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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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52
I
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J
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38
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l
s
y
s
t
e
m
in
s
t
a
b
i
li
t
y
[
8
]
,
[
9
]
.
T
h
e
r
e
f
o
r
e
,
b
alan
cin
g
t
h
e
d
c
-
lin
k
ca
p
ac
ito
r
v
o
ltag
e
in
3
L
N
P
C
co
n
v
er
ter
s
is
cr
u
cial
f
o
r
m
ain
tain
in
g
s
y
s
tem
s
tab
ilit
y
an
d
p
er
f
o
r
m
an
ce
,
wh
i
le
v
ar
io
u
s
s
tr
ateg
ies
h
av
e
b
ee
n
d
ev
elo
p
e
d
to
ad
d
r
ess
th
is
ch
all
en
g
e.
Fo
r
in
s
tan
ce
,
Sin
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M)
at
tem
p
ts
to
ac
h
iev
e
n
eu
tr
al
-
p
o
in
t
b
alan
ce
b
y
in
jectin
g
a
ze
r
o
-
s
eq
u
en
ce
s
ig
n
al
in
to
t
h
e
m
o
d
u
latio
n
s
ig
n
al.
Ho
wev
er
,
th
is
ap
p
r
o
ac
h
is
o
f
ten
in
e
f
f
ec
tiv
e
u
n
d
er
d
y
n
am
ic
lo
a
d
co
n
d
itio
n
s
,
lead
in
g
to
in
s
tab
il
ity
an
d
lo
w
-
f
r
eq
u
en
cy
o
s
ci
llat
io
n
s
in
ca
p
ac
ito
r
v
o
ltag
es
[
1
0
]
,
[
1
1
]
.
Similar
ly
,
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
S
VM
)
u
s
es
r
ed
u
n
d
a
n
t
s
witch
in
g
s
tates
to
co
n
tr
o
l
ca
p
a
cito
r
v
o
ltag
es,
b
u
t
its
ef
f
ec
tiv
en
ess
is
lim
ited
b
y
th
e
co
m
p
lex
ity
an
d
co
m
p
u
tatio
n
al
d
em
an
d
s
o
f
t
h
e
alg
o
r
ith
m
[
1
2
]
,
[
1
3
]
.
Oth
e
r
m
eth
o
d
s
,
lik
e
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
PW
M
(
SHE
-
PW
M)
,
tar
g
et
s
p
ec
if
ic
h
ar
m
o
n
ics
b
y
s
o
lv
in
g
n
o
n
-
lin
ea
r
eq
u
atio
n
s
f
o
r
s
witch
in
g
an
g
les.
Alth
o
u
g
h
SHE
-
PW
M
ca
n
im
p
r
o
v
e
v
o
ltag
e
b
ala
n
ce
,
th
e
co
m
p
lex
ity
o
f
r
ea
l
-
tim
e
ca
lcu
latio
n
s
o
f
ten
lim
its
its
ef
f
ec
tiv
en
ess
,
p
ar
ticu
lar
ly
in
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
[
1
4
]
,
[
1
5
]
.
I
n
h
ig
h
-
s
p
ee
d
ap
p
licatio
n
s
,
v
ir
tu
al
s
p
a
ce
v
ec
to
r
m
o
d
u
latio
n
(
VSVP
W
M)
ca
n
r
ed
u
ce
s
witch
in
g
lo
s
s
es
b
u
t
s
tr
u
g
g
les
with
th
e
co
m
p
lex
ity
o
f
r
ea
l
-
tim
e
v
e
cto
r
ad
ju
s
tm
en
ts
,
lead
in
g
to
p
o
ten
tial d
elay
s
in
v
o
l
ta
g
e
b
ala
n
cin
g
[
1
6
]
.
Vir
tu
al
f
lu
x
d
ir
ec
t
p
o
wer
co
n
tr
o
l
(
VFDPC
)
em
er
g
es
as
a
r
o
b
u
s
t
s
o
lu
tio
n
[
1
7
]
,
[
1
8
]
to
th
ese
c
h
allen
g
es.
Un
lik
e
tr
ad
itio
n
al
s
tr
ateg
ies
[
1
9
]
,
VFDPC
d
ir
ec
tly
co
n
tr
o
ls
th
e
p
o
wer
f
lo
w
th
r
o
u
g
h
t
h
e
c
o
n
v
er
ter
,
s
tab
ilizin
g
th
e
n
eu
tr
al
p
o
in
t
v
o
ltag
e
with
o
u
t
r
ely
in
g
o
n
co
m
p
lex
m
o
d
u
l
atio
n
o
r
p
r
ed
ictiv
e
m
o
d
els.
I
n
t
e
g
r
a
t
i
n
g
a
c
a
p
a
c
i
t
o
r
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a
l
a
n
c
i
n
g
s
o
l
u
ti
o
n
w
i
t
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i
n
t
h
e
V
F
DP
C
f
r
a
m
e
w
o
r
k
is
c
r
u
c
i
a
l
f
o
r
t
h
e
s
t
a
b
l
e
o
p
e
r
a
t
i
o
n
o
f
3
L
N
PC
c
o
n
v
e
r
t
e
r
s
.
T
h
e
c
a
p
a
c
i
t
o
r
b
a
l
a
n
ci
n
g
a
l
g
o
r
i
t
h
m
w
o
r
k
s
b
y
a
d
j
u
s
t
i
n
g
t
h
e
r
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d
u
n
d
a
n
t
s
w
it
c
h
i
n
g
s
t
a
t
es
t
o
en
s
u
r
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v
e
n
v
o
l
t
a
g
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d
i
s
t
r
i
b
u
ti
o
n
a
c
r
o
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s
t
h
e
D
C
-
l
i
n
k
c
a
p
a
c
i
t
o
r
s
[
2
0
]
.
T
h
i
s
a
p
p
r
o
a
c
h
h
e
l
p
s
t
o
m
i
t
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g
a
te
t
h
e
a
d
v
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r
s
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f
f
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c
ts
o
f
v
o
l
t
a
g
e
d
r
i
f
t
s
a
n
d
r
i
p
p
l
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s
a
t
t
h
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n
e
u
t
r
al
p
o
i
n
t
,
e
n
s
u
r
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n
g
c
o
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s
t
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t
a
n
d
b
a
l
a
n
c
e
d
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p
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r
a
t
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o
n
[
21
]
.
B
y
m
a
i
n
t
a
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n
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v
o
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d
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a
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ly
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c
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it
h
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d
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b
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t
y
o
f
3
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N
PC
c
o
n
v
e
r
t
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s
[
2
2
]
.
T
h
e
VF
D
PC
m
e
t
h
o
d
p
r
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v
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s
p
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c
i
s
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c
o
n
t
r
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l
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v
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p
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we
r
f
l
o
w
,
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f
f
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c
ti
v
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ai
n
t
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ca
p
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it
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v
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b
al
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,
a
n
d
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d
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s
t
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v
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s
t
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s
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h
i
s
l
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t
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m
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2.
M
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L
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Fig
u
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1
s
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u
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At
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eu
tr
a
l p
o
in
t c
la
m
p
ed
A
C
-
DC
…
(
A
z
z
id
d
in
Mo
h
a
ma
d
R
a
z
a
li)
65
o
n
,
t
h
e
co
n
v
er
ter
in
p
u
t
ter
m
i
n
al
a
is
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n
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ec
ted
to
t
h
e
n
eu
tr
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l
p
o
in
t
th
r
o
u
g
h
o
n
e
o
f
th
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cla
m
p
in
g
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io
d
es.
T
h
e
v
o
ltag
e
ac
r
o
s
s
ea
ch
o
f
th
e
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ca
p
ac
ito
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wh
ich
is
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o
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ally
eq
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al
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o
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t
h
e
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v
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Vd
c.
W
ith
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f
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ite
v
alu
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f
o
r
C
1
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d
C
2
,
th
e
ca
p
ac
ito
r
ca
n
b
e
c
h
ar
g
e
d
o
r
d
is
ch
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e
d
b
y
n
eu
t
r
al
cu
r
r
en
t,
ca
u
s
in
g
n
eu
tr
al
-
p
o
in
t
v
o
ltag
e
d
ev
iatio
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.
T
h
e
s
witch
es
1
,
2
,
̅
1
,
̅
2
,
1
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2
,
̅
1
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2
,
1
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d
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1
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2
ar
e
co
m
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lim
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y
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o
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n
.
Nex
t,
th
e
s
witch
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g
s
tate
d
ef
in
itio
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s
in
NP
C
ar
e
s
h
o
wn
in
T
a
b
le
1
.
T
h
e
ter
m
[
P
]
d
en
o
tes
th
at
th
e
u
p
p
e
r
two
s
witch
es
in
leg
A
ar
e
t
u
r
n
e
d
o
n
.
[
O]
in
d
icate
s
th
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in
n
e
r
two
s
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d
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e
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ar
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o
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er
ate
in
a
co
m
p
lem
en
tar
y
m
an
n
e
r
.
T
ab
le
1
.
Switch
in
g
s
tates f
o
r
NPC
S
w
i
t
c
h
i
n
g
st
a
t
e
S
w
i
t
c
h
i
n
g
st
a
t
u
s (
p
h
a
se
A
)
1
,
2
1
,
2
P
ON
ON
O
F
F
O
F
F
O
O
F
F
ON
ON
O
F
F
N
O
F
F
O
F
F
ON
ON
T
h
e
th
r
ee
-
p
h
ase
3
L
NPC
h
as
a
to
tal
o
f
2
7
co
m
b
i
n
atio
n
s
o
f
s
witch
in
g
s
tates
as
ca
n
b
e
s
ee
n
in
th
e
v
o
ltag
e
v
ec
to
r
s
[
2
3
]
.
T
h
o
s
e
v
ec
to
r
s
ar
e
ar
r
an
g
e
d
in
to
f
o
u
r
ca
teg
o
r
ies,
as
g
iv
en
in
T
ab
le
2
.
T
h
e
2
7
s
witch
in
g
s
tates
li
s
ted
in
th
e
tab
le
co
r
r
esp
o
n
d
to
1
9
v
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ltag
e
v
ec
to
r
s
th
at
ar
e
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ased
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n
th
eir
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a
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n
itu
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(
len
g
th
)
c
o
m
p
u
t
e
th
e
v
ec
to
r
r
e
p
r
esen
tatio
n
in
th
e
s
p
ac
e
v
ec
to
r
[
2
4
]
.
T
h
e
th
e
s
u
b
-
in
d
e
x
L,
M,
a
n
d
S
a
r
e
r
elate
d
to
lar
g
e,
m
e
d
iu
m
,
an
d
s
m
all
v
ec
to
r
s
as illu
s
tr
ated
in
Fig
u
r
e
2
[
2
5
]
.
T
ab
le
2
.
Dif
f
e
r
en
t switch
in
g
s
tates o
f
th
r
ee
-
lev
el
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o
n
v
er
te
r
s
S
w
i
t
c
h
i
n
g
st
a
t
e
s
V
e
c
t
o
r
c
l
a
ss
i
f
i
c
a
t
i
o
n
V
e
c
t
o
r
ma
g
n
i
t
u
d
e
V
0
(
P
P
P
,
N
N
N
,
O
O
O
)
Ze
r
o
v
e
c
t
o
r
0
V
S
_
1
(
P
O
O
/
O
N
N
)
;
V
S
_
2
(
P
P
O
/
O
O
N
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V
S
_
3
(
O
P
O
/
N
O
N
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;
V
S
_
4
(
O
P
P
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O
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V
s_
5
(
O
P
P
/
N
N
O
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;
V
S
_
6
(
P
O
P
/
O
N
O
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mal
l
v
e
c
t
o
r
1
/
3
V
d
V
M
_
1
(
P
O
N
)
;
V
M
_
2
(
O
P
N
)
;
V
M
_
3
(
N
P
O
)
V
M
_
4
(
N
O
P
)
;
V
M
_
1
(
O
N
P
)
;
V
M
_
6
(
P
N
O
)
M
e
d
i
u
m
v
e
c
t
o
r
√
3
/
3
V
d
V
L_
1
(
P
N
N
)
;
V
L
_
2
(
P
P
N
)
;
V
L_
3
(
N
P
N
)
V
L_
4
(
N
P
P
)
;
V
L
_
5
(
N
N
P
)
;
V
L
_
6
(
P
N
P
)
La
r
g
e
v
e
t
o
r
2
/
3
V
d
Fig
u
r
e
2
.
Secto
r
d
ec
o
m
p
o
s
itio
n
o
f
th
r
ee
-
lev
el
s
p
ac
e
v
ec
to
r
d
iag
r
am
3.
T
H
RE
E
-
L
E
VE
L
NP
C
V
I
RT
UAL
-
F
L
U
X
DIR
E
C
T
P
O
WE
R
CO
NT
RO
L
(
3
L
NP
C
V
F
DP
C)
T
h
e
b
lo
c
k
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
VFDPC
in
NPC
AC
-
D
C
co
n
v
er
ter
s
is
s
h
o
wn
i
n
Fig
u
r
e
3
.
I
t
is
ap
p
ar
en
t
to
s
ee
th
at
th
e
v
o
ltag
e
s
en
s
o
r
h
as
b
ee
n
elim
in
ated
.
T
h
e
v
ir
tu
al
f
lu
x
co
n
ce
p
t
f
o
r
m
u
ltil
ev
el
co
n
v
er
ter
s
NPC
to
p
o
lo
g
y
th
e
co
n
v
er
ter
p
o
le
v
o
ltag
e,
V
con,
an
,
V
conv
,
bn
,
an
d
V
conv,
cn
ca
n
b
e
o
b
tain
e
d
b
y
u
s
in
g
th
e
in
p
u
t
f
r
o
m
th
e
s
witch
in
g
s
tates
o
f
t
h
e
co
n
v
er
ter
s
,
S
a1
,
b1,
c1
,
S
a2,
b2,
c2
an
d
ca
p
ac
ito
r
v
o
ltag
es,
v
dc1
,
v
dc2
f
r
o
m
u
p
p
er
a
n
d
lo
wer
.
T
h
en
,
th
e
co
n
v
er
ter
p
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o
lta
g
e,
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con,
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,
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conv,
bn
,
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d
V
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cn
h
as
b
ee
n
tr
an
s
f
o
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ed
f
r
o
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th
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b
c
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r
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n
ce
f
r
am
e
in
to
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αβ
-
r
ef
er
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ce
f
r
am
e
u
s
in
g
C
lar
k
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tr
an
s
f
o
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m
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.
T
h
e
in
p
u
t
f
r
o
m
g
r
id
v
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tu
al
f
lu
x
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cu
r
r
en
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b
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ef
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ce
-
f
r
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e
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u
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m
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th
e
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n
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tan
eo
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P
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ac
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ile,
th
e
r
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r
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r
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b
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m
u
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ly
in
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52
I
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u
r
e
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B
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d
iag
r
am
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o
r
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NPC
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W
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e
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alan
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th
r
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u
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e
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=
3
2
̄
,
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,
∗
(
1
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th
e
d
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iv
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n
o
f
in
p
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e
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u
r
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o
llo
ws:
=
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,
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3
2
{
(
(
̅
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)
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=
3
2
{
|
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(
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k
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t
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[
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[
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3
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(
2
+
2
)
3
2
(
5
)
,
=
2
1
−
(
1
+
1
)
3
1
+
2
2
−
(
2
+
2
)
3
2
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
A
n
a
lysi
s
o
f V
F
DP
C
fo
r
th
r
ee
-
leve
l n
eu
tr
a
l p
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t c
la
m
p
ed
A
C
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DC
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(
A
z
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id
d
in
Mo
h
a
ma
d
R
a
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67
n
ex
t
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y
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p
h
ase
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tr
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q
u
an
titi
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abc
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c
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d
i
n
ates
wh
ich
ar
e
d
ef
in
ed
b
y
x
a,
b,
c
ca
n
f
u
r
th
er
b
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tr
an
s
f
o
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m
ed
in
to
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co
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d
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ates b
y
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s
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g
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e
tr
an
s
f
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r
m
atio
n
m
atr
ix
.
[
]
=
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
]
th
e
g
r
id
v
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tu
al
f
lu
x
v
ec
to
r
in
a
s
tatio
n
ar
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f
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e
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is
d
ef
in
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d
as
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r
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in
a
s
tatio
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e
f
er
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ce
f
r
am
e
,
as sh
o
wn
in
(
7
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:
,
,
=
∫
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(
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)
by
ap
p
l
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g
t
h
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v
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f
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(
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,
t
h
e
g
r
i
d
v
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ca
n
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e
esti
m
ated
as sh
o
wn
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:
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(
,
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(
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in
p
r
ac
tice,
th
e
v
alu
e
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ter
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f
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esis
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lecte
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ce
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e
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ch
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ctan
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ce
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L
.
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h
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o
r
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i
n
(
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ca
n
b
e
r
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itten
in
th
e
s
tati
o
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ar
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o
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ates
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q
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m
ag
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n
d
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m
p
lex
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es a
s
s
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o
wn
i
n
(
9
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to
(
1
0
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=
∫
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(
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=
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1
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th
en
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h
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at
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g
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h
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(
1
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m
ig
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ate
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et
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ich
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ese
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r
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en
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T
h
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s
,
a
lo
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p
ass
f
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s
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ted
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i
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ato
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wev
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ce
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te
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er
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s
e
it
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ce
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er
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th
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p
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ase
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d
m
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g
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o
f
th
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ir
t
u
al
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o
m
p
o
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ts
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lc
u
latio
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s
.
T
o
m
i
n
im
ize
th
ese
er
r
o
r
s
,
in
(
1
1
)
an
d
(
1
2
)
ar
e
an
aly
ze
d
an
d
ad
o
p
te
d
in
th
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ir
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m
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ce
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u
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w
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ar
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tic
at
all
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r
eq
u
en
cies.
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h
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αβ
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co
m
p
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e
n
ts
o
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th
e
ac
tu
al
co
n
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ter
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l
f
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e
ca
lcu
lated
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ased
o
n
th
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o
p
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at
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g
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eq
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with
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f
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esti
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ate
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n
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ter
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le
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o
wn
in
Fig
u
r
e
4
.
,
=
,
′
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′
(
)
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1
1
)
,
=
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′
(
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(
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Fig
u
r
e
4
.
C
o
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o
l b
lo
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k
s
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ir
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L
NP
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VFDP
C
Hen
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y
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l
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P
in
a
n
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r
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p
o
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,
Q
in
o
f
th
e
PW
M
AC
-
DC
co
n
v
er
ter
in
a
s
tatio
n
ar
y
f
r
a
m
e
ca
n
b
e
wr
itten
as:
=
3
2
(
,
,
−
,
,
)
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
38
,
No
.
1
,
Ap
r
il
20
25
:
63
-
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68
=
3
2
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,
,
+
,
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ac
co
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d
if
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tiatio
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f
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p
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n
b
e
r
ep
r
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ted
as
s
h
o
w
n
in
(
1
5
)
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d
(
1
6
)
,
r
esp
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tiv
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:
=
3
2
(
,
,
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,
,
−
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,
−
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,
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(
15
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=
3
2
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,
,
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,
,
+
,
,
+
,
,
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T
h
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s
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m
is
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wn
in
Fig
u
r
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5
f
o
r
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d
Fig
u
r
e
6
f
o
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s
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p
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p
ar
ticu
lar
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ter
v
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to
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V
n
.
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h
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e
f
o
r
e,
to
g
e
n
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ate
th
e
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t
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p
atib
le
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p
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le
as
s
h
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w
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in
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3
,
th
e
r
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s
e
o
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m
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g
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q
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i
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ch
s
ec
to
r
h
as
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im
p
l
e
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d
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e
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th
e
ch
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g
e
o
f
ac
tiv
e
a
n
d
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e
p
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.
Fo
r
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x
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f
o
r
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e
a
n
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le
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r
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0
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t
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3
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t
h
e
ap
p
licatio
n
o
f
s
h
o
r
t
v
o
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e
v
ec
to
r
s
(
V
S_3
V
S_4
V
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V
S_6
)
,
m
ed
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m
v
o
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e
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ec
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(
V
M_3
V
M_4
V
M_5
)
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lo
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g
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o
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e
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ec
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s
(
V
L_3
V
L_4
V
L_5
)
,
an
d
ze
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o
v
o
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s
(
V
0
V
7
)
ca
p
a
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ce
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f
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itiv
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tim
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er
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th
e
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p
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wer
.
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s
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e
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e
p
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s
to
in
cr
ea
s
e
wh
ile
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o
s
e
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ec
to
r
s
ar
e
ap
p
lied
.
Ho
wev
er
,
th
r
o
u
g
h
th
e
im
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lem
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f
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o
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e
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ec
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(
V
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)
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o
r
s
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o
r
t,
m
ed
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m
(
V
M_6
V
M_1
)
,
an
d
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o
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g
(
V
L_1
V
L_2
)
g
e
n
er
ate
a
n
e
g
ativ
e
-
tim
e
d
er
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ativ
e
th
at
in
ten
d
s
to
d
ec
r
ea
s
e
th
e
ac
tiv
e
p
o
wer
.
T
h
at
in
f
o
r
m
atio
n
i
s
b
ein
g
ap
p
lied
to
th
e
r
em
ain
i
n
g
1
1
s
ec
to
r
s
.
T
h
is
o
p
er
atin
g
is
ca
r
r
y
o
n
f
o
r
th
e
r
e
ac
tiv
e
p
o
wer
c
h
ar
ac
ter
is
tics
wh
en
th
e
im
p
l
em
en
tatio
n
f
r
o
m
s
h
o
r
t
(
V
S_2
V
S_3
V
S_4
)
,
m
ed
iu
m
(
V
M_1
V
M_3
)
,
lo
n
g
(
V
L_2
V
L_3
V
L_4
)
,
an
d
ze
r
o
(
V
0
V
7
)
v
o
ltag
e
v
ec
to
r
s
d
ec
id
e
o
n
to
d
eliv
er
a
p
o
s
itiv
e
tim
e
-
d
er
iv
ativ
e
o
f
r
ea
ctiv
e
p
o
wer
.
T
h
e
n
b
y
a
p
p
ly
in
g
t
h
e
v
o
l
tag
e
v
ec
to
r
s
f
r
o
m
s
h
o
r
t
(
V
S_5
V
S_6
)
,
m
ed
i
u
m
(
V
M_
5
V
M_6
)
,
an
d
lo
n
g
(
V
L_5
V
L_6
)
b
r
in
g
to
a
n
e
g
ativ
e
tim
e
-
d
er
i
v
at
iv
e
wh
ich
r
ed
u
ce
th
e
r
ea
ctiv
e
p
o
wer
.
T
h
e
s
am
e
o
p
er
atin
g
h
as b
ee
n
a
p
p
lied
f
o
r
th
e
r
em
ain
in
g
1
1
s
ec
to
r
s
in
r
e
ac
tiv
e
p
o
wer
d
e
r
iv
ativ
es.
Fig
u
r
e
5
.
Dif
f
e
r
en
tiatio
n
c
h
ar
a
cter
is
tics
u
n
d
er
d
if
f
er
e
n
t v
o
lta
g
e
v
ec
to
r
V
n
f
o
r
ac
tiv
e
p
o
we
r
Fig
u
r
e
6
.
Dif
f
e
r
en
tiatio
n
c
h
ar
a
cter
is
tics
u
n
d
er
d
if
f
er
e
n
t v
o
lta
g
e
v
ec
to
r
V
n
f
o
r
r
ea
ctiv
e
p
o
we
r
4.
T
H
E
P
RO
P
O
SE
D
B
A
L
ANC
E
D
CO
NT
RO
L
S
T
RA
T
E
G
Y
O
p
er
atin
g
a
th
r
ee
-
lev
el
NPC
AC
-
DC
co
n
v
er
ter
in
v
o
lv
es
b
y
a
p
p
ly
in
g
a
s
h
o
r
t
-
am
p
litu
d
e
v
o
ltag
e
v
ec
to
r
,
wh
ich
can
p
o
te
n
tially
d
is
r
u
p
t
th
e
b
alan
ce
b
etwe
en
th
e
u
p
p
er
an
d
lo
wer
ca
p
ac
ito
r
v
o
ltag
es,
s
p
ec
if
ically
V
c1
(
u
p
p
er
ca
p
ac
it
o
r
v
o
ltag
e)
an
d
V
c2
(
lo
wer
ca
p
ac
ito
r
v
o
ltag
e
)
.
T
h
ese
v
o
ltag
e
v
ec
to
r
s
ar
e
r
ep
r
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ted
with
in
an
"in
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h
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a
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n
"
in
th
e
v
o
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g
e
s
p
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e
v
ec
to
r
d
iag
r
a
m
as
s
h
o
wn
in
Fig
u
r
e
2
,
wh
er
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ea
c
h
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ec
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r
o
f
f
er
s
two
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s
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le
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witch
in
g
s
tate
s
:
P
-
ty
p
e
an
d
N
-
ty
p
e.
Selectin
g
th
e
a
p
p
r
o
p
r
iate
s
witch
in
g
s
tate
is
cr
u
cial,
as
P
-
ty
p
e
an
d
N
-
ty
p
e
s
tates p
r
o
d
u
ce
o
p
p
o
s
ite
ef
f
ec
ts
o
n
th
e
ca
p
ac
ito
r
v
o
lta
g
es
as c
an
b
e
s
ee
n
in
T
a
b
le
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
A
n
a
lysi
s
o
f V
F
DP
C
fo
r
th
r
ee
-
leve
l n
eu
tr
a
l p
o
in
t c
la
m
p
ed
A
C
-
DC
…
(
A
z
z
id
d
in
Mo
h
a
ma
d
R
a
z
a
li)
69
T
ab
le
3
.
Switch
in
g
s
tates f
o
r
NPC
Ty
p
e
o
f
sw
i
t
c
h
i
n
g
s
t
a
t
e
S
w
i
t
c
h
i
n
g
st
a
t
e
Ef
f
e
c
t
t
o
w
a
r
d
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
P
-
t
y
p
e
[
P
P
O
]
,
[
P
O
O
]
,
[
P
O
P
]
,
[
O
O
P
]
,
[
O
P
P
]
,
[
O
P
O
]
,
V
1
< V
2
N
-
t
y
p
e
[
O
O
N
]
,
[
O
N
N
]
,
[
O
N
O
]
,
[
N
N
O
]
,
[
N
O
O
]
,
[NON]
V
1
> V
2
T
h
e
P
-
ty
p
e
s
witch
in
g
s
tate
d
ec
r
ea
s
es
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
u
p
p
er
ca
p
ac
ito
r
(
V
c1
)
b
y
ca
u
s
in
g
it
to
d
is
ch
ar
g
e,
w
h
ich
r
esu
lts
in
V
c1
d
r
o
p
p
in
g
b
el
o
w
V
c2
.
I
n
c
o
n
t
r
ast,
th
e
N
-
ty
p
e
s
witch
in
g
s
tate
in
cr
ea
s
es
V
c1
b
y
d
is
ch
ar
g
in
g
th
e
lo
wer
ca
p
ac
it
o
r
(
C
2
)
,
p
o
ten
tially
ca
u
s
in
g
V
c1
to
ex
ce
ed
V
c2
.
T
h
is
v
o
ltag
e
im
b
alan
ce
b
etwe
en
V
c1
an
d
V
c2
ca
n
s
ig
n
if
ican
tly
af
f
ec
t
th
e
c
o
n
v
e
r
ter
’
s
p
er
f
o
r
m
an
ce
an
d
s
tab
ilit
y
.
Ach
iev
in
g
an
d
m
ain
tain
i
n
g
a
b
alan
ce
d
v
o
ltag
e
b
etwe
en
V
c1
an
d
V
c2
is
ess
en
tial
to
av
o
i
d
is
s
u
es
s
u
ch
as
s
h
o
r
t
cir
cu
its
.
T
h
ese
is
s
u
es
ca
n
ar
is
e
if
th
e
v
o
ltag
e
d
if
f
er
e
n
ce
b
etwe
en
th
e
ca
p
ac
ito
r
s
b
ec
o
m
es
to
o
lar
g
e,
lead
in
g
to
p
o
ten
tial
d
am
ag
e
to
th
e
p
o
we
r
s
witch
es
an
d
co
m
p
r
o
m
is
in
g
th
e
co
n
v
e
r
ter
’
s
f
u
n
ctio
n
ality
.
E
f
f
ec
tiv
e
m
an
a
g
em
en
t
o
f
th
e
s
witch
in
g
s
tates
is
th
er
ef
o
r
e
v
ital f
o
r
t
h
e
s
af
e
an
d
ef
f
ic
ien
t o
p
e
r
atio
n
o
f
th
e
c
o
n
v
er
ter
.
T
o
m
itig
ate
th
ese
ch
allen
g
es,
t
h
e
b
alan
cin
g
s
tr
ateg
y
b
lo
ck
d
i
ag
r
am
is
s
h
o
wn
i
n
Fig
u
r
e
7
.
T
h
is
d
iag
r
am
r
ep
r
esen
ts
a
s
ig
n
al
p
r
o
ce
s
s
in
g
o
r
co
n
tr
o
l
s
y
s
tem
m
o
d
el,
wh
e
r
e
two
in
p
u
t
s
ig
n
als,
V
c1
an
d
V
c2
,
ar
e
f
ir
s
t
s
u
b
tr
ac
ted
to
p
r
o
d
u
ce
a
d
if
f
er
e
n
ce
s
ig
n
al
.
T
h
is
d
if
f
er
en
ce
is
th
en
p
ass
ed
th
r
o
u
g
h
a
r
elay
b
l
o
ck
,
wh
ic
h
lik
ely
in
tr
o
d
u
ce
s
d
ec
is
io
n
-
m
ak
in
g
lo
g
ic,
s
u
ch
a
s
ac
tiv
atin
g
o
r
d
ea
ctiv
atin
g
th
e
s
ig
n
a
l
b
ased
o
n
a
s
p
ec
if
ic
th
r
esh
o
ld
,
1
o
r
0
.
T
h
e
co
n
v
er
ted
s
ig
n
al
is
th
e
n
m
u
lt
ip
lied
b
y
a
co
n
s
tan
t
v
alu
e
o
f
1
an
d
an
o
th
er
d
ata
ty
p
e
co
n
v
er
s
io
n
f
o
llo
ws,
p
r
ep
ar
in
g
th
e
s
ig
n
al
f
o
r
o
u
tp
u
t,
wh
ich
is
lab
eled
"Bs
"
to
r
ep
r
esen
ts
th
e
b
alan
cin
g
s
tatu
s
an
d
is
d
ir
ec
te
d
to
th
e
MA
T
L
AB
Fu
n
ctio
n
b
lo
c
k
f
o
r
s
witch
in
g
s
tates.
Fig
u
r
e
7
.
B
lo
ck
d
iag
r
am
f
o
r
b
alan
cin
g
s
tr
ateg
y
A
n
o
p
tim
ized
s
witch
i
n
g
ta
b
le,
p
r
esen
ted
in
T
ab
le
4
,
h
as b
ee
n
d
ev
elo
p
ed
f
o
r
t
h
e
th
r
ee
-
le
v
el
NPC
AC
-
DC
co
n
v
er
ter
.
T
h
is
tab
le
is
th
e
r
esu
lt o
f
ex
ten
s
iv
e
an
aly
s
is
,
tak
in
g
in
to
ac
co
u
n
t th
e
ef
f
ec
ts
o
f
d
if
f
er
en
t v
o
lta
g
e
v
ec
to
r
s
o
n
b
o
th
ac
tiv
e
an
d
r
e
ac
tiv
e
p
o
wer
f
lo
ws,
as
well
a
s
th
eir
im
p
ac
t
o
n
th
e
b
alan
cin
g
s
tatu
s
(
B
s
)
o
f
th
e
ca
p
ac
ito
r
s
.
T
h
e
B
s
p
ar
am
eter
d
ir
ec
ts
th
e
ch
o
ice
o
f
s
witch
in
g
s
tate:
B
s
=
1
in
d
icate
s
th
at
t
h
e
P
-
ty
p
e
s
witch
in
g
s
tate
s
h
o
u
ld
b
e
em
p
lo
y
ed
.
I
n
t
h
is
s
tate,
th
e
u
p
p
er
ca
p
ac
ito
r
v
o
ltag
e
(
V
c1
)
will
d
ec
r
ea
s
e,
h
el
p
in
g
to
p
r
ev
e
n
t
Vc1
f
r
o
m
b
ec
o
m
i
n
g
t
o
o
h
ig
h
r
ela
tiv
e
to
V
c2
.
Mean
wh
ile
,
B
s
=
0
s
ate
s
ig
n
al
th
e
ap
p
licati
o
n
o
f
th
e
N
-
ty
p
e
is
ap
p
r
o
p
r
iate.
Her
e,
th
e
u
p
p
e
r
ca
p
ac
ito
r
v
o
ltag
e
(
V
c1
)
will
in
cr
ea
s
e,
en
s
u
r
in
g
th
at
V
c1
d
o
es
n
o
t
f
all
to
o
lo
w
co
m
p
ar
ed
to
V
c2
.
B
y
u
s
in
g
th
i
s
o
p
tim
ized
s
witch
in
g
tab
le,
t
h
e
co
n
v
e
r
ter
ca
n
d
y
n
am
ically
ad
ju
s
t
th
e
s
witch
in
g
s
tates
to
m
ain
tain
a
b
alan
ce
d
v
o
ltag
e
b
etwe
en
Vc1
an
d
V
c2
.
T
h
is
n
o
t
o
n
ly
p
r
ev
en
ts
p
o
ten
ti
al
s
h
o
r
t
cir
c
u
its
an
d
d
am
ag
e
to
p
o
wer
s
witch
es b
u
t
also
en
s
u
r
es th
e
o
v
e
r
all
s
tab
ilit
y
an
d
ef
f
icien
cy
o
f
th
e
c
o
n
v
e
r
ter
’
s
o
p
er
atio
n
.
T
ab
le
4
.
Switch
in
g
s
tates f
o
r
NPC
P
o
w
e
r
e
r
r
o
r
st
a
t
u
s
S
e
c
t
o
r
p
o
s
i
t
i
o
n
(
θ
n
)
a
n
d
c
o
n
v
e
r
t
e
r
v
o
l
t
a
g
e
v
e
c
t
o
r
(
V
n
)
d
P
d
Q
B
S
θ
1
θ
2
θ
3
θ
4
θ
5
θ
6
θ
7
θ
8
θ
9
θ
10
θ
11
θ
12
0
0
-
V
L
_1
V
M
_1
V
L
_2
V
M
_2
V
L
_3
V
M
_3
V
L
_4
V
M
_4
V
L
_5
V
M
_5
V
L
_6
V
M
_6
0
1
-
V
M
_1
V
L
_2
V
M
_2
V
L
_3
V
M
_3
V
L
_4
V
M
_4
V
L
_5
V
M
_5
V
L
_6
V
M
_6
V
L
_1
1
0
V
S
_5
V
S
_5
V
S
_6
V
S
_6
V
S
_1
V
S
_1
V
S
_2
V
S
_2
V
S
_3
V
S
_3
V
S
_4
V
S
_4
1
OOP
OOP
P
O
P
P
O
P
P
O
O
P
O
O
PPO
PPO
O
P
O
O
P
O
O
P
P
O
P
P
0
NNO
NNO
ONO
ONO
ONN
ONN
OON
OON
NON
NON
NNO
NNO
1
1
V
S
_4
V
S
_4
V
S
_5
V
S
_5
V
S
_6
V
S
_6
V
S
_1
V
S
_1
V
S
_2
V
S
_2
V
S
_3
V
S
_3
1
O
P
P
O
P
P
OOP
OOP
P
O
P
P
O
P
P
O
O
P
O
O
PPO
PPO
O
P
O
O
P
O
0
NNO
NNO
NNO
NNO
ONO
ONO
ONN
ONN
OON
OON
NON
NON
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
38
,
No
.
1
,
Ap
r
il
20
25
:
63
-
75
70
5.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
T
h
e
th
r
ee
-
lev
el
AC
-
DC
co
n
v
er
ter
s
y
s
tem
u
s
in
g
th
e
p
r
o
p
o
s
ed
s
witch
in
g
lo
o
k
-
u
p
tab
le
in
3
L
NPC
VFDP
C
is
s
im
u
lated
in
MA
T
L
AB
/Si
m
u
lin
k
b
lo
ck
d
iag
r
am
.
T
h
e
m
ain
p
ar
a
m
eter
u
s
ed
in
t
h
e
s
im
u
latio
n
is
g
iv
en
in
T
ab
le
5
.
T
h
er
ef
o
r
e
Fig
u
r
e
8
s
h
o
w
th
e
r
esu
lts
th
at
o
b
tain
f
r
o
m
th
e
s
im
u
latio
n
an
d
co
n
s
is
ts
o
f
s
ix
s
u
b
p
lo
ts
f
r
o
m
d
i
f
f
er
en
t
asp
ec
t
o
f
elec
tr
ical
s
ig
n
als.
T
h
e
f
ir
s
t
s
u
b
p
lo
t
Fig
u
r
e
8
(
a)
illu
s
tr
ates
th
e
p
h
a
s
e
v
o
ltag
es
Va
,
Vb
,
an
d
Vc
o
v
e
r
tim
e,
d
ep
icted
as si
n
u
s
o
id
al
wav
ef
o
r
m
s
with
1
2
0
⸰
p
h
ase
s
h
if
ts
,
ch
ar
ac
ter
is
tic
o
f
a
b
alan
ce
d
th
r
ee
-
p
h
ase
AC
s
y
s
tem
.
T
h
e
v
o
ltag
e
s
ex
h
ib
it
co
n
s
is
ten
t
am
p
litu
d
e
an
d
f
r
e
q
u
en
c
y
,
in
d
icatin
g
a
s
tab
le
s
o
u
r
ce
.
Su
b
p
lo
t
Fig
u
r
e
8
(
b
)
s
h
o
ws
th
e
p
h
ase
cu
r
r
en
ts
I
a
,
I
b
,
an
d
I
c
o
v
er
tim
e,
wh
ich
also
f
o
llo
w
s
in
u
s
o
id
al
p
atter
n
s
.
I
n
Fig
u
r
e
8
(
c)
r
ep
r
esen
ts
th
e
u
n
i
ty
p
o
wer
f
ac
t
o
r
o
p
er
atio
n
wh
er
e
th
e
p
h
ase
A
v
o
ltag
e
an
d
c
u
r
r
en
t
ar
e
i
n
p
h
ase.
Me
an
wh
ile,
th
e
esti
m
ated
in
s
t
an
tan
eo
u
s
ac
tiv
e
p
o
wer
an
d
r
e
ac
tiv
e
p
o
wer
ar
e
s
h
o
w
n
in
Fig
u
r
e
8
(
d
)
.
I
t
is
clea
r
to
s
ee
th
at
th
e
r
ea
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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v
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s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
I
n
d
o
n
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J
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g
&
C
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m
p
Sci
,
Vo
l.
38
,
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1
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Ap
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20
25
:
63
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f
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