Light detection and ranging (lidar) systems have gained a great importance in today's wake characteristic measurements. The aim of this measurement campaign is to track the wake meandering and in a further step to validate the wind speed deficit in the meandering frame of reference (MFR) and in the fixed frame of reference using nacelle-mounted lidar measurements. Additionally, a comparison of the measured and the modeled wake degradation in the MFR was conducted. The simulations were done with two different versions of the dynamic wake meandering (DWM) model. These versions differ only in the description of the quasi-steady wake deficit. Based on the findings from the lidar measurements, the impact of the ambient turbulence intensity on the eddy viscosity definition in the quasi-steady deficit has been investigated and, subsequently, an improved correlation function has been determined, resulting in very good conformity between the new model and the measurements.

Wake calculation of neighboring wind turbines is a key aspect of every wind farm development. The aim is to estimate both energy yield of the whole wind farm and loads on single turbines as accurately as possible.
One of the main models for calculating the wake-induced turbulence in a wind farm is the so-called Frandsen model (see, for example,

Lidar systems are highly suitable for wake validation purposes. In particular, the so-called scanning lidar systems offer great potential for detailed wake analysis. These lidars are capable of scanning a three-dimensional wind field, so that the line-of-sight (LOS) wind speed can be measured subsequently at different positions in the wake, thus enabling the detection of the wake meandering as well as the shape of the wind speed deficit in the MFR. That is the reason why such a device is used in the measurement campaign outlined here. Several different measurement campaigns with ground-based and nacelle-mounted lidar systems have already been carried out in the last years, some of them even with the purpose of tracking wake meandering and validation of wake models.

In

Additionally, in

It should be noted that the references listed here are only the most essential, on which the present measurement campaign builds. Several campaigns including either lidar systems or meandering observations as well as wake model validations have been conducted in the past. The outlined analysis transfers some of the procedures of tracking the wake meandering to measurement results from an onshore wind farm with small turbine distances. Particular focus is put on the investigation of the wind speed deficit's shape in the MFR and the degradation of the wind speed deficit in the downstream direction. The latter can be captured very well with the used nacelle-mounted pulsed scanning lidar systems due to the fact that it measures simultaneously in different downstream distances. Thus, a detailed comparison of the predicted degradation of the wind speed deficit between the DWM model and the measurement results is possible. Furthermore, the collected lidar measurements are used to recalibrate the DWM model, which enables a more precise modeling of the wake degradation. As a consequence, the calculation of loads and energy yield of the wind farm can be improved.

The remaining document is arranged as follows: in Sect.

The investigated onshore wind farm (Fig.

Wind farm layout with measurement equipment.

Met mast measurement equipment and lidar positions.

Power and thrust coefficients over wind speed for the N117 3 MW and the N117 2.4 MW turbines.

The lidar data are filtered in accordance with the wind direction, so that lidar data without free inflow of the wake-generating turbine as well as lidar measurements in the induction zone of another turbine are rejected. This leads to the remaining wind direction sectors listed in Table

Filter according to the wind direction determined by the met mast (free inflow at met mast and wind turbine and no induction zone from other turbines).

Filter according to the normal power production determined by the turbine's SCADA system.

Filter according to yaw misalignment.

Filter according to the SNR of the lidar measurements.

Filter according to scan time.

Group all data sets in turbulence intensity bins with a bin width of 2 %.

Considered wind direction sectors per wake-generating turbine in the measurement campaign. Wind direction sectors without free inflow of the met mast and the turbine as well as measurements in the induction zone of another turbine are omitted.

Lidar systems measure the line-of-sight velocity. The wind speed in the downstream direction is then 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 meandering time series and the wake's horizontal displacement are determined with the help of a Gaussian fit.

Wind speed deficit at a downstream distance of

Since the vertical meandering is neglected, the measurement results are fitted to a one-dimensional Gaussian curve defined as follows:

Method for the determination of the mean wind speed deficit in the HMFR.

The entire method of calculating the wind speed deficit in the HMFR is illustrated in Fig.

One of the most challenging parts of this specific measurement campaign is the low ray update rate of the lidar system, which is considerably smaller than in the previously introduced measurement campaigns

Simulated and simulated “measured” meandering time series

The lidar simulations indicate that the Gauss fit works more reliably under optimal operating conditions, i.e., at optimal tip speed ratio, when the wind speed deficit is most pronounced and the power coefficient

The measured wind speed deficit in the HMFR is consecutively compared to the DWM model, which is based on the assumption that the wake behaves as 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

Components of the DWM model

One key point of the model is the quasi-steady wake deficit or rather the wind speed deficit in the MFR.
In this study, two calculation methods for the quasi-steady wake deficit are compared with the lidar measurement results. A similar comparison of these models to met mast measurements in the FFR was published in

For the first method the following formulae are given to calculate the initial deficit. Hence, the boundary conditions for solving the thin shear layer equations are

The second investigated method defines the initial deficit by the following equations

The meandering of the wind speed deficit is calculated from the large turbulence scales of the ambient turbulent wind field. Thus, the vertical and horizontal movements are calculated from an ideal low-pass-filtered ambient wind field. The cutoff frequency of the low-pass filter is specified by the ambient wind speed and the rotor radius as

The wind speed deficit measured by the lidar systems is used to recalibrate the wake degradation downstream or to be more precise the eddy viscosity description. In

A similar behavior but even more pronounced can be seen in the results in Sect.

The measurement campaign lasted from January to July 2019. Both lidar systems, introduced in Sect.

Meandering time series

Wind speed deficit in the HMFR for an ambient turbulence intensity of 11.7 %

The used lidar system is capable of measuring several range gates simultaneously in 30 m intervals. The results of all detected range gates for the data set presented in Fig.

Wind speed deficit in the FFR for a turbulence intensity of 11.7 %

Figure

Similar results as exemplarily shown in Figs.

Number of measured and considered data sets per turbulence intensity for the lidar systems on WTG 1 and WTG 2.

Shear exponent over the ambient turbulence intensity for all considered data sets.

Figure

Measured mean value (line) and standard deviation (bar) of the mean value of the minimal wind speed in the HMFR for different turbulence intensity bins with a bin width of 2 %.

Comparison of measurements and simulations of the minimum wind speed deficit in the HMFR for different turbulence intensities. The recalibrated model is denoted DWM-Keck-c.

Figure

The recalibration of the DWM model and accordingly the normalized eddy viscosity definition in the DWM model are based on a least-squares fit of the minimum of the simulated normalized wind speed to the minimum of the measured normalized wind speed for several downstream distances. The definition of the eddy viscosity along with the recalibrated parameters are explained in detail in Sect.

RMSE between the lidar-measured and the simulated normalized minimum wind speed in the wake.

The results of the recalibrated DWM model, denoted Keck-c in Fig.

Simulated minimal normalized wind speed in the MFR

Figure

The study compares measurements of the wind speed deficit with DWM model simulations. The measurement campaign consists of two nacelle-mounted lidar systems in a densely packed onshore wind farm. The lidar measurements were prepared by lidar and wind field simulations to examine whether the scan pattern is suitable for the outlined analysis. Several wind speed deficits that were simultaneously measured at different downstream distances are presented along with their associated meandering time series. The one-dimensional scan worked reliably in the field campaign, thus delivering lidar data for a multitude of different ambient conditions. These measurements are compared to the simulated wind speed deficit in the HMFR. The simulation result of the DWM-Keck model is in good agreement, whereas the DWM-Egmond model yields a too low degradation of the wind speed deficit. Furthermore, even the DWM-Keck model shows some discrepancies to the measurements at low turbulence intensities, which is why a recalibrated DWM model was proposed. The recalibrated model improves the correlation with measurements at low turbulence intensities and leads to an agreement at high turbulence intensities, which are as good as the original model, thus resulting in a very good overall conformity with the measurements.

Future work will include the analysis of two-dimensional scans as well as measurements with more range gates and higher spatial resolutions. Increasing the number of range gates and scan points will lead to longer scan times, hence preventing further analysis of the wind speed deficit in the MFR and the determination of the meandering time series. Nevertheless, a validation of the wind speed deficit in the FFR with higher resolutions and more distances seems reasonable to also prove the validity of the outlined calibration for further distances. Furthermore, the analyzed models will be assessed in load as well as power production simulations and compared to the particular measurement values from the wind farm. Simulations have shown that the recalibration of the DWM-Keck model can lead to up to 13 % lower loads in the turbulence-dependent components in cases with small turbine distances and low turbulence intensities, whereas for higher turbulence intensities (

Meandering time series

Comparison of measurements and simulations of the minimum wind speed deficit in the HMFR for different turbulence intensities. The recalibrated model is denoted DWM-Keck-c.

Comparison of measurements and simulations of the minimum wind speed deficit in the HMFR for different turbulence intensities. The recalibrated model is denoted DWM-Keck-c.

Access to lidar and met mast data as well as the source code used for post-processing the data and simulations can be requested from the authors.

IR performed all simulations, post-processed and analyzed the measurement data, and wrote the paper. LS and DS gave technical advice in regular discussions and reviewed the paper. PD and MB reviewed the paper and supervised the investigations.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

The content of this paper was developed within the 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 Helge Aagaard Madsen and Vasilis Pettas.