Environmental Engineering Reference
In-Depth Information
e
2
k
i
þ
0
:
0068k
116
k
i
C
p
ð
k
;
b
Þ¼
0
:
5176
0
:
4b
5
ð
3
:
4
Þ
where
k
þ
0
:
08b
0
:
035
1
k
i
¼
b
3
þ
1
To obtain the maximum active power extraction from the wind, the power
coefficient Eq. (
3.4
) should be kept the optimal value, i.e.,
dk
C
p
ð
k
;
b
Þ
k
¼
k
opt
d
¼
0
ð
3
:
5
Þ
which can lead to C
pmax
(k
opt
, b) = max{C
pmax
(k, b)} for k = k
opt
.
The optimal maximum output power and torque of a turbine can be obtained,
respectively, as follows from Eqs. (
3.2
), (
3.3
) and (
3.5
):
P
m max
¼
K
opt
x
wopt
ð
3
:
6
Þ
T
m max
¼
K
opt
x
wopt
ð
3
:
7
Þ
where K
opt
is a constant determined by the characteristics of the wind turbine and
given by the following equation:
K
opt
¼
1
2
C
p
ð
k
;
b
Þ
qpr
5
ð
3
:
8
Þ
3.3 Maximum Power Point Tracking
The electrical load of the generator in Fig.
3.1
should be regulated suitably for
maximizing the active power extraction of a wind turbine at any given instant. It
can be neither too large nor too small for a particular wind speed, otherwise the
operating point of the wind turbine will deviate from the optimal power point and
the efficiency of the wind turbine will be lower [
16
]. The wind turbine can only
generate a maximum power for a particular wind speed and can acquire more
power from the wind by decreasing or increasing the load on the generator via
regulating the speed of the generator.
A lot of methods on the MPPT have been proposed. The simplest method is
based on the tip speed of the wind turbine. Assume that the optimal value of the tip
speed ratio can be obtained from Eq. (
3.5
), the optimal speed of the wind turbine
can be calculated from Eq. (
3.14
) by:
