Environmental Engineering Reference
In-Depth Information
the control systems, we filtered the generator speed measurement for both the
torque and pitch controllers using a recursive, single-pole low-pass filter with
exponential smoothing.
The 5 MW reference wind turbine given by FAST contains a torque controller.
In Region 3, this controller maintains constant the generator power, thus the
generator torque is inversely proportional to the filtered generator speed, or,
s
c
¼
P
ref
x
g
;
ð
15
:
1
Þ
where P
ref
is the reference power and x
g
is the filtered generator speed. This
controller will be referred as the baseline torque controller.
15.5.2 Chattering Torque Control
In this subsection a chattering torque controller is proposed [
15
].
The electrical power-tracking error is defined as
e
¼
P
e
P
ref
;
ð
15
:
2
Þ
where P
e
is the electrical power and P
ref
is the reference power. We impose a first-
order dynamic to this error,
e
¼
ae
K
a
sgn
ð
e
Þ
a
;
K
a
[ 0
;
ð
15
:
3
Þ
and consider that the electrical power is described as [
2
,
3
,
5
,
11
]
P
e
¼
s
c
x
g
;
ð
15
:
4
Þ
where s
c
is the torque control and x
g
is the generator speed. By substitution of
Eqs. (
15.2
) and (
15.4
) into (
15.3
), and assuming that P
ref
is a constant function, we
obtain
s
c
x
g
þ
s
c
x
g
¼
a
ð
s
c
x
g
P
ref
Þ
K
a
sgn
ð
P
e
P
ref
Þ;
which, can also be written as
:
s
c
¼
1
x
g
s
c
ð
ax
g
þ
x
g
Þ
aP
ref
þ
K
a
sgn
ð
P
e
P
ref
Þ
ð
15
:
5
Þ
Theorem 1 The proposed controller 5 ensures finite time stability [
4
]. Moreover,
the settling time can be chosen by properly defining the values of the parameters
a and K
a
.
