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1138
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1139
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un
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s
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d:
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I
sI
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1
L
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(2)
T
h
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s
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s
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d
t
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R
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s
f
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l
l
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s
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V
dc
I
dc
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3
2
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E
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I
sR
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E
sI
I
sI
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(4)
W
h
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r
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,
3
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i
s
t
ra
n
s
f
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r
m
a
t
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c
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s
t
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f
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f
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e
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p
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a
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ra
m
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l
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t
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d
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F
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5
,
t
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E
SR
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n
d
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SI
c
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n
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de
f
i
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e
d
a
s
f
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l
l
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s
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sR
=
E
s
c
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s
θ
s
=
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V
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o
s
θ
s
E
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=
E
s
si
n
θ
s
=
K
cs
V
dc
si
n
θ
s
(5)
W
h
e
r
e
:
K
CS
i
s
c
o
n
s
t
a
nt
pe
rt
a
i
n
i
ng
b
e
t
w
e
e
n
t
h
e
D
C
a
n
d
A
C
v
o
l
t
a
ge
s
.
In
a
V
S
C
o
f
12
pul
s
e
s
,
t
h
e
K
cs
=
2
√
6π
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T
h
e
r
e
f
o
r
e
,
(4)
b
e
c
o
m
e
s
:
V
dc
I
dc
=
3
2
(
K
cs
V
dc
c
o
s
θ
s
I
sR
+
K
cs
V
dc
si
n
θ
s
I
sI
)
(6)
I
dc
=
3
2
(
K
cs
c
o
s
θ
s
I
sR
+
K
cs
si
n
θ
s
I
sI
)
(7)
By
s
u
b
s
t
i
t
ut
i
o
n
,
t
h
e
v
a
l
ue
o
f
Idc
i
n
e
qu
a
t
i
o
n
(
3)
i
s
a
s
f
o
l
l
ow
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
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s
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a
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J
E
l
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c
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20
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4
7
1142
dV
dc
d
t
=
−
1
C
s
(
3
2
(
K
cs
c
o
s
θ
s
I
sR
+
K
cs
si
n
θ
s
I
sI
)
+
dV
dc
R
P
)
(8)
S
ub
s
t
i
t
ut
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t
h
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v
a
l
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s
o
f
a
nd
f
r
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m
(
5)
i
n
t
o
(2)
,
o
n
e
m
a
y
ob
t
a
i
n:
[
I
sR
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I
sI
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=
[
−
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L
s
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w
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L
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c
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s
θ
s
−
E
tR
K
cs
V
dc
s
in
θ
s
−
E
tI
]
(9)
S
T
A
T
CO
M
c
i
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c
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t
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n
F
i
g
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5
c
a
n
b
e
m
o
de
l
e
d
by
s
t
a
t
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s
pa
c
e
i
n
R
-
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f
r
a
m
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ri
v
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d
f
r
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m
(8)
a
n
d
(9)
a
s
f
o
l
l
ow
s
:
[
I
sR
̇
I
sI
̇
V
dc
̇
]
=
[
−
R
s
L
s
w
o
K
cs
c
o
s
θ
s
L
s
−
w
o
−
R
s
L
s
K
cs
s
i
n
θ
s
L
s
−
1
.
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o
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C
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−
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.
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θ
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C
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R
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s
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[
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I
sI
V
dc
]
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[
−
1
L
s
0
0
−
1
L
s
0
0
]
[
E
tR
E
tI
]
(10)
4.
F
U
ZZY
-
L
O
G
I
C
(F
L)
B
A
S
ED
C
O
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R
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[24
,
25].
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nput
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ub
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t
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r
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w
e
l
l
-
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d
a
s
(
-
B
,
-
M
,
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S
,
Z
,
+
S
,
+
M
,
+
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h
e
r
e
e
a
c
h
i
nput
i
s
f
uz
z
i
f
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e
d
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n
t
o
7F
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va
r
i
a
b
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t
h
e
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L
c
oo
r
di
n
a
t
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d
c
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t
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o
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l
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r
ha
s
49
r
u
l
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s
.
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a
b
l
e
1
r
e
p
r
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s
e
n
t
s
t
h
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i
n
f
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r
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c
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r
ul
e
b
a
s
e
.
Co
nt
r
o
l
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g
n
a
l
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a
r
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g
e
n
e
r
a
t
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d
by
t
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L
c
o
nt
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o
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l
e
r.
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a
b
l
e
1
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L
C
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ul
e
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a
s
e
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/
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M
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Z
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M
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M
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Z
-
S
-
S
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M
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M
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5.
S
TA
TC
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EX
P
ER
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n
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o
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of
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Evaluation Warning : The document was created with Spire.PDF for Python.
IS
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2502
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4752
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a
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+
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[
1]
A
bde
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-
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khe
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.
,
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M
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g
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.
,
A
g
a
r
w
a
l
S
.
K
.
“
V
o
l
t
a
g
e
C
o
nt
r
o
l
a
nd
D
y
na
m
i
c
P
e
r
f
or
m
a
nc
e
o
f
P
o
w
e
r
T
r
a
ns
m
i
s
s
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o
n
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y
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m
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i
ng
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T
A
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nd
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t
s
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m
pa
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n
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t
h
S
V
C
.
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n
t
e
r
na
t
i
ona
l
J
ou
r
na
l
of
A
dv
a
nc
e
s
i
n
E
ng
i
ne
e
r
i
ng
and
T
e
c
hn
ol
ogy
.
J
a
nu
a
r
y
2012
.
[
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H
a
que
M
.
H
.
“
A
ppl
i
c
a
t
i
o
n
o
f
U
P
F
C
t
o
E
nha
nc
e
T
r
a
ns
i
e
n
t
S
t
a
b
i
l
i
t
y
L
i
m
i
t
.
”
P
ow
e
r
E
ngi
ne
e
r
i
ng
Soc
i
e
t
y
G
e
ne
r
al
M
e
e
t
i
ng
.
J
un
e
(
20
07)
;
pp
.
1
-
6.
[
9]
H
i
ng
o
r
a
ni
,
N
.
G
.
“
P
o
w
e
r
E
l
e
c
t
r
o
n
i
c
s
a
nd
F
l
e
xi
bl
e
A
C
T
r
a
ns
m
i
s
s
i
o
n
S
y
s
t
e
m
.
”
I
E
E
E
P
ow
e
r
E
ngi
ne
e
r
i
ng
r
e
v
i
e
w
.
J
ul
y
1988
.
[
10]
J
a
nu
s
z
e
w
s
k
i
M
.
,
M
a
c
ho
w
s
ki
J
.
,
B
i
a
l
e
kJ
.
“
A
ppl
i
c
at
i
on
of
t
he
di
r
e
c
t
L
y
apu
nov
M
e
t
h
od
t
o
i
m
p
r
ov
e
dam
p
i
n
g
o
f
P
ow
e
r
s
w
i
ngs
b
y
C
on
t
r
o
l
o
f
U
P
F
C
.
”
I
E
E
P
r
o
c
e
e
di
ng
s
G
e
ne
r
a
t
i
o
n,
T
r
a
ns
m
i
s
s
i
o
n&
D
i
s
t
r
i
bu
t
i
o
n
.
M
a
r
c
h(
2004
)
;
V
o
l
.
15
1,
N
o
.
2,
pp.
2
52
-
260
.
[
11]
K
a
z
e
m
i
A
.
,
S
o
hr
f
o
r
o
uz
a
ni
M
.
V
.
“
P
o
w
e
r
s
y
s
t
e
m
da
m
pi
ng
us
i
ng
f
u
z
z
y
c
o
nt
r
o
l
l
e
d
f
a
c
t
s
de
v
i
c
e
s
.
”
E
l
e
c
t
r
i
c
al
P
ow
e
r
and
E
ne
r
gy
Sy
s
t
e
m
s
28
.
(
20
06)
;
349
–
357
.
[
12]
M
a
m
da
ni
,
E
.
H
.
“
T
w
e
nt
y
y
e
ar
s
of
f
u
z
z
y
c
on
t
r
o
l
:
E
x
pe
r
i
e
nc
e
s
ga
i
n
e
d
and
l
e
s
s
ons
l
e
ar
n
t
.
”
P
r
o
c
e
e
d
i
ng
s
o
f
t
he
2nd
I
E
E
E
I
nt
e
r
na
t
i
o
na
l
C
o
nf
e
r
e
nc
e
o
n
F
uz
z
y
S
y
s
t
e
m
s
.
1
993;
(
pp
.
339
–
3
44)
,
S
a
n
F
r
a
nc
i
s
c
o
,
C
A
.
[
13]
K
i
s
ho
r
e
P
.
V
.
,
R
e
ddy
S
.
R
.
.
V
o
l
t
a
g
e
S
a
g
M
i
t
i
g
a
t
i
o
n
i
n
E
i
g
ht
B
us
S
y
s
t
e
m
us
i
ng
D
–
S
T
A
T
C
O
M
f
o
r
P
o
w
e
r
Q
ua
l
i
t
y
I
m
pr
o
v
e
m
e
nt
.
I
n
t
e
r
nat
i
o
nal
J
our
nal
o
f
E
ng
i
ne
e
r
i
ng
Sc
i
e
nc
e
an
d
T
e
c
hno
l
og
y
.
2
010;
v
o
l
um
e
2
(
4
)
,
52
9
–
537
.
[
14]
K
undur
P
.
P
o
w
e
r
S
y
s
t
e
m
S
t
a
bi
l
i
t
y
a
nd
C
o
nt
r
o
l
.
M
c
G
r
aw
-
H
i
l
l
.
1994
;
N
e
w
Y
o
r
k
.
[
15]
L
i
m
y
i
ngc
ha
r
o
e
n
S
.
,
A
nna
kk
a
g
e
U
.
D
.
,
P
a
h
a
l
a
w
a
t
ht
ha
N
.
C
.
“
F
uz
z
y
l
og
i
c
ba
s
e
d
uni
f
i
e
d
po
w
e
r
f
l
o
w
c
o
nt
r
o
l
l
e
r
s
f
o
r
t
r
a
ns
i
e
n
t
s
t
a
b
i
l
i
t
y
i
m
pr
o
v
e
m
e
nt
.
”
I
E
E
P
r
o
c
e
e
di
ng
s
G
e
ne
r
a
t
i
o
n,
T
r
a
ns
m
i
s
s
i
o
n&
D
i
s
t
r
i
bu
t
i
o
n
.
1
998;
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o
l
.
1
45
,
N
o
.
3
,
pp.
22
5
-
232.
[
16]
M
a
h
da
d
,
B
.
,
T
.
B
o
ukt
i
r
,
K
.
S
r
a
i
r
i
.
“
A
t
h
r
e
e
-
phas
e
pow
e
r
f
l
ow
m
ode
l
i
z
at
i
on
:
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t
o
ol
f
or
op
t
i
m
a
l
l
oc
a
t
i
on
and
c
o
nt
r
ol
of
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A
C
T
S
de
v
i
c
e
s
i
n
unb
al
a
nc
e
d
pow
e
r
s
y
s
t
e
m
s
.
”
T
h
e
32n
d
A
nnua
l
C
o
nf
e
r
e
nc
e
o
f
t
he
I
E
E
E
I
ndus
t
r
i
a
l
E
l
e
c
t
r
o
ni
c
s
S
o
c
i
e
t
y
.
2006;
C
o
ns
e
r
v
a
t
o
i
r
e
N
a
t
i
o
na
l
d
e
s
A
r
t
s
&
M
e
t
i
e
r
s
P
a
r
i
s
,
F
R
A
N
CE
,
P
a
g
e
(
s
)
:
2238
-
224
3,
1
-
42
4
4
-
0136
-
4
/
06
.
[
17]
M
a
t
hu
r
R
.
M
.
,
R
a
j
i
v
K
.
V
.
“
T
hy
r
i
s
t
o
r
B
a
s
e
d
F
A
C
T
S
C
o
nt
r
o
l
l
e
r
s
f
or
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l
e
c
t
r
i
c
a
l
T
r
a
n
s
m
i
s
s
i
o
n
S
y
s
t
e
m
s
.
”
I
E
E
E
pr
e
s
s
s
e
r
i
e
s
o
n
P
ow
e
r
E
ngi
ne
e
r
i
n
g,
J
ohn
W
i
l
e
y
&
Son
s
L
T
D
.
200
2.
[
18]
M
a
n
ue
l
S
.
A
l
v
a
r
e
z
-
A
l
v
a
r
a
do
,
D
i
l
a
n
J
a
y
a
w
e
e
r
a
.
“
S
m
a
r
t
M
a
i
n
t
e
n
a
nc
e
M
o
de
l
f
o
r
O
pe
r
a
t
i
o
na
l
P
l
a
nn
i
ng
o
f
S
t
a
t
i
c
S
y
nc
hr
o
no
us
C
o
m
pe
ns
a
t
o
r
s
.
”
I
E
E
E
M
i
l
an
P
ow
e
r
T
e
c
h
.
20
19
[
19]
S
a
de
g
hz
a
de
h
S
.
M
.
,
E
hs
a
n
M
.
,
S
a
i
d
N
.
H
.
,
F
e
u
i
l
l
e
t
R
.
.
“
I
m
pr
o
v
e
m
e
nt
o
f
T
r
a
ns
i
e
n
t
S
t
a
bi
l
i
t
y
L
i
m
i
t
i
n
P
o
w
e
r
S
y
s
t
e
m
L
i
ne
s
U
s
i
ng
F
uz
z
y
C
o
nt
r
o
l
o
f
F
A
C
T
S
D
e
v
i
c
e
s
.
”
I
E
E
E
T
r
an
s
ac
t
i
on
s
o
n
P
ow
e
r
Sy
s
t
e
m
s
.
1998;
V
o
l
.
13
,
N
o
.
3
.
[
20]
S
r
i
v
a
s
t
a
S
.
K
.
“
A
dv
a
nc
e
d
P
o
w
e
r
E
l
e
c
t
r
o
ni
c
s
B
a
s
e
d
F
a
c
t
s
C
o
nt
r
o
l
l
e
r
s
a
nd
O
v
e
r
v
i
e
w
.
”
A
s
i
an
P
ow
e
r
E
l
e
c
t
r
on
i
c
s
J
our
nal
.
D
e
c
e
m
be
r
2
010;
v
o
l
um
e
4,
N
o
.
3.
[
21]
S
w
a
r
o
o
pa
n
N
M
.
J
.
,
S
o
m
a
s
unda
r
a
m
P
.
“
T
r
ans
i
e
nt
S
t
ab
i
l
i
t
y
E
nh
anc
e
m
e
nt
w
i
t
h
U
P
F
C
.
”
I
E
T
-
U
K
I
nt
e
r
n
at
i
ona
l
C
o
nf
e
r
e
nc
e
o
n
I
nf
o
r
m
a
t
i
o
n
a
nd
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o
m
m
uni
c
a
t
i
o
n
T
e
c
hno
l
o
gy
i
n
E
l
e
c
t
r
i
c
a
l
S
c
i
e
nc
e
s
(
I
C
T
E
S
)
.
D
e
c
.
(
20
07)
;
pp.
51
0
-
516
.
[
22]
Y
a
ng
Z
.
,
S
he
n
C
.
,
Z
h
a
ng
L
.
,
C
r
o
w
M
.
L
.
,
A
t
c
i
t
t
y
S
.
“
I
nt
e
g
r
a
t
i
o
n
o
f
a
S
t
a
t
C
o
m
a
nd
b
a
t
t
e
r
y
e
ne
r
gy
s
t
o
r
a
g
e
.
”
I
E
E
E
T
r
ans
ac
t
i
ons
on
P
ow
e
r
Sy
s
t
e
m
s
.
M
a
y
2001;
v
o
l
.
1
6,
no
.
2,
p
p.
25
4
-
260.
[
23]
H
y
unW
oo
L
e
e
,
J
u
ng
-
W
o
o
k
P
a
r
k
.
“
A
n
I
m
pr
ov
e
d
ST
A
T
C
O
M
bas
e
d
on
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y
b
r
i
d
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odu
l
a
r
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u
l
t
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l
e
v
e
l
C
o
nv
e
r
t
e
r
.
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34
t
h
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nt
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na
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o
na
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hn
i
c
a
l
C
o
nf
e
r
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nc
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o
n
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i
r
c
ui
t
s
/
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y
s
t
e
m
s
,
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o
m
put
e
r
s
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nd
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o
m
m
uni
c
a
t
i
o
ns
(
I
T
C
-
C
S
C
C
)
.
12
A
u
g
us
t
2019
[
24]
Z
ha
ng
X
.
P
.
,
R
e
ht
a
nz
C
.
,
P
a
l
B
.
“
F
l
e
xi
bl
e
A
C
T
r
a
ns
m
i
s
s
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o
n
S
y
s
t
e
m
s
:
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o
de
l
l
i
ng
a
nd
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o
nt
r
o
l
.
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pr
i
nge
r
-
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e
r
l
ag
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e
r
l
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n
H
e
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de
l
be
r
.
2
006
.
[
25]
A
.
Y
.
H
a
s
s
a
n,
S
.
A
.
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.
W
a
h
s
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.
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C
E
D
S
1202
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nt
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Se
ar
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h
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p
t
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m
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z
e
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D
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of
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M
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.
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w
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t
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nt
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y
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t
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m
s
C
o
nf
e
r
e
nc
e
(
M
E
P
C
O
N
)
.
2018;
C
a
i
r
o
,
E
g
y
pt
,
pp
.
11
26
-
1133
.
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