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in
e
th
e
o
p
ti
m
al
lo
ca
tio
n
s
f
o
r
ca
p
ac
ito
r
p
lace
m
en
tat
c
an
d
id
ate
b
u
s
e
s
f
ir
s
tl
y
a
n
d
t
h
e
n
th
e
o
p
ti
m
al
s
izi
n
g
o
f
ca
p
ac
ito
r
s
is
ca
lcu
lated
.
An
o
th
er
i
s
s
i
m
u
lta
n
eo
u
s
l
y
d
o
n
e
a
d
eter
m
i
n
atio
n
b
o
th
t
h
e
o
p
ti
m
al
lo
ca
tio
n
a
n
d
s
izin
g
o
f
ca
p
ac
ito
r
s
.
R
e
f
er
en
ce
s
[
3
-
5
]
h
av
e
u
s
ed
a
f
u
zz
y
tech
n
iq
u
eto
f
i
n
d
th
e
m
o
s
t
s
u
i
tab
le
p
o
s
itio
n
s
f
o
r
ca
p
ac
ito
r
p
lace
m
e
n
t
w
h
ile
r
ea
l
co
d
ed
g
en
etic
alg
o
r
it
h
m
(
R
C
G
A
)
[
3
]
,
p
ar
ticle
s
w
ar
m
o
p
t
i
m
izatio
n
(
P
SO)
[
4
]
an
d
d
if
f
er
en
tial
e
v
o
lu
tio
n
(
D
E
)
[
5
]
an
d
m
u
lti
ag
e
n
t
P
SO
(
MA
P
SO)
[
5
]
h
av
e
b
ee
n
ap
p
lied
f
o
r
s
izi
n
g
o
f
ca
p
ac
ito
r
s
.
Si
m
ilar
to
m
eth
o
d
s
ab
o
v
e,
r
ef
er
en
ce
s
[
6
-
1
1
]
an
d
[
1
2
]
h
av
e
also
lo
ca
ted
th
e
ca
n
d
id
ate
b
u
s
es
b
y
u
s
i
n
g
lo
s
s
s
e
n
s
it
iv
i
t
y
f
ac
to
r
(
L
SF
)
an
d
th
e
n
th
e
o
p
ti
m
al
ca
p
a
cito
r
s
izes
h
av
e
b
ee
n
d
o
n
e
b
y
t
i
m
e
-
v
ar
y
i
n
g
i
n
er
tia
w
ei
g
h
ti
n
g
P
SO
(
T
VI
W
P
SO)
[
6
]
,
m
ax
i
m
u
m
lo
ad
-
ab
ilit
y
in
d
ex
(
M
L
I
)
[
7
]
,
g
en
etic
al
g
o
r
ith
m
(
G
A
)
[
8
]
,
in
er
tia
w
ei
g
h
ti
n
g
P
SO
(
I
W
P
SO)
[
9
]
,
an
t
co
lo
n
y
o
p
ti
m
iz
atio
n
(
A
C
O)
al
g
o
r
it
h
m
[
1
0
]
,
m
o
d
if
ied
h
ar
m
o
n
y
alg
o
r
ith
m
(
MH
A
)
[
1
1
]
an
d
ar
tif
icia
l
b
ee
co
lo
n
y
alg
o
r
it
h
m
(
A
B
C
)
[
1
2
]
.
Dis
s
i
m
ilar
to
th
e
p
r
ev
io
u
s
m
eth
o
d
s
,
teac
h
i
n
g
lear
n
i
n
g
b
ased
o
p
tim
izatio
n
(
T
L
B
O)
[
1
3
]
,
h
y
b
r
id
m
e
th
o
d
o
f
ch
ao
tic
s
ea
r
ch
,
o
p
p
o
s
itio
n
-
b
ased
lear
n
in
g
,
DE
an
d
q
u
an
t
u
m
m
e
ch
an
ic
s
(
HC
ODE
Q)
[
1
4
]
,
p
a
r
ticle
s
w
ar
m
o
p
ti
m
izat
io
n
ap
p
r
o
ac
h
es
(
P
SOs
)
[
1
5
]
an
d
f
lo
w
er
p
o
llin
atio
n
alg
o
r
it
h
m
(
FP
A
)
[
1
6
]
h
av
e
s
o
lv
ed
s
u
ch
OC
L
SD
p
r
o
b
lem
b
y
co
n
s
id
er
in
g
lo
ca
tio
n
s
an
d
s
ize
o
f
ca
p
ac
ito
r
as
co
n
tr
o
l
v
ar
iab
les
o
f
ea
ch
s
o
l
u
tio
n
.
O
n
th
e
o
th
er
h
a
n
d
,
v
o
lta
g
e
en
h
an
ce
m
e
n
t
ca
n
b
e
r
ea
ch
ed
b
y
u
s
in
g
w
in
d
tu
r
b
in
es
an
d
p
h
o
to
v
o
ltaic
s
y
s
te
m
s
[
1
7
,
1
8
]
,
n
et
w
o
r
k
r
ec
o
n
f
i
g
u
r
atio
n
[
1
9
-
2
1
]
,
an
d
d
is
tr
ib
u
ted
g
en
er
ato
r
s
[
2
2
]
.
I
n
th
is
p
ap
er
,
MSA
i
s
ap
p
lied
to
OC
L
SD
p
r
o
b
le
m
.
T
h
e
r
esu
lts
o
b
tai
n
ed
f
r
o
m
MS
A
ar
e
co
m
p
eted
w
it
h
th
e
l
atel
y
r
ep
o
r
ted
r
esu
lts
.
Mo
th
s
w
ar
m
al
g
o
r
ith
m
(
MS
A
)
w
as
e
v
o
lv
ed
b
y
A
l
-
Attar
A
li
Mo
h
a
m
ed
in
2
0
1
7
[
2
3
]
an
d
em
p
lo
y
ed
f
o
r
s
o
lv
i
n
g
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
s
s
u
c
h
as
co
m
b
in
ed
ec
o
n
o
m
ic
an
d
e
m
is
s
io
n
d
is
p
atc
h
[
2
4
]
an
d
im
ag
e
s
e
g
m
e
n
tatio
n
[
2
5
,
2
6
]
.
I
n
s
u
m
m
ar
y
,
t
h
e
n
o
v
e
lt
y
a
n
d
co
n
tr
ib
u
tio
n
of
th
e
p
ap
er
ar
e
as f
o
llo
w
s
:
T
h
e
f
ir
s
t a
p
p
licatio
n
o
f
MS
A
f
o
r
d
if
f
er
en
t c
ase
o
f
in
s
talli
n
g
c
ap
ac
ito
r
s
in
r
ad
ial
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
De
m
o
n
s
tr
atio
n
o
f
th
e
e
f
f
ec
ti
v
e
n
es
s
o
f
th
e
n
u
m
b
er
o
f
ca
p
ac
ito
r
s
f
o
r
v
o
ltag
e
e
n
h
a
n
ce
m
e
n
t
Sh
o
w
a
d
etail
o
f
MS
A
p
r
o
ce
d
u
r
e
f
o
r
u
p
d
atin
g
n
e
w
s
o
lu
tio
n
s
Su
cc
es
s
f
u
l
l
y
ap
p
l
y
M
S
A
f
o
r
s
o
lv
in
g
O
C
L
SD p
r
o
b
le
m
MS
A
ca
n
r
ea
ch
h
i
g
h
er
q
u
al
it
y
s
o
lu
tio
n
s
t
h
an
o
th
er
o
n
e
s
.
2.
M
O
DE
L
O
F
T
H
E
O
C
L
SD
P
RO
B
L
E
M
2
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n
C
o
n
n
ec
ti
n
g
s
er
ies
ca
p
ac
ito
r
s
o
r
p
ar
allel
ca
p
ac
ito
r
s
to
t
h
e
b
u
s
es
o
f
d
i
s
tr
ib
u
tio
n
s
y
s
te
m
ca
n
s
ig
n
i
f
ica
n
tl
y
r
ed
u
ce
to
tal
ac
ti
v
e
p
o
w
er
lo
s
s
es
as
w
ell
as
en
h
a
n
ce
to
th
e
o
p
er
atio
n
s
tab
ilit
y
o
f
th
e
p
o
w
er
s
y
s
te
m
.
So
,
m
in
i
m
izi
n
g
to
tal
ac
tiv
e
p
o
w
er
lo
s
s
e
s
(
PL
)
is
a
k
e
y
d
u
t
y
i
n
ad
d
r
ess
in
g
OC
L
SD
p
r
o
b
lem
.
I
ts
m
at
h
e
m
at
ical
f
o
r
m
u
la
is
g
i
v
en
b
y
2
1
M
i
n
i
m
i
z
e
Nb
cc
c
P
L
I
R
(
1
)
2
.
2
.
Co
ns
t
ra
ints
2
.
2
.
1
.
Co
ns
t
ra
ints o
f
ba
la
ncing
po
w
er
s
y
s
t
e
m
I
n
d
is
tr
ib
u
tio
n
s
y
s
te
m
,
s
u
m
o
f
to
tal
lo
ad
d
e
m
a
n
d
an
d
ac
tiv
e
p
o
w
er
lo
s
s
esi
n
li
n
es
m
u
s
t
b
e
eq
u
al
to
g
en
er
atio
n
p
o
w
er
as
f
o
llo
w
s
:
G
P
L
D
P
L
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
0
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
4
5
1
4
-
4521
4516
2
.
2
.
2
.
T
he
v
o
lt
a
g
e
re
s
t
rict
i
o
n
T
h
e
v
o
ltag
e
at
b
u
s
e
s
is
li
m
ited
b
y
it
s
lo
w
er
b
o
u
n
d
an
d
u
p
p
er
b
o
u
n
d
b
elo
w
:
m
in
m
a
x
;
1
,
.
.
.
,
i
b
u
s
V
V
V
i
N
(
3
)
2
.
2
.
3
.
Ca
pa
cit
o
r
s
ize
re
s
t
rict
i
o
n
Selectin
g
s
ize
o
f
ca
p
ac
ito
r
s
f
o
r
co
n
n
ec
ti
n
g
to
d
is
tr
ib
u
tio
n
s
y
s
te
m
ca
n
r
ed
u
ce
p
o
w
er
lo
s
s
o
r
lead
to
o
v
er
co
m
p
e
n
s
atio
n
.
Su
c
h
o
v
er
co
m
p
en
s
atio
n
n
o
t
o
n
l
y
m
ak
e
p
o
w
er
lo
s
s
ex
tr
a
b
u
t
al
s
o
p
ar
tly
i
m
p
ac
t
s
o
n
th
e
s
tab
ilit
y
o
f
t
h
e
s
y
s
te
m
.
I
n
th
is
p
ap
er
,
ca
p
ac
ito
r
s
’
s
ize
an
d
lo
ca
tio
n
ar
e
s
elec
ted
to
b
e
co
n
tr
o
l
v
a
r
iab
les
m
ea
n
w
h
ile
s
ize
is
a
co
n
ti
n
u
o
u
s
v
ar
iab
le
b
u
t
lo
ca
tio
n
i
s
a
d
is
cr
ete
v
ar
iab
le.
Size
o
f
ca
p
ac
ito
r
m
u
s
t
be
r
estricte
d
b
y
t
h
e
m
in
i
m
u
m
an
d
m
ax
i
m
u
m
r
ated
p
o
w
er
o
f
ca
p
ac
ito
r
as th
e
f
o
llo
w
i
n
g
in
eq
u
a
lit
y
:
m
i
n
m
a
x
;
1
,
.
.
.
,
kc
Q
Q
Q
k
N
(
4
)
2
.
2
.
4
.
Rest
rict
io
n o
f
bra
nch
curr
ent
T
h
e
cu
r
r
en
t
r
u
n
n
i
n
g
o
n
b
r
an
c
h
esi
s
eq
u
al
o
r
s
m
aller
t
h
an
t
h
e
m
ax
i
m
u
m
c
u
r
r
en
t
o
f
co
n
d
u
ct
o
r
th
at
ca
n
b
e
s
u
b
j
ec
ted
.
I
t is p
r
esen
ted
as
in
(
5
)
,
m
a
x
;
1
,
.
.
.
,
cc
I
I
c
N
b
(
5
)
3.
M
E
T
H
O
D
3
.
1
.
M
o
t
h
s
w
a
rm
a
lg
o
rit
h
m
I
n
MS
A
[
2
3
]
,
th
e
o
p
ti
m
al
s
o
l
u
tio
n
o
f
t
h
e
co
n
s
id
er
ed
p
r
o
b
le
m
r
elate
d
to
a
li
g
h
t
s
o
u
r
ce
o
f
t
h
e
m
o
o
n
i
s
co
n
s
id
er
ed
as
t
h
eb
est
m
o
t
h
s
w
ar
m
p
o
s
itio
n
an
d
its
f
itn
e
s
s
i
s
th
e
lu
m
i
n
e
s
ce
n
ce
in
ten
s
it
y
o
f
t
h
e
m
o
o
n
.
Fro
m
an
i
n
itial
m
o
t
h
s
i
n
p
o
p
u
latio
n
Gr
,
th
e
y
ar
e
ass
i
g
n
ed
th
r
ee
g
r
o
u
p
s
w
it
h
Gr1
,
Gr2
an
d
Gr3
b
y
b
asin
g
o
n
th
eir
ca
lc
u
lated
f
i
tn
e
s
s
.
I
n
w
h
i
ch
,
m
o
t
h
s
i
n
G
r
1
ar
e
ca
lled
P
a
th
f
in
d
er
s
t
h
at
ta
k
e
o
n
f
i
n
d
in
g
th
e
li
g
h
t so
u
r
ce
s
to
d
ir
ec
t
th
e
s
w
ar
m
,
t
h
o
s
e
f
r
o
m
Gr
2
ar
e
n
a
m
ed
P
r
o
s
p
ec
to
r
s
th
at
f
in
d
t
h
e
f
o
o
d
ac
co
r
d
i
n
g
to
t
h
e
p
o
s
itio
n
s
d
eter
m
in
ed
b
y
P
ath
f
i
n
d
er
s
a
n
d
th
o
s
e
f
r
o
m
t
h
e
last
g
r
o
u
p
ar
e
ca
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NUM
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ize
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ase
2
:
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ate
s
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tal
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o
f
t
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at
th
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d
if
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n
t b
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s
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s
C
ase
3
:
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u
d
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h
e
in
s
tallatio
n
o
f
f
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ca
p
ac
ito
r
s
at
f
o
u
r
d
if
f
er
en
t b
u
s
e
s
C
ase
4
:
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n
s
p
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t
s
f
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v
e
ca
p
ac
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r
s
at
f
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v
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d
if
f
er
e
n
t b
u
s
e
s
.
4
.
1
.
P
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m
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t
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n
T
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p
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w
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lo
s
s
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f
th
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ated
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2
]
.
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h
is
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e
ca
n
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ed
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ce
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ti
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g
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p
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s
.
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n
p
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eter
m
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n
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ate
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it
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th
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2088
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8708
I
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s
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r
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o
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tain
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f
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d
o
th
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m
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ter
m
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a
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a
r
ed
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ctio
n
o
f
p
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(
RPL
)
in
k
W
a
n
d
in
(
%).
C
o
l
u
m
n
3
o
f
th
e
s
e
tab
les
s
h
o
w
s
t
h
at
th
e
p
o
w
er
lo
s
s
es
v
al
u
e
g
o
tten
b
y
MS
A
i
s
al
w
a
y
s
b
etter
t
h
an
o
th
er
m
et
h
o
d
s
f
o
r
all
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s
e
s
.
T
h
at
o
f
MS
A
is
3
2
.
3
1
k
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f
o
r
ca
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1
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0
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r
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is
f
r
o
m
3
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6
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m
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1
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7
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,
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d
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k
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0
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9
6
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f
o
r
ca
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4
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s
v
al
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i
n
g
t
h
e
r
ed
u
ctio
n
o
f
p
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w
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s
s
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MS
A
ca
n
r
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ch
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p
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th
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o
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er
m
eth
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d
s
b
y
f
r
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m
0
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2
9
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k
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m
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k
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1
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,
0
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f
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e
3
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d
f
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o
m
0
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8
k
W
to
1
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2
1
k
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f
o
r
ca
s
e
4
.
T
h
e
r
ed
u
ctio
n
o
f
p
o
w
er
lo
s
s
co
r
r
esp
o
n
d
in
g
to
th
e
i
m
p
r
o
v
e
m
e
n
t
p
er
ce
n
ta
g
e
o
f
MS
A
o
v
er
o
th
er
o
n
e
s
is
p
r
esen
ted
in
co
l
u
m
n
5
o
f
T
ab
les
5
-
8
.
Fro
m
t
h
ese
co
m
p
ar
is
o
n
s
,
it
ca
n
b
e
s
ee
n
th
at
MS
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ca
n
r
ea
ch
b
etter
o
p
ti
m
al
r
es
u
lt
t
h
an
o
t
h
er
m
et
h
o
d
s
f
o
r
all
ca
s
es.
I
n
ad
d
itio
n
,
t
h
e
v
o
lta
g
e
at
b
u
s
es is
also
p
r
ese
n
ted
i
n
Fig
u
r
e
2
.
Su
c
h
f
ig
u
r
e
s
h
o
w
s
t
h
e
i
m
p
r
o
v
e
m
e
n
t o
f
v
o
ltag
e
s
in
ca
s
es
w
ith
o
r
w
it
h
o
u
t i
n
s
ta
ll
in
g
ca
p
ac
ito
r
s
.
T
ab
le
5
.
C
o
m
p
ar
is
o
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et
w
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n
r
esu
lt
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tain
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f
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m
M
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A
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d
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m
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f
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e
1
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e
t
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T
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t
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l
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W
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k
W
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%
H
EM
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2
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8
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T
ab
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6
.
C
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ed
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d
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m
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e
t
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K
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k
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[
8
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1
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3
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3
4
-
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T
ab
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7
.
C
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w
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esu
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b
tain
ed
f
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m
M
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A
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d
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th
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m
e
th
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f
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e
3
M
e
t
h
o
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T
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t
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l
K
V
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k
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%
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[
9
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1
2
0
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3
0
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3
0
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4
1
.
3
2
M
S
A
1
2
5
8
2
9
.
9
0
-
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Dete
r
min
in
g
o
p
tima
l lo
ca
tio
n
a
n
d
s
iz
e
o
f c
a
p
a
cito
r
s
in
…
(
T
h
a
n
h
Lo
n
g
Du
o
n
g
)
4519
T
ab
le
8
.
C
o
m
p
ar
is
o
n
b
et
w
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n
r
esu
lt
s
o
b
tain
ed
f
r
o
m
M
S
A
an
d
o
th
er
m
e
th
o
d
s
f
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r
ca
s
e
4
M
e
t
h
o
d
T
o
t
a
l
K
V
A
R
a
d
d
e
d
P
o
w
e
r
l
o
ss (k
W
)
R
P
L
I
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k
W
R
P
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I
n
%
P
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[
4
]
1
0
2
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3
0
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5
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8
2
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2
D
E
[
5
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1
1
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1
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2
1
3
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9
1
M
S
A
1
2
6
3
2
9
.
7
5
-
-
Fig
u
r
e
2
.
T
h
e
v
o
ltag
e
i
m
p
r
o
v
e
m
en
t
w
it
h
an
d
w
it
h
o
u
t i
n
s
talli
n
g
ca
p
ac
ito
r
s
4
.
2
.
Dis
cu
s
s
io
n
T
h
e
n
u
m
b
er
o
f
ca
p
ac
ito
r
s
in
s
tal
led
o
n
to
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
h
a
s
asig
n
i
f
ica
n
t
i
m
p
ac
t
o
n
r
ed
u
cin
g
th
e
p
o
w
er
lo
s
s
as
w
ell
a
s
i
m
p
r
o
v
i
n
g
t
h
e
q
u
alit
y
o
f
v
o
lta
g
es
at
b
u
s
e
s
i
n
th
e
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
.
T
h
e
s
elec
tio
n
o
f
ca
p
ac
ito
r
n
u
m
b
er
n
ee
d
s
to
b
e
ca
lcu
lated
a
n
d
an
al
y
ze
d
ca
r
ef
u
ll
y
.
Fo
r
t
h
is
v
ie
w,
Fig
u
r
es
3
a
n
d
4
h
a
v
e
b
ee
n
p
l
o
tted
to
s
h
o
w
a
n
alter
atio
n
o
f
p
o
w
er
lo
s
s
v
al
u
es
a
n
d
i
m
p
r
o
v
e
m
e
n
t
o
f
v
o
ltag
e
s
w
it
h
d
if
f
er
e
n
t
n
u
m
b
er
s
o
f
in
s
t
alled
ca
p
ac
ito
r
s
.
A
s
s
h
o
w
n
i
n
Fig
u
r
e
3
,
th
e
v
al
u
e
o
f
p
o
w
er
l
o
s
s
d
ec
r
ea
s
es
f
r
o
m
3
2
.
3
1
k
W
to
2
9
.
7
5
k
W
c
o
r
r
es
p
o
n
d
in
g
to
f
r
o
m
ca
s
e
o
f
ad
d
ed
t
w
o
ca
p
ac
ito
r
s
to
ca
s
e
o
f
ad
d
ed
f
o
u
r
ca
p
ac
ito
r
s
.
On
th
e
o
th
er
h
a
n
d
,
Fig
u
r
e
s
ee
s
v
o
ltag
e
is
also
h
ig
h
l
y
i
m
p
r
o
v
ed
,
n
a
m
el
y
f
r
o
m
0
.
9
6
5
co
r
r
esp
o
n
d
in
g
to
t
w
o
-
ca
p
ac
ito
r
in
s
ta
llatio
n
to
0
.
9
6
9
9
p
u
co
r
r
esp
o
n
d
in
g
to
f
i
v
e
-
ca
p
ac
ito
r
in
s
ta
llatio
n
.
Fig
u
r
e
3
.
T
h
e
ch
an
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e
o
f
p
o
w
e
r
lo
s
s
v
al
u
e
b
y
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I
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2088
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8708
I
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4521
4520
p
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Gr
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CI
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[1
]
S
u
li
m
a
n
,
M
.
Y.,
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Vo
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p
ro
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ter
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trica
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En
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1
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4
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p
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0
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[2
]
Ha
q
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e
.
M
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H,
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lac
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Ka
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Ka
ly
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
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(
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4521
[6
]
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ra
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a
sh
.
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a
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,
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[9
]
El
sh
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A
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A
b
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G
a
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1
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r
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g
(
IJ
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)
,
v
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l
.
7
,
n
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.
6
,
pp.
3226
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3234
,
2
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0
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2
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ter
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3
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4
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6
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Ja
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ter
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p
p
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.
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