Environmental Engineering Reference
In-Depth Information
Figure 12.1
Independently-controlled neutral leg under consideration
1
Note that
V
a
v
e
is half of the voltage shift
ε
defined in the previous chapter, i.e.
V
a
v
e
=
2
ε
.
According to Kirchhoff's laws, there are
di
L
dt
+
u
N
=
L
N
R
N
i
L
,
i
N
=
i
L
+
i
c
(12.3)
where
R
N
is the equivalent series resistance of the inductor, and
C
N
1
dV
+
C
N
2
dV
−
i
c
=
dt
+
dt
.
(12.4)
Actually, (12.1) and (12.2) determine the coordinate transformation
V
V
−
0
V
DC
V
a
v
e
.
51
=
.
−
0
.
51
Hence, (12.4) can be re-formulated as
C
N
2
)
dV
a
v
e
dt
C
N
1
−
C
N
2
dV
DC
dt
i
c
=
(
C
N
1
+
+
.
2
Define a new voltage variable (actually, a disturbance signal)
C
N
1
−
C
N
2
V
DC
2
.
V
0
=−
(12.5)
C
N
1
+
C
N
2
This reflects the effect of the possibly mismatched capacitors
C
N
1
and
C
N
2
and the effect of
the possible variations of
V
DC
. Then the last formula for
i
c
becomes
C
N
2
)
d
(
V
a
v
e
−
V
0
)
i
c
=
(
C
N
1
+
.
(12.6)
dt
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