Wake redirection is an active wake control (AWC) concept that is known to have a high potential for increasing the overall power production of wind farms. Being based on operating the turbines with intentional yaw misalignment to steer wakes away from downstream turbines, this control strategy requires careful attention to the load implications. However, the computational effort required to perform an exhaustive analysis of the site-specific loads on each turbine in a wind farm is unacceptably high due to the huge number of aeroelastic simulations required to cover all possible inflow and yaw conditions. To reduce this complexity, a practical load modeling approach is based on “gridding”, i.e., performing simulations only for a subset of the range of environmental and operational conditions that can occur. Based on these simulations, a multi-dimensional lookup table (LUT) can be constructed containing the fatigue and extreme loads on all components of interest. Using interpolation, the loads on each turbine in the farm can the be predicted for the whole range of expected conditions. Recent studies using this approach indicate that wake redirection can increase the overall power production of the wind farm and at the same time decrease the lifetime fatigue loads on the main components of the individual turbines. As the present level of risk perception related to operation with large yaw misalignment is still substantial, it is essential to increase the confidence level in this LUT-based load modeling approach to further derisk the wake redirection strategy. To this end, this paper presents the results of a series of studies focused on the validation of different aspects of the LUT load modeling approach. These studies are based on detailed aeroelastic simulations, two wind tunnel tests, and a full-scale field test. The results indicate that the LUT approach is a computationally efficient methodology for assessing the farm loads under AWC, which achieves generally good prediction of the load trends.
When wind turbines are grouped into wind farms, they affect each other’s performance through their wakes. In the wake, wind turbines experience a decreased wind velocity and increased turbulence. For this reason, waked turbines will produce less power at below rated wind speeds and suffer increased fatigue loading. Below rated, the conventional “greedy” control approach aims at maximizing the power capture for each turbine, thereby disregarding the interactions between the turbines through their wakes. This approach is not optimal with respect to the total power production of the whole wind farm. Active wake control (AWC) is an approach to operate the turbines cooperatively with the goal of mitigating the wake effects to maximize the power production of the whole farm while at the same time trying to reduce the fatigue loading on the turbines
There are two concepts to AWC. The first concept, known as induction control, adjusts the axial induction of the windward turbines below their optimum for power production in order to reduce the velocity deficit and turbulence in the wake
In
The LUT contains the fatigue loads and statistics from a large number of aero-elastic simulations with different wind speeds, turbulence intensities, wake profiles (wake deficit width, depth, and location with respect to the rotor), yaw misalignments, and pitch angle offsets. For given inflow conditions in front of a specific wind turbine in a wind farm, calculated using a wake model such as FarmFlow
To increase the confidence level of the load LUT approach, it needs to be properly validated. That is the purpose of this work, which has the following objectives:
Evaluate if interpolation of the loads in the LUT is an accurate enough method for predicting the loads for conditions that are not present in the LUT. Evaluate the accuracy of the loads calculated using the conventional aeroelastic simulations, using blade element momentum (BEM) theory. Complex turbine conditions that result from large yaw misalignments violate the assumptions of BEM and its usual correction models. Validate the predictions with respect to wake-induced loads, which are very pronounced load contributors in wind farms. Evaluate if the LUT load model predictions can be generalized for different turbine scales.
To this end, a series of validations studies have been performed based on detailed simulations, wind tunnel measurements, and full-scale field tests. These studies are outlined in Sects.
This section describes the wind farm modeling used in this study, as well as the LUT table approach to fatigue load modeling.
The wind farm model used in this study is FarmFlow
The wake model was improved in
The FarmFlow model supports simulations with active wake control (AWC), allowing each turbine to be operated at a different power and thrust coefficient (induction control) or with different yaw misalignment (wake redirection). Implementation of induction control in FarmFlow is rather straightforward by applying different power and thrust curves for induction control. The implementation of the wake redirection control is more complicated and is described below. Since FarmFlow uses prescribed axial and radial pressure gradients in the near-wake region in order to induce the wake, i.e., the deceleration and expansion of the flow behind the rotor, implementation of yaw misalignment is realized by prescribing these pressure gradients with respect to the yaw angle instead of the flow direction. The effect of this deflection is validated from measurements in a scaled wind
farm and with wind tunnel measurements
In addition to that, the width of the wake is reduced by a factor
In the previous subsection, the wind farm model FarmFlow was summarized. In this section, a load module is described that enables the estimation of the loading on each turbine at a number of locations. This allows the evaluation of the effect of AWC on the turbine loads. Besides analysis, the load module enables the inclusion of the loads into the AWC optimization. The load module consists of pre-calculated database, constructed using detailed aeroelastic simulations with the software tool Focus/Phatas. The simulations are performed with a single fictive wind turbine model in the 4 MW range operating in a wake situation that covers the entire wide range of operating conditions which the turbine can encounter during operation in a wind farm. To keep the computational load manageable, only single bell-shaped wake profiles are considered. In practice, a turbine can experience more complex wake situations resulting from wakes from multiple turbines. However, studies with several offshore wind farms with different types of layouts indicated that, in such situations, one of the wakes hitting the rotor strongly dominates the other one(s) in terms of wake deficit. A situation where a turbine gets two equally strong wakes at both sides of its rotor is, clearly, difficult to imagine as that would imply two upstream turbines to be located at the same distance upstream, and therefore they should stand next to each other. Alternatively, they could be at a different distance but have quite different thrust coefficients, which is even less realistic to assume. Notice that extending the load database to model, for instance, double-bell shaped wake profiles would have given rise to a significantly larger number of aeroelastic simulations necessary to populate the database. It was therefore decided that the resulting increase in computational complexity does not weigh against the expected added value in practice.
Visualization of the parameters used for describing the wake conditions in front of a turbine.
The following formulation is used for the bell-shaped wake deficit profile
The operating conditions which have been simulated with Focus/Phatas consist of combinations of the following parameters (see Fig.
Signals stored in the load database.
For each combination of these wake parameters, normal production simulations for six different wind realizations (seeds) have been performed. The simulations are performed with complete three-dimensional wind field that is generated to match the selected values for the wake parameters. This results in a total number of 673 596 cases, which were subsequently reduced to 100 926 simulations by skipping unnecessary and duplicate cases, such as yaw misalignments and pitch offsets at wind speeds for which the farm operates at its rated power or different wake widths and locations for zero wake depth (implying no wake at all). The simulations took several days of computation time on a moderately sized computer cluster of about 150 cores. The results from all these simulations are stored into a LUT that comprises the load database module. The lookup table contains, for each simulated scenario, the calculated fatigue loads and/or statistics (min, max, mean, and SD) at a large number of different locations throughout the turbine. These are summarized in Table
For the simulations under yaw misalignment it needs to be pointed out that, even though the underlying BEM theory is generally considered as inaccurate under yawed conditions, recent studies
During a farm simulation, FarmFlow determines the wake conditions in front of each turbine, from which the above-listed parameters of a single bell-shaped wake are approximated using least-squares fitting. These wake parameters are subsequently used as input to the load database to interpolate the corresponding loads on locations. By doing this for the whole range of relevant ambient wind conditions (wind speeds, wind directions, turbulence intensities), and given the corresponding distributions, the lifetime fatigue loads are calculated for each component at each turbine in the farm. It should be noted that the wake properties, calculated by FarmFlow, concern the undisturbed by the rotor inflow conditions in front of each turbine. The same holds for the wind fields generated for the Foxus/Phatas simulations.
In this section, validation by simulations is performed. Firstly, in the next section the interpolation properties of the LUT load database are studied using conventional BEM simulations. In the section that follows, higher-fidelity simulations are used to assess the prediction capabilities of the LUT approach with respect to yaw-induced loads.
The focus of this section is to evaluate if linear interpolation using the LUT load database is a suitable method for determining the fatigue loads of wind turbines. This would be the case if the LUT database were sufficiently populated which, therefore, is what will be essentially evaluated here. For this purpose, Focus/Phatas aeroelastic simulations were performed for a number of operational conditions, listed in Table
Wake parameters for validation of the interpolation properties of the farm modeling approach.
Visualization of interpolation and BEM simulation results. The loads are normalized with respect to the loads in nominal (offset-free) free-stream operation at a wind speed of 8 m s
The results from these comparisons are shown in Fig.
In can be seen from Fig.
Next, the precision of the LUT load modeling for yawed flow conditions is studied, as those inherent for wake redirection AWC. As explained in Sect.
For this reason, the Aerodynamic Wind Turbine Simulation Module (AWSM)
In this study, the yaw-induced fatigue loads from AWSM simulations are compared to those from BEM simulations. To this end, AWSM and BEM simulations are performed using DTU 10 MW reference wind turbine
In the simulations, turbulent inflow at 8 m s
High-fidelity simulation cases. Different yaw angles are used to evaluate the precision of BEM versus free vortex model.
In Fig. The higher turbulence intensity results in higher fatigue loads, both for BEM and AWSM. Moreover, by moving from 5 % to 15 % turbulence, the relative load increase is comparable for both models. The relative load changes due to misalignment are much smaller than those due to turbulence. The results here suggest that yaw misalignment can increase the turbine loads in the range of 10 %–15 %. However, it can also be observed that the impact of turbulence intensity on the loads is much more pronounced, up to 250 % in this example. Since the simulated turbulence intensities (5 % and 10 %) are quite representative of the turbulence levels for wind turbines operating in free stream and a single wake, respectively, it can be stated that wake-induced loading is more pronounced that yaw-induced loading. In other words, a downstream turbine operating in a wake of another turbine will experience much higher loading than a turbine in free stream. Since wake redirection control moves the wake away from downstream turbines, it is expected to have a positive effect on the loads there since these will operated at lower turbulence levels. This fact is seen as the reason that wake redirection control can result in lower fatigue loading; see Taking the zero yaw angle as a reference, the load trends are generally well captured by BEM for both positive and negative misalignments. This implies that in terms of relative load impacts by AWC, the BEM-based LUT approach seems suitable. In the absolute sense, BEM significantly overpredicts the loads as compared to AWSM. This is completely in line with earlier findings by
Normalized blade root DEL as a function of yaw angle for the AWSM and BEM models.
The focus of this section is to validate the LUT load model against wind tunnel measurements under misaligned inflow conditions. This is done using measurements gathered in the New Mexico project
The objective of the New Mexico project
Selected load cases from Mexico experiments.
Normalized blade root out-of-plane loads: Mexico wind tunnel measurements vs. LUT database prediction
Figure
In the CL-Windcon experiments
CL-Windcon single-turbine experiment cases.
The results are shown in Fig.
CL-Windcon and load module tower base fore–aft moment as a function of yaw, for low turbulence
Wind conditions at EWTW:
EWTW's layout.
In the low turbulence case, a similar trend is observed between the LUT prediction and the tunnel experiment. The database overestimates the loads and, more importantly, the tower loads decrease with yaw misalignment. For high turbulence, however, a big discrepancy is observed with respect to the effect of the turbulence intensity on the loads: due to the much higher turbulence, the LUT load predictions are much higher, while the wind tunnel measurements do not share this trend. Further analysis of the results indicated that this is due to the inertial loads being the main contributor to fatigue loads. Due to the small scale of the turbine, the tower frequency (around 14 Hz) is well outside the bandwidth of the turbulence excitation. At the same time it is very close to the rotational frequency of the rotor, getting excited by the rotor (aerodynamic and mass) imbalance. This deterministic excitation outweighs by much the impact of the turbulence on the loads. As a result, the turbulence intensity has practically no impact on the tower fatigue loading in this wind tunnel experiment.
Due to this, it is concluded that in terms of tower bottom loads these measurements are unrealistic for a real-life modern wind turbine and are therefore considered not suitable for validation of the LUT load model.
In this section, the LUT load model is compared against full-scale field measurements. The measurements are performed at the ECN's Wind Turbine Test Site Wieringermeer (EWTW), the Netherlands. The farm consists of five research turbines which are oriented in a single line with a mutual distance of 3.8 D (see Fig.
Given the wind turbines and site conditions, a FarmFlow model is built and used to estimate the inflow conditions for each turbine for the whole range of wind speeds and wind direction.
These are subsequently used to interpolate the loads from the LUT, as explained in Sect.
Comparison of LUT load prediction to EWTW measurements for 6, 7, and 8 m s
Comparison of LUT load prediction to EWTW measurements at 9 and 10 m s
For the analysis, ambient wind speeds of 6, 7, 8, 9, and 10 m s
Since the farm layout consists of a single row of turbines, there are only sectors of wind directions in which the measured turbine is in wake: around 95 and 275
The wind direction sectors for which the measured turbine T2 is in a wake condition are clearly identifiable in Figs.
This paper presented the results of a number of studies focused on the validation of the LUT approach to modeling the loads on turbines in wind farms. The approach represents a computationally attractive way to study the impact of wake redirection AWC on the turbine loads. The validation studies included conventional (BEM) and detailed (free vortex wake) simulations, data from two wind tunnel measurements performed under yaw misalignment, and full-scale field measurements.
The BEM simulations were used to evaluate the interpolation properties of the LUT. The results indicated that, for the chosen resolution of the LUT, the interpolated loads accurately approximate the simulated loads.
The free vortex wake simulations with the AWSM code confirmed earlier findings that the fatigue loads predicted by BEM models tend to significantly overpredict the loads from AWSM simulations. This implies that using BEM models (as those used to construct the LUT) is a conservative, though safe, approach to assess the loads on turbines. Another observation, applicable to both BEM and AWSM, is that the loads are shown to increase significantly for higher turbulence levels. This is also consistent with other results showing the wake-induced loading is much more pronounced than the loading due to misalignment. This is also the main reason that, as discussed in
The wind tunnel experiments proved very useful for validating the yaw LUT prediction of the yaw-induced load. The New Mexico experiment indicated that the sensitivity of the blade out-of-plane loads to changes in the yaw misalignment angle is very well modeled by the LUT approach even though the tunnel test is performed with a much smaller turbine. An interesting observation is that due to lack of wind shear in the tunnel experiment, the lowest blade loading was achieved at zero yaw misalignment, while the presence of shear in the simulations used for creation of the LUT resulted in the lowest loads at non-zero, positive yaw angle. This is also consistent with previous studies. The CL-Windcon tunnel tests involved experiments with two levels of artificially generated turbulence. Unfortunately, the measured tower loads proved to be very insensitive to variations in the turbulence. The reason for that was that for this scaled turbine model, the main contributor to the tower loads is the relatively high tower frequency, excited primarily by effects occurring once per rotor revolution due to aerodynamic and/or mass imbalance. These outweighed by much the fatigue loads induced by (low frequency) turbulence. As a result of that, the CL-Windcon measurements were not useful for assessing the accuracy of the wake-induced load predictions by the LUT, but they did confirm the findings with respect to yaw-induced loading.
The field measurements on EWTW were compared to the LUT load predictions for a range of wind speeds. The agreement was very good, especially for the blade root bending moments. With respect to tower loads the LUT estimates generally overpredicted the measurements for the wind directions with waked inflow. The measured tower loads were also found less sensitive to variations in the inflow conditions than the blade loads.
Finally, the LUT database is created with a wind turbine model and controller according to the current “common practice”. As such, it may not be representative of specific cases such as wind turbines with soft-soft towers, low induction rotors, and advanced control algorithms including IPC, tower damping, lidar-based control, etc. For the more standard cases, the results from this paper suggest that the LUT approach is suitable for different wind turbine types when it comes to predicting the load trends (making it possible to judge whether under AWC loads increase or decrease, and by how much), rather than the absolute loads.
Data are not available due to confidentiality issues.
HMR performed the entire analysis and prepared a first draft as part of his MSc final project, which he performed at the ECN part of TNO. SK supervised HMR on a daily basis, performed simulations, and helped with the analysis and interpretation of the results. SK had a major role in the preparation of the final version of the manuscript. JWvW and BD had an advisory role as formal supervisors from the TU Delft.
The authors declare that they have no conflict of interest.
Koen Boorsma is acknowledged for the support he provided in setting up the AWSM simulations.
This paper was edited by Sandrine Aubrun and reviewed by two anonymous referees.