Observations of large coherent fluctuations are used to define a probabilistic model of coherent gusts with direction change. The gust model provides the joint description of the gust rise time, amplitude, and directional changes with a 50-year return period. The observed events are from a decade of measurements from a coastal site in western Denmark, making the derived gust model site specific. In conjunction with the gust model, a yaw controller is presented in this study to investigate the load implications of the joint gust variables. These loads are compared with the design load case of the extreme coherent gust with direction change (ECD) from the IEC 61400-1 Ed.4 wind turbine safety standard. Within the framework of our site-specific gust model we find the return period of the ECD to be approximately 460 years. From the simulations we find that for gusts with a relatively long rise time the blade root flapwise bending moment, for example, can be reduced by including the considered yaw controller. From the extreme load comparison of the ECD and the modeled gusts we see that by including the variability in the gust parameters the load values from the modeled gusts are between 20 % and 74 % higher than the IEC gusts.

In the process of designing a wind turbine, designers have to consider a balance between cost and structural safety. Wind turbine safety standards like the IEC 61400-1 Ed.4

The present study addresses the extreme coherent gust with direction change (ECD) which is used for DLC 1.4 for ultimate load analysis. For certain turbines this load case can drive the ultimate loading of, for example, the blade root flapwise bending moment

In a previous study

A yaw controller ensures that the wind turbine is aligned with the mean wind speed direction. Yaw control is important for increasing the power production

The aim of this paper is to investigate how 50-year coherent gusts (based on observations) impact wind turbine loads and how they compare to the DLC 1.4 of the IEC standard. This will be achieved through three steps.

Derive a probabilistic gust model by extrapolating the observed gust variables to a 50-year return period. As the gust variables form a 3D space, the extrapolation is done with the Nataf distribution model

Develop a yaw controller to be incorporated in the load simulations, as the observed gusts may have a relatively long rise time, and a real wind turbine could start to yaw under such wind conditions.

We simulate thousands of points on the 3D gust variable surface to identify critical load regions. The load simulations are performed using the aeroelastic software HAWC2

The amplitude of the extreme coherent gust with direction change (ECD) is

In the present study we consider wind speed fluctuations that may be assumed to be coherent across the rotor of any multi-megawatt wind turbine. Such large coherent fluctuations have been detected and characterized in a previous study

A wavelet transform is made to identify both the exact timing of the wind speed increase and the total length of the time window defined from the wavelet scale.

An idealized ramp function (a modified error function) is fitted to the measurements within a window defined from the wavelet scale. The parameters from the fit of the ramp function define the rise time (

The direction change is characterized as the maximum difference in the 30 s moving average directional data during the window defined in the wavelet analysis.

Figure

The marginal fitted and empirical cumulative distributions of gust amplitude

In this section we derive an environmental surface that provides the 50-year return period of the joint coherent gust variables,

Here the joint probability distribution of the variables is given by the Nataf distribution model, which is defined by

The Nataf transformation of a random vector

The first step in constructing the environmental surface of coherent gust variables is to calculate the exceedance probability (

Before performing the Nataf transformation, the correlation coefficients of

The estimated correlation coefficients and the evaluated empirical expressions for

We can now determine

Figure

The 50-year return period surface of

The 50-year return period surface, sliced at different rise times. The color scale shows the rise time for the 92 coherent gust events.

We see from the gust variables on the 10 s rise-time contour in Fig.

In this section we briefly describe the HAWC2 software that was used for performing aeroelastic simulations and the HAWC2 yaw controller that was specially developed for this study.

HAWC2

When a yaw error is measured, different strategies are used to determine whether the wind turbine must yaw for a given misalignment. The yaw controller presented in

The 2D wind vector,

The moving average, used to trigger the initiation of the yaw sequence, is computed as

Similarly, the moving average used to stop the yaw action is defined:

To ensure a proper function of the simple yaw controller, the condition

The wind turbine starts yawing once

Figure

Although a more elaborate study regarding yaw control should be considered, the simple long/short time-averaging approach is chosen here in order not to trigger a yaw action too early (hence 120 s averaging window for the start trigger) while avoiding overshooting after a zero yaw error has been reached (using the 10 s averaging window for the stop trigger).

The yaw mechanism is modeled as a second-order dynamical system with a frequency of 5 Hz and a damping ratio of 0.7. There is no limit on the maximum and minimum yaw angle, allowing a full rotation of the system. It is possible to constrain the response of the second-order model in velocity and acceleration. A typical yaw sweep sequence, yawing 360

This section contains the results from the HAWC2 simulations. The simulations consist of 3219 points on the 50-year joint gust variable surface with different rise times, amplitudes, and direction changes. The gust surface has been sliced to limit the presentation of simulation results to relevant ranges. The simulation results are shown for a rise-time range of 4–400 s, where the lower rise-time threshold for this range is chosen from considerations of the shortest possible fluctuation turnover time for which the wind field can be considered coherent across the rotor of the DTU 10 MW wind turbine. Further, when considering curves with the same

Absolute maxima of a selection of load channels with yaw control for gusts starting at 10 m s

We have simulated the IEC ECD coherent gust for comparison. All simulations have been performed both with and without yaw control, and all gust simulations, including the IEC simulation, start from 10 m s

In this section we focus on the load simulations that were performed with the yaw controller, as we believe that these simulations best represent the load response of a real operating wind turbine.

Figures

Simulation results with yaw control. The absolute maximum responses are shown with the color scale on the 3D gust variable surface of rise time, amplitude, and direction change. The relevant channel is indicated on the right of the color bar legend:

Simulation results with yaw control. The absolute maximum responses are shown with the color scale on the 2D gust variable domain of acceleration and direction change. Notice the IEC ECD gust in all panels is the single outlier. The relevant channel is indicated on the right of the color bar legend:

In Fig.

The blade root flapwise moments also show a circular shape on the surface with moderately high load responses for a large range of the gust variables on the surface (Fig.

For the tower-top yawing moment a large area (on the right of the 3D gust domain) with high loading corresponds to gusts with high amplitudes, wide range of high rise times, and large changes in direction. The yaw controller is active when the absolute highest tower-top yaw moments occur in the simulations, and the shape of the high-load area is strongly influenced by the current implementation of the yaw controller.

The absolute maxima of the response of selected load channels over the considered gust surface are compared with the IEC ECD definition in Table

The difference between what drives the tower-top yawing moment and the tower-base resultant moments is illustrated in Fig.

Simulations with yaw control.

An example time series of the gust resulting in the highest tower-bottom resultant load and tower-top acceleration is compared with the IEC ECD gust in Fig.

Simulations without yaw control

Absolute maxima of a selection of load channels without yaw control for gusts starting at 10 m s

The simulations on the gust variable surface were performed both with and without the yaw controller. This was done to investigate the differences in load response between the two simulation sets. Table

In Fig.

In this analysis we chose to extrapolate the multivariate distribution model with a relatively new method, namely the ISORM. Although the IFORM is recommended in the IEC standard, it has been shown to underestimate the probability behind the surface of considered design variables

According to the probabilistic gust model derived in this analysis, the IEC ECD gust is conservative. That is, with the combination of coherent gust variables, the IEC gust is more extreme and falls outside the 3D gust parameter surface. By increasing the return period to 460 years, the IEC gust is matched on the surface of the probabilistic gust surface. Though we did find that the IEC gust is more conservative with regards to the gust variables, it is interesting to see that higher loads can be reached with simulations from the probabilistic gust model. By including variability in the gust parameters, we were able to identify critical regions on the gust parameter surface that lead to loads that are significantly higher (up to 74 %) than those that come from the simulation of the IEC ECD gust.

The current analysis is based on data from a single site and is therefore likely to be site specific. Although previous studies on coherent structures

We also note that all the results shown in Figs.

Although not discussed in the current work, the aerodynamic response under yawed inflow conditions is another topic of concern since the accuracy of the blade element momentum method (BEM) may decrease as the yaw error increases, and generally such results should be considered carefully. However, the BEM implementation used in HAWC2 employs a yawed inflow correction and assumes non-constant induction across an angular ring element (see

In this work observations of coherent gusts are used to obtain an environmental surface with a 50-year return period with the Nataf distribution model. The surface is a 3D gust variable space of rise time, amplitude, and direction change. There is a large variability within the modeled gust variables, where the direction change and amplitude may exceed the ECD values, though in these cases with a considerably longer rise time. For modeled gusts with 10 s rise time, the maximum amplitude is 8.3 m s

The modeled gust variable surface can match the values of the IEC ECD gust parameters by using a return period of approximately 460 years.

We choose 3219 points on the surface to simulate for wind turbine response, where the simulations are performed with and without a yaw controller that is specially developed in this study.

The effect of the yaw controller is seen for the modeled gusts, where we see that the absolute maximum of all the considered load responses is lowered by including the yaw controller, especially for gusts with a relatively long rise time in which the blade root torsion and flapwise bending moments are significantly reduced when the wind turbine yaws.

From the comparison of the modeled gusts and the IEC ECD, we find that, even though the modeled gusts are not as severe in terms of gust variables, the difference in observed extreme loads is higher. From the considered load component channels, the largest difference is seen for the tower-base resultant moment, which is 74.2 % higher for the modeled gust compared with the IEC gust. Similarly, the blade root torsion load is 63.9 % higher for the modeled gust, and the blade root flapwise, blade root edgewise, and tower-top yaw moments are around 20 % higher than the simulated ECD gust. The maximum loads for TB

In the current work we have used the basic DTU Wind Energy controller with the specific DTU 10 MW tuning parameters. We acknowledge that our simulation results depend on the general response of the controller. While it is out of the scope of the current study, an improved controller (tuning) could change the response significantly, and follow-up work could consider this aspect. Similarly, an improved tuning of the simple yaw controller could be performed to establish in more detail how yaw control can affect the loads and how much inertial loading a yawing and rotating turbine can experience.

Gust for which the tower-bottom resultant bending moment TB

Gust for which the tower-top yawing moment TT

The data with the coherent gust variables and a Python code with the probabilistic gust model are available at

HAWC2 input files of the DTU 10 MW as used for the study, dynamic-link libraries (DLLs) used for the controller, and the source code to the yaw controller are available at

ÁH made the gust analysis and gust model. AMU developed the yaw controller. DRV performed HAWC2 load simulations. ÁH wrote the main body of the paper. DRV and AMU contributed with the writing of Sects. 4–7 and the Appendix. All authors commented on the paper.

DTU Wind Energy develops, supports, and distributes HAWC2 on commercial terms.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Ásta Hannesdóttir would like to thank Mark Kelly for comments and discussion around the coherent gust distribution model.

This paper was edited by Julie Lundquist and reviewed by two anonymous referees.