Environmental Engineering Reference
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The corresponding plant transfer function is then
=
D
1
D
2
+
A
)
−
1
B
1
B
2
,
P
C
1
(
sI
−
or, in short,
A B
1
B
2
C
1
D
1
D
2
P
=
.
(13.4)
13.2.4 State-space Realisation of the Generalised Plant P
Since there are harmonics in the neutral current, the weighting function
W
can be chosen as a
resonant filter
A
w
B
w
W
=
,
C
w
0
with a high gain at the vicinity of the line frequency while providing small gains at all the
other frequencies. It can be designed to cover the fundamental frequency only or to cover the
fundamental frequency and some harmonic frequencies, e.g. the 3rd and 5th harmonics, as
well. From Figure 13.4, the following equations can be obtained:
A B
1
B
2
C
1
D
1
D
2
i
N
u
y
=
i
C
+
ξ
n
=
ξ
n
+
⎡
⎣
⎤
A
0
B
1
n
i
N
u
B
2
⎦
,
=
(13.5)
ξ
C
1
D
1
D
2
z
1
=
W
(
i
C
+
ξ
n
)
⎡
⎣
⎤
A
w
A
0
B
1
n
i
N
u
B
w
B
2
⎦
=
C
w
0
C
1
ξ
D
1
D
2
⎡
⎤
⎡
⎤
A
0
0
B
1
B
2
n
i
N
u
⎣
⎦
⎣
⎦
,
=
B
w
C
1
A
w
B
w
ξ
B
w
D
1
B
w
D
2
(13.6)
0
C
w
0
0
0
z
2
=
μ
u
.
(13.7)
Combining equations (13.5), (13.6) and (13.7), the realisation of the generalised plant is
obtained as
⎡
⎤
A
0
0
B
1
B
2
⎣
⎦
B
w
C
1
A
w
B
w
ξ
B
w
D
1
B
w
D
2
P
=
0
C
w
0
0
0
.
(13.8)
μ
----------------------------------------------
C
1
0
0
0
0
0
ξ
D
1
D
2
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