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ta
g
e
o
f
t
h
e
u
s
e
o
f
T
C
S
C
w
i
th
a
f
u
z
z
y
co
n
tr
o
ller
o
v
er
f
i
x
ed
ca
p
ac
ito
r
o
p
e
r
atio
n
is
p
r
esen
ted
i
n
[
7
]
.
An
au
to
m
atic
F
AC
T
S
d
ev
ice
allo
ca
tio
n
p
r
o
ce
s
s
b
ased
o
n
ev
o
lu
tio
n
ar
y
al
g
o
r
ith
m
to
en
h
a
n
ce
t
h
e
v
o
ltag
e
s
tab
ilit
y
o
f
p
o
w
er
s
y
s
te
m
s
i
s
p
r
o
p
o
s
ed
in
R
ef
er
en
ce
[
8
]
.
I
n
R
ef
er
en
ce
[
9
]
,
a
m
u
lti
-
o
b
j
ec
tiv
e
f
r
a
m
e
w
o
r
k
is
p
r
o
p
o
s
ed
f
o
r
co
n
g
e
s
tio
n
m
a
n
ag
e
m
e
n
t
w
h
er
e
t
h
r
e
e
co
m
p
etin
g
o
b
j
ec
tiv
e
f
u
n
c
tio
n
s
i
n
cl
u
d
in
g
to
tal
o
p
er
atin
g
co
s
t,
v
o
lta
g
e
a
n
d
t
r
an
s
ie
n
t
s
tab
ilit
y
m
ar
g
i
n
s
ar
e
o
p
ti
m
ized
s
i
m
u
lta
n
eo
u
s
l
y
.
A
lo
ca
l
f
u
zz
y
b
ased
d
am
p
i
n
g
co
n
tr
o
ller
f
o
r
T
C
SC
to
i
m
p
r
o
v
e
tr
an
s
ien
t
s
ta
b
ilit
y
o
f
p
o
w
er
s
y
s
te
m
s
i
s
p
r
o
p
o
s
ed
in
[
1
0
]
.
I
n
R
e
f
er
e
n
ce
[
1
1
]
,
th
e
p
o
w
e
r
s
y
s
te
m
s
tab
ilit
y
i
n
cl
u
d
in
g
th
e
e
f
f
ec
ts
o
f
F
AC
T
S
co
n
tr
o
ller
s
is
p
r
o
p
o
s
ed
.
A
p
r
o
ce
d
u
r
e
f
o
r
m
o
d
ellin
g
a
n
d
o
p
ti
m
al
tu
n
i
n
g
th
e
p
ar
a
m
eter
s
o
f
T
C
SC
co
n
tr
o
ller
f
o
r
th
e
p
o
w
er
s
y
s
te
m
tr
an
s
ie
n
t
s
tab
ilit
y
is
p
r
o
p
o
s
ed
in
R
e
f
er
e
n
ce
[
1
2
]
.
R
ef
er
e
n
ce
[
1
3
]
p
r
o
p
o
s
es
th
e
u
s
e
o
f
s
p
ec
i
f
ic
F
AC
T
S
d
ev
ices
an
d
W
A
MS
s
y
s
te
m
s
to
m
ax
i
m
ize
to
tal
tr
an
s
f
er
ca
p
ab
ilit
y
g
en
er
all
y
d
ef
i
n
ed
as
t
h
e
m
a
x
i
m
u
m
p
o
w
er
tr
an
s
f
er
tr
an
s
ac
tio
n
i
n
C
e
n
tr
al
-
E
ast
-
E
u
r
o
p
e
p
o
w
er
s
y
s
te
m
.
T
h
e
ap
p
licatio
n
o
f
M
u
lti
-
Ob
j
ec
tiv
e
Ge
n
etic
A
l
g
o
r
ith
m
t
o
s
o
lv
e
t
h
e
Vo
ltag
e
Stab
ilit
y
C
o
n
s
tr
ain
ed
Op
ti
m
al
P
o
w
er
F
l
o
w
p
r
o
b
le
m
is
p
r
o
p
o
s
ed
in
[
1
4
]
.
A
m
at
h
e
m
atica
l
d
er
iv
atio
n
f
o
r
th
e
v
o
lta
g
e
d
ep
en
d
en
c
y
o
f
a
C
o
n
tr
o
llab
le
Ser
ies
C
o
m
p
en
s
ato
r
an
d
a
S
tatic
S
y
n
ch
r
o
n
o
u
s
Ser
ies
C
o
m
p
en
s
ato
r
in
a
s
i
n
g
le
-
lo
ad
in
f
in
i
tiv
e
-
b
u
s
m
o
d
el
is
p
r
o
p
o
s
ed
in
R
ef
er
e
n
ce
[
1
5
]
.
T
h
e
P
r
o
p
o
s
ed
So
lu
tio
n
:
I
n
o
r
d
er
to
im
p
r
o
v
e
t
h
e
T
r
an
s
ien
t
Stab
ilit
y
(
T
S)
m
ar
g
in
,
a
s
er
ies
F
AC
T
S
d
ev
ice
h
a
s
b
ee
n
i
m
p
le
m
en
ted
in
t
h
is
p
ap
er
.
A
f
u
zz
y
co
n
tr
o
ll
ed
T
C
SC
h
a
s
b
ee
n
u
s
ed
,
an
d
t
h
e
r
es
u
lts
h
i
g
h
li
g
h
t
th
e
e
f
f
ec
ti
v
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
in
i
m
p
r
o
v
i
n
g
t
h
e
tr
an
s
ien
t
s
tab
il
it
y
o
f
a
p
o
w
er
s
y
s
te
m
.
T
h
e
T
r
a
j
ec
to
r
y
Sen
s
iti
v
it
y
A
n
al
y
s
i
s
(
T
SA
)
h
as
b
ee
n
u
s
ed
to
m
ea
s
u
r
e
t
h
e
tr
an
s
ien
t
s
tab
ili
t
y
co
n
d
itio
n
o
f
th
e
s
y
s
te
m
.
T
h
e
T
C
SC
is
m
o
d
ele
d
b
y
a
v
ar
iab
le
ca
p
ac
ito
r
,
th
e
v
alu
e
o
f
w
h
ich
c
h
an
g
es
w
it
h
th
e
f
ir
in
g
an
g
le.
I
t is s
h
o
w
n
t
h
at
T
SA
ca
n
b
e
u
s
ed
in
th
e
d
esi
g
n
o
f
t
h
e
co
n
tr
o
ll
er
.
T
h
e
o
p
ti
m
al
lo
ca
tio
n
s
o
f
t
h
e
T
C
SC
co
n
tr
o
ller
f
o
r
d
if
f
er
e
n
t
f
a
u
lt
co
n
d
itio
n
s
ca
n
also
b
e
id
en
tif
ied
w
it
h
th
e
h
elp
o
f
T
SA
.
T
h
e
s
tu
d
ies
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t
in
o
r
d
er
to
im
p
r
o
v
e
t
h
e
T
r
an
s
ie
n
t
S
tab
ilit
y
(
T
S)
o
f
W
SC
C
3
m
ac
h
in
e
9
b
u
s
s
y
s
te
m
.
T
h
is
p
ap
er
d
ep
icts
th
e
ad
v
an
ta
g
e
o
f
t
h
e
u
s
e
o
f
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
b
y
u
s
i
n
g
th
e
T
C
S
C
.
T
h
e
r
em
ai
n
d
er
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
Sectio
n
2
d
escr
ib
e
ab
o
u
t
th
e
tr
an
s
ie
n
t
s
tab
ilit
y
an
al
y
s
is
a
n
d
th
e
m
o
d
elin
g
o
f
th
e
s
y
s
te
m
.
Sect
io
n
3
p
r
esen
t
s
th
e
tr
a
n
s
ie
n
t
s
tab
il
it
y
o
f
m
u
l
ti
-
m
ac
h
in
e
s
y
s
te
m
.
T
h
e
m
o
d
eli
n
g
o
f
T
C
SC
a
n
d
p
o
w
er
s
y
s
te
m
is
p
r
ese
n
ted
in
Sectio
n
4
.
T
h
e
tr
aj
ec
t
o
r
y
s
e
n
s
it
iv
i
t
y
a
n
al
y
s
i
s
is
p
r
esen
ted
in
Sectio
n
5
.
Sect
io
n
6
p
r
esen
t
s
r
es
u
lts
a
n
d
d
is
c
u
s
s
io
n
.
Fin
a
ll
y
,
Sectio
n
7
b
r
in
g
s
o
u
t
co
n
tr
ib
u
tio
n
s
w
it
h
co
n
cl
u
d
i
n
g
r
e
m
ar
k
s
.
2.
T
RANS
I
E
NT
S
T
AB
I
L
I
T
Y
ANALY
SI
S
T
h
e
tr
an
s
ien
t
s
tab
ili
t
y
s
t
u
d
ie
s
p
r
o
v
id
e
in
f
o
r
m
atio
n
r
elate
d
t
o
th
e
ca
p
ab
ilit
y
o
f
p
o
w
er
s
y
s
te
m
to
r
e
m
ain
in
s
y
n
c
h
r
o
n
i
s
m
d
u
r
i
n
g
m
aj
o
r
d
is
tu
r
b
an
ce
s
r
esu
ltin
g
f
r
o
m
e
ith
er
t
h
e
lo
s
s
o
f
g
e
n
er
ati
o
n
o
r
tr
an
s
m
i
s
s
io
n
f
ac
ilit
ies,
s
u
d
d
en
o
r
s
u
s
tai
n
e
d
lo
ad
ch
an
g
es,
o
r
m
o
m
en
ta
r
y
f
au
l
ts
.
Sp
ec
if
ical
l
y
,
th
e
s
e
s
tu
d
ie
s
p
r
o
v
id
e
t
h
e
ch
an
g
es
i
n
v
o
lta
g
e
s
,
cu
r
r
en
t
s
,
p
o
w
er
s
,
s
p
ee
d
s
,
an
d
to
r
q
u
e
s
o
f
m
ac
h
i
n
es
o
f
p
o
w
er
s
y
s
t
e
m
,
as
w
ell
as
t
h
e
ch
an
g
es
i
n
s
y
s
te
m
v
o
lta
g
e
s
an
d
p
o
w
er
f
lo
w
s
,
d
u
r
i
n
g
an
d
i
m
m
ed
iatel
y
f
o
llo
w
i
n
g
a
d
is
t
u
r
b
an
ce
.
T
r
an
s
ien
t
s
tab
ili
t
y
a
n
al
y
s
i
s
is
p
er
f
o
r
m
ed
b
y
co
m
b
in
i
n
g
th
e
s
o
lu
t
io
n
o
f
al
g
eb
r
aic
eq
u
at
io
n
s
d
escr
ib
in
g
t
h
e
n
et
w
o
r
k
w
i
th
n
u
m
er
ical
s
o
lu
ti
o
n
o
f
d
if
f
er
e
n
tia
l
E
q
u
at
io
n
s
[
1
6
]
.
T
h
e
s
o
lu
tio
n
o
f
t
h
e
n
e
t
w
o
r
k
eq
u
atio
n
s
r
etai
n
s
th
e
id
en
tit
y
o
f
t
h
e
s
y
s
te
m
,
an
d
th
er
eb
y
p
r
o
v
id
es
ac
ce
s
s
to
s
y
s
te
m
v
o
ltag
e
s
an
d
cu
r
r
en
ts
d
u
r
in
g
th
e
tr
an
s
ie
n
t
p
er
io
d
.
M
o
d
elin
g
o
f
t
h
e
s
y
s
te
m
is
p
r
ese
n
ted
n
e
x
t:
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
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n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
0
1
9
:
8
8
4
-
8
9
3
886
2
.
1
.
Sy
nchro
no
us
m
a
chi
ne
m
o
de
l
T
h
e
s
y
n
c
h
r
o
n
o
u
s
m
ac
h
in
e
is
r
ep
r
esen
ted
b
y
a
v
o
ltag
e
s
o
u
r
c
e,
in
b
ac
k
o
f
a
tr
an
s
ie
n
t
r
ea
cta
n
ce
,
th
a
t
is
co
n
s
ta
n
t
i
n
m
ag
n
it
u
d
e,
b
u
t
c
h
an
g
e
s
i
n
a
n
g
u
lar
p
o
s
itio
n
.
I
f
t
h
e
r
o
t
atio
n
al
p
o
w
er
lo
s
s
es
o
f
th
e
m
ac
h
in
e
d
u
e
to
s
u
c
h
e
f
f
ec
t
s
as
w
i
n
d
ag
e
a
n
d
f
r
ictio
n
ar
e
ig
n
o
r
ed
,
th
en
th
e
a
cc
eler
atin
g
p
o
w
er
eq
u
al
s
t
h
e
d
if
f
er
e
n
ce
b
et
w
ee
n
m
ec
h
a
n
ical
an
d
elec
tr
ica
l
p
o
w
er
[
6
]
.
T
h
e
class
ical
m
o
d
el
ca
n
b
e
d
escr
ib
ed
b
y
t
h
e
f
o
llo
w
in
g
s
et
o
f
d
i
f
f
er
e
n
tia
l
an
d
alg
eb
r
aic
eq
u
atio
n
s
:
Differ
en
tia
l E
q
u
a
tio
n
s
:
(
1
)
(
)
(
2
)
A
lg
eb
r
a
ic
E
q
u
a
tio
n
s
:
(
3
)
2
.
2
.
Repre
s
ent
a
t
io
n o
f
l
o
a
ds
P
o
w
er
s
y
s
te
m
lo
ad
s
,
o
th
er
th
a
n
m
o
to
r
s
ar
e
r
ep
r
esen
ted
b
y
e
q
u
iv
ale
n
t
cir
cu
its
,
an
d
ca
n
b
e
tr
ea
ted
in
s
ev
er
al
w
a
y
s
d
u
r
i
n
g
t
h
e
tr
an
s
i
en
t
p
er
io
d
.
T
h
e
co
m
m
o
n
l
y
u
s
ed
r
ep
r
esen
tatio
n
s
ar
e
eith
er
s
tatic
i
m
p
ed
an
ce
o
r
ad
m
itta
n
ce
to
g
r
o
u
n
d
,
co
n
s
ta
n
t
r
ea
l
an
d
r
ea
cti
v
e
p
o
w
er
,
o
r
a
co
m
b
in
at
io
n
o
f
t
h
ese
r
e
p
r
esen
tatio
n
s
[
1
7
]
.
T
h
e
p
ar
am
eter
s
as
s
o
ciate
d
w
i
th
s
tat
ic
i
m
p
ed
an
ce
a
n
d
co
n
s
t
an
t
cu
r
r
en
t
r
ep
r
esen
tatio
n
s
ar
e
o
b
tain
ed
f
r
o
m
th
e
s
ch
ed
u
led
b
u
s
lo
ad
s
.
T
h
e
b
u
s
v
o
ltag
e
s
ar
e
ca
lcu
lated
f
r
o
m
a
lo
ad
f
lo
w
s
o
l
u
tio
n
f
o
r
th
e
p
o
w
er
s
y
s
te
m
p
r
io
r
to
a
d
is
tu
r
b
an
ce
[
5
]
.
T
h
e
in
itial
v
alu
e
o
f
t
h
e
cu
r
r
en
t
f
o
r
a
co
n
s
tan
t
c
u
r
r
en
t
r
ep
r
esen
tatio
n
i
s
o
b
tain
ed
f
r
o
m
th
e
f
o
llo
w
in
g
eq
u
at
io
n
,
(
4
)
T
h
e
s
tatic
ad
m
itta
n
ce
(
Yp
o
)
is
u
s
ed
to
r
ep
r
esen
t th
e
lo
ad
at
b
u
s
P
,
an
d
ca
n
b
e
o
b
tain
ed
f
r
o
m
[
1
8
]
,
(
5
)
T
h
e
d
iag
o
n
al
ele
m
e
n
ts
o
f
ad
m
ittan
ce
m
atr
ix
(
YB
u
s
)
co
r
r
esp
o
n
d
in
g
to
th
e
lo
ad
b
u
s
ar
e
m
o
d
if
ied
u
s
i
n
g
Yp
o
.
2
.
3
.
Si
m
ula
t
io
n o
f
f
a
ults
A
f
a
u
lt
at
o
r
n
ea
r
a
b
u
s
is
s
i
m
u
lated
b
y
ap
p
r
o
p
r
iatel
y
ch
a
n
g
in
g
th
e
s
el
f
-
ad
m
it
tan
ce
o
f
t
h
e
b
u
s
.
Fo
r
a
th
r
ee
-
p
h
ase
f
a
u
lt,
t
h
e
f
a
u
lt
i
m
p
ed
a
n
ce
is
ze
r
o
,
an
d
t
h
e
f
a
u
lted
b
u
s
h
a
s
th
e
s
a
m
e
p
o
ten
tial
a
s
th
e
g
r
o
u
n
d
.
T
h
is
in
v
o
lv
e
s
p
lacin
g
in
f
i
n
ite
s
h
u
n
t
ad
m
itta
n
ce
,
s
o
t
h
at
t
h
e
b
u
s
v
o
lta
g
e
i
s
in
e
f
f
ec
t
ze
r
o
.
T
h
e
f
au
lt
i
s
r
e
m
o
v
ed
b
y
r
es
to
r
in
g
t
h
e
s
h
u
n
t a
d
m
itta
n
ce
to
th
e
ap
p
r
o
p
r
iate
v
alu
e
d
ep
en
d
in
g
o
n
th
e
p
o
s
t
-
f
au
l
t s
y
s
t
e
m
co
n
f
i
g
u
r
atio
n
.
2
.
4
.
Sin
g
le
m
a
chine c
o
nn
ec
t
ed
t
o
a
n infinit
e
bu
s
T
h
e
tr
an
s
ien
t
s
tab
ilit
y
p
er
tain
s
to
th
e
s
tab
ilit
y
u
n
d
er
lar
g
e
d
i
s
tu
r
b
an
ce
s
.
Hen
ce
,
t
h
e
n
o
n
-
li
n
ea
r
ties
o
f
th
e
m
o
d
el
h
a
v
e
to
b
e
co
n
s
id
er
ed
in
th
e
an
al
y
s
is
.
A
s
a
n
al
y
tical
s
o
l
u
tio
n
s
ar
e
n
o
t
av
a
il
ab
le
f
o
r
th
e
s
w
i
n
g
eq
u
atio
n
,
n
u
m
er
ical
m
e
th
o
d
s
h
av
e
to
b
e
u
s
ed
.
3.
T
RANS
I
E
NT
S
T
AB
I
L
I
T
Y
O
F
M
UL
T
I
-
M
ACH
I
NE
P
O
WE
R
SY
ST
E
M
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
d
eter
m
i
n
in
g
th
e
s
tab
ilit
y
o
f
m
u
l
ti
-
m
ac
h
i
n
e
s
y
s
te
m
i
s
d
escr
ib
ed
n
ex
t:
S
tep
1
:
Fro
m
t
h
e
p
r
e
-
f
a
u
lt
lo
ad
f
lo
w
d
ata,
d
eter
m
i
n
e
(
v
o
ltag
e
b
e
h
in
d
tr
a
n
s
ie
n
t
r
e
ac
tan
ce
)
f
o
r
al
l
g
en
er
ato
r
s
.
T
h
is
estab
lis
h
es
g
en
er
ato
r
em
f
m
a
g
n
it
u
d
es
|
|
,
w
h
ich
r
e
m
a
in
s
co
n
s
ta
n
t
d
u
r
in
g
th
e
s
tu
d
y
,
an
d
in
itial r
o
to
r
an
g
le
(
)
Als
o
,
r
ec
o
r
d
p
r
im
e
m
o
v
er
in
p
u
ts
to
g
e
n
er
ato
r
s
,
S
tep
2
:
A
u
g
u
m
e
n
t
th
e
lo
ad
f
l
o
w
n
et
w
o
r
k
b
y
t
h
e
g
e
n
er
ato
r
tr
an
s
ie
n
t
r
ea
cta
n
ce
s
.
Sh
if
t
n
e
t
w
o
r
k
b
u
s
e
s
b
eh
in
d
th
e
tr
an
s
ien
t r
ea
ctan
ce
s
.
S
tep
3
:
Fin
d
f
o
r
v
ar
io
u
s
n
et
w
o
r
k
co
n
d
it
io
n
s
:
d
u
r
in
g
f
au
l
t
,
p
o
s
t
f
au
lt
(
f
au
l
ted
lin
e
clea
r
ed
)
,
af
ter
lin
e
r
ec
lo
s
u
r
e.
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
Tr
a
n
s
ien
t sta
b
ilit
y
en
h
a
n
ce
men
t u
s
in
g
th
yris
to
r
co
n
tr
o
lled
s
eries
co
mp
en
s
a
to
r
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
887
S
tep
4
:
Fo
r
f
au
lted
m
o
d
e,
f
i
n
d
g
en
er
ato
r
o
u
tp
u
ts
f
r
o
m
p
o
w
e
r
an
g
le
eq
u
atio
n
s
,
an
d
s
o
lv
e
t
h
e
s
w
i
n
g
eq
u
at
io
n
s
b
y
u
s
i
n
g
t
h
e
s
tep
b
y
s
tep
/p
o
in
t
b
y
p
o
in
t
m
et
h
o
d
o
r
an
y
i
n
teg
r
at
io
n
al
g
o
r
ith
m
s
s
u
c
h
a
s
m
o
d
if
ied
E
u
ler
’
s
m
et
h
o
d
,
R
u
n
g
a
K
u
tta
f
o
u
r
t
h
o
r
d
er
m
et
h
o
d
,
etc.
S
tep
5
:
Kee
p
r
ep
ea
tin
g
th
e
ab
o
v
e
s
tep
f
o
r
p
o
s
t
-
f
au
lt
m
o
d
e
an
d
af
ter
li
n
e
r
ec
lo
s
u
r
e
m
o
d
e.
S
tep
6
:
E
x
a
m
i
n
e
δ(
t)
p
lo
ts
f
o
r
all
th
e
g
e
n
er
ato
r
s
,
an
d
estab
li
s
h
th
e
a
n
s
w
er
to
th
e
s
tab
ilit
y
q
u
esti
o
n
.
3
.
1
.
Alg
o
rit
h
m
f
o
r
net
w
o
rk
re
du
ct
io
n t
ec
hn
iq
ue
T
o
p
r
e
p
ar
e
th
e
s
y
s
te
m
d
ata
f
o
r
s
tab
ilit
y
s
tu
d
y
,
th
e
f
o
llo
w
i
n
g
p
r
eli
m
in
ar
y
ca
lcu
latio
n
s
ar
e
r
eq
u
ir
ed
:
a)
A
ll
s
y
s
te
m
d
ata
ar
e
co
n
v
er
ted
to
a
co
m
m
o
n
b
ase.
b)
T
h
e
lo
ad
s
ar
e
co
n
v
er
ted
to
eq
u
iv
a
len
t
i
m
p
ed
an
ce
s
o
r
ad
m
itt
an
ce
s
.
T
h
e
n
ee
d
ed
d
ata
f
o
r
th
i
s
s
tep
ar
e
o
b
tain
ed
f
r
o
m
th
e
lo
ad
f
lo
w
s
t
u
d
y
[
1
9
]
.
T
h
er
ef
o
r
e,
if
a
ce
r
tai
n
lo
ad
b
u
s
h
a
s
a
v
o
ltag
e
V
L
,
p
o
w
er
P
L
,
r
ea
ctiv
e
p
o
w
er
Q
L
,
an
d
cu
r
r
en
t I
L
f
lo
w
i
n
g
in
to
th
e
lo
ad
ad
m
ittan
ce
Y
L
=G
L
+j
B
L
,
th
e
n
,
(
)
(
6
)
T
h
e
eq
u
iv
alen
t sh
u
n
t a
d
m
i
ttan
ce
at
th
at
b
u
s
i
s
g
i
v
e
n
b
y
,
YL
=P
L
/V
L
2
–
j
(
QL
/VL
2
)
(
7
)
c)
T
h
e
in
ter
n
al
v
o
lta
g
es
o
f
th
e
g
e
n
er
ato
r
s
E
i∟
ar
e
ca
lcu
lated
f
r
o
m
t
h
e
lo
ad
f
lo
w
d
ata.
T
h
ese
in
ter
n
al
an
g
le
s
m
a
y
b
e
co
m
p
u
ted
f
r
o
m
th
e
p
r
e
-
tr
an
s
ien
t te
r
m
i
n
al
v
o
lt
ag
es V
∟
α
a
s
f
o
llo
w
s
:
L
et
t
h
e
ter
m
in
a
l
v
o
lta
g
e
b
e
u
s
ed
te
m
p
o
r
ar
il
y
as
a
r
e
f
er
en
c
e.
I
f
w
e
d
e
f
i
n
e
I
=I
1
+j
I
2
,
th
en
f
r
o
m
t
h
e
r
elatio
n
P
+j
Q
=
VI
*
.
W
e
h
av
e
I
1
+
j
I
2
=
(
P
–
j
Q)
/V,
s
in
ce
E
∟
δ
’
=
V+
j
x
d
’
I
.
W
e
co
m
p
u
te
[
2
0
]
,
E
∟
δ
’
=
(
V+
QXd
’
/V)
+
j
(
P
X
d
’
/V)
(
8
)
T
h
e
in
itial g
e
n
er
ato
r
an
g
le
δ0
is
th
e
n
o
b
tain
ed
b
y
ad
d
in
g
th
e
p
r
e
-
tr
an
s
ie
n
t
v
o
ltag
e
a
n
g
le
α
t
o
δ’
,
o
r
δ0
=
δ’
+
α
.
d)
T
h
e
Yb
u
s
m
atr
i
x
f
o
r
ea
ch
n
et
w
o
r
k
co
n
d
it
io
n
is
ca
lc
u
lated
.
e)
Fin
all
y
,
w
e
el
i
m
in
ate
a
ll
t
h
e
n
o
d
es
ex
ce
p
t
f
o
r
th
e
i
n
ter
n
al
g
en
er
ato
r
n
o
d
es,
a
n
d
o
b
tain
th
e
Yb
u
s
m
atr
i
x
f
o
r
t
h
e
r
ed
u
ce
d
n
e
t
w
o
r
k
.
T
h
e
r
ed
u
ctio
n
ca
n
b
e
ac
h
i
ev
ed
b
y
m
atr
ix
o
p
er
atio
n
,
all
th
e
n
o
d
es
h
av
e
ze
r
o
in
j
ec
tio
n
c
u
r
r
en
ts
e
x
ce
p
t
f
o
r
th
e
i
n
ter
n
al
g
e
n
er
at
o
r
n
o
d
es.
T
h
is
p
r
o
p
er
ty
is
u
s
e
d
to
o
b
tain
th
e
n
et
w
o
r
k
r
ed
u
ctio
n
,
a
n
d
is
ex
p
lain
ed
b
elo
w
,
I
=Y
V
(
9
)
Y
an
d
V
m
a
tr
ices
ar
e
p
ar
titi
o
n
ed
ac
co
r
d
in
g
l
y
.
V
n
h
a
s
th
e
d
i
m
e
n
s
io
n
(
n
*
1
)
,
Vr
h
as
t
h
e
d
i
m
en
s
io
n
(
r
*
1
)
.
E
x
p
an
d
i
n
g
t
h
e
ab
o
v
e
m
a
tr
ix
,
I
n
=Y
n
n
V
n
+Y
n
r
Vr
(
1
0
)
0
=Y
r
n
Vn
+Y
r
r
Vr
(
1
1
)
W
h
er
e
th
e
s
u
b
s
cr
ip
t
'
n
'
is
u
s
ed
to
r
e
p
r
esen
t
th
e
g
e
n
er
at
o
r
n
o
d
es,
an
d
th
e
s
u
b
s
cr
ip
t
'
r
'
is
u
s
e
d
f
o
r
th
e
r
em
ai
n
i
n
g
n
o
d
es.
Fro
m
w
h
ich
,
w
e
eli
m
i
n
ate
V,
to
f
in
d
I
n
=
(
Yn
n
-
Y
n
r
Yr
r
-
1
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h
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h
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ated
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f
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t.
3
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2
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Va
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h
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ited
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s
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is
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er
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.
W
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th
e
Flex
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an
s
m
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io
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y
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te
m
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AC
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S)
tech
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h
a
s
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ee
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d
em
o
n
s
tr
ated
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h
at
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ar
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m
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en
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atio
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h
i
g
h
l
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f
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o
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n
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lo
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th
e
l
in
e
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d
in
i
m
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r
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ilit
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r
ies
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p
ac
ito
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v
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ee
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cc
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l
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et
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r
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t
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ted
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p
ac
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o
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ce
t
h
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f
ec
t
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ea
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ce
o
f
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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I
n
t J
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p
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3
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3
.
T
hy
risto
r
co
ntr
o
lled ser
ies ca
pa
cit
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r
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T
CSC)
T
C
SC
co
n
s
i
s
ts
o
f
th
e
s
er
ies
co
m
p
e
n
s
at
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g
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p
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ito
r
s
h
u
n
ted
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a
T
h
y
r
is
to
r
C
o
n
tr
o
lle
d
R
ea
cto
r
(
T
C
R
)
as
s
h
o
w
n
in
F
ig
u
r
e
1
.
I
n
a
p
r
ac
tical
T
C
SC
i
m
p
le
m
e
n
tatio
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,
s
e
v
er
al
s
u
ch
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asic
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m
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e
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ato
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a
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ted
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er
ies to
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e
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esire
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o
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e
r
ati
n
g
an
d
o
p
er
atin
g
ch
ar
ac
ter
is
tics
[
2
1
]
.
X
P
X
F
C
X
C
V
S
-
+
Fig
u
r
e
1
.
Sch
e
m
atic
d
iag
r
a
m
o
f
T
C
SC
T
h
is
ar
r
an
g
e
m
e
n
t
i
s
s
i
m
ilar
in
s
tr
u
ctu
r
e
to
th
e
T
h
y
r
is
t
o
r
S
w
i
tch
ed
Ser
ies
C
ap
ac
it
o
r
(
T
SS
C
)
,
an
d
if
t
h
e
i
m
p
ed
a
n
ce
o
f
t
h
e
r
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cto
r
(
XL
)
is
s
u
f
f
icie
n
tl
y
s
m
al
ler
th
an
t
h
at
o
f
t
h
e
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p
ac
ito
r
(
XC
)
,
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e
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it
ca
n
b
e
o
p
er
ated
in
an
ON/OFF
m
a
n
n
er
lik
e
t
h
e
T
SS
C
.
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w
ev
er
,
th
e
b
asic
id
ea
b
eh
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n
d
th
e
T
C
S
C
s
ch
e
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e
i
s
to
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r
o
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e
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tin
u
o
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s
l
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ar
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le
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p
ac
ito
r
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y
m
ea
n
s
o
f
p
ar
tially
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n
ce
li
n
g
t
h
e
ef
f
e
ctiv
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m
p
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s
ati
n
g
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p
ac
itan
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y
t
h
e
T
C
R
.
T
C
R
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th
e
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u
n
d
a
m
e
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tal
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te
m
f
r
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en
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o
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l
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ar
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le
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m
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ce
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n
tr
o
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le
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ela
y
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g
le
α
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h
e
s
tead
y
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tate
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m
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ce
o
f
th
e
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C
S
C
is
t
h
at
o
f
a
p
ar
allel
L
C
cir
cu
i
t,
co
n
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i
s
ti
n
g
o
f
a
f
i
x
ed
c
ap
ac
itiv
e
i
m
p
ed
a
n
ce
(
Xc)
,
an
d
a
v
ar
iab
le
in
d
u
c
ti
v
e
i
m
p
ed
a
n
c
e,
XL
(
α
)
,
th
at
i
s
.
(
)
(
)
(
1
3
)
W
h
er
e
XL
(
α
)
=X
L
*
π/(
π
-
2
α
-
s
i
n
α
)
,
X
L
≤
XL
(
α
)
≤
∞,
XL
=ω
L
.
T
C
SC
p
r
esen
ts
a
tu
n
ab
le
p
ar
allel
L
C
cir
cu
it
to
th
e
l
i
n
e
c
u
r
r
en
t
th
at
is
s
u
b
s
tan
tiall
y
a
co
n
s
tan
t
alter
n
a
tin
g
c
u
r
r
en
t
s
o
u
r
ce
.
As
t
h
e
i
m
p
ed
an
c
e
o
f
t
h
e
co
n
tr
o
lled
r
ea
cto
r
(
XL
(
α
)
)
is
v
ar
ied
f
r
o
m
it
s
m
a
x
i
m
u
m
(
in
f
i
n
it
y
)
to
w
ar
d
its
m
i
n
i
m
u
m
(
ω
L
)
,
t
h
e
T
C
SC
in
cr
ea
s
es
it
s
m
i
n
i
m
u
m
ca
p
ac
itiv
e
i
m
p
ed
a
n
ce
,
XT
C
SC
m
i
n
=X
c=
1
/ω
C
,
(
an
d
t
h
er
eb
y
t
h
e
d
e
g
r
ee
o
f
s
er
ies
ca
p
ac
iti
v
e
co
m
p
e
n
s
at
io
n
)
u
n
t
il
p
ar
allel
r
eso
n
an
ce
at
Xc=
XL
(
α
)
i
s
est
ab
lis
h
ed
,
a
n
d
XT
C
SC
m
a
x
t
h
eo
r
etica
ll
y
b
ec
o
m
e
s
in
f
in
ite.
4.
M
O
DE
L
I
N
G
O
F
T
C
SC
T
h
e
o
v
er
all
r
ea
ctan
ce
XC
o
f
t
h
e
T
C
SC
[
2
]
is
g
i
v
en
i
n
ter
m
s
o
f
th
e
f
ir
in
g
a
n
g
le
α
as [
2
2
]
,
(
)
(
1
4
)
W
h
er
e
(
)
(
)
,
,
√
,
[
(
)
]
(
)
an
d
(
)
I
n
t
h
is
p
ap
er
,
it is
co
n
s
id
er
ed
th
at
t
h
e
T
C
S
C
i
s
o
p
er
ated
o
n
l
y
in
th
e
ca
p
ac
iti
v
e
m
o
d
e.
T
h
e
c
ap
ac
itiv
e
r
ea
cta
n
ce
(
XFC
)
o
f
th
e
T
C
SC
is
ch
o
s
e
n
as
h
alf
o
f
th
e
r
ea
ctan
ce
o
f
t
h
e
lin
e
in
w
h
ic
h
th
e
T
C
SC
i
s
p
lace
d
,
an
d
th
e
T
C
R
r
ea
ctan
ce
(
XP
)
is
ch
o
s
en
to
b
e
1
/3
o
f
XFC
.
I
n
th
e
n
e
x
t
s
tep
,
a
co
n
tr
o
ller
is
e
m
p
lo
y
ed
alo
n
g
w
it
h
th
e
T
C
S
C
.
T
h
e
b
lo
ck
d
iag
r
am
o
f
t
h
e
co
n
tr
o
l
s
ch
e
m
e
u
s
ed
is
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
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
Tr
a
n
s
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t sta
b
ilit
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n
ce
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t u
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in
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eries
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en
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to
r
(
S
u
r
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ed
d
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a
lku
ti
)
889
K
P
+
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/
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r
e
f
T
C
S
C
C
T
C
S
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C
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n
t
r
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l
l
e
r
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u
r
e
2
.
B
lo
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iag
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a
m
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f
co
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tr
o
l sch
e
m
e
T
h
e
ac
tiv
e
p
o
w
er
f
lo
w
(
P
)
t
h
r
o
u
g
h
th
e
li
n
e
co
n
tai
n
in
g
T
C
S
C
i
s
ta
k
en
as
t
h
e
co
n
tr
o
l
v
ar
iab
le.
I
t
is
co
m
p
ar
ed
w
i
th
t
h
e
r
ef
er
en
ce
v
al
u
e
o
f
ac
ti
v
e
p
o
w
er
f
l
o
w
(
P
r
ef
)
,
an
d
th
e
er
r
o
r
is
f
e
d
to
a
P
r
o
p
o
r
tio
n
al
I
n
teg
r
al
(
P
I
)
co
n
tr
o
ller
.
T
h
e
o
u
tp
u
t
o
f
t
h
e
P
I
is
th
e
f
ir
in
g
a
n
g
le
o
f
t
h
e
T
C
SC
(
α
)
.
T
h
is
α
i
s
p
ass
ed
t
h
r
o
u
g
h
a
li
m
iter
to
k
ee
p
it
w
it
h
in
th
e
c
ap
ac
itiv
e
o
p
er
atio
n
zo
n
e
o
f
t
h
e
T
C
SC
(
b
et
w
ee
n
1
4
5
◦
an
d
1
8
0
◦
)
.
T
h
e
o
u
tp
u
t
o
f
th
e
l
i
m
iter
is
s
u
p
p
lied
to
t
h
e
f
ir
in
g
cir
cu
it
o
f
T
C
SC
.
T
h
e
c
ap
ac
itan
ce
o
f
T
C
SC
(
C
T
C
S
C
)
is
i
n
cl
u
d
ed
in
t
h
e
lin
e
d
y
n
a
m
ics.
5.
T
RAJ
E
C
T
O
RY
S
E
NS
I
T
I
V
I
T
Y
ANA
L
YS
I
S
Mu
lti
-
m
ac
h
in
e
p
o
w
er
s
y
s
te
m
i
s
r
ep
r
esen
ted
b
y
a
s
et
o
f
d
if
f
er
en
tial e
q
u
at
io
n
s
,
̇
(
)
(
)
(
1
5
)
T
h
e
s
en
s
iti
v
itie
s
o
f
s
tate
tr
aj
ec
to
r
ies
w
it
h
r
esp
ec
t
to
s
y
s
te
m
p
ar
a
m
eter
s
ca
n
b
e
f
o
u
n
d
b
y
p
er
tu
r
b
in
g
f
r
o
m
it
s
n
o
m
in
a
l v
al
u
e
.
T
h
e
eq
u
atio
n
s
o
f
tr
aj
ec
to
r
y
s
e
n
s
it
iv
i
t
y
[
2
]
ar
e,
̇
*
+
*
+
(
)
(
1
6
)
W
h
er
e
⁄
.
T
h
e
s
en
s
iti
v
itie
s
ca
n
b
e
f
o
u
n
d
i
n
a
s
i
m
p
ler
w
a
y
b
y
u
s
i
n
g
th
e
n
u
m
er
ical
m
et
h
o
d
.
5
.
2
.
Q
ua
ntif
ica
t
io
n o
f
t
ra
j
ec
t
o
ry
s
ens
it
iv
it
y
(
T
S)
a
nd
it
s
i
m
p
lica
t
io
n
T
r
a
j
ec
to
r
y
s
e
n
s
it
iv
i
ties
(
⁄
)
an
d
(
⁄
)
g
iv
es
t
h
e
in
f
o
r
m
atio
n
ab
o
u
t
th
e
ef
f
ec
t
o
f
ch
a
n
g
e
o
f
p
ar
a
m
eter
o
n
i
n
d
iv
id
u
al
s
ta
te
v
ar
iab
les,
an
d
h
e
n
ce
o
n
t
h
e
g
e
n
er
ato
r
s
o
f
t
h
e
s
y
s
te
m
.
Ho
w
e
v
er
,
to
k
n
o
w
t
h
e
o
v
er
all
s
y
s
te
m
co
n
d
it
io
n
,
w
e
n
ee
d
to
s
u
m
u
p
all
th
ese
i
n
f
o
r
m
atio
n
.
T
h
e
n
o
r
m
o
f
th
e
s
e
n
s
iti
v
ities
o
f
an
d
ar
e
ca
lcu
lated
.
T
h
e
s
en
s
iti
v
it
y
n
o
r
m
f
o
r
m
m
ac
h
i
n
e
s
y
s
te
m
i
s
g
i
v
en
b
y
,
√
∑
[
(
)
(
)
]
(
1
7
)
A
n
e
w
ter
m
ƞ
(
E
T
A
)
is
d
e
f
in
ed
as
th
e
in
v
er
s
e
o
f
t
h
e
m
ax
i
m
u
m
o
f
SN,
i.e
.
,
(
)
⁄
.
As th
e
s
y
s
te
m
m
o
v
es
t
o
w
ar
d
s
in
s
tab
il
it
y
,
t
h
e
o
s
cil
latio
n
i
n
tr
aj
ec
to
r
y
s
en
s
iti
v
it
y
(
T
S)
w
ill b
e
m
o
r
e
r
esu
lt
in
g
i
n
lar
g
er
v
al
u
es
o
f
SN.
T
h
is
w
i
ll
r
esu
lt
in
th
e
s
m
a
ller
v
al
u
es
o
f
η
.
I
d
ea
ll
y
,
η
s
h
o
u
ld
b
e
z
er
o
at
th
e
p
o
in
t
o
f
in
s
tab
il
it
y
.
T
h
er
ef
o
r
e,
th
e
v
al
u
e
o
f
η
g
iv
e
s
u
s
an
i
n
d
i
ca
tio
n
o
f
d
is
ta
n
ce
f
r
o
m
i
n
s
tab
ili
t
y
.
I
n
t
h
i
s
p
ap
er
,
η
i
s
u
s
ed
f
o
r
ass
es
s
i
n
g
t
h
e
r
elativ
e
s
tab
ilit
y
co
n
d
itio
n
s
o
f
th
e
s
y
s
te
m
w
it
h
d
if
f
er
en
t
v
alu
e
s
o
f
f
au
lt
clea
r
in
g
ti
m
e,
s
y
s
te
m
lo
ad
an
d
f
ir
in
g
an
g
le
o
f
T
C
SC
.
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
i
s
p
ap
er
,
W
SC
C
3
m
ac
h
i
n
e
n
i
n
e
-
b
u
s
s
y
s
te
m
[
2
2
]
is
co
n
s
id
er
ed
to
s
h
o
w
t
h
e
ef
f
ec
t
iv
e
n
es
s
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
A
t
h
r
ee
-
p
h
a
s
e
f
au
lt
is
s
i
m
u
lated
in
o
n
e
o
f
th
e
lin
e
s
o
f
t
h
e
n
i
n
e
-
b
u
s
s
y
s
te
m
.
T
h
e
s
i
m
u
latio
n
i
s
d
o
n
e
i
n
th
r
ee
s
tep
s
.
T
o
s
tar
t
w
i
th
,
th
e
p
r
e
-
f
a
u
lt
s
y
s
te
m
i
s
r
u
n
f
o
r
a
s
m
all
ti
m
e.
T
h
en
,
a
s
y
m
m
etr
ical
f
a
u
lt
is
a
p
p
lied
at
o
n
e
en
d
o
f
t
h
e
li
n
e.
Si
m
u
latio
n
o
f
t
h
e
f
a
u
lted
co
n
d
itio
n
co
n
ti
n
u
es
till
th
e
f
a
u
lt
is
clea
r
ed
af
ter
a
ti
m
e
tcl.
T
h
en
,
th
e
p
o
s
t
-
f
a
u
lt
s
y
s
te
m
is
s
i
m
u
lated
f
o
r
a
lo
n
g
er
ti
m
e
(
s
a
y
5
s
ec
)
to
o
b
s
er
v
e
th
e
n
at
u
r
e
o
f
t
h
e
tr
a
n
s
ie
n
t
s
.
T
h
e
f
a
u
lt
m
a
y
b
e
o
f
s
el
f
-
c
lear
in
g
t
y
p
e
(
i.e
.
,
is
o
la
tio
n
o
f
li
n
e
i
s
n
o
t
r
eq
u
ir
ed
f
o
r
f
a
u
lt
clea
r
a
n
ce
)
o
r
m
a
y
b
e
clea
r
ed
b
y
i
s
o
latin
g
th
e
f
au
lted
li
n
e.
T
ab
le
1
p
r
esen
ts
th
e
n
o
r
m
alize
d
v
alu
e
s
o
f
eta
(
ƞ
)
f
o
r
th
e
n
i
n
e
b
u
s
te
s
t s
y
s
te
m
w
it
h
T
C
SC
p
lac
ed
in
d
if
f
er
e
n
t
f
au
l
t lo
ca
tio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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I
n
t J
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&
C
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p
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n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il 2
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1
9
:
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8
4
-
8
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3
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T
ab
le
1
.
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r
m
al
ized
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(
E
T
A
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Valu
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o
f
9
B
u
s
S
y
s
te
m
f
o
r
T
C
S
C
P
lace
d
in
Dif
f
er
en
t
Fau
l
t
L
o
ca
tio
n
s
F
a
u
l
t
a
t
b
u
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n
e
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so
l
a
t
e
d
L
i
n
e
4
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5
L
i
n
e
5
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7
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i
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e
4
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6
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i
n
e
6
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L
i
n
e
7
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8
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i
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e
8
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5
4
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5
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2
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1
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9
9
5
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3
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0
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9
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4
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3
1
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4
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6
0
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8
2
0
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2
0
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1
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0
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4
1
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0
1
3
6
6
-
9
1
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0
0
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0
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9
6
8
0
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9
0
1
---
1
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0
1
9
0
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9
2
7
8
7
-
8
1
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0
2
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1
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6
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1
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0
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3
9
1
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8
3
0
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9
3
0
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7
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0
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9
5
1
---
Her
e,
tr
aj
ec
to
r
y
s
e
n
s
itiv
it
y
m
e
th
o
d
is
u
s
ed
to
f
in
d
t
h
e
lo
ca
ti
o
n
,
w
h
ic
h
i
m
p
r
o
v
e
s
t
h
e
s
tab
ili
t
y
m
ar
g
i
n
to
m
a
x
i
m
u
m
.
Fig
u
r
e
3
p
r
ese
n
ts
t
h
e
c
h
ar
ac
ter
is
tic
s
o
f
r
elati
v
e
r
o
to
r
an
g
le
f
o
r
th
e
f
au
lt
at
7
th
b
u
s
,
li
n
e
5
-
7
is
o
p
en
ed
w
it
h
f
a
u
lt c
lear
i
n
g
t
i
m
e
o
f
0
.
0
8
7
3
s
ec
,
w
h
er
ea
s
w
i
th
5
0
% c
o
m
p
en
s
atio
n
h
a
s
b
ee
n
d
ep
icted
in
Fig
u
r
e
4
.
Fig
u
r
e
3
.
Fau
lt a
t 7
th
b
u
s
,
li
n
e
5
-
7
is
o
p
en
ed
.
C
lear
in
g
ti
m
e
0
.
0
8
7
3
Sec
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u
r
e
4
.
Fau
lt a
t 7
th
b
u
s
,
li
n
e
5
-
7
is
o
p
en
ed
.
C
lear
in
g
ti
m
e
is
0
.
0
8
7
3
Sec,
w
i
th
5
0
% c
o
m
p
en
s
atio
n
W
h
en
T
C
SC
S
is
p
lace
d
in
li
n
e
6
-
9
,
th
e
r
elati
v
e
r
o
to
r
an
g
le
is
d
ep
icted
in
Fi
g
u
r
e
5
,
wh
ich
r
ep
r
ese
n
ts
t
h
e
i
m
p
r
o
v
ed
tr
an
s
ie
n
t
s
tab
ilit
y
o
f
th
e
s
y
s
te
m
.
Fi
g
u
r
e
6
d
ep
icts
th
e
r
elativ
e
r
o
to
r
an
g
le
f
o
r
th
e
f
a
u
lt
at
7
t
h
b
u
s
,
lin
e
5
-
7
is
o
p
en
ed
a
n
d
th
e
f
a
u
lt
clea
r
in
g
ti
m
e
i
s
0
.
1
8
s
ec
.
T
h
e
r
elativ
e
r
o
to
r
an
g
le
f
o
r
th
e
f
au
lt
at
7
t
h
b
u
s
,
li
n
e
5
-
7
is
o
p
en
ed
w
it
h
t
h
e
f
a
u
lt c
l
ea
r
in
g
ti
m
e
o
f
0
.
2
2
s
ec
an
d
5
0
% f
i
x
ed
co
m
p
en
s
atio
n
i
s
d
ep
icted
in
Fig
u
r
e
7
.
0
0.
5
1
1.
5
2
2.
5
0
500
1000
1500
2000
2500
t
im
e
in
s
ec
rela
t
iv
e
rot
or
ang
le
in
deg
del
t
a21
del
t
a31
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0.
5
1
1.
5
2
2.
5
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0
20
40
60
80
t
im
e
in
s
ec
rela
t
iv
e
rot
or
ang
le
in
deg
del
t
a21
del
t
a31
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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m
p
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2
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t u
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to
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co
n
tr
o
lled
s
eries
co
mp
en
s
a
to
r
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
891
Fig
u
r
e
5
.
Fau
lt a
t 7
th
b
u
s
,
li
n
e
5
-
7
is
o
p
en
ed
.
C
lear
in
g
ti
m
e
is
0
.
0
8
7
3
s
ec
w
ith
Kp
=0
.
8
,
Ki=9
.
T
C
SC
is
p
lace
d
in
li
n
e
6
-
9
Fig
u
r
e
6
.
Fau
lt a
t 7
th
b
u
s
,
li
n
e
5
-
7
is
o
p
en
ed
.
C
lear
in
g
ti
m
e
is
0
.
1
8
Sec
Fig
u
r
e
7
.
Fau
lt a
t 7
th
b
u
s
,
li
n
e
5
-
7
is
o
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en
ed
.
C
lear
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g
ti
m
e
is
0
.
2
2
Sec
w
it
h
5
0
% f
i
x
ed
co
m
p
en
s
atio
n
T
C
SC
ca
u
s
es
i
m
p
r
o
v
e
m
e
n
t
o
f
s
y
s
te
m
s
tab
il
it
y
co
n
d
itio
n
t
h
e
m
o
s
t,
w
h
e
n
i
t
is
p
lace
d
in
l
in
e
6
-
9
o
r
lin
e
5
-
7
.
T
h
er
ef
o
r
e,
w
e
s
h
all
s
tu
d
y
th
e
e
f
f
ec
t
o
f
T
C
SC
(
alo
n
g
w
ith
co
n
tr
o
ller
)
in
th
e
s
e
t
w
o
lo
ca
tio
n
s
.
An
o
th
er
in
ter
esti
n
g
i
s
s
u
e
is
th
e
co
m
p
ar
is
o
n
b
et
w
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ts
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s
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p
ac
i
to
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d
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h
e
e
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f
ec
ts
o
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a
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co
n
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o
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co
m
b
i
n
atio
n
(
w
i
th
s
u
i
tab
l
y
c
h
o
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en
co
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tr
o
ller
co
n
s
ta
n
ts
)
o
n
t
h
e
tr
an
s
ie
n
t
s
tab
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n
d
itio
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ar
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esti
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ated
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d
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er
e.
Fro
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th
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i
m
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la
tio
n
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ie
s
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e
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n
clu
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ed
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at
th
e
i
m
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r
o
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e
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in
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h
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a
n
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u
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e
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it
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t
h
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m
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.
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h
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g
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li
g
h
t
th
e
ef
f
ec
ti
v
e
n
ess
o
f
t
h
e
ap
p
licatio
n
o
f
T
C
SC
alo
n
g
w
ith
a
c
o
n
tr
o
ller
in
i
m
p
r
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v
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t
h
e
tr
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s
ie
n
t
s
tab
ili
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y
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f
a
p
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s
y
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te
m
.
7.
CO
NCLU
SI
O
NS
T
h
is
p
ap
er
p
r
esen
ts
t
h
e
i
m
p
r
o
v
e
m
e
n
ts
o
f
tr
an
s
ien
t
s
tab
ilit
y
u
s
in
g
T
C
S
C
.
A
cc
u
r
ate
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n
al
y
s
i
s
o
f
t
h
e
tr
an
s
ie
n
t
s
tab
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y
r
eq
u
ir
es
t
h
e
d
etailed
m
o
d
eli
n
g
o
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g
e
n
er
atin
g
u
n
it
s
,
an
d
o
th
er
eq
u
ip
m
en
ts
.
I
n
th
i
s
p
ap
er
,
th
e
tr
an
s
ien
t
s
tab
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y
a
s
s
es
s
m
en
t
o
f
W
SC
C
-
9
b
u
s
s
y
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te
m
i
s
d
o
n
e
f
o
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d
if
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er
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t
ca
s
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s
s
u
c
h
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a
u
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s
el
f
clea
r
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y
p
e,
f
a
u
lt
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r
ed
b
y
lin
e
r
e
m
o
v
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l,
etc.
T
h
e
d
am
p
in
g
o
f
th
e
s
y
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te
m
i
s
in
co
r
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ated
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d
th
e
an
al
y
s
i
s
g
iv
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s
t
h
e
b
etter
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h
e
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ase
s
t
u
d
ies
d
ep
icts
t
h
e
o
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ti
m
a
l
lo
ca
tio
n
o
f
f
i
x
ed
co
m
p
en
s
ati
o
n
in
t
h
e
W
S
C
C
9
b
u
s
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y
s
te
m
as
li
n
e
6
-
9
,
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ased
o
n
th
e
f
ir
s
t
s
w
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p
ea
k
v
alu
e
r
ed
u
ctio
n
.
T
h
e
T
C
SC
co
n
tr
o
ller
h
as
b
ee
n
m
o
d
eled
an
d
i
m
p
le
m
e
n
ted
o
n
t
h
e
W
S
C
C
9
b
u
s
s
y
s
te
m
at
th
e
o
p
ti
m
al
lo
ca
tio
n
.
T
h
e
r
es
u
lts
h
ig
h
li
g
h
t
th
e
ef
f
ec
ti
v
e
n
es
s
o
f
th
e
ap
p
licatio
n
o
f
t
h
e
T
C
S
C
in
i
m
p
r
o
v
i
n
g
t
h
e
tr
an
s
ie
n
t st
ab
ilit
y
o
f
p
o
w
er
s
y
s
te
m
.
ACK
NO
WL
E
D
G
M
E
NT
S
T
h
is
r
esear
ch
w
o
r
k
h
a
s
b
ee
n
ca
r
r
ied
o
u
t
b
ased
o
n
t
h
e
s
u
p
p
o
r
t
o
f
“
W
o
o
s
o
n
g
U
n
i
v
er
s
it
y
's
A
ca
d
e
m
ic
R
esear
ch
Fu
n
d
in
g
-
2
0
1
8
”.
RE
F
E
R
E
NC
E
S
[1
]
Ku
n
d
u
r
P
,
P
a
se
rb
a
J,
“
De
f
in
it
io
n
a
n
d
Clas
sif
ica
ti
o
n
o
f
P
o
w
e
r
S
y
ste
m
S
tab
il
it
y
,
”
IEE
E
T
ra
n
sa
c
t
io
n
s
o
n
Po
we
r
S
y
ste
ms
,
2
0
0
4
;
1
9
(
2
):
1
3
8
7
-
1
4
0
1
.
[2
]
Ch
a
tt
e
rjee
D,
G
h
o
sh
A
,
“
T
CS
C
c
o
n
tr
o
l
d
e
sig
n
f
o
r
tran
sie
n
t
sta
b
il
it
y
i
m
p
ro
v
e
m
e
n
t
o
f
a
m
u
lt
i
-
m
a
c
h
in
e
p
o
w
e
r
s
y
ste
m
u
sin
g
traje
c
to
ry
se
n
siti
v
it
y
,
”
El
e
c
t
ric
Po
we
r S
y
ste
ms
Res
e
a
rc
h
,
2
0
0
7
;
7
7
:
4
7
0
-
4
8
3
.
[3
]
Ku
m
a
r
P
S
,
“
T
ra
n
sie
n
t
S
tab
il
it
y
En
h
a
n
c
e
m
e
n
t
o
f
P
o
w
e
r
S
y
ste
m
Us
in
g
TCS
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
Co
m
p
u
ter
E
n
g
i
n
e
e
rin
g
,
2
0
1
2
;
2
(3
)
:
3
1
7
-
3
2
4
.
[4
]
Ro
ss
o
D,
Ca
n
iza
re
s
C
A
,
Do
n
a
V
M
,
“
A
stu
d
y
o
f
TCS
C
c
o
n
tro
ll
e
r
d
e
sig
n
f
o
r
p
o
w
e
r
s
y
ste
m
sta
b
il
it
y
i
m
p
ro
v
e
m
e
n
t,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
st
e
ms
,
2
0
0
3
;
1
8
(
4
):
1
4
8
7
-
1
4
9
6
.
[5
]
S
h
a
n
k
a
r
R,
S
riv
a
sta
v
a
J,
“
T
ra
n
si
e
n
t
S
tab
il
it
y
S
tu
d
y
b
y
Us
in
g
T
h
y
risto
r
Co
n
tr
o
ll
e
d
S
e
ries
Co
m
p
e
n
sa
to
r
Co
n
tr
o
ll
e
r
f
o
r
S
in
g
le
M
a
c
h
in
e
In
f
in
it
e
Bu
s
(S
M
IB)
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
S
c
ien
c
e
a
n
d
I
n
n
o
v
a
ti
v
e
T
e
c
h
n
o
l
o
g
y
,
2
0
1
3
;
2
(
5
):
3
0
-
3
4
.
[6
]
Ku
m
k
ra
tu
g
P
,
“
T
h
e
E
ffe
c
t
o
f
T
h
y
risto
r
Co
n
tro
ll
e
d
S
e
ries
Ca
p
a
c
it
o
r
o
n
T
ra
n
sie
n
t
S
tab
il
it
y
o
f
S
in
g
le
M
a
c
h
in
e
In
f
in
it
e
Bu
s
S
y
ste
m
w
it
h
th
e
Ex
a
c
t
S
h
o
rt
T
ra
n
sm
i
ss
io
n
L
in
e
M
o
d
e
l,
”
Ame
ric
a
n
J
o
u
r
n
a
l
o
f
A
p
p
l
ied
S
c
ien
c
e
s
,
2
0
1
2
;
9
(3
):
4
2
5
-
4
2
8
.
[7
]
S
rin
iv
a
sa
Ra
o
G
,
S
ru
jan
a
A
,
“
T
ra
n
sie
n
t
S
tab
il
it
y
Im
p
ro
v
e
m
e
n
t
o
f
M
u
lt
i
-
m
a
c
h
in
e
P
o
w
e
r
S
y
st
e
m
Us
in
g
F
u
z
z
y
Co
n
tr
o
ll
e
d
T
CS
C,
”
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
A
d
v
a
n
c
e
me
n
ts
i
n
Res
e
a
rc
h
&
T
e
c
h
n
o
l
o
g
y
,
2
0
1
2
;
1
(
2
):
1
6
2
-
1
7
2
.
[8
]
Na
sc
i
m
e
n
to
S
,
G
o
u
v
ê
a
Jr
M
M
,
“
V
o
lt
a
g
e
S
tab
i
li
ty
En
h
a
n
c
e
m
e
n
t
in
P
o
w
e
r
S
y
ste
m
s
w
it
h
A
u
t
o
m
a
ti
c
F
a
c
ts
De
v
ice
A
ll
o
c
a
ti
o
n
,
”
En
e
rg
y
Pr
o
c
e
d
ia
,
2
0
1
7
;
1
0
7
:
6
0
-
6
7
.
[9
]
Esm
a
il
i
M
,
S
h
a
y
a
n
f
a
r
H
A
,
M
o
sle
m
i
R,
“
L
o
c
a
ti
n
g
se
ries
F
A
C
T
S
d
e
v
ic
e
s
f
o
r
m
u
lt
i
-
o
b
jec
ti
v
e
c
o
n
g
e
stio
n
m
a
n
a
g
e
m
e
n
t
im
p
ro
v
in
g
v
o
lt
a
g
e
a
n
d
tran
sie
n
t
sta
b
il
it
y
,
”
Eu
ro
p
e
a
n
J
o
u
rn
a
l
o
f
O
p
e
ra
ti
o
n
a
l
Res
e
a
rc
h
,
2
0
1
4
;
2
3
6
(2
):
7
6
3
-
7
7
3
.
[1
0
]
Ba
k
h
sh
i
M
,
Ho
lak
o
o
ie
M
H,
Ra
b
iee
A
,
“
F
u
z
z
y
b
a
s
e
d
d
a
m
p
in
g
c
o
n
tro
ll
e
r
f
o
r
T
CS
C
u
sin
g
lo
c
a
l
m
e
a
su
re
m
e
n
ts
to
e
n
h
a
n
c
e
tran
si
e
n
t
sta
b
il
it
y
o
f
p
o
w
e
r
s
y
ste
m
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
P
o
we
r
&
En
e
rg
y
S
y
ste
ms
,
2
0
1
7
;
8
5
:
1
2
-
2
1
.
[1
1
]
Co
lv
a
ra
L
D,
A
r
a
u
jo
S
CB,
F
e
str
a
it
s
EB,
“
S
tab
il
it
y
a
n
a
l
y
sis
o
f
p
o
w
e
r
s
y
ste
m
in
c
lu
d
in
g
f
a
c
ts
(
TCS
C)
e
ff
e
c
ts
b
y
d
irec
t
m
e
th
o
d
a
p
p
ro
a
c
h
,
”
I
n
ter
n
a
t
io
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
,
2
0
0
5
;
2
7
(
4
):
2
6
4
-
2
7
4
.
[1
2
]
Ra
u
tray
S
K,
Ch
o
u
d
h
u
ry
S
,
M
ish
ra
S
,
Ro
u
t
P
K,
“
A
P
a
rti
c
le S
w
a
r
m
Op
ti
m
iza
ti
o
n
b
a
se
d
A
p
p
ro
a
c
h
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,
2
0
1
2
;
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:
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1
-
3
8
.
[1
3
]
Ko
lcu
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,
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ň
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,
Ka
n
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ra
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issio
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tral
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p
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0
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6
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9
(2
7
):
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7
6
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3
8
1
.
[1
4
]
Ro
se
ly
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JP
,
De
v
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ra
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D,
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sh
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,
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n
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g
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l
,
2
0
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4
;
5
(3
):
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8
9
-
8
0
1
.
[1
5
]
G
a
sp
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ric
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ih
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li
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R,
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h
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m
p
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il
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ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
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e
c
trica
l
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we
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&
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e
rg
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ste
ms
,
2
0
1
5
;
6
4
:
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0
4
0
-
1
0
4
8
.
[1
6
]
Re
d
d
y
S
S
,
“
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ti
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l
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lac
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stio
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th
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late
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r
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st
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m
,
”
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ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
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e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
2
0
1
8
;
8
(
3
):
1
3
3
6
-
1
3
4
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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&
C
o
m
p
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n
g
I
SS
N:
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0
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8
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8708
Tr
a
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eries
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(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
893
[1
7
]
T
rip
a
th
i
A
,
Ra
o
KU
,
V
e
n
k
a
tes
h
a
L
,
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M
u
lt
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-
M
a
c
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in
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ta
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in
g
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y
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m
ic
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v
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rsio
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c
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e
,
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ter
n
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ti
o
n
a
l
J
o
u
rn
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trica
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n
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r E
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g
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g
(
IJ
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)
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2
0
1
7
;
7
(
6
):
3
1
7
6
-
3
1
8
9
.
[1
8
]
Wa
rtan
a
IM
,
Ag
u
stin
i
N
P
,
S
in
g
h
JG
,
“
Op
ti
m
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l
In
teg
ra
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o
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n
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w
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b
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En
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rid
b
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rin
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m
a
ll
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ig
n
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l
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tab
il
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stra
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t,
”
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ter
n
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ti
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o
u
rn
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l
o
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tr
ica
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a
n
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Co
mp
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ter
En
g
i
n
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rin
g
(
IJ
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)
,
2
0
1
7
;
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(5
):
2
3
2
9
-
2
3
3
7
.
[1
9
]
Re
d
d
y
S
S
,
“
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n
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n
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a
n
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m
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n
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V
o
lt
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g
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ro
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p
ro
v
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t
in
a
H
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b
rid
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o
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r
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ste
m
w
it
h
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A
C
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n
tr
o
ll
e
rs
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ap
p
li
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g
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n
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rin
g
Res
e
a
r
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h
,
2
0
1
7
;
1
2
(
9
):
1
1
9
5
-
1
2
0
3
.
[2
0
]
A
c
e
v
e
d
o
L
F
,
Bo
th
ia
-
V
a
rg
a
s
G
,
C
a
n
d
e
lo
JE,
“
Dy
n
a
m
ic
V
o
lt
a
g
e
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tab
il
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m
p
a
riso
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o
f
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h
e
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m
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l
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n
d
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in
d
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w
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r
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e
n
e
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ti
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w
it
h
Dif
fe
re
n
t
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tatic
a
n
d
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n
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m
ic
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o
a
d
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o
d
e
ls,
”
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
m
p
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ter
En
g
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n
e
e
rin
g
(
IJ
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)
,
2
0
1
8
;
8
(3
):
1
4
0
1
-
1
4
1
1
.
[2
1
]
Ou
k
e
n
n
o
u
A
,
S
a
n
d
a
li
A
,
El
m
o
u
m
e
n
S
,
“
Co
o
rd
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n
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ted
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lac
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m
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n
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in
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tri
c
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tw
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rk
b
a
s
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d
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n
Ka
lai
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sm
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ro
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sk
y
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r
g
a
in
in
g
S
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ti
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n
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lt
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g
e
De
v
i
a
ti
o
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In
d
e
x
,
”
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
E
n
g
in
e
e
rin
g
(
IJ
EC
E)
,
2
0
1
8
;
8
(6
)
:
4
0
7
9
-
4
0
8
8
.
[2
2
]
A
n
d
e
rso
n
P
M
,
F
o
u
d
AA
,
“
P
o
w
e
r
S
y
st
e
m
Co
n
tro
l
a
n
d
S
tab
il
it
y
,
”
Io
wa
S
t
a
te Un
ive
rs
it
y
Pre
ss
,
Ame
s,
Io
wa
,
1
9
7
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.