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h
e
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tec
ti
o
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o
f
p
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l
v
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s
y
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l
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h
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g
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b
il
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e
a
v
y
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s
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st
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ice
s:
th
e
v
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g
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sta
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il
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y
m
a
r
g
in
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c
to
r
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a
n
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e
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o
ll
a
p
se
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re
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ictio
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x
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n
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e
,
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e
p
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im
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e
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tran
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a
l
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ti
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s
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n
d
o
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ti
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siz
e
s.
Tw
o
ty
p
e
s
o
f
F
A
C
T
S
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re
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se
d
in
th
i
s
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re
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r
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CS
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a
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d
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ti
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v
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r
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p
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sa
to
r
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V
C).
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h
e
o
b
je
c
ti
v
e
f
u
n
c
ti
o
n
o
f
t
h
e
p
r
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lem
is
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i
tt
e
d
u
sin
g
p
a
rti
c
le
sw
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r
m
o
p
ti
m
i
z
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ti
o
n
(
P
S
O).
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h
e
p
ro
p
o
se
d
m
e
th
o
d
is
v
e
r
if
ied
u
sin
g
sim
u
latio
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tes
t
o
n
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la
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1
3
2
k
V
n
e
tw
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h
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p
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e
Ir
a
q
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p
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w
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m
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e
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lt
s
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se
rv
e
d
th
a
t
im
p
ro
v
e
m
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n
t
th
e
v
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lt
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g
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sta
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,
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e
v
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p
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n
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n
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re
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se
d
.
K
ey
w
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r
d
s
:
P
SO
SVC
T
C
SC
Vo
ltag
e
s
tab
ili
t
y
i
n
d
ices
W
ea
k
b
u
s
d
etec
tio
n
T
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is i
s
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n
a
c
c
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ss
a
rticle
u
n
d
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r th
e
CC B
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SA
li
c
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se
.
C
o
r
r
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s
p
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A
uth
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r
:
Gh
as
s
an
A
b
d
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Sal
m
an
Dep
ar
t
m
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t o
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E
lectr
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ch
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s
E
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ee
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Un
i
v
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D
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ah
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Di
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r
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ail:
g
h
a
s
s
a
n
p
o
w
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z
@
g
m
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il
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Ma
in
tain
in
g
v
o
ltag
e
s
tab
ilit
y
o
f
th
e
p
o
w
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s
y
s
tem
is
o
n
e
o
f
th
e
m
aj
o
r
p
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lem
s
d
u
e
to
th
e
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r
eq
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en
t
v
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ltag
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llap
s
e
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at
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elate
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ce
s
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o
v
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ad
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s
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tem
s
an
d
ch
an
g
in
g
o
p
er
atin
g
co
n
d
itio
n
s
.
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er
ef
o
r
e,
th
e
v
o
ltag
e
p
o
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t
is
k
n
o
w
n
as
a
h
ea
v
y
lo
ad
ed
p
o
in
t
[
1
-
3
]
.
T
h
e
s
h
o
r
tag
e
in
th
e
ca
p
ab
ilit
y
o
f
th
e
s
y
s
tem
to
m
ee
t
th
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d
em
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d
o
f
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p
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is
th
e
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ain
r
ea
s
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n
o
f
v
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ltag
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p
r
o
f
ile
d
eter
io
r
atio
n
.
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h
e
s
y
s
tem
is
co
n
s
id
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u
n
s
tab
le
w
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v
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m
ag
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itu
d
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s
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e
s
f
o
r
th
e
s
am
e
b
u
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f
th
e
s
y
s
tem
[
4
-
7
]
.
T
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o
r
e,
th
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is
to
id
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s
p
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itiates
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at
th
e
p
r
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b
lem
o
f
v
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s
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.
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h
e
ex
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tin
g
m
eth
o
d
o
f
d
etec
tin
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th
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w
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k
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s
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ar
e
alm
o
s
t
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ased
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v
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in
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ices.
Ho
w
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m
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s
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th
e
s
y
s
tem
s
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r
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[
8
-
1
1
]
.
T
h
e
f
lex
ib
le
alter
n
atin
g
cu
r
r
en
t
tr
an
s
m
is
s
io
n
s
y
s
tem
(
FA
C
T
S)
d
ev
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ca
n
ac
h
iev
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a
s
af
e
an
d
co
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t
-
e
f
f
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tiv
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s
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lu
tio
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if
th
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ar
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ap
p
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o
p
r
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in
s
talled
in
th
e
p
o
w
er
s
y
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tem
.
A
m
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g
th
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en
tire
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C
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th
e
T
h
y
r
is
to
r
co
n
tr
o
lled
s
er
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co
m
p
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s
ato
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an
d
s
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co
m
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ar
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s
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ap
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th
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p
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m
eth
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d
d
u
e
to
th
eir
h
i
g
h
ly
lead
in
g
f
lex
ib
ilit
y
[
1
2
-
1
8
]
.
T
C
SC
as
an
ef
f
icien
t
s
er
ies
co
m
p
en
s
atio
n
co
n
tr
o
ller
ca
n
b
e
u
tili
ze
d
in
tr
an
s
m
is
s
io
n
lin
e,
f
o
r
co
n
tr
o
l
th
e
p
o
w
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f
lo
w
in
p
o
w
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s
y
s
tem
,
w
h
ile
SVC
as
an
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f
icien
t
s
h
u
n
t
co
m
p
en
s
atio
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co
n
tr
o
ller
ca
n
b
e
in
j
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ted
r
ea
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p
o
w
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a
t
b
u
s
es,
f
o
r
ad
j
u
s
ted
th
e
v
o
ltag
es
o
f
p
o
w
er
s
y
s
tem
[
1
9
-
2
1
]
.
A
llo
ca
tin
g
th
ese
FA
C
T
S
d
ev
ices
r
esu
lts
in
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
in
ch
ar
ac
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is
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o
f
v
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ltag
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s
tab
ilit
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ar
g
in
o
f
th
e
lar
g
e
-
s
ca
le
p
o
w
er
s
y
s
tem
s
[
2
2
-
2
6
]
.
I
n
th
e
ex
is
tin
g
liter
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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s
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g
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E
P
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an
d
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
[
2
7
-
3
2
]
.
I
n
th
is
p
ap
er
,
a
P
SO
-
b
ased
m
eth
o
d
o
lo
g
y
is
p
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g
f
o
r
f
in
d
in
g
th
e
o
p
tim
al
s
izes
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d
s
elec
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g
th
e
o
p
tim
al
lo
ca
tio
n
s
o
f
th
e
FA
C
T
S
d
ev
ices
.
Ho
w
ev
er
,
th
is
p
ap
er
f
o
cu
s
es
o
n
th
e
s
ettin
g
an
d
p
lace
m
en
t
o
f
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C
SC
an
d
SVC
co
n
tr
o
ller
,
f
o
r
im
p
r
o
v
em
en
t
th
e
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
o
f
Diy
ala
1
3
2
k
V
p
o
w
er
s
y
s
tem
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
aim
s
to
im
p
r
o
v
e
th
e
v
o
ltag
e
s
tab
ilit
y
o
f
th
e
I
r
aq
i
p
o
w
er
g
r
id
b
y
in
s
tallin
g
th
e
p
r
o
p
o
s
er
FA
C
T
S
d
ev
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in
th
e
w
ea
k
est
b
u
s
ac
co
r
d
in
g
to
its
v
o
ltag
e
s
tab
ilit
y
in
d
ices.
Mu
lti
-
o
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j
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tiv
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is
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e
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s
s
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o
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e
s
tab
ilit
y
m
ar
g
in
,
an
d
th
e
v
o
ltag
e
s
tab
ilit
y
d
ev
iatio
n
ar
e
em
p
lo
y
ed
f
o
r
o
p
tim
izin
g
th
e
o
p
tim
al
lo
ca
tio
n
s
an
d
s
izes
o
f
FA
C
T
S
d
ev
ices.
B
o
th
T
C
SC
an
d
SVC
b
e
ab
le
o
f
im
p
r
o
v
in
g
th
e
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
an
d
th
er
ef
o
r
e,
en
h
an
cin
g
th
e
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
t
h
e
m
at
h
e
m
a
t
ical
f
o
r
m
u
latio
n
o
f
t
h
e
v
o
lta
g
e
s
tab
ilit
y
p
r
o
b
lem
,
th
e
in
d
ice
s
o
f
v
o
lta
g
e
s
tab
ilit
y
,
an
d
t
h
e
m
o
d
eli
n
g
o
f
th
e
F
AC
T
S
d
ev
ices
ar
e
g
iv
en
i
n
s
ec
tio
n
2
,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
f
o
r
m
u
latio
n
o
f
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
w
it
h
th
e
P
SO
al
g
o
r
ith
m
i
s
p
r
esen
ted
i
n
s
ec
tio
n
3
,
s
i
m
u
lat
io
n
test
s
an
d
d
is
c
u
s
s
io
n
ar
e
p
r
o
v
id
ed
in
s
ec
tio
n
4
f
o
ll
o
w
ed
b
y
th
e
co
n
clu
s
io
n
s
in
s
e
ctio
n
5
.
2.
F
O
RM
UL
AT
I
O
N
O
F
VO
L
T
A
G
E
S
T
AB
I
L
I
T
Y
AND
F
ACTS
D
E
V
I
CE
S
T
h
is
s
ec
tio
n
p
r
o
v
id
es
th
e
f
o
r
m
u
las
o
f
m
o
d
elin
g
th
e
tw
o
in
d
ices
o
f
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
w
ith
th
e
d
etec
tio
n
tech
n
iq
u
es
o
f
th
e
w
ea
k
est
b
u
s
an
d
th
e
m
o
d
elin
g
o
f
th
e
tw
o
ty
p
es
o
f
FA
C
T
S
d
ev
ices.
I
n
th
is
p
ap
er
,
th
e
o
v
er
all
p
er
f
o
r
m
an
ce
o
f
p
o
w
er
s
y
s
tem
is
en
h
an
ce
m
en
t
b
y
u
s
in
g
s
er
ies
an
d
s
h
u
n
t
FA
C
T
S
d
ev
ices
w
h
ich
ar
e
th
e
T
C
SC
an
d
SVC
.
2
.
1
.
Vo
l
t
a
g
e
s
t
a
bil
it
y
m
a
rg
in f
a
ct
o
r
(
dS
/dY)
T
h
e
(
d
S/d
Y)
in
d
ex
d
escr
ib
es
th
e
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
b
ased
o
n
T
h
ev
en
in
th
eo
r
em
r
an
g
es
f
r
o
m
0
(
n
o
-
lo
ad
)
to
1
(
v
o
ltag
e
-
co
llap
s
e
p
o
in
t)
.
B
ased
o
n
th
is
in
d
ex
,
th
e
v
o
ltag
e
co
llap
s
e
p
o
in
t
is
r
ea
ch
ed
w
h
en
th
e
(
d
S/d
Y)
f
ac
to
r
is
clo
s
e
to
ze
r
o
.
Hen
ce
,
th
e
w
ea
k
est
b
u
s
in
s
y
s
tem
is
th
e
clo
s
est
o
n
e
to
ze
r
o
.
Ho
w
ev
er
,
th
e
m
o
d
el
is
r
ep
r
esen
ted
b
y
th
e
f
o
llo
w
in
g
eq
u
atio
n
s
[
8
,
9
]
:
=
ℎ
√
ℎ
2
+
2
+
2
ℎ
co
s
(
−
)
(
1
)
T
h
e
lo
ad
is
s
u
p
p
lied
b
y
th
e
ap
p
ar
en
t p
o
w
er
,
=
2
whe
r
e
=
1
=
ℎ
2
ℎ
2
+
2
+
2
ℎ
co
s
(
−
)
(
2
)
=
ℎ
2
(
1
−
ℎ
2
2
)
(
1
+
ℎ
2
2
+
2
ℎ
co
s
(
−
)
)
2
(
3
)
w
h
er
e,
is
th
e
p
h
ase
an
g
le
o
f
im
p
ed
an
ce
ℎ
an
d
is
th
e
p
h
ase
an
g
le
o
f
im
p
ed
an
ce
.
2
.
2
.
Vo
l
t
a
g
e
c
o
lla
ps
e
predict
io
n ind
e
x
(
VCP
I
)
T
h
e
VC
P
I
in
d
ex
is
d
er
iv
ed
f
r
o
m
th
e
b
asic
p
o
w
er
f
lo
w
eq
u
atio
n
to
d
eter
m
i
n
e
th
e
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
.
T
h
e
v
o
ltag
e
co
llap
s
e
p
o
in
t
is
m
et
w
h
en
VC
P
I
f
ac
to
r
is
clo
s
e
to
o
n
e,
an
d
th
e
w
ea
k
est
b
u
s
in
s
y
s
tem
is
th
at
clo
s
est to
o
n
e.
Ho
w
ev
er
,
th
e
m
o
d
el
ca
n
b
e
r
ep
r
esen
ted
as f
o
llo
w
s
[
1
0
,
1
1
]
:
=
1
−
∑
′
=
1
≠
(
4
)
I
n
(
4
)
′
is
r
ep
r
esen
ted
b
y
,
′
=
∑
=
1
≠
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
8
4
-
992
986
I
n
th
is
p
ar
t,
th
e
lo
ad
is
in
cr
ea
s
ed
r
eg
ar
d
in
g
as
lo
ad
in
g
f
ac
to
r
(
)
w
h
ich
lead
s
to
v
o
ltag
e
co
llap
s
e
p
o
in
t o
f
p
o
w
er
s
y
s
tem
s
.
=
,
=
(
6
)
w
h
er
e,
is
th
e
v
o
lta
g
e
p
h
aso
r
at
b
u
s
k
,
is
th
e
v
o
ltag
e
p
h
a
s
o
r
at
b
u
s
m
,
is
th
e
ad
m
itta
n
ce
b
et
w
ee
n
b
u
s
k
an
d
m
,
is
th
e
ad
m
i
ttan
ce
b
et
w
ee
n
b
u
s
k
an
d
j
,
k
is
th
e
m
o
n
ito
r
in
g
b
u
s
,
m
is
th
e
o
th
er
b
u
s
co
n
n
ec
ted
to
b
u
s
k
an
d
is
th
e
lo
ad
in
g
f
ac
to
r
.
2
.
3
.
M
o
dellin
g
o
f
T
CSC
T
h
e
T
C
SC
is
th
e
s
er
ies
ty
p
es
o
f
FA
C
T
S
d
ev
ice
an
d
co
n
n
e
cted
b
etw
ee
n
tw
o
b
u
s
es
s
h
o
w
n
in
Fig
u
r
e
1
.
T
h
e
T
C
SC
o
p
er
ates
eith
er
in
d
u
ctiv
e
o
r
ca
p
ac
itiv
e
b
y
m
o
d
if
icatio
n
t
h
e
r
ea
ctan
ce
o
f
tr
an
s
m
is
s
io
n
lin
e,
an
d
th
e
m
o
d
el
ca
n
b
e
r
ep
r
esen
ted
b
y
th
e
f
o
llo
w
in
g
eq
u
atio
n
s
[
2
3
,
2
8
]
:
=
+
(
7
)
=
∗
(
8
)
−
0
.
8
≤
≤
0
.
2
(
9
)
w
h
er
e,
is
th
e
r
ea
ctan
ce
o
f
th
e
tr
an
s
m
is
s
io
n
lin
e,
is
th
e
T
C
SC
r
ea
ctan
ce
an
d
is
th
e
co
ef
f
icien
t
d
ep
en
d
in
g
o
n
r
ea
ctan
ce
o
f
th
e
tr
an
s
m
is
s
io
n
lin
e
lo
ca
tio
n
.
Fig
u
r
e
1
.
T
C
SC
s
tr
u
ct
u
r
e
m
o
d
el
2
.
4
.
M
o
dellin
g
o
f
SVC
T
h
e
m
o
s
t
p
o
p
u
lar
co
n
f
ig
u
r
atio
n
o
f
s
h
u
n
t
ty
p
e
co
n
n
ec
ted
FA
C
T
S
d
ev
ice
is
th
e
SVC
th
at
is
s
h
o
w
n
in
Fig
u
r
e
2
.
T
h
e
SVC
o
p
er
ates e
ith
er
ca
p
ac
itiv
e
o
r
in
d
u
ctiv
e
b
y
in
j
ec
tio
n
o
r
ab
s
o
r
b
in
g
r
ea
ctiv
e
p
o
w
er
to
th
e
b
u
s
,
an
d
th
e
m
o
d
el
ca
n
b
e
r
ep
r
esen
ted
as f
o
llo
w
s
[
2
3
,
2
8
]
:
=
(
1
0
)
=
−
2
(
1
1
)
−
100
≤
≤
100
(
1
2
)
w
h
er
e,
is
th
e
c
u
r
r
en
t
d
r
a
w
n
b
y
SV
C
,
is
th
e
v
o
lta
g
e
at
k
ith
b
u
s
,
is
t
h
e
s
u
s
ce
p
ta
n
ce
o
f
S
VC
a
n
d
is
th
e
r
ea
cti
v
e
p
o
w
er
in
j
ec
ted
in
to
th
e
b
u
s
(
in
d
u
cti
v
e
o
r
ca
p
a
citiv
e)
.
Fig
u
r
e
2
.
SVC
s
tr
u
ct
u
r
e
m
o
d
el
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
I
mp
r
o
ve
men
t th
e
vo
lta
g
e
s
ta
b
i
lity
ma
r
g
in
o
f I
r
a
q
i p
o
w
er sys
t
em
u
s
in
g
...
(
Gh
a
s
s
a
n
A
b
d
u
lla
h
S
a
lma
n
)
987
3.
P
RO
P
O
SE
D
M
E
T
H
O
DO
L
O
G
Y
I
n
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
th
e
o
p
ti
m
al
lo
ca
tio
n
a
n
d
v
al
u
e
o
f
T
C
SC
an
d
SVC
co
n
tr
o
ller
is
d
eter
m
in
ed
b
y
u
s
i
n
g
P
SO a
lg
o
r
it
h
m
b
ased
o
n
m
u
lti
-
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
.
3
.
1
.
F
o
r
m
ula
t
io
n o
f
m
ulti
-
o
bje
ct
iv
e
f
un
ct
io
ns
T
h
e
o
p
tim
al
s
izi
n
g
a
n
d
lo
ca
t
io
n
o
f
T
C
SC
a
n
d
SV
C
d
ev
i
ce
s
ar
e
f
o
u
n
d
b
ased
o
n
f
o
u
r
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
.
T
h
i
s
p
ap
er
p
r
o
p
o
s
es
i
m
p
r
o
v
ed
f
o
r
m
u
latio
n
s
to
th
at
d
escr
ib
ed
in
[
8
-
1
1
,
2
4
,
2
5
]
.
T
h
e
m
o
d
i
f
icatio
n
s
i
m
p
le
m
en
ted
o
n
t
h
e
tr
ad
itio
n
al
in
d
ice
s
i
s
p
r
o
p
o
s
ed
in
s
u
c
h
a
w
a
y
t
h
at
n
o
r
m
alize
t
h
e
tar
g
et
o
f
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
a
n
d
f
ac
ilit
ate
co
n
v
e
r
g
en
ce
o
f
th
e
p
r
o
b
lem
.
T
w
o
o
f
t
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
s
ar
e
m
i
n
i
m
ized
an
d
t
w
o
f
u
n
ctio
n
s
ar
e
m
a
x
i
m
ized
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
s
ar
e
s
u
m
m
a
r
ized
b
elo
w
:
3
.
1
.
1
.
P
o
w
er
lo
s
s
es ind
ex
(
P
L
I
)
B
ased
o
n
th
is
o
b
j
ec
tiv
e
f
u
n
ct
io
n
,
th
e
ac
ti
v
e
p
o
w
er
lo
s
s
es
ar
e
co
m
p
u
ted
w
it
h
an
d
w
it
h
o
u
t
F
AC
T
S
co
n
tr
o
ller
.
T
h
e
P
L
I
is
m
i
n
i
m
iz
ed
an
d
ca
n
b
e
f
o
r
m
u
la
ted
as [
2
4
,
2
5
]
:
=
∑
[
2
+
2
−
2
c
os
]
=
1
(
1
3
)
=
−
(
1
4
)
w
h
er
e
−
≤
0
.
W
h
er
e,
is
th
e
n
u
m
b
er
o
f
tr
an
s
m
is
s
io
n
li
n
es,
is
th
e
co
n
d
u
ctan
ce
o
f
b
r
an
c
h
b
et
w
ee
n
b
u
s
i
a
n
d
b
u
s
j
,
is
t
h
e
v
o
ltag
e
m
a
g
n
it
u
d
e
at
b
u
s
i
,
is
t
h
e
v
o
ltag
e
m
ag
n
it
u
d
e
at
b
u
s
j
,
is
t
h
e
p
h
ase
an
g
le
d
i
f
f
er
en
ce
,
is
th
e
to
tal
p
o
w
er
lo
s
s
es
w
it
h
T
C
SC
&
SV
C
an
d
is
th
e
to
tal
p
o
w
er
lo
s
s
e
s
w
it
h
o
u
t T
C
SC
&
SV
C
.
3
.
1
.
2
.
Vo
lt
a
g
e
m
a
rg
in ind
e
x
(
VM
I
)
B
ased
o
n
th
is
o
b
j
ec
tiv
e
f
u
n
c
t
io
n
,
th
e
v
o
lta
g
e
p
r
o
f
ile
o
f
lo
ad
b
u
s
es
is
co
m
p
u
ted
,
w
it
h
an
d
w
ith
o
u
t
F
A
C
T
S
co
n
tr
o
ller
.
T
h
e
ac
ce
p
tab
le
v
al
u
es
o
f
b
u
s
v
o
ltag
e
a
r
e
(
1
±
0
.
5
)
.
T
h
e
VM
I
is
m
ax
i
m
ized
a
n
d
ca
n
b
e
f
o
r
m
u
lated
as [
2
4
,
2
5
]
:
=
∑
(
−
)
≠
1
(
1
5
)
w
h
er
e
−
≥
0
.
W
h
er
e,
is
th
e
v
o
ltag
e
m
ag
n
it
u
d
e
w
it
h
T
C
SC
&
SVC
a
n
d
is
th
e
v
o
lta
g
e
m
ag
n
it
u
d
e
w
it
h
o
u
t T
C
S
C
&
S
VC
.
3
.
1
.
3
.
dS
/dY
dev
ia
t
io
n
(
∆dS/
dY)
T
h
is
o
b
j
ec
tiv
e
f
u
n
ctio
n
co
m
p
u
tes
t
h
e
d
ev
iatio
n
o
f
d
S/d
Y
f
o
r
lo
ad
b
u
s
es
w
it
h
a
n
d
w
i
th
o
u
t
F
A
C
T
S
co
n
tr
o
ller
.
T
h
e
∆d
S/d
Y
is
m
a
x
i
m
ized
an
d
ca
n
b
e
f
o
r
m
u
lated
as [
8
,
9
]
:
∆
=
∑
[
(
)
−
(
)
]
≠
1
(
1
6
)
w
h
er
e
(
)
−
(
)
≥
0
.
W
h
er
e,
(
)
is
th
e
Vo
lta
g
e
Stab
ilit
y
Ma
r
g
i
n
Fac
to
r
w
i
t
h
T
C
SC
&
SVC
a
n
d
(
)
is
th
e
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
f
ac
to
r
w
it
h
o
u
t T
C
SC
&
SV
C
.
3
.
1
.
4
.
VCP
I
dev
ia
t
io
n
(
∆V
CP
I
)
T
h
is
o
b
j
ec
tiv
e
f
u
n
ctio
n
co
m
p
u
tes
th
e
d
e
v
iatio
n
o
f
V
C
P
I
f
o
r
lo
ad
b
u
s
es
w
it
h
a
n
d
w
it
h
o
u
t
F
AC
T
S
co
n
tr
o
ller
.
T
h
e
∆V
C
P
I
is
m
i
n
i
m
ized
an
d
ca
n
b
e
f
o
r
m
u
la
ted
as [
1
0
,
1
1
]
:
∆
=
∑
(
−
)
≠
1
(
1
7
)
w
h
er
e
−
≤
0
.
W
h
er
e,
is
th
e
v
o
lta
g
e
co
llap
s
e
p
r
ed
ictio
n
in
d
ex
w
it
h
T
C
SC
&
SV
C
an
d
is
th
e
v
o
ltag
e
co
llap
s
e
p
r
ed
ic
tio
n
in
d
ex
w
it
h
o
u
t
T
C
SC
&
SVC
.
T
h
er
ef
o
r
e,
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
(
J
)
is
g
i
v
e
n
b
y
:
=
0
.
25
∗
(
−
−
∆
+
∆
)
(
1
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
8
4
-
992
988
3
.
2
.
P
a
rt
icle
s
wa
r
m
o
pti
m
iz
a
t
io
n
(
P
SO
)
B
ased
o
n
t
h
e
P
SO
a
lg
o
r
it
h
m
,
th
e
p
ar
a
m
e
ter
s
o
f
ea
c
h
p
ar
ticl
e
ar
e
u
p
d
ated
i
n
ea
c
h
iter
atio
n
ac
co
r
d
in
g
to
th
e
f
o
llo
w
i
n
g
f
o
r
m
u
las t
h
at
ar
e
s
i
m
u
lati
n
g
t
h
e
p
o
s
itio
n
an
d
v
elo
cit
y
o
f
ea
c
h
b
ir
d
in
b
ir
d
s
’
s
w
ar
m
s
[
3
3
-
3
5
]
.
+
1
=
[
+
∅
1
1
(
,
−
)
+
∅
2
2
(
,
−
)
]
(
1
9
)
+
1
=
+
+
1
(
2
0
)
=
2
2
−
∅
−
√
∅
2
−
4∅
,
∅
1
+
∅
2
=
∅
>
4
(
2
1
)
w
h
er
e,
+
1
is
t
h
e
p
o
s
itio
n
o
f
p
ar
ticle
at
k
+1
,
is
th
e
p
o
s
itio
n
o
f
p
ar
ticle
at
k
,
+
1
r
ep
r
esen
t
t
h
e
v
elo
cit
y
o
f
th
e
p
ar
ticle
at
k
+1
,
r
ep
r
ese
n
t
th
e
v
elo
cit
y
o
f
th
e
p
ar
ticle
at
k
,
r
ep
r
esen
t
in
er
tia
w
ei
g
h
t
p
ar
am
eter
,
∅
1
an
d
∅
2
ar
e
t
w
o
p
o
s
i
tiv
e
n
u
m
b
er
s
ca
lled
ac
ce
ler
atio
n
co
n
s
ta
n
t
s
ar
e
u
s
u
all
y
s
et
to
b
e
2
an
d
2
.
1
r
esp
ec
tiv
el
y
,
an
d
1
,
2
ar
e
r
an
d
o
m
n
u
m
b
er
in
t
h
e
in
ter
v
al
[
0
,
1
]
.
3
.
2
.
1
.
P
ro
po
s
ed
a
lg
o
rit
hm
T
h
e
p
r
o
p
o
s
ed
P
SO
-
b
ased
alg
o
r
ith
m
o
f
allo
ca
ti
n
g
an
d
s
izi
n
g
t
h
e
F
AC
T
S
d
ev
ices
f
o
r
im
p
r
o
v
in
g
v
o
ltag
e
s
tab
ilit
y
is
i
m
p
le
m
en
t
ed
as f
o
llo
w
s
[
3
6
-
3
8
]
:
Step
1
:
Sp
ec
if
y
t
h
e
P
SO p
ar
am
eter
s
: i
n
itia
l v
elo
cit
y
,
n
u
m
b
e
r
o
f
p
ar
ticles an
d
m
a
x
iter
atio
n
.
Step
2
:
I
n
itialize
F
AC
T
S lo
ca
tio
n
an
d
s
izi
n
g
f
o
r
ea
ch
p
ar
ticl
e
(
T
C
SC
o
r
SVC
co
n
tr
o
ller
.
Step
3
:
Ru
n
Ne
w
to
n
R
ap
h
s
o
n
p
o
w
er
f
lo
w
p
r
o
g
r
a
m
a
n
d
co
m
p
u
te
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
.
Step
4
:
Dete
r
m
in
e
a
n
d
s
to
r
e
p
b
est an
d
g
b
est
f
o
r
all
p
ar
ticles.
Step
5
:
C
h
ee
k
m
a
x
iter
atio
n
i
s
r
ea
ch
ed
(
Yes o
r
No
)
,
if
Yes g
o
to
s
tep
7
,
w
h
ile
if
No
g
o
to
s
tep
6
.
Step
6
:
Up
d
ate
v
elo
cit
y
a
n
d
p
ar
ticle
p
o
s
itio
n
an
d
r
ep
ea
t th
e
p
r
o
ce
s
s
u
n
ti
l to
r
ea
ch
m
a
x
iter
atio
n
(
g
o
to
s
tep
3
).
Step
7
:
P
r
in
t th
e
s
to
r
e
r
esu
lt (
o
p
ti
m
al
p
lace
m
e
n
t a
n
d
v
al
u
e
o
f
FAC
T
S d
ev
ice)
.
R
eg
ar
d
in
g
T
C
SC
,
t
h
e
p
ar
ticle
s
ar
e
d
ef
in
ed
a
s
a
v
ec
to
r
w
h
ic
h
co
n
tain
s
t
h
e
lo
ca
tio
n
s
o
f
(
li
n
e
n
u
m
b
er
)
an
d
s
izes
o
f
T
C
SC
co
n
tr
o
ller
.
W
h
er
ea
s
,
th
e
SV
C
v
ec
to
r
in
clu
d
es
t
h
e
SV
C
b
u
s
lo
ca
tio
n
s
an
d
th
eir
s
izes
a
s
s
h
o
w
n
b
elo
w
[
6
,
3
2
]
:
:
[
]
(
2
2
)
:
[
]
(
2
3
)
w
h
er
e,
is
t
h
e
li
n
e
lo
ca
tio
n
n
u
m
b
er
o
f
T
C
SC
,
is
th
e
s
izi
n
g
o
f
T
C
SC
,
is
th
e
b
u
s
lo
ca
tio
n
n
u
m
b
er
o
f
SV
C
an
d
is
th
e
s
iz
in
g
o
f
SV
C
.
4.
SI
M
UL
AT
I
O
N
T
E
ST
S
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
e
v
al
u
ated
u
s
in
g
s
i
m
u
latio
n
s
te
s
ts
o
n
Di
y
ala
1
0
-
b
u
s
w
h
ic
h
i
s
a
p
ar
t
o
f
t
h
e
I
r
aq
i
1
3
2
k
V
p
o
w
er
g
r
id
.
T
h
e
s
i
n
g
le
-
li
n
e
d
iag
r
a
m
o
f
t
h
e
te
s
t
s
y
s
te
m
is
s
h
o
w
n
i
n
Fig
u
r
e
3
.
T
h
e
d
at
a
o
f
Diy
al
a
1
0
-
b
u
s
test
s
y
s
te
m
ar
e
g
i
v
en
i
n
[
2
4
-
2
6
]
.
MA
T
L
A
B
R
2
0
1
7
a
is
u
s
ed
f
o
r
i
m
p
le
m
en
t
in
g
t
h
e
a
lg
o
r
it
h
m
.
T
w
o
ca
s
e
s
t
u
d
ies
ar
e
ca
r
r
ied
o
u
t
to
e
v
alu
a
te
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
b
e
f
o
r
e
an
d
af
ter
allo
ca
ti
n
g
o
f
F
A
C
T
S
d
ev
ices:
Fig
u
r
e
3
.
Sin
g
le
-
lin
e
d
ia
g
r
a
m
o
f
d
i
y
ala
1
0
-
b
u
s
s
y
s
te
m
(
1
3
2
k
V)
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
I
mp
r
o
ve
men
t th
e
vo
lta
g
e
s
ta
b
i
lity
ma
r
g
in
o
f I
r
a
q
i p
o
w
er sys
t
em
u
s
in
g
...
(
Gh
a
s
s
a
n
A
b
d
u
lla
h
S
a
lma
n
)
989
4
.
1
.
Det
ec
t
io
n o
f
t
he
w
e
a
k
es
t
bu
s
I
n
o
r
d
er
to
s
tu
d
y
t
h
e
v
o
ltag
e
co
llap
s
e
p
o
in
t
an
d
d
etec
t
w
ea
k
est
b
u
s
in
th
e
s
y
s
te
m
,
t
h
e
v
o
lta
g
e
s
tab
ilit
y
m
ar
g
in
ar
e
ca
r
r
ied
o
u
t
o
n
Di
y
ala
1
0
-
b
u
s
te
s
t
s
y
s
te
m
w
it
h
t
w
o
t
y
p
es
o
f
s
tab
il
it
y
in
d
ex
:
(
d
S/d
Y)
an
d
VC
P
I
.
R
eg
ar
d
in
g
t
h
e
f
ir
s
t
in
d
ex
(
d
S/d
Y)
,
th
e
lo
ad
ad
m
itta
n
ce
o
f
t
h
e
test
s
y
s
te
m
i
s
i
n
cr
ea
s
ed
in
a
r
an
g
e
o
f
s
i
x
s
tep
s
(
f
r
o
m
th
e
b
ase
ca
s
e
o
f
t
h
e
lo
ad
to
s
ix
ti
m
es o
f
th
e
lo
ad
)
.
T
h
e
in
cr
e
m
en
tal
i
n
cr
ea
s
i
n
g
o
f
t
h
e
s
y
s
te
m
’
s
lo
ad
w
h
ile
ap
p
l
y
i
n
g
f
ir
s
t
i
n
d
ex
le
ad
s
to
th
e
r
esp
o
n
s
e
s
h
o
w
n
i
n
Fi
g
u
r
e
4
w
h
ic
h
r
ev
ea
l
s
t
h
e
r
an
k
o
f
th
e
b
u
s
e
s
ac
co
r
d
in
g
th
eir
v
o
ltag
e
co
llap
s
e.
T
h
e
w
ea
k
e
s
t b
u
s
is
t
h
e
clo
s
est o
n
e
to
ze
r
o
w
h
ic
h
i
s
B
L
D
Z
b
u
s
.
On
th
e
o
t
h
er
h
an
d
,
f
o
r
th
e
V
C
P
I
in
d
ex
,
th
e
lo
ad
(
ac
tiv
e
an
d
r
ea
ctiv
e
p
ar
ts
)
o
f
th
e
tes
t
s
y
s
te
m
i
s
in
cr
ea
s
ed
in
s
tep
s
f
r
o
m
t
h
e
b
a
s
e
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ase
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ig
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ai
n
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L
D
Z
b
u
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n
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er
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e
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y
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b
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t F
AC
T
d
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s
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o
w
n
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T
ab
le
1
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Fig
u
r
e
4
.
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S/d
Y
v
s
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ad
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it
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ce
Fig
u
r
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5
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v
s
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ad
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ac
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le
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R
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r
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r
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2
3
4
5
6
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R
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H
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2
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dev
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T
h
e
p
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SO
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ased
alg
o
r
ith
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is
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ted
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o
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lace
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en
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m
ee
t
t
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ti
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iza
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n
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tr
ai
n
t
s
.
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h
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n
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m
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eg
ar
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in
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t
h
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m
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m
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t
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ar
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n
,
b
o
th
T
C
S
C
a
n
d
SVC
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n
tr
o
ller
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e
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lo
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d
in
th
is
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ap
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.
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h
e
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SO
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g
o
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m
i
s
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ate
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d
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n
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y
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i
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m
izi
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g
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h
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o
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j
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(
1
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)
.
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m
th
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s
i
n
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le
-
l
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d
ia
g
r
a
m
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Di
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la
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er
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y
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te
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is
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i
n
Fi
g
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r
e
3
,
all
th
e
s
in
g
le
li
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its
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f
r
o
m
li
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to
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5
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ar
e
ass
ig
n
ed
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ca
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ta
lli
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g
t
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C
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n
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o
ller
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h
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r
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ar
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m
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m
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d
m
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m
u
m
lo
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tio
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n
u
m
b
er
o
f
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esp
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m
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th
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f
r
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m
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m
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ased
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p
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u
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4
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t
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2
9
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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8
8
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8708
I
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t J
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&
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p
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n
g
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Vo
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11
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2
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p
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:
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990
T
h
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e
n
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o
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th
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test
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y
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te
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p
er
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m
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d
u
e
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th
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F
AC
T
S
d
ev
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(
T
C
SC
an
d
SVC
)
is
d
e
m
o
n
s
tr
ated
i
n
t
h
e
Fig
u
r
es
6
an
d
7
u
s
i
n
g
t
h
e
r
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n
s
e
to
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e
t
w
o
in
d
ices
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d
S/d
Y
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d
VC
P
I
)
.
Fro
m
Fig
u
r
e
6
,
it
is
e
v
id
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t
th
a
t
t
h
e
v
o
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s
tab
ilit
y
m
ar
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f
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L
DZ
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ce
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d
d
in
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e.
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n
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h
e
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er
h
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d
,
t
h
e
VC
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also
i
m
p
r
o
v
ed
as it b
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m
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m
o
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s
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le
o
n
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cr
ea
s
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g
as s
h
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w
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g
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r
e
7
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u
r
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6
.
d
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v
s
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m
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at
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L
D
Z
b
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s
Fig
u
r
e
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.
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s
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ad
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g
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at
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L
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s
Fig
u
r
e
8
ill
u
s
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ate
s
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e
b
eh
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v
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r
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f
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h
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o
b
j
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f
u
n
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n
to
d
eter
m
i
n
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t
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o
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ti
m
a
l
v
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s
a
n
d
lo
ca
tio
n
s
o
f
T
C
S
C
an
d
SV
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c
o
n
tr
o
ller
d
u
r
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t
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e
o
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izati
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n
p
r
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ce
s
s
.
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t
ca
n
b
e
o
b
s
er
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ed
th
at
th
e
SV
C
h
a
s
m
i
n
i
m
u
m
a
n
d
f
aster
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n
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g
e
n
ce
co
m
p
ar
ed
w
it
h
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C
SC
to
ac
h
iev
e
t
h
e
o
b
j
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tiv
e
f
u
n
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n
.
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r
th
er
m
o
r
e,
th
e
o
v
er
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p
er
f
o
r
m
a
n
ce
is
i
m
p
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ed
f
o
r
t
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e
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le
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u
s
e
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th
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s
y
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te
m
b
y
e
n
h
an
ce
d
t
h
e
v
o
ltag
e
p
r
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ile,
p
h
a
s
e
an
g
le
d
i
f
f
er
en
ce
an
d
p
o
w
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s
s
es.
Fi
g
u
r
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9
illu
s
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ate
s
th
e
v
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ltag
e
p
r
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f
ile
o
f
th
e
te
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t
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te
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d
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ter
in
s
ta
lli
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g
t
h
e
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AC
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d
ev
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s
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er
e
t
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g
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o
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b
u
s
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L
D
Z
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A
a
n
d
KNK
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ig
n
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ican
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e
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2
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%.
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u
r
e
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.
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er
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ate
o
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o
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j
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n
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Fig
u
r
e
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.
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ltag
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p
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m
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wo
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ir
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tab
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a
r
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in
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ased
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h
e
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et
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ased
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e
P
SO
alg
o
r
it
h
m
p
r
o
v
id
es
v
alid
ate
s
o
lu
tio
n
s
w
h
e
n
i
m
p
le
m
e
n
ted
f
o
r
F
A
C
T
S d
ev
ices o
n
p
o
w
er
s
y
s
te
m
s
.
RE
F
E
R
E
NC
E
S
[1
]
C.
W
.
T
a
y
lo
r,
“
P
o
w
e
r
S
y
ste
m
V
o
lt
a
g
e
S
tab
il
it
y
,
”
Ne
w
Yo
rk
,
M
c
G
r
a
w
-
Hill
,
1
9
9
4
.
[2
]
P
.
Ku
n
d
u
r,
e
t
a
l.
,
“
De
f
in
it
io
n
a
n
d
Clas
si
f
ica
ti
o
n
o
f
P
o
w
e
r
S
y
st
e
m
S
tab
il
it
y
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
1
9
,
p
p
.
1
3
8
7
-
1
4
0
1
,
2
0
0
4
.
[3
]
S
.
Kih
w
e
le,
“
En
h
a
n
c
e
m
e
n
t
o
f
V
o
l
tag
e
S
tab
il
it
y
M
a
rg
in
Us
in
g
F
A
C
T
S
De
v
ice
s
f
o
r
1
3
2
k
V
T
a
n
z
a
n
ia
G
rid
Ne
tw
o
rk
,
”
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
E
lec
tro
n
ics
,
I
n
fo
rm
a
t
io
n
,
a
n
d
C
o
mm
u
n
ica
ti
o
n
,
2
0
1
9
,
p
p
.
1
-
3
.
[4
]
T
.
He
,
e
t
a
l.
,
“
Id
e
n
t
if
i
c
a
ti
o
n
o
f
we
a
k
lo
c
a
ti
o
n
s
in
b
u
lk
tran
sm
is
sio
n
s
y
ste
m
s
u
sin
g
v
o
lt
a
g
e
sta
b
il
it
y
m
a
rg
in
in
d
e
x
,
”
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
Pr
o
b
a
b
il
ist
ic M
e
th
o
d
s
Ap
p
li
e
d
to
Po
w
e
r S
y
ste
ms
,
2
0
0
4
,
p
p
.
8
7
8
-
8
8
2
.
[5
]
S.
A
.
S
o
li
m
a
n
,
e
t
a
l.
,
“
P
o
w
e
r
S
y
ste
m
V
o
lt
a
g
e
S
tab
il
it
y
M
a
rg
in
id
e
n
ti
f
ica
ti
o
n
Us
in
g
L
o
c
a
l
M
e
a
su
re
m
e
n
ts,
”
L
a
rg
e
En
g
i
n
e
e
rin
g
S
y
ste
ms
Co
n
fer
e
n
c
e
o
n
P
o
we
r E
n
g
in
e
e
rin
g
,
2
0
0
3
,
p
p
.
1
0
0
-
1
0
4
.
[6
]
S
.
Ch
a
n
sa
re
e
w
it
ta
y
a
a
n
d
P
.
Jira
p
o
n
g
,
“
P
o
w
e
r
tran
sf
e
r
c
a
p
a
b
il
it
y
e
n
h
a
n
c
e
m
e
n
t
w
it
h
m
u
lt
it
y
p
e
F
A
C
T
S
c
o
n
tro
ll
e
rs
u
sin
g
h
y
b
rid
p
a
rti
c
le sw
a
r
m
o
p
ti
m
iz
a
ti
o
n
,
”
El
e
c
trica
l
E
n
g
in
e
e
rin
g
,
v
o
l.
9
7
,
p
p
.
1
1
9
-
1
2
7
,
2
0
1
5
.
[7
]
S
.
K.
A
.
H
a
ss
a
n
a
n
d
F
.
M
.
T
u
a
i
m
a
h
,
“
Op
ti
m
a
l
lo
c
a
ti
o
n
o
f
u
n
if
ied
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
r
g
e
n
e
ti
c
a
lg
o
rit
h
m
b
a
se
d
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
P
EDS
)
,
v
o
l.
1
1
,
n
o
.
2
,
p
p
.
8
8
6
-
8
9
4
,
2
0
2
0
.
[8
]
A
.
W
isz
n
ie
w
s
k
i,
“
Ne
w
c
rit
e
ria
o
f
v
o
lt
a
g
e
sta
b
il
it
y
m
a
r
g
in
f
o
r
th
e
p
u
rp
o
se
o
f
lo
a
d
sh
e
d
d
in
g
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
Po
we
r De
li
v
e
ry
,
v
o
l.
2
2
,
p
p
.
1
3
6
7
-
1
3
7
1
,
2
0
0
7
.
[9
]
A
.
R.
P
h
a
d
k
e
,
e
t
a
l.
,
“
A
n
e
w
tec
h
n
i
q
u
e
f
o
r
o
n
-
li
n
e
m
o
n
it
o
rin
g
o
f
v
o
lt
a
g
e
sta
b
il
it
y
m
a
r
g
in
u
sin
g
lo
c
a
l
sig
n
a
ls
,
”
i
n
Fi
ft
e
e
n
th
N
a
ti
o
n
a
l
P
o
we
r S
y
ste
ms
Co
n
fer
e
n
c
e
,
2
0
0
8
,
p
p
.
4
8
8
-
4
9
2
.
[1
0
]
V.
Ba
lam
o
u
ro
u
g
a
n
,
e
t
a
l
.
,
“
T
e
c
h
n
i
q
u
e
f
o
r
o
n
li
n
e
p
re
d
ictio
n
o
f
v
o
lt
a
g
e
c
o
ll
a
p
se
,
”
IEE
Pro
c
e
e
d
i
n
g
s
-
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l.
1
5
1
,
2
0
0
4
,
p
p
.
4
5
3
-
4
6
0
.
[1
1
]
M
.
Niz
a
m
,
e
t
a
l
.
,
“
D
y
n
a
m
ic
v
o
lt
a
g
e
c
o
ll
a
p
se
p
re
d
ictio
n
o
n
a
p
ra
c
ti
c
a
l
p
o
w
e
r
s
y
ste
m
u
sin
g
p
o
w
e
r
t
ra
n
sf
e
r
sta
b
il
it
y
in
d
e
x
,
”
IEE
E
5
t
h
S
t
u
d
e
n
t
C
o
n
fer
e
n
c
e
o
n
Res
e
a
rc
h
a
n
d
De
v
e
lo
p
me
n
t
,
2
0
0
7
,
p
p
.
1
-
6
.
[1
2
]
J.
L
a
k
k
ired
d
y
,
e
t
a
l
.
,
“
S
tea
d
y
sta
te
v
o
lt
a
g
e
sta
b
il
it
y
e
n
h
a
n
c
e
m
e
n
t
u
sin
g
sh
u
n
t
a
n
d
se
ries
F
A
CT
S
d
e
v
ice
s,
”
IEE
E
Clem
so
n
Un
ive
rs
it
y
Po
we
r S
y
ste
ms
Co
n
fer
e
n
c
e
,
2
0
1
5
,
p
p
.
1
-
5
.
[1
3
]
A
.
S
o
d
e
-
Yo
m
e
,
e
t
a
l
.
,
“
A
c
o
m
p
r
e
h
e
n
siv
e
c
o
m
p
a
riso
n
o
f
F
A
C
T
S
d
e
v
ice
s
f
o
r
e
n
h
a
n
c
in
g
sta
ti
c
v
o
lt
a
g
e
sta
b
il
it
y
,
”
2
0
0
7
IE
EE
P
o
we
r
En
g
in
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
2
0
0
7
,
p
p
.
1
-
8
.
[1
4
]
M.
A
.
Ka
m
a
rp
o
sh
ti
a
n
d
H.
L
e
sa
n
i,
“
Ef
f
e
c
ts
o
f
S
TAT
COM,
T
CS
C,
S
S
S
C
a
n
d
U
P
F
C
o
n
sta
ti
c
v
o
lt
a
g
e
sta
b
il
it
y
,
”
El
e
c
trica
l
En
g
in
e
e
rin
g
,
v
o
l
.
9
3
,
p
p
.
3
3
-
4
2
,
2
0
1
1
.
[1
5
]
M
.
Zad
e
h
b
a
g
h
e
ri,
e
t
a
l.
,
“
Re
v
ie
w
o
f
th
e
UP
F
C
Diff
e
r
e
n
t
M
o
d
e
ls
i
n
Re
c
e
n
t
Ye
a
rs,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
)
,
v
o
l
.
4
,
n
o
.
3
,
p
p
.
3
4
3
-
3
5
5
,
2
0
1
4
.
[1
6
]
I.
Az
i
m
a
n
d
F
.
Ra
h
m
a
n
,
“
G
e
n
e
ti
c
A
lg
o
rit
h
m
B
a
se
d
Re
a
c
ti
v
e
P
o
w
e
r
M
a
n
a
g
e
m
e
n
t
b
y
S
V
C,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
4
,
n
o
.
2
,
p
p
.
2
0
0
-
2
0
6
,
2
0
1
4
.
[1
7
]
C.
L
i,
e
t
a
l
.
,
“
Op
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
m
u
lt
i
-
ty
p
e
F
A
C
T
S
d
e
v
ice
s
in
p
o
w
e
r
s
y
st
e
m
s
b
a
se
d
o
n
p
o
w
e
r
f
lo
w
e
n
tro
p
y
,
”
J
o
u
rn
a
l
o
f
M
o
d
e
rn
Po
we
r
S
y
ste
ms
a
n
d
Clea
n
E
n
e
rg
y
,
v
o
l.
2
,
p
p
.
1
7
3
-
1
8
0
,
2
0
1
4
.
[1
8
]
N.
Yo
rin
o
,
e
t
a
l.
,
“
A
n
e
w
f
o
r
m
u
latio
n
f
o
r
F
A
CT
S
a
ll
o
c
a
ti
o
n
f
o
r
se
c
u
rit
y
e
n
h
a
n
c
e
m
e
n
t
a
g
a
in
st
v
o
lt
a
g
e
c
o
ll
a
p
se
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
st
e
ms
,
v
o
l.
1
8
,
p
p
.
3
-
1
0
,
2
0
0
3
.
[1
9
]
S
.
M
o
ll
a
z
e
i,
e
t
a
l.
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
iza
ti
o
n
o
f
p
o
w
e
r
s
y
ste
m
p
e
r
f
o
r
m
a
n
c
e
w
it
h
T
CS
C
u
sin
g
th
e
M
O
P
S
O
a
lg
o
rit
h
m
,
”
2
0
0
7
IEE
E
Po
we
r E
n
g
in
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
T
a
m
p
a
,
F
L
,
2
0
0
7
,
p
p
.
1
-
8
.
[2
0
]
R.
M
in
g
u
e
z
,
e
t
a
l.
,
“
Op
ti
m
a
l
Ne
t
w
o
rk
P
lac
e
m
e
n
t
o
f
S
V
C
De
v
ice
s,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
vo
l
.
2
2
,
n
o
.
4
,
p
p
.
1
8
5
1
-
1
8
6
0
,
2
0
0
7
.
[2
1
]
B.
Ku
m
a
r,
e
t
a
l.
,
“
P
lac
e
m
e
n
t
o
f
F
A
C
T
S
c
o
n
tro
ll
e
rs
u
si
n
g
m
o
d
a
l
c
o
n
tro
ll
a
b
il
i
ty
in
d
ice
s
to
d
a
m
p
o
u
t
p
o
w
e
r
s
y
ste
m
o
sc
il
latio
n
s,
”
IET
Ge
n
e
ra
t
io
n
,
T
r
a
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l.
1
,
p
p
.
2
0
9
-
2
1
7
,
2
0
0
7
.
[2
2
]
N.
S
h
a
rm
a
,
e
t
a
l.
,
“
A
n
o
v
e
l
p
lac
e
m
e
n
t
stra
teg
y
f
o
r
F
A
CT
S
c
o
n
tr
o
ll
e
rs,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
De
li
v
e
ry
,
v
o
l.
1
8
,
p
p
.
9
8
2
-
9
8
7
,
2
0
0
3
.
[2
3
]
M.
A
.
Ka
m
a
rp
o
sh
ti
,
e
t
a
l.
,
“
Co
m
p
a
riso
n
o
f
S
V
C,
S
T
AT
COM,
T
CS
C,
a
n
d
U
P
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C
Co
n
tr
o
ll
e
rs
f
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r
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tatic
Vo
lt
a
g
e
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tab
il
it
y
Ev
a
lu
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ted
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y
Co
n
ti
n
u
a
ti
o
n
P
o
w
e
r
F
lo
w
M
e
th
o
d
,
”
IEE
E
8
th
An
n
u
a
l
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
Co
n
fer
e
n
c
e
,
V
a
n
c
o
u
v
e
r,
BC,
2
0
0
8
,
p
p
.
1
-
8
.
[2
4
]
G.
A
.
S
a
l
m
a
n
,
e
t
a
l.
,
“
Im
p
le
m
e
n
tatio
n
Op
ti
m
a
l
L
o
c
a
ti
o
n
a
n
d
S
izi
n
g
o
f
UP
F
C
o
n
Ira
q
i
P
o
w
e
r
S
y
st
e
m
G
rid
(1
3
2
k
V)
Us
in
g
Ge
n
e
ti
c
A
lg
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
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y
ste
ms
(
IJ
PE
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S
)
,
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l.
9
,
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o
.
4
,
p
p
.
1
6
0
7
-
1
6
1
5
,
2
0
1
8
.
[2
5
]
G.
A
.
S
a
l
m
a
n
,
“
I
m
p
le
m
e
n
tatio
n
S
V
C
a
n
d
T
CS
C
to
Im
p
ro
v
e
m
e
n
t
th
e
Eff
ica
c
y
o
f
Di
y
a
la
El
e
c
tri
c
Ne
t
w
o
rk
(1
3
2
k
V
),
”
Ame
ric
a
n
J
o
u
rn
a
l
o
f
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
(
AJER)
,
v
o
l.
4
,
p
p
.
1
6
3
-
1
7
0
,
2
0
1
5
.
[2
6
]
H.
I.
Hu
ss
e
in
,
e
t
a
l.
,
“
P
h
a
se
M
e
a
su
re
m
e
n
t
Un
it
s
b
a
se
d
F
A
C
T
’s
De
v
ice
s
f
o
r
th
e
I
m
p
ro
v
e
m
e
n
t
o
f
P
o
w
e
r
S
y
ste
m
s
Ne
tw
o
rk
s
Co
n
tro
ll
a
b
i
li
ty
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
8
8
8
-
8
9
9
,
2
0
1
8
.
[2
7
]
K.
V
e
n
k
a
tes
w
a
rlu
,
e
t
a
l.
,
“
I
m
p
ro
v
e
m
e
n
t
o
f
V
o
lt
a
g
e
S
tab
il
it
y
a
n
d
Re
d
u
c
e
P
o
w
e
r
L
o
ss
e
s
b
y
Op
ti
m
a
l
P
lac
e
m
e
n
t
o
f
U
P
F
C
d
e
v
ice
b
y
u
sin
g
GA
a
n
d
P
S
O,
”
I
n
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
En
g
in
e
e
rin
g
S
c
ie
n
c
e
s
Res
e
a
rc
h
,
v
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l.
1
,
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o
.
2
,
p
p
.
6
6
-
7
5
,
2
0
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Evaluation Warning : The document was created with Spire.PDF for Python.
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11
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.
2
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r
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2
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992
[2
8
]
S
.
G
e
rb
e
x
,
e
t
a
l.
,
“
Op
ti
m
a
l
lo
c
a
ti
o
n
o
f
m
u
lt
i
-
t
y
p
e
F
A
C
T
S
d
e
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ice
s
in
a
p
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r
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y
ste
m
b
y
m
e
a
n
s
o
f
g
e
n
e
ti
c
a
lg
o
rit
h
m
s,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
1
6
,
p
p
.
5
3
7
-
5
4
4
,
2
0
0
1
.
[2
9
]
C.
Ro
d
ríg
u
e
z
a
n
d
M
.
A
.
Rio
s,
“
S
izin
g
a
n
d
lo
c
a
ti
o
n
o
f
sh
u
n
t
F
A
C
T
S
d
e
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s
in
p
o
w
e
r
s
y
ste
m
u
sin
g
g
e
n
e
ti
c
a
lg
o
rit
h
m
s,
”
2
0
1
3
IEE
E
Gr
e
n
o
b
l
e
Co
n
fer
e
n
c
e
,
G
re
n
o
b
le,
2
0
1
3
,
p
p
.
1
-
6
.
[3
0
]
W
.
On
g
s
a
k
u
l
a
n
d
P
.
Jira
p
o
n
g
,
“
Op
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
F
A
C
T
S
d
e
v
ice
s
to
e
n
h
a
n
c
e
to
tal
tran
sf
e
r
c
a
p
a
b
il
it
y
u
sin
g
e
v
o
lu
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
,
”
Pro
c
e
e
d
in
g
s
o
f
t
h
e
IEE
E
In
ter
n
a
ti
o
n
a
l
S
y
mp
o
siu
m
o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
(
IS
CAS
)
,
v
o
l.
5
,
2
0
0
5
,
pp
.
4
1
7
5
-
4
1
7
8
.
[3
1
]
H.
S
h
a
h
e
e
n
,
e
t
a
l.
,
“
Op
ti
m
a
l
lo
c
a
ti
o
n
a
n
d
p
a
ra
m
e
ters
se
tt
in
g
o
f
u
n
ifi
e
d
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
r
b
a
se
d
o
n
e
v
o
lu
ti
o
n
a
ry
o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
s,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
IE
EE
P
o
we
r E
n
g
in
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
2
0
0
7
,
p
p
.
1
-
8
.
[3
2
]
D.
M
o
n
d
a
l
,
e
t
a
l.
,
“
Op
ti
m
a
l
p
lac
e
m
e
n
t
a
n
d
p
a
ra
m
e
ter
se
tt
in
g
o
f
S
V
C
a
n
d
T
CS
C
u
sin
g
P
S
O
to
m
it
ig
a
te
s
m
a
ll
sig
n
a
l
sta
b
il
it
y
p
ro
b
lem
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
4
2
,
p
p
.
3
3
4
-
3
4
0
,
2
0
1
2
.
[3
3
]
J.
Ke
n
n
e
d
y
a
n
d
R.
Eb
e
r
h
a
rt,
“
P
a
rti
c
le
sw
a
r
m
o
p
ti
m
iz
a
ti
o
n
i
n
,
”
Pr
o
c
e
e
d
in
g
s
o
f
th
e
IE
EE
I
n
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
Ne
u
r
a
l
Ne
two
rk
s
,
1
9
9
5
,
p
p
.
1
9
4
2
-
1
9
4
8
.
[3
4
]
J.
Ke
n
n
e
d
y
a
n
d
R.
M
e
n
d
e
s,
“
Ne
ig
h
b
o
rh
o
o
d
to
p
o
l
o
g
ies
in
f
u
ll
y
-
in
f
o
rm
e
d
a
n
d
b
e
sto
f
-
n
e
ig
h
b
o
rh
o
o
d
p
a
rt
icle
sw
a
r
m
s,
”
IEE
E
In
ter
n
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
S
o
f
t
Co
m
p
u
ti
n
g
in
In
d
u
stria
l
A
p
p
li
c
a
ti
o
n
s
,
2
0
0
3
,
p
p
.
4
5
-
50
.
[3
5
]
Y.
d
e
l
V
a
ll
e
,
e
t
a
l.
,
“
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
:
Ba
sic
Co
n
c
e
p
t
s,
V
a
rian
ts
a
n
d
A
p
p
li
c
a
ti
o
n
s
i
n
P
o
w
e
r
S
y
ste
m
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Evo
l
u
ti
o
n
a
ry
Co
mp
u
t
a
ti
o
n
,
v
o
l.
1
2
,
p
p
.
1
7
1
-
1
9
5
,
2
0
0
8
.
[3
6
]
G.
A
.
S
a
lma
n
,
e
t
a
l.
,
“
E
n
h
a
n
c
e
m
e
n
t
T
h
e
D
y
n
a
m
ic
S
tab
il
it
y
o
f
T
h
e
Ira
q
'
s
P
o
w
e
r
S
tatio
n
Us
in
g
P
ID
C
o
n
tro
ll
e
r
Op
ti
m
ize
d
b
y
F
A
a
n
d
P
S
O
Ba
se
d
o
n
Dif
fe
re
n
t
Ob
jec
ti
v
e
F
u
n
c
ti
o
n
s,
”
El
e
k
tro
teh
n
išk
i
Ves
tn
ik
,
v
o
l.
8
5
,
p
p
.
4
2
-
4
8
,
2
0
1
8
.
[3
7
]
H.
I.
Hu
ss
e
in
,
e
t
a
l
.
,
“
Em
p
lo
y
m
e
n
t
o
f
P
S
O alg
o
rit
h
m
to
im
p
ro
v
e
th
e
n
e
u
ra
l
n
e
tw
o
rk
tec
h
n
iq
u
e
f
o
r
ra
d
ial
d
istri
b
u
ti
o
n
s
y
ste
m
sta
t
e
e
sti
m
a
ti
o
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
n
S
ma
rt
S
e
n
sin
g
a
n
d
I
n
telli
g
e
n
t
S
y
ste
ms
,
v
o
l.
1
2
,
p
p
.
1
-
1
0
,
2
0
1
9
.
[3
8
]
G.
A
.
S
a
l
m
a
n
,
e
t
a
l.
,
“
A
p
p
li
c
a
ti
o
n
o
f
a
rti
f
icia
l
in
telli
g
e
n
c
e
tec
h
n
iq
u
e
s
f
o
r
L
F
C
a
n
d
A
V
R
s
y
ste
m
s
u
sin
g
P
ID
c
o
n
tro
ll
e
r,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
)
,
v
o
l.
1
0
,
n
o
.
3
,
p
p
.
1
6
9
4
-
1
7
0
4
,
2
0
1
9
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
G
h
a
ss
a
n
Abd
u
ll
a
h
S
a
l
m
a
n
re
c
e
iv
e
d
h
is
B.
S
c
.
d
e
g
re
e
in
e
n
g
in
e
e
rin
g
o
f
P
o
w
e
r
a
n
d
El
e
c
tri
c
a
l
M
a
c
h
in
e
s
in
2
0
0
6
f
ro
m
th
e
Un
iv
e
rsit
y
o
f
Di
y
a
l
a
.
He
re
c
e
iv
e
d
h
is
M
.
S
c
.
d
e
g
re
e
in
El
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tri
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l
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g
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g
in
2
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1
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ro
m
t
h
e
Un
iv
e
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y
o
f
T
e
c
h
n
o
lo
g
y
,
Ba
g
h
d
a
d
,
Ira
q
.
Cu
rre
n
tl
y
,
h
e
is
an
A
s
sista
n
t
P
ro
f
e
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o
r
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t
Un
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e
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o
f
Di
y
a
la,
B
a
q
u
b
a
h
,
Ira
q
.
His
re
se
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r
c
h
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se
s
o
n
p
o
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e
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s
y
ste
m
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ti
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iza
ti
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n
,
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o
w
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s
y
st
e
m
o
p
e
ra
ti
o
n
a
n
d
c
o
n
tro
l,
F
A
C
T
S
d
e
v
ice
s,
p
o
w
e
r
s
y
ste
m
se
c
u
rit
y
a
n
d
p
o
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m
sta
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il
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y
.
H
a
tim
G
h
a
d
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b
a
n
Ab
o
o
d
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d
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ra
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ted
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t
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e
Un
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e
rsity
o
f
Diy
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in
2
0
0
6
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g
in
El
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tri
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P
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En
g
in
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.
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.
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ield
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s.
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