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: