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is
cu
s
s
ed
.
Fin
all
y
,
a
n
al
y
zi
n
g
th
e
s
p
ec
if
ic
v
al
u
es
o
f
t
h
e
s
y
s
te
m
a
n
d
also
ap
p
lied
s
i
m
u
latio
n
s
o
n
Mir
a
m
o
d
es
o
f
o
s
c
illatio
n
b
et
w
ee
n
d
i
f
f
er
e
n
t
g
e
n
er
ato
r
ar
ea
s
o
f
th
e
s
tu
d
ied
s
y
s
te
m
w
il
l b
e
d
ea
lt
w
ith
.
2.
M
O
DE
L
I
N
G
2
.
1
.
T
he
M
o
delin
g
o
f
t
he
T
ra
ns
m
is
s
io
n L
ines
o
f
H
VDC
a
nd
H
VAC
HVDC
tr
a
n
s
m
is
s
io
n
s
y
s
te
m
s
ar
e
p
ar
ticu
lar
ly
i
m
p
o
r
tan
t
n
o
w
ad
a
y
s
an
d
b
ec
au
s
e
o
f
t
h
e
ir
s
p
ec
ial
f
ea
t
u
r
es,
t
h
e
y
ar
e
g
etti
n
g
m
o
r
e
atten
tio
n
.
T
h
ese
s
y
s
te
m
s
i
n
tr
an
s
m
i
tti
n
g
th
e
p
o
w
er
f
o
r
l
o
n
g
d
i
s
ta
n
ce
s
,
lo
n
g
u
n
d
er
g
r
o
u
n
d
tr
a
n
s
m
i
s
s
io
n
li
n
es,
a
n
d
co
n
n
ec
ti
n
g
t
w
o
p
o
w
er
n
et
w
o
r
k
s
w
i
th
o
u
t
d
i
s
tu
r
b
an
ce
s
h
av
e
w
id
e
ap
p
licatio
n
s
.
On
e
p
r
o
b
le
m
o
f
th
ese
li
n
es
is
h
i
g
h
co
s
t
o
f
c
o
n
v
er
ti
n
g
AC
to
DC
eq
u
ip
m
en
t
an
d
v
ice
v
er
s
a,
th
o
u
g
h
it
is
ec
o
n
o
m
ical
l
y
f
ea
s
ib
le
f
o
r
th
e
HVDC
tr
an
s
m
is
s
i
o
n
[
1
1
]
.
Fo
r
ex
am
p
le,
in
t
h
e
tr
an
s
m
i
s
s
io
n
d
is
ta
n
ce
o
f
o
v
er
6
0
0
k
m
an
d
u
n
d
er
g
r
o
u
n
d
ca
b
le
tr
an
s
m
is
s
io
n
(
m
o
r
e
th
an
5
0
k
m
)
to
co
n
n
ec
t
th
e
is
l
an
d
s
to
th
e
n
et
w
o
r
k
th
er
e
ar
e
co
n
d
itio
n
s
t
h
at
j
u
s
tify
t
h
e
HVD
C
s
y
s
te
m
ec
o
n
o
m
ical
l
y
.
W
h
ile
HV
DC
lin
es
r
eq
u
ir
e
o
n
l
y
2
co
n
d
u
cto
r
s
th
at
i
s
o
n
e
w
it
h
a
p
o
s
itiv
e
v
o
lta
g
e
a
n
d
an
o
th
er
w
it
h
a
n
eg
ati
v
e
v
o
ltag
e
i
n
r
ela
tio
n
to
th
e
g
r
o
u
n
d
,
at
least
th
r
ee
co
n
d
u
cto
r
s
ar
e
n
ee
d
ed
f
o
r
HVA
C
tr
a
n
s
m
is
s
io
n
l
i
n
es.
T
h
u
s
,
t
h
e
a
m
o
u
n
t
o
f
s
eq
u
en
ce
an
d
tr
an
s
itio
n
cu
r
r
en
t i
n
A
C
a
n
d
DC
tr
an
s
m
i
s
s
io
n
l
in
e
s
ca
n
b
e
d
eter
m
i
n
ed
as f
o
llo
w
s
[
1
2
,
21
]:
√
(
1
)
√
(
2
)
(
3
)
(
4
)
T
h
e
r
r
eliab
ilit
y
o
f
HVD
C
li
n
e
s
is
m
o
r
e
th
a
n
HV
AC
lin
e
s
,
b
ec
au
s
e
d
esp
ite
a
f
a
u
lt
in
o
n
e
o
f
th
e
t
w
o
co
n
d
u
cti
v
e
lin
e
s
th
e
tr
a
n
s
m
i
s
s
io
n
p
o
w
er
ca
n
s
t
ill
b
e
p
ass
ed
th
r
o
u
g
h
t
h
e
o
th
er
co
n
d
u
cto
r
w
i
th
o
u
t
a
n
y
p
r
o
b
le
m
.
Giv
e
n
t
h
at
th
e
HVD
C
li
n
e
in
clu
d
es
t
w
o
co
n
d
u
c
to
r
s
,
in
co
m
p
ar
i
s
o
n
w
it
h
t
h
e
s
i
m
ilar
H
VAC
i
t
r
eq
u
ir
es
les
s
s
p
ac
e
an
d
t
h
er
ef
o
r
e
r
eq
u
ir
es
s
m
aller
b
ase
s
,
an
d
a
s
a
r
e
s
u
lt
i
s
les
s
co
s
tl
y
to
in
s
tall
th
a
n
H
VAC.T
h
e
m
a
x
i
m
u
m
v
o
ltag
e
r
a
n
g
e
o
f
ea
c
h
AC
s
y
s
t
e
m
is
:
√
√
(
5
)
An
d
th
e
m
ax
i
m
u
m
s
y
s
te
m
v
o
l
tag
e
o
f
D
C
is
:
(
6
)
T
h
er
e
is
n
o
p
r
o
b
lem
o
f
m
ai
n
t
ain
i
n
g
s
y
n
c
h
r
o
n
izatio
n
b
et
w
e
en
t
w
o
s
y
s
te
m
s
o
f
A
C
th
at
ar
e
co
n
n
ec
ted
b
y
an
HVD
C
li
n
e.
I
n
ad
d
itio
n
,
th
e
s
a
m
e
f
r
eq
u
en
c
y
o
f
t
w
o
n
et
w
o
r
k
s
o
f
AC
t
h
at
ar
e
co
n
n
e
cted
b
y
an
HVD
C
lin
e
is
n
o
t
n
ee
d
ed
.
Mo
r
eo
v
er
,
in
ca
s
e
o
f
s
h
o
r
t
cir
cu
it
o
cc
u
r
r
en
ce
in
o
n
e
o
f
th
e
t
w
o
AC
n
et
w
o
r
k
s
th
at
ar
e
co
n
n
ec
ted
b
y
a
D
C
li
n
e,
t
h
e
s
h
o
r
t
-
cir
c
u
it
c
u
r
r
en
t
is
n
o
t
tr
a
n
s
f
er
r
ed
to
an
o
t
h
er
n
et
w
o
r
k
,
b
ec
au
s
e
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
is
g
en
er
al
l
y
a
r
ea
ctiv
e
cu
r
r
en
t
an
d
i
n
th
e
D
C
s
y
s
t
e
m
r
ea
ctiv
e
c
u
r
r
en
t
is
n
o
t
tr
an
s
f
er
r
ed
an
d
eq
u
als
1
.
T
h
e
tr
an
s
m
i
s
s
io
n
p
o
w
er
f
r
o
m
a
DC
li
n
e
ca
n
b
e
ea
s
il
y
co
n
tr
o
lled
b
y
its
th
y
r
i
s
to
r
r
ec
tif
ier
an
d
b
e
m
ai
n
tai
n
ed
in
a
ce
r
tain
a
m
o
u
n
t.
Sin
ce
r
ea
ctiv
e
c
u
r
r
en
t
d
o
esn
’
t
e
x
is
t
i
n
DC
li
n
es,
HV
DC
li
n
e
lo
s
s
es
ar
e
f
e
w
er
th
an
t
h
e
li
n
es
o
f
HV
AC
.
I
n
HV
A
C
li
n
es
,
t
h
e
tr
an
s
m
i
s
s
io
n
p
o
w
er
is
eq
u
al
an
d
d
u
e
to
tr
an
s
ie
n
t
m
o
d
e
s
in
t
h
e
s
e
lin
e
s
,
th
e
a
n
g
l
e
o
f
S
in
n
o
r
m
al
co
n
d
itio
n
m
u
s
t
b
e
less
t
h
a
n
3
0
d
eg
r
ee
s
.
So
,
AC
li
n
es
f
ac
e
li
n
e
len
g
th
a
n
d
tr
an
s
m
i
s
s
io
n
p
o
w
er
li
m
itatio
n
s
a
n
d
s
er
ies
ca
p
ac
ito
r
s
ar
e
u
s
ed
to
ad
d
r
ess
th
e
p
r
o
b
lem
.
B
u
t,
i
n
HVDC
li
n
es
t
h
er
e
w
i
ll
b
e
n
o
s
tab
ilit
y
co
n
s
tr
ai
n
ts
.
A
l
th
o
u
g
h
d
u
e
to
th
e
h
ig
h
co
s
t
o
f
A
C
to
DC
an
d
DC
to
AC
co
n
v
er
ter
s
th
e
co
s
t
o
f
HVD
C
lin
es
i
s
v
er
y
h
ig
h
,
f
o
r
lo
n
g
d
is
tan
ce
lin
e
s
f
r
o
m
6
0
0
to
9
0
0
k
m
a
n
d
p
o
w
er
s
m
o
r
e
th
an
1
0
0
MW
,
DC
li
n
es
w
ill
b
e
less
co
s
tl
y
t
h
an
AC
li
n
es
.
T
h
is
is
s
u
e
is
p
ar
tic
u
lar
l
y
m
o
r
e
s
ig
n
i
f
ica
n
t
f
o
r
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
3
,
Sep
tem
b
er
2
0
1
7
:
1
2
7
4
-
1284
1276
DC
ca
b
les
t
h
at
f
o
r
d
is
ta
n
ce
s
o
f
5
0
to
1
0
0
k
m
w
o
u
ld
b
e
m
o
r
e
ec
o
n
o
m
ical.
At
t
h
e
t
i
m
e
o
f
t
w
o
AC
n
et
w
o
r
k
s
co
n
n
ec
tio
n
,
HVDC
a
s
y
n
c
h
r
o
n
o
u
s
s
y
s
te
m
w
ill
b
e
u
s
ed
.
I
n
HVDC
s
y
s
te
m
,
t
h
e
ca
p
ac
it
y
o
f
lo
ad
p
o
r
tio
n
w
i
ll
in
cr
ea
s
e
in
a
w
a
y
th
at
t
h
e
le
v
e
l
an
d
t
h
e
p
ath
o
f
p
o
w
er
tr
a
n
s
m
is
s
io
n
ca
n
b
e
s
p
ec
i
f
icall
y
a
n
d
b
r
o
ad
ly
co
n
tr
o
lled
an
d
in
ca
s
e
o
f
DC
s
o
u
r
ce
s
o
n
th
e
w
a
y
it
ca
n
b
e
s
u
p
p
lied
.
I
n
ad
d
itio
n
,
th
er
e
w
ill
b
e
n
o
n
ee
d
f
o
r
co
m
m
o
n
f
r
eq
u
en
c
y
i
n
th
e
n
et
w
o
r
k
a
n
d
t
h
e
ea
r
th
ca
n
b
e
u
s
ed
as t
h
e
r
etu
r
n
li
n
e
[
19
].
2
.
2
.
M
o
delin
g
o
f
Sta
t
ic
Va
r
Co
m
pens
a
t
o
r
(
SVC)
SVC
is
co
n
n
ec
ted
to
th
e
n
et
w
o
r
k
i
n
a
p
ar
allel
w
a
y
an
d
as
Fig
u
r
e
(
1
)
s
h
o
w
s
t
h
e
f
ea
t
u
r
es
o
f
VI
v
o
ltag
e
o
f
SVC
cu
r
r
en
t
m
a
y
a
p
p
ea
r
in
in
d
u
ctiv
e
o
r
ca
p
ac
itiv
e
r
ea
ctiv
e
m
o
d
es.
I
n
th
e
lar
g
er
ca
p
ac
ito
r
cu
r
r
en
t,
SVC
tr
a
n
s
f
o
r
m
s
to
a
ca
p
ac
ito
r
an
d
its
r
ea
ctiv
e
p
o
w
er
ch
a
n
g
e
s
as a
f
u
n
c
tio
n
o
f
v
o
ltag
e.
Fig
u
r
e
1.
Vo
ltag
e
-
t
h
e
SV
C
c
u
r
r
en
t c
h
ar
ac
ter
i
s
tics
(
V
-
I)
W
ith
p
r
o
p
er
co
o
r
d
in
atio
n
o
f
c
ap
ac
ito
r
s
w
itc
h
i
n
g
an
d
r
ea
cto
r
co
n
tr
o
l,
th
e
r
ea
cti
v
e
o
u
tp
u
t
c
an
b
e
co
n
s
id
er
ed
as
s
h
i
f
ti
n
g
co
n
ti
n
u
o
u
s
l
y
b
et
w
ee
n
ca
p
ac
itiv
e
an
d
in
d
u
cti
v
e
v
al
u
es [
1
3
,
2
0
,
21
].
Fig
u
r
e
2.
T
h
e
s
tr
u
ctu
r
e
o
f
SV
C
No
w
,
i
f
w
e
m
o
d
el
SV
C
as s
h
o
w
n
i
n
Fi
g
u
r
e
(
2
)
th
e
f
o
r
m
u
lat
i
o
n
w
o
u
ld
b
e
as f
o
llo
w
s
[
1
4
]
:
(
)
(
)
(
7
)
W
h
er
e
th
er
e
is
t
h
e
f
ir
i
n
g
a
n
g
l
e
o
f
th
y
r
is
to
r
,
t
h
e
i
m
p
ac
t
o
f
t
h
e
SVC
r
ea
cta
n
ce
ca
n
b
e
ac
h
ie
v
ed
b
y
t
h
e
p
ar
allel
co
m
b
i
n
atio
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Th
e
C
o
o
r
d
in
a
ted
C
o
n
tr
o
l o
f F
A
C
TS
a
n
d
HV
DC
u
s
in
g
H
-
I
n
fi
n
ity
R
o
b
u
s
t
Meth
o
d
…
(
M
.
Za
d
eh
b
a
g
h
eri
)
1277
(
(
)
(
)
)
(
8
)
S
VC
S
u
s
ce
p
ta
n
ce
is
p
r
ese
n
ted
in
E
q
u
atio
n
(
9
)
w
h
ile
i
ts
p
r
o
f
i
le
as a
f
u
n
ctio
n
o
f
t
h
e
f
ir
e
a
n
g
l
e
is
s
h
o
w
n
i
n
Fig
u
r
e
(
3
)
(
(
)
(
)
)
(
9
)
Fig
u
r
e
3.
SVC
eq
u
i
v
ale
n
t s
u
s
c
ep
tan
ce
as a
f
u
n
c
tio
n
o
f
t
h
e
f
ir
e
an
g
le
2
.
3
.
T
CSC
M
o
dellin
g
T
h
e
o
r
ig
in
al
d
esi
g
n
o
f
co
n
tr
o
l
led
s
er
ies
o
f
ca
p
ac
ito
r
alo
n
g
w
it
h
th
y
r
is
to
r
,
w
h
ic
h
w
as
p
r
o
p
o
s
ed
as
t
h
e
m
et
h
o
d
o
f
"
r
ap
id
a
d
j
u
s
t
m
en
t
o
f
n
et
w
o
r
k
i
m
p
ed
a
n
ce
"
b
y
"
Vitan
at
il
"
et
al
in
1
9
8
6
h
as
b
ee
n
s
h
o
w
n
i
n
Fig
u
r
e
(
4
)
.
I
n
th
e
i
m
p
le
m
en
ta
t
io
n
o
f
th
e
T
C
SC
,
s
ev
er
al
co
m
p
en
s
ato
r
s
o
f
th
i
s
t
y
p
e
ca
n
b
e
co
n
n
ec
ted
in
s
er
ies
to
ac
h
ie
v
e
a
n
o
m
i
n
al
v
o
lta
g
e
an
d
g
o
o
d
p
er
f
o
r
m
a
n
ce
c
h
ar
ac
t
er
is
tics
.
T
h
i
s
co
n
f
i
g
u
r
atio
n
is
s
tr
u
ct
u
r
all
y
s
i
m
ilar
to
T
SS
C
,
an
d
if
t
h
e
X
L
r
ea
cto
r
im
p
ed
an
ce
i
s
en
o
u
g
h
s
m
alle
r
th
an
X
c
ca
p
ac
ito
r
im
p
ed
an
ce
,
it
ca
n
f
u
n
ctio
n
as
o
f
f
a
n
d
o
n
li
k
e
T
SS
C
.
Ho
wev
er
,
th
e
m
ai
n
id
ea
b
eh
i
n
d
th
e
T
C
SC
d
esi
g
n
is
cr
ea
ti
n
g
a
ca
p
ac
ito
r
w
ith
m
o
n
o
to
n
o
u
s
c
h
an
g
e
s
b
y
eli
m
i
n
ati
n
g
p
ar
t
o
f
th
e
e
f
f
ec
ti
v
e
ca
p
ac
it
y
o
f
ca
p
ac
ito
r
b
y
t
h
e
T
C
R
.
Si
n
ce
T
C
R
i
n
t
h
e
m
ai
n
f
r
eq
u
en
c
y
o
f
s
y
s
te
m
i
s
r
ea
ctiv
e
i
m
p
ed
an
ce
w
it
h
m
o
n
o
to
n
o
u
s
ch
a
n
g
es
w
h
ic
h
i
s
c
o
n
tr
o
lled
b
y
d
ela
y
an
g
le,
th
e
i
m
p
ed
an
ce
o
f
p
er
m
an
en
t
m
o
d
e
o
f
T
C
S
C
i
s
t
h
e
i
m
p
ed
an
ce
o
f
a
p
ar
allel
L
C
c
ir
cu
it
th
at
in
c
lu
d
es
X
C
f
i
x
ed
ca
p
ac
ito
r
im
p
ed
an
ce
a
n
d
X
C
v
ar
iab
le
in
d
u
c
tiv
e
i
m
p
ed
an
ce
.
T
h
is
m
ea
n
s
t
h
at:
Fig
u
r
e
4.
T
h
e
in
itial d
esig
n
o
f
C
o
n
tr
o
lled
Ser
ies C
ap
ac
ito
r
with
t
h
y
r
i
s
to
r
(
)
(
)
(
)
(
1
0
)
I
n
E
q
u
atio
n
11
w
e
h
av
e
:
(
)
(
)
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
3
,
Sep
tem
b
er
2
0
1
7
:
1
2
7
4
-
1284
1278
w
h
er
e
an
d
α
is
a
d
ela
y
a
n
g
le
w
h
ic
h
h
a
s
b
ee
n
m
ea
s
u
r
ed
f
r
o
m
t
h
e
p
ea
k
p
o
in
t
v
o
lta
g
e
o
f
ca
p
ac
ito
r
(
o
r
its
eq
u
i
v
ale
n
t,
ze
r
o
p
o
in
t o
f
lin
e
v
o
ltag
e)
T
h
er
ef
o
r
e,
T
C
SC
d
e
m
o
n
s
tr
ates
an
L
C
p
ar
allel
cir
cu
it
w
h
i
ch
is
ad
j
u
s
tab
le
to
th
e
cu
r
r
en
t
w
h
ic
h
is
ess
e
n
tiall
y
a
co
n
s
tan
t
s
o
u
r
ce
o
f
alter
n
ati
n
g
cu
r
r
en
t.
B
y
c
h
an
g
i
n
g
th
e
i
m
p
ed
an
ce
o
f
th
e
co
n
tr
o
lled
r
ea
cto
r
(
)
f
r
o
m
t
h
e
m
a
x
i
m
u
m
v
al
u
e
(
i
n
f
i
n
ite)
to
its
m
in
i
m
u
m
v
alu
e
,
T
C
SC
i
n
cr
ea
s
es
i
ts
m
i
n
i
m
u
m
ca
p
ac
ito
r
i
m
p
ed
an
ce
,
⁄
(
in
co
n
s
eq
u
e
n
c
e
in
cr
ea
s
es
t
h
e
d
eg
r
ee
o
f
c
o
m
p
e
n
s
at
io
n
an
d
s
er
ie
s
ca
p
ac
ito
r
)
ac
c
o
r
d
in
g
l
y
t
h
e
p
ar
allel
in
ten
s
if
icatio
n
m
o
d
e
(
(
)
)
is
cr
ea
ted
w
h
ic
h
is
th
eo
r
etica
ll
y
i
n
f
in
i
te.
F
u
r
th
er
f
all
(
)
ca
u
s
es
t
h
e
i
m
p
ed
a
n
ce
o
f
T
C
SC
to
b
ec
o
m
e
i
n
d
u
c
tiv
e
an
d
to
g
et
to
i
ts
m
i
n
i
m
u
m
v
alu
e
w
h
er
e
i
n
f
ac
t
th
e
ca
p
ac
ito
r
is
b
y
p
ass
ed
b
y
T
C
R
.
T
h
u
s
,
b
y
co
n
v
e
n
tio
n
al
ar
r
an
g
e
m
e
n
t o
f
T
C
S
C
in
w
h
ich
th
e
i
m
p
ed
an
ce
o
f
th
e
T
C
R
r
ea
cto
r
is
s
m
aller
t
h
a
n
t
h
e
ca
p
ac
ito
r
i
m
p
ed
an
ce
,
T
C
S
C
h
a
s
t
w
o
o
p
er
atin
g
r
an
g
e
ar
o
u
n
d
th
e
en
h
a
n
ce
m
en
t
p
o
in
t o
f
its
i
n
ter
n
al
cir
c
u
it:
a.
⁄
w
h
er
e
(
)
is
t
h
e
ca
p
ac
ito
r
.
b.
w
h
er
e
(
)
is
in
d
u
ctiv
e.
T
h
e
m
e
n
tio
n
ed
r
an
g
e
is
s
h
o
wn
in
Fi
g
u
r
e
(
5
)
an
d
(
6
)
.
T
C
S
C
s
tead
y
s
tate
m
o
d
el
th
a
t
w
a
s
d
escr
ib
ed
ab
o
v
e
is
b
ased
o
n
T
C
R
in
an
SVC
en
v
ir
o
n
m
e
n
t
w
h
er
e
T
C
R
is
s
u
p
p
lied
b
y
a
v
o
lta
g
e
s
o
u
r
ce
.
T
h
is
m
o
d
el
is
u
s
e
f
u
l
f
o
r
o
b
tain
i
n
g
a
g
e
n
er
al
u
n
d
er
s
tan
d
i
n
g
o
f
t
h
e
ac
t
u
al
b
eh
av
io
r
o
f
t
h
e
T
C
S
C
.
Ho
w
e
v
er
,
in
t
h
e
d
esig
n
o
f
T
C
SC
,
T
C
R
i
s
clo
s
ed
i
n
p
ar
allel
w
it
h
a
ca
p
ac
ito
r
r
ath
er
t
h
an
a
co
n
s
tan
t
v
o
ltag
e
s
o
u
r
ce
.
D
y
n
a
m
ic
b
alan
ce
b
et
w
ee
n
th
e
ca
p
ac
ito
r
an
d
in
d
u
cto
r
d
r
iv
es
o
u
t
o
p
er
atin
g
v
o
ltag
e
f
o
r
m
t
h
e
o
r
ig
i
n
al
co
n
d
itio
n
o
f
s
i
n
e
w
a
v
e
w
h
ic
h
is
co
n
n
ec
ted
to
a
co
n
s
ta
n
t f
lo
w
o
f
lin
e.
Fig
u
r
e
5.
C
h
ar
ac
ter
is
t
ic
o
f
i
m
p
ed
an
ce
ag
ain
s
t t
h
e
d
ela
y
an
g
l
e
in
T
C
SC
Dee
p
er
an
al
y
s
is
o
f
t
h
e
i
n
ter
a
ctio
n
i
s
n
ec
es
s
ar
y
to
u
n
d
er
s
ta
n
d
t
h
e
ac
t
u
al
p
h
y
s
ical
p
er
f
o
r
m
an
ce
a
n
d
d
y
n
a
m
ic
b
eh
a
v
io
r
o
f
T
C
SC
,
e
s
p
ec
iall
y
i
n
ter
m
s
o
f
it
s
i
m
p
ed
an
ce
in
f
r
eq
u
e
n
cies
u
n
d
er
s
y
n
ch
r
o
n
izer
.
Fig
u
r
e
6.
Sh
o
w
s
v
o
ltag
e
r
ev
er
s
e
b
y
T
C
R
; (
A
)
t
h
e
li
n
e
cu
r
r
en
t a
n
d
r
elev
an
t c
ap
ac
ito
r
v
o
ltag
e,
(
B
)
th
e
T
C
SC
eq
u
iv
ale
n
t c
ir
c
u
it a
t th
e
t
i
m
e
o
f
th
e
f
ir
e,
(C
)
th
e
r
es
u
lti
n
g
ca
p
ac
ito
r
v
o
ltag
e
an
d
r
elev
a
n
t T
C
R
cu
r
r
en
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Th
e
C
o
o
r
d
in
a
ted
C
o
n
tr
o
l o
f F
A
C
TS
a
n
d
HV
DC
u
s
in
g
H
-
I
n
fi
n
ity
R
o
b
u
s
t
Meth
o
d
…
(
M
.
Za
d
eh
b
a
g
h
eri
)
1279
I
E
E
E
d
ef
in
es
T
C
S
C
as
co
m
p
en
s
atio
n
ca
p
ac
itiv
e
r
ea
cta
n
c
e
w
h
ic
h
i
n
cl
u
d
es
a
s
er
ie
s
o
f
ca
p
ac
ito
r
b
an
k
s
i
n
p
ar
allel
w
it
h
th
y
r
is
to
r
an
d
in
d
u
cto
r
in
s
er
ies
to
p
r
o
d
u
ce
a
s
er
ies
o
f
v
ar
iab
le
ca
p
a
citiv
e
r
ea
ctan
ce
i
n
tr
an
s
m
is
s
io
n
li
n
e
s
.
So
m
o
d
if
ie
d
t
w
o
p
ar
t e
q
u
atio
n
s
a
n
d
th
e
i
n
j
ec
tio
n
p
o
w
er
s
f
o
r
T
C
SC
.
(
)
(
1
2
)
(
)
(
)
(
1
3
)
(
)
(
1
4
)
(
)
(
)
(
1
5
)
T
h
er
ef
o
r
e,
th
e
in
j
ec
tio
n
p
o
w
er
s
ca
n
b
e
ex
p
r
ess
ed
as
f
o
llo
w
s
:
(
)
(
1
6
)
(
)
(
1
7
)
(
)
(
1
8
)
(
)
(
1
9
)
I
n
th
e
ab
o
v
e
E
q
u
atio
n
s
:
(
)
(
)
(
(
)
)
(
2
0
)
(
)
(
)
(
(
)
)
(
2
1
)
(
)
(
2
2
)
(
)
(
)
(
2
3
)
3.
RO
B
UST
CO
NT
RO
L
L
E
R
DE
S
I
G
N
(
)
R
o
b
u
s
t
co
n
tr
o
ller
d
esi
g
n
i
s
u
s
ed
f
o
r
t
h
e
d
a
m
p
i
n
g
o
f
lo
w
f
r
e
q
u
en
c
y
o
s
ci
llatio
n
m
o
d
es.
Fo
r
th
e
d
esi
g
n
o
f
th
is
t
y
p
e
o
f
co
n
tr
o
ller
,
th
r
e
e
o
p
er
atin
g
p
o
in
t
s
ar
e
co
n
s
id
er
ed
.
T
h
e
f
ir
s
t
o
p
er
atin
g
p
o
i
n
t
i
s
r
elate
d
to
th
e
ti
m
e
w
h
e
n
th
e
h
ea
v
y
lo
ad
is
co
n
n
ec
ted
to
th
e
g
e
n
er
ato
r
.
T
h
e
s
ec
o
n
d
o
p
er
atin
g
p
o
in
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ig
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s
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er
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r
[
1
5
,
19
].
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f
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t si
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w
s
:
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2
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2
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].
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u
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4.
SIMUL
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y
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d
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ass
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s
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n
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SVC
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w
as
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s
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.
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4
.
1
.
T
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ph
a
s
e:
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Res
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E
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Are
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Fig
u
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s
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u
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2
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ato
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ase
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u
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.
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0
5
10
15
20
25
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5
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1
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
3
,
Sep
tem
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er
2
0
1
7
:
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2
7
4
-
1284
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4
.
3
.
T
he
t
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a
s
e:
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po
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t
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ass
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1
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u
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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1283
5.
CO
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SI
O
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T
h
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p
ap
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p
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w
f
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s
s
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o
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s
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y
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m
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tab
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g
.
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n
ad
d
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n
,
in
th
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s
s
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d
y
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co
o
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d
in
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p
o
w
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f
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ap
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f
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d
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b
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g
d
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f
f
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t
a
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ea
s
w
a
s
in
v
es
tig
a
ted
.
T
h
is
m
eth
o
d
ca
n
s
i
g
n
if
ican
t
l
y
i
n
cr
ea
s
e
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e
e
f
f
icien
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y
o
f
th
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s
y
s
te
m
b
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t
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e
F
AC
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S a
n
d
HVDC e
q
u
ip
m
e
n
t.
RE
F
E
R
E
NC
E
S
[1
]
L
i,
Yo
n
g
,
Ch
risti
a
n
Re
h
tan
z
,
S
v
e
n
Rü
b
e
rg
,
L
o
n
g
f
u
L
u
o
,
a
n
d
Yiji
a
Ca
o
.
"
W
id
e
-
a
re
a
ro
b
u
st
c
o
o
rd
in
a
ti
o
n
a
p
p
r
o
a
c
h
o
f
HV
DC
a
n
d
F
A
C
T
S
c
o
n
tro
ll
e
rs
f
o
r
d
a
m
p
in
g
m
u
lt
ip
le
in
tera
re
a
o
sc
il
latio
n
s"
.
P
o
w
e
r
De
li
v
e
r
y
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
2
7
,
n
o
.
3
(2
0
1
2
):
1
0
9
6
-
1
1
0
5
.
[2
]
Ch
a
p
m
a
n
,
J.
W
.
,
M
.
D.
Ili
c
,
C.
A
.
Kin
g
,
L
.
En
g
,
a
n
d
H.
Ka
u
fm
a
n
.
"
S
tab
il
izin
g
a
m
u
lt
im
a
c
h
in
e
p
o
w
e
r
s
y
ste
m
v
ia
d
e
c
e
n
tralize
d
f
e
e
d
b
a
c
k
li
n
e
a
rizin
g
e
x
c
it
a
ti
o
n
c
o
n
tr
o
l"
.
P
o
w
e
r
S
y
st
e
m
s,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
8
,
n
o
.
3
(1
9
9
3
)
:
8
3
0
-
8
3
9
.
[3
]
Da
sh
,
P
.
K.,
A
.
C.
L
iew
,
a
n
d
A
.
Ro
u
tray
.
"
De
sig
n
o
f
ro
b
u
st
c
o
n
tr
o
ll
e
rs
f
o
r
HV
DC
li
n
k
s
in
A
C
-
DC
p
o
w
e
r
s
y
ste
m
s"
.
El
e
c
tri
c
p
o
w
e
r
s
y
ste
m
s res
e
a
r
c
h
3
3
,
n
o
.
3
(
1
9
9
5
):
2
0
1
-
2
0
9
.
[4
]
Hs
u
,
Yu
a
n
-
Yih
,
a
n
d
L
i
W
a
n
g
.
"
Da
m
p
in
g
o
f
a
p
a
ra
ll
e
l
a
c
-
d
c
p
o
we
r
s
y
ste
m
u
sin
g
P
ID
p
o
w
e
r
s
y
ste
m
sta
b
il
ize
rs
a
n
d
re
c
ti
f
ier cu
rre
n
t
re
g
u
lato
rs"
.
En
e
rg
y
Co
n
v
e
rsio
n
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
3
,
n
o
.
3
(1
9
8
8
):
5
4
0
-
5
4
7
.
[5
]
Ho
ss
e
in
z
a
d
e
h
,
Na
ss
e
r,
a
n
d
A
k
h
ta
r
Ka
la
m
.
"
A
ru
le
-
ba
se
d
f
u
z
z
y
p
o
w
e
r
s
y
ste
m
sta
b
il
ize
r
tu
n
e
d
b
y
a
n
e
u
ra
l
n
e
tw
o
rk
"
.
En
e
rg
y
Co
n
v
e
rsio
n
,
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
1
4
,
n
o
.
3
(
1
9
9
9
):
7
7
3
-
7
7
9
.
[6
]
S
h
a
m
so
ll
a
h
i,
P
.
,
a
n
d
O.
P
.
M
a
li
k
.
"
A
n
a
d
a
p
ti
v
e
p
o
w
e
r
s
y
ste
m
st
a
b
il
ize
r
u
sin
g
on
-
li
n
e
train
e
d
n
e
u
ra
l
n
e
tw
o
rk
s
"
.
En
e
rg
y
Co
n
v
e
rsio
n
,
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
1
2
,
n
o
.
4
(
1
9
9
7
):
3
8
2
-
3
8
7
.
[7
]
Ch
u
n
g
,
T
.
S
.
,
a
n
d
F
a
n
g
Da
-
Zh
o
n
g
.
"
F
u
z
z
y
lo
g
ic
c
o
n
tro
ll
e
r
f
o
r
e
n
h
a
n
c
in
g
o
sc
il
lato
ry
sta
b
il
it
y
o
f
AC/DC
in
terc
o
n
n
e
c
ted
p
o
w
e
r
s
y
ste
m
"
.
El
e
c
tri
c
P
o
w
e
r
S
y
ste
m
s Re
se
a
rc
h
6
1
,
n
o
.
3
(
2
0
0
2
):
2
2
1
-
2
2
6
.
[8
]
L
u
,
J.,
M
.
H.
Na
h
rir,
a
n
d
Do
n
a
ld
A
.
P
ierre
.
"
A
f
u
z
z
y
lo
g
ic
-
b
a
s
e
d
a
d
a
p
ti
v
e
p
o
w
e
r
s
y
ste
m
st
a
b
i
li
z
e
r
f
o
r
m
u
lt
i
-
m
a
c
h
in
e
s
y
ste
m
s
"
.
El
e
c
tri
c
p
o
w
e
r
sy
ste
m
s re
se
a
rc
h
6
0
,
n
o
.
2
(
2
0
0
1
):
1
1
5
-
1
2
1
.
[9
]
Yo
o
n
,
Ja
e
Yo
u
n
g
.
"
A
g
e
n
e
ti
c
a
l
g
o
rit
h
m
a
p
p
ro
a
c
h
t
o
d
e
sig
n
a
n
o
p
t
im
a
l
f
u
z
z
y
c
o
n
tro
ll
e
r
f
o
r
re
c
ti
f
ier
c
u
rre
n
t
c
o
n
tro
l
in
H
V
DC
sy
ste
m
"
.
In
Ev
o
l
u
ti
o
n
a
r
y
Co
m
p
u
tatio
n
P
ro
c
e
e
d
i
n
g
s,
1
9
9
8
.
IE
EE
W
o
rl
d
C
o
n
g
re
ss
o
n
Co
m
p
u
tatio
n
a
l
In
telli
g
e
n
c
e
.
T
h
e
1
9
9
8
I
EE
E
I
n
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
,
p
p
.
4
0
4
-
4
0
9
.
IEE
E,
1
9
9
8
.
[1
0
]
W
e
n
,
Ji
y
u
,
S
h
ij
ie
Ch
e
n
g
,
a
n
d
O.
P
.
M
a
li
k
.
"
A
s
y
n
c
h
ro
n
o
u
s
g
e
n
e
ra
to
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it
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ti
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ler
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d
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n
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d
w
it
h
a
g
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ti
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a
l
g
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rit
h
m
"
.
In
P
o
w
e
r
In
d
u
stry
Co
m
p
u
ter
A
p
p
li
c
a
ti
o
n
s.
1
9
9
7
.
2
0
t
h
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
,
p
p
.
106
-
1
1
1
.
IEE
E,
1
9
9
7
.
[1
1
]
P
a
d
iy
a
r,
K.
R.
H
V
DC
p
o
w
e
r
tran
sm
issio
n
sy
st
e
m
s:
tec
h
n
o
lo
g
y
a
n
d
sy
ste
m
in
tera
c
ti
o
n
s.
Ne
w
A
g
e
In
tern
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ti
o
n
a
l,
1
9
9
0
.
[1
2
]
A
l
f
u
h
id
,
A
.
S
.
,
M
.
S
.
M
a
h
m
o
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d
,
a
n
d
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.
A
.
A
l
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S
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e
d
.
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o
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li
n
g
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n
d
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o
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tr
o
l
HV
DC P
o
w
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y
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m
"
.
El
e
c
ric
P
o
w
e
r
S
y
te
m
R
e
s (1
9
9
8
):
7
8
7
-
7
8
1
.
[1
3
]
Zh
a
n
g
,
X
iao
-
P
in
g
,
C
h
risti
a
n
Re
h
tan
z
,
a
n
d
Bik
a
sh
P
a
l.
F
lex
ib
le
A
C
tran
sm
issio
n
sy
ste
m
s:
m
o
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e
ll
i
n
g
a
n
d
c
o
n
tr
o
l.
S
p
rin
g
e
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S
c
ien
c
e
&
Bu
si
n
e
ss
M
e
d
ia,
2
0
1
2
.
[1
4
]
P
a
r
n
ian
i,
M
.
,
a
n
d
M
.
R.
Ira
v
a
n
i
.
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Op
ti
m
a
l
ro
b
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tr
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to
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"
.
In
G
e
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e
ra
ti
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n
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T
ra
n
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m
issio
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n
d
Distri
b
u
ti
o
n
,
IE
E
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ro
c
e
e
d
i
n
g
s
-
,
v
o
l.
1
4
5
,
n
o
.
3
,
p
p
.
3
0
1
-
3
0
7
.
IET
,
1
9
9
8
.
[1
5
]
Ch
a
u
d
h
u
ri
,
Ba
lark
o
,
Bik
a
sh
C.
P
a
l,
A
rg
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s
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Zo
l
o
tas
,
Im
a
d
M
.
Ja
im
o
u
k
h
a
,
a
n
d
T
im
C.
G
re
e
n
.
"
M
ix
e
d
-
se
n
siti
v
it
y
a
p
p
ro
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c
h
t
o
H∞
c
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t
ro
l
o
f
p
o
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r
sy
ste
m
o
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latio
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e
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p
lo
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in
g
m
u
lt
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le
F
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CT
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d
e
v
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s
"
.
P
o
w
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r
S
y
st
e
m
s,
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E
T
ra
n
sa
c
ti
o
n
s o
n
1
8
,
n
o
.
3
(
2
0
0
3
):
1
1
4
9
-
1
1
5
6
.
[1
6
]
Ng
a
m
ro
o
,
Iss
a
ra
c
h
a
i.
"
De
si
g
n
o
f
ro
b
u
st
H∞
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S
S
v
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rm
a
li
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rim
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to
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Circu
it
s
a
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2
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2
0
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tern
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ti
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v
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3
,
p
p
.
1
2
9
-
1
3
2
.
IEE
E
,
2
0
0
1
.
[1
7
]
Zad
e
h
b
a
g
h
e
ri,
M
a
h
m
o
u
d
,
Ra
h
i
m
Ild
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ra
b
a
d
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a
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g
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Ne
jad
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a
n
d
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.
"
A
N
e
w
S
tru
c
tu
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n
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m
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V
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lt
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g
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sto
re
r
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se
d
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n
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s
y
m
m
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tri
c
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l
Γ
-
S
o
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rc
e
In
v
e
rters
to
Co
m
p
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n
sa
te
V
o
lt
a
g
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Distu
rb
a
n
c
e
s
in
P
o
w
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r
Distrib
u
ti
o
n
Ne
tw
o
rk
s"
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
le
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
8
,
n
o
.
1
(
2
0
1
7
):
3
4
4
.
[1
8
]
Zad
e
h
b
a
g
h
e
ri,
M
a
h
m
o
u
d
,
Ra
h
im
Ild
a
ra
b
a
d
i,
M
a
ji
d
Ba
g
h
a
e
i
Ne
jad
,
a
n
d
T
o
le S
u
ti
k
n
o
.
"
Re
v
ie
w
o
f
D
y
n
a
m
ic V
o
lt
a
g
e
Re
sto
re
r
A
p
p
li
c
a
ti
o
n
f
o
r
Co
m
p
e
n
sa
ti
o
n
o
f
V
o
lt
a
g
e
Ha
rm
o
n
ics
in
P
o
w
e
r
S
y
ste
m
s"
.
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
C
o
mp
u
ter
S
c
ien
c
e
5
,
n
o
.
1
(2
0
1
7
):
5
8
-
7
1
.
[1
9
]
Zad
e
h
b
a
g
h
e
ri,
M
a
h
m
o
u
d
,
a
n
d
A
m
in
P
a
y
e
d
a
r.
"
T
h
e
F
e
a
sib
il
it
y
S
tu
d
y
o
f
Us
in
g
S
p
a
c
e
V
e
c
to
r
M
o
d
u
latio
n
I
n
v
e
rters
in
Tw
o
-
L
e
v
e
l
o
f
In
teg
ra
ted
P
h
o
to
v
o
lt
a
ic
S
y
ste
m
"
.
In
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
C
o
mp
u
ter
S
c
ien
c
e
1
4
.
2
(2
0
1
5
):
2
0
5
-
2
1
4
.
[2
0
]
Zad
e
h
b
a
g
h
e
ri,
M
a
h
m
o
u
d
,
Ra
h
im
Ild
a
ra
b
a
d
i,
a
n
d
M
a
ji
d
Ba
g
h
a
e
i
Ne
jad
.
"
Re
v
ie
w
o
f
th
e
UP
F
C
Dif
fe
re
n
t
M
o
d
e
ls
in
Re
c
e
n
t
Ye
a
rs
"
.
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
i
v
e
S
y
ste
ms
(
IJ
PE
DS
)
4.
3
(2
0
1
4
):
3
4
3
-
3
5
5
.
[2
1
]
Zad
e
h
b
a
g
h
e
ri,
M
a
h
m
o
u
d
,
Ra
h
im
Ild
a
ra
b
a
d
i,
a
n
d
M
a
ji
d
Ba
g
h
a
e
i
Ne
jad
.
"
A
Re
v
ie
w
o
n
S
p
e
e
d
C
o
n
tro
l
T
e
c
h
n
iq
u
e
s
o
f
S
e
p
a
ra
tel
y
Ex
c
it
e
d
DC
M
o
to
r
"
.
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
1
3
.
1
(
2
0
1
5
)
:
106
-
1
1
3
.
B
I
O
G
RAP
H
IE
S
O
F
AUTH
O
RS
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