15  Planning, operation and economics of wind farm projects  517 
0
500
1000
1500
2000
2500
3000
3500
4000
2 3 4 5 6 7 8 9 10 11 12
Mittlere Jahresw indgeschw indigkeit v
m.a
 in m/s
Flächenspezifischer Jahresertrag E
a
 in kWh/m²
15
v
N
= 16 m/s
14
13
12
11
10
9
8
Annahmen: -Wind nach Rayleigh-Häufigkeitsverteilung 
-WKA-Leistungsbeiwert c
p
 = 0,41 = const
-Luftdichte 
U
 = 1,2 kg/m³
v
N 
v
N 
v
aus
 / v
N 
= 
2,0
v
ein
 / v
N 
= 
0,25
P
N 
Area-specific annual yield in kWh / m²
Annual mean wind speed v in m/s at hub height
_
Assumptions: - Rayleigh wind frequency distribution
- WEC power coefficient c
P
= 0.41 = const
- air density
P
R
P
R
v
cut-in
/v
R
=
0.25
v
R
v
cut-out
/v
R
=
2.0
v
R
0
500
1000
1500
2000
2500
3000
3500
4000
2 3 4 5 6 7 8 9 10 11 12
Mittlere Jahresw indgeschw indigkeit v
m.a
 in m/s
Flächenspezifischer Jahresertrag E
a
 in kWh/m²
15
v
N
= 16 m/s
14
13
12
11
10
9
8
Annahmen: -Wind nach Rayleigh-Häufigkeitsverteilung 
-WKA-Leistungsbeiwert c
p
 = 0,41 = const
-Luftdichte 
U
 = 1,2 kg/m³
v
N 
v
N 
v
aus
 / v
N 
= 
2,0
v
ein
 / v
N 
= 
0,25
P
N 
Area-specific annual yield in kWh / m²
Annual mean wind speed v in m/s at hub height
_
Assumptions: - Rayleigh wind frequency distribution
- WEC power coefficient c
P
= 0.41 = const
- air density
P
R
P
R
v
cut-in
/v
R
=
0.25
v
R
v
cut-out
/v
R
=
2.0
v
R
0
500
1000
1500
2000
2500
3000
3500
4000
2 3 4 5 6 7 8 9 10 11 12
Mittlere Jahresw indgeschw indigkeit v
m.a
 in m/s
Flächenspezifischer Jahresertrag E
a
 in kWh/m²
15
v
N
= 16 m/s
14
13
12
11
10
9
8
Annahmen: -Wind nach Rayleigh-Häufigkeitsverteilung 
-WKA-Leistungsbeiwert c
p
 = 0,41 = const
-Luftdichte 
U
 = 1,2 kg/m³
v
N 
v
N 
v
aus
 / v
N 
= 
2,0
v
ein
 / v
N 
= 
0,25
P
N 
Area-specific annual yield in kWh / m²
Annual mean wind speed v in m/s at hub height
_
Annual mean wind speed v in m/s at hub height
_
Assumptions: - Rayleigh wind frequency distribution
- WEC power coefficient c
P
= 0.41 = const
- air density
P
R
P
R
v
cut-in
/v
R
=
0.25
v
R
v
cut-out
/v
R
=
2.0
v
R
 
Fig. 15-23  Area-specific annual yield versus mean wind speed at hub height  
At v = v
R
 there is a sharp corner in the power curve P = P(v). Between v
R
 and the 
cut-out wind speed v
cut-out
 = 2 v
R
 the wind turbine constantly operates at rated 
power  P
R
. 
The integral of the energy yield, cf. equation (4.20), is now applied to the  
period of a year T = 8,760 h 
 
dvvPvvhTE )(),(
0
³
f
  . (15.5) 
Using the area of one square metre as reference area for calculating the power 
gives the area-specific annual energy yield E
a
 of the wind turbine shown in 
Fig. 15-23 depending on its rated wind speed v
R
 (turbine) and the annual mean 
wind speed 
v
 (site). Here, it becomes apparent that reasonable designs will use a 
rated wind speed of v
R
 = 2 
v
, i.e. twice the annual mean wind speed (in praxi: v
R
 
= 11...15 m/s). If the sharp corner in the power curve is moved to a higher rated 
wind speed v
R
, i.e. if a bigger generator is installed, the annual energy yield is in-
creased only slightly. 
This is shown even more clearly in Fig. 15-24 where the annual energy yield  - 
which contains a lot of partial load hours - is converted into the full load equiva-
lence (i.e. capacity factor) which is the ratio of the annual energy yield E
a
 to the 
product of rated power and the time period of a year: E
a
.
v
.
R
 
= P
R
  8,760 h. The 
curves of full load equivalence versus the ratio of the rated wind speed to the  
annual mean wind speed, v
R 
/ 
v
 in Fig. 15-24 reveal the following: