Environmental Engineering Reference
In-Depth Information
F
3
ð
s
Þ¼
H
ð
s
Þ¼¼
X
r
ð
s
Þ
T
gd
ð
s
Þ
¼
A
T
ð
s
Þ
Q
ð
s
Þ¼
A
T
ð
s
Þ
n
l33
ð
s
Þ
½
rad/s
½
Nm
;
ð
14
:
37b
Þ
d
tf
ð
s
Þ
14.4.3 Rotor Speed Versus Wind Speed Transfer Function
F
1
(S)
The gain of the rotor-speed versus wind-speed transfer function X
rs
(s)/v
1
(s) is
identified experimentally by changing the wind speed to different values—see
Fig.
14.15
a-c for v
1m
= 3.68, 4.22 and 4.75 m/s, t \ 30 s-, v
1
= v
1m
+ v
1a
sin(2pft+ h), as shown in Eq. (14.38).
X
rs
ð
s
Þ
v
1
ð
s
Þ
¼
k
wv
s
1
s
þ
1
ð
14
:
38a
Þ
where: k
wv
¼
160
:
87; s
1
¼
1
:
35 s, v
1a
= 0.125 m/s, f = 0.2 Hz, h = 58, X
rs
in
rpm and v
1
in m/s.
The plant F
1
(s) in Fig.
14.14
and expressions (
14.27
) and (
14.28
) are (metric
system):
F
1
ð
s
Þ¼
D
1
ð
s
Þ¼
X
r
ð
s
Þ
k
wv
s
1
s
þ
1
c
2
;
½
rad/s
½
m/s
v
1
ð
s
Þ
¼
ð
14
:
38b
Þ
14.5 Control System Design
14.5.1 Rotor Speed Control System
The Quantitative feedback theory (QFT)—see [
2
-
4
]—has demonstrated to be an
excellent controller design methodology to deal with the compromises between
several, often conflicting, performance specifications, model uncertainty, and
practical implementation. Its transparent design process allows the designer to
consider all these compromises simultaneously, and to find the controller that
satisfies the set of requested performance specifications for every plant within the
model uncertainty while using the minimum amount of feedback. In this section,
we present the QFT design of the controller to regulate the rotor speed of the wind
turbines with the pitch angle actuators.
14.5.1.1 Control Objectives and Configuration
The main objective of the pitch control system (see Fig.
14.10
in Region 3) is: (a)
to regulate the rotor speed at the rated (nominal) value X
r
= X
r-ref
; (b) to reject the
