To provide comprehensive information that will assist in making decisions regarding the adoption of lidar-assisted control (LAC) in wind turbine design, this paper investigates the impact of different turbulence models on the coherence between the rotor-effective wind speed and lidar measurement. First, the differences between the Kaimal and Mann models are discussed, including the power spectrum and spatial coherence. Next, two types of lidar systems are examined to analyze the lidar measurement coherence based on commercially available lidar scan patterns. Finally, numerical simulations have been performed to compare the lidar measurement coherence for different rotor sizes. This work confirms the association between the measurement coherence and the turbulence model. The results indicate that the lidar measurement coherence with the Mann turbulence model is lower than that with the Kaimal turbulence model. In other words, the potential value creation of LAC based on simulations during the wind turbine design phase, evaluated using the Kaimal turbulence model, will be diminished if the Mann turbulence model is used instead. In particular, the difference in coherence is more significant for larger rotors. As a result, this paper suggests that the impacts of different turbulence models should be considered uncertainties while evaluating the benefits of LAC.

Turbine-mounted lidar sensors provide preview information about the inflow wind to be used for improving wind turbine control, which is referred to as wind-turbine-integrated lidar-assisted control (LAC). LAC is a promising technology for reducing wind turbine loads and the levelized cost of energy (LCOE)

The topic of the optimal lidar scan pattern for wind energy applications is critical for the widespread deployment of LAC. Both practical considerations for overcoming the obstacles of LAC application and for optimizing lidar scan patterns were discussed at the International Energy Agency (IEA) Wind Task 32 workshop

According to current wind turbine design requirements in the IEC standard

With the advent of larger rotor sizes and more flexible wind turbines, evaluating the value creation of LAC is becoming increasingly important. The analysis in this work is based on the framework proposed by

The remainder of this paper is organized as follows: Sect.

Two different turbulence models are commonly used to evaluate the design loads in the IEC standard

The advantage of the Kaimal model is that the one-dimensional spectra are expressed as simple analytic expressions. The wind disturbance is described as turbulent velocity fluctuations and is assumed to be a stationary and random vector field with zero-mean Gaussian statistics. The power spectral densities (PSDs) of each wind component are given in a non-dimensional form:

For the longitudinal velocity component

The cross-power spectral density (CPSD)

According to the IEC standard

The Mann turbulence model

The three-dimensional fluctuations around the mean wind speed

Because of homogeneity, the covariance tensor is a function of the separation vector

All second-order statistics of turbulence, such as variances and cross spectra, can be derived from the covariance tensor. The spectral tensor is given by

For three-dimensional turbulent velocity vector

The Mann model is based on three adjustable parameters:

The co-coherence

The theoretical turbulence models are quite complicated, especially for the Mann model, although the application of the Mann model only requires three parameters (

The coordinate system of the wind box as well as the lidar scan patterns is shown in Fig.

Coordinate system of wind box and lidar scan patterns. The wind box is shown using the color map. Two corners are marked as black squares (corner 1 and corner 2). Two commercial CW lidar scan patterns are shown:

To generate the wind boxes for further analysis, two different turbulence simulators are used. The Kaimal model can be generated using the turbulence simulator TurbSim

All numerical simulations are performed for a wind field with mean wind speed

Settings for generating the turbulence box.

Since the Mann turbulence fields are normally rescaled to the specified turbulence intensity inside HAWC2, the parameter

The method used in TurbSim is the Veers approach

The differences between the Mann and Kaimal models are discussed in this section.

Co-coherence at different separation distances.

Figure

A clear trend can be seen in Fig.

For vertical separations in Fig.

The co-coherence with the Mann model is negative in some frequency ranges, which is not the case for the exponential coherence model with the Kaimal model expressed in Fig.

With the advent of larger rotor sizes, lidar measurements must scan a larger area upstream of the rotor. So the findings above indicate that the choice of the turbulence model strongly influences the correlation between the lidar measurement and true REWS. This impact should be considered while evaluating the benefits of LAC.

Two different scan patterns based on commercial nacelle-mounted lidars are investigated here to illustrate the impact of different turbulence models on lidar measurement coherence: a 4-beam scan pattern (Fig.

As suggested by

The optimal lidar scan parameters for maximizing coherence bandwidth. Optimal scan radii

The LOS velocity at one measurement point from a lidar system can be expressed as

The velocity measured by a real scanning lidar is a spatial average of the LOS velocities along the lidar beam, which is described by the range-weighting function. The range-weighting function for continuous-wave lidars is expressed as follows

The REWS is modeled as a sum of the

The method of reconstructing the REWS from lidar measurements has been discussed by

no lateral

no shears or inflow angles.

In order to investigate the impact of different turbulence models on lidar measurement coherence, numerical simulations have been performed. Apart from the Vestas V52 with a 52 m rotor diameter, two other reference wind turbines are used, including the National Renewable Energy Laboratory (NREL) 5 MW reference turbine with a 126 m rotor diameter

The numerical simulations include 18 random turbulence boxes with different seeds for each turbulence model. The simulation time is 600 s. Therefore, the combination of two types of lidars, three different rotor sizes and two turbulence models results in 12 separate scenarios and 18 random realizations for each scenario.

For indicating the measurement quality, the wavenumber

For reducing fatigue loads using LAC, detecting eddies with a length as small as 1

By optimizing the lidar scan pattern, the measurement coherence bandwidth can be maximized, but the cost of the lidar will increase as well. Meanwhile, the benefits of fatigue load reduction may reach a plateau. Generally speaking, the lower the value of

Based on the simulation results, the magnitude-squared coherence

Magnitude-squared coherence

The key findings of this study are included in the following discussion. For brevity, the magnitude-squared coherence with the Mann model is represented by

For the Vestas V52 turbine in Fig.

For the NREL 5 MW turbine in Fig.

For the DTU 10 MW turbine in Fig.

The additional measurement points with the circular scan provide an obvious improvement in measurement coherence in the frequency band

A novel finding in this work is that the coherence with the Mann model is lower that with the Kaimal model for large rotors, and this difference becomes larger with increasing rotor size. Conversely, for small rotor sizes, the coherence with the Mann model is higher than that with the Kaimal model. The differences between

In summary, these results provide important insights into the impact of different turbulence models on lidar measurement coherence. If the wind conditions at a site agree more closely with the Mann model, the lower coherence with the Mann model will diminish the advantages of LAC because inappropriate blade pitch actions in response to the lidar measurements will deteriorate the turbine structural loading. It can therefore be suggested that the turbulence model needs to be carefully considered while integrating the LAC solution with larger-rotor turbine designs.

This work confirms the association between lidar measurement coherence, the turbulence model and rotor size. Our results suggest that this impact should be considered an uncertainty when evaluating the benefits of LAC during the wind turbine design phase. Note that the impacts on the load reduction need to be further investigated using reference turbines and aero-elastic tools following the IEC standards. More broadly, further research should be undertaken to provide guidelines on how to determine the optimal scan pattern for different site-specific atmospheric conditions and rotor sizes. Field validation is strongly recommended to mitigate the risk induced by site-specific wind conditions if LAC is adopted, especially for large rotors.

The turbulence box data could be made available on request.

LD was involved in the conceptualization of the project, the creation of the methodology, the use of software, the investigation and the writing of the original draft of this paper. WHL was involved in the conceptualization of the project, the creation of the methodology, the investigation and the writing of the original draft of this paper. ES was involved in the creation of the methodology, the investigation and the writing of the original draft of this paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work or allow others to do so for US Government purposes.

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The authors want to thank Jakob Mann for providing the inputs of theoretical-coherence results with the Mann model and his suggestions on the manuscript.

This research was supported by the Energy Technology Development and Demonstration Program (EUDP) for the project “Lidar-assisted control for reliability improvement” (LICOREIM, grant no. 64019-0580).

This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under contract no. DE-AC36-08GO28308. Funding was provided by the US Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office.

This paper was edited by Joachim Peinke and reviewed by two anonymous referees.