Publishers version - DTU Orbit

Normalized C r = C r
P Q 2
W (r)
b
Coherence
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
Blade Span (%)
0 10 20 30 40 40 50 60 60 70 80 90 100
0 6.3 12.6 18.9 25.2 31.5 37.8 44.1 50.4 56.7 63
Spanwise Position, r (m)
10 -3
Weighting, U = 11.4 m/s
r = 25% R
r = 50% R
r = 70% R
r = 84% R
r = 100% R
Point to Blade Effective Wind Speed Coherence
10 -2
10 -1
Frequency (Hz)
r = 25% R
r = 50% R
r = 70% R
r = 84% R
r = 100% R
Figure 139: Coherence between the wind speeds at single points along the blade and overall
blade effective wind speed for the NREL 5-MW model at U = 11.4 m/s.
Thescanradius r ofthecircularlyscanninglidarshouldbe chosentoproducehighmeasurement
coherence between the measured wind and the blade effective wind speed. Figure 139
shows the coherence between perfectly measured u wind speeds at various points along the
blade and blade effective wind speed. Coherence is highest for wind speed measurements near
the outboard region of the blade, where torque production is highest. Note that low-frequency
coherence happens to be maximized when the wind is measured at 70% blade span rather
than at 84% span, where the peak of the weighting function is located, due to the particular
spatial coherence model used. For control purposes, it is more important to maximize
coherence at low frequencies, where the power in the turbulence spectrum is concentrated.
10.5.1 Range Weighting
As illustrated by the magenta curve on the lidar beam in Fig. 133, a CW lidar measures
weighted line-of-sight wind speeds along the entire beam, where the peak of the weighting
function is located at the intended focus point. A weighted line-of-sight lidar measurement
can be described as
(234)
uwt,los = −ℓxuwt −ℓyvwt −ℓzwwt
where ˆ ℓ = [ℓx,ℓy,ℓz] is the unit vector in the direction that the lidar is pointing. uwt,
vwt, and wwt are the weighted velocities along the lidar beam such that the vector uwt =
[uwt,vwt,wwt] is given by
∞
uwt = u Rℓ
ℓ+[0,0,h] W(Fℓ,Rℓ)dRℓ (235)
0
DTU Wind Energy-E-Report-0029(EN) 203
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