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nte
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l J
o
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Appl
ied P
o
wer
E
ng
i
neer
ing
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I
J
AP
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)
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
,
p
p
.
3
0
7
~
3
1
4
I
SS
N:
2252
-
8
7
9
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,
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: 1
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1
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4
.
p
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314
307
J
o
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e
:
h
ttp
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//ij
a
p
e.
ia
esco
r
e.
co
m
Simula
tion o
f
bo
o
st
AC
-
AC
co
nv
ert
er using
sing
le
-
ph
a
se ma
trix
co
nv
erte
r
Z
ey
nep B
a
la
Dura
na
y
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H
a
nifi
G
uld
em
ir
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
-
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
,
Tec
h
n
o
l
o
g
y
F
a
c
u
lt
y
,
F
irat
U
n
iv
e
rsit
y
,
E
laz
ig
,
T
u
r
k
e
y
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ap
r
4
,
2
0
21
R
ev
is
ed
J
u
n
2
4
,
2
0
21
Acc
ep
ted
J
u
l
23
,
2
0
21
G
e
n
e
r
a
ll
y
,
AC
-
AC
c
o
n
v
e
rters
a
re
imp
lem
e
n
ted
u
sin
g
th
y
risto
rs.
T
h
e
se
c
o
n
v
e
rters
g
e
n
e
ra
te
h
a
rm
o
n
ics
a
n
d
h
a
v
e
a
l
o
w
p
o
we
r
fa
c
to
r
.
T
o
e
li
m
in
a
te
th
e
se
p
ro
b
lem
s
m
a
tri
x
c
o
n
v
e
rt
e
rs
(M
C)
a
re
b
e
c
o
m
e
u
se
d
a
s
AC
-
AC
c
o
n
v
e
rter.
M
a
tri
x
c
o
n
v
e
rters
h
a
v
e
th
e
c
a
p
a
b
il
it
y
o
f
b
e
i
n
g
u
se
d
a
s
fre
q
u
e
n
c
y
c
h
a
n
g
e
r,
re
c
ti
fier,
i
n
v
e
rter
a
n
d
c
h
o
p
p
e
r.
In
th
is
w
o
rk
,
it
is
p
r
o
p
o
se
d
to
a
c
h
iev
e
th
e
d
e
sire
d
o
u
t
p
u
t
o
f
A
C
-
AC
Bo
o
st
c
o
n
v
e
rter
u
si
n
g
si
n
g
le
p
h
a
se
m
a
tri
x
c
o
n
v
e
rter
(S
P
M
C).
Th
e
o
p
e
ra
ti
o
n
o
f
sin
g
le
-
p
h
a
se
AC
-
AC
b
o
o
st
c
o
n
v
e
rter
u
si
n
g
MC
is
stu
d
ied
i
n
th
is
p
a
p
e
r.
T
h
e
o
u
t
p
u
t
v
o
l
tag
e
o
f
th
is
b
o
o
st
c
o
n
v
e
rter
is
h
ig
h
e
r
th
a
n
t
h
e
AC
i
n
p
u
t
su
p
p
ly
v
o
lt
a
g
e
.
in
s
u
late
d
g
a
te
b
i
p
o
lar
tran
sisto
rs
(
IG
BTs
)
a
re
u
se
d
a
s
t
h
e
sw
it
c
h
i
n
g
e
lem
e
n
ts
in
t
h
e
S
P
M
C
p
o
we
r
c
ircu
it
.
S
in
u
so
i
d
a
l
P
u
lse
wi
d
th
m
o
d
u
lati
o
n
(S
P
WM
)
tec
h
n
i
q
u
e
i
s
a
p
p
li
e
d
t
o
g
e
n
e
ra
te
sw
it
c
h
in
g
sig
n
a
ls
t
o
o
b
tain
th
e
o
u
t
p
u
t
v
o
lt
a
g
e
.
T
h
e
m
o
d
e
l
o
f
t
h
e
m
a
tri
x
c
o
n
v
e
rter
is
c
o
n
stru
c
t
e
d
in
M
ATLAB/
S
imu
li
n
k
p
r
o
g
ra
m
m
in
g
so
ftwa
re
p
a
c
k
a
g
e
.
Th
e
b
e
h
a
v
i
o
r
o
f
S
P
M
C
is
sim
u
late
d
wi
th
v
a
rio
u
s
sw
it
c
h
in
g
fre
q
u
e
n
c
ies
.
T
h
e
si
m
u
latio
n
re
su
lt
s
to
g
e
th
e
r
wit
h
h
a
rm
o
n
ic
sp
e
c
tru
m
a
n
d
t
o
tal
h
a
rm
o
n
ic
d
ist
o
rti
o
n
(THD)
v
a
lu
e
s
a
re
p
re
se
n
ted
.
S
u
c
c
e
ss
fu
l
o
p
e
ra
ti
o
n
o
f
b
o
o
st S
P
M
C
is ac
h
iev
e
d
.
K
ey
w
o
r
d
s
:
AC
-
AC
co
n
v
er
ter
B
o
o
s
t c
o
n
v
er
ter
Ma
tr
ix
co
n
v
e
r
ter
Pu
ls
e
wid
th
m
o
d
u
latio
n
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Z
ey
n
ep
B
ala
Du
r
an
a
y
Dep
ar
tm
en
t o
f
E
lectr
ical
-
E
lectr
o
n
ics E
n
g
in
ee
r
in
g
Fira
t
Un
iv
er
s
ity
E
lazig
2
3
1
1
9
,
T
u
r
k
e
y
E
m
ail: z
b
d
u
r
a
n
ay
@
f
ir
at.
ed
u
.
t
r
1.
I
NT
RO
D
UCT
I
O
N
So
m
e
in
d
u
s
tr
ial
a
p
p
licatio
n
s
r
eq
u
ir
e
a
n
AC
-
AC
co
n
v
e
r
s
io
n
.
AC
v
o
ltag
e
c
o
n
tr
o
ller
s
with
th
y
r
is
to
r
s
wer
e
p
er
f
o
r
m
e
d
th
is
AC
-
AC
c
o
n
v
er
s
io
n
.
T
h
is
ty
p
e
o
f
cir
cu
it
s
d
is
to
r
ts
v
o
ltag
e
an
d
cu
r
r
en
t
wav
ef
o
r
m
an
d
h
av
e
a
lo
w
p
o
wer
f
ac
to
r
.
T
h
er
ef
o
r
e,
p
o
wer
f
ac
to
r
c
o
r
r
ec
tio
n
a
n
d
h
ar
m
o
n
ic
r
ed
u
ctio
n
ar
e
n
ec
ess
ar
y
f
o
r
th
ese
v
o
ltag
e
r
e
g
u
lato
r
s
.
T
o
o
v
er
c
o
m
e
th
ese
p
r
o
b
lem
s
m
atr
ix
co
n
v
er
ter
s
h
as
tak
en
p
lace
o
f
th
e
AC
v
o
ltag
e
co
n
tr
o
ller
s
.
I
n
a
m
atr
i
x
c
o
n
v
e
r
ter
(
MC)
cir
cu
it
th
e
r
e
ar
e
in
p
u
t
an
d
o
u
tp
u
t
lin
es.
Ma
tr
ix
co
n
v
er
ter
co
n
s
is
ts
o
f
b
id
ir
ec
tio
n
al
s
witch
es
ar
r
a
n
g
e
d
in
m
atr
ix
f
o
r
m
,
c
o
n
n
ec
ted
b
etwe
en
in
p
u
t
an
d
o
u
tp
u
t
lin
e
s
.
T
h
e
o
u
tp
u
t
lin
es
ar
e
co
n
n
ec
ted
t
o
in
p
u
t
lin
es
in
ac
co
r
d
a
n
ce
with
a
s
tr
ateg
y
[
1
]
.
T
h
is
co
n
v
e
r
ter
to
p
o
lo
g
y
h
as
th
e
ad
v
an
tag
e
o
f
n
o
d
c
lin
k
s
to
r
ag
e
elem
en
t
[
2
]
.
Up
to
n
o
w,
m
an
y
ty
p
es
o
f
r
e
s
ea
r
ch
ar
e
d
o
n
e
o
n
s
in
g
le
p
h
a
s
e
m
atr
ix
co
n
v
er
ter
(
SP
MC
)
in
th
e
f
ield
o
f
AC
-
AC
[
3
]
-
[
5
]
,
DC
-
DC
[
6
]
,
[
7
]
,
DC
-
AC
[
8
]
,
[
9
]
an
d
AC
-
DC
[
10
]
,
[
1
1
]
c
o
n
v
e
r
s
io
n
.
MC
to
p
o
lo
g
y
is
f
i
r
s
t
p
r
o
p
o
s
ed
in
[
1
2
]
a
n
d
t
h
e
SP
MC
cir
cu
it
was
f
ir
s
t
im
p
lem
en
ted
in
[
1
3
]
.
T
h
is
SP
MC
im
p
lem
en
tatio
n
h
as
a
m
atr
ix
o
f
in
p
u
t
a
n
d
o
u
t
p
u
t
li
n
es
with
s
witch
in
g
elem
e
n
ts
wh
ich
co
n
n
ec
t
t
h
e
in
p
u
t
to
th
e
o
u
tp
u
t.
T
h
e
s
witch
es
in
th
e
co
n
v
er
ter
cir
cu
it
ar
e
b
o
t
h
ca
p
a
b
le
o
f
c
o
n
d
u
ctin
g
c
u
r
r
en
t
in
b
o
t
h
d
ir
ec
tio
n
s
th
at
is
b
id
ir
ec
tio
n
a
l
an
d
ca
p
ab
le
o
f
b
lo
c
k
in
g
v
o
ltag
e.
Ma
n
y
r
esear
ch
w
o
r
k
s
h
av
e
b
ee
n
d
o
n
e
o
n
SP
MC im
p
lem
en
tatio
n
[
4
]
-
[
9
]
,
[
14
]
-
[
1
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
87
92
I
n
t J
Ap
p
l
Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
0
7
–
314
308
Ma
tr
ix
co
n
v
er
ter
s
ca
n
p
r
o
d
u
ce
an
o
u
tp
u
t
with
v
ar
iab
le
v
o
ltag
es
an
d
f
r
eq
u
e
n
cies.
V
ar
i
o
u
s
cir
cu
it
to
p
o
lo
g
ies
s
u
c
h
as
f
r
eq
u
en
cy
ch
an
g
er
,
r
ec
tifie
r
,
in
v
e
r
ter
an
d
ch
o
p
p
er
ca
n
b
e
c
o
n
s
tr
u
cted
with
th
e
MC
with
s
im
p
le
s
tr
u
ctu
r
e
an
d
h
ig
h
r
eli
ab
ilit
y
.
B
ec
au
s
e
th
e
b
o
o
s
t
M
C
is
p
o
o
r
ly
s
tu
d
ied
in
th
e
liter
atu
r
e,
it
is
aim
ed
to
em
p
h
asize
th
e
b
o
o
s
t c
h
ar
ac
ter
is
tics
o
f
th
e
m
atr
ix
co
n
v
e
r
ter
.
T
h
er
ef
o
r
e,
i
n
th
is
s
tu
d
y
,
a
s
in
g
le
-
p
h
ase
b
o
o
s
t A
C
-
AC
m
atr
ix
co
n
v
er
ter
is
s
tu
d
ie
d
wh
ich
h
as
a
h
i
g
h
er
o
u
tp
u
t
v
o
ltag
e
th
an
a
lo
w
in
p
u
t
v
o
lt
ag
e.
I
n
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
is
to
r
s
(
I
GB
T
s
)
a
r
e
u
s
ed
as
s
witch
in
g
elem
en
ts
in
th
e
SP
MC
cir
cu
it.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
o
b
tain
ed
t
h
r
o
u
g
h
d
u
t
y
cy
cle
co
n
tr
o
l
o
f
s
witch
in
g
d
ev
ic
e
u
s
in
g
t
h
e
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M)
tech
n
iq
u
e.
A
r
esis
tiv
e
lo
ad
is
u
s
ed
with
an
L
C
f
ilte
r
f
o
r
r
em
o
v
in
g
r
i
p
p
les
at
th
e
lo
ad
.
An
in
d
u
ctan
ce
is
co
n
n
ec
ted
in
s
er
ies
with
t
h
e
in
p
u
t
s
u
p
p
ly
f
o
r
b
o
o
s
t
o
p
er
atio
n
.
A
m
o
d
el
o
f
SP
MC
f
o
r
b
o
o
s
t
AC
-
AC
o
p
er
atio
n
is
d
ev
elo
p
ed
in
Si
m
u
lin
k
.
T
h
e
v
alid
atio
n
o
f
th
e
m
o
d
el
is
p
er
f
o
r
m
ed
th
r
o
u
g
h
s
im
u
latio
n
s
.
T
h
e
m
o
d
el
is
test
ed
with
d
if
f
er
e
n
t
s
witch
in
g
f
r
eq
u
e
n
cies.
T
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
e
s
u
cc
ess
f
u
l
b
o
o
s
t
o
p
er
atio
n
o
f
SP
MC.
2.
SI
NG
L
E
P
H
AS
E
B
O
O
S
T
A
C
-
AC
M
A
T
RIX CO
N
VE
R
T
E
R
On
e
o
f
th
e
p
r
ac
tical
p
r
o
b
lem
s
f
ac
ed
in
th
e
im
p
lem
en
tatio
n
o
f
MC
is
co
m
m
u
tatio
n
.
Du
e
to
h
av
in
g
n
o
f
r
ee
wh
ee
l
p
ath
s
,
th
e
s
af
e
tr
an
s
f
er
o
f
th
e
cu
r
r
en
t
b
etwe
en
th
e
s
witch
es
is
d
if
f
icu
lt.
T
h
e
s
witch
in
g
h
as
to
b
e
s
o
d
o
n
e
as
to
m
ai
n
tain
co
n
tin
u
o
u
s
lo
ad
cu
r
r
en
t
a
n
d
p
r
ev
en
t
s
h
o
r
t
cir
cu
it.
T
h
e
co
m
m
u
tatio
n
o
f
c
u
r
r
e
n
t
ca
n
g
en
er
ate
o
v
er
v
o
ltag
es
th
at
ca
n
d
is
tu
r
b
t
h
e
s
em
ico
n
d
u
cto
r
s
witch
es.
Fo
r
in
d
u
ctiv
e
l
o
ad
s
,
a
t
th
e
s
witch
tu
r
n
o
f
f
in
s
tan
ts
th
er
e
n
ee
d
to
b
e
an
alt
er
n
ativ
e
cu
r
r
en
t
f
lo
w
p
ath
th
at
av
o
id
s
o
v
e
r
v
o
ltag
es.
Fo
r
th
is
,
f
o
u
r
b
id
ir
ec
tio
n
al
s
witch
es
in
wh
ich
cu
r
r
en
t
f
lo
w
in
b
o
th
d
i
r
ec
tio
n
s
ar
e
u
s
ed
i
n
th
e
SP
MC
cir
cu
it
as
in
Fig
u
r
e
1.
An
a
n
tip
ar
allel
I
GB
T
an
d
d
io
d
e
p
air
s
,
as
r
ep
r
esen
ted
in
Fig
u
r
e
2
,
is
co
n
n
e
cted
to
o
b
tain
th
e
b
id
ir
ec
tio
n
al
s
witch
es.
Dio
d
es
ar
e
u
s
ed
to
a
d
d
r
e
v
er
s
e
b
lo
ck
i
n
g
ca
p
a
b
ilit
y
to
b
id
ir
ec
tio
n
al
s
witch
es.
S
1
a
S
1
b
S
2
a
S
2
b
S
3
a
S
3
b
S
4
a
S
4
b
L
o
a
d
Vi
(
t
)
Fig
u
r
e
1
.
Sin
g
le
p
h
ase
m
atr
ix
co
n
v
er
ter
I
G
B
T
I
G
B
T
DI
OD
E
D
I
O
D
E
S
1
a
S
1
b
C
u
r
r
e
n
t
f
l
o
w
C
u
r
r
e
n
t
f
l
o
w
Fig
u
r
e
2
.
A
b
id
ir
ec
tio
n
al
s
witch
T
h
e
s
tu
d
ied
co
n
v
e
r
ter
cir
cu
it
t
o
p
o
lo
g
y
is
g
iv
en
in
Fig
u
r
e
3
.
A
lo
ad
is
co
n
n
ec
ted
to
th
e
o
u
t
p
u
t
o
f
th
e
co
n
v
er
ter
.
T
h
is
lo
ad
co
m
p
r
is
e
s
a
r
esi
s
tiv
e
lo
ad
an
d
an
L
C
f
i
lter
.
An
in
d
u
cto
r
L
is
co
n
n
ec
t
ed
in
s
er
ies
with
th
e
s
u
p
p
ly
to
p
r
o
v
i
d
e
b
o
o
s
t o
p
er
at
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
imu
la
tio
n
o
f
b
o
o
s
t A
C
-
A
C
co
n
ve
r
ter u
s
in
g
s
in
g
le
-
p
h
a
s
e
ma
tr
ix
co
n
ve
r
ter
(
Zeyn
ep
B
a
la
D
u
r
a
n
a
y
)
309
S
1
a
S
1
b
S
2
a
S
2
b
S
3
a
S
3
b
S
4
a
S
4
b
Vi
(
t
)
L
L
1
C
L
o
a
d
Fig
u
r
e
3
.
SP
MC c
ir
cu
it
3.
SI
NU
SO
I
DA
L
P
WM
Du
e
to
its
s
im
p
licity
,
SP
W
M
is
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
u
s
ed
m
eth
o
d
s
in
p
o
wer
elec
tr
o
n
ic
cir
cu
its
f
o
r
d
ig
itally
co
n
tr
o
l
o
f
th
e
s
witch
in
g
co
m
m
u
tatio
n
[
1
7
]
.
T
h
is
m
o
d
u
latio
n
tec
h
n
iq
u
e
h
as
ad
v
an
ta
g
es
o
f
r
ed
u
ce
d
f
ilter
in
g
r
eq
u
ir
em
en
t
s
,
less
m
ath
em
a
tical
ca
lcu
latio
n
s
,
an
d
h
i
g
h
tr
a
n
s
m
itted
o
f
ef
f
ec
tiv
e
p
o
wer
.
I
n
SP
W
M
m
eth
o
d
,
wh
ich
is
p
r
e
s
en
ted
in
Fig
u
r
e
4
,
b
asically
,
a
h
ig
h
f
r
eq
u
e
n
cy
s
awto
o
th
s
h
ap
ed
ca
r
r
ier
s
ig
n
al,
Vc,
is
co
m
p
ar
ed
with
a
s
in
u
s
o
id
al
r
ef
er
en
ce
s
ig
n
al,
Vr
,
with
th
e
d
esire
d
f
r
eq
u
en
cy
.
T
h
e
s
witch
in
g
tim
es
ar
e
d
eter
m
in
ed
b
y
th
e
i
n
ter
s
ec
t p
o
in
ts
o
f
th
e
r
ef
e
r
en
ce
an
d
ca
r
r
ie
r
wav
es [
6
]
-
[
13
].
0
0
.
0
0
2
0
.
0
0
4
0
.
0
0
6
0
.
0
0
8
0
.
01
0
.
0
1
2
0
.
0
1
4
0
.
0
1
6
0
.
0
1
8
0
.
02
-
1
-
0
.
5
0
0
.
5
1
V
c
,
V
r
1
,
V
r
2
0
0
.
0
0
2
0
.
0
0
4
0
.
0
0
6
0
.
0
0
8
0
.
01
0
.
0
1
2
0
.
0
1
4
0
.
0
1
6
0
.
0
1
8
0
.
02
0
1
P
W
M
p
0
0
.
0
0
2
0
.
0
0
4
0
.
0
0
6
0
.
0
0
8
0
.
01
0
.
0
1
2
0
.
0
1
4
0
.
0
1
6
0
.
0
1
8
0
.
02
T
i
m
e
(
S
e
c
)
0
1
P
W
M
n
Fig
u
r
e
4
.
PW
M
s
ig
n
al
p
r
o
d
u
ct
io
n
T
h
e
m
o
d
u
latio
n
s
ch
em
e
u
s
e
s
th
e
SP
W
M
tech
n
iq
u
e
to
o
b
tain
a
s
ig
n
al
wh
ich
r
esem
b
les
o
f
th
e
r
ef
er
en
ce
s
in
u
s
o
id
al
s
ig
n
al.
T
h
at
is
,
th
e
p
r
o
d
u
ce
d
s
ig
n
al
im
p
licitly
in
clu
d
es
th
e
a
m
p
li
tu
d
e
an
d
f
r
e
q
u
en
c
y
in
f
o
r
m
atio
n
o
f
t
h
e
m
o
d
u
latin
g
wav
e.
SP
W
M
s
ch
em
e
b
lo
ck
d
iag
r
am
is
g
iv
en
i
n
Fig
u
r
e
5
.
T
h
e
r
atio
o
f
m
a
g
n
itu
d
e
o
f
t
h
e
r
ef
er
e
n
ce
wa
v
e
(
Vr
)
t
o
th
e
m
ag
n
i
tu
d
e
o
f
th
e
ca
r
r
ier
wa
v
e
(
Vc)
is
d
ef
in
ed
as
th
e
m
o
d
u
latio
n
in
d
ex
(
Mi)
.
Gen
er
ally
,
th
e
ca
r
r
ier
s
ig
n
al
Vc
h
as
a
f
ix
e
d
am
p
litu
d
e.
T
h
e
o
u
tp
u
t
v
o
ltag
e
ca
n
b
e
ch
a
n
g
ed
b
y
c
o
n
tr
o
llin
g
th
e
Mi
[
1
8
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
87
92
I
n
t J
Ap
p
l
Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
0
7
–
314
310
R
e
f
1
R
e
f
2
P
W
M
_
p
P
W
M
_
n
a
b
0
.
5
M
o
d
u
l
a
t
i
o
n
İ
n
d
e
x
C
a
r
r
i
e
r
Fig
u
r
e
5
.
PW
M
s
ig
n
al
p
r
o
d
u
ct
io
n
b
lo
c
k
4.
SPMC
M
O
DE
S
SP
MC
h
as
d
if
f
er
en
t
to
p
o
lo
g
i
es
an
d
o
p
er
atio
n
m
o
d
es
d
e
p
en
d
in
g
o
n
co
m
m
u
tatio
n
s
ch
em
e.
T
h
ese
m
o
d
es o
f
SP
MC a
r
e
ch
o
p
p
er
,
b
u
ck
,
b
o
o
s
t,
r
ec
tifie
r
,
r
ec
tifie
r
with
p
o
wer
f
ac
to
r
co
r
r
ec
tio
n
a
n
d
cy
clo
c
o
n
v
e
r
ter
.
On
e
o
f
th
e
o
p
e
r
atio
n
m
o
d
e
o
f
th
e
m
atr
ix
c
o
n
v
e
r
ter
s
is
AC
-
AC
co
n
v
er
ter
o
r
cy
clo
c
o
n
v
e
r
t
er
.
I
n
th
is
m
o
d
e,
th
e
m
atr
ix
co
n
v
er
ter
is
u
s
ed
to
o
b
tain
AC
v
o
ltag
e
wit
h
v
a
r
iab
le
am
p
litu
d
e
an
d
f
r
e
q
u
en
cy
with
o
u
t
DC
lin
k
.
T
h
e
c
o
n
tr
o
l sy
s
tem
is
u
s
e
d
to
p
r
o
d
u
ce
SP
W
M
p
atter
n
s
t
o
co
n
tr
o
l th
e
p
o
wer
s
witch
es
.
4
.
1
.
B
o
o
s
t
AC
-
AC
o
pera
t
io
n
T
h
e
b
o
o
s
t
AC
-
AC
co
n
v
er
ter
h
as
f
o
u
r
o
p
er
atio
n
m
o
d
es
as
s
h
o
wn
in
Fig
u
r
e
6
.
T
wo
o
f
t
h
e
o
p
er
atio
n
m
o
d
es
o
cc
u
r
in
t
h
e
f
i
r
s
t
h
alf
p
er
io
d
an
d
th
e
o
th
e
r
two
o
p
e
r
atio
n
m
o
d
es
o
cc
u
r
in
th
e
n
e
x
t
h
alf
p
er
i
o
d
.
T
h
e
cu
r
r
en
t
f
lo
w
f
o
r
co
m
m
u
tatio
n
s
w
itch
es
is
r
ep
r
esen
te
d
b
y
b
o
ld
lin
e
an
d
th
e
co
n
t
r
o
l
(
SP
W
M)
s
wi
tch
is
r
ep
r
esen
ted
b
y
th
e
d
o
tted
lin
e.
Mo
d
e
1
is
th
e
ch
ar
g
i
n
g
o
p
e
r
atio
n
m
o
d
e
a
n
d
s
tar
ts
wh
en
b
o
th
s
witch
es
S1
a
an
d
S3
a
ar
e
clo
s
ed
.
T
h
e
in
p
u
t
cu
r
r
en
t th
r
o
u
g
h
th
e
i
n
d
u
cto
r
r
i
s
es.
Mo
d
e
2
is
th
e
d
is
ch
ar
g
in
g
o
p
e
r
atio
n
m
o
d
e.
T
h
is
m
o
d
e
s
tar
ts
wh
en
s
witch
es
S1
a
an
d
S4
a
ar
e
clo
s
ed
wh
ile
S3
a
is
o
p
en
.
T
h
e
cu
r
r
en
t
f
lo
win
g
t
h
r
o
u
g
h
S3
a
in
m
o
d
e
1
is
tr
an
s
f
er
r
ed
to
th
e
l
o
ad
in
m
o
d
e
2
.
T
h
e
in
d
u
cto
r
cu
r
r
en
t
d
ec
r
ea
s
es till S3
a
h
as
tu
r
n
ed
o
n
ag
ain
.
T
h
e
lo
ad
r
ec
eiv
es th
e
s
to
r
ed
en
er
g
y
o
f
th
e
in
d
u
cto
r
L
.
T
h
e
o
th
er
two
m
o
d
es h
av
e
th
e
s
am
e
o
p
er
atio
n
d
u
r
i
n
g
th
e
n
e
x
t h
alf
p
e
r
io
d
.
S
1
a
S
1
b
S
2
a
S
2
b
S
3
a
S
3
b
S
4
a
S
4
b
Vi
(
t
)
L
L
o
a
d
S
1
a
S
1
b
S
2
a
S
2
b
S
3
a
S
3
b
S
4
a
S
4
b
Vi
(
t
)
L
L
o
a
d
(
a)
(
b
)
Fig
u
r
e
6
.
B
o
o
s
t A
C
-
AC
co
n
v
e
r
ter
to
p
o
l
o
g
y
:
(
a
)
Po
s
itiv
e
cy
cl
e
,
(
b
)
Neg
ati
v
e
cy
cle
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
imu
la
tio
n
o
f
b
o
o
s
t A
C
-
A
C
co
n
ve
r
ter u
s
in
g
s
in
g
le
-
p
h
a
s
e
ma
tr
ix
co
n
ve
r
ter
(
Zeyn
ep
B
a
la
D
u
r
a
n
a
y
)
311
5.
M
O
DE
L
I
NG
AN
D
SI
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L
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SU
L
T
S
T
h
e
b
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o
s
t
SP
MC
is
m
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eled
u
s
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g
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T
L
AB
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lin
k
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T
h
e
co
n
v
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ter
cir
cu
it
p
ar
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ar
e
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ted
in
T
ab
le
1
.
T
h
e
Simu
lin
k
m
o
d
el
o
f
b
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o
s
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AC
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co
n
v
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MC
an
d
s
w
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in
g
s
ig
n
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p
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o
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r
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u
r
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an
d
Fig
u
r
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r
esp
ec
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T
h
e
co
m
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ar
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h
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lar
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r
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wav
e
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ce
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with
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b
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lin
k
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is
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Fig
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.
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ates
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I
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87
92
I
n
t J
Ap
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312
Fig
u
r
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9
.
Switch
in
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al
g
o
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ith
m
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b
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s
t SPMC
T
h
e
b
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o
s
t
SP
MC
m
o
d
el
is
s
i
m
u
lated
with
th
e
p
ar
a
m
eter
s
lis
ted
in
T
ab
le
1
.
Fig
u
r
e
1
0
a
n
d
Fig
u
r
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1
p
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f
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d
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z
r
esp
ec
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.
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h
e
m
o
d
u
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i,
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et
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5
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V
p
ea
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in
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t
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s
ed
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th
e
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im
u
latio
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h
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r
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ce
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t
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6
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3
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p
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k
f
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r
s
witch
in
g
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r
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en
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f
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KHz
an
d
5
1
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1
V
p
ea
k
f
o
r
s
witch
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r
eq
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e
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o
f
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0
KHz.
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u
r
e
1
0
.
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MC o
u
tp
u
t v
o
lta
g
e
with
s
witch
in
g
f
r
eq
u
en
cy
f
c=
5
KHz
Fig
u
r
e
1
1
.
SP
MC o
u
tp
u
t v
o
lta
g
e
with
s
witch
in
g
f
r
eq
u
en
cy
f
c=
1
0
KHz
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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SS
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8
7
9
2
S
imu
la
tio
n
o
f
b
o
o
s
t A
C
-
A
C
co
n
ve
r
ter u
s
in
g
s
in
g
le
-
p
h
a
s
e
ma
tr
ix
co
n
ve
r
ter
(
Zeyn
ep
B
a
la
D
u
r
a
n
a
y
)
313
Fig
u
r
e
12
(
a
)
an
d
1
2
(
b
)
r
ep
r
e
s
en
t
th
e
s
p
ec
tr
u
m
an
aly
s
is
f
o
r
m
ea
s
u
r
in
g
T
HD
o
f
o
u
tp
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t
v
o
ltag
e
f
o
r
s
witch
in
g
f
r
eq
u
en
cies
5
KHz
an
d
1
0
KHz
r
esp
ec
tiv
ely
.
I
t
ca
n
b
e
s
ee
n
in
th
e
s
im
u
latio
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s
p
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esen
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d
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ea
s
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g
th
e
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r
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ier
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e
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n
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s
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th
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o
u
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t
v
o
ltag
e
.
T
h
e
s
im
u
latio
n
s
s
h
o
w
th
at
th
e
o
u
tp
u
t
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o
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e
is
ab
o
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t
3
tim
es
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ig
h
er
th
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at
o
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e
i
n
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t.
T
h
e
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ar
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tio
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HD)
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6
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7
1
%
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o
r
5
Kh
z
an
d
1
0
Kh
z
s
witch
in
g
f
r
eq
u
en
cies
r
esp
ec
tiv
ely
.
T
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
ca
lcu
lated
f
o
r
th
e
s
im
u
latio
n
s
p
r
esen
ted
s
tay
s
with
in
th
e
s
tan
d
ar
d
s
.
T
h
e
I
E
E
E
s
tan
d
ar
d
f
o
r
T
HD
is
5
% [
1
9
]
,
[
20
].
(
a)
(
b
)
Fig
u
r
e
1
2
.
Har
m
o
n
ic
s
p
ec
t
r
u
m
o
f
o
u
tp
u
t v
o
ltag
e
:
(
a)
f
c=
5
K
Hz,
(
b
)
f
c=
1
0
KHz
6.
CO
NCLU
SI
O
N
A
s
tu
d
y
o
f
b
o
o
s
t
AC
-
AC
co
n
v
er
ter
u
s
in
g
SP
MC
i
s
s
tu
d
ied
in
th
is
p
ap
er
.
T
h
e
s
y
s
tem
is
im
p
lem
en
ted
in
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
en
t.
T
h
e
c
o
n
v
e
r
ter
cir
c
u
it
i
s
co
n
s
tr
u
cted
u
s
in
g
I
GB
T
an
d
d
io
d
e
p
air
s
w
h
ich
ar
e
s
o
co
n
n
ec
ted
to
allo
w
b
id
ir
ec
tio
n
al
cu
r
r
en
t
f
lo
w.
T
h
e
s
y
s
tem
is
s
im
u
lated
with
d
if
f
er
en
t
s
witch
in
g
f
r
eq
u
e
n
cies.
T
h
e
s
im
u
latio
n
r
esu
lts
h
av
e
s
h
o
wn
th
at
th
e
b
o
o
s
t
AC
-
A
C
co
n
v
er
ter
with
SP
MC
p
r
o
d
u
ce
h
ig
h
er
AC
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
a
g
i
v
en
AC
s
u
p
p
ly
v
o
ltag
e
.
I
t
h
a
s
b
ee
n
o
b
s
er
v
ed
f
r
o
m
th
e
s
i
m
u
latio
n
r
esu
lts
th
at
ch
an
g
in
g
th
e
m
o
d
u
latio
n
in
d
e
x
h
as n
o
e
f
f
ec
t o
n
th
e
v
al
u
e
o
f
o
u
tp
u
t
v
o
ltag
e.
RE
F
E
R
E
NC
E
S
[1
]
Z.
Id
r
is,
M
.
K.
Ha
m
z
a
h
a
n
d
M
.
F
.
S
a
i
d
o
n
,
"
Im
p
lem
e
n
tatio
n
o
f
si
n
g
le
-
p
h
a
se
m
a
tri
x
c
o
n
v
e
rter
a
s
a
d
irec
t
AC
-
AC
c
o
n
v
e
rter
with
c
o
m
m
u
tati
o
n
stra
t
e
g
ies
,
"
2
0
0
6
3
7
t
h
I
EE
E
Po
we
r
El
e
c
tro
n
ics
S
p
e
c
ia
li
sts
Co
n
fer
e
n
c
e
,
2
0
0
6
,
p
p
.
1
-
7
,
d
o
i:
1
0
.
1
1
0
9
/p
e
sc
.
2
0
0
6
.
1
7
1
2
1
0
6
.
[2
]
K.
P
.
S
h
a
ik
,
S
.
Ka
rimu
ll
a
a
n
d
S
.
M
.
Irsh
a
d
,
"
S
imu
lati
o
n
o
f
sin
g
l
e
p
h
a
se
b
u
c
k
b
o
o
st
m
a
tri
x
c
o
n
v
e
rter
with
o
u
t
c
o
m
m
u
tatio
n
iss
u
e
s,
"
Eu
r
o
p
e
a
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
,
v
o
l.
2
0
,
n
o
.
2
,
p
p
.
2
0
5
-
2
1
4
,
2
0
1
8
,
d
o
i:
1
0
.
3
1
6
6
/
EJEE
.
2
0
.
2
0
5
-
2
1
4
.
[3
]
A.
Kh
o
e
i
a
n
d
S
.
Y
u
v
a
ra
jan
,
"
S
in
g
le
-
p
h
a
se
AC
-
AC
c
o
n
v
e
rters
u
si
n
g
p
o
we
r
M
OSF
ET
s,
"
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l
.
3
5
,
n
o
.
3
,
p
p
.
4
4
2
-
4
4
3
,
A
u
g
.
1
9
8
8
,
d
o
i
:
1
0
.
1
1
0
9
/
4
1
.
3
1
1
9
.
[4
]
A.
K.
G
o
la
a
n
d
V.
Ag
a
rwa
l
,
"
Im
p
lem
e
n
tatio
n
o
f
a
n
e
fficie
n
t
a
lg
o
rit
h
m
fo
r
a
sin
g
le p
h
a
se
m
a
tri
x
c
o
n
v
e
rter
,
"
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
,
v
o
l
.
9
,
n
o
.
2
,
p
p
.
1
9
8
-
2
0
6
,
2
0
0
9
.
[5
]
H.
F
.
Ra
sh
a
g
,
"
Op
ti
m
iza
ti
o
n
o
f
e
fficie
n
c
y
f
o
r
p
o
we
r
s
y
ste
m
u
si
n
g
th
re
e
p
h
a
se
AC
t
o
AC
m
a
tri
x
c
o
n
v
e
rter
with
t
h
e
a
lg
o
rit
h
m
o
f
f
u
z
z
y
c
o
n
tr
o
ll
e
r,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
A
p
p
li
e
d
P
o
we
r
En
g
in
e
e
rin
g
(IJ
AP
E)
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
1
2
9
-
1
3
3
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
/i
jap
e
.
v
8
.
i2
.
p
p
1
2
9
-
1
3
3
.
[6
]
Z.
M
.
No
o
r,
N.
F
.
A.
Ra
h
m
a
n
a
n
d
M
.
K.
Ha
m
z
a
h
,
"
S
im
u
latio
n
o
f
DC
t
o
DC
c
o
n
v
e
rter
u
si
n
g
sin
g
l
e
p
h
a
se
m
a
tri
x
c
o
n
v
e
rter t
o
p
o
lo
g
y
,
"
2
0
1
0
IEE
E
S
y
mp
o
si
u
m o
n
I
n
d
u
stria
l
E
lec
tro
n
ics
a
n
d
Ap
p
li
c
a
t
io
n
s (IS
IEA
)
,
2
0
1
0
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314
314
[1
1
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D.
M
.
B
u
k
a
ri,
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Ba
h
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ro
m
,
A.
Id
ris
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.
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m
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a
h
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B
o
o
st
re
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ti
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sin
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p
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stria
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p
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2
]
L.
G
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i,
a
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d
B.
R
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P
e
ll
y
,
S
ta
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q
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h
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3
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A.
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Wein
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4
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5
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6
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Clare
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