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th
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g
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g
le
m
o
d
e
l,
a
s
re
v
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a
led
b
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t
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e
sim
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re
su
lt
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re
fo
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a
m
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m
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e
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th
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sh
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m
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a
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sim
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h
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o
f
t
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e
tr
a
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sm
issio
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tw
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rk
s.
K
ey
w
o
r
d
s
:
FAC
T
S
d
ev
ices
Firin
g
an
g
le
Static v
ar
co
m
p
en
s
ato
r
Var
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s
u
s
ce
p
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Vo
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T
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is i
s
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d
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r th
e
CC B
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-
SA
li
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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
:
Sam
s
o
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Olad
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Ay
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Dep
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C
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T
o
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Ar
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L
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b
a
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W
ay
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I
b
ad
a
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Nig
er
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ail:
s
am
s
o
n
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ed
u
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ng
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ay
a
n
lad
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@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Sev
er
al
d
if
f
icu
lties
co
n
f
r
o
n
t
tr
an
s
m
is
s
io
n
s
y
s
tem
s
,
jeo
p
ar
d
izin
g
th
eir
p
er
f
o
r
m
a
n
ce
.
A
m
o
n
g
t
h
ese
d
if
f
icu
lties
ar
e
v
o
ltag
e
m
ag
n
i
tu
d
e
f
lu
ctu
atio
n
s
,
p
o
wer
lo
s
s
es,
an
d
v
o
ltag
e
r
eg
u
latio
n
.
R
esear
ch
er
s
f
r
o
m
all
ac
r
o
s
s
th
e
wo
r
ld
h
av
e
d
ev
is
ed
v
ar
io
u
s
s
o
lu
tio
n
s
to
s
o
m
e
o
f
th
ese
is
s
u
es.
So
m
e
o
f
th
e
s
o
lu
tio
n
s
in
clu
d
e
s
h
u
n
t
ca
p
ac
ito
r
p
lace
m
en
t
[
1
]
-
[4
]
,
d
is
tr
ib
u
tio
n
g
en
er
atio
n
in
c
o
r
p
o
r
atio
n
[
5]
-
[7
]
,
an
d
th
e
p
la
ce
m
en
t
o
f
f
lex
ib
le
alter
n
atin
g
cu
r
r
en
t
tr
a
n
s
m
is
s
io
n
s
y
s
tem
s
(
FA
C
T
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co
n
tr
o
ller
s
[
8]
-
[
1
0
]
,
am
o
n
g
o
th
er
s
.
FAC
T
S
d
ev
ices
h
av
e
f
o
u
n
d
a
wid
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r
a
n
g
e
o
f
ap
p
licatio
n
s
i
n
tr
a
n
s
m
is
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n
s
y
s
tem
s
f
o
r
v
o
ltag
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co
n
tr
o
l
b
ec
a
u
s
e
o
f
th
eir
ad
ap
tab
ilit
y
[
1
1
].
FAC
T
S
d
ev
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ar
e
elec
tr
o
n
ic
-
b
ased
r
ea
ctiv
e
co
m
p
e
n
s
ato
r
s
th
at
ar
e
p
r
o
f
icien
t
at
s
u
p
p
ly
in
g
o
r
co
n
s
u
m
in
g
r
ea
ctiv
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p
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we
r
f
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o
m
n
etwo
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k
s
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ased
o
n
th
e
n
et
wo
r
k
r
eq
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ir
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m
en
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o
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at
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p
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f
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r
m
a
n
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o
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t
h
e
n
etwo
r
k
m
ay
b
e
im
p
r
o
v
ed
[
1
2]
-
[
1
4
]
.
FAC
T
S
d
ev
ices
co
m
e
in
v
ar
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u
s
f
o
r
m
s
an
d
th
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c
o
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n
ec
tio
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s
,
as
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th
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m
an
ce
s
,
d
if
f
er
f
r
o
m
o
n
e
an
o
th
er
.
T
h
e
s
tatic
v
ar
co
m
p
en
s
ato
r
(
SVC
)
,
wh
ich
co
m
es
in
n
u
m
er
o
u
s
v
ar
ian
ts
,
is
o
n
e
o
f
th
e
s
ev
er
a
l
ty
p
es
o
f
FAC
T
S
d
ev
ices
[
1
5]
-
[
1
7
]
.
T
h
e
two
p
r
im
a
r
y
SV
C
m
o
d
els
ar
e
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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p
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Po
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E
n
g
I
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2252
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8
7
9
2
C
o
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a
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(
A
b
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s
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921
v
ar
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s
h
u
n
t
s
u
s
ce
p
tan
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m
o
d
el
an
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th
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f
ir
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g
an
g
le
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o
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el.
B
o
th
o
f
th
ese
m
o
d
els
ar
e
ca
p
ab
le
o
f
b
o
o
s
tin
g
tr
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s
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is
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io
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m
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ce
d
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e
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u
s
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o
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e
tr
an
s
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is
s
io
n
n
etwo
r
k
s
[
1
8
].
A
s
u
b
s
tan
tial
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o
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ty
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Par
ticl
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s
war
m
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(
PS
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was
u
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d
in
[
1
9
]
to
ass
ig
n
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s
tatic
s
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n
ch
r
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o
u
s
co
m
p
en
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r
(
STAT
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to
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p
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o
v
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m
ag
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e
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s
.
As
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I
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E
1
4
-
b
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s
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ly
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o
f
FAC
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d
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m
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it
with
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q
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ST
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.
T
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ap
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licatio
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h
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f
ir
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ly
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h
m
(
FA)
to
o
p
tim
i
ze
SVC
an
d
STAT
C
OM
f
o
r
v
o
ltag
e
m
ag
n
itu
d
e
en
h
a
n
ce
m
en
t
a
n
d
l
o
s
s
m
itig
atio
n
o
n
th
e
I
E
E
E
1
4
-
b
u
s
n
etwo
r
k
is
d
o
cu
m
e
n
ted
in
[
20
]
.
Acc
o
r
d
in
g
to
th
e
a
n
aly
s
is
,
th
e
in
s
tallatio
n
o
f
SVC
an
d
STAT
C
OM
d
ev
ices
en
h
an
ce
d
th
e
s
y
s
tem
v
o
ltag
e
m
a
g
n
itu
d
es
wh
ile
s
im
u
ltan
eo
u
s
ly
lo
wer
in
g
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
we
r
lo
s
s
es.
No
n
eth
eless
,
th
e
r
esear
c
h
d
id
n
o
t e
x
p
l
o
r
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
ese
d
ev
ices
u
n
d
er
d
if
f
er
e
n
t n
etwo
r
k
co
n
d
itio
n
s
,
wh
ich
co
u
ld
af
f
ec
t t
h
eir
ap
p
licab
ilit
y
.
Me
tah
eu
r
is
tic
alg
o
r
ith
m
s
wer
e
u
s
ed
in
[
2
1
]
to
s
o
lv
e
r
ea
ctiv
e
p
o
wer
p
lan
n
i
n
g
p
r
o
b
lem
s
u
s
in
g
FAC
T
S
co
n
tr
o
ller
s
.
Fo
r
th
e
test
s
ce
n
ar
io
s
,
th
e
I
E
E
E
3
0
-
an
d
I
E
E
E
5
7
-
b
u
s
n
etwo
r
k
s
wer
e
u
tili
ze
d
.
T
h
e
lo
a
d
f
lo
w
an
aly
s
is
tech
n
iq
u
e
was
u
tili
ze
d
to
esti
m
ate
th
e
lo
ca
tio
n
o
f
t
h
e
th
y
r
is
to
r
-
co
n
tr
o
lled
s
er
ies
ca
p
ac
ito
r
(
T
C
SC
)
,
an
d
th
e
v
o
lta
g
e
co
llap
s
e
p
r
o
x
i
m
ity
in
d
icatio
n
m
eth
o
d
was
em
p
lo
y
ed
t
o
o
b
tain
th
e
SVC
p
o
s
itio
n
.
T
h
is
s
tu
d
y
,
h
o
wev
er
,
d
id
n
o
t
ac
c
o
u
n
t
f
o
r
d
y
n
am
ic
ch
an
g
es
in
th
e
n
etw
o
r
k
lo
ad
,
wh
ich
m
ig
h
t
in
f
l
u
en
ce
th
e
e
f
f
ec
tiv
en
ess
o
f
th
e
p
lace
m
e
n
t stra
teg
ies.
Ma
g
ad
u
m
et
a
l
.
[2
2
]
s
o
lv
e
d
v
o
ltag
e
in
s
tab
ilit
y
b
y
em
p
lo
y
in
g
f
u
zz
y
lo
g
ic
to
o
p
tim
ize
u
n
if
ied
p
o
wer
f
lo
w
co
n
tr
o
ller
(
UPFC
)
p
lace
m
en
t.
T
h
e
MiPo
wer
s
o
f
twar
e
p
ac
k
ag
e
was
u
s
ed
to
r
u
n
th
e
s
im
u
latio
n
u
s
in
g
th
e
I
E
E
E
1
4
b
u
s
s
y
s
tem
.
T
h
e
U
PF
C
lo
ca
tio
n
im
p
r
o
v
ed
n
etw
o
r
k
v
o
ltag
e
s
tab
ilit
y
s
u
b
s
tan
tially
.
T
h
e
lim
itatio
n
h
er
e
is
th
e
r
elian
ce
o
n
f
u
zz
y
l
o
g
ic,
wh
ich
m
ay
n
o
t
ca
p
tu
r
e
a
ll
th
e
n
u
a
n
ce
s
o
f
th
e
n
etwo
r
k
d
y
n
am
ics
an
d
m
ig
h
t
r
eq
u
ir
e
e
x
ten
s
iv
e
tu
n
in
g
o
f
th
e
f
u
zz
y
r
u
les f
o
r
d
if
f
er
e
n
t scen
a
r
io
s
.
Su
b
r
am
an
i
et
a
l
.
[2
3
]
im
p
r
o
v
ed
UPFC
b
y
u
tili
zin
g
PS
O
f
o
r
o
p
tim
al
d
e
v
ice
p
o
s
itio
n
an
d
p
ar
am
ete
r
tu
n
in
g
,
wh
ich
r
e
d
u
ce
s
ac
tiv
e
lo
s
s
es
an
d
en
h
an
ce
s
n
etwo
r
k
v
o
ltag
e
s
tab
ilit
y
.
T
o
v
al
id
ate
th
e
p
r
o
p
o
s
e
d
ap
p
r
o
ac
h
,
s
im
u
latio
n
s
wer
e
p
er
f
o
r
m
e
d
u
s
in
g
th
e
I
E
E
E
1
4
-
b
u
s
s
y
s
tem
.
Ho
wev
er
,
th
e
s
tu
d
y
d
id
n
o
t
co
m
p
ar
e
PS
O
wi
th
o
th
er
o
p
tim
izatio
n
tech
n
iq
u
es,
leav
in
g
o
p
en
th
e
q
u
esti
o
n
o
f
wh
eth
er
PS
O
is
th
e
m
o
s
t
ef
f
ec
tiv
e
m
eth
o
d
f
o
r
th
is
p
u
r
p
o
s
e.
T
h
e
m
u
lti
-
o
b
jectiv
e
g
en
etic
alg
o
r
ith
m
(
MO
GA)
was
u
s
ed
in
[
2
4
]
to
a
n
aly
ze
o
v
er
all
lo
s
s
m
in
im
izatio
n
an
d
lin
e
co
n
g
esti
o
n
en
h
a
n
ce
m
en
t
b
y
ca
lc
u
latin
g
th
e
a
p
p
r
o
p
r
iate
p
lace
m
en
ts
an
d
c
o
m
p
en
s
atio
n
r
ates
o
f
T
C
SC
d
ev
ices.
T
o
co
n
f
ir
m
th
e
p
o
ten
cy
o
f
t
h
e
tech
n
iq
u
e,
it
was
ev
alu
ated
o
n
th
e
I
E
E
E
3
0
-
b
u
s
test
n
etwo
r
k
.
W
h
ile
ef
f
ec
tiv
e,
th
is
ap
p
r
o
ac
h
d
id
n
o
t
co
n
s
id
er
th
e
im
p
ac
t
o
f
o
th
er
FAC
T
S
d
ev
ices,
s
u
ch
as
S
VC
o
r
STAT
C
OM
,
o
n
th
e
o
v
er
all
n
et
wo
r
k
p
er
f
o
r
m
a
n
ce
.
Desp
ite
th
ese
ad
v
an
ce
s
,
th
er
e
r
em
ain
s
a
n
ee
d
f
o
r
a
f
o
cu
s
ed
co
m
p
ar
is
o
n
b
etwe
en
d
if
f
er
e
n
t
ty
p
es
o
f
SVC
s
in
co
n
tr
o
llin
g
b
u
s
v
o
ltag
e
m
ag
n
itu
d
es
to
im
p
r
o
v
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
p
er
f
o
r
m
a
n
ce
.
T
h
is
r
esear
ch
was
co
n
d
u
cted
to
co
m
p
a
r
e
th
e
ca
p
ab
ilit
ies
o
f
two
k
e
y
ty
p
e
s
o
f
SVC
s
in
co
n
tr
o
llin
g
t
h
e
v
o
ltag
e
m
a
g
n
itu
d
es
at
th
e
b
u
s
es
wh
er
e
th
ey
ar
e
p
lace
d
to
b
o
o
s
t
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
tr
an
s
m
is
s
io
n
n
etw
o
r
k
.
T
h
e
two
b
asic
ty
p
es
o
f
SVC
s
wer
e
m
o
d
eled
m
ath
em
atica
lly
an
d
ad
d
e
d
to
th
e
New
to
n
-
R
ap
h
s
o
n
lo
ad
f
lo
w
alg
o
r
ith
m
.
MA
T
L
AB
co
d
es
wer
e
d
ev
el
o
p
ed
to
im
p
lem
en
t
th
e
tech
n
iq
u
e
an
d
wer
e
e
x
ec
u
ted
o
n
th
e
I
E
E
E
3
0
-
b
u
s
tr
an
s
m
is
s
io
n
s
y
s
tem
.
T
h
e
p
r
im
ar
y
co
n
tr
ib
u
tio
n
o
f
th
is
p
ap
er
ex
ten
d
s
to
o
f
f
e
r
in
g
co
m
p
r
eh
en
s
iv
e
in
s
ig
h
ts
in
to
th
e
p
er
f
o
r
m
an
ce
v
a
r
iatio
n
s
am
o
n
g
s
tatic
v
ar
co
m
p
e
n
s
ato
r
m
o
d
els,
f
ac
ilit
atin
g
a
n
u
an
ce
d
u
n
d
er
s
tan
d
in
g
o
f
th
eir
ef
f
ec
tiv
en
ess
u
n
d
er
d
iv
er
s
e
t
r
an
s
m
is
s
io
n
n
etwo
r
k
co
n
d
itio
n
s
.
T
h
is
a
n
aly
s
is
aid
s
in
n
o
t
o
n
l
y
id
e
n
tify
in
g
o
p
tim
al
m
o
d
els
f
o
r
p
r
ec
is
e
v
o
ltag
e
co
n
tr
o
l
b
u
t
also
lay
s
th
e
g
r
o
u
n
d
wo
r
k
f
o
r
r
ef
in
i
n
g
v
o
ltag
e
co
n
tr
o
l
s
tr
ateg
ies,
th
u
s
b
o
ls
ter
in
g
th
e
s
tab
ilit
y
an
d
ef
f
icien
cy
o
f
tr
an
s
m
is
s
io
n
n
etwo
r
k
s
.
T
h
is
s
tu
d
y
'
s
n
o
v
elty
r
ests
in
a
f
o
cu
s
ed
co
m
p
a
r
is
o
n
b
etwe
en
two
SVC
m
o
d
els,
em
p
h
asizin
g
th
eir
co
m
p
u
tatio
n
al
s
p
ee
d
a
n
d
ef
f
ec
tiv
en
ess
in
r
eg
u
latin
g
b
u
s
v
o
ltag
e
m
ag
n
it
u
d
e
with
in
tr
an
s
m
is
s
io
n
n
etwo
r
k
s
.
2.
M
E
T
H
O
D
I
n
its
s
im
p
lest
f
o
r
m
,
th
e
s
tatic
v
ar
co
m
p
en
s
ato
r
(
SVC
)
co
n
s
is
t
s
o
f
a
p
a
r
allel
co
n
n
ec
tio
n
b
etwe
en
a
b
an
k
o
f
ca
p
ac
ito
r
s
an
d
a
th
y
r
is
to
r
-
co
n
tr
o
lled
r
ea
cto
r
(
T
C
R
)
.
T
h
is
co
n
f
ig
u
r
atio
n
o
p
e
r
ates
s
im
ilar
ly
to
a
p
ar
allel
-
co
n
n
ec
te
d
v
ar
iab
le
s
u
s
ce
p
tan
ce
,
wh
er
e
th
e
SVC
r
e
g
u
lates
th
e
v
o
ltag
e
m
ag
n
itu
d
e
at
th
e
co
n
n
ec
tio
n
p
o
in
t
to
th
e
s
y
s
tem
b
y
eith
er
g
en
er
atin
g
o
r
ab
s
o
r
b
in
g
r
ea
ctiv
e
p
o
wer
.
T
h
is
ca
p
a
b
ilit
y
allo
ws
th
e
SVC
to
p
r
o
v
id
e
r
a
p
id
ad
ju
s
tm
en
ts
to
r
ea
ctiv
e
p
o
wer
an
d
v
o
ltag
e
lev
els
as
n
ee
d
ed
[
2
5
]
.
T
h
e
th
y
r
is
to
r
’
s
f
ir
in
g
an
g
le
co
n
tr
o
l m
ec
h
an
is
m
en
ab
les th
e
SVC
to
r
ea
ct
alm
o
s
t in
s
tan
tan
eo
u
s
ly
to
c
h
an
g
es in
s
y
s
tem
co
n
d
itio
n
s
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
s
ch
e
m
atic
r
ep
r
esen
tatio
n
o
f
th
e
SVC
.
T
h
e
SVC
is
co
n
n
ec
ted
to
t
h
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
th
r
o
u
g
h
a
th
r
ee
-
p
h
ase,
t
h
r
ee
-
win
d
i
n
g
tr
a
n
s
f
o
r
m
e
r
.
T
h
is
tr
an
s
f
o
r
m
er
f
ea
tu
r
es
tw
o
Evaluation Warning : The document was created with Spire.PDF for Python.
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s
ec
o
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d
ar
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win
d
in
g
s
:
o
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f
ig
u
r
ed
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c
o
n
n
ec
tio
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f
o
r
th
e
s
ix
-
p
u
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T
C
R
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an
d
th
e
o
th
er
c
o
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i
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ed
as
a
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n
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ec
tio
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o
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th
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th
r
ee
-
p
h
ase
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p
ac
ito
r
b
an
k
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f
lo
atin
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tar
p
o
in
t
[
1
8
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.
I
t
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also
ass
u
m
ed
th
at
all
th
r
ee
win
d
in
g
s
o
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o
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m
er
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th
e
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p
o
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ts
f
lo
atin
g
to
allo
w
f
o
r
e
f
f
ec
tiv
e
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
an
d
v
o
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e
r
eg
u
latio
n
.
Sin
ce
tr
an
s
m
is
s
io
n
n
etwo
r
k
lin
es
ar
e
tr
an
s
p
o
s
ed
at
r
eg
u
lar
in
ter
v
als,
w
h
ich
r
esu
lts
in
th
e
ass
u
m
p
tio
n
t
h
at
th
ese
n
etwo
r
k
s
o
p
er
ate
as
b
ala
n
ce
d
s
y
s
tem
s
,
th
e
f
o
llo
win
g
s
u
b
-
s
ec
tio
n
s
d
escr
ib
e
th
e
two
s
in
g
le
-
p
h
ase
m
o
d
els
o
f
SVC
.
I
T
C
R
c
I
T
C
R
b
I
T
C
R
a
I
T
C
R
1
I
T
C
R
2
I
T
C
R
3
I
Ca
I
Cb
I
Cc
C
3
C
3
C
2
n
B
r
a
nc
h
3
B
r
a
nc
h 2
B
r
a
nc
h 1
I
a
I
b
I
c
V
a
V
b
V
c
Fig
u
r
e
1
.
T
h
r
ee
-
p
h
ase
SVC
r
ep
r
esen
tatio
n
co
n
s
is
tin
g
o
f
th
y
r
is
to
r
-
co
n
tr
o
lled
r
ea
cto
r
s
an
d
f
ix
ed
ca
p
ac
ito
r
s
[
1
8
]
2
.
1
.
Sh
un
t
v
a
ria
ble su
s
ce
pta
nce
m
o
de
T
h
e
SVC
m
ay
r
ea
lly
b
e
th
o
u
g
h
t
o
f
as
a
co
n
tr
o
llab
le
r
ea
ct
an
ce
with
eith
er
r
ea
ctan
ce
lim
itatio
n
s
o
r
f
ir
in
g
an
g
le
co
n
s
tr
ain
ts
[
2
6
]
.
T
h
e
an
alo
g
o
u
s
cir
cu
it
s
ee
n
in
Fig
u
r
e
2
is
u
s
ed
to
d
ev
elo
p
b
o
th
th
e
lin
ea
r
ized
eq
u
atio
n
s
n
ee
d
ed
b
y
New
to
n
'
s
ap
p
r
o
ac
h
an
d
th
e
SVC
n
o
n
l
in
ea
r
p
o
wer
eq
u
atio
n
s
.
R
ef
er
r
in
g
to
Fig
u
r
e
2
,
th
e
SVC
's cu
r
r
en
t d
r
aw
is
:
S
VC
=
S
V
C
(
1
)
an
d
th
e
r
ea
ctiv
e
p
o
wer
in
jecte
d
at
b
u
s
k
,
as we
ll a
s
th
e
r
ea
ctiv
e
p
o
wer
e
x
tr
ac
ted
b
y
th
e
SV
C
,
is
g
iv
en
as (
2
)
.
=
=
−
2
S
VC
(
2
)
T
h
e
eq
u
iv
ale
n
t
s
u
s
ce
p
tan
ce
S
VC
is
ass
u
m
ed
to
r
ep
r
esen
t
th
e
s
tate
v
ar
iab
le
an
d
th
e
lin
ea
r
iz
ed
eq
u
atio
n
is
g
iv
en
as
(
3
)
.
[
]
(
)
=
[
0
0
0
]
(
)
[
S
V
C
S
V
C
]
(
)
(
3
)
T
h
e
v
ar
iab
le
s
h
u
n
t su
s
ce
p
tan
c
e
B
SVC
is
r
ev
is
ed
af
ter
ea
ch
r
ep
etitio
n
in
ac
co
r
d
an
ce
with
(
4
)
.
S
VC
(
)
=
S
VC
(
−
1
)
+
(
S
V
C
S
V
C
)
(
)
S
VC
(
−
1
)
(
4
)
T
h
e
to
tal
SVC
s
u
s
ce
p
tan
ce
r
eq
u
ir
ed
to
k
ee
p
t
h
e
bus
v
o
ltag
e
m
ag
n
itu
d
e
at
th
e
d
esire
d
le
v
e
l
is
r
ep
r
esen
ted
b
y
th
e
ch
an
g
in
g
s
u
s
ce
p
tan
ce
[
2
7
]
.
T
h
e
th
y
r
is
to
r
f
ir
in
g
an
g
le
is
d
eter
m
in
ed
o
n
ce
th
e
le
v
el
o
f
co
r
r
ec
tio
n
h
as
b
ee
n
estab
lis
h
ed
.
Ho
wev
er
,
d
u
e
to
t
h
e
n
o
n
lin
e
ar
r
elatio
n
s
h
ip
b
etw
ee
n
th
e
SVC
s
u
s
ce
p
tan
ce
an
d
th
e
th
y
r
is
to
r
f
ir
i
n
g
an
g
le,
th
is
co
m
p
u
tatio
n
r
e
q
u
ir
es a
n
iter
ativ
e
s
o
lu
tio
n
[
2
8
]
.
2
.
2
.
F
iring
-
a
ng
le
m
o
del
B
y
ad
d
r
ess
in
g
th
e
th
y
r
is
to
r
-
c
o
n
tr
o
lled
r
ea
cto
r
(
T
C
R
)
f
ir
in
g
an
g
le
α
as
a
s
tate
v
ar
iab
le
in
th
e
p
o
wer
f
lo
w
d
er
i
v
atio
n
,
an
alter
n
ativ
e
S
VC
m
o
d
el
m
a
y
b
e
u
s
ed
to
av
o
id
th
e
ex
tr
a
iter
ativ
e
p
r
o
ce
d
u
r
e
[
2
9
]
.
Her
e,
"SVC
"
i
s
u
s
ed
to
r
ef
er
to
th
e
v
ar
iab
le.
T
h
e
SVC
'
s
p
o
s
itiv
e
s
e
q
u
en
ce
s
u
s
ce
p
tan
ce
is
p
r
o
v
id
e
d
as in
(
5
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l
Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
C
o
mp
a
r
a
tive
a
n
a
lysi
s
o
f tw
o
s
ta
tic
va
r
co
mp
en
s
a
to
r
mo
d
els
in
vo
lta
g
e
c
o
n
tr
o
l …
(
A
b
d
u
lr
a
s
a
q
Jimo
h
)
923
=
−
2
{
−
[
2
(
−
S
VC
)
+
(
2
S
VC
)
]
}
(
5
)
T
h
e
lin
ea
r
ized
SVC
eq
u
atio
n
i
s
p
r
o
v
id
ed
f
r
o
m
(
5
)
as
(
6
)
.
[
]
(
)
=
[
0
0
0
2
2
[
(
2
S
VC
)
−
1
]
]
(
)
[
S
VC
]
(
)
(
6
)
T
h
e
v
ar
iab
le
f
ir
in
g
a
n
g
le
is
r
ev
is
ed
af
ter
ea
ch
iter
atio
n
in
ac
co
r
d
an
ce
with
(
7
)
.
(
)
=
(
−
1
)
+
(
)
(
7
)
T
h
e
New
to
n
-
R
ap
h
s
o
n
p
o
wer
f
lo
w
tech
n
iq
u
e
was
im
p
lem
en
ted
f
o
r
b
o
th
SVC
m
o
d
els
b
ased
o
n
th
eir
m
ath
em
atica
l
f
o
r
m
u
latio
n
s
,
an
d
MA
T
L
AB
s
cr
ip
ts
an
d
f
u
n
ctio
n
s
wer
e
d
ev
elo
p
ed
to
p
er
f
o
r
m
th
e
s
im
u
latio
n
s
.
T
h
e
d
ata
r
e
q
u
ir
ed
f
o
r
t
h
e
s
im
u
latio
n
s
wer
e
o
b
tain
ed
f
r
o
m
[
30
].
I
S
V
C
B
S
V
C
Fig
u
r
e
2
.
Var
iab
le
s
h
u
n
t su
s
ce
p
tan
ce
[
1
8]
,
[
2
6
]
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
in
v
esti
g
atio
n
r
esu
lts
o
f
t
h
e
two
SVC
m
o
d
els
ar
e
p
r
esen
ted
.
T
h
e
s
im
u
latio
n
s
u
s
ed
a
p
r
ec
is
io
n
lev
el
o
f
1
e
-
1
0
a
n
d
wer
e
p
er
f
o
r
m
ed
o
v
er
2
0
iter
atio
n
s
.
Fig
u
r
e
3
s
h
o
ws
th
e
I
E
E
E
3
0
-
b
u
s
p
o
wer
f
lo
w
s
o
lu
tio
n
.
I
t
was
d
is
co
v
er
ed
th
at
s
o
m
e
b
u
s
es
h
ad
v
o
ltag
e
m
a
g
n
itu
d
es
l
ess
th
an
1
.
0
p
.
u
.
T
h
er
e
f
o
r
e,
SVC
s
wer
e
in
s
ta
lled
on
th
ese
b
u
s
es
to
ex
p
lo
r
e
th
e
ca
p
ab
ilit
ies
o
f
th
e
two
ty
p
es
o
f
SVC
m
o
d
els
in
r
e
g
u
latin
g
th
e
v
o
ltag
e
to
t
h
e
d
esire
d
lev
el.
I
n
th
e
n
etwo
r
k
u
n
d
er
i
n
v
esti
g
atio
n
,
s
im
u
latio
n
s
wer
e
co
n
d
u
cted
b
y
s
eq
u
en
t
ially
ad
d
in
g
SVC
s
.
I
n
itially
,
o
n
e
SVC
was
in
s
tal
led
at
th
e
f
ir
s
t
s
elec
ted
b
u
s
,
f
o
llo
wed
b
y
two
SVC
s
at
th
e
f
ir
s
t
two
s
elec
ted
b
u
s
es,
th
r
ee
SVC
s
at
th
e
f
ir
s
t
th
r
ee
s
elec
ted
b
u
s
es,
an
d
f
in
ally
f
o
u
r
SVC
s
at
th
e
f
ir
s
t
f
o
u
r
s
elec
ted
b
u
s
es.
B
u
s
es
n
u
m
b
er
ed
1
8
,
2
0
,
2
4
,
a
n
d
2
5
wer
e
ch
o
s
en
b
ec
au
s
e
t
h
eir
v
o
ltag
e
m
ag
n
itu
d
es
wer
e
l
ess
th
an
1
.
0
p
.
u
.
,
as
d
ep
icted
in
Fig
u
r
e
3
.
T
h
e
v
o
ltag
e
m
a
g
n
itu
d
es
at
t
h
ese
b
u
s
es
wer
e
in
itially
a
d
ju
s
ted
to
1
.
0
p
.
u
.
an
d
s
u
b
s
eq
u
en
tly
to
1
.
0
5
p
.
u
.
to
as
s
ess
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
S
VC
s
in
r
eg
u
latin
g
th
e
v
o
ltag
e
lev
els.
T
h
e
s
im
u
latio
n
r
esu
lts
f
o
r
th
e
two
d
if
f
er
en
t SVC
m
o
d
els ar
e
s
h
o
wn
in
T
ab
le
1
,
with
th
e
SVC
v
o
ltag
e
m
ag
n
itu
d
es r
eg
u
lated
to
1
.
0
p
.
u
.
T
h
e
s
u
s
ce
p
tan
ce
v
alu
es f
o
r
b
o
th
m
o
d
els,
as
p
r
esen
ted
in
T
ab
le
1
,
wer
e
f
o
u
n
d
to
b
e
id
en
tical,
in
d
icatin
g
co
n
s
is
ten
t
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
ca
p
ab
ilit
ies.
Fig
u
r
e
4
f
u
r
th
er
elu
cid
ates
th
e
co
m
p
ar
is
o
n
o
f
v
o
ltag
e
p
r
o
f
ile
s
b
etwe
en
th
e
b
ase
ca
s
e
an
d
th
e
s
ce
n
ar
io
s
wh
er
e
t
h
e
two
d
i
f
f
er
en
t
SVC
m
o
d
els
wer
e
d
ep
lo
y
ed
o
n
th
e
s
elec
ted
b
u
s
es.
T
h
is
co
m
p
ar
is
o
n
d
em
o
n
s
tr
ates
h
o
w
b
o
th
m
o
d
els
ef
f
ec
tiv
ely
en
h
an
ce
d
th
e
n
etwo
r
k
'
s
v
o
ltag
e
s
tab
ilit
y
b
y
m
ain
tain
in
g
th
e
b
u
s
v
o
ltag
e
m
ag
n
itu
d
es
with
in
th
e
d
esire
d
r
an
g
e.
T
h
e
id
en
tical
s
u
s
ce
p
tan
ce
v
alu
es
s
u
g
g
est
th
at
b
o
th
m
o
d
els
p
r
o
v
id
e
co
m
p
a
r
ab
le
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
u
n
d
er
s
tead
y
-
s
tate
co
n
d
itio
n
s
.
Ho
wev
er
,
as
s
h
o
wn
in
T
a
b
le
1
,
t
h
e
v
a
r
iab
le
s
h
u
n
t
s
u
s
ce
p
tan
ce
m
o
d
el
ex
h
ib
ite
d
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
v
e
r
th
e
f
ir
in
g
an
g
le
m
o
d
el
in
ter
m
s
o
f
co
m
p
u
ta
tio
n
al
ef
f
icien
cy
.
Sp
ec
if
ically
,
th
e
v
ar
iab
le
s
h
u
n
t
s
u
s
ce
p
tan
ce
m
o
d
el
r
eq
u
ir
ed
f
ewe
r
iter
atio
n
s
to
co
n
v
e
r
g
e
an
d
ac
h
iev
ed
s
h
o
r
ter
s
im
u
latio
n
tim
es,
h
ig
h
lig
h
tin
g
its
ef
f
icien
cy
in
r
ea
c
h
in
g
a
s
t
ea
d
y
-
s
tate
s
o
lu
tio
n
.
T
h
is
in
d
ic
ates
th
at
th
e
v
ar
iab
le
s
h
u
n
t
s
u
s
ce
p
tan
ce
m
o
d
el
is
m
o
r
e
c
o
m
p
u
tatio
n
ally
ef
f
icien
t,
wh
ich
ca
n
b
e
p
a
r
ticu
lar
ly
a
d
v
an
tag
eo
u
s
in
r
ea
l
-
tim
e
ap
p
licatio
n
s
wh
er
e
q
u
ick
r
esp
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g
b
o
m
o
so
,
Oy
o
S
ta
te,
Nig
e
ria
in
2
0
1
2
a
n
d
a
n
M
.
S
c
.
in
p
o
we
r
sy
ste
m
e
n
g
in
e
e
rin
g
fro
m
Ob
a
fe
m
i
Aw
o
lo
w
o
Un
iv
e
rs
it
y
,
I
le
-
Ife
,
Os
u
n
S
tate
,
Ni
g
e
ria
in
2
0
1
9
.
He
b
a
r
g
e
d
h
is
P
h
.
D.
a
t
Ob
a
fe
m
i
Aw
o
lo
wo
Un
iv
e
rsit
y
,
Il
e
-
Ife
,
Os
u
n
S
tate
in
2
0
2
4
.
His res
e
a
rc
h
in
tere
sts a
re
p
rima
ril
y
in
th
e
a
re
a
s
o
f
p
o
we
r
sy
ste
m
o
p
t
i
m
iza
ti
o
n
,
a
n
d
p
o
we
r
sy
ste
m
sta
b
il
it
y
.
He
c
a
n
b
e
c
o
n
tac
ted
at
e
m
a
il
:
sa
m
so
n
.
a
y
a
n
lad
e
@lc
u
.
e
d
u
.
n
g
o
r
a
y
a
n
lad
e
o
lad
a
y
o
@g
m
a
i
l.
c
o
m
.
Fu
n
so
K
e
h
in
d
e
Ar
i
y
o
re
c
e
iv
e
d
b
a
c
h
e
lo
r
o
f
sc
ien
c
e
(B.
S
c
.
)
in
e
lec
tro
n
ic
a
n
d
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fr
o
m
Ob
a
fe
m
i
Aw
o
lo
wo
Un
i
v
e
rsity
,
Ile
-
Ife
,
Os
u
n
S
tate
,
Nig
e
ria
i
n
2
0
0
4
,
m
a
ste
r
o
f
sc
ien
c
e
in
p
o
we
r
sy
st
e
m
e
n
g
in
e
e
rin
g
fr
o
m
Ob
a
fe
m
i
Aw
o
lo
wo
Un
i
v
e
rsity
,
Ile
-
Ife
,
Os
u
n
S
tate
,
Nig
e
ria
a
n
d
P
h
.
D
.
i
n
p
o
we
r
sy
ste
m
,
Ob
a
fe
m
i
Aw
o
l
o
wo
U
n
iv
e
rsit
y
,
Ile
-
Ife
,
Os
u
n
S
tate
,
Nig
e
ria
.
Cu
rre
n
tl
y
,
h
e
is
a
se
n
io
r
lec
tu
re
r
a
t
De
p
a
rtme
n
t
o
f
El
e
c
tro
n
ic
a
n
d
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
,
Ob
a
fe
m
i
Aw
o
lo
w
o
Un
iv
e
rsity
,
Ile
-
Ife
,
Os
u
n
S
tate
,
Nig
e
ria.
His
re
se
a
rc
h
in
tere
sts
a
re
p
o
we
r
sy
ste
m
p
o
we
r
q
u
a
li
ty
,
p
o
we
r
sy
ste
m
a
n
a
ly
sis,
a
n
d
p
o
we
r
sy
ste
m
m
o
d
e
li
n
g
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
fu
n
so
a
ri
y
o
@y
a
h
o
o
.
c
o
m
.
Mo
se
s
Ta
iwo
Adeba
y
o
re
c
e
iv
e
d
t
h
e
e
n
g
in
e
e
rin
g
d
e
g
re
e
in
e
l
e
c
tri
c
a
l
e
n
g
in
e
e
rin
g
fro
m
th
e
Un
iv
e
rsit
y
o
f
Ilo
rin
i
n
2
0
0
2
,
t
h
e
M
.
Tec
h
.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
lec
tro
n
ic
e
n
g
in
e
e
rin
g
p
o
we
r
o
p
ti
o
n
fr
o
m
F
e
d
e
ra
l
Un
i
v
e
rsity
o
f
Tec
h
n
o
lo
g
y
,
A
k
u
re
,
O
n
d
o
S
tate
in
2
0
1
4
.
Cu
rre
n
tl
y
,
h
e
is
th
e
p
o
we
r
c
o
n
tr
o
l
a
n
d
a
u
to
m
a
ti
o
n
sp
e
c
ialist
with
Ca
d
b
u
r
y
Nig
e
ri
a
Li
m
it
e
d
,
Ag
id
i
n
g
b
i,
La
g
o
s
,
a
n
d
is
a
lso
p
u
rsu
i
n
g
a
P
h
.
D.
d
e
g
re
e
a
t
Ob
a
fe
m
i
Aw
o
lo
wo
Un
iv
e
rsity
,
Ile
-
Ife
,
Os
u
n
S
tate
,
Nig
e
ria.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
d
e
b
a
y
o
taiw
o
@g
m
a
il
.
c
o
m
.
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