Publishers version - DTU Orbit

hh hub
1.6
1.4
1.2
1.0
0.8
0.6
0.4
measurements
fit
Α fit 0.12
RSS 0.03
a
6.5 7 7.5
wind speedlidarms
hh hub
1.6
1.4
1.2
1.0
0.8
0.6
0.4
measurements
fit
Α fit 0.14
RSS 0.15
b
6.5 7 7.5
wind speedlidarms
Figure 93: Example of measured wind profiles and their fit to a power law profile. (a) RSS ≤
0.1, (b) RSS > 0.1
According to this classification, profile (a) in Figure 93 would be in group 1 and profile (b)
in group 2. The value of 0.1 was chosen here as threshold for the RSS, because it gave two
groups of data showing two trends (shown below) while being statistically comparable (as
they count similar numbers of data: 511 in group 1 and 396 in group 2). It is recognized that
this threshold is somewhat arbitrary and should subsequently be “fine-tuned” using a large
number of datasets.
7.4 Equivalent wind speed
7.4.1 Standard power curve for the two groups of wind profiles
Figure 94 shows the standard scatter plot of the power (a) and the Cp (b) as function of the
wind speed at hub height. Cp is defined as in the current IEC standard 61400-12-1:
Cp =
P
0.5ρu 3 hub A,
(165)
where P is the electrical power output of the turbine and A is the rotor swept area. The two
colours represent the two groups of wind profiles: points obtained with the group 1 profiles
(RSS ≤ 0.1) are displayed in black and those obtained with group 2 profiles (RSS > 0.1) are
displayed in red.
Figures 94(a) and (b) show two trends (one for each group) leading to two mean power
curves and Cp curves (obtained after binning the data into 0.5 m s −1 wind speed bins and
averaging as required by the IEC 614000-12-1 standard) (Figures 94(c) and (d)). The power
output of the turbine for a given wind speed (at hub height) is smaller for data from group
2 (non power-law profiles) than for data from group 1 and the data from group 2 generally
give a lower Cp.
What might appear here, for the non-power law profiles, as an underperformance of the
wind turbine is an overestimation of the kinetic energy flux of the wind. Indeed, the Cp
definition given by Eq. (165) implicitly assumes that the wind speed is constant over the
entire rotor swept area:
or, in other words, the wind speed shear is ignored.
u(z) = uhub KEhub = 0.5ρu 3 hubA, (166)
150 DTU Wind Energy-E-Report-0029(EN)