Lidar systems installed on the nacelle of wind turbines can provide a preview of incoming turbulent wind. Lidar-assisted control (LAC) allows the turbine controller to react to changes in the wind before they affect the wind turbine. Currently, the most proven LAC technique is the collective pitch feedforward control, which has been found to be beneficial for load reduction. In literature, the benefits were mainly investigated using standard turbulence parameters suggested by the IEC 61400-1 standard and assuming Taylor's frozen hypothesis (the turbulence measured by the lidar propagates unchanged to the rotor). In reality, the turbulence spectrum and the spatial coherence change by the atmospheric stability conditions. Also, Taylor's frozen hypothesis does not take into account the coherence decay of turbulence in the longitudinal direction. In this work, we consider three atmospheric stability classes, unstable, neutral, and stable, and generate four-dimensional stochastic turbulence fields based on two models: the Mann model and the Kaimal model. The generated four-dimensional stochastic turbulence fields include realistic longitudinal coherence, thus avoiding assuming Taylor's frozen hypothesis. The Reference Open-Source Controller (ROSCO) by NREL is used as the baseline feedback-only controller. A reference lidar-assisted controller is developed and used to evaluate the benefit of LAC. Considering the NREL 5.0

Traditionally, wind turbine control only relies on the feedback (FB) control strategy. For the above-rated wind operations, the generator speed change caused by the turbulence wind is measured, and the blade pitch is adjusted to maintain the rated rotor/generator speed. This means that the turbine reacts to the wind disturbance only after it has been affected. A nacelle lidar scanning in front of the turbine can provide a preview of the incoming turbulence. Based on the preview, a rotor-effective wind speed (REWS) can be derived and used to provide a feedforward pitch signal. The feedforward pitch signal can be simply added to the conventional feedback controller

To utilize the lidar measurement for LAC, a correlation study is necessary to determine how much the lidar-estimated REWS is correlated with the actual REWS that acts on the turbine rotor. Some facts that could have an impact on the measurement correlation are listed below:

According to the IEC standard, two turbulence models are commonly used for wind turbine design as provided by the

Once the lidar measurement coherence is analyzed, a filter needs to be designed to filter out uncorrelated information in the lidar-estimated REWS. Because the filter introduces a certain time delay

When evaluating the benefits of LAC,

The recent developments in turbulence simulation tools,

The variation of turbulence parameters from the standard values given by

Top view of a turbulence field showing the eddy structures under different atmospheric stability, simulated using the

In this work, we summarize how the turbulence spectrum and spatial coherence can vary by atmospheric stability from literature. Three atmospheric stability classes, unstable, neutral, and stable, are considered. For each atmospheric stability class, the Mann model parameters are collected, and then the Kaimal model parameters are fitted to have similar spectra and coherence compared to the Mann model. Then the four-dimensional stochastic turbulence fields are generated using the

This paper is organized as follows: Sect.

In this section, we first introduce the

The

At a certain moment, the velocity field can be described by

The one-dimensional (along the longitudinal wavenumber) cross-spectra of all velocity components with separations

The Kaimal model given by

The turbulence evolution refers to the phenomenon that the eddy structure changes when the turbulence propagates from upstream to downstream. It is often represented using longitudinal coherence.

A space–time tensor that extends the three-dimensional Mann spectral tensor

In the space–time tensor, the turbulence field is assumed to travel with a mean reference wind speed

On the other hand,

To include the exponential longitudinal coherence model into the analysis of lidar measurement correlation, a general “direct product” approach is used to combine the lateral-vertical coherence and the longitudinal coherence

Atmospheric stability indicates the buoyancy effect on the turbulence generation, and it is usually related to the temperature gradient by height. It is interesting to investigate its impact on the filter design of LAC since the turbine will experience different atmospheric stability conditions during operation. The filter is necessary to filter out the uncorrelated frequencies in the REWS estimated by lidar, as will be discussed later in Sect.

The Mann model parameters under different atmospheric stability classes (based on the work of

As for the Kaimal model, we chose the parameters listed by the

Except for the spectra and

The fitted parameters for the exponential longitudinal coherence model.

Based on the study by

In this section, the definitions of REWS and the REWS estimated by lidar will first be discussed. Then the auto-spectra of these two signals and the cross-spectrum between them will be presented. In the end, we summarize the wind preview quality of the investigated four-beam lidar for the NREL 5.0

As discussed by

For the Mann model, as derived by

As for the Kaimal model, the spectrum is derived by

Lidar utilizes the Doppler spectrum contributed by the aerosol backscatters within the probe volume to determine wind measurement. It is necessary to include the probe volume averaging effect.

The front view of the NREL 5.0

Since lidar only provides the wind speed in the LOS direction, the

For the Kaimal model, the auto-spectrum can be derived based on the Fourier transform:

When turbulence evolution is considered with the Mann model,

Similarly, following

To evaluate the preview quality of lidar measurement, one can calculate the lidar–rotor coherence by

In this work, we chose the medium-size NREL 5.0

Parameters of the optimal four-beam pulsed lidar system. Optimized according to the measurement coherence bandwidth using the space–time tensor model. The definitions of the angles are shown in Fig.

With the optimized lidar trajectory, we show the coherence

Except for the coherence, another indicator of how well the lidar predicts the REWS can be the following transfer function

The transfer functions under the three investigated stability classes are shown in Fig.

By the turbulence spectral model, which represents the mean spectral properties, we can obtain the expected Wiener transfer function gain. However, in real operation, the Wiener filter design is more complicated and requires a higher-order filter. In contrast, a linear filter that has similar damping as the Wiener filter can also provide a similar filtering effect as the Wiener filter. The linear filter is usually designed to have a cutoff frequency at

The dependency of cutoff frequencies in hertz on the mean wind speed. The cutoff frequency corresponds to

Apart from the case that all measurement gates (see the caption of Fig.

In this section, we introduce the lidar-assisted turbine controller theory and its integration into OpenFAST aeroelastic simulation.

To configure LAC in the OpenFAST aeroelastic simulation, we chose to use the Bladed-style interface

The overall OpenFAST and LAC interface. LDP: lidar data processing. FFP: feedforward pitch. ROSCO: the reference FB controller.

As mentioned before, the lidar measurement data need to be processed before they can be used for control. The first sub-DLL is the lidar data processing (LDP) which calculates the lidar-estimated REWS from the lidar LOS speed.

In reality, the lidar usually does not measure all beam directions simultaneously. Instead, it sequentially measures from one direction to the next direction. This sequential measurement property is later simulated using the lidar module in the aeroelastic simulation (see Sect.

A typical variable-speed wind turbine is controlled by a blade pitch and generator torque controller. A baseline collective feedback blade pitch control is achieved by a proportional-integral (PI) controller

For better code accessibility, the recently developed open-source reference controller, ROSCO (v2.6.0) by

The collective feedforward pitch control proposed by

The overall control diagram. FFC: feedforward pitch controller; FBC: collective feedback pitch controller; GTC: generator torque controller. Note that the real-time pitch angle (

A feedforward pitch (FFP) sub-DLL is programmed to be responsible for filtering the lidar-estimated REWS and provide feedforward pitch rate at correct time. A first-order low-pass filter with the following transfer function:

The leading time and required leading time for pitch feedforward signal.

Another point for the feedforward pitch command is that it is only activated when the REWS is above 14

In this section, we use the open-source aeroelastic simulation tool OpenFAST to further evaluate the benefits of LAC. The simulation results will be presented and discussed.

Previously, OpenFAST (v3.0) was modified to integrate a lidar simulation module

To include the turbulence evolution for the aeroelastic simulation, four-dimensional stochastic turbulence fields are required. We use the newly developed

For the turbulence field generated by the

For the Kaimal-model-based 4D wind fields,

For both types of 4D turbulence fields, the time step is chosen to be 0.5

For each stability class, we generate 4D turbulence fields with 12 different random seed numbers. For each turbulent wind field, the OpenFAST simulation is executed with the following configurations: (a) FB control using ROSCO only and (b) feedforward+feedback (FFFB) control using lidar measurements. All the degrees of freedom for a fixed-bottom turbine except for the yawing are activated. Each simulation is executed for 31

In Fig.

The time series collected from OpenFAST simulation. The case with the Mann model and neutral stability parameters is shown. Note the same 3D wind field

Panel (a) compares the REWS estimated by the lidar data processing algorithm and that estimated by the extended Kalman filter (EKF)

Panel (b) shows that the rotor speed obviously fluctuates less using FFFB control compared to that using FB control only. Also, the peak values with FFFB control are smaller.

The tower fore–aft bending moment

In panel (f), we show the pitch action between the two control strategies. The pitch angles in the FFFB control generally lead that by the FB-only control in time, as expected. The pitch angle trajectories are overall similar between the FFFB and FB-only controls.

Lastly, the generator power is shown in panel (g). Here, we can see that the generator power fluctuates even though the constant power torque control mode is activated. The reason is that ROSCO uses low-pass-filtered generator speed to calculate the generator torque command by

We estimate the spectra from the collected time series using the

Before comparing the OpenFAST outputs spectra, the spectra of the REWS by the input turbulent wind fields are first compared in Fig.

The auto-spectra of REWS. “theo.”: theoretical spectra by the models discussed in Sect.

In Figs.

Panels (a), (b), and (c) compare the rotor speed spectra between FFFB and FB controls under three stability classes. The FFFB control generally reduces the rotor speed spectrum in the frequency range from 0.01 to 0.1

The auto-spectra estimated from OpenFAST output time series. The simulation results are obtained using the Mann model. The mean wind speed is 16

The auto-spectra estimated from OpenFAST output time series. The simulation results are obtained using the Kaimal model. The mean wind speed is 16

The comparison of the tower fore–aft bending moment is shown in panels (d), (e), and (f). In neutral and stable cases, the main benefits bought by FFFB control are the reductions in the frequency range from 0.01–0.2

Panels (g), (h), and (i) show the blade root out-of-plane moment of blade one. There are slight reductions in the blade root out-of-plane moment in the frequency range from 0.02 to 0.1

The comparison of low-speed shaft torque is shown by the panels (j), (k), and (l). Using FFFB control brings some benefits in the frequency range from 0.01 to 0.1

Overall, the relative reductions in the spectra bought by adding FF control mainly lie in the frequency range where the lidar–rotor transfer function is above zero. For very low-frequency ranges, the turbine motions are naturally damped; thus, no obvious benefits are brought by adding the pitch feedforward signal. Based on the spectral analysis, we found reductions significantly in rotor speed, some in tower fore–aft moment, and slightly in low-speed shaft torque. Also, the reductions are observed by both turbulence models in three different atmospheric stability classes.

To further evaluate the benefits of LAC, we calculate the DEL using the rainflow counting method

Comparison of DEL (

Comparison of DEL (

Figure

There are overall obvious reductions of the tower fore–aft bending moment DEL in all the investigated atmospheric stability classes. The largest reduction is found to be 16.7 % by a mean wind speed of 22

As for the low-speed shaft torque, the DEL is reduced by more than 4.0 % under the unstable case for wind speed above 18

The DEL of the blade out-of-plane moment is reduced by introducing LAC. More benefits (about 2.7 %–6.0 %) are found under the unstable case. In the neutral stability, the reduction is better at 20

The SD of rotor speed is found to be reduced significantly using FFFB control. The reductions are more than 20 % and up to 40 %. Also, it can be seen that the reductions are more significant under higher mean wind speeds, which is similar in all the three atmosphere stability classes.

Introduction of the FF pitch also generally helps to reduce the standard deviation of pitch rate (speed)

As for the electrical power SD, it is reduced obviously by about 16 % in the unstable case for wind speed above 18

With the same mean wind speed but under different stability cases, the electricity productions are similar either using LAC or not. For all the stability conditions, the electricity productions are lower at wind speeds below 14

The results using the Kaimal model are shown in Fig.

In terms of tower fore–aft bending moment, the reductions of DEL are from 10.4 % to 13.4 % with a mean wind speed from 18 to 20

The results of low-speed shaft DEL show a similar trend to that using the Mann model. On average, for wind speed above 16

Generally, the reduction of the blade root load simulated using the Kaimal model is similar to that based on the Mann model. On average, for wind speed above 16

The SD of rotor speed is found to be reduced obviously using FFFB control. The reductions are more than 15 % and are up to 30 %. The result shows a similar trend to that of the Mann-model-based result. However, we can also see the reduction is less than that shown by the Mann model.

The pitch actions show high similarity with that simulated using the Mann model. At mean wind speeds from 16 to 20

Since the variation in electrical power is highly linked with the rotor speed, the reductions in the SD of power lie around 10 %, 13 %, and 11 %, respectively, under the three investigated stability classes. These values are smaller than those observed using the Mann model.

The electricity production shows very similar results to those simulated by the Mann model. Using LAC has a marginal impact on electricity production.

In general, the benefits of LAC in load reduction by a four-beam lidar are clear. However, we also show that there are some uncertainties and differences when assessing LAC by different IEC turbulence models. Among the compared turbine loads, LAC has the most significant load reduction effect in the tower base fore–aft bending moment. There are also considerable reductions in speed and power variations. The electrical power generation is not significantly affected by introducing LAC. The load reductions also show differently under different turbulence parameters represented by different atmosphere stability classes. For different stability conditions but the same mean wind speed, it can be seen that the LAC benefits for the load reduction are overall highest in the unstable, medium in neutral, and lowest in stable atmospheric classes. The reason could be the difference in turbulence length scales. The turbulence length scale is lower under a stable condition, which means the peak of the turbulence spectrum appears at a higher wavenumber/frequency (based on the conversion

This paper evaluates lidar-assisted wind turbine control under various turbulence characteristics using a four-beam liar and the NREL 5.0

Currently, two turbulence models (the Mann model and the Kaimal model) are provided by the IEC standard for turbine aeroelastic simulation. The recent research has made it possible to generate 4D stochastic turbulence fields in aeroelastic simulation for both the Mann model and the Kaimal model, which allows for simulating lidar measurements more realistically and assessing the potential benefits by lidar-assisted control more reasonably. When evaluating the benefits of lidar-assisted control, previous research uses the Kaimal model with fixed-turbulence spectral parameters provided by the IEC standard

Based on the defined three turbulence cases, we analyzed the coherence between the rotor-effective wind speed and the one estimated by lidar. The NREL 5.0

To further analyze the impact of atmospheric stability for lidar-assisted control, a reference lidar-assisted control package is developed and used in this work. The lidar-assisted control package includes several DLL modules written in FORTRAN: (1) a wrapper DLL that calls all sub-DLLs sequentially, (2) the lidar data processing DLL that estimates the REWS and records the leading time of the REWS, (3) a feedforward pitch module that filters the REWS and activates the feedforward rate at the correct time, and (4) a modified reference FB controller (ROSCO) which can receive a feedforward command.

The benefits of lidar-assisted control are evaluated using both the Mann model and the Kaimal-model-based 4D turbulence. The simulations are performed for the mean wind speed level from 12 to 24

With this work, we show that the mean wind speed, the turbulence spectrum, coherence, and the used turbulence models all have certain impacts on the results of evaluating lidar-assisted control. In this paper, the same turbulence intensity level is assumed for different atmospheric conditions. However, in reality, the turbulence intensity depends on the stability conditions of the atmosphere. In the future, we recommend assessing the benefits of lidar-assisted control depending on site-specific turbulence characteristics and statistics. Also, it is necessary to consider the uncertainties in turbulence models when performing load analysis using aeroelastic simulations.

The OpenFASTv3.0 version with a lidar simulator integrated can be accessed via

Simulation data of this paper are available upon request from the corresponding author.

FG conceived the concept, performed the simulations, and prepared the paper. DS supported by verifying the simulations, provided general guidance, and reviewed the paper. PWC provided suggestions and revised and reviewed the paper.

The contact author has declared that none of the authors has any competing interests.

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

This research received financial support from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 858358 (LIKE – Lidar Knowledge Europe).

This research has been supported by the European Commission, Horizon 2020 Framework Programme (LIKE (grant no. 858358)).

This paper was edited by Jan-Willem van Wingerden and reviewed by Eric Simley and one anonymous referee.