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Coherence
1
0.8
0.6
0.4
0.2
0
10 −3
Geometry Errors, r = 41 m
10 −2
10 −1
Frequency (Hz)
10 0
d = 30 m
d = 60 m
d = 90 m
d = 120 m
d = 150 m
Figure 141: Measurement coherence for a hub-mounted lidar with a scan radius of 41 m at
five different preview distances. Only geometry errors are included.
Coherence
1
0.8
0.6
0.4
0.2
0
10 −3
10 −2
Wind Evolution, r = 41 m
10 −1
Frequency (Hz)
10 0
d = 30 m
d = 60 m
d = 90 m
d = 120 m
d = 150 m
Figure 142: Measurement coherence for a hub-mounted lidar with a scan radius of 41 m at
five different preview distances. Only wind evolution errors are included.
10.5.3 Wind Evolution
A major source of preview measurement error is the evolution of the turbulence between
the time it is measured by the lidar and the time it appears at the turbine rotor as a wind
disturbance. While for a fixed scan radius r, measurement errors due to the measurement
geometry decrease as preview distance increases, errors due to wind evolution become more
severe, since there is additional time for the turbulence to evolve.
Wind evolution can be described by a coherence function between wind speeds at two
points separated in the longitudinal (along-wind) direction. A popular longitudinal coherence
formula used in the wind turbine control community (Bossanyi et al. 2012b; Schlipf et al.
2012a; Laks et al. 2013) is presented in Kristensen (1979). The Kristensen coherence formula
is a function of frequency, longitudinal separation, mean wind speed, turbulent kinetic energy,
and a turbulence length scale. Wind evolution becomes more severe when longitudinal separation
or turbulent kinetic energy are increased and becomes less severe as mean wind speed
increases. Longitudinal coherence curves using the Kristensen (1979) formula are shown in
Fig. 142 for several preview distances. A mean wind speed of 13 m/s is used with a turbulence
intensity of 10%. Wind evolution tends to affect high frequencies more than low frequencies
and, as a result, very low-frequencystructures in the wind do not change significantlybetween
the measurement point and the turbine.
The IEC von Karman wind model used in this chapter only defines spatial coherence in
the transverse and vertical (yz) plane. This model assumes that wind speeds are perfectly
DTU Wind Energy-E-Report-0029(EN) 205