Environmental Engineering Reference
In-Depth Information
where P
g
is the power supplied by the electrical generator, g
c
the efficiency
from the output of the generator to the grid connection, q is the air density,
A
r
= p r
2
the rotor effective surface, r
b
the rotor radius, C
p
the aerodynamic
power coefficient (see also Sect.
14.3.3
), v
1
the undisturbed upstream wind
speed, g
g
the electrical generator efficiency, T
r
the mechanical torque at the
shaft due to the wind, X
r
the rotor speed, P
a
the power at the shaft given by
the aerodynamics, and k is the tip speed ratio,
k
¼
X
r
r
b
=
v
1
ð
14
:
8
Þ
• Region 2. It is the transition between a torque control with fixed pitch mode
(Region 1) to a fixed torque with a variable pitch mode (Region 3).
• Region 3. The objective in this region is to limit and control the incoming
power at rated power, regulate the rotor speed and minimize the mechanical
loads. This is done by means of controlling the rotor speed X
r
by changing the
pitch angles b (Pitch control).
• Region 4. An extended mode in very high winds can be obtained by means of
varying the pitch closed-loop performance. Through a rotor speed X
r
limita-
tion, the extreme loads can be reduced.
14.3.2 Power Generation According to the Number of Blades
It is well known that in the ideal scenario of an infinite number of blades and no
losses the upper limit for the aerodynamic rotor power coefficient is the Betz limit:
C
pmax
= 0.593. For a real situation, considering a finite number of blades N,
typical frictional losses, and rotating wakes in the out-coming airflow, the aero-
dynamic power coefficient C
p
is always smaller than the Betz limit. Figure
14.11
a
presents some typical C
p
curves versus the tip speed ratio k and for different pitch
angles b. A numerical approximation of the aerodynamic power coefficient C
p
is
given by the following equations (see [
2
], Chap. 12),
exp
ð
c
5
=
k
i
Þ
c
2
k
i
C
P
k
; ðÞ¼
c
1
c
3
b
c
4
1
ð
14
:
9
Þ
1
k
þ
c
6
b
c
7
b
3
þ
1
k
i
¼
where: c
1
¼
0
:
39 ;
c
2
¼
116 ; c
3
¼
0
:
4 ; c
4
¼
5 ;
c
5
¼
16
:
5 ;
c
6
¼
0
:
089 ;
c
7
¼
0
:
035
The maximum value of these curves (maximum power coefficient C
pmax
)
depends on the number of blades N. An experimental expression that presents the
