Wind Farm Lab Test-Bench for Research/Education on Optimum Design and Cooperative Control of Wind Turbines - Wind Turbine Control and Monitoring - page 414

2
4

3
5

l 11 ðÞ l 32 ðÞ K FX K TV K FV K TX

ð Þ þ K FV

1 l 32 ðÞ K TX
l 21 ðÞ l 32 ðÞ K FX K TV K FV K TX

ð Þ þ K FV

1 l 32 ðÞ K TX
l 32 ðÞ K TV

D ð s Þ¼ ð 14 : 26 Þ

1 l 32 ðÞ K TX
l 42 ðÞ K TV
1 l 32 ðÞ K TX
l 52 ðÞ K TV
1 l 32 ðÞ K TX

The rotational speed X r of the wind turbine rotor is continuously modified (a)
by the controllers and actuators, which changes the blade pitch angles b d and the
electrical torque T gd ; (b) by the wind speed v 1 ; and (c) through the dynamics of
the rotor speed X r itself (see Fig. 14.13 ).
The transfer functions of the rotor speed X r (s) versus the demanded blade pitch
angle b d (s), the demanded electrical torque T gd (s), and the wind speed v 1 (s), are
(see Fig. 14.13 and Ref. [ 2 ], Chap. 12, for details),

X r ð s Þ¼ F 1 ð s Þ v 1 ð s Þþ F 2 ð s Þ b d ð s Þþ F 3 ð s Þ T gd ð s Þ ð 14 : 27 Þ

where,

F 1 ð s Þ¼ K TV n l32 ð s Þ
d tf ð s Þ

¼ D 1 ð s Þ ð 14 : 28 Þ

F 2 ð s Þ¼ K Tb n l32 ð s Þ A b ð s Þ
d tf ð s Þ

¼ P ð s Þ ð 14 : 29 Þ

F 3 ð s Þ¼ n l33 ð s Þ A T ð s Þ
d tf ð s Þ

¼ H ð s Þ ð 14 : 30 Þ

and,

n l32 ð s Þ¼ I g I w s 4 þð B h I w þ I g B l þ I g B h R t Þ s 3 þð B h B l þ I g K l þ I g K h R t
þ K h I w Þ s 2 þ h B l þ B h K l Þ s þ K h K l

ð 14 : 31 Þ

n l33 ð s Þ¼ B h R t B l s 2 R t ð K h B l þ B h K l Þ s K h R t K l ð 14 : 32 Þ