cid:58)(cid:58)(cid:58) of (cid:58)(cid:58)(cid:58) the cases compared to the measurements. Additionally, the frequency response of the structure is investigated and it is calculated by FAST.Farm in good agreement with the measurements. In general, the calculation of fatigue loads is improved with a wake-added turbulence model added to FAST.Farm in the course of this study. exists. Consequently, higher TI values lead to higher loads at the the this holds true it was found that also also (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) found (cid:58)(cid:58)(cid:58) that (cid:58) low ambient TI conditions can lead to high wake loads. This shows that there is some uncertainty in modeling the environmental conditions and wake features that should be investigated in future. for tower-base loading. It was shown that FAST.Farm predicts the mean power deﬁcit with high accuracy compared to the measurements. Additionally, the PDF of generator speed was calculated in strong agreement with the measurements for the free- freestream and downstream turbine. Fatigue loads were analyzed in terms of DELs of the bending moments at the blade root in the ﬂapwise direction and the tower base in the fore-aft FA direction. Distributions over wind direction show a good match between simulations and measurements with deviations of less than 10 % for most of the investigated wind directions.

turbulence and the individual wake deficits from each rotor. When multiple wakes overlap, the superposition of axial wake deficits is based on a root-sum-square method.
Some of the unique innovations of FAST.Farm relative to DWM implementations in other simulation tools include: 60 -Improvement of wake advection, deflection, and merging; -Calibration of wake-related model parameters against results from high-fidelity large-eddy simulations :::: LES; -Ability to solve all wind turbines and the farm-wide disturbed wind field in parallel; -Optional inclusion of a wind-farm-wide super controller (not used in this paper); and -Optional inclusion of large-eddy simulation-generated :::::::::::: LES-generated ambient wind data (not used in this paper).

Implementation of wake-added turbulence
Besides modeling wake deficit and wake meandering, the DWM model by Larsen et al. (2008) includes modeling of wake-70 added turbulence. This term describes the generation of turbulence behind a wind turbine rotor due to shear forces in the wake, as well as the breakdown of mainly the tip and root vortices. The contribution of wake-added turbulence to the total turbulence level inside a turbine's wake is higher for low ambient turbulence conditions (Madsen et al. (2010)). Therefore, the inclusion of wake-added turbulence is especially important for offshore conditions where ambient turbulence levels are often low (i.e. below ::: less :::: than : 10 %). Preliminary results in the course of this work (see Fig. A1) supported this observation and led to the 75 implementation of a wake-added turbulence feature in FAST.Farm, which was not present in previous versions. In summary, it was :: is seen that the tower loads are strongly influenced by wake-added turbulence and the corresponding improvement of FAST.Farm lead :::: leads to an increase in accuracy. In contrast, Fig. A1 indicates , that the blade loads are not very sensitive to wake-added turbulence.
The herein presented implementation of wake-added turbulence in FAST.Farm follows mainly the approach by Larsen et al. 80 (2008) and Madsen et al. (2010), which is included in the IEC 61400-1 standard (IEC (2019)). In addition to the ambient turbulence domain, it uses a new wake-added turbulence domain defined in the meandering frame of reference. This domain is generated with Mann's spectral turbulence model (Mann (1994)), defining turbulence as homogeneous and isotropic with a length scale that equals the rotor diameter. The domain should have a fine spatial discretization to resolve the smaller turbulent scales of the wake-added turbulence.

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The wake-added turbulence velocity components are scaled with the factor k mt defined by Eq. 1. It is composed by ::: (1).

Alpha ventus measurement data base
The wind farm alpha ventus is located 45 km north of the German island Borkum in the North Sea. It consists of twelve turbines with a rated power of 5 MWform, which is shown in Fig. 2. This study focuses on the turbines AV4 and AV5, which are Senvion 120 5M turbines with a rotor diameter of 126 m and a hub height of 92 m. They are mounted on a jacket substructure and are located approximately 6.7 D apart. Within the initiative Research at alpha ventus (RAVE, 2021) measurement data from both turbines have been acquired since 2011. For example, these data were used in load validation studies for freestream conditions by Kaufer and Cheng (2013) and Popko et al. (2021). For this work, we used data from the period 01/2016 − 07/2018 because of good availability and quality. In front of turbine AV4, the Fino 1 :::::: FINO1 : met mast is located at a distance of approximately 3.2 D providing environmental data.

Turbine measurements
The turbines are equipped with load sensors at various locations. Additionally, data from the turbine's SCADA system is ::: are available. The time resolution of all sensors is 50 Hz. The following list explains the sensors used in this study and their calibration.

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-SCADA: Generator power, generator speed and blade-pitch angle measurements are directly taken from the SCADA system. -Nacelle yaw position: These data are also available through the SCADA system. Over longer time periods, a drift was observed in the data. This was corrected by using nacelle rotation events and correlating the known tower-base strain gauge positions with the nacelle-yaw signal. In this way, sensor offset values were derived to make the data consistent 135 over time.
-Tower-base bending moments were calculated from strain gauges located above the transition piece. The strain gauges are placed at four locations separated by 90 • ::: 90 • around the tower cylinder. By combining the strain gauge measurements with the nacelle's yaw position, fore-aft :::: (FA) and side-side :::: (SS) bending moments were derived. Nacelle rotation events during turbine shutdown and calm wind conditions were used to determine calibration factors in terms of slope and 140 offset.
-Blade-root bending moments in edgewise and flapwise direction are measured via four strain gauges placed near the blade root. They were calibrated with rotor idling events during calm winds , as well as 10-min mean operational data.
The measurements were made consistent over time by adjusting slope and offset. Strain gauge signals were combined to reduce cross-talk effects.

Environmental data
Meteorological and sea conditions are measured at the Fino 1 :::::: FINO1 met mast and are available as 10-min statistics. Wind speed is measured with cup anemometers at 7 locations starting at 41.5 m height above sea level (a.s.l.) and going up with approx. 10 m :::::::: increasing :: in ::::::: approx. ::::: 10-m : increments to 100 m height a.s.l. Wind speed data is :: are : corrected for met mast shadow effects as explained by Westerhellweg et al. (2011). Vertical wind shear is described in terms of the power law exponent 150 α, which is derived by fitting the power law on the wind speed measurements from all available heights of the met mast.
Wind direction is taken from the wind vane located at 91.5 m height :::::: 91.5-m :::::: height, : with the correction given by Westerhellweg et al. (2010). An additional offset of +3 • is applied on wind direction, which was derived by correlating the wake deficit of turbine AV4 with the measured wind direction at Fino 1. :::::: FINO1. : Atmospheric stability is estimated by using the power law shear exponent α and applying the limits given in Table 1.

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This simplified approach is motivated by Westerhellweg et al. (2014) and has the advantage of good sensor availability. It is considered to be sufficient for this study because it only serves as refinement for environmental conditions and specific analyzes on :::::: analyses :: of : atmospheric stability are excluded.

Filtering approach 165
The measurement data are clustered in 10-min events for which the statistics are calculated to allow appropriate filtering. In particular, the following filter criteria were applied: -Only events are considered which have a data availability of more than 99 %.
-Wind direction is constrained from 257 • to 287 • to ensure that only wake effects of turbine AV4 affect AV5. At the boundaries of this wind direction sector, nearly freestream conditions exist for both turbines; effects from wind farm 170 blockage are ignored.
-Both turbines are operated under normal conditions. For example, down-regulation, startup : , : or shutdown events are omitted. events where the difference in the mean yaw position is below ::: less :::: than : 6 • .

Calibration of aeroelastic simulation model
The aeroelastic simulation model was generated with structural and aerodynamic information provided by the manufacturer.
Simulations were performed with the original turbine controller. In addition, a thorough calibration of the simulation model of both turbines AV4 and AV5 was performed to match the turbines measured load characteristic in the field as close ::::: closely : as possible. This involves the determination of structural damping of the first tower eigenmodes in the fore-aft (FA ) and side-side 205 (SS ) :: FA ::: and ::: SS : direction by analyzing turbine shutdown events.
Furthermore, imbalances in the rotating system were identified by looking at the frequency response during freestream events with low TI conditions. The imbalances were introduced for each blade i as variation in blade mass B M,i , variation in blade flapwise B FK,i and edgewise B EK,i stiffness, and blade-pitch offset B PO,i . A summary of the introduced imbalances in the simulation model is listed in Table 2. Using these values, : we were able to reproduce the turbines' frequency response from the 210 field at the desired sensor locations with satisfactory accuracy. It is noted , that these imbalances do not necessarily reflect the real existing imbalances; however, this approach was regarded as the best solution overcoming missing exact blade calibration measurements such as static blade deflection tests.

Initial results
A check of the turbine characteristics during freestream conditions as well as an analysis of the environmental conditions is 250 presented, before taking wake effects into account in Sect. 4. Figure 3 illustrates results of the comparison between simulations and field measurements for close to freestream conditions. This freestream sector of 240 • − 257 • was detected beforehand by correlating loads of turbine AV5 with the wind direction. In total, : 2980 simulations were conducted with the software OpenFAST, which employs the same aeroelastic model as described 255 for FAST.Farm but without wind farm-wide effects, enabling faster simulation times. Although an individual calibration of both turbines AV4 and AV5 was conducted, the differences in the considered aggregated load quantities is negligible; hence, only the results of the AV4 calibration is shown in Fig. 3.

Investigation of turbine characteristics in freestream conditions
For the operational sensors of generator power ( Fig. 3 (a)) and blade-pitch angle ( Fig. 3 (b)), a discrepancy of less than 5 % is found between the data of turbines AV4, AV5 and simulations described as OpenFAST. The damage equivalent load (DEL , 260 see Eq. 4) :::: DEL : computed for the fore-aft ::: FA bending moment at tower-base (Fig. 3 (c)) shows : a :::: close :::::: match with a difference of less than 7 % a close match in below rated conditions (4 − 12 m s −1 ). In the above rated conditions, simulations agree well with measurements from turbine AV4; the loads of turbine AV5 are up to 20 % higher compared to turbine AV4. This difference is most likely related to an imbalance in the rotor system during blade-pitch actuation. Loads at the blade root are compared by means of DEL of the bending moment in the flapwise direction in Fig. 3 (d). It is observed that measurements of both turbines 265 as well as simulations match each other well with differences of less than 10 % for wind speeds up to 16 m s −1 .
Overall, the simulations can predict the measured load quantities in freestream conditions with high accuracy. This indicates that the aeroelastic simulation model is set up appropriately and that the meteorological conditions are transferred into realistic wind fields. The exact representation of hydrodynamic excitation in terms of wave loads is considered of less importance because the substructure is quite rigid and only sensors above the sea water level are taken into account in this study.

Distribution of environmental conditions
For the analyzed wind speed bins, the TI distribution over wind direction is shown in Fig. 4. The mean TI for wind speed bin I calculates to ≈ 6.4 % and ≈ 5.9 % for wind speed bin II. Highest TI values are found in unstable atmospheric conditions whereas lowest TI values occur in stable conditions. Especially in wind speed bin II, more events are found towards wind directions from the southwest, which is the predominant wind direction. A more uniform event distribution with regard to the 275 wind direction is found for wind speed bin I. Figure 5 depicts the distribution of the power law shear exponent α over wind direction. It can be seen that wind speed bin II contains higher α values on average compared to wind speed bin I.

Turbine performance: detailed results
A more detailed analysis of the turbine performance is shown in Fig. 7 , by plotting the probability density function (PDF) of 290 the generator speed. The PDF was calculated for each 10-min event in the wind sector corresponding to full-wake conditions.
Afterwards, mean value with error range expressed as 15 th and 85 th percentiles across the PDFs of all events were derived. In  both wind speed bins, a reduction of generator speed is found for the waked turbine, caused by the wind speed deficit from the upstream turbine. In wind speed bin I, the downstream turbine operates near the cut-in wind speed, which is indicated by the peak around the normalized generator speed of 0.6 in Fig. 7 (a). From Fig. 7 (b), it can be seen that a wider range of generator 295 speeds is covered by the waked turbine compared to the freestream turbine. This can be related to a varied operational point due to the wake deficit. Additionally, it can be partly attributed to the increased turbulence in the wake originating from wake-added    Figure 8 shows results of the fatigue loads expressed as DEL of the blade-root bending moment in the flapwise direction. By comparing the two wind speed bins, different load distributions over wind direction for the waked turbine are observed. For wind speed bin I (Fig. 8 (a)), a dip in the DEL for the downstream turbine occurs around full wake conditions at 272 • ); this is not visible for wind speed bin II (Fig. 8 (b)). Influencing factors on the load distribution for the waked turbine are the wind the :::: aim ::: was : to reduce the uncertainty arising from the different combinations. Hence, it is seen for both wind speed bins that FAST.Farm agrees well with the measurements and predicts the increase in loads and trends over wind direction with good accuracy. Overall, a load increase by approx. :: of :::::::::::: approximately factor 1.7 (wind speed bin I) and factor 2 ::: 2.0 (wind speed bin II) are identified for the waked turbine. Figure 9 displays the DELs of the tower-base bending moment in the fore-aft :: FA : direction. In contrary to the fatigue loads at the blade-root, a higher increase in loads for the waked turbine is observed for wind speed bin I compared to wind speed bin II. In particular, DELs are increased by factor ≈ 2.4 (wind speed bin I) and factor ≈ 2 ::::: ≈ 2.0 (wind speed bin II) for the waked turbine compared to the DELs of the freestream turbine. FAST.Farm produces results in good agreement with the measurements in terms of magnitude and wind direction dependency. For most of the considered wind directions, the discrepancy in the mean 315 value per bin between FAST.Farm and the measurements is below ::: less :::: than : 10 %; in some wind directions, : the difference is increased to ≈ 25 %. The uncertainty range per bin indicated by the percentile range is predicted by FAST.Farm with good agreement to the measurements.   density (PSD) was calculated. Then mean values for each frequency with corresponding uncertainty range expressed as 15 th and 85 th percentiles were determined. They are shown for the blade-root bending moment in the flapwise direction ( Fig.10 (a)) and the tower-base bending moment in the fore-aft ::: FA direction ( Fig. 10 (b)).

Structural loads: frequency response
In case of the blade (Fig. 10 (a)), an increase of energy at the blade passing frequency 1P is observed for the waked turbine 325 compared to the freestream turbine. It comes along with a reduction of the blade passing frequency (freestream: 1P ≈ 0.15 Hz, wake: 1P ≈ 0.13 Hz) due to the reduced wind speed inside the wake and consequently a reduction of rotor speed. The magnitude of the first blade passing frequency of turbine AV5 is predicted by FAST.Farm with :: to :: be : a factor of 3 higher compared to the measurements. In contrast, the excitation of the second blade passing frequency 2P indicated by the peaks between 0.2−0.3 Hz is higher in the measurements. A possible explanation is the modeling of the wake, : which has a circular ::::::: Gaussian : shape in 330 FAST.Farm. In reality, the wake is more likely to be skewed ::::::: distorted, leading to smoother transitions to undisturbed winds.

Discussion
The present investigation concentrates on two wind speed bins in below rated conditions. This choice is motivated by the connected high rotor thrust conditions and hence strong wake effects. Moreover, analyses :: of :::::::: quantities : over wind direction are enabled. Another reason is that the behavior of both turbines AV4 and AV5 is comparable in the measurements : , whereas 345 in above rated conditions : , : differences occur even under ambient inflow for both turbines (see Fig. 3 (c)). For the analysis of structural loads, we focus on sensors and directions that are mainly affected by the change of turbulence characteristics in the wake, i.e. tower-base fore-aft :: FA : bending moment and blade-root flapwise bending moment.
A crucial part of this load validation is the generation of adequate wind fields representing the environmental conditions at alpha ventus. Especially, coherence and turbulence scale have an influence on wake meandering magnitude, which in turn 350 effects ::::: affects : the loads of the downstream turbine (see also Shaler et al. (2019b) ::: and ::::::::::::::::::::::: Wise and Bachynski (2020)). Unstable and neutral atmospheric conditions imply greater turbulent length scales and more ::::: larger coherent turbulent structures than stable conditions. This leads to higher wake meandering magnitudes and higher load levels for the downstream turbine. For the loads at the blade-root, adequate capturing of wake meandering is most important, whereas for the loads at the tower-base, both wake meandering and wake-added turbulence must be modeled. We observed that in the simulations, : a direct relationship 355 between ambient TI conditions and wake loads exist ::::: exists. Consequently, higher ambient TI values lead to higher loads at the downstream turbine. In the measurements, this relationship holds true but it was found that also ::: also :::::: found ::: that : low ambient TI conditions can lead to high wake loads. This shows that there is some uncertainty in modeling the environmental conditions and wake features that should be investigated in future.
In offshore full-scale load validation, there are many potential sources of uncertainty. Starting with the modeling of environ-360 mental , conditions ::::::::: conditions, : we aimed to minimize those uncertainties by making use of findings by :::: from previous research, which is available for the site. However, there are limits in the methods used. For example, in the coherence model of the wind field, there is no directional dependency of coherence considered and coherence is only dependent on the velocity components u, v, w. In the considered period of measurements and wind direction sector, alpha ventus operates in the wake of the wind farm "Trianel Borkum I", which is located ≈ 6.5 km ::::::: ≈ 6.5 km : east. The flow structures evolving from this farm-wake are likely to 365 be different from ideal freestream conditions, for which the wind field generation method was originally derived. Overall, order to reduce the input uncertainties, we followed a one-to-one simulation approach where the measured environmental conditions are utilized directly as simulation inputs.
Distributions over wind direction show a good match between simulations and measurements with deviations of less than 10 % for most of the investigated wind directions.
More detailed insights in the aforementioned structural load quantities were provided by PSD analyses. They show that FAST.Farm calculates trends in the structural response with good agreement to the measurements in :: the : frequency domain.

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In particular, excitation at the tower base of the waked turbine is reproduced with FAST.Farm, which can be attributed to the wake-added turbulence feature in FAST.Farm added in the course of this study. However, by looking at the PSD at blade root, it is indicated that not all phenomena are captured sufficiently by FAST.Farm, leaving room for further improvements.
It was demonstrated that the proposed one-to-one simulation approach works well for the validation in offshore single wake conditions. It is concluded that calibration of the aeroelastic model with respect to imbalances as well as appropriate transfer 385 of environmental conditions to simulations are important. Hereby : is ::::::::: important. :::: Here, a differentiation of atmospheric stability helps to refine simulation inputs such as coherence in the wind field, but also indicates that especially stable atmospheric conditions remain challenging to model for capturing the loads of a waked turbine.
Code and data availability. The version of FAST.Farm including the wake-added turbulence model, which was used to create the results presented in this paper is different than the official version released by NREL, but is available under . NREL has plans 390 to incorporate an updated version of the present implementation in a future release of FAST.Farm The measurement data used in this study can be accessed via the "Bundesamt für Seeschifffahrt und Hydrographie" (BSH (2021)). A data usage agreement must be signed with the BSH in advance.
the national joint research project RAVE -OWP Control (FKZ 0324131B) and is part of the research done in the WindForS research cluster.