Publishers version - DTU Orbit

A 9
A 8
A 7
A 6
A 5
A 4
A 3
A 2
A 1
U 9
U 8
U 7
U 6
U 5
U 4
U 3
U 2
U 1
Figure 95: Rotor swept area divided into 9 segments corresponding to the 9 heights where
lidar observations are performed. Each wind speed is assumed to be constant in each segment
7.4.3 Equivalent wind speed definition
Intuitively, thepoweroutputoftheturbineshouldbemorecloselyrelatedtothe kineticenergy
flux derived from the whole profile than that derived from the wind speed at hub height. We
should then consider the power output of the turbine as a function of the kinetic energy flux.
In order to do so, an equivalent wind speed is suggested:
Then Cp becomes:
Cp =
P
0.5ρ0u 3 eq
P
ueq =
A =
i
0.5ρ0
u 3 i
Ai
A
i
1/3
ρi
ρ0
. (168)
P
1/3
3
ui
=
i0.5ρiu3 iAi = . (169)
KEprofile
Figure 97 shows plots comparable to the plots in Figure 94: in Figure 97, the power and
Cp are plotted as a function of the equivalent wind speed defined in Eq. (168) (instead of the
wind speed at hub height in Figure 87) and Cp is calculated according to Eq. (169) (instead
of Eq. (165) in Figure 94). In Figure 97, profiles from both groups follow the same trend.
The mean power and Cp curves obtained with each group of points overlap each other. This
shows that the difference in power curves between the two groups shown in Figure 97 was
mainly due to the error in kinetic energy flux.
7.4.4 Choice of instrument
The question now is: can any remote sensing instrument be used to measure a power curve
and reduce the scatter with the equivalent wind speed method? Figures 98(a) and (b) show
152 DTU Wind Energy-E-Report-0029(EN)
P
Ai
A
A