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f
g
etti
n
g
s
tu
c
k
at
lo
ca
l
o
p
ti
m
a.
An
t
co
lo
n
y
o
p
ti
m
izatio
n
[
8
]
,
Fire
f
l
y
al
g
o
r
ith
m
[
9
]
,
B
ac
ter
ial
Fo
r
ag
in
g
al
g
o
r
ith
m
[
1
0
]
Fro
g
L
ea
p
in
g
a
lg
o
r
it
h
m
[
1
1
]
,
A
r
tif
icial
B
ee
C
o
lo
n
y
alg
o
r
ith
m
[
1
2
]
,
P
a
r
ticle
Sw
ar
m
Op
ti
m
izatio
n
al
g
o
r
ith
m
[
1
3
]
,
Sim
u
lated
An
n
ea
lin
g
[
1
4
]
an
d
Gen
etic
a
lg
o
r
ith
m
[
1
5
]
w
er
e
ap
p
lied
f
o
r
h
ar
m
o
n
ic
r
ed
u
ct
io
n
i
n
m
u
lti
lev
el
i
n
v
er
ter
.
B
u
t
th
e
T
HD
r
ed
u
ctio
n
d
o
es n
o
t c
o
m
p
l
y
w
it
h
t
h
e
I
E
E
E
s
tan
d
ar
d
5
1
9
.
W
alsh
f
u
n
c
tio
n
m
et
h
o
d
h
as b
ee
n
r
ep
o
r
ted
in
[
1
6
]
.
Her
e
s
w
itch
in
g
a
n
g
les
ar
e
o
b
tain
ed
b
y
s
o
l
v
i
n
g
l
in
ea
r
e
q
u
atio
n
s
.
T
h
e
m
et
h
o
d
f
ail
s
[
1
7
]
if
it
i
s
r
eq
u
ir
ed
to
f
i
n
d
m
o
r
e
an
g
les
i
n
t
h
e
s
a
m
e
i
n
ter
v
al.
T
h
e
en
er
g
y
m
a
n
a
g
e
m
en
t
s
y
s
te
m
w
i
th
ca
s
ca
d
ed
m
u
l
tilev
el
i
n
v
er
ter
h
a
s
b
ee
n
r
ep
o
r
ted
in
[
1
8
]
.
Har
m
o
n
ic
a
n
al
y
s
is
o
f
s
e
v
e
n
a
n
d
n
in
e
le
v
el
i
n
v
er
ter
w
er
e
ca
r
r
ied
o
u
t
i
n
[
1
9
]
.
T
h
e
o
p
tim
izatio
n
m
e
th
o
d
s
ap
p
lied
f
o
r
h
ar
m
o
n
ic
r
ed
u
ctio
n
o
n
e
w
a
y
o
r
t
h
e
o
t
h
er
lead
s
to
p
r
em
at
u
r
e
co
n
v
er
g
e
n
ce
,
d
if
f
ic
u
lt
y
i
n
f
in
d
i
n
g
th
e
i
n
itia
l
g
u
e
s
s
,
T
HD
n
o
t
co
m
p
lia
n
ce
w
it
h
t
h
e
I
E
E
E
5
1
9
s
tan
d
ar
d
,
i
n
co
n
s
is
te
n
c
y
o
f
t
h
e
o
p
tim
a
l so
lu
tio
n
f
o
r
th
e
v
ar
y
in
g
m
o
d
u
la
tio
n
i
n
d
ex
w
er
e
t
h
e
m
aj
o
r
p
r
o
b
l
em
s
f
ac
ed
.
I
n
th
is
p
ap
er
p
atter
n
s
ea
r
ch
alg
o
r
ith
m
h
a
s
b
ee
n
u
til
ized
to
ca
lcu
late
th
e
s
w
itc
h
i
n
g
a
n
g
le
f
o
r
th
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
ter
w
i
th
t
h
e
a
i
m
to
m
i
n
i
m
ize
t
h
e
to
t
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
Ma
tlab
s
o
f
t
w
ar
e
w
as
u
s
ed
to
s
i
m
u
late
t
h
e
th
ir
teen
le
v
el,
f
i
f
teen
lev
el
a
n
d
s
ev
e
n
tee
n
le
v
el
in
v
er
ter
w
i
th
r
esi
s
ti
v
e
lo
ad
,
r
esis
ti
v
e
-
in
d
u
cti
v
e
lo
ad
an
d
m
o
to
r
lo
ad
.
2.
CASCAD
E
D
H
-
B
RID
G
E
I
N
VE
R
T
E
R
C
ascad
ed
H
-
b
r
id
g
e
in
v
er
ter
ac
q
u
ir
es
t
h
e
in
p
u
t
f
r
o
m
m
a
n
y
l
D
C
s
o
u
r
ce
s
an
d
g
e
n
er
ates
a
s
tep
p
ed
w
a
v
e
f
o
r
m
.
A
s
t
h
e
n
u
m
b
er
o
f
l
ev
els
o
f
t
h
e
i
n
v
er
ter
in
cr
ea
s
e
s
,
th
e
w
a
v
e
f
o
r
m
ap
p
r
o
ac
h
es
s
i
n
u
s
o
id
r
ed
u
ci
n
g
th
e
to
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
.
A
k
-
lev
el
i
n
v
er
ter
co
n
s
i
s
t
o
f
(
k
-
1
)
/
2
H
-
b
r
id
g
es.
Fo
u
r
s
w
i
tch
in
g
d
ev
ices
ar
e
r
eq
u
ir
ed
f
o
r
ea
ch
b
r
id
g
e.
S
w
i
tch
in
g
d
e
v
ices
ca
n
b
e
o
f
I
GB
T
,
Po
w
er
MO
SF
E
T
,
SC
R
etc.
Her
e
S
C
R
h
as
b
ee
n
u
s
ed
as
a
s
w
itc
h
in
g
d
ev
ice.
T
h
ir
teen
lev
el
in
v
er
ter
w
ith
r
esi
s
ti
v
e
in
d
u
ctiv
e
lo
ad
is
s
h
o
w
n
in
t
h
e
Fig
u
r
e
1
.
T
h
e
in
v
er
ter
co
n
s
is
t si
x
H
-
b
r
id
g
e
s
co
n
n
ec
te
d
in
s
er
ies an
d
h
en
ce
it c
o
n
tai
n
s
t
w
e
n
t
y
f
o
u
r
s
w
itc
h
es.
Fig
u
r
e
1
.
13
-
lev
el
in
v
er
ter
w
it
h
R
L
lo
ad
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
2
9
2
–
3
2
9
8
3294
Ma
th
e
m
atica
l
eq
u
atio
n
s
f
o
r
m
in
i
m
izi
n
g
th
e
h
ar
m
o
n
ic
s
h
a
v
e
b
ee
n
f
o
r
m
u
lated
b
y
f
o
u
r
ier
an
al
y
s
i
s
T
h
e
f
o
llo
w
in
g
eq
u
atio
n
r
ep
r
esen
ts
f
u
n
d
a
m
en
ta
l
co
m
p
o
n
en
t,
t
h
ir
d
h
ar
m
o
n
ic
s
,
f
i
f
t
h
h
ar
m
o
n
ics,
s
ev
en
t
h
h
ar
m
o
n
ic
s
,
n
in
th
h
ar
m
o
n
ics a
n
d
e
lev
e
n
t
h
h
ar
m
o
n
ics
f
o
r
th
e
1
3
-
le
v
el
in
v
er
ter
Fu
n
d
a
m
e
n
tal
C
o
m
p
o
n
e
n
t
4
π
√
2
(
V
1
c
os
θ
1
+
V
2
c
os
θ
2
+
V
3
c
os
θ
3
+
V
4
c
os
θ
4
+
V
5
c
os
θ
5
+
V
6
c
os
θ
6
)
=
2
3
0
;
T
h
ir
d
Har
m
o
n
ic
E
q
u
at
io
n
V
1
co
s
3
θ
1
+V
2
co
s
3
θ
2
+V
3
co
s
3
θ
3
+V
4
co
s
3
θ
4
+V
5
co
s
3
θ
5
+ V
6
co
s
3
θ
6
=0
;
Fif
t
h
Har
m
o
n
ic
E
q
u
at
io
n
V
1
co
s
5
θ
1
+V
2
co
s
5
θ
2
+V
3
co
s
5
θ
3
+V
4
co
s
5
θ
4
+V
5
co
s
5
θ
5
+ V
6
co
s
5
θ
6
=0
;
Sev
e
n
th
Har
m
o
n
ic
E
q
u
atio
n
V
1
co
s
7
θ
1
+V
2
co
s
7
θ
2
+V
3
co
s
7
θ
3
+V
4
co
s
7
θ
4
+V
5
co
s
7
θ
5
+ V
6
co
s
7
θ
6
=0
;
Nin
t
h
Har
m
o
n
ic
E
q
u
atio
n
V
1
co
s
9
θ
1
+V
2
co
s
9
θ
2
+V
3
co
s
9
θ
3
+V
4
co
s
9
θ
4
+V
5
co
s
9
θ
5
+ V
6
co
s
9
θ
6
=0
;
E
lev
en
th
Har
m
o
n
ic
E
q
u
a
tio
n
V
1
co
s
1
1
θ
1
+V
2
co
s
1
1
θ
2
+V
3
co
s
1
1
θ
3
+V
4
co
s
1
1
θ
4
+V
5
co
s
1
1
θ
5
+
V
6
co
s
1
1
θ
6
=0
;
W
h
er
e
V
1
, V
2
, V
3
, V
4
, V
5
&
V
6
ar
e
th
e
in
p
u
t d
c
v
o
lta
g
es
f
o
r
s
ix
H
-
b
r
d
g
e
in
v
er
ter
s
.
θ
1
, θ
2
, θ
3
, θ
4
, θ
5
&
θ
6
ar
e
th
e
s
w
i
tch
i
n
g
an
g
les
f
o
r
s
i
x
H
-
b
r
id
g
e
in
v
er
ter
s
3.
P
AT
T
E
RN
S
E
AR
CH
AL
G
O
RIT
H
M
P
atter
n
s
ea
r
ch
al
g
o
r
ith
m
ca
n
b
e
u
s
ed
to
f
i
n
d
t
h
e
m
i
n
i
m
u
m
o
f
th
e
f
u
n
ctio
n
ca
l
led
o
b
j
ec
tiv
e
f
u
n
ctio
n
w
it
h
co
n
s
tr
ai
n
t
s
.
I
t
ta
k
es
t
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
w
i
th
t
h
e
in
it
ial
r
a
n
d
o
m
v
a
l
u
es.
P
att
er
n
s
ea
r
c
h
m
et
h
o
d
p
er
f
o
r
m
s
t
h
e
s
eq
u
en
ce
o
f
iter
a
tio
n
s
f
o
r
co
n
v
er
g
en
ce
.
On
ce
f
i
n
ite
n
u
m
b
er
o
f
iter
at
io
n
i
s
r
ea
ch
ed
it
s
w
i
tch
e
s
to
th
e
lo
w
er
co
s
t
f
u
n
c
tio
n
.
Me
s
h
s
ize
p
la
y
s
a
r
o
le
in
s
et
tin
g
t
h
e
s
ea
r
ch
alo
n
g
th
e
s
ea
r
ch
d
ir
ec
tio
n
.
T
h
e
d
ef
au
lt
v
alu
e
o
f
th
e
m
e
s
h
s
ize
is
o
n
e.
So
m
e
ti
m
es
s
o
l
u
tio
n
g
o
t
m
a
y
n
o
t
b
e
o
p
tim
u
m
.
So
to
i
m
p
r
o
v
e
o
p
ti
m
alit
y
o
f
th
e
s
o
lu
ti
o
n
m
es
h
s
ca
li
n
g
h
a
s
to
b
e
d
o
n
e.
T
h
e
n
u
m
b
er
o
f
f
u
n
ct
io
n
ev
a
lu
at
io
n
w
i
ll
b
e
m
i
n
i
m
u
m
w
i
th
ap
p
r
o
p
r
iate
s
ca
lin
g
,
r
ed
u
ci
n
g
t
h
e
co
m
p
u
tat
io
n
ti
m
e.
T
h
e
P
atter
n
Sear
ch
a
lg
o
r
ith
m
[
2
0
]
is
g
iv
e
n
b
y
L
et
x
0
∈
R
n
an
d
∆
0
>
0
b
e
g
iv
e
n
.
Fo
r
k
=
0
,
1
,
.
.
.
,
(
a)
C
o
m
p
u
te
f
(
x
k
).
(
b
)
Dete
r
m
i
n
e
a
s
tep
s
k
u
s
i
n
g
a
n
ex
p
lo
r
ato
r
y
m
o
v
es a
l
g
o
r
ith
m
.
(
c)
C
o
m
p
u
te
ρ
k
=
f
(
x
k
)
−
f
(
x
k
+ s
k
).
(
d
)
I
f
ρ
k
>
0
th
e
n
x
k+
1
= x
k
+ s
k
.
Oth
er
w
is
e
x
k
+
1
= x
k
.
(
e)
Up
d
ate
C
k
an
d
∆
k
.
T
o
d
ef
in
e
a
p
ar
tic
u
lar
p
atter
n
s
ea
r
c
h
m
eth
o
d
,
it
i
s
n
ec
es
s
ar
y
to
s
p
ec
i
f
y
t
h
e
b
asis
m
at
r
ix
B
,
th
e
g
en
er
ati
n
g
m
atr
i
x
C
k
,
th
e
ex
p
l
o
r
ato
r
y
m
o
v
e
s
to
b
e
u
s
ed
to
p
r
o
d
u
ce
a
s
tep
s
k
,
a
n
d
t
h
e
al
g
o
r
ith
m
s
f
o
r
u
p
d
atin
g
C
k
an
d
∆
k
.
Her
e
p
atter
n
s
ea
r
c
h
alg
o
r
it
h
m
h
a
s
b
ee
n
ap
p
lied
to
d
eter
m
i
n
e
t
h
e
s
w
itc
h
i
n
g
an
g
les
o
f
t
h
e
ca
s
ca
d
ed
H
-
b
r
id
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[1
]
R.
S
.
R
.
Ba
b
u
,
e
t
a
l
.
,
“
A
Clo
se
d
L
o
o
p
Co
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o
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o
f
Qu
a
d
ra
ti
c
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st
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o
n
v
e
rter
Us
in
g
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n
tr
o
ll
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r
,
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IJ
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tra
n
sa
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ti
o
n
s
B:
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p
li
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n
s
,
v
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l
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2
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,
p
p
.
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6
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.
[2
]
R.
D
.
He
n
d
e
rso
n
a
n
d
P
.
J.
Ro
se
,
“
Ha
r
m
o
n
ics
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h
e
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ff
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ts
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p
o
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e
r
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ty
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n
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e
rs,”
IEE
E
T
ra
n
s
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ti
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n
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o
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n
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u
stry
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p
.
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8
–
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,
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9
4
.
[3
]
N.
S
u
re
sh
a
n
d
R.
S
.
R
.
Ba
b
u
,
“
Re
v
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r
m
o
n
ics
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n
d
it
s
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li
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in
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ti
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trate
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5
.
[4
]
D.
S
h
m
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o
v
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,
“
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th
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e
f
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su
re
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e
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t
in
terp
r
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,
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n
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.
[5
]
J
.
R
o
d
ríg
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z
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e
t
a
l
.
,
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M
u
l
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In
v
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rters
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ies
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n
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ra
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.
[6
]
M.
G
.
V
.
K
u
m
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e
t
a
l
.
,
“
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m
p
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riso
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u
lt
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rters
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,
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ter
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ti
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rn
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d
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1
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p
.
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9
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0
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2
.
[7
]
T.
R.
S
u
m
it
h
ira
,
e
t
a
l
.
,
“
El
im
in
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ti
o
n
o
f
Ha
r
m
o
n
ics
in
M
u
lt
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lev
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l
In
v
e
rters
Co
n
n
e
c
ted
to
S
o
lar P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
s
Us
in
g
A
NFIS
:
A
n
Ex
p
e
rime
n
tal
Ca
se
S
tu
d
y
,
”
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o
u
rn
a
l
o
f
A
p
p
li
e
d
Res
e
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rc
h
a
n
d
T
e
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h
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o
l
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g
y
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v
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1
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p
.
1
2
4
-
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3
2
,
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0
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3
.
[8
]
I.
A
d
e
y
e
m
o
,
e
t
a
l
.
,
“
A
n
t
Co
lo
n
y
Op
ti
m
isa
ti
o
n
A
p
p
ro
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c
h
t
o
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
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im
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a
ti
o
n
i
n
M
u
lt
il
e
v
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l
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v
e
rter
,
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IM
PA
CT
:
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ter
n
a
ti
o
n
a
l
J
o
u
rn
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l
o
f
Res
e
a
rc
h
in
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n
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g
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y
,
v
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l.
3
,
p
p
.
31
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42
,
2
0
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5
.
[9
]
M
.
G
.
S
u
n
d
a
ria
,
e
t
a
l
.
,
“
A
p
p
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c
a
ti
o
n
o
f
im
p
ro
v
e
d
f
iref
l
y
a
lg
o
rit
h
m
f
o
r
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ro
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ra
m
m
e
d
P
W
M
in
m
u
lt
il
e
v
e
l
in
v
e
rter
w
it
h
a
d
ju
sta
b
le DC so
u
rc
e
s
,
”
Ap
p
li
e
d
S
o
ft
C
o
mp
u
ti
n
g
,
2
0
1
5
.
[1
0
]
T.
S
.
Ba
b
u
,
e
t
a
l
.
,
“
S
e
lec
ti
v
e
v
o
lt
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g
e
h
a
r
m
o
n
ic
e
li
m
in
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ti
o
n
in
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in
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e
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b
a
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teria
l
f
o
ra
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n
g
a
lg
o
rit
h
m
,
”
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wa
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n
d
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l
u
ti
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n
a
ry
C
o
mp
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t
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ti
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n
,
2
0
1
5
.
[1
1
]
H
.
L
o
u
,
e
t
a
l
.
,
“
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u
n
d
a
m
e
n
tal
m
o
d
u
latio
n
stra
teg
y
w
it
h
se
lec
ti
v
e
h
a
r
m
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n
ic
e
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m
in
a
ti
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ter
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.
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6
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.
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8
]
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.
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.
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ter
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,
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.
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p
.
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0
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ter
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.
T
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o
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,
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f
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a
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rn
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p
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AUTH
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RS
First au
t
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r.
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.
P
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As
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P
ro
f
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m
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.
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re
a
s
o
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in
tere
st
a
re
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Dig
it
a
l
P
ro
tec
ti
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.