The estimation of the cost of energy of offshore wind farms has a high uncertainty, which is partly due to the lacking accuracy of information on wind conditions and wake losses inside of the farm. Wake models that aim to reduce the uncertainty by modeling the wake interaction of turbines for various wind conditions need to be validated with measurement data before they can be considered as a reliable estimator. In this paper a methodology that enables a direct comparison of modeled with measured flow data is evaluated. To create the simulation data, a model chain including a mesoscale model, a large-eddy-simulation (LES) model and a wind turbine model is used. Different setups are compared to assess the capability of the method to reproduce the wind conditions at the hub height of current offshore wind turbines. The 2-day-long simulation of the ambient wind conditions and the wake simulation generally show good agreements with data from a met mast and lidar measurements, respectively. Wind fluctuations due to boundary layer turbulence and synoptic-scale motions are resolved with a lower representation of mesoscale fluctuations. Advanced metrics to describe the wake shape and development are derived from simulations and measurements but a quantitative comparison proves to be difficult due to the scarcity and the low sampling rate of the available measurement data. Due to the implementation of changing synoptic wind conditions in the LES, the methodology could also be beneficial for case studies of wind farm performance or wind farm control.
Offshore wind energy still remains an expensive alternative
to onshore wind energy, which has been established as one of the cheapest
options to generate electricity.
One of the reasons for the comparatively high costs of offshore wind energy is the scarcity of
long-term atmospheric measurements at existing or planned wind farms.
The resource assessment at these locations is difficult and prone to large
errors
Only a few offshore wind farms deploy permanent met masts that allow for studying
the influence of atmospheric conditions on wind farm performance.
The available measurements indicate that due to the generally lower level of turbulent kinetic energy offshore compared to onshore,
the wakes of the wind turbines are frequently more persistent, which leads to higher
wake losses at downwind turbines even over larger distances.
An even lower turbulence level caused by stable atmospheric stratification leads
to a further increase in wake losses
Several numerical models have been developed with the purpose of calculating the optimal layout of
offshore wind farms under consideration of the wake losses.
Simplified engineering models allow a fast calculation of
multiple wind scenarios and an optimization of wind farm layouts
A high-fidelity solution for wind farm simulations are large-eddy simulations (LESs).
Coupled with wind turbine models, LESs provide a detailed solution of the flow
inside of a wind farm with a high representation of the relevant physics.
Due to the high computational costs, LESs of offshore wind farms have been
restricted to simulations of idealized atmospheric conditions or
to case studies of specific situations, e.g.,
In addition to performance measurements from the data acquisition system of wind turbines, which are often kept confidential, flow measurements using the light detection and ranging methodology (lidar) have become a widespread tool for scientific research. To optimize this technique for model validation, the lidar measurement campaigns have to be designed and postprocessed to allow for a meaningful comparison with simulations. One aspect of the measurement design is the measurement of free flow conditions, which can be used as meteorological boundary conditions for the simulations.
Especially offshore the measurement or derivation of boundary conditions to set
up simulations is challenging.
For example, onshore LESs are often run with boundary conditions derived from
near-surface measurements (e.g., heat flux measurements) and are compared to
wind profiles derived from lidar devices
In this paper we investigate a methodology to use profiles and boundary
conditions derived from a mesoscale simulation for a continuous LES of an offshore wind
turbine wake over several hours.
The purpose is to evaluate if this model chain can be used to conduct wake simulations
in a wind field with the same turbulent properties and the same profile shape as measured.
Measurements from an offshore met mast are used for the evaluation.
The model chain is further evaluated by a comparison of the flow distortion by a wind turbine model
with the wind field extracted from lidar measurements
Recently, long-term LESs of multiple days up to 1 year have been run with this approach to study the changes
of meteorological conditions at a measurement site
The case study that is analyzed in this paper is based on measurements on 20 February 2014 at the German offshore wind farm Alpha ventus.
Two independent data sets were used for comparison with the model results.
The simulated ambient wind conditions without turbines were compared to
measurements from the met mast FINO1 located at
The lidar measurements, which were used for comparison with the simulated
wakes, are part of a measurement campaign that took place from August 2013
until March 2014. During the analyzed day, two long-range lidar devices
(Windcube WLS200S) executed single elevation plan position indicator scans in
the wake of turbine AV10 with one lidar positioned on FINO1 and the other one
on the converter station of the wind farm (Fig.
The line of sight velocities of the lidars were combined and averaged to get
a 10 min mean horizontal vector wind field at hub height
Revision 1928 of the Parallelized Large-eddy Simulation Model (PALM)
The momentum relaxation has no physical justification but is used to prevent
a drift of the model from the large-scale state.
The term depends on the difference between the horizontal average
The equation for scalars
Time dependency of the external forcing is achieved by prescribing profiles of the time-variant geostrophic wind, source terms of horizontal momentum and scalar properties, and of the large-scale state of the relaxation term. The surface fluxes are calculated by making use of the Monin–Obukhov similarity theory, with the values of the surface pressure, temperature and humidity also prescribed by the time-dependent large-scale state.
In this section we analyze the simulation of the ambient conditions with the
large-scale forcing derived from the output of a mesoscale simulation.
Different parameters are modified to analyze their influence on the results.
In Sect.
The lidar measurements were conducted on 20 February 2014.
After filtering according to the criteria mentioned in Sect.
Layout of Alpha ventus and position of the two lidars that were used for the construction of the wind field. Circular segments denote the scan areas of the lidars. The green box denotes the region of the vector wind field reconstruction.
Meteorological conditions on 20 February 2014,
as measured at FINO1.
The wind direction at FINO1 is southwest during the
night and south during the rest of the day, with an increase in the wind
speed at hub height of the Alpha ventus wind turbines (90 m) from about 8
COSMO-DE wind speed and direction on 20 February 2014 at 07:00 UTC on the model level of 73.5 m. The black square marks the averaging domain surrounding FINO1 and the blue squares mark the neighboring domains that are used for the calculation of the gradients.
The profiles for the large-scale tendencies are calculated from the operational analysis
of the COSMO-DE model
Following
Time series for 19 and 20 February 2014 of
Time development of the vertical input profiles for the LES run.
We analyzed the influence of the size of the averaging domain on the profiles required
by the LES model by comparing three different quadratic domain sizes with
grid lengths of
The comparison of the different averaging domains (Fig.
Figure
Comparison of the different simulation setups and the RMSE of the
difference between the time series of simulated wind direction and wind speed
of simulations
Comparison of
To transfer the input profiles from the COSMO-DE time steps and height levels to the LES model, they were linearly interpolated on the vertical LES grid and on the time steps of the simulation. The LESs were initialized with the set of large-scale profiles on 19 February at 00:00 UTC and nudging was applied only after 6 h to enable a free development of turbulence in the first simulation hours.
All simulations had a domain size of 3200 m
Five different simulations with a rather coarse grid were run with different
configurations (Table
For evaluation we selected the 10 min mean wind speed and direction at 70 m,
as they are close to the hub height and also available from the COSMO-DE model.
For better comparison the raw 10 min values from the anemometers and wind vanes were
smoothed by means of a 1 h running mean.
The RMSE between each simulation time series and the references is
compared in Table
The evaluation shows that switching off momentum advection appears to have the largest
influence on the wind speed and wind direction deviation from the input data.
Figure
The more highly resolved simulation run, which was used as the basis for the turbine simulations,
was computed with a relaxation time constant of
The time series of the domain-averaged results of
LES wind speed and wind direction follow the general trend of the input and measurement data. The averaged magnitude of the turbulent fluctuations on the 10 min scale is also reproduced. The largest discrepancy between simulation and measurements exists in the shear of the vertical wind profile which is almost constantly lower in the LES.
The destabilization of the boundary layer is observable as a decrease of the vertical shear of
the LES and the measurements (Fig.
The comparison of modeled and measured time series shows that the measurements
contain additional fluctuations that are not replicated by the model chain of mesoscale and
microscale models. Figure
Power spectral density derived from the 1 Hz measurements at 90 m height and the simulation time series at 90 m. Grey and black lines represent different window sizes for the Fourier transformation. The short black lines denote the slope of the Kolmogorov cascade.
The wind turbine wake simulations are run with the same
domain and setup as the high-resolution simulation
Comparison of the simulated state of the boundary layer with the measured state during the 15 10 min time periods of the lidar measurements. The night period is between 01:00 and 01:40 UTC, the morning period between 05:40 and 07:30 UTC, and the evening period between 21:40 and 22:10 UTC.
Normalized wind fields from LES and
lidar measurements. The third column shows horizontal cross sections
along the lines at constant
An enhanced actuator disc model with rotation (ADM-R)
is used to calculate the forces of the wind turbine
on the flow
Figure
Fitted functions to the wake at 01:30 UTC.
Scatter plots of the properties derived
from the Gaussian-like fit to the wake profiles of
For the wind turbine the three periods represent different operating conditions.
With a rated wind speed of the turbine of 12.5 ms
Figure
The 10 min averaging does not apparently filter all turbulent structures of the measured wake field. This is most probably due to the much lower sampling rate of the lidar measurements. Approximately 8000 single values contribute to the average on the 20 m grid in the LES, considering a time step of about 2 Hz and the original grid resolution of 5 m. In contrast, the sample velocities contributing to the lidar average vary from 100 to 350 individual line-of-sight wind speed values and are not evenly distributed in space and time.
The results show that the unrotated wakes (Fig.
In the following an attempt is made to make a quantitative comparison between
the measured and simulated wakes. To derive statistics of the wakes, the
profiles of all 15 time intervals were fitted to a curve consisting of two
Gaussian-like functions:
A direct comparison of the wake properties at selected downstream distances
is presented in Fig.
As demonstrated in this paper, the forcing of LES with mesoscale-model profiles allows for time-dependent LESs that change according to the synoptic meteorological conditions. Thus, a transient state of the atmospheric boundary layer can be used for the analysis of wind farm model performance. This allows, for example, for a direct validation of wake simulations with measured data, which represents a different approach from the classical statistically derived validation data for wind farm models.
The comparison of the ambient flow created by the model chain with met mast data indicates
that the synoptic trend of wind speed and direction is maintained and that the average properties
of the simulated wind profile during the 2-day period are close to the properties of the measured wind profile.
Time series and power spectra, however, reveal a gap of energy contained in the mesoscale fluctuation range.
These fluctuations might be partly resolved with a much larger LES domain, if they originate from thermal effects
As this paper only looks at a very short time period, we refrain from drawing general conclusions about the model chain's ability to replicate the evolving state of the
atmospheric boundary layer
and refer to Schalkwijk et al. (2015) and Heinze et al. (2017), who analyze longer time periods.
For wind energy purposes we think that the mesoscale model remains the crucial part of the presented model chain to improve the
spectral and vertical representation of the wind field.
However, at least for the spectral part, current combinations of models and reanalysis data do not appear to be sufficient
The comparison of the wake simulations with the measured wakes represents one of the suggested applications of the model chain. Instead of averaging over similar wind profile states, a direct time series comparison is performed. The visual comparison of simulated with measured wakes shows a good match, indicating that wind direction and wake profile are well replicated. Derived wake statistics of the downstream development, however, reveal that the available measurement data still require a more statistical treatment to be able to draw a conclusion about the goodness of the wake representation in the simulations.
Alternatives to the presented approach for LES of wind turbines in the atmospheric boundary layer are idealized quasi-stationary setups or nested LESs inside a mesoscale model.
Both of these approaches have advantages and disadvantages compared to the method in this paper.
An idealized setup enables the study of an identified quasi-stationary state of the atmospheric boundary layer in detail, as in Vollmer et al. (2016) and Mirocha et al. (2015), for example,
or the replication of an idealized transient state
The approach of a nested LES domain inside of a mesoscale-model domain might enable the inclusion of frequencies of the flow in the range
of mesoscale fluctuations or the advection of a different level of turbulence created by upstream obstacles. However, it needs a large LES domain for the development of microscale turbulence
In this paper we introduce and test a method to simulate a wind turbine wake in the offshore atmospheric boundary layer with LESs driven by forcing derived from a mesoscale simulation. The methodology enables the simulation of a transient state of the atmospheric boundary layer for the evaluation of wind farm performance or the validation of wake simulations. The comparison with met mast data shows that the model chain is able to reproduce the synoptic trends and the boundary layer turbulence of the marine wind field during the 2 days analyzed. Most of the mesoscale fluctuations found in the measurements are not replicated, which is most likely related to the deficiencies of the mesoscale model. The wake simulations are compared to lidar measurements downstream of an Alpha ventus turbine. In certain periods the modeled and measured wakes are very similar, as especially the wind direction matches well. A direct comparison of measures to describe the downstream wake development proves to be difficult with a high scatter of the measured wakes. Thus, the limited data set of the lidar measurements and the still-prevailing turbulent structures in the 10 min averages of the data make it difficult to validate the performance of the whole model chain. We think that the methodology might be especially valuable for transient non-neutral states of the atmospheric boundary layer, in which the boundary conditions to set up LESs are difficult to derive. In these cases, the method presented might not only be valuable for the comparison of simulations with measurement data but could also be applied to study wind turbine or wind farm control in changing wind conditions.
The simulation data and the model implementation code could be made available in the framework of a cooperation agreement. Please contact the corresponding author for further information.
The authors declare that they have no conflict of interest.
The authors gratefully acknowledge the efforts of the Wind Energy Systems group of ForWind who carried out the lidar measurements at Alpha ventus, including Jörge Schneemann, Davide Trabucchi, Juan-Jose Trujillo and Stephan Voß. The work presented in this study was conducted within the German national research projects “GWWakes” and “OWEA Loads” (FKZ 0325397A and 0325577B), funded by the Federal Ministry for Economic Affairs and Energy (BMWi) and within the project “ventus efficiens” (ZN3024, Ministry for Science and Culture of Lower Saxony). Computer resources have been partly provided by the North-German Supercomputing Alliance (HLRN). We thank the Deutscher Wetterdienst (DWD) for providing analysis data. We thank the BSH and DEWI for providing measurement data from FINO1 (FINO project by BMWi). Edited by: Luciano Castillo Reviewed by: two anonymous referees