Physics of Wind Parks - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 136

Fig. 6.1 Schematic of momentum loss and replenishment in an indefinitely large wind park. The
undisturbed flow is approaching from left

¼ 1

z
L

z
L ¼ 0

/ m for ð 6 : 10 Þ

z
L

for z

L [ 0
with x = (1 - b z/L * ) 1/4 and the Obukhov length L * defined in ( 3.11 ). We use
a = 5 and b = 16 in ( 6.10 ). Assuming a logarithmic wind profile, the friction
velocity, u * is given by:

1 þ a

W 1

h
z 0

h
L

u ¼ u h j ln ð 6 : 11 Þ

where W is given by ( 3.15 ) for unstable conditions and the first equation of ( 3.21 )
for neutral and stable conditions.
Following Frandsen ( 2007 ), we define the wind park drag coefficient, c t as a
function of the park area A, the rotor area 0.25pD 2 , the number of turbines N and
the turbine thrust coefficient C T :

NpD 2
A

c t ¼ 1
8

C T ð 6 : 12 Þ

C T is about 0.85 for lower wind speeds around the cut-in wind speed and
decreases around and above the rated wind speed of the turbines with increasing
wind speed (Barthelmie et al 2006 ; Jimenez et al 2007 ). The exact value depends
on the construction of the turbine and its operation. We use the following empirical