Environmental Engineering Reference
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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 )
 
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