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Based on above analysis the impossible combination was expressed in Table 2.
The symbols
(
)
denote combination type of equivalent
inductance, TSC, FC and PPF. For example the symbol
FC
i i =
1, 2,
, 20, 21
in Table 2 denote
FC
18
following topology sets
(
)
(5)
FC
=
ZZ ZZZ
,
,
,
,
18
TSC
1
TSC
2
Ls
Fc
PPF
Table 2. parameters of a capacitor
+
+
+
+
term
Z
Z
Z
Z
Z
Z
Z
Ls
Fc
Ls
PPF
Ls
Fc
PPF
Z
FC 1
FC 8
FC 15
TSC
1
Z
FC 2
FC 9
FC 16
TSC
2
Z
FC 3
FC 10
FC 17
TSC
3
Z
Z
+
FC 4
FC 11
FC 18
TSC
1
TSC
2
Z
+
Z
FC 5
FC 12
FC 19
TSC
1
TSC
3
Z
Z
+
FC 6
FC 13
FC 20
TSC
2
TSC
3
+
+
FC 7
FC 14
FC 21
Z
Z
Z
TSC
1
TSC
2
TSC
3
The difficulty of proposed device is how to avoid the parallel resonance of
variables of Figure 5 occur in condition of the harmonic currents in Figure2 and Table
I. Considering the Ls is fixed it is necessary to determine the other parameters such
( ) (
)
.
By the thermodynamics modeling method the PPF consists of 5 factors which set is
expressed as
and
C
LC
,
i =
1, 2,3,5
i
i
F
{
}
=
S
contactor 5,fuse5,
L
,
C
(6)
PPF
55
In Eq.(6), considering the factors such as contactor5 fuse5 are linear, their voltage
and current are determined by the L and C by the Kirchhoff law. When
calculating, they can be seen as linear node of directed edge. So the set of the Eq.(6)
can be simplified as
{
}
PPF S L = (7)
Similarly, the basic factors of TSC thermodynamics modeling such as breaker,
(
,
55
)
(
)
(
)
fuse
ii =
1, 2, 3
ki
i =
1, 2, 3
fuse
ii =
1, 2, 3
and
. The factor breaker
can also
be seen as linear node of directed edge. The set of the TSC can be written as
{ } (
)
S L C = = (8)
The basic factors of thermodynamics modeling of the proposed compensation devices
can be expressed as
,
1, 2,3
TSC
i
i
{
} {
} (
)
= = = (9)
According to thermodynamics, under the power constraint E , the set S
SLS S C
,
,
,
LLCC i
,
,
,
1, 2,3,5
s
PPF
TSC
F
s
i
i
F
can be
characterized by the following equations
{
(
)
}
Eui
=
,
,
ui
,
j
=
1,2,3,5
(10)
Ls
C
Lj
Cj
F
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