Can wind lidars measure turbulence?A. SatheJ. MannJ. GottschallM. Courtney

Acknowledgements – 1. EU FP6 Upwind Project2. EU FP7 SafeWind Project

Risø DTU, Danmarks Tekniske Universitet

What do we mean by turbulence?Estimation of Reynolds stress tensor,

2

2

2

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'''''

'''''

wvwuw

wvvuv

wuvuu

Rij

Why should we measure turbulence?

1. Design of wind turbines2. Power curve of a wind turbine3. Validation of wind profile models at greater heights, e.g. using momentum

flux measurementThe aim is to reduce the overall cost of wind energy!

Many other applications in fields other than wind energy, e.g. Bridge design

Risø DTU, Danmarks Tekniske Universitet

How can we measure turbulence?• Sonic anemometers (current industry standard)• Cup anemometers• Hot wire anemometers

So, what is the problem?

Remote sensors that do not need a tower1. Wind lidars2. Sodars3. Any other remote sensing instrument

All these instruments need a meteorological mast • They are very expensive, both onshore and particularly offshore• They have a fixed structure to the ground, and hence, cannot be moved

easily

What is the alternative?

Risø DTU, Danmarks Tekniske Universitet

What are the challenges for remote sensors?• They should measure exactly what they are supposed to measure – Mean

wind speeds, Turbulence etc.• They should be cheaper than or at least as expensive as the current

standard measurement systems

What are wind lidars?

rv

N

E

S

W

w

hv

)cos,sinsin,sin(cos)(),,,(

),)(()()(

nwvuv

dnvnv fr

22

cossinsinsincos)(

vuv

wvuv

h

r

Risø DTU, Danmarks Tekniske Universitet

What are the challenges for the measurement of turbulence?

E

rv

N

S

W

w

hv

dssndnvnsv fr ))()(()()()(

Which wind lidars are currently available?• Windcube – a pulsed lidar developed by Leosphere • ZephIR – a continuous-wave (CW) lidar developed by Qinetiq, Natural

power

fds

Risø DTU, Danmarks Tekniske Universitet

How are the wind speeds retrieved?

Windcube ZephIRE

N

S

W

sin2

sin2

,sincos

rWrEEW

rSrNNS

EWNSwc

vvu

vvu

uuu

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,)sin()(sin1

,)cos()(sin1

dvw

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rqq

dssndnvnsv fr ))()(()()()(

rNv

rEvrSvrWv

Risø DTU, Danmarks Tekniske Universitet

How accurate is the turbulence measured by lidars?

ZephIR

Risø DTU, Danmarks Tekniske Universitet

Can we understand why lidars do not measure turbulence precisely?

tensorvelocity spectral3D

dkdkdkdkkk

dvv

ij

ijtrueji

)(

,),,,(

)(

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)()()(

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)()()(

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2

Point measurements

Risø DTU, Danmarks Tekniske Universitet

Can we understand why lidars do not measure turbulence precisely?

conjugate Complex *lidar respective the for function weightingingCorrespond X

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nj

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)(

)()()( *''

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2

Assumptions in modelling• The terrain is horizontally homogeneous• The spatial structure of turbulence flow is well described by the spectral

tens or model of Mann(1994)

Risø DTU, Danmarks Tekniske Universitet

Can we understand why lidars do not measure turbulence precisely?

• Only neutral conditions are shown• The model compares reasonably well with the measurements from both lidars• Large systematic errors are observed for both lidars in turbulence measurements

Model

Measurements

Ideal caseIdeal case

Variation with wind direction

ZephIR Windcube

Risø DTU, Danmarks Tekniske Universitet

How can we measure turbulence using lidars?Directly using the variances of line-of-sight velocities

sincossin2coscossin2cossinsin2

cossinsincossin''''2''

22'222'222'2'

wvwuvu

uvuvr

• Avoids averaging due to conical scanning

• Averaging only along the beam direction

• In principle, only 6 beams are required to measure Reynolds stress tensor

Risø DTU, Danmarks Tekniske Universitet

How can we measure turbulence using lidars?

How did we arrive at this configuration?

beam vertical172,45 beams, 5

Assumptions in modelling• The terrain is horizontally homogeneous• The spatial structure of turbulence flow is well described by the spectral

tensor model of Mann(1994)

ss1 and of consistingMatrix

ancessight vari-of-linestresses, Reynolds

,1

M

SΣ

SMΣ

450

,3600

),,(

f

2SΣΣ

Risø DTU, Danmarks Tekniske Universitet

Comparing the 6 beam configuration with the conical scanning method

• For ZephIR, the improvement is not significant except for w variance• The line-of-sight averaging effect is quite significant, especially for the ZephIR.• For the Windcube, the variances using 6 beam is quite different from the conical scanning method• Better results with the Windcube for the conical scanning method is due to luck (contribution of the cross components). The errors are quite

large for different stability conditions using the conical scanning method as compared to the 6-beam method.

Conical scanning

6-beam

Conical scanning

6-beam

Ideal caseIdeal case

ZephIR Windcube

Risø DTU, Danmarks Tekniske Universitet

Conclusions• Using the conical scanning method, turbulence cannot be measured

precisely due to large systematic errors arising from spatial averaging• In principle, the 6 beam configuration reduces systematic errors due to

conical averaging. Windcube errors are reduced significantly• We need to somehow negate the line-of-sight averaging effect from both

lidars, especially the ZephIR

Future work• 6-beam experiment using a short-range windscanner developed at Risø

DTU• Mann et.al(2010) developed a spatial filter model for the ZephIR to negate

the line-of-sight averaging effect, but needs measurements. Averaged doppler spectra will be used instead of using the radial velocities derived from the individual doppler spectra.

Risø DTU, Danmarks Tekniske Universitet

Thank you