Environmental Engineering Reference
In-Depth Information
The generalized coordinates q
i
are (see also Fig.
14.12
):
q
¼½
q
i
¼
y
t
T
½
c
r
h
g
h
l
ð
14
:
12
Þ
where y
t
is the axial displacement of the nacelle, c is the angular displacement of
the blades out of the plane of rotation, h
r
is the rotor angular position, h
g
is the
generator angular position and h
l
the gearbox low-speed shaft position.
The Energy and dissipation function equations, E
k
,E
p
,D
n
are:
E
k
¼
m
1
2
y
t
þ
m
2
2
ð
r
b
c
þ
y
t
Þ
2
þ
I
r
2
h
r
þ
I
g
2
h
g
þ
I
w
2
h
l
ð
14
:
13
Þ
E
p
¼
K
t
2
y
t
þ
N
2
K
b
ð
r
b
c
Þ
2
þ
K
l
ð
h
r
h
l
Þ
2
þ
K
h
2
ð
R
t
h
l
h
g
Þ
2
ð
14
:
14
Þ
2
D
n
¼
B
t
2
y
t
þ
N
2
B
b
ð
r
b
c
Þ
2
þ
B
l
2
ð
h
r
h
l
Þ
2
þ
B
h
ð
R
t
h
l
h
g
Þ
2
ð
14
:
15
Þ
2
Based on Eqs. (
14.11
) through (
14.15
), the state space description for the wind
turbine is (see [
2
], Chap. 12, for details):
x
¼
Ax
þ
Bu; y
¼
Cx
ð
14
:
16
Þ
2
4
3
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
K
t
m
1
NK
b
r
b
m
1
B
t
m
1
NB
b
r
b
m
1
0
0
0
0
0
0
A
¼
K
t
m
1
r
b
ð
m
1
þ
m
2
Þ
NK
b
m
1
m
2
B
t
m
1
r
b
ð
m
1
þ
m
2
Þ
NB
b
m
1
m
2
0
0
0
0
0
0
K
l
I
r
K
l
I
r
B
l
I
r
B
l
I
r
0
0
0
0
0
0
K
h
I
g
K
h
R
t
I
g
B
h
I
g
B
h
R
t
I
g
0
0
0
0
0
0
K
l
þ
K
h
R
t
I
w
B
l
þ
B
h
R
t
I
w
K
l
I
w
K
h
R
t
I
w
B
l
I
w
B
h
R
t
I
w
0
0
0
0
ð
14
:
17
Þ
2
4
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
00
1
m
1
1
r
p
r
b
ð
14
:
18
Þ
B
¼
1
m
1
r
b
ð
m
1
þ
m
2
Þ
r
p
1
00
m
2
r
b
1
I
r
0
0
0
0
I
g
0
0
0
