Environmental Engineering Reference
In-Depth Information
wind disturbances (effect of v
1
variation); and (c) to avoid over-speed situations
(with significant DX
r
) that can be dangerous for the turbine.
Based on Figs.
14.13
and
14.14
and Eqs. (
14.27
)-(
14.3
8), Fig.
14.16
shows a
simplified block diagram for the rotor speed/pitch control system.
14.5.1.2 Modeling
The dynamics between the rotor-speed X
rs
(t), given by the pitch angle sensor at the
nacelle, and the controller signal b
di
(t) at the actuator input was calculated in
Eqs. (
14.34
) and (
14.35
), and is summarized here for convenience—see Eq. (
14.39
).
X
rs
ð
s
Þ½
rpm
b
di
ð
s
Þ½
k
1
1
¼
P
1
ð
s
Þ
r
tg
A
b
ð
s
Þ¼
r
tg
2
þ
2 f
1
s
2
2
þ
2 f
3
s
x
n1
x
n1
þ
1
x
n2
x
n2
þ
1
ð
14
:
39
Þ
with:
k
1
2
5
:
4756
;
4
:
6733
½
10%
;
x
n1
2
0
:
675
10%
½
rad/sec
;
f
1
2
0
:
4815
10%
½
x
n2
¼
5 rad
=
s
;
f
2
¼
0
:
83
;
r
tg
¼
1
=
140
where the rotor-speed X
r
(s) is in rpm (the rotor sensor gives the information in
rpm) and the demanded pitch angle b
di
in degrees (the NXT motor needs degrees).
The QFT templates of this model—Eq. (
14.39
)—, including the parametric
uncertainty, are calculated with the QFT Control Toolbox [
2
,
3
] and are shown in
Fig.
14.17
.
14.5.1.3 Control Specifications
The performance specifications required for the rotor speed controllers include
robust stability and robust disturbance rejection. They are defined in Eqs. (
14.40
)
and (
14.41
).
Specification 1 (Robust Stability).
X
r
ð
jx
Þ
X
r
Pj
ðÞ
Gj
ðÞ
1
þ
Pj
ðÞ
Gj
ðÞ
¼
l
¼
1
:
3
; 8
x
ð
14
:
40
Þ
ref
ð
jx
Þ
This stability specification, l = 1. 3 in magnitude Eq. (
14.40
), is introduced in
the QFT Control Toolbox [
2
,
3
]. It implies a gain margin of 4.95 dB and a phase
margin of 45.23.
