Environmental Engineering Reference
In-Depth Information
not contribute to the shift according to (11.10). Hence, the root-mean-square value of the
shift is
1
2
31
2
j
E
=
j
=
1
ε
j
2
π
fI
j
31
j
=
=
2
·
1
2
ω
i
C
N
π
f
31
j
=
1
2
j
2
I
j
.
=
ω
2
i
C
N
Another important issue in engineering is how the control signal
u
N
behaves. The transfer
function from
i
N
to
u
N
is
sL
N
(
sK
i
C
N
+
K
v
)
T
u
(
s
)
=
s
2
L
N
C
N
+
sK
i
C
N
+
K
v
o
)
sL
N
(
s
ω
i
+
ω
=
o
.
(11.12)
s
2
+
s
ω
i
+
ω
Moreover, when
ω
o
=
ω
i
,
s
(
s
+
ω
i
)
T
u
(
s
)
=
i
ω
i
L
N
.
2
s
2
+
s
ω
i
+
ω
The Bode plot is shown in Figure 11.8. There is a small peak of about 3 dB near
ω
o
. This does
not cause a large control signal
u
N
. In the frequency range under consideration, the control
signal can be calculated as
u
N
≈
2
π
f
N
L
N
I
N
,
(11.13)
where
f
N
is the frequency of the neutral current
i
N
with a peak value of
I
N
(assuming there
is only one frequency component to simplify the exposition). This coincides with the analysis
ω
i
60
ω
o
=
ω
i
40
ω
o
=0.5
ω
i
20
0
-20
10
1
10
2
10
3
Frequency(rad/sec)
10
4
10
5
Figure 11.8
Frequency response from
i
N
to control signal
u
N
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