The outlined analysis validates the dynamic wake meandering (DWM) model based on loads and power production measured at an onshore wind farm with small turbine distances. Special focus is given to the performance of a version of the DWM model that was previously recalibrated at the site. The recalibration is based on measurements from a turbine nacelle-mounted lidar system. The different versions of the DWM model are compared to the commonly used Frandsen wake-added turbulence model. The results of the recalibrated wake model agree very well with the measurements, whereas the Frandsen model overestimates the loads drastically for short turbine distances. Furthermore, lidar measurements of the wind speed deficit as well as the wake meandering are incorporated in the DWM model definition in order to decrease the uncertainties.

Wake models are a key aspect in every site-specific load calculation procedure. The used wake model has significant impact on predicted loads and the power output of the whole wind farm; hence, an accurate wake model is of major importance for a wind farm design optimization process. Planning a new wind farm is a highly iterative process, where time-consuming calculations are avoided as much as possible, so the complexity and the accuracy of the model need to be well balanced.

Simple analytical wake models can be divided into models estimating either the mean wind speed reduction in the wake or the wake-induced turbulence. While the former serves as a basis for power calculations, the latter is necessary to compute loads.
One of the main simple analytical models for calculating the wake-induced turbulence in a wind farm is the so-called Frandsen model (see, e.g.,

The dynamic wake meandering (DWM) model investigated here is strongly influenced by the work of

The DWM model has proven to be more accurate in load prediction than the commonly used Frandsen wake-added turbulence model

Besides the validation of the recalibrated model according to power output and loads, in the present study, lidar wake measurements are integrated into the load simulation to support the calculation and decrease the uncertainties. The measured wind speed deficit in the MFR and the time series of the meandering are introduced successively. Related studies with a different approach of integrating the lidar measurements are

Hereafter, in Sect.

Wind farm layout with measurement equipment

The analyzed wind farm is located southeast of Hamburg, Germany. The terrain is mostly flat, and no further wind farms are located in the immediate vicinity. Only at a distance of more than 1 km the terrain becomes slightly hilly (approximately 40 m difference in altitude). The distance to the next wind farm is approximately 3 km. The wind farm layout is depicted in Fig.

Met mast (MM) measurement equipment and lidar positions

Lastly, at three turbines, load measurement equipment is installed. The tower top and bottom as well as blade flapwise and edgewise bending moments are measured with strain gauges at WTG 2 and WTG 5. WTG 3 is only equipped with strain gauges at the tower. The strain gauges at the tower top are installed 3.4 m below the nacelle and the strain gauges at the tower bottom are placed 1.5 m above the floor panel. The edgewise and flapwise moments are measured at a distance of 1.5 m from the blade root. Besides the installed measurement equipment, the turbine's supervisory control and data acquisition (SCADA) system is used to determine the operational conditions of the turbines.

Considered wind direction sectors for wake-free inflow and analyzed wake sectors.

Measurement results from April 2019 to May 2020 have been used in the analysis.
The data are filtered and sorted in accordance with the ambient conditions (e.g., ambient wind speed, turbulence intensity and wind direction) determined by the met mast and the operational states of the turbine tracked by the SCADA system so that all filtering is based on 10 min statistics from the met mast or the SCADA system. Only measurement results where the turbines operate under normal power production are included in the analysis. In the night, the turbines work in a reduced mode for noise-reduction purposes, so no data could be gathered during the night. The wind direction sectors for free inflow and wake conditions are summarized in Table

The measured lidar data are filtered by the power intensity from the returned laser beam, which is closely related to the signal-to-noise ratio (SNR) of the measurements. Furthermore, the scan time is observed, so only results with a sufficient scan time to track the wake meandering are considered.
Lidar systems measure the LOS velocity. The wind speed in the downstream direction is calculated from the lidar's LOS velocity and the geometric dependency of the position of the laser beam relative to the main flow direction as outlined in

The loads are simulated with the commercial software alaska/Wind

The multibody model is connected to an aerodynamic code, which includes the blade element momentum (BEM) theory

Furthermore, the multibody model is connected to a controller, which uses the generator speed and the pitch angle from the multibody simulation to calculate the generator torque and the pitch speed and returns them to the multibody model. The pitch velocity refers to the rotational speed of the pitch blade angular velocity about the pitch axis during a pitching motion. The controller used for the simulations is the actual controller implemented in the turbines of the analyzed wind farm. Hence, a reliable comparison with the measured loads can be achieved.

The inflow wind conditions can be divided into deterministic and stochastic contributions. Deterministic contributions, like the mean wind speed and the shear effects, are imposed on the turbulent wind field. The stochastic contributions are simulated based on a Kaimal spectrum and a coherence function

Components of the DWM model

The following analysis covers simulated power, blade root flapwise and edgewise bending moments as well as tower bottom bending moments.
To compare the measured loads with simulations, sensors at the precise position of the strain gauges are added to the turbine model in alaska/Wind. The locations of the strain gauges are given in Sect.

The measured loads under wake conditions are compared to the simulated loads, which incorporate the DWM model to simulate the inflow at the wake-affected turbine.
As mentioned before, the DWM model is based on the assumption that the wake behaves like a passive tracer in the turbulent wind field. Consequently, the movement of the passive structure, i.e., the wake deficit, is driven by large turbulence scales

One part of the model is the quasi-steady wake deficit, or rather the wind speed deficit in the MFR, which consists of a definition of the initial deficit emitted by the wake-generating turbine and the degradation of the deficit downstream

“DWM-Egmond” based on the definitions in

“DWM-Keck” adopted from

“DWM-Keck-c”, a recalibrated version of the “DWM-Keck” model based on lidar measurements from the wind farm underlying here

Another aspect of the model is the description of the wake meandering. In this work, it is calculated based on the large turbulence scales of the ambient turbulent wind field, which is generated by a Kaimal spectrum and a coherence function

The third part of the DWM model is the definition of the small-scale turbulence generated by the wake shear itself as well as by blade tip and root vortices. This small-scale turbulence is calculated with a scaled homogeneous turbulent wind field, which is also generated by a Kaimal spectrum. The scaling is implemented in accordance with

Incorporation of lidar measurements into the DWM model;

In the previous section, a recalibrated version of the DWM model has been introduced. The lidar systems have been used to recalibrate the DWM model to decrease the uncertainties of load simulations in wake conditions. In a next step, the lidar measurements will be successively incorporated into the wake simulation. A schematic illustration of the process is illustrated in Fig.

The lidar system measures in the induction zone of the downstream turbine, where the wind speed is decreased due to the upstream effect of the subsequent turbine. However, its influence must be excluded from the measurement results to use the measured wind speed deficit in the wake model. The simple induction model defined in

Time series

The time series of the meandering and the horizontal displacement of the wake are determined with the help of a Gaussian fit in accordance with

correction of the measured wind speed by the induction zone model;

fitting of a Gaussian curve to the wind speed distribution along the horizontal direction determined by a measured horizontal line scan and determination of the horizontal displacement of the wake;

transfer of the measured wind speed deficit to the HMFR by shifting the scan points according to the determined displacement;

interpolation of the scanned wind speed deficit in the HMFR to a regular grid;

repetition of steps 1 to 4 until a certain number of scans is reached (e.g., approximately 37 for a 10 min time series);

calculation of the mean wind speed deficit in the HMFR from all scans; and

fitting of the measured mean wind speed deficit to the Bastankhah wake model described in

Wind speed deficit in the HMFR, measured and simulated with the calibrated DWM-Keck-c model as well as fitted to a Gaussian-shaped wake model (DWM-meas).

An example of the measured and simulated time series of the meandering as well as the power spectrum is shown in Fig.

An example of a measured wind speed deficit over the radial distance from the hub center in the HMFR in comparison to the simulated one with the recalibrated DWM model is illustrated in Fig.

Measured and simulated power

In order to validate the aerodynamic load simulations, the following section contains a comparison of measured and simulated loads under wake-free inflow conditions. The section shows results from WTG 2 under normal operating conditions. The met mast as well as WTG 2 are exposed to wake-free inflow conditions. Thus, the met mast is suitable to determine all ambient conditions.
The mean value of the measured and simulated normalized power curve is depicted in Fig.

Measured nacelle anemometer wind speed at WTG 2 over the met mast wind speed.

The power curve is normalized by the measured power in the smallest wind speed bin.
The error bars in the curves illustrate the standard deviation in each wind speed bin. All data sets are divided into wind speed bins with a width of 1 m s

Measured and simulated power deficit

The results of the measured and simulated flapwise blade root bending moment are illustrated in Fig.

The following section summarizes the measured and simulated fatigue loads under normal operation conditions for the wake sector. The ambient conditions for the simulations are determined by the met mast so that only results with wake-free inflow at the met mast are included in the evaluation. The results of the measured and simulated normalized power deficit, where WTG 2 experiences the wake of WTG 1, are shown in Fig.

The results are normalized by the measured power at wake-free inflow on the left side of the power deficit curve. The measurements were gathered during an ambient wind speed of 6 m s

The DELs of the flapwise blade root bending moment under wake conditions are illustrated in Fig.

The two maxima are differently pronounced, which derives from the aerodynamic force and the rotor tilt.
The aerodynamic forces on a blade segment are a function of the apparent wind velocity, which is a vector composed of the motion of the blade and the incoming wind. Due to the turbine tilt, the apparent wind velocity is slightly lower during the upward movement, and the aerodynamic force is reduced. The blade faces slightly away from the wind direction during the upward movement, whereas during the downward movement, the blade faces slightly more towards the wind direction, which results in an increase of the aerodynamic force. At wake conditions, the increase is stronger when the wind speed deficit coincides with the upward movement of the rotor, so a higher alternating load at the blade occurs and the maximum is more pronounced in comparison to the case where the wind speed coincides with the downwind movement of the rotor. A schematic illustration of phenomenon is depicted in the Appendix in Fig.

The results of the edgewise blade root bending moment are depicted in Fig.

Bias between the measured and simulated fatigue loads and the root-mean-square error for the flapwise blade root bending moment

The tower bottom bending moment is illustrated in Fig.

Measured and simulated power at an ambient wind speed of 8 m s

A similar analysis as the one presented in Fig.

Figure

This section compares results for different downstream distances at an ambient wind speed of 8 m s

WTG 2 in the wake of WTG 1

WTG 5 in the wake of WTG 2

WTG 5 in the wake of WTG 1

Measured and simulated flapwise blade root bending moment

Bias between the measured and simulated fatigue loads and the root-mean-square error for the flapwise blade root bending moment

The results of the flapwise and edgewise blade root moments as well as the tower bottom bending moments are shown in Fig.

Measured and simulated power over the wind direction

The bias of accumulated DELs over all wind directions as well as the RMSE are depicted in Fig.

Measured and simulated flapwise blade root bending moment over the wind direction

Measured and simulated edgewise blade root bending moment over the wind direction

Measured and simulated tower bottom fore-aft bending moment over the wind direction

In the following, the recalibrated DWM model is compared to a constrained simulation with lidar measurements of the meandering and the wind speed deficit. The method to incorporate the wind speed deficit in the HMFR as well as the meandering itself is explained in Sect.

The normalized simulated power over the normalized measured power is illustrated in Fig.

The results of the flapwise blade root bending moment are given in Fig.

The outlined analysis validates the DWM model based on power and load measurements at an onshore wind farm with small turbine distances. Special focus is put on a calibrated version of the DWM model

Schematic illustration of the flapwise blade root bending moment according to

Schematic illustration of the edgewise blade root bending moment according to

Access to lidar and met mast data can be requested from the authors.

IR performed all simulations, postprocessed and analyzed the measurement data and wrote the paper. LS monitored the load measurements and data acquisition. Furthermore, LS, DS and ND gave technical advice in regular discussions and reviewed the paper. PD and MB supervised the investigations and reviewed the paper and its revision.

The authors declare that they have no conflict of interest.

The content of this paper was developed within project NEW 4.0 (North German Energy Transition 4.0).

This research has been supported by the Federal Ministry for Economic Affairs and Energy (BMWI) (grant no. 03SIN400).

This paper was edited by Sandrine Aubrun and reviewed by two anonymous referees.