In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
4
6
1
~1
4
6
8
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1461-1468
1461
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Multilevel inverter w
i
th MPWM-
LFT sw
itching strategy for
voltage TH
D
minimizati
o
n
M
.
H. Yatim,
A. Pon
niran
,
A.
N
.
K
asiran
Faculty of E
l
ectr
i
cal
a
nd
E
l
ectron
i
c
Engin
eering,
Uni
versiti
T
u
n
H
u
s
s
e
in
O
n
n
M
a
l
a
ys
ia
,
M
a
l
a
ys
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
l
2
3,
201
8
Re
vise
d Jan
1
9
, 2019
Ac
ce
p
t
ed
M
ar 2
8
,
2
019
Th
is
p
aper
p
resen
t
s
a
prop
os
ed
m
odif
i
ed
p
u
l
se
w
i
d
th
m
o
d
u
l
a
tio
n
–
low
f
r
equ
e
ncy
tri
a
ngular
(
M
P
WM
-LF
T
)
s
w
it
chi
ng
strateg
y
f
or
m
in
im
iza
tion
of
vo
lt
age
THD
with
i
m
p
le
m
e
n
t
atio
n
o
f
a
sy
mm
etric
m
u
lti
l
evel
i
nv
e
r
t
er
(
A
M
L
I
)
to
po
lo
gy
o
n
t
h
e
red
u
ced
n
u
m
ber
o
f
s
w
i
tch
i
n
g
d
evices
(
RN
S
D
)
ci
rc
uit
st
ruct
ure.
P
rin
c
ip
ally
,
MPWM
-LFT
a
b
l
e
to
p
ro
duce
o
p
ti
m
u
m
ang
l
e
of
t
h
e
ou
tp
ut
volt
a
ge
l
evel
i
n
order
to
m
in
imi
ze
to
ta
l
h
a
rmo
n
i
c
d
istor
tion
(THD)
.
I
n
th
is
s
tud
y
,
5-l
e
vel
redu
ced
n
um
b
e
r
of
s
wi
tch
i
n
g
d
evi
ces
c
i
r
cui
t
s
tructur
e
i
s
sel
ected
a
s
a
ci
rcui
t
co
n
f
i
g
u
r
atio
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f
o
r
asym
m
e
t
r
ic
(
7-lev
e
l
st
r
uctu
re)
m
u
lti
l
evel
i
n
v
erter.
F
o
r
s
w
i
t
c
hing
s
t
rat
e
gy,
M
PW
M
u
s
ed
l
ow
s
wi
t
ch
i
ng
f
r
equ
e
ncy
in
p
rodu
cin
g
s
ig
nal
an
d
n
e
eds
h
i
gh
er
o
utp
u
t
v
o
ltage
l
ev
els
to
achi
e
ve
l
ow
t
otal
h
arm
o
n
i
c
distortio
n.
I
n
con
t
ras
t
,
sin
u
s
o
i
d
a
l
pu
lse
wid
t
h
modul
a
tion
u
s
ed
h
igh
sw
itch
i
n
g
f
requ
e
n
cy
i
n
ord
e
r
t
o
m
in
imize
t
ota
l
h
a
rmon
ic
d
i
s
to
r
t
ion
.
B
y
o
p
tim
iz
ing
a
n
gle
a
t
t
h
e
o
utpu
t
vo
lta
g
e
us
in
g
M
P
WM
-LF
T
s
w
i
t
c
hi
ng
st
rateg
y
,
t
h
e
v
o
l
t
ag
e
TH
D
is
l
ow
er
a
s
com
p
ar
ed
t
o
M
P
W
M
a
n
d
S
P
W
M
s
w
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t
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h
i
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g
s
t
r
a
t
e
g
i
e
s
.
M
P
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M
-
L
F
T
s
w
i
t
c
h
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n
g
s
t
r
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t
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o
b
ta
in
s
11
.
6
%
of
v
ol
ta
ge
T
HD
f
o
r
t
h
e
7
-le
v
e
l
a
sy
mme
tr
ic
t
op
olog
y
as
com
p
ared
t
o
M
P
WM
a
nd
SPW
M
s
w
itchi
ng
s
trat
egi
e
s
with
t
he
v
o
l
t
a
g
e
T
HD
are 21
.5%
and
17.5
%
res
pecti
v
e
l
y f
r
om th
e
exp
erim
en
t
a
l w
o
rk
s
K
eyw
ord
s
:
A
s
ymm
e
tric
mult
ile
ve
l
inve
rt
er,
Re
duce
d
n
umb
e
r of sw
itch
i
ng
dev
i
ce
s,
S
i
nus
o
i
da
l p
u
l
se
w
idt
h
modu
la
ti
o
n
,
To
tal ha
rmo
n
ic
d
istort
i
o
n
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
s
ma
rashid P
onn
iran
(
A
.
P
onnira
n
)
,
Fa
cult
y
o
f
E
l
e
c
t
rica
l
and
E
l
e
c
t
r
on
ic E
n
g
i
n
ee
rin
g
,
U
n
i
v
ersi
ti
T
un
H
u
ssei
n
O
nn
Ma
lays
ia,
86
4
00 Pa
rit Ra
ja,
Joh
o
r,
M
alays
i
a,
Em
ail:
asma
r@u
t
hm.
e
du.
my
1.
I
N
TR
OD
U
C
TI
O
N
G
e
nera
lly,
p
o
w
e
r
i
n
v
e
r
ters
a
r
e
one
o
f
c
o
n
v
erte
r
tha
t
c
o
n
v
e
r
tin
g
d
i
r
ec
t
cur
r
ent
(DC)
t
o
a
l
t
e
rna
t
ing
curr
ent
(
A
C)
for
a
n
y
s
yste
ms tha
t re
q
u
ir
e
d
t
hi
s ty
pe of po
w
e
r
c
on
versi
o
n [1]. M
ult
i
l
e
v
el in
v
er
t
e
rs
(
MLI
)
h
a
v
e
bec
o
me
a
s
ele
c
ti
o
n
f
or
u
ses
in
e
lec
t
ric
ut
il
ity
a
nd
for
me
dium
t
o
h
ig
h
pow
er
i
nd
us
tri
a
l
ap
p
l
i
c
a
t
ions
.
In
a
rec
e
nt
num
ber
of
y
ea
rs,
the
ind
u
s
t
ry
h
as
b
e
g
u
n
t
o
reque
st
g
re
at
er
p
ow
er
e
qu
i
p
me
nt
,
w
h
ich
n
o
w
r
eac
h
e
s
t
h
e
meg
a
wat
t
l
ev
el
a
n
d
st
a
r
t
to
g
ro
w
ev
e
n
f
u
r
th
er.
Fo
r
t
h
es
e
ca
u
s
e
s
,
M
L
I
h
a
ve
b
ee
n
de
ve
lo
pe
d
a
s
t
he
k
ey
f
or
w
o
rki
n
g
w
ith
h
i
g
her
v
o
l
t
a
g
e
leve
ls.
G
e
nera
l
l
y,
M
LI
c
o
n
s
i
s
t
s
of
an
a
rra
y
o
f
po
wer
se
mi
co
ndu
c
t
o
r
s
an
d
di
re
c
t
c
u
rre
n
t
(DC
)
v
ol
t
a
g
e
s
ou
rces,
t
h
en
t
h
e
out
put
v
olt
a
g
e
s
wi
th
s
t
e
ppe
d
w
a
veform
s
w
ill
b
e
ge
ne
rate
d.
M
LI
con
s
is
t
s
o
f
thr
e
e
ma
i
n
d
iffe
rent
t
op
olo
g
i
es,
i.
e.,
neutra
l
p
o
i
n
t
c
l
a
m
p
m
u
l
t
i
l
ev
el
i
n
v
erte
r
(NPCMLI),
f
l
y
i
n
g
ca
paci
t
o
r
mu
l
tile
ve
l
in
verte
r
(
F
C
MLI)
a
nd
c
a
s
ca
de
d
H
-
br
i
dge
m
u
l
ti
le
ve
l
i
n
ve
rte
r
(
CH
BMLI)
[2]
.
S
p
e
c
ifica
l
l
y
,
m
u
l
t
i
l
e
v
el
i
nv
e
r
ter
has
t
h
e
adva
n
t
age
s
o
f
gene
rat
in
g
b
e
t
t
er
o
ut
put
qual
ity
b
y
c
o
n
s
id
e
r
ati
on
numbe
r of le
v
e
l
a
nd m
o
d
u
l
a
t
i
o
n
tec
h
ni
q
u
e
u
s
e
d
[3].
Bas
i
ca
ll
y,
t
he
p
rima
ry
o
bj
e
c
t
ive
i
n
c
re
ati
n
g
m
u
lt
ile
ve
l
inve
r
t
e
rs
i
s
t
o
m
ainta
i
n
a
lo
w
harm
onic
di
st
ort
i
o
n
(
TH
D
)
a
t
out
pu
t
si
de
by
c
o
n
s
i
d
er
ing
less
n
u
m
be
rs
o
f
sem
i
c
o
n
duc
t
o
r
de
vice
s
[4,
5].
S
e
ve
ral
impro
v
e
m
e
n
ts
h
ad
b
ee
n
do
ne
i
n
order
to
p
r
o
duce
hi
g
h
e
ffic
i
e
nc
y
co
n
v
erte
r.
F
or
e
xam
p
le
,
seve
ral
rese
arc
h
ers
are
focus
i
ng
o
n
r
educ
i
ng
se
m
i
con
d
u
ct
or
d
evice
s
b
y
r
earrang
in
g
t
he
c
i
r
c
u
it
co
nfig
ura
t
i
o
n
[6,
7]
.
S
e
ve
ral
to
pol
o
g
ie
s
ha
d
be
e
n
i
ntro
d
u
c
e
d
in
o
rde
r
t
o
r
e
duce
t
h
e
n
u
mbe
r
o
f
s
em
ico
n
duc
t
o
r
de
vice
s
[8,
9]
s
uc
h
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
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El
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c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
146
1
– 1
468
1
462
symm
etric
mul
t
i
le
ve
l
inve
r
t
er
(
SMLI)
a
nd
a
s
ym
m
e
tric
m
ultile
ve
l
in
ver
t
e
r
(
A
M
LI
)
w
h
ich
i
m
prov
e
con
v
e
n
t
i
ona
l
m
u
lti
le
ve
l
i
n
ve
rter
s
truc
ture
s. The
o
b
v
i
ous
d
i
f
fer
en
c
e
b
et
ween
s
y
m
met
r
i
c
a
n
d
a
sy
mme
t
r
i
c
i
s
th
e
DC
s
ou
rce
s
.
W
h
ereb
y
,
i
n
sy
mmet
ri
c
t
opol
ogy
a
l
l
DC
s
o
u
r
ce
s
volt
a
ge
a
r
e
s
a
m
e,
m
e
a
nw
h
ile
i
n
a
s
y
m
m
e
tric
to
pol
o
gy e
a
c
h
D
C source
v
ol
t
a
ge
i
s
d
i
f
f
er
en
t
[10]
.
Har
monics
i
s
one
o
f
the
i
ssu
es
[
1
1
,
1
2
]
c
onsi
d
er
ed
b
ec
a
u
s
e
i
t
m
a
y
ca
use
over
h
e
a
t
i
ng,
i
n
c
rea
s
i
n
g
o
f
vo
lta
ge
s
tress
i
n
t
he
p
a
ssive
c
om
po
ne
nt
s
an
d
m
a
lo
per
a
t
i
on
i
n
th
e
elec
t
r
o
n
i
c
d
e
v
ice
s
.
In
s
ho
r
t
,
it
ca
n
l
ead
t
o
the
reduc
ti
on
of
t
he
e
qu
i
p
m
e
nt’s
life
s
pa
n.
T
he
refor
e
,
so
m
e
s
tan
d
a
rd
s
mu
st
b
e
co
mp
l
i
e
d
wi
th
,
su
ch
a
s
th
e
IEEE
Std
519-
1992
[
13]
.
According
to
I
EEE
S
td
5
19-1992,
h
ar
moni
c
vo
l
t
a
g
e
o
n
p
ow
e
r
s
ys
tem
of
6
9
k
V
a
nd
bel
o
w
m
u
st
b
e
l
i
m
i
t
e
d
to
5
%
TH
D
w
ith
eac
h
m
a
ximu
m
ind
i
vi
d
u
al
h
a
r
m
on
ic
i
s
3
%
,
w
h
il
e
IEC
st
a
n
dar
d
[1
3,
1
4]
s
h
o
w
s
t
he
T
H
D
tha
t
l
im
it
s
t
o
8
%
for
l
o
w
v
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t
a
g
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a
p
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tio
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I
n
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ile
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l
in
verter
,
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n
p
u
t
v
o
l
t
a
g
e
and
c
u
rre
nt
a
r
e
c
hop
pe
d
bas
e
d
o
n
t
he
s
w
i
t
c
hi
n
g
s
i
g
nal
w
h
ic
h
gen
er
at
es
t
he
d
es
ired
o
u
t
p
u
t
w
a
v
eform
s
.
The
ou
tpu
t
vol
ta
ge
a
nd
c
ur
ren
t
h
a
v
e
harm
on
i
c
s
a
t
t
he
s
w
i
tc
hi
n
g
freq
ue
n
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y,
w
hic
h
c
a
n
b
e
red
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ce
d
b
y
usin
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pass
ive
fi
lters.
Bas
i
ca
l
l
y,
t
he
s
w
itc
h
i
ng
fre
que
nc
y
a
n
d
pa
ssive
f
i
l
t
e
r
s
ha
ve
a
s
ig
ni
fi
c
a
n
t
r
o
l
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i
n
r
ed
uc
i
n
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t
h
e
harm
on
ics.
B
y
de
cre
a
si
ng
t
h
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sw
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fr
eq
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50
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d
u
c
e
d
a
n
d
t
h
e
q
u
a
l
i
t
y
of
t
he
o
ut
p
u
t
v
o
lta
ge
c
an be
i
m
pr
ove
d a
s
w
el
l.
In
add
iti
on,
t
he
f
ilter
size
and
sw
itc
hi
n
g
l
oss a
r
e
reduc
ed.
Thi
s
p
ap
e
r
p
re
se
nt
s
t
h
e
p
r
op
osed
M
P
W
M
-
LFT
swi
t
c
hi
ng
s
t
r
at
e
g
y
fo
r
min
i
miz
a
tio
n
of
v
ol
t
a
ge
T
H
D
wi
t
h
i
mp
l
e
me
nt
at
io
n
of
A
M
L
I
t
opo
log
y
o
n
th
e
RNSD
c
i
r
cu
i
t
st
ru
ct
ure.
M
P
W
M-LF
T
sw
i
t
c
h
i
n
g
s
t
r
a
te
gy
a
b
l
e
to
e
n
h
a
n
c
e
t
he
m
i
n
im
izat
i
o
n
of
t
he
v
o
l
t
a
ge
T
H
D
by
o
p
t
i
miz
i
n
g
t
h
e
angl
e
a
t
t
he
out
put
v
olt
a
g
e
i
n
op
en
-l
o
o
p
system
a
s
c
o
mpared
t
o
M
P
WM
a
nd
S
PWM
s
w
itching
s
trat
e
g
i
e
s.
I
n
ad
d
i
ti
on,
i
t
a
l
s
o
a
ble
t
o
r
educe
t
h
e
sw
it
c
h
i
n
g
lo
ss
a
n
d
i
n
c
rea
s
e
d
t
he
e
ffic
ie
nc
y
of
t
he
c
on
ve
rter.
T
he
ref
o
re,
it
sh
ow
s
tha
t
t
he
M
P
W
M-
LF
T
sw
it
c
h
i
n
g
strat
e
gy
i
s
the
bes
t
s
w
itc
h
i
n
g
s
tra
t
egy
for
ope
n-l
o
o
p
s
y
s
t
e
m
i
n
o
rd
e
r
t
o
g
e
t
th
e
l
o
w
e
r
vol
t
a
ge
T
HD
and
red
u
ce
d t
h
e
sw
i
t
c
h
i
ng
los
s
a
s w
e
ll.
2.
VOLTAGE
T
HD M
INI
M
I
Z
ATIO
N
BY
M
PW
M
-
LFT
AND
ASYM
M
E
T
RIC TOPO
LOG
Y
WITH RNSD CI
R
CUIT
STRUCTURE
2.1.
Prin
c
i
p
l
e
of as
y
mme
tr
i
c
top
olo
g
y
Th
e
co
mmo
n
ad
v
a
nt
a
g
e
of
a
sy
mmet
ri
c
to
pol
ogy
i
s
th
at
i
t
i
s
a
b
l
e
t
o
g
ener
a
t
e
a
h
i
gh
le
ve
l
o
f
o
u
t
pu
t
vo
lta
ge
by
us
i
ng
the
sam
e
s
tr
uct
u
re
o
f
sym
m
e
tric
t
o
p
o
l
o
g
y
[
1
5
,
16]
;
as
a
n
exam
p
l
e,
a
sy
m
m
e
tric
t
o
p
o
lo
gy
w
i
t
h
d
i
f
f
e
r
e
n
t
D
C
v
o
l
t
a
g
e
s
,
i
.
e
.
,
V
d
c
1
=
V
d
c
,
V
d
c
2
=
2
V
d
c
,
V
d
c
3
=
4
V
d
c
,
V
d
c
4
=
8
V
d
c
a
s
c
o
m
p
a
r
e
d
t
o
t
h
e
D
C
s
our
ce
v
o
lta
ge
o
f
s
y
m
m
e
t
ric
t
o
pol
og
y,
i
.
e
.,
V
dc1
=
V
d
c2
=V
dc
3.
Asy
mme
t
r
i
c
t
o
pol
ogy
h
a
s
d
i
f
f
e
re
nt
val
u
es
o
f
D
C
s
ou
r
ce
vo
ltage
a
nd
the
mod
u
l
at
i
on
tec
h
n
i
qu
e
i
s
c
om
p
l
e
x
a
nd
t
h
e
le
ve
l
ca
n
be
u
p
g
ra
de
d
up
to
tw
o le
ve
l
s
h
igh
e
r.
F
igure
1 s
how
s t
h
e
c
i
rcu
i
t
struc
t
ure
t
h
at
ha
s
b
e
en
s
el
ec
te
d
fo
r
AM
LI. B
ased
o
n
th
e
sel
e
c
t
e
d
circ
u
i
t
s
t
ruc
t
ure,
i
t
is
a
b
l
e
t
o
p
ro
duce
five
l
e
v
el
s
o
f
o
u
t
p
u
t
vol
tage
s.
B
y
a
ppl
yi
n
g
t
he
a
s
y
mm
etric
p
r
in
c
i
ple
in
th
i
s
s
truc
ture
,
it
is
a
b
l
e
to
p
rod
u
ce
u
p
to
7
l
e
v
e
l
o
f
o
u
t
put
v
o
l
tages.
T
here
fore
,
the
num
ber
of
s
w
i
tc
hin
g
dev
i
ce
s
an
d
se
mic
ond
uc
tor
lo
sses a
r
e reduc
e
d
.
2.2.
RNSD circuit
co
n
f
ig
ura
t
io
n
Th
e
s
e
l
ect
e
d
c
ircu
i
t
st
ru
ct
u
r
e
i
s
t
h
e
R
NSD
stru
ct
u
r
e
[
1
7
]
,
wh
i
c
h
is
t
he
i
m
p
rovem
e
n
t
o
f
th
e
casc
a
de
d
H
-
bridge
s
truc
t
u
r
e
.
Ba
sic
a
l
l
y
,
the
s
t
r
u
c
t
ure
i
s
d
iv
ide
d
i
n
t
o
tw
o
p
a
r
t
s
,
w
h
i
c
h
a
r
e
S
1
a
n
d
S
2
a
s
p
a
r
t
1
a
n
d
S
A
,
S
B
,
S
C
a
n
d
S
D
a
r
e
p
a
r
t
2
o
r
a
l
s
o
k
n
o
w
n
a
s
H
-
b
r
i
d
g
e
.
P
a
r
t
1
a
c
t
s
a
s
t
h
e
m
a
in
p
a
r
t
for
p
r
od
uci
n
g
the
le
ve
l
a
n
d
p
a
rt
2
o
p
e
rat
e
s
f
o
r
t
h
e
po
sit
i
ve
a
n
d
n
eg
a
t
i
v
e
o
f
t
h
e
out
put
v
ol
tage.
T
h
i
s
s
elec
te
d
s
t
ruc
t
u
r
e
can
p
ro
d
u
ce
f
i
v
e
leve
ls
o
f o
u
t
p
u
t
vo
lta
ge
w
he
n
i
t
fol
low
s
t
he ca
s
cade
d
a
nd
s
ymm
e
tric pr
i
n
c
ip
les. B
u
t
the
sele
c
t
ed
s
truc
tur
e
ca
n
a
l
so
o
p
e
ra
t
e
i
n
p
r
odu
c
i
ng
s
eve
n
l
ev
el
s
o
f
out
put
v
o
l
t
a
g
e
w
h
e
n
t
h
e
b
in
a
r
y
met
hod
o
f
asymme
t
r
i
c
t
opolo
g
y
i
s
implem
e
n
te
d.
F
i
gur
e
1
s
how
s
the
pr
op
ose
d
s
truct
u
re
f
or
a
5
-leve
l
sym
m
e
tric
a
nd
7-
le
vel
a
s
ym
m
e
tric
M
LI
.
Com
p
ar
i
n
g
t
h
e
num
ber
of
s
w
itc
hi
n
g
d
e
v
i
c
es
o
f
ca
scade
d
s
truc
tu
r
e
w
i
t
h
t
h
e
s
e
l
e
c
t
e
d
s
t
r
u
c
t
u
r
e
,
t
h
e
5
-
l
e
v
e
l
ca
sc
ade
d
s
truc
ture
c
o
n
t
ai
ns
e
igh
t
u
nits
o
f
sw
itc
hes
w
h
ile
t
he
p
ro
p
o
se
d
RN
S
D
c
irc
u
it
s
t
r
u
ct
ure
us
i
n
g
symm
etric
t
o
p
o
lo
gy
onl
y
req
u
ire
s
s
i
x
u
nit
of
s
w
itc
he
s
a
n
d
pro
d
u
ces
t
he
s
am
e
level
a
s
t
he
c
a
s
ca
de
d
circ
u
i
t
st
ru
ct
u
r
e
.
F
o
r
a
7
-l
e
v
el
c
as
cade
d
c
i
r
cui
t
st
r
u
ct
u
r
e
,
1
2
u
n
i
t
s
o
f
sw
itc
he
s
ar
e
neede
d
f
o
r
t
he
s
truc
ture
w
h
ile
o
nl
y
six
sw
i
t
c
h
es
a
re
r
equ
i
red
for
the
pro
p
o
se
d
RN
S
D
c
ircui
t
s
truc
tu
re
u
si
ng
t
h
e
bin
a
ry
m
et
hod
o
f
asy
mme
t
r
i
c
to
pol
o
gy a
n
d p
r
od
uce
s
the
s
a
m
e le
v
e
l of
o
u
t
pu
t v
o
l
t
a
g
e
as
t
he
c
a
s
cade
d
c
i
r
cui
t
s
t
r
uc
t
u
re.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Mu
lti
lev
e
l i
n
ve
rt
e
r
w
ith M
P
W
M
-L
FT
sw
itc
h
i
ng s
t
ra
t
e
gy fo
r v
o
l
t
age
TH
D
min
i
miza
ti
o
n
(M. H.
Y
a
t
i
m)
1
463
F
i
gur
e
1.
Red
u
c
ed
num
ber
of
s
w
i
t
c
h
i
n
g
d
e
v
i
ces
c
ir
c
u
i
t
s
tr
u
c
t
u
r
e
2.
3.
Opt
i
mum
a
n
g
l
e
a
t
the o
utp
u
t
v
o
ltag
e lev
e
l
Vol
t
a
g
e
THD
ca
n
be
m
inim
ized
b
y
inc
r
ea
sing
t
h
e
l
e
v
e
l
of
o
u
t
pu
t
vo
lta
ge
a
nd
u
s
i
ng
S
P
WM
switc
h
i
n
g
s
trat
egy.
O
t
h
er
t
ha
n
tha
t
,
wit
h
o
ptim
um
a
n
g
l
e
a
t
t
he
o
u
tp
ut
v
o
l
tage
l
e
v
e
l
,
the
v
o
lta
ge
T
HD
is
m
i
ni
m
i
ze
d
a
n
d
is
b
e
t
t
e
r
tha
n
t
he
S
P
W
M
sw
i
t
c
h
i
ng
s
t
r
a
te
gy
[1
8]
.
The
most
c
om
mon
m
e
th
od
t
o
d
e
t
er
min
e
t
h
e
op
t
i
mum
a
n
g
l
e
at
t
he
o
ut
p
u
t
vol
tage
i
s
usin
g
se
le
c
tive
har
m
onic
e
l
i
min
a
ti
on
(
SHE
)
,
wh
ere
i
t
n
eed
s
a
cl
os
e-
lo
o
p
s
ys
t
e
m
[1
9]
a
n
d
i
s
mor
e
c
om
p
l
i
c
a
t
e
d
[
20,
21]
.
Ther
e
f
or
e,
t
he
o
p
tim
al
a
ng
le
a
t
t
h
e
ou
t
p
u
t
v
olta
ge
l
e
v
el
for
t
h
e
m
i
n
i
m
i
za
tio
n
o
f
v
olta
ge
T
HD
us
in
g
t
h
e
MP
WM
s
witc
h
i
n
g
s
t
r
a
t
e
g
y
c
a
n
b
e
d
e
t
e
r
m
i
n
e
d
b
y
im
pr
o
v
em
ent
s
o
f
MP
WM
a
nd
S
P
W
M
sw
i
t
c
h
in
g
str
a
te
g
i
e
s
.
F
r
om
t
he
p
r
in
ci
pl
e
of
i
mp
rov
e
d
swi
t
ch
ing
st
rat
e
g
y
b
as
ed
o
n
M
P
WM
a
nd
S
PWM
swit
ch
ing
st
rat
e
gi
es,
th
e
ang
l
e
a
t
t
h
e
ou
tpu
t
v
olt
a
ge
l
ev
e
l
o
r
known
a
s
a
l
p
h
a
a
n
g
l
e
c
a
n
b
e
ge
ner
a
t
e
d
an
d
a
p
plie
d
in
o
r
d
e
r
t
o
ge
t
low
e
r
vol
tage
T
H
D
than
t
h
e
S
P
W
M
sw
it
chi
n
g
stra
t
e
gy.
I
t
is
e
asier
an
d
les
s
c
o
mpl
i
ca
te
d
t
o
u
se
M
PW
M
swit
c
h
i
n
g
s
tr
a
t
e
g
y
as
c
omp
a
r
e
d
to
t
he
S
P
W
M
s
w
itc
h
i
n
g
s
tr
a
t
e
g
y
.
The
s
w
i
tc
hi
n
g
c
ontr
o
l
f
o
r
the
ha
r
d
w
a
r
e
s
e
t
u
p
is ea
s
i
e
r us
in
g MP
WM switc
h
i
n
g
stra
t
egy as
c
o
mpa
r
ed
t
o
S
P
WM
s
w
i
t
c
h
i
n
g
s
t
r
ate
g
y
a
n
d
r
e
duc
es
t
he
c
o
s
t
[2
2]
.
F
i
gu
r
e
2
s
ho
ws
t
h
e
e
xa
mp
l
e
o
f
t
h
e
an
gl
e
a
t
t
h
e
o
u
tp
ut
v
o
lta
g
e
l
ev
el
f
o
r
a
7
-l
ev
el
M
L
I
u
si
ng
M
PWM
swi
t
c
h
i
n
g
s
t
r
a
t
e
g
y
.
T
h
e
w
i
d
t
h
,
W
f
o
r
e
a
c
h
st
ai
rc
ase
mu
st
di
f
f
e
r i
n
o
r
d
e
r
t
o
p
r
oduc
e l
o
we
r
v
o
l
t
a
g
e
T
HD t
h
a
n
t
h
e
S
PWM
s
w
i
t
c
h
i
n
g
s
t
r
a
t
eg
y
.
F
i
gur
e
2.
E
xa
mple
o
f
a
n
g
l
e
a
t
t
he
o
u
t
p
u
t
v
ol
ta
ge
l
e
v
el
f
or
vol
t
age
THD minimization
2.
4.
V
o
lt
a
g
e
t
h
d
min
i
m
i
zat
i
on
b
y
p
r
op
osin
g
mod
i
f
i
e
d
p
u
l
se
w
id
t
h
m
od
u
lat
i
on
w
it
h
l
o
w
f
r
eq
u
e
n
c
y
of
t
r
ia
ng
u
l
a
r
w
av
e (M
PW
M
-
LFT
)
B
a
si
ca
lly
,
th
e
p
r
in
c
i
pl
e
o
f
t
he
p
rop
o
sed
m
o
dif
i
ed
p
ul
se
w
i
d
t
h
m
od
u
l
a
t
i
o
n
w
i
t
h
l
ow
f
r
e
que
ncy
o
f
tria
ng
u
l
ar
w
av
e
(MP
W
M-LF
T)
s
wi
tc
hin
g
s
trate
gy
is
t
he
s
a
m
e
wi
th
t
h
e
pr
i
n
ci
p
l
e
of
t
he
S
P
W
M
sw
itch
i
ng
str
a
t
e
gy
[
23]
w
he
r
e
i
t
c
o
m
p
ar
es
t
he
t
r
i
a
n
g
u
lar
w
a
ve
w
i
t
h
the
si
ne
w
a
v
e.
T
he
d
if
fer
e
nce
i
s
t
he
s
w
i
tc
h
i
n
g
f
r
e
que
n
c
y
tha
t
i
s
ap
p
lie
d
i
n
t
he
t
r
i
a
n
gu
lar
w
a
ve
i
s
50
H
z
a
nd
s
hi
ft
ed
9
0
o
a
s
sh
ow
n
i
n
F
ig
ur
e
3,
w
hi
c
h
i
s
di
ffere
n
t
wi
th
t
he
t
yp
ica
l
S
PWM
sw
itc
h
i
ng
s
trate
gy
t
h
at
u
s
u
al
ly
u
se
s
m
o
r
e
t
ha
n
1
kH
z.
H
ow
ev
er
,
the
m
odu
la
tio
n
s
i
g
n
al
g
e
n
e
r
ate
d
from
the
5
0
H
z
o
f
t
ria
n
g
u
l
ar
w
ave
i
s
the
sa
me
w
it
h
the
MP
WM
p
ri
nci
p
l
e
.
The
si
gna
l
ca
n
be
a
pp
l
i
ed
f
or
t
he
m
ulti
le
vel i
n
v
e
r
t
er
s
tr
uct
u
r
e
i
n
o
r
d
e
r
t
o
g
e
t
t
h
e
opt
i
m
u
m
poi
n
t
o
f
t
h
e
angl
e
at
t
he
ou
t
p
u
t
v
o
l
tage
l
eve
l
.
O
n
e
o
f
t
he
a
d
v
a
n
ta
ge
s
of
u
s
i
n
g
l
ow
s
w
itc
h
i
n
g
f
r
e
q
u
e
ncy
i
s
t
ha
t
i
t
r
e
d
uc
e
s
t
h
e
s
w
itc
hi
ng
lo
sses
c
o
m
p
ar
e
d
t
o
S
P
WM
s
w
itc
hi
n
g
s
tr
a
t
e
gy,
w
h
i
ch
u
ses
a
hig
h
s
w
i
t
c
hing
fr
eq
uenc
y
[
2
4
]
.
T
he
or
et
ica
l
ly,
t
h
e
sw
itc
h
i
n
g
l
os
se
s
for
th
is
t
ec
hn
i
que
w
i
l
l
be
t
he
s
a
m
e
a
s
t
he
M
P
W
M
sw
itc
h
i
n
g
s
tr
ate
g
y.
F
i
gur
e
3
sh
ow
s
t
h
e
m
odu
la
tin
g
me
th
od
for
the
7-
le
vel
a
s
ymm
e
tric
m
ult
i
l
eve
l
i
nv
e
r
te
r
.
B
y
usi
n
g
t
h
i
s
m
odu
la
ti
on
s
i
gn
al,
the
ou
t
p
u
t
v
ol
ta
ge
l
e
v
els
ge
ner
a
ted
a
r
e
au
tom
a
tica
l
l
y
a
t
t
h
e
op
tim
u
m
an
g
l
e
a
t
t
he
o
ut
p
u
t
v
o
lta
ge
l
ev
el
a
nd
obs
er
ved
b
y
t
h
e
p
e
r
ce
nt
a
g
e
of
vol
ta
ge
T
H
D
.
S
1
S
2
V
dc
1
V
dc
2
D
1
D
2
S
A
S
C
S
D
S
B
Lo
a
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
6
1
–
1
468
1
464
It
h
as
b
ee
n
pr
o
v
ed
by
t
h
e
sim
u
la
t
i
o
n
a
n
d
e
x
p
erim
en
t
tha
t
t
he
v
o
lt
ag
e
TH
D
o
b
t
a
i
n
e
d
b
y
t
hi
s
met
hod
i
s
l
o
w
e
r
t
h
a
n
t
h
e
S
P
W
M
a
n
d
M
P
W
M
s
w
i
t
c
h
i
n
g
s
t
r
a
t
e
g
i
e
s
.
T
h
e
w
a
v
e
f
or
m
of
t
he
s
ta
ir
c
a
se
out
pu
t
vo
l
t
a
g
e
is
the
near
est
t
o
t
he
s
i
n
e
w
a
v
e
for
m
.
S
o
,
it
i
s
p
r
o
ved
t
h
a
t
t
he
v
ol
ta
ge
T
H
D
is
t
he
l
o
w
est
am
on
g
t
h
e
o
t
he
r
switching
strateg
i
e
s
.
Th
e
an
g
l
e at
t
h
e
o
utpu
t
v
o
ltag
e
lev
e
l
can
b
e
deter
m
i
n
ed
by
u
s
i
n
g
si
multa
ne
ou
s
eq
uat
i
o
n
:
360
0.
02
o
le
v
e
l
t
(
1
)
Whe
r
e
t
level
i
s
th
e
t
i
me
o
f
t
h
e e
x
ch
ang
e
l
e
v
el, i
.e.
, t
i
m
e
f
r
om l
ev
el
o
n
e
t
o
leve
l
tw
o.
T
he
α
i
s t
h
e a
ngle
a
t
t
he
o
u
t
pu
t
v
o
l
t
a
g
e
le
ve
l.
T
he
s
i
m
ula
t
ion
r
e
su
lts
f
or
the
m
od
u
l
a
t
i
o
n s
i
g
n
al
t
hat
c
o
m
p
a
r
e
s
t
he
t
r
i
a
ngu
l
a
r
w
a
ve
w
i
t
h
t
he
s
i
n
e
w
a
ve i
s sh
ow
n i
n
F
ig
ur
e.
4
w
h
i
c
h i
s
i
n MP
W
M
s
w
i
tc
h
i
n
g
s
t
r
a
teg
y
f
or
m
.
Ther
e
for
e
,
i
t
s
ho
w
s
t
ha
t
t
h
e
th
eo
ry
a
n
d
p
rin
c
ipl
e
o
f
th
is
m
e
t
hod
h
av
e
b
e
en
m
o
d
i
f
i
e
d
fro
m
S
P
W
M
sw
itc
h
i
n
g
s
t
r
ateg
y
pr
inc
i
ple
.
T
h
e
m
odu
la
tio
n
s
i
g
n
al
s
i
n
F
i
g
ur
e
4
ne
e
d
t
o
b
e
r
ear
r
a
nge
d
sam
e
a
s
th
e
swit
c
h
i
n
g
se
qu
en
c
e
o
f
M
P
WM
s
wi
tch
i
ng
str
a
t
e
gy
tha
t
f
o
l
l
o
w
t
h
e
mo
de
o
f
oper
a
t
i
o
n
o
f
t
h
e
R
N
S
D
s
tr
uct
u
r
e
s
.
F
i
gur
e
5
sh
ow
s
t
h
e
si
m
u
lat
i
on
r
e
s
u
l
t
f
or
the
7-
le
vel
a
s
ym
m
e
tr
ic
t
op
o
l
og
y
w
i
th
t
he
p
r
o
p
o
sed
M
P
WM-
L
F
T
s
w
i
t
c
h
in
g
s
t
r
a
te
gy.
I
t
is
p
ro
ve
d
tha
t
u
sin
g
the
pr
i
n
c
i
ple
o
f
S
P
W
M
sw
itc
hin
g
s
tr
ate
g
y
c
a
n
gene
r
a
te
t
h
e
M
P
W
M-
LF
T
switc
h
i
ng
s
tra
t
e
gy.
T
he
r
esu
lt
a
l
s
o
inc
l
ude
s
t
h
e
sine
w
a
v
e
as
t
he
r
efere
n
ce
in
o
rder
t
o
o
b
se
rve
tha
t
the
sta
i
r
c
ase
c
a
n
be
e
a
s
i
l
y
f
i
lter
e
d
an
d
for
m
a
si
ne
w
a
v
e.
I
t
is
a
lso
pro
v
e
d
t
h
a
t
t
h
e
ou
tpu
t
v
olta
ge
i
s
t
h
e
ne
a
r
e
st
f
or
m
to
s
i
n
e
w
a
ve
c
om
p
a
r
e
d
t
o
t
he
M
P
W
M
a
nd SP
WM
s
w
i
tc
h
i
n
g
stra
t
e
g
ie
s.
F
i
gur
e
4.
M
o
d
u
la
t
i
o
n
s
i
g
nal
s
F
i
gur
e
3.
M
et
h
od
o
f
m
od
ula
t
i
o
n
F
i
gur
e
5.
S
im
ul
a
t
ion
r
e
su
l
t
s
o
f
out
pu
t
v
o
l
t
a
g
e
using
the
pr
o
pos
e
d
M
PWM-LF
T s
w
i
t
c
hing
st
r
at
e
g
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Mu
lti
lev
e
l i
n
ve
rt
e
r
w
ith M
P
W
M
-L
FT
sw
itc
h
i
ng s
t
ra
t
e
gy fo
r v
o
l
t
age
TH
D
min
i
miza
ti
o
n
(M. H.
Y
a
t
i
m)
1
465
3.
RESU
L
T
S
A
ND ANALY
S
ES
To
tal
ha
rm
o
n
i
c
d
is
tor
t
i
o
n
(THD)
o
f
the
o
u
t
p
u
t
v
ol
ta
ge
i
s
an
i
mp
or
ta
n
t
p
ar
a
m
e
t
er
t
ha
t
is
o
b
s
er
ved
e
i
t
h
e
r
i
n the
pr
inc
i
ple,
s
im
u
l
a
t
i
o
n or
h
a
r
dw
a
r
e.
S
ever
al
f
act
or
s aff
e
c
t
the
v
ol
ta
ge TH
D
,
s
uc
h
as i
n
a m
u
lti
le
ve
l
in
ver
t
e
r
,
incr
e
a
s
i
ng
the num
be
r
of
o
u
t
p
u
t
vo
lta
ge
l
eve
l
g
e
n
e
r
at
e
d
a
n
d
u
s
i
n
g
t
h
e
c
o
r
r
e
c
t
s
w
i
t
c
h
i
n
g
s
t
r
a
t
e
g
y
c
a
n
pr
oduc
e
a
low
e
r
vo
lta
ge
T
H
D
t
ha
n
t
h
e
c
o
n
v
en
t
i
o
n
a
l
M
LI
[
7]
.
Ther
ef
or
e
,
t
he
i
m
p
lem
e
n
t
at
i
on
o
f
a
sym
m
etr
i
c
t
o
p
o
l
o
g
y
i
s
a
b
l
e
t
o
i
n
c
r
e
a
s
e
t
h
e
l
e
v
e
l
o
f
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
a
n
d
m
a
in
t
a
ins
the
str
u
ct
ure
in
o
r
d
er
t
o
re
duc
e
t
h
e
TH
D
of
t
he
o
u
t
pu
t
v
o
l
ta
ge.
A
n
o
t
her
fa
ct
or
t
ha
t
c
a
n
r
ed
uce
the
v
ol
ta
ge
T
H
D
i
s
t
h
e
su
ita
bi
li
ty
o
f
t
h
e
sw
i
t
c
h
i
n
g
str
a
t
e
gy
a
p
pl
ie
d.
T
his
s
t
ud
y
f
o
cu
ses
o
n
t
hr
ee
t
y
p
es
o
f
sw
i
t
c
hi
n
g
stra
t
e
gi
e
s
,
wh
ich
are
th
e
M
P
WM,
SP
W
M
a
nd
M
P
WM-
L
F
T
s
w
i
t
c
h
i
n
g
s
tr
a
t
e
g
i
e
s.
T
he
or
et
i
c
al
l
y
,
S
P
WM
s
w
itc
h
i
n
g
st
r
a
te
gy
ca
n
pr
o
duce
muc
h
l
ow
e
r
vo
l
t
age
TH
D
[
25]
a
s
c
o
m
p
ar
e
d
t
o
MP
W
M
s
w
itc
h
i
n
g
s
tr
a
t
e
g
y.
B
u
t
,
b
y
op
t
i
miz
i
n
g
t
he
a
n
g
le
a
t
t
h
e
ou
tpu
t
vo
l
t
age
le
ve
l
usin
g
MP
WM-
L
F
T
s
w
itc
h
i
n
g
s
tr
ate
gy,
t
he
v
ol
ta
ge
T
H
D
is
l
ow
e
r
t
ha
n
S
P
WM
switc
h
i
n
g
strat
e
g
y
.
F
i
gur
e
6
show
s
t
h
e
r
e
su
lt
of
t
he
e
x
p
e
r
ime
n
t
for
t
h
e
7-
le
vel
asy
m
m
e
t
r
i
c
t
o
pol
og
y
us
in
g
the
M
P
WM
switc
h
i
n
g
s
tra
t
e
gy
w
h
i
l
e
F
i
g
u
re
8
s
hows
the
r
e
su
lt
o
f
t
h
e
exper
i
m
e
n
t
f
o
r
t
h
e
7-
le
ve
l
asym
m
e
tr
ic
t
o
pol
og
y
us
in
g
t
h
e
S
P
WM
s
w
i
tc
hi
ng
s
t
r
a
t
e
g
y
.
The
nu
mbe
r
o
f
the
o
u
t
p
u
t
l
e
v
e
l
i
s
t
h
e
sam
e
f
or
a
l
l
r
esul
ts
a
nd
i
t
s
how
s
t
h
at
t
h
e
s
e
l
ecte
d
s
t
r
u
c
tu
re
o
p
e
rat
e
s
we
ll
e
v
e
n
in
e
xp
erimen
t
an
d
pr
o
v
e
s
t
h
at
a
s
y
m
m
e
t
r
i
c
to
pol
o
g
y
ca
n
b
e
im
pl
e
m
e
n
te
d.
T
he
v
olta
ge
T
H
D
of
t
h
e
o
ut
pu
t
vo
l
t
age
us
in
g
MP
WM
a
n
d
S
PWM
sw
i
t
ch
i
ng
s
t
r
a
te
g
i
es
a
r
e
21.
5
%
a
n
d
1
7.
5
%
r
espec
t
i
v
e
l
y
as
s
h
o
w
n
i
n
F
i
gur
e
7
a
nd
F
i
gur
e
9.
i
t
ca
n
be
s
a
i
d
tha
t
,
the
vo
l
t
a
g
e
T
H
D
is
m
i
ni
m
i
ze
d
w
h
e
n
S
P
W
M
sw
it
c
h
in
g
s
t
r
a
teg
y
i
s
a
p
p
l
ied
i
n
t
he
R
N
S
D
c
i
r
cui
t
s
tr
uct
u
r
e
w
i
t
h
t
h
e
sam
e
num
ber
of
ou
t
p
u
t
v
ol
t
a
ge
l
e
v
e
l
.
F
i
gur
e
6.
O
utp
u
t
v
o
l
ta
ge
l
e
v
e
l
o
f
ex
per
i
m
e
n
t
al
r
esul
ts
u
s
i
n
g
M
P
W
M
s
wi
tch
i
ng
st
r
at
e
g
y
F
i
g
u
r
e
7
. Freq
u
e
n
c
y
sp
ectrum o
f
o
u
t
pu
t
vol
tag
e
u
s
i
n
g
MP
W
M
s
wit
c
h
i
ng
st
r
a
t
e
gy
Th
e
s
e
c
ond
c
omp
a
ri
s
o
n
i
s
b
et
we
en
t
h
e
M
P
W
M
swit
c
h
i
n
g
st
r
a
t
e
gy
a
n
d
t
h
e
pr
opo
se
d
MP
WM-
L
F
T
sw
itc
h
i
n
g
s
tr
a
t
egy
base
d
on
the
ex
per
i
m
e
n
t
al
r
e
s
u
l
ts.
F
i
gu
r
e
6
a
n
d
F
i
g
u
r
e
1
0
s
h
o
w
t
h
e
w
a
v
e
f
o
r
m
s
d
i
f
f
e
r
e
n
c
e
be
t
w
ee
n
MP
WM
s
w
itc
hi
ng
s
t
r
a
teg
y
a
n
d
t
he
M
P
W
M-
LF
T
sw
it
c
h
i
ng
str
a
t
e
gy.
T
he
w
id
th
o
f
e
a
c
h
s
ta
irc
a
se
i
s
no
t
t
h
e
sam
e
f
or
t
he
M
P
W
M-
LF
T
sw
i
t
c
h
in
g
str
a
te
g
y
d
ue
t
o
t
h
e
o
p
t
im
u
m
a
ngle
a
t
t
he
outp
u
t
v
ol
ta
g
e
l
eve
l
g
e
n
e
ra
t
e
d
wh
e
r
e
t
r
i
a
ngu
l
a
r
w
a
v
e
i
s
ov
erl
a
ppi
ng
w
i
t
h
th
e
re
f
e
r
e
n
ce
w
a
v
e,
w
hic
h
is t
h
e
s
i
ne
w
a
v
e.
S
ome
of
t
he
pu
lses
i
n
t
h
e
MPW
M
-LFT
a
re
w
ider
a
nd
s
om
e
a
r
e
sm
al
l
e
r
t
h
a
n
t
he
c
o
m
m
on
MP
W
M
s
w
itc
h
i
ng
s
tr
a
t
e
gy.
H
e
nce
,
t
he
T
H
D
a
t
the
o
u
tp
ut
volta
ge
i
s
r
e
d
u
ce
d
a
nd
i
s
b
e
tte
r
t
ha
n
i
n
t
he
S
P
W
M
sw
it
c
h
ing
s
t
r
a
te
gy.
I
t
i
s
a
l
s
o
pr
ove
d
t
h
a
t
i
n
t
h
e
ope
n-
l
o
o
p
s
ys
t
e
m
,
m
ini
m
um
v
o
l
ta
ge
T
H
D
c
a
n
be
achie
ve
d
b
y
c
a
l
c
u
lat
i
on
a
nd
es
ti
ma
t
i
o
n
of
a
n
g
l
e
a
t
t
h
e
ou
t
p
u
t
v
ol
ta
ge
l
eve
l
.
I
n
a
dd
iti
on,
f
i
n
d
i
ng
t
he
o
p
ti
mu
m
a
ngle
a
t
t
h
e
out
put
v
olt
a
g
e
l
ev
e
l
i
s
a
b
l
e
to
m
i
n
im
i
z
e
th
e
vo
l
t
a
g
e
TH
D
bet
t
er
t
ha
n
t
h
e
SP
WM
s
w
i
t
c
h
i
n
g
s
t
r
a
teg
y
w
hic
h
i
s
we
ll
k
n
o
wn
a
s
the
co
m
m
on
m
odu
la
tio
n
te
chn
i
que
f
or
t
h
e
m
ult
ile
ve
l
i
n
v
e
r
t
er.
B
a
sic
a
lly,
t
h
e
s
t
airc
ase
o
f
t
he
M
P
W
M-LF
T
swi
t
c
h
in
g
str
a
t
e
gy
i
s
d
i
ff
e
r
ent
fr
om
t
he
m
axim
um
v
ol
t
a
ge
t
o
z
e
r
o
.
T
h
e
w
i
d
th
f
r
o
m
t
h
e
ma
ximum
vo
lta
ge
t
ow
ar
d
s
z
e
r
o
sli
g
h
t
ly
c
h
a
ng
e
s
d
ep
endi
ng
o
n
t
h
e
opt
i
m
u
m
a
n
g
l
e
a
t
t
h
e
outp
u
t
v
o
lta
g
e
l
e
v
el
f
or
m
in
imu
m
volta
ge
T
H
D
.
T
he
vo
l
t
age
TH
D
o
f
t
he
o
ut
p
u
t
v
o
lta
ge us
i
n
g
S
P
W
M
a
n
d
MP
WM-
L
F
T
s
w
i
t
c
h
i
ng
s
t
r
a
t
eg
i
e
s
a
r
e
1
7
.
5%
a
nd
1
1
.
6%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
6
1
–
1
468
1
466
r
e
spec
tive
l
y
as
s
how
n
i
n
F
ig
ur
e
9
and
F
i
g
u
r
e
11.
it
ca
n
be
s
ai
d
t
h
a
t
,
t
h
e
v
o
l
t
a
g
e
T
H
D
i
s
m
i
n
i
m
i
z
e
d
w
h
e
n
MP
WM-LFT
s
witc
h
i
n
g
s
tra
t
e
gy
is
a
p
p
l
i
e
d
i
n
t
h
e
R
N
S
D
c
ircu
it
stru
c
t
ur
e
w
i
t
h
t
he
s
a
m
e
numbe
r
of
o
u
t
pu
t
vo
l
t
age
l
e
ve
l.
F
i
gur
e
8.
O
utp
u
t
v
o
l
ta
ge
l
e
v
e
l
o
f
ex
per
i
m
e
n
t
al
r
esul
ts
u
s
i
n
g
M
P
W
M
s
wi
tch
i
ng
st
r
at
e
g
y
F
i
gur
e
9.
F
r
eque
n
c
y
spec
tr
u
m
o
f
o
u
t
p
ut
v
o
lta
ge
u
s
i
ng
S
P
W
M
sw
itc
h
i
ng st
ra
t
e
gy
F
i
gur
e
1
0
.
O
u
tpu
t
v
olta
ge
l
e
v
e
l
o
f
ex
per
i
m
e
nta
l
r
esul
ts
u
s
i
ng
M
PWM-LF
T switch
i
ng s
t
rate
g
y
F
i
gur
e
1
1
.
Fr
e
que
nc
y
spec
t
r
u
m
o
f
out
p
u
t
v
o
l
t
a
ge
u
si
ng
MP
WM-
L
F
T
switchi
n
g
s
trate
g
y
Conc
e
p
tua
l
ly,
by
i
ncr
eas
in
g
the
num
ber
o
f
o
u
t
pu
t
v
o
l
t
a
ge
l
e
v
e
l
,
t
he
v
ol
u
m
e
a
n
d
s
i
ze
o
f
f
i
lter
ar
e
r
e
duce
d
s
i
g
n
i
f
i
can
t
l
y
du
e
t
o
t
he
m
in
imiz
a
tio
n
o
f
v
ol
t
a
g
e
T
H
D
.
T
he
r
e
f
o
r
e
,
it
can
b
e
c
onc
lu
de
d
tha
t
by
op
t
i
miz
i
n
g
a
n
g
l
e
a
t
t
h
e
out
pu
t
v
o
l
t
a
ge
l
e
v
e
l
u
sin
g
M
P
W
M-
LF
T
sw
i
t
c
h
i
ng
s
t
r
at
egy
a
b
l
e
t
o
mi
nimi
z
e
t
he
vo
l
t
age
TH
D
at
t
he
out
p
u
t
vo
l
t
a
g
e
bet
t
er
t
ha
n
MP
W
M
a
nd
S
P
WM
s
w
i
tc
hi
n
g
s
t
r
ate
g
ie
s.
I
n
addi
t
i
on,
t
he
sw
itc
h
i
n
g
l
oss
r
e
duct
i
on
us
i
ng
the
pr
o
p
o
s
e
d
M
P
W
M-
LF
T
sw
itc
hi
n
g
s
t
rat
e
gy
i
s
si
gnif
i
c
a
nt
a
s
c
o
mpa
r
ed
t
o
ty
p
i
cal
S
P
W
M
sw
itch
i
ng
str
a
t
e
gy.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Mu
l
til
evel
i
n
vert
e
r
wit
h
MPWM-LF
T
swi
t
c
h
in
g
st
rat
e
g
y
f
o
r vo
lt
a
g
e
T
HD
mi
ni
mi
zat
i
on
(M.
H.
Y
a
ti
m)
1
467
4.
CONCL
U
S
ION
Bas
i
ca
ll
y,
b
y
com
p
ar
ing
t
h
e
MP
WM
a
nd
S
P
WM
s
w
itc
h
i
ng
s
t
ra
t
e
g
i
e
s
,
S
P
W
M
sw
i
t
c
h
in
g
s
t
rate
gy
show
s
a
be
t
t
e
r
v
o
l
tage
T
H
D
qua
li
ty
a
s
c
o
mp
a
r
ed
t
o
MP
WM
s
w
i
tc
hi
n
g
st
ra
t
e
g
y
f
or
t
h
e
m
ult
ile
ve
l
i
nve
rte
r
.
I
n
th
i
s
p
a
p
e
r
,
a
sw
itc
hi
n
g
s
tra
t
e
gy
is
p
r
o
p
o
se
d
t
o
i
m
p
ro
ve
t
h
e
m
in
imiz
a
t
ion
of
t
he
v
olta
ge
T
H
D
.
T
h
e
p
ropos
ed
MP
WM-L
F
T
i
s
b
y
i
m
p
rov
i
ng
the
pri
n
c
i
p
l
e
o
f
S
P
W
M
by
a
ppl
y
i
n
g
5
0
H
z
sw
itc
h
i
n
g
f
re
que
ncy
a
t
t
h
e
tria
ng
u
l
ar
w
ave
and
p
h
ase-s
h
i
f
ted
9
0
o
.
By
c
om
pari
ng
w
ith
s
ine
w
a
ve
a
nd
tria
n
g
u
l
a
r
50
H
z
,
th
e
si
gna
l
gene
ra
ted
w
i
l
l
b
e
in
M
P
W
M
for
m
a
nd
a
l
so
w
it
h
o
p
t
i
mum
ang
l
e
a
t
t
h
e
out
put
v
o
l
t
a
g
e
l
ev
el
.
Thi
s
s
wit
c
h
i
ng
st
r
a
te
gy
o
b
t
a
i
n
s
1
1.
6%
o
f
volta
ge
T
H
D
f
or
t
he
7
-le
v
e
l
a
s
y
m
m
e
t
ri
c
to
p
o
l
ogy
a
s
c
o
mpared
t
o
M
P
WM
a
nd
S
P
W
M
s
w
i
t
c
h
i
n
g
s
t
r
a
t
e
g
i
e
s
w
i
t
h
t
h
e
v
o
l
t
a
g
e
T
H
D
a
r
e
2
1
.
5
%
a
n
d
1
7
.
5
%
r
e
spec
t
i
ve
ly
.
It
can
b
e
c
o
n
c
lu
d
e
d
tha
t
t
he
T
H
D
a
t
t
h
e
o
u
t
p
ut
v
o
l
tage
l
ev
el
c
a
n
b
e
red
u
ce
d
by
de
t
e
rm
i
n
i
n
g
the
opt
im
um
a
ng
le
a
t
t
h
e
ou
t
put
vo
lta
ge
l
e
v
e
l
u
s
i
ng
MP
WM
-LF
T
s
w
itch
i
n
g
s
tr
ate
gy.
T
h
r
ee
sw
itc
hi
n
g
stra
te
gie
s
h
av
e
be
e
n
a
pp
l
i
e
d
a
nd
MPWM-L
FT
s
ho
w
s
t
h
e
l
ow
est
v
o
lta
ge
T
H
D
that
b
een
o
b
t
a
i
o
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ACKNOW
LEDG
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MEN
T
S
The
a
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thors w
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ke to e
x
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s the
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r
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p
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t
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to t
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e
U
n
i
ve
rs
iti T
un H
u
ssei
n
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nn Ma
lays
ia for
the f
u
ndi
ng
su
pp
ort,
re
s
ear
ch gr
a
nts
G
P
P
S
,
Tie
r
1
V
ot
U
85
8 a
nd
Resea
r
ch
F
und,
U
TH
M
REFE
RENCES
[1]
M
.
M
a
l
i
n
o
w
s
k
i
,
K
.
G
o
p
a
k
u
m
a
r
,
J
.
R
o
d
r
i
g
u
e
z
,
a
n
d
M
.
A
.
P
e
r
e
z
,
"
A
Survey
o
n
Ca
scaded
M
u
ltil
evel
I
nverters,
"
IEEE
Trans
.
Ind
.
El
ec
t
r
on
,
vol.
57(7
)
,
p
p
.
2
19
7-2206
,
2
01
0.
[2]
E
.
B
a
b
a
e
i
,
S
.
A
l
i
l
u
,
S
.
L
a
a
l
i
,
a
n
d
S
.
M
e
m
b
e
r
,
"
A
N
e
w
G
e
n
e
r
a
l
T
o
pology
f
or
C
ascaded
M
ul
tilevel
Inverters
W
i
t
h
Re
d
u
c
e
d
N
u
m
b
e
r
of
C
o
m
po
ne
nts
Ba
se
d
o
n
D
e
v
e
l
op
e
d
H
-Bridg
e
,
"
IE
E
E
Trans. Ind.
E
l
ectr
o
n
,
vo
l.
6
1
(
8),
pp
.
3
932
-39
3
9
, 2
014
.
[3]
O.
L
.
Ji
mene
z,
R
.
A.
V
ar
gas,
J
.
Ag
uay
o
,
J.
E
.
A
r
au,
G.
V
ela,
a
n
d
A.
C
lau
d
i
o
,
"
T
HD
i
n
cascade
m
u
lti
l
evel
i
nv
erter
s
y
m
m
e
t
r
i
c
a
n
d
a
s
y
m
m
e
t
r
i
c
,
"
P
r
o
c
.
IE
EE Elect
ron
.
Robot.
A
u
tomo
t. M
ech
. Con
f
.
C
E
R
M
A
2
0
11
,
pp
.
2
89-2
9
5
,
2
0
1
1.
[4]
M
.
M
o
s
a,
R
.
S
.
B
al
og,
H
.
Ab
u-Ru
b,
a
n
d
M
.
Elbu
lu
k,
"
A
m
odifi
e
d
s
y
m
m
e
tri
c
a
nd
a
sy
mm
etric
m
u
ltil
evel
p
o
w
er
in
verter
w
it
h
redu
ce
d
nu
mb
er
o
f
po
wer
switc
h
e
s
con
t
ro
ll
e
d
b
y
M
P
C,"
in
I
E
E
E
Ap
p
l
ie
d
P
o
w
e
r E
l
e
c
tr
on
ic
s
Con
f
eren
ce an
d E
x
po
siti
on (
APEC)
,
p
p
.
4
8
8
-
49
3,
2
01
7.
[5]
A.
M
ok
hb
e
r
do
ra
n
a
nd
A.
A
ja
mi
,
"
S
ym
me
tric
a
nd
A
sym
m
e
t
r
i
c
De
sign
an
d
I
m
p
l
e
m
ent
a
ti
on
o
f
N
e
w
Cascad
ed
Multilevel
Inver
t
er T
opology,"
I
E
EE
T
r
a
n
s
.
Po
w
e
r E
l
e
c
t
ro
n
,
vol.
2
9
(
12),
pp
.
67
12-67
24
,
2
0
1
4
.
[6]
G.
S
.
Z
i
noviev
a
nd
N
.
N.
L
o
p
atkin,
"
Evol
u
t
i
o
n
of
m
ul
tilevel
vo
l
ta
ge
s
o
u
r
c
e
i
nv
e
r
te
rs,"
i
n
9th In
te
rna
t
ion
a
l
Con
f
eren
ce on
Act
u
a
l
P
r
o
b
l
e
ms
of
El
ectro
ni
c In
str
u
m
e
n
t
En
gin
e
e
r
i
n
g
, v
o
l
. 0
1,
pp
.
12
5
-1
36
, 20
0
8
.
[7]
H
.
H
.
H
.
a
n
d
A
.
P
.
a
n
d
A
.
N
.
K
.
a
n
d
M
.
A
.
H
.
a
n
d
D
.
A
.
G
.
a
n
d
M
.
H.
Y
atim,
"A
S
in
g
l
e
Ph
ase
7
-
L
e
vel
Cas
cade
Inv
e
rter
T
op
ol
o
g
y
w
i
t
h
R
educed
N
um
ber
o
f
S
witches
o
n
R
esisti
ve
L
o
a
d
b
y
U
s
i
n
g
P
W
M
,
"
J.
Ph
ys.
Conf. Ser
.
,
vo
l.
995
(1),
p
.
1
2
061
,
2
01
8.
[8]
S
.
S
.
L
a
ndg
e,
V
.
S
.
K
am
b
l
e,
a
n
d
S
.
S.
S
h
i
ng
are,
"
S
i
mu
la
t
i
o
n
o
f
S
e
ven
Lev
e
l
Asymm
etri
c
M
u
lti
l
ev
e
l
I
nvert
er,"
Int
.
J. Electr.
E
l
ectr
o
n,
v
o
l
.
4
(
1),
p
p
.
18
7-19
6,
2
0
1
4
.
[9]
M
.
H
.
Ya
tim,
A.
P
onniran
,
M
.
A
.
Z
ai
n
i
,
M
.
S
.
S
h
ai
li,
N.
A
.
S.
N
gam
i
du
n
,
a
n
d
A
.
N
.
K
as
i
r
an,
"S
ymm
e
trical
a
n
d
Asymmetr
i
cal
M
ulti
l
e
vel
Inver
t
er
S
t
r
uctu
res
wit
h
R
educed
N
um
ber
o
f
Sw
itch
in
g
D
e
vi
ces,"
In
do
nes.
J.
Elect
r. Eng
.
Com
put.
S
c
i.
,
vol.
11
(1
),
p
p.
1
4
4
-15
1
,
201
8.
[10]
D. P.
R.
M
s.
T.P
rathib
a,
"
Per
f
or
m
a
nce An
aly
s
is o
f
S
y
m
m
e
tri
cal a
nd
Asymm
etr
i
c
a
l
,
"
J. E
l
ectr
.
E
n
g
.
, vo
l
. 1
, p
p
. 1-
7
.
[11]
S
.
K
.
D
a
s
h
,
B.
N
ayak,
an
d
J.
B
.
S
a
hu
,
"
S
el
ecti
v
e
Harm
on
ic
E
lim
i
na
t
i
on
o
f
a
n
El
even
L
evel
I
n
v
erter
Us
in
g
W
h
ale
Op
ti
mizati
o
n
Tech
ni
que,
"
v
ol
.
9
(
4),
p
p.
1
9
44-1
951,
201
8.
[12]
M
.
N
agaraju
and
M
.
K. K
u
m
a
r, "An
aly
s
i
s
of
seri
es /
p
a
r
allel
m
u
l
ti
lev
e
l i
n
v
e
rt
er with
s
y
mm
etri
cal an
d
as
y
m
m
e
tri
cal
c
o
nfig
ura
t
io
ns
,"
v
o
l
.
1
0
(1
),
p
p
. 3
00
-30
6
, 2
01
9.
[13]
T.
M
.
Bl
oom
i
n
g
and
D
.
J
.
Carn
ov
ale,
"
App
l
i
cati
on
of
I
EEE
S
T
D
5
1
9-
1
9
9
2
Ha
r
m
on
ic
L
i
m
it
s,
"
in
Co
nfer
en
ce
Reco
rd
of 20
06
An
nua
l
Pu
l
p
and P
aper Ind
u
str
y
T
echn
i
cal
Confer
ence
, pp
.
1
-9
, 2
00
6.
[14]
M
.
K
.
R.
N
oo
r
et
a
l
.,
"
O
ptimizat
io
n
of
P
F
C
S
EP
IC
C
o
n
v
e
rt
er
P
ara
meters
D
esign
f
o
r
M
i
n
i
mizat
ion
of
T
HD
a
nd
Vo
lt
age
Rip
p
l
e
,"
Int
.
J. En
g
.
&
Amp
;
T
echn
o
l
,
v
o
l
7
(4
.3
0
)
,
i
s
su
e
30
,
DOI-1
0.
1
4
4
19/ijet.
v7i
4
.
30.
222
74
,
Nov
. 20
1
8
.
[15]
A.
P
rayag
and
S.
B
odkhe,
"Novel
B
a
s
ic
B
loc
k
o
f
Multilevel
Inver
ter
Using
Reduced
Number
o
f
O
n
-Stat
e
S
w
i
tches
and
Cascad
ed
C
ircu
it
To
polo
gy,
"
vol.
2
01
7
,
2
01
7
.
[16]
B.
M
.
Redd
y,
Y
.
V
.
S
.
Redd
y,
a
n
d
M
.
V.
K
um
ar,
"
M
o
d
eli
ng
an
d
S
i
m
ul
a
t
i
on
o
f
1
2
7
L
ev
el
O
ptim
a
l
M
ulti
le
v
e
l
Inverter w
i
t
h
L
o
wer
Num
b
er o
f
Sw
i
t
ches
a
nd Mi
nim
u
m T
H
D
,
" v
o
l.
9
(4
), p
p.
1
76
5-1
7
7
3
, 2
01
8.
[17]
M.
H
.
Yatim, A
.
Po
n
n
iran,
A.
A
.
Bak
a
r, A.
N.
K
a
s
iran,
K.
R
. No
o
r, an
d
J
. N
.
J
um
a
d
ri
l, "
A
n
aly
s
i
s
of
S
y
m
m
et
ric an
d
As
ymm
e
tri
c
M
ul
tilevel
Inv
e
rter
T
op
ol
og
i
e
s
Usi
n
g
Redu
c
e
d N
u
m
b
er
of
S
w
i
t
c
h
i
n
g
D
evi
ces C
i
r
cui
t
S
t
r
u
c
t
u
r
e
,
"
Int.
J.
Eng
.
&
A
m
p; Te
c
h
no
l
,
v
o
l
7
(4.
3
0
)
,
is
su
e
30,
D
OI-1
0.
1
441
9/ij
e
t
.
v7i
4.
3
0
.
2
21
27
,
N
ov
.
2
01
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
6
1
–
1
468
1
468
[18]
M.
A
wai
s
,
H.
I
ly
as,
H.
B
.
Yo
un
us,
M.
A
.
Ra
za,
a
nd
T
.
Ab
bas,
"
Op
tima
l
s
witching
a
ngl
e
s
f
o
r
mini
mizat
i
o
n
of
t
o
t
al
h
a
rm
oni
c
d
i
st
ortio
n
i
n
s
in
g
l
e
ph
ase
c
a
s
cad
ed
m
ultil
e
vel
in
vert
e
rs
,
"
i
n
1
9
t
h
In
ternat
io
nal M
u
lti
-Topi
c Con
f
er
ence
(I
N
M
I
C
)
, p
p.
1-
6
, 20
1
6
.
[19]
S
.
D
.
P
a
ti
l
an
d
S
.
G
.
Kad
w
an
e
,
"
A
p
p
licat
io
n
of
opt
imi
zati
on
t
e
c
hn
iq
ue
i
n
S
H
E
cont
rolled
multilevel
in
verter,
"
i
n
In
ter
natio
nal Co
nf
erence
on
En
ergy,
Commu
n
ica
t
i
o
n
,
Da
ta
An
a
l
yti
c
s and
So
ft
Com
p
u
t
i
ng
(
I
CECDS)
,
pp
.
2
6
-
30
, 2
01
7.
[20]
J
.
N
apo
l
es
et a
l
.
,
"
S
el
ec
t
i
ve
H
armoni
c
M
itigat
i
o
n
Techni
que
f
o
r
Cascaded
H
-Br
i
d
g
e
C
on
vert
ers
w
i
t
h
N
on
equ
a
l
DC
Li
nk
V
o
l
t
a
g
e
s,
"
IEEE Tr
ans
.
I
n
d
.
El
ectron
.
,
vol.
60
(5),
pp.
1
9
6
3
-
19
71,
2
0
1
3
.
[21]
B.
A
s
h
o
k
a
nd
A
.
R
ajen
dran
,
"S
elect
iv
e
Harm
o
n
ic
E
lim
i
na
t
i
on
o
f
M
ul
ti
le
ve
l
In
ve
rte
r
U
s
i
n
g
S
H
E
P
W
M
Te
c
h
niqu
e
,
"
In
t.
J.
Soft
Com
p
u
t
.
Eng.
,
vol.
3
(2
),
pp.
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9
-
82
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3
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[22]
A
.
A
.
Bakar,
M
.
U.
W
ahyu
,
A.
P
o
nni
ran,
a
n
d
T
.
T
a
u
f
ik,
"
S
i
m
u
l
ati
on
a
n
d
A
n
a
ly
si
s
of
M
ul
tiph
a
se
B
oo
st
C
on
ve
rte
r
wi
th
S
o
f
t-
S
w
i
t
c
hi
n
g
f
o
r
R
e
n
e
w
a
b
le
E
ne
r
g
y
Ap
pl
ic
a
t
i
o
n
,
"
In
t. J.
P
o
wer
El
ec
t
r
o
n
. Dri
ve Sys
t
.
(
I
JPEDS)
,
vo
l 8
(
4)
2
01
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[23]
D
.
T
.
N
u
g
r
oho
,
A.
N
.
A
z
is
,
an
d
T.
N
og
uch
i
,
"
S
im
plifi
e
d
fi
ve-l
e
v
e
l
v
ol
ta
g
e
s
o
u
rc
e
inv
e
rte
r
w
ith
le
ve
l-ph
a
s
e
-
s
hi
fte
d
carri
ers
b
a
sed
modu
latio
n t
echn
i
qu
e,
"
vo
l.
1
3
(
2
)
,
p
p
.
46
1-46
8,
2019
.
[24]
A.
N
.
Kasiran,
A
.
Po
nn
i
r
an,
A.
A
.
Bak
a
r,
M
.
H.
Y
at
i
m
,
M
.
K
.
R.
No
or,
an
d
J.
N
.
J
u
m
a
dril,
"
Im
pl
e
m
ent
a
ti
on
of
Res
onan
t
a
n
d
P
as
si
ve
L
ossles
s
S
n
ub
ber
Circu
its
f
o
r
D
C-DC
B
oos
t
Converter,"
Int
.
J.
E
n
g
.
&
Am
p.
T
echno
l
,
v
o
l
7
(
4.
3
0
),
i
ssue
30
DO
I-1
0
.
144
19
/ijet
.
v7i4.
30
.
2
2
276,
N
ov.
2
01
8
.
[25]
G
.
J
.
Rus
h
i
r
aj
a
nd
P
.
N
.
K
apil,
"
Anal
ysis
o
f
d
i
f
f
e
rent
m
odul
ati
on
t
echniqu
es
f
or
m
u
ltilevel
i
nvert
ers,"
i
n
In
ter
natio
nal
Conf
erence on El
e
c
t
r
i
c
al
,
E
l
ectr
onics
,
an
d Optimiz
a
t
ion T
echn
i
q
u
es
(
I
CEEOT)
,
p
p
.
3
0
17-3
0
2
4
,
201
6.
BIOGRAPHI
E
S
OF
AUT
HORS
M
ohd
H
afizie
Y
at
im
r
ecei
ved
th
e
ba
ch
elo
r
’s
d
eg
ree
i
n
e
le
ctri
cal
e
ng
in
e
e
r
ing
te
c
hno
lo
gy
(
po
we
r
)
fro
m
U
n
i
ve
rsit
i
Tu
n
Hus
s
e
i
n
On
n
Ma
l
a
ysia,
Pari
t
Ra
ja,
M
a
laysia,
i
n
20
17
a
n
d
t
he
m
a
s
te
r’
s
deg
r
ee
i
n
electrical
e
ng
in
eering
also
from
U
n
i
v
ers
i
t
i
T
u
n
H
u
s
se
in
O
n
n
M
a
l
ay
si
a,
i
n
20
19.
H
e
is
current
ly
w
o
r
k
i
ng
t
o
w
a
rd
P
hD
i
n
electri
cal
e
n
g
i
n
eerin
g
also
a
t
Univ
ersi
ti
T
un
Hu
ss
ein
O
nn
M
a
lays
ia.
H
i
s
re
search
i
n
t
eres
t
incl
ud
es
pow
er
c
o
n
v
e
rt
ers:
t
opo
lo
gi
es
a
nd
s
t
r
uctures
,
h
ig
h
p
o
w
e
r
den
s
it
y
conv
erter an
d m
u
lt
il
evel conv
erters
.
As
maras
h
i
d
P
onniran
recei
ved
th
e
b
achel
or’s
d
eg
ree
i
n
e
lect
ri
ca
l
e
n
gine
e
r
in
g
from
Un
ive
r
sit
i
Tu
n
Hu
ss
ein
O
n
n
M
a
l
a
ysi
a
,
P
a
rit
Raj
a
,
M
a
laysia,
i
n
2
0
02,
a
nd
t
h
e
m
a
st
er’s
d
eg
ree
i
n
e
l
e
ct
rical
eng
i
neeri
n
g
(po
w
er)
fro
m
Univ
e
r
siti
T
ek
no
lo
g
i
M
alay
si
a
,
J
oho
r
B
ah
ru
,
M
a
l
a
ys
ia
,
in
2
0
0
5
.
T
hen,
he
r
ec
eiv
e
d
the
P
h
D
degree
i
n
elect
rical
e
ngi
neeri
ng
f
r
om
t
he
N
agao
ka
U
n
i
v
e
rsity
o
f
Techn
o
l
o
g
y
,
Na
gao
k
a,
J
apan
.
H
e
i
s
curren
tly
w
orki
ng
a
s
lectu
r
er
w
i
t
h
Univers
iti
Tun
Hussein
On
n
M
a
l
a
ysi
a
.
H
i
s
research
i
n
t
eres
t
i
n
cl
udes
power
c
onv
erter,
u
nd
e
r
g
r
ou
nd
p
o
w
e
r
c
a
b
le
i
n
di
st
ri
buti
o
n
si
de,
and
dem
a
nd
s
i
d
e
man
a
gem
e
n
t
o
f
power
c
o
n
su
mpt
ion
.
M
ohd
A
m
i
rul
Nai
m
K
asi
r
an
r
eceived
the
bac
h
elo
r’s
d
eg
ree
in
e
lec
tri
cal
e
ng
in
eering
(pow
er)
fro
m
U
n
i
ve
rsit
i
Tu
n
Hus
s
e
i
n
On
n
Ma
l
a
ysia,
Pari
t
Ra
ja,
M
a
laysia,
i
n
20
17
a
n
d
t
he
m
a
s
te
r’
s
deg
r
ee
i
n
electrical
e
ng
in
eering
also
from
U
n
i
v
ers
i
t
i
T
u
n
H
u
s
se
in
O
n
n
M
a
l
ay
si
a,
i
n
20
19.
H
e
is
current
ly
w
o
r
k
i
ng
t
o
w
a
rd
P
hD
i
n
electri
cal
e
n
g
i
n
eerin
g
also
a
t
Univ
ersi
ti
T
un
Hu
ss
ein
O
nn
M
a
lays
ia.
H
i
s
re
search
i
n
t
eres
t
incl
ud
es
pow
er
c
o
n
v
e
rt
ers:
t
op
o
lo
gi
es
a
nd
s
t
r
uctures
,
h
ig
h
p
o
w
e
r
den
s
it
y
conv
erter an
d m
u
lt
il
evel conv
erters
.
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