Analysis of Wind Speed Measurements using Continuous …eces.colorado.edu/~simley/Documents/SimleyEtAl_AIAA_2011.pdf · Analysis of Wind Speed Measurements using Continuous Wave LIDAR

Analysis of Wind Speed Measurements using

Continuous Wave LIDAR for Wind Turbine Control �y

Eric Simleyz Lucy Y. Pao x Rod Frehlich { Bonnie Jonkman k Neil Kelley ��

Light Detection and Ranging (LIDAR) systems are able to measure the speed of incom-ing wind before it interacts with a wind turbine rotor. These preview wind measurementscan be used in feedforward control systems designed to reduce turbine loads. However,the degree to which such preview-based control techniques can reduce loads by reacting toturbulence depends on how accurate the incoming wind �eld can be measured. This studyexamines the accuracy of di�erent measurement scenarios that rely on coherent continuous-wave Doppler LIDAR systems to determine their applicability to feedforward control. Inparticular, the impacts of measurement range and angular o�set from the wind directionare studied for various wind conditions. A realistic case involving a scanning LIDAR unitmounted in the spinner of a wind turbine is studied in depth, with emphasis on choices forscan radius and preview distance. The e�ects of turbulence parameters on measurementaccuracy are studied as well.

Nomenclature

d measurement preview distanceF focal distancek wind velocity wavenumber (m�1)r scan radius for spinning LIDARRMS root mean square�u standard deviation of u component of wind velocityTI turbulence intensity� LIDAR measurement angle�u mean u wind speedu� friction velocityU�D average friction velocity over rotor disk� angle between laser and wind velocity vector angle in the rotor plane! rotational rate of spinning LIDAR

�This work was supported in part by the US National Renewable Energy Laboratory. Additional industrial support is alsogreatly appreciated. The authors also thank Alan Wright, Fiona Dunne, and Jason Laks for discussions on desired characteristicsof wind speed measurement devices that can enable preview-based control methods for wind turbines.yEmployees of the Midwest Research Institute under Contract No. DE-AC36-99GO10337 with the U.S. Dept. of Energy

have authored this work. The United States Government retains, and the publisher, by accepting the article for publication,acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish orreproduce the published form of this work, or allow others to do so, for the United States Government purposes.zGraduate Student, Dept. of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO, Student

Member AIAA.xRichard and Joy Dorf Professor, Dept. of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder,

CO, Member AIAA.{Senior Research Associate, Cooperative Institute for Research in Environmental Sciences, Boulder, CO 80309.kSenior Scientist, National Wind Technology Center, NREL, Golden, CO 80401, AIAA Member.��Principal Scientist, National Wind Technology Center, NREL, Golden, CO 80401, AIAA Member.

1 of 16

American Institute of Aeronautics and Astronautics

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-263

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. Under the copyright claimed herein, the U.S. Government has a royalty-free license to exercise all rights for Governmental purposes. All other rights are reserved by the copyright owner.

I. Introduction

Wind speed measurements in front of a wind turbine can be used as part of feedforward or preview-based controllers to help mitigate structural loads caused by turbulent wind conditions. Prior analyses haveshown that improvements to turbine load performance can be achieved with knowledge of the incoming wind�eld.1{3 A block diagram of such a control strategy is shown in Fig. 1. Upstream wind is measured, providingan estimate of the wind speeds that will eventually reach the turbine. In reality, the turbulent structures inthe wind will evolve between the time they are measured and when they reach the turbine, causing errors inthe preview wind measurements.4 In this paper, we focus on the preview measurement stage, ignoring windevolution. Thus, our model assumes the validity of Taylor’s frozen turbulence hypothesis, which states thatturbulent eddies tend to remain unchanged while convecting with the average wind velocity.5

Figure 1. A block diagram illustrating how LIDAR can be used in a preview based combined feedfor-ward/feedback control scenario. Although wind measured using LIDAR will evolve between preview mea-surement and contact with the turbine, we do not study wind evolution in this paper.

Although various optical and acoustical methods exist for measuring wind speeds, coherent DopplerLIDAR (LIght Detection And Ranging) provides the most accurate and versatile way to provide remotemeasurements.6 The two main coherent LIDAR technologies that are currently available are continuouswave (CW) LIDAR and pulsed LIDAR. In this paper, we provide an analysis of using CW LIDAR to providepreview wind measurements, although a brief discussion of pulsed LIDARs is also included. Aside from thetechnological merits of CW LIDAR, the recent application of �ber telecommunications technology to LIDARinstrumentation has made infrared, CW LIDAR an economical and eye-safe technology for measuring windvelocity in front of a turbine.6

While some improvement can be gained by measuring wind speeds upwind of the hub location, it ismuch more advantageous to be able to measure the wind that will appear at each individual blade.7 Acommercially available ZephIR LIDAR, developed by Natural Power, mounted in the spinner of a windturbine has been successfully tested in the �eld, illustrating the ability of the technology to be applied toindividual turbine control.8 Therefore, we provide a detailed analysis of preview wind measurements at avariety of blade span positions using a spinning LIDAR mounted in the hub of a 5 MW turbine. Analysesare provided using a model of a CW LIDAR developed for the National Renewable Energy Laboratory’s(NREL’s) FAST code.9 The LIDAR measurement scenarios investigated involve NREL’s reference 5 MWmodel10 with turbulent wind inputs generated using NREL’s TurbSim code.11,12

This paper is organized as follows. In Section II we present the principal equation used in our LIDARmeasurement model, called the \range weighting function," as well as the geometry of LIDAR measurements.The processes through which range weighting and measurement geometry cause measurement errors arediscussed here. Results from simulation are provided in Section III describing the e�ects of wind turbulenceparameters on wind speed measurement error. A hub mounted spinning LIDAR scenario is investigated heretoo, with a focus on the optimal preview distances for wind speed measurements at given fractions of therotor radius. Section IV concludes the paper and provides a discussion of plans for future research involvingLIDAR and wind evolution modeling.

2 of 16


II. LIDAR Measurement Theory

The analysis of LIDAR performance examined here uses the coordinate system shown in Fig. 2 (a). Theground referenced x, y, and z axes are de�ned such that -z is pointing in the direction of gravity and x isnominally pointing in the downwind direction. However, depending on the wind conditions being simulated,the x axis may not be aligned with the average wind direction. The wind speed vector is de�ned by u, v,and w components, where u is the streamwise component . Nominally, the u, v, and w axes are aligned withthe x, y, and z axes, respectively, since the FAST simulations simply \march" the wind toward the turbinein the x direction. The 5 MW model used for our LIDAR studies has a hub height of 90 meters and a rotorradius of 63 meters.

Figure 2. Coordinate system and measurement variables referred to in the discussions. (a) The x, y, zcoordinate system along with the LIDAR measurement angle, �, and the angle between the LIDAR beam andthe wind speed vector, �. (b) Variables referred to in the analysis of a spinning LIDAR including previewdistance, d, and scan radius, r.

The LIDAR measurement model we have created introduces two imperfections to wind speed measure-ments. Range weighting is the e�ect inherent to CW LIDAR that applies a spatial �lter along the laserbeam causing wind speeds at locations other than the focal distance to contribute to the measured value.The other primary source of error in wind speed measurements is due to estimating the u component ofthe wind velocity vector given a single line-of-sight measurement. This is sometimes called the \cyclopsdilemma." Control systems utilizing preview wind speed measurements primarily focus on the componentof the wind that is perpendicular to the rotor plane, nominally the u component. In our simulations, themean streamwise wind direction is aligned with the x axis, so we are assuming that the rotor plane is alwaysperpendicular to the x axis. Therefore, our LIDAR measurements estimate the component of wind alignedwith the x axis, which will be treated as equivalent to the u component for the rest of the paper. When theLIDAR is staring in the x direction, there will be no geometrical measurement errors because the v and wcomponents do not contribute to the detected radial velocity. If the laser is instead pointed in a directionother than along the x axis, unknown v and w components contribute to the measurement and an estimateof the u component must be formed.

A. Range Weighting

CW LIDAR determines the radial wind speed at a speci�c location by focusing the laser beam at thatlocation instead of relying on range gates and timing circuitry like a pulsed system. However, rather thanonly detecting the wind speed at the focal point, wind speed values along the entire laser beam are integrated

3 of 16


according to a Lorentzian range weighting function W (R), inherent in the physics of a focused LIDAR system,to yield the detected value. Our model assumes that range weighting occurs only along an in�nitely thinbeam. The wind speed measurement due to range weighting at a focal distance F is determined by

vwgt(F ) =Z 1�1

vr(R)W (R)dR (1)

where vr(R) is the radial velocity at a range R along the laser beam.13 In the case when the e�ects ofrefractive turbulence on laser propagation are ignored, the range weighting function for a focal distance ofF is given by

W (R) =KN

R2 + (1� RF )2R2

R

(2)

where RR is the Rayleigh range and KN is a normalizing constant so thatZ 1�1

W (R)dR = 1: (3)

The Rayleigh range is given by

RR =�a2

2

�(4)

where � is the laser wavelength and a2 is the e�2 intensity radius of the Gaussian laser beam.The analyses in this study assume � = 1:565 �m and a2 = 2:8 cm, which are characteristic of the

commercially available ZephIR Doppler LIDAR system. W (R) is presented in Fig. 3 for several ranges thatmight be desired in wind preview control applications. Clearly, as the range of the measurement increases,the detected velocity contains increasingly signi�cant contributions from a greater length along the beam.The spatial averaging e�ect of range weighting causes the LIDAR beam to low-pass �lter the wind speedsit measures. As focal distance increases, the cut-o� frequency of the equivalent �lter decreases. Frequencyresponses for the range weighting functions shown in Fig. 3 as well as those for focal distances of 200 and250 meters are provided in Fig. 4. Note that typical focal distances for the ZephIR LIDAR are less than 200meters.

Figure 3. Normalized range weighting functions, W (R), for the ZephIR LIDAR at a variety of focal distances,F . The range weighting functions spatially average the wind along the laser beam. As focal distance increases,spatial averaging along a greater length of the beam occurs.

B. Measurement Geometry

A single LIDAR unit is capable of measuring only radial wind velocity, yet the wind velocity at a givenlocation is a vector quantity consisting of u, v, and w components. Therefore, a single LIDAR cannot

4 of 16


Figure 4. The frequency responses of the normalized range weighting �lters for a variety of focal distancesalong with the -3 dB bandwidths of the �lters.

determine the entire wind vector quantity. Instead, the assumption that the measured radial wind speedis due to the u component alone with v = w = 0 is made, since ideally u � v; w. When the LIDAR ispointing upwind at an angle � o� of the x axis, it is assumed that the angle � , which is formed between theinstantaneous wind vector and LIDAR beam, is equal to � (although � and � will di�er if the instantaneouswind direction is not aligned with the x axis, as is almost always the case). The detected radial velocity isthen given by

vr =pu2 + v2 + w2 cos� (5)

and, under the assumption that v = w = 0 (� = �), the estimate of u is

u =vr

cos �: (6)

When the LIDAR is pointing nearly along the x axis, and � is small, errors due to the LIDAR geometrywill be small since the measured radial velocity will be dominated by the u component of wind speed. As� increases, the radial velocity measured by the LIDAR will contain more contributions from the v and wcomponents. For large angles o� of the x axis where the u component becomes close to orthogonal to theLIDAR direction, � is close to �=2 and an approximation for the u estimate is

u �pu2 + v2 + w2

�=2� ��=2� �

: (7)

For large � and � close to �=2, the u estimate is very sensitive to mismatches between � and � , andmeasurements will likely contain severe errors.

An analysis of large angle errors has shown that for a variable u velocity, and a transverse wind speedcomponent with magnitude � =

pv2 + w2 and uniformly distributed random direction in the yz plane will

cause an RMS error of�err =

� tan �p2

(8)

where � is the measurement angle o� of the x axis. Furthermore, for stochastic wind �elds where themagnitude

pv2 + w2 varies with time, the RMS error is given by

�err =�RMS tan �p

2(9)

5 of 16


where �RMS is the RMS value of the transverse wind speed magnitude, orpv2 + w2.a The most revealing

feature of this relationship is that in the absence of range weighting, measurement errors will scale withtan �.

C. Combined Range Weighting and Geometrical Errors

An analysis has been provided for range weighting errors and measurement angle errors separately, but inpractice measurement errors are caused by a combination of the two sources. For very large �, angular errorstend to dominate, while for moderate to small � and large focal distances, range weighting dominates theoverall error. Figure 5 (a) illustrates how measurement errors follow a tan � trend for large � as well ashow range weighting will dominate overall errors for small � and great enough focal distances. The scenarioused to generate the four curves in Fig. 5 (a) is illustrated in Fig. 5 (b). The focal distances in the fourmeasurement scenarios are di�erent and vary as F = �Z

sin � . Thus the curves representing large �Z havegreater focal distances, and represent errors that are dominated by range weighting, at smaller �.

Figure 5. The combined e�ects of measurement angle and range weighting on overall measurement error.(a) Four curves showing RMS measurement error vs. measurement angle. The curves represent LIDARmeasurements at four di�erent �xed �Z values as a function of measurement angle �. For each �Z, thefocal distance F varies with measurement angle. The four di�erent measurement scenarios are illustrated in(b). Each LIDAR is pointed at a di�erent elevation, �Z, above the LIDAR unit, that does not vary withmeasurement angle. At any given measurement angle, the focal distance is then given by F = �Z

sin �. Note that

the chosen �Z represent 25%, 50%, 75%, and 100% blade span for the 5 MW turbine model investigated inthis research. For larger � (which corresponds to smaller F for a constant �Z), measurement error follows thetan � curve. Each solid curve in (a) begins a transition (at a di�erent measurement angle) from predominantlyrepresenting angular errors to being dominated by range weighting errors. The �Z = 63 m curve divergesfrom tan � at roughly 40:2� and F = 97:6 meters, the �Z = 47:25 m curve diverges at 33:3� and F = 86:2 meters,the �Z = 31:5 m curve diverges at 27:1� and F = 69:1 meters, and the �Z = 15:75 m curve diverges at 20:3� andF = 45:5 meters.

To graphically illustrate how range weighting and measurement angles a�ect wind speed measurements,Fig. 6 compares actual u components of wind speed as well as the measured wind speeds for a variety of Fand �. For F = 10 and F = 25 meters, range weighting has little impact on detected wind while for largerF , the low-pass �ltering e�ect of the measurement process can clearly be observed in Fig. 6 (a). Fig. 6 (b)illustrates how severe wind speed errors can be for moderate to large �.

For the analysis of a spinning LIDAR described in Section III C, another possible source of measurementerror exists. The ZephIR LIDAR being modeled provides a velocity sample at a rate of 50 Hz. For a LIDARthat is pointed at some angle � and spinning around the x axis, the focal point will travel along the circlebeing scanned while returns are being integrated to form a velocity estimate. This \blurring" e�ect could

aA derivation of �err is provided in the Appendix

6 of 16


Figure 6. Examples of (a) range weighting errors for a variety of F and (b) measurement angle errors for avariety of �. The measurements in (b) involve focal distances less than 10 m, so all visible discrepancies fromthe true wind speed are solely due to geometrical errors.

cause another source of spatial averaging error. The arc length that the focal point traverses during a sampleperiod is equal to

l =2�r!

50(10)

where ! is the rotational rate of the LIDAR in s-1 and r is the scan radius as de�ned in Fig. 2 (b). Ourstudies of this source of error show that the blurring e�ect causes insigni�cant errors for ! less than 4 Hz.Since it is unlikely that a spinning LIDAR would scan at a rate higher than 4 Hz, we have ignored this sourceof error. It is possible that the resolution of the wind �les used during simulation is not high enough toreveal the severity of the spatial averaging that would occur. Investigating the e�ect with higher resolutionwind �elds is an area of future work.

III. Simulation Results

Simulations were performed in FAST to assess the performance of CW LIDAR in realistic previewmeasurement scenarios. All wind �elds used were generated for use with a 5 MW turbine model with ahub height of 90 meters. RMS wind speed measurement errors were analyzed for a forward staring LIDAR(� = 0) at the hub location to assess the e�ects of range weighting alone for a variety of wind conditions. Idealpreview control systems might include LIDAR units mounted in the blades so that preview measurementscan be made in front of outboard sections of the blades, avoiding geometrical measurement errors. However,since a more economical and realistic method involves placing a single scanning LIDAR angled o� of the xaxis in the spinner of a turbine, we analyze spinning LIDAR performance for di�erent blade span positionsand preview distances.

A. Wind Conditions

In order to test the performance of CW LIDAR in realistic wind environments, simulations were run usinga variety of wind �les generated with the Great Plains-Low Level Jet (GP LLJ) spectral model in TurbSim,

7 of 16


characteristic of wind observed near Lamar, Colorado.2,12 A library of wind �les consisting of below rated(mean u component of wind speed �u = 9 m/s), rated (�u = 11.4 m/s), and above rated (�u = 13 m/s)conditions with various stability and friction velocity values was used for the simulations. A total of 31 wind�elds, 630 seconds in length were stochastically generated for each of the �ve varieties of wind conditionsavailable at the three mean wind speeds. The wind �les are sampled at 20 samples/second and contain 31by 31 points in the yz plane. A summary of the library of wind �les used is provided in Table 1. Althoughcoherent structures have been generated to be superimposed over some of the wind �les, the results in thispaper do not include coherent structures.

Table 1. A summary of the Great Plains-Low Level Jet wind �elds used for wind speed measurement analysis.Uhub indicates the reference streamwise wind speed, RiTL indicates the turbine layer gradient Richardsonnumber, and �D indicates the wind shear power law exponent. U�D is the average friction velocity, de�ned

in Eq. 11, of wind at the hub, top of the rotor, and bottom of the rotor. TIU , TIV , and TIW are the meanturbulence intensities of the u, v, and w components of wind speed, de�ned in Eq. 12, respectively. For thewind scenarios that do not have power law wind shears, jet height indicates the height of the center of the jet,which is hub height for the 5 MW model.

Simulation ID Uhub (m/s) RiTL �D U�D (m/s) TIU (%) TIV (%) TIW (%) Jet Height (m)

BR1 9 -0.1 0.123 0.399 6.61 8.14 6.33 N/A

BR2 9 0.02 0.235 0.341 8.00 7.47 5.68 N/A

BR3 9 0.2 0.273 0.135 3.61 4.71 2.73 N/A

BR4 9 0.02 N/A 0.29 7.07 6.68 4.97 90

BR5 9 0.2 N/A 0.158 4.26 4.90 3.08 90

R1 11.4 -0.1 0.086 0.451 6.31 7.15 5.82 N/A

R2 11.4 0.02 0.134 0.414 7.67 7.03 5.46 N/A

R3 11.4 0.2 0.365 0.149 3.62 3.47 2.56 N/A

R4 11.4 0.02 N/A 0.29 5.76 5.32 4.02 90

R5 11.4 0.2 N/A 0.158 3.61 3.54 2.56 90

AR1 13 -0.1 0.077 0.514 6.54 7.14 5.69 N/A

AR2 13 0.02 0.139 0.422 6.93 6.22 4.82 N/A

AR3 13 0.2 0.363 0.135 3.17 2.85 2.16 N/A

AR4 13 0.02 N/A 0.289 5.12 4.55 3.46 90

AR5 13 0.2 N/A 0.16 3.39 3.02 2.27 90

B. Impact of Turbulence on Measurement Errors

It is important to be able to judge the �delity of wind speed measurements in a variety of wind conditions todetermine when preview measurements will be reliable enough for use in control systems. RMS measurementerror over an entire 10 minute wind �eld is used as a metric to compare LIDAR performance in this section.The amount of measurement error is not directly related to the mean wind speed of a wind �eld but ratherto the turbulence parameters. For a forward staring LIDAR at hub height, the wind shear pro�le will nota�ect wind speed errors either. Parameters that will likely impact range weighting errors are the Richardsonnumber, de�ning vertical stability, the turbulence intensity (TI), and the local friction velocity, in m/s,de�ned as

u� =qju0w0j (11)

where u0 = u � �u and w0 = w � �w. Because range weighting acts as a �lter on the wind �eld, anotherapproach is to study the impact of range weighting for a variety of spectral shapes. In this research, this wasnot possible since all GP LLJ wind spectra, once normalized by some value, have roughly the same spectralshape.

The turbulence intensities of the three wind components, given by

TIu = �u=u

TIv = �v=u

TIw = �w=u

(12)

8 of 16


where �u, �v, and �w are the standard deviations of the u, v, and w wind speed components, respectively,are common ways of describing wind conditions3 and are also easy to measure. The turbulence intensityvalue most commonly used to describe wind conditions is TIu. Since it is the standard deviation of the windthat causes measurement errors rather than the turbulence intensity, the variable actually analyzed here isTIu multiplied by the mean wind speed, or the standard deviation of the u component, �u. Results showingthe RMS errors between true wind speeds at the hub location and wind passed through a range weighting�lter are shown in Fig. 7 as functions of �u.

Results for all 31 seeds for each of the 15 wind conditions are provided for a total of 465 wind conditionsdue to the fact that the various stochastic realizations of the 15 basic wind types have varying amounts ofTI. While the results show that there is a general trend between �u and RMS error, it is clear that all seedswithin one basic wind type produce roughly the same amount of error regardless of �u. At a focal distanceof 200 meters, it appears that �u plays more of a role in determining RMS error. A possible reason for thisis that at F = 200 m, the range weighting �lter has a very low cuto� frequency, 0:0022 m-1. Only turbulentfeatures with wavelengths on the order of 450 meters or above are able to pass through the �lter and it islikely that a TI value captures the low frequency uctuations very well.

Figure 7. RMS wind speed measurement errors for a LIDAR pointed along the -x axis at hub height for variousfocal distances as functions of standard deviation of the u component of wind speed. Results are shown for all465 wind �les generated for use with the 5 MW model. See Table 1 for more details about the wind conditionsanalyzed.

Rather than treating standard deviation of wind speed as a reliable variable for estimating measurementerror, a variable common to all of the realizations of a basic wind type is desired. Local friction velocity,or u�, is a good �gure for judging measurement errors because all seeds of a main wind type have the samelocal u� values for the GP LLJ spectral model analyzed here. In fact, local u� values control the scalingof the velocity spectra in the GP LLJ model.b In addition, u� has been shown to be a good indicator ofthe number of high-loading events on a turbine14,15 and may therefore be a useful value for analyzing theperformance of a controller based on wind preview measurements. Results of RMS errors between true and

bWhile the GP LLJ spectra scale with u�, other spectral models such as the IEC models scale with �u.

9 of 16


measured wind are included in Fig. 8 as functions of local u� at hub height. It is important to note thatthe friction velocity referred to in this analysis is the local u� at hub height rather than the average frictionvelocity over the entire rotor disk, U�D, shown in Table 1. Clearly, local u� provides a much better indicatorof forward-looking LIDAR performance, especially for the 25, 50, and 100 meter focal distances. When theLIDAR is focused at a distance of 200 meters, local u� is still a reasonably good indicator of RMS error,but there tends to be more variation within a basic wind type. This is consistent with the results in Fig. 7revealing an increasing dependence on �u for errors at greater focal distances.

Figure 8. RMS wind speed measurement errors for a LIDAR pointed along the -x axis at hub height forvarious focal distances as functions of the local friction velocity u�. Results are shown for all 465 wind �lesgenerated for use with the 5 MW model. See Table 1 for more details about the wind conditions analyzed.

C. Hub Mounted Spinning LIDAR Analysis

By mounting a LIDAR in the spinner of a wind turbine, the LIDAR can be o�set at an angle � and focusedat a distance F so that measurements will be made at a radius r and a preview distance d in front of theturbine (see Fig. 2 (b)). In addition to the rotational rate of the turbine rotor, which may be too slow forthe measurement rate desired, an additional rotational rate can be introduced. Since this method has beensuccessfully tested on a 2.5 MW turbine with a ZephIR LIDAR,8 it is reasonable to assume that a likelymeasurement technique for a preview control implementation will involve a spinning LIDAR.

Observations based on the results in Fig. 5 encouraged the study of \optimal" preview distances forspeci�c scan radii, r, and wind conditions. The optimal preview distance is de�ned here as the distance for agiven r that provides the lowest RMS measurement error while using a LIDAR mounted at the hub location.Although wind evolution would cause even more error between the measured wind speed and the wind speedthat reaches the rotor, Taylor’s frozen turbulence hypothesis is assumed here, meaning that the optimalpreview distance is judged based on measurement errors alone. RMS errors for a given r are calculated byaveraging over all rotor angles, (see Fig. 2 (b)). Measurement errors are shown as functions of previewdistance for 14 di�erent blade span radii in Fig. 9 for the AR1 and AR3 wind conditions. The AR1 wind type

10 of 16


is the most turbulent of all wind types analyzed here, while AR3 has relatively benign conditions. Figure10 summarizes the minimum errors detected and the corresponding preview distances for the 14 blade spanpositions analyzed in Fig. 9.

Figure 9. RMS measurement error as a function of preview distance for various scan radii, assuming a spinningLIDAR mounted in the spinner of a wind turbine. The optimal (minimum RMS error) preview points areplotted as well for each scan radii. (a) Results for the high turbulence AR1 wind type. (b) Results for therelatively calm AR3 wind condition. The 14 radii analyzed correspond to the 14 sample locations along they and z axes in the TurbSim �le that are less than or equal to blade span. We found that by modeling windmeasurements on the TurbSim grid points, wind speeds more indicative of the intended turbulence conditionscould be acquired. For this reason, measurement errors are formed by averaging wind speed measurements at = 0, 90, 180, and 270 degrees, the angles where it is guaranteed that a measurement will lie on a grid pointfor the chosen scan radii.

The optimal measurement distance can be roughly described as the point at which both geometricalerrors and range weighting errors are low. For shorter distances measurement angle errors will cause error toincrease, and for greater distances the low-pass �ltering e�ect of range weighting will cause more signi�canterror. The results of Fig. 9 show that the optimal measurement distance is a strong function of r. As rincreases, the optimal preview distance is greater because of the large measurement angle required to focusat a radius r. In addition, for the calmer wind condition, AR3, optimal preview distances tend to be closerto the turbine than for the AR1 case. In Fig. 9 (a), one can see that for very large preview distances, allerror curves tend to converge, because range weighting dominates over the low angular errors caused by verysmall �.

Results for AR3 in Fig. 9 (b) reveal a very interesting phenomenon. At great enough preview distances,measurements at smaller scan radii produce errors that are greater than those resulting from larger radii.This is a counterintuitive result because for a given preview distance larger scan radii should produce greater

11 of 16


Figure 10. Optimal (minimum RMS error) measurement errors and preview distances corresponding to Fig. 9as functions of scan radius, r.

measurement errors, since � is greater and the measurement angle errors have more of an impact. However,by observing how local u� varies with height, some insight into this phenomenon can be gained. In SectionIII B, we found u� to be a good indicator of the amount of measurement error that can be expected.Normalized pro�les of u� for AR1 through AR5 are shown in Fig. 11. The ratio of u� at 50% blade spanabove hub height to u� at hub height, for example, is 0.62 for AR3, while it is 0.83 for AR1. This meansthat measurements at 50% blade span will be far less corrupted by turbulence compared to measurements athub height for AR3 than they would be for AR1. Beyond a certain preview distance, for AR3, the decreasein range weighting error due to lower turbulence causes overall error to be lower for larger scan radii, eventhough the measurement angles are greater. For AR1, the ratio between turbulence levels at hub heightand larger blade radii is not great enough to counteract the increase in error due to greater measurementangles, �. Therefore, the curves representing measurement error for small scan radii, r, in Fig. 9 (a) do noteventually intersect and become greater than the curves corresponding to larger r, as they do in Fig. 9 (b).

Figure 11. Height pro�les of u� for AR1 through AR5. All pro�les have been normalized to their maximumvalue of u�.

Previous LIDAR-based preview control studies have required knowledge of wind speeds concentratedheavily between 60% to 80% rotor radius3 and at 75% rotor radius1,2 because of maximum power extractionat these spans. To re ect the interest in wind speed measurements at these spans, simulations were performedfor all 15 wind types for a scan radii of 75% blade span along with 50% and 100% blade span for comparison.

12 of 16


Results from these simulations are included in Fig. 12, which displays the average minimum measurementerror achieved for each wind condition along with the preview distance at which the minimum error wasmeasured. Minimum achievable RMS error is clearly a much stronger function of wind condition than optimalpreview distance. For the high-interest 75% blade span scan radius, typical optimal preview distances for avariety of wind conditions are between 110 and 150 meters.

Figure 12. Minimum RMS measurement errors and corresponding optimal preview distances for measurementsusing a spinning LIDAR located at the hub of a wind turbine for scan radii of 53.7%, 76.7%, and 99.7% bladespan (33.83 m, 48.33 m, and 62.83 m, respectively). The scanned radii correspond to the grid points closestto 50%, 75%, and 100% blade span containing wind speed samples in the TurbSim �les.

IV. Conclusions and Future Work

In this paper we have provided an analysis of the application of continuous-wave (CW) Doppler LIDARto preview wind measurements on a wind turbine. Speci�cally, we analyzed the two main sources of errorduring CW LIDAR measurement, including range weighting and geometrical errors, and the measurementscenarios where each source is dominant. Figures 5 and 6 suggest that measurement angles greater than 45degrees should be used with caution because of the large errors introduced by the relatively strong v andw components of radial velocity. The local friction velocity, u�, was shown through simulation to provide agood indication of the amount of wind speed measurement error due to range weighting. An analysis of arealistic hub mounted spinning LIDAR measurement scenario for a 5 MW turbine was made, with resultsrevealing the preview distances that one might expect to provide the minimum RMS error for speci�c scanradii. Initial results for wind preview based feedforward controllers utilizing the CW LIDAR model developedin this study are documented in Dunne et al.16 and Laks et al.17

On-going work involving CW LIDAR modeling includes investigating random LIDAR errors due to

13 of 16


optical and electronic noise. Measurement noise likely varies with turbulence conditions and a model ofnoise is desirable in a future LIDAR model. Analysis of measurements of coherent structures, such asKelvin-Helmholtz billows, in the wind �elds is needed. Studies have shown that coherent structures causesevere turbine loads,14 and it is a goal of wind preview based controllers to mitigate the loads caused bycoherent structures. Therefore, it is essential to determine the �delity that LIDAR measurements of coherentstructures can achieve.

Although this paper studied a CW LIDAR model, several companies have pulsed LIDAR models on themarket for wind turbine applications. Pulsed LIDARs rely on transmitting a pulse and collecting returnsfrom di�erent \range gates." Since pulsed LIDARs do not focus the laser at the measurement range, theirrange weighting functions do not vary with measurement distance, making their analysis easier than forCW LIDARs. However, pulsed LIDARs cannot be focused at arbitrary ranges. Instead, measurements arereturned for range gates separated by distances on the order of 30 meters. A brief comparison of pulsed andCW technologies is presented in Fig. 13.

Figure 13. A comparison of CW and pulsed LIDARs. The CW LIDAR is modeled after the ZephIR while thepulsed LIDAR is representative of the Leosphere Windcube. (a) A comparison of RMS errors for a forwardstaring LIDAR con�guration using the AR1 wind condition at ranges corresponding to range gates similar tothose of the Windcube. Note that range weighting functions for pulsed LIDARs do not vary with measurementdistance and the minor variations visible are due to simulation imperfections. At a range of about 135 meters,both LIDAR technologies produce the same amount of measurement error. (b) A comparison of the pulsedrange weighting function and the CW range weighting function at F = 135 meters. At the range where bothtechnologies produce the same error, the pulsed LIDAR has a wider range weighting function while the CWrange weighting function has more signi�cant \tails."

As shown in Fig. 1, wind evolution presents another source of wind preview uncertainty that was notdiscussed in this work. Future e�orts in wind evolution modeling and simulation are required to fully assessthe e�ectiveness of LIDAR wind preview measurements for control applications. An implication of the studies

14 of 16


in this paper is that it may be impractical for a LIDAR unit based in the spinner of a wind turbine to provideaccurate wind preview measurements at large scanning radii close to the turbine. To avoid measurementerrors due to geometry, one possibility is to measure the wind farther away from the turbine and delay themeasurements before they are input to a controller if the controller requires very short preview times.c Weanticipate that with the addition of wind evolution modeling, optimal preview distances such as those shownin Figs. 10 and 12 will no longer be valid because wind evolution will likely cause shorter preview distances tobe favored, since wind evolves more over greater distances. As a result, it may be di�cult to provide highlyaccurate preview measurements to a controller using a hub mounted spinning LIDAR. More simulationsusing LIDAR and wind evolution models are required to fully understand the capabilities of LIDAR-basedwind preview measurements.

Appendix

Without loss of generality, consider a LIDAR measurement of wind velocity where the LIDAR is locatedat the origin (see Fig. 2 (a)) and the measurement point is contained in the xz plane with y = 0, upwindfrom the LIDAR. Consider the wind to have a positive u component, aligned with the x direction, which willbe referred to as U . The wind velocity vector has a transverse component in the yz plane with magnitude� =

pv2 + w2 and uniformly distributed random angle, , in the yz plane. If the LIDAR measures this

wind velocity with a measurement angle �, the detected radial velocity is given by

ur = cos � � U + sin � sin � �: (13)

The estimate of the u component, using Eq. 6, is given by

u =ur

cos �= U + tan � sin � � (14)

and therefore the measurement error, u� u, is

err(u) = tan � sin � �: (15)

When many wind speed measurements are made, the RMS measurement error is calculated as

�err =q

tan2 � sin2 � �2: (16)

Since � is constant and and � are independent random variables, Eq. 16 becomes

�err = tan �q

sin2 p�2: (17)

Finally, since the RMS value of sin2 isp

22 , the RMS measurement error is given by

�err =tan � � �RMSp

2(18)

where �RMS is the RMS magnitude of the transverse wind component.

References

1J. Laks, L. Pao, A. Wright, N. Kelley, and B. Jonkman, \Blade pitch control with preview wind measurements," in Proc.48th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA-2010-251, Jan. 2010.

2F. Dunne, L. Pao, A. Wright, B. Jonkman, and N. Kelley, \Combining standard feedback controllers with feedforwardblade pitch control for load mitigation in wind turbines," in Proc. 48th AIAA Aerospace Sciences Meeting, Orlando, FL,AIAA-2010-250, Jan. 2010.

3D. Schlipf and M. K�uhn, \Prospects of a collective pitch control by means of predictive disturbance compensation assistedby wind speed measurements," in Proc. German Wind Energy Conference (DEWEK), Bremen, Germany, Nov. 2008.

4D. Schlipf, D. Trabucchi, O. Bischo�, M. Hofs�a�, J. Mann, T. Mikkelsen, A. Rettenmeier, J. Trujillo, and M. K�uhn,\Testing of frozen turbulence hypothesis for wind turbine applications with a scanning lidar system," in Proc. InternationalSymposium for the Advancement of Boundary Layer Remote Sensing, Paris, France, Jun. 2010.

cLaks et al.1 �nd that an \optimal" preview time for a 600 kW wind turbine is 0.45 s, which for above-rated wind speedsof 18 m/s means preview wind measurements are needed only 8.1 meters in front of the turbine.

15 of 16


5G. Taylor, \The spectrum of turbulence," in Proceedings of the Royal Society of London, 1938.6M. Harris, M. Hand, and A. Wright, \Lidar for turbine control," National Renewable Energy Laboratory, NREL/TP-

500-39154, Golden, CO, Tech. Rep., Jan. 2006.7J. Laks, L. Pao, and A. Wright, \Combined feedforward/feedback control of wind turbines to reduce blade ap bending

moments," in Proc. 47th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA-2009-687, Jan. 2009.8T. Mikkelsen, K. Hansen, N. Angelou, M. Sj�oholm, M. Harris, P. Hadley, R. Scullion, G. Ellis, and G. Vives, \Lidar wind

speed measurements from a rotating spinner," in Proc. European Wind Energy Conference, Warsaw, Poland, Apr. 2010.9J. Jonkman and M. Buhl, \FAST user’s guide," National Renewable Energy Laboratory, NREL/EL-500-38230, Golden,

CO, Tech. Rep., 2005.10J. Jonkman, S. Butter�eld, W. Musial, and G. Scott, \De�nition of a 5-MW reference wind turbine for o�shore system

development," National Renewable Energy Laboratory, NREL/TP-500-38060, Golden, CO, Tech. Rep., 2009.11N. Kelley and B. Jonkman, \Overview of the TurbSim stochastic in ow turbulence simulator," National Renewable

Energy Laboratory, NREL/TP-500-39796, Golden, CO, Tech. Rep., 2007.12B. Jonkman, \TurbSim user’s guide: Version 1.50," National Renewable Energy Laboratory, NREL/TP-500-46198,

Golden, CO, Tech. Rep., 2009.13R. Frehlich and M. Kavaya, \Coherent laser performance for general atmospheric refractive turbulence," Applied Optics,

vol. 30, no. 36, pp. 5325{5352, Dec. 1991.14N. Kelley, R. Osgood, J. Bialasiewicz, and A. Jakubowski, \Using wavelet analysis to assess turbulence/rotor interactions,"

Wind Energy, vol. 3, pp. 121{134, 2000.15N. Kelley, \The identi�cation of in ow uid dynamics parameters that can be used to scale fatigue loading spectra of

wind turbine spectral components," National Renewable Energy Laboratory, NREL/TP-442-6008, Golden, CO, Tech. Rep.,1993.

16F. Dunne, L. Y. Pao, A. D. Wright, B. Jonkman, N. Kelley, and E. Simley, \Adding feedforward blade pitch control forload mitigation in wind turbines: Non-causal series expansion, preview control, and optimized FIR �lter methods," in Proc.49th AIAA Aerospace Sciences Meeting, Orlando, FL, Jan. 2011.

17J. Laks, L. Pao, E. Simley, A. Wright, N. Kelley, and B. Jonkman, \Model predictive control using preview measurementsfrom lidar," in Proc. 49th AIAA Aerospace Sciences Meeting, Orlando, FL, Jan. 2011.

16 of 16
