Environmental Engineering Reference
In-Depth Information
• For v
1m
= 3.68 m/s
k
1
¼
4
:
1067
;
x
n1
¼
0
:
675 rad
=
s
;
f
1
¼
0
:
4815
• For v
1m
= 4.22 m/s
k
1
¼
5
:
4756
;
x
n1
¼
0
:
675 rad
=
s
;
f
1
¼
0
:
4815
• For v
1m
= 4.75 m/s
k
1
¼
5
:
4756
;
x
n1
¼
0
:
675 rad
=
s
;
f
1
¼
0
:
4815
• For all v
1
x
n2
¼
5 rad
=
s
;
f
2
¼
0
:
83
;
r
tg
¼
1
=
140
Now, the complete plant F
2
(s) in Fig.
14.14
and expressions (
14.27
) and
(
14.29
) is:
F
2
ð
s
Þ¼
P
ð
s
Þ¼
X
r
ð
s
Þ
b
d
ð
s
Þ
¼
c
2
P
1
ð
s
Þ
r
tg
A
b
ð
s
Þ
c
1
¼
c
2
K
Tb
n
l32
ð
s
Þ
d
tf
ð
s
Þ
½
rad/sec
½
rad
r
tg
A
b
ð
s
Þ
c
1
;
ð
14
:
36
Þ
Figures
14.15
a-c present the first set of experiments for v
1m
= 3.68, 4.22, and
4.75 m/s respectively, and with constant T
gd
. They show (a) the experimental rotor
speed X
rs
in rpm, measured with the rotor speed Glide-Wheel sensor when the
nacelle pitch angle b changes as a step input from 0 to 5; and (b) the estimated
rotor speed using Eq. (
14.34
) for the same pitch angle b.
Figure
14.15
d presents the second set of experiments, with v
1
= 0 and a con-
stant T
gd
, showing (a) the experimental pitch angle b measured with the nacelle
Glide-Wheel sensor when a 0 to 700 step is applied to the actuator input b
di
and
(b) the estimated nacelle pitch angle using Eq. (
14.35
) for the same actuator input
b
di
.
14.4.2 Rotor-Speed Versus Electrical-Torque Transfer
Function F
3
(S)
The dominant dynamics of the rotor-speed versus electrical-torque transfer func-
tion X
rs
(s)/T
g
(s) is identified experimentally by applying step inputs to the elec-
trical torque of the wind turbines under different wind speeds and a constant pitch
angle (see Figs.
14.14
and
14.24
). The experimental rotor speed X
rs
is measured
with the rotor speed Glide-Wheel sensor (in rpm), and the applied electrical torque
