Environmental Engineering Reference
In-Depth Information
Fig. 14.25 Experimental
estimation of the C
p
/k
characteristic of the 6-blade
rotor wind turbine, b = 0
Cp = -0.259 Lambda
2
+ 0.640 Lambda + -0.168
0.25
0.2
0.15
0.1
0.05
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
tip speed ratio: Lambda
14.6.4 Estimation of the C
p
/k Characteristic of the 6-Blade
Rotor Wind Turbine
This section estimates the C
p
/k characteristic of a 6-blade wind turbine. For a
constant wind speed v
1m
= 3.65 m/s, pitch angle b = 0 and yaw angle a = 0,
the demanded electrical torque T
gd
of the generator is changed from a minimum to
a maximum value (R
load
= 133 to 0 ohm). As a result the rotor speed X
r
and the
generated power P
g
of the wind turbine change. Knowing the generator efficiency
g
g
at different rotor speeds—Eq. (
14.46
) and Fig.
14.20
a, and using Eq. (
14.7
)
with
r
2
= 0.0531 m
2
,
the
turbine's
parameters
(r
b
= 0.13 m,
A
r
= p
q = 1.225 kg/m
3
),
the
C
p
/k characteristic
of
the
wind
turbine
is
calculated
according to Eq. (
14.47
), as shown in Fig.
14.25
.
P
g
=
g
g
k
¼
X
r
r
b
v
1m
C
p
¼
;
ð
14
:
47
Þ
0
:
5 q A
r
v
1m
The maximum aerodynamic power coefficient is C
pmax
= 0.227 at an optimum
tip-speed ratio k
opt
= 1.224. A second order polynomial approach of the experi-
mental data is shown in Eq. (
14.48
).
C
p
¼
0
:
259 k
2
þ
0
:
640 k
0
:
168
ð
14
:
48
Þ
14.6.5 Power Curve for the 6-Blade Rotor Wind Turbine
After the estimation of the aerodynamic power coefficient at different tip-speed
ratios for a 6-blade rotor wind turbine (C
p
/k characteristic, Sect.
14.6.4
) and the
estimation of the generator efficiency at different rotor speeds—see Eq. (
14.46
)