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.
2, June
2
01
9, pp.
662~
6
7
1
ISSN: 2088-
8694,
DOI
:
10.115
91/ijpeds.
v10.
i
2.662-671
662
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
Comparison of m
u
ltiple m
odulat
i
o
n t
e
c
hni
que
s
for various
topologies of m
u
l
t
ilevel con
verters for singl
e
phase
AC
motor drive
Laith
M.
A
k
r
am
A
lsaqa
l
1
,
Ahme
d M. T. Ibrah
eem Alnai
b
2
,
Om
ar Ta
l
a
l
M
ah
mo
od
3
1,
2
D
e
p
a
rtem
en
t o
f
El
ectrical P
o
w
er E
ng
.
Te
c
h
no
lo
gie
s
,
Northe
r
n
Te
c
hni
cal U
nivers
ity,
Iraq
3
D
epartem
e
n
t
of
El
ectrical Tech
no
lo
gies, N
o
rt
he
rn
T
echn
i
cal
Un
i
ve
rs
it
y
,
Ira
q
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Au
g
1
7
,
2
018
Re
vise
d N
ov
1
9
,
201
8
A
c
c
e
pte
d
D
ec 11,
2
0
1
8
Th
ere
are
vario
u
s
typ
e
s
o
f
M
ul
tilevel
Con
v
erters
(
M
C
s
)
i
n
add
i
t
ion
to
v
a
rio
u
s
typ
e
s
o
f
m
o
d
u
l
a
t
io
n
te
c
h
niqu
e
s
f
or
t
he
se
t
yp
e
s
o
f
MCs;
the
chal
len
g
es
i
n
s
e
lect
ing
t
h
e
best
o
n
e
o
f
th
em
w
it
h
regard
t
o
t
h
e
a
m
o
un
t
o
f
t
he
requ
ired
o
f
com
p
on
ent
s
,
an
d
i
t
s
harm
on
ics
con
t
ent
.
S
o,
a
c
om
p
a
r
ison
s
tud
y
a
m
o
n
g
th
e
s
e
ty
p
e
s
ha
s
b
e
e
n
d
o
n
e
in
t
h
i
s
p
a
pe
r.
F
or
c
om
pa
riso
n
s
tu
dy
,
t
h
e
sim
u
l
a
tio
n
o
f
s
e
v
en
l
ev
el
o
f
t
w
o
po
pul
ar
t
opo
lo
gi
es
o
f
M
C
s:
N
eu
tral
P
o
i
nt
Clam
p
e
d
(N
P
C
)
co
nv
erter,
a
n
d
C
ascad
ed-M
Cs
w
ere
carried
out
w
ith
M
a
tl
ab
/Si
m
u
lin
k
s
o
f
t
ware
p
rogram
.
Th
ese
co
nvert
ers
are
used
t
o
d
r
iv
e
a
si
ngle
ph
a
s
e
cap
acit
o
r
s
t
art
m
o
to
r
d
r
ive.
M
ulticarrier
m
odu
lati
o
n
c
ont
rol
tech
ni
ques
are
u
s
e
d
f
o
r
c
o
n
trollin
g
t
h
e
M
Cs
;
t
h
es
e
tech
ni
ques
i
nv
ol
ve
t
wo
m
a
in
t
yp
e:
L
evel
S
h
i
ft
ed
C
arrier
(
LS
C),
and
Ph
ase
S
h
if
ted
Ca
rri
er
(
P
S
C).
Th
e
com
p
ariso
n
i
s
m
a
de
w
it
h
respect
t
o
t
h
e
p
e
rf
orm
a
nce
factors
as,
th
e
am
plit
ude
o
f
t
h
e
T
ot
a
l
H
arm
o
n
i
c
Disto
r
tion
(TH
D
),
a
nd
th
e
D
C
-b
us
ut
ilizat
ion
perf
orm
a
n
ce
w
h
ich
measured
b
y
Roo
t
M
ean
S
qu
are
o
f
t
he
o
u
t
p
u
t
vo
lt
age
Vrm
s
a
t
v
a
riabl
e
m
od
u
l
atio
n
i
n
d
i
ces
a
nd
v
a
riab
le
carrie
r
fre
q
ue
n
c
y.
Based
o
n
s
i
m
u
l
atio
n
resu
lt
s
it'
s
f
o
u
nd,
t
hat
t
h
e
casc
a
d
e
d-M
C
w
i
th
P
S
C
mo
du
la
t
i
o
n
me
t
h
o
d
g
i
v
e
s
b
e
s
t
r
e
su
lt
s,
i
n
a
d
di
ti
on
t
o
t
h
e
A
l
te
r
n
at
ive
P
h
as
e
Opposition
D
isposit
i
on
A
POD
-
L
S
C
mo
dulatio
n
tech
ni
qu
e
(
w
it
h
even
nu
m
b
er
o
f
m
odul
ati
on
f
r
equen
c
y)
g
ener
at
e
th
e
ou
tp
ut
volt
a
ge
w
it
h
a
low
e
r
harm
o
n
ic
c
ont
en
t
com
p
ared wit
h t
h
e o
t
h
e
r techn
i
ques
.
K
eyw
ord
s
:
C
a
sc
ad
ed
M
C
s
LSC
Mu
lt
ile
ve
l C
o
n
v
erte
rs
NPC-MCs
PS
C
THD
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:
Ahm
e
d M.
T. I
braheem
Aln
a
ib,
Depa
rtem
ent o
f
E
lectr
i
c
a
l P
o
wer
Eng.
T
echno
l
o
g
i
es,
N
o
rther
n
Tec
h
n
i
c
a
l
U
ni
ver
s
it
y,
M
osul,
Ira
q.
Em
ail:
ahm
e
d_
alna
i
b
8
5
@
ya
h
oo.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
Mu
l
t
i
le
ve
l
c
o
n
v
e
r
ter
is
m
ater
ia
li
z
e
d
a
s
a
n
a
p
p
ro
priate
a
l
t
er
nat
e
to
n
um
ero
u
s
di
ffic
u
l
ties
pro
duce
d
b
y
the
c
o
n
v
e
n
tio
nal
c
o
nver
t
er
p
ar
tic
ula
r
l
y
i
n
me
dium
a
n
d
hi
g
h
p
ow
e
r
app
l
ica
t
i
o
ns
[
1].
Mu
lti
lev
e
l
pow
e
r
con
v
er
t
e
r
i
s
a
power
e
lec
t
ro
n
i
c
sy
stem
t
ha
t
syn
t
hes
i
ze
s
a
requ
i
re
d
hig
h
o
ut
p
u
t
v
o
l
t
a
g
e
fr
om
num
er
o
u
s
leve
ls
of D
C vo
lta
ge
s
a
s
in
p
u
t
s,
a
h
i
gh ou
t
p
u
t
v
o
l
t
a
ge i
s gener
a
te at
t
h
e o
u
t
p
u
t w
ith
ou
t
u
s
i
n
g
a
t
r
a
n
sf
orm
e
r or
w
ith a
trans
f
or
me
r
w
i
t
h
s
m
a
l
l
t
ra
nsf
o
rm
ation
ra
tio.
Th
is
m
e
t
ho
do
lo
g
y
h
as
s
e
v
er
a
l
b
e
n
efit
s
a
s
c
on
t
r
aste
d
wi
th
t
he
st
a
ndard
p
ow
e
r
c
on
ver
s
i
on
m
a
nner.
I
t
lea
d
s
to
d
e
c
re
ase
v
o
l
tage
stress
on
t
h
e
loa
d
a
n
d
t
o
pro
v
i
d
e
w
a
ve
for
m
s
w
ith
a
h
i
gh
po
w
e
r
qual
i
t
y
.
F
o
r
opera
t
i
n
g
a
t
hig
h
e
r
v
o
lta
ge
s
the
p
o
w
e
r
s
w
i
t
c
h
e
s
are
c
onne
ct
e
d
i
n
a
se
ri
e
s
t
ype
lin
ki
n
g
w
h
i
ch
i
s an esse
n
tia
l fe
ature
of
M
LI. Th
u
s t
h
e sw
itc
hi
n
g
lo
sses
wi
ll
b
e
re
d
u
c
ed
and
t
h
e
effi
ci
e
n
cy
wil
l
incre
a
se [2].
As
a
r
esu
l
t
o
f
a
ll
t
he
se
b
e
n
e
f
its,
it is
s
ug
ges
t
e
d
for
num
er
o
u
s app
l
ica
t
i
o
ns
f
or
e
xam
p
l
e
A
C motor
dri
v
es,
un
i
n
ter
r
u
p
t
e
d
p
ow
er
s
up
p
l
ies,
f
l
e
x
i
ble
A
C
t
ra
nsm
i
ssion
s
y
s
t
e
m
s,
s
tati
c
V
A
R
c
om
pensa
t
o
r
s,
a
ctive
f
ilt
ers,
e
l
e
ct
ri
c
an
d
hy
b
r
id
e
l
e
c
t
ri
c
ve
hi
cl
es
,
in
a
ddi
t
i
o
n
to
it
i
s pro
p
o
se
d fo
r renew
a
ble en
er
gy
s
ource
s
a
s
sol
a
r
ph
o
t
o
v
o
l
t
a
i
c
(P
V
)
,
w
i
nd
tur
b
i
n
e
ge
ner
a
t
i
o
n
s
o
u
rce
,
a
nd
fue
l
c
el
l
s
u
p
p
l
y
.
E
spe
c
ia
l
l
y
t
he
casc
a
de
d
c
o
n
v
er
t
e
r
ty
pe i
t pre
f
e
rred
to o
per
a
te w
ith t
he
se
so
u
ses
be
cause
i
t re
qui
r
e
d isolated D
C
s
u
pply [
1
,
3
]
.
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
Co
mp
ressio
n
of
mu
l
t
i
pl
e mo
du
lat
i
o
n
t
ech
niqu
e
s
fo
r va
ri
ou
s t
o
pol
og
i
e
s
of
…
(La
i
t
h
M.
A
k
ra
m
Al
sa
qal
)
66
3
The
r
e
ar
e
ma
inl
y
t
hre
e
t
ype
s
of
M
Cs
c
o
n
f
i
gura
t
i
o
ns
u
se
d
i
n
i
n
d
u
st
r
i
al
a
p
p
li
c
a
t
i
on
s:
N
eu
t
r
al
P
oi
nt
Cla
m
pe
d
(
N
PC),
C
asc
a
d
ed
H
-br
i
dge
s
in
ve
r
t
e
r
,
a
nd
F
l
yin
g
c
a
p
ac
it
o
rs
(
F
L
C)
t
y
p
e
i
nver
t
e
r
.
A
hu
ge
a
m
o
u
n
t
o
f
stor
age
c
a
pac
i
t
o
r
is
r
eq
uire
d
in
F
L
C
-M
C
ty
pe
i
n
v
e
r
ter,
i
t
'
s
dif
fic
u
lt
t
o
o
b
ta
i
n
t
he
p
r
e
-c
harg
in
g
ca
pa
ci
tors,
mor
e
d
iffic
u
lt
t
o
pack
a
g
e
a
n
d
t
h
o
s
e
b
u
l
k
y
ca
pac
i
t
o
rs
a
re
e
xpe
ns
i
v
e.
I
n
add
i
t
i
o
n
,
it
h
as
t
he
p
rob
l
em
o
f
hig
h
vo
lta
ge
u
nba
la
nce
.
N
P
C
a
nd
casc
a
de
d-M
C
a
re
u
sua
lly
u
se
d
f
o
r
mot
or
d
ri
ve
a
n
d
pow
er
qua
lit
y
i
m
pro
v
e
m
e
nt
app
l
ica
t
i
o
ns
[
4
,
5
]
.
S
o
i
n
t
his
pa
per
t
h
ese
t
w
o
la
t
e
r
t
y
pe
s
w
a
s
s
i
m
ul
at
ed
i
n
ou
r
wo
rk
w
i
t
h
s
ev
en
l
e
v
e
l
,
th
e
sing
le
p
ha
se
c
a
p
aci
t
o
r
start
i
s
e
mplo
ye
d
a
s
l
oa
d
f
o
r
t
h
e
sim
u
la
te
d
c
o
n
v
e
r
ters
b
e
cause
t
hi
s
type
o
f
mo
tors
a
r
e
the m
o
s
t
usual in hom
e
a
pplica
ti
o
n
,
and sm
all in
d
u
str
i
e
s
.
2.
SEVEN LE
V
E
L NEUTRAL
P
OI
NT
C
LAM
P
E
D
M
U
L
T
I
LE
V
E
L CONVERTER
I
n
N
P
C
-M
C,
s
hari
ng
a
c
om
mon
D
C
s
ource
a
nd
i
t
i
s
s
u
b
d
i
vi
de
d
b
y
u
si
ng
ca
p
a
c
i
t
o
r
and
t
h
e
v
o
lt
ag
e
ac
ross
e
a
c
h
c
a
p
aci
t
o
r
is
V
D
C
.
The
numbe
r
of
v
o
lta
ge
l
e
v
e
l
s
in
M
C
ca
n
b
e
i
ncr
ease
d
b
y
add
i
ng
the
ad
d
iti
on
a
l
c
a
p
a
c
ito
rs, d
i
o
d
e
s
an
d po
we
r d
e
vi
c
e
s
.
T
h
e
c
lamp
i
n
g
di
od
e
s
a
re
u
sed
to
lim
it st
r
e
ss
o
n
the
pow
er
de
v
ic
e [
6
, 7]
.
N
P
C-MC
c
ha
l
l
en
ge
s
to
over
c
om
e
spec
if
i
c
o
f
the
w
e
ak
ne
sses
of
c
as
ca
d
e
d-M
C
s
s
o
rts,
s
uc
h
as
i
t
do
e
s
n
o
t
nec
e
ss
i
t
a
t
e
se
p
a
r
a
ted
D
C
s
u
p
p
lie
s.
A
l
t
hou
g
h
,
t
h
ese
t
y
pes
of
i
n
v
e
r
ters
h
a
v
in
g
s
o
m
e
d
is
adva
n
t
age
or
p
r
o
b
l
e
m
like
dc
l
ink
u
n
b
a
l
a
n
ce
[4]
.
G
e
nera
lly
i
n
M
C
,
p
h
ase
v
o
l
t
age
(i.
e
.
vo
l
t
a
g
e
ac
ros
s
one
l
eg)
of
a
n
k-
l
e
vel
c
o
n
v
erte
r
has
k
le
ve
ls
to
ge
ther
w
i
t
h
z
e
r
o
re
fer
e
nce
le
vel,
a
n
d
t
hus
t
he
l
ine
vo
l
t
a
g
e
l
e
v
e
l
(
v
o
l
t
a
g
e
betw
e
e
n
t
w
o
i
n
v
e
r
ter
l
e
gs)
has
k′
leve
l,
i
s equa
l
t
o
2k -
1
le
v
els,
s
o t
h
e
ou
tpu
t
v
ol
ta
ge
o
f
se
ve
n
(
l
i
ne
) leve
l
,
ha
s
f
our
(
phase
le
g
)
leve
l [6].
The
com
p
o
n
e
n
t
re
qu
ire
m
e
n
t
for
th
is
t
y
p
e
o
f
c
onve
rte
r
s
a
s
f
ol
l
o
w
ing
:
N
um
ber
of
D
C
l
i
n
k
ca
paci
t
o
r=
k-1,
numbe
r
of
c
l
a
m
p
in
g
d
i
ode
s
for
ea
ch
p
ha
se
l
eg
=(k-
1)*(k-
2),
and
n
u
m
b
er
o
f
m
a
in
p
ow
er
sw
it
c
h
es
f
or
e
ac
h
p
h
ase
leg
of
c
on
verte
r
=
2
k-2.
S
o,
f
or
s
even
l
e
vel
(4
p
ha
se
l
e
v
e
l
)
N
P
C-M
C
,
t
h
ee
D
C
bu
s
ca
paci
t
o
rs
a
r
e
u
se
d
(C1,
C
2,
a
nd
C
3
)
as
s
ho
w
n
i
n
F
i
gure
1
(a).
Id
ea
l
l
y
vol
t
a
g
e
a
cro
s
s
e
ach
c
a
p
acit
o
r
shou
ld
be
t
hir
d
o
f
t
h
e
am
pl
i
t
ud
e
o
f
t
he
D
C
S
u
p
p
l
y
(
V
D
C
/3),
a
nd
t
h
er
efo
r
e
,
t
h
e
v
o
lta
ge
s
tre
s
s
o
f
e
ve
ry
d
e
v
i
c
e
w
ill
be
dec
r
ea
se
d
t
o
o
ne
c
a
p
ac
it
or
v
olta
ge
l
e
v
e
l
V
D
C
/
3
t
hr
o
u
g
h
c
la
mpi
n
g
d
io
d
e
s.
M
ore
over,
s
i
x
pow
er
s
w
i
t
c
hes
an
d
six
of
pow
e
r
s
w
i
tc
h
and
six
of c
l
a
mpi
n
g di
o
d
es
a
re
used
fo
r
eac
h phase
le
g
.
3.
SEVEN LE
V
E
L CASCAD
ED M
UL
TILEVEL
C
O
N
VE
RTER
The
c
a
sca
d
ed-
M
C
is
one
o
f
t
h
e
s
t
an
dar
d
c
onve
rter
t
y
p
es
u
se
d
for
h
igh
po
we
r
a
p
pli
c
at
ion
s
.
Com
p
ar
ed
t
o
o
t
her
type
s
of
M
Cs,
t
h
is
t
y
p
e
re
qu
i
r
es
s
m
a
ll
est
am
o
un
t
of
c
ompo
ne
nt
s
f
o
r
sam
e
volta
ge
l
e
v
el
w
itho
u
t
f
urt
h
e
r
c
lam
p
ing
d
i
ode
s
or
v
o
l
t
a
ge
b
a
l
a
n
c
i
n
g
c
apac
it
ors
.
The
modu
lar
i
t
y
p
ro
per
t
y
(
i
.
e
.
sim
p
l
e
r
modu
lar
a
rran
g
e
m
e
n
t
)
o
f
t
h
e
s
e
t
y
pes
of
c
onve
r
t
ers
al
low
s
t
o
pra
c
t
i
c
a
l
ly
b
u
ild
in
g
h
i
g
h
n
u
m
b
er
o
f
le
ve
ls
f
or
the
casc
a
d
e
d
-M
Cs
b
y
assem
b
l
i
ng
t
he
u
n
i
ts
w
i
t
h
e
a
se
p
ac
kag
i
ng.
T
he
w
ork
i
n
g
o
f
the
casc
a
de
d-
MC
can
b
e
si
m
p
ly
c
om
pre
h
e
n
de
d.
T
he
o
utp
u
t
v
o
l
t
a
ge
i
s
eq
ui
va
len
t
t
o
the
ac
cu
mu
lat
i
on
o
f
th
e
ou
tpu
t
v
o
l
t
a
g
e
o
f
th
e
in
div
i
dua
l un
i
t
s
t
ha
t
a
r
e co
up
l
e
d i
n
s
er
i
e
s. The
N
o.
o
f
H
-
bridg
e mo
d
u
les
(
H
) w
h
i
c
h
is e
q
u
iva
l
e
n
t to t
he N
o. of
D
C
s
up
p
l
y
de
pe
nd
s
on
t
he
w
h
o
l
e
N
o.
o
f
p
o
s
i
tive
,
n
ega
t
ive
a
n
d
re
fere
nce
le
ve
ls
(
k
′
)
o
f
t
h
e
ca
sc
ad
ed
-MC
.
T
h
e
fo
l
l
ow
i
n
g
eq
ua
ti
o
n
gi
v
es t
he
r
ela
t
i
on b
e
tw
ee
n
H
a
nd
k
′
is [8-
10
]
.
1
/
2
(
1
)
Num
b
er
o
f
m
a
in
p
ower
s
wi
tche
s
f
o
r
ca
sc
aded-
M
C
=
2
k
′
-
2.S
o
f
or
i
m
p
lem
e
n
t
a
t
io
n
se
ven
le
v
e
l
ca
sc
ade
d
-
M
C,
t
hree
o
f
H
-
bri
dge
(
w
h
ic
h
e
q
ual
t
o
t
he
n
um
ber
o
f
D
C
s
o
u
r
ce),
a
nd
tw
el
ve
o
f
p
o
w
e
r
sw
itc
he
s
are
r
e
qu
ired.
O
n
e
d
i
sa
d
v
an
t
a
ge
o
f
the
s
e
t
y
pes
of
c
on
vert
er
s,
i
t
s
nee
d
s
s
e
pa
rate
D
C
p
o
w
er
s
ource
s
t
h
ere
by
li
m
i
ti
ng
i
t
s
u
t
il
ity
a
n
d
a
p
p
l
i
c
a
tio
ns.
A
se
ven
le
ve
l
c
a
s
c
a
d
ed-
M
C
com
p
r
i
se
s
of
3
c
a
s
c
a
de
H
-bri
dg
es
a
s
di
sp
la
ye
d i
n
F
i
gur
e 1(
b).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
2, June
2
019
: 66
2
–
6
71
66
4
(a)
(b)
F
i
gure
1. Bl
o
c
k
dia
gr
am
of
sim
u
lat
i
on o
f
s
e
v
en
l
e
v
e
l
c
onv
e
r
ter:
(
a
)
N
PC
-
M
C
,
(
b
)
C
as
c
a
d
ed
-MC
4.
SINGLE
P
H
A
S
E
CAPA
C
ITOR-START
M
O
T
OR:
S
i
ngle
-
p
h
ase i
nduc
tio
n mo
to
rs are
t
y
p
ica
l
ly
t
w
o
-p
o
l
e or fo
u
r-po
le,
ra
ted
a
t
2 hp or l
e
s
s,
w
hile s
lo
w
e
r
and
grea
ter
m
o
t
o
r
c
a
n
b
e
m
a
n
u
fa
c
t
ured
f
or
s
pec
i
a
l
u
se
s
[1
1
]
.
Th
e
w
o
rk
i
s
c
a
rr
i
e
d
o
u
t
o
n
1
H
P
,
220
V
,
50
H
z
sing
le
pha
se
c
a
p
ac
it
or
s
tar
t
m
otor
a
s
loa
d
f
or
t
he
s
e
v
e
n
l
e
v
el
i
n
ve
r
t
er
a
t
all
c
i
rcu
i
t
co
n
f
i
g
ura
t
i
o
ns,
t
h
e
motor
has t
h
e
par
a
m
e
ter
li
s
t
ed
i
n
Ta
ble
1.
Ta
b
l
e 1.
Mot
or
spec
i
fica
t
i
o
n
s
Pa
r
a
mete
r
Va
lue
Ma
in
w
inding
sta
t
or
r
e
s
i
s
ta
n
c
e
(
R
sm
)
4 Ω
Ma
in
w
inding
sta
t
or
l
ea
k
a
ge
i
nduc
t
a
nce
(
L
sm
)
0.
0203
H
A
uxili
a
r
y
windi
n
g
s
t
a
tor
re
sista
n
ce
(
R
sa
)
6.
5
Ω
A
uxili
a
r
y
windi
n
g
s
t
a
tor
l
e
a
k
a
g
e
induc
ta
n
c
e
(
L
sa
)
0.
021
H
Ma
in
w
inding
r
o
t
o
r
re
sis
t
a
n
c
e
(
R
′
rm
)
3.
61
Ω
Ma
in
w
inding
r
o
t
o
r
le
a
k
a
g
e
induc
t
a
n
c
e
(
L
′
rm
)
0.
0304
H
Ma
in
w
inding m
u
t
u
a
l
i
nduc
t
a
n
c
e
(
L
m
)
0.
1954
H
C
o
m
b
in
e
d
rotor a
nd loa
d
i
n
e
rtia
c
o
e
ffic
i
e
n
t (
J
)
0.
0142
4 K
g
.m
2
C
a
p
a
c
itor-Sta
r
t
(C)
40 µ
F
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
Co
mp
ressio
n
of
mu
l
t
i
pl
e mo
du
lat
i
o
n
t
ech
niqu
e
s
fo
r va
ri
ou
s t
o
pol
og
i
e
s
of
…
(La
i
t
h
M.
A
k
ra
m
Al
sa
qal
)
66
5
4.1.
Mu
lticarr
i
e
r
m
od
u
l
at
ion
tech
n
i
qu
es
M
odul
a
t
i
o
n
t
e
c
h
niq
u
e
u
se
d
fo
r
MC
s
can
b
e
c
l
a
s
si
fi
e
d
i
n
t
o
t
w
o
ca
teg
o
ries
:
Lo
w
S
w
it
c
h
in
g
F
r
equenc
y
(LS
F
)
a
s
sele
ctive
ha
rm
on
i
c
e
lim
i
n
at
ion
m
e
t
h
od
w
h
ic
h
op
e
r
at
ed
a
t
sw
i
t
c
hi
ng
fre
q
u
e
n
c
y
equa
l
t
o
a
fre
que
nc
y
o
f
o
u
t
pu
t
vo
l
t
a
g
e
,
a
nd
H
i
gh
S
w
itc
hi
n
g
F
re
quenc
y
(H
S
F
)
f
or
h
i
gh
sw
i
t
c
hi
n
g
freq
u
e
n
c
y
i
s
con
s
i
d
ere
d
a
b
ove
1
KHz
a
s
S
p
ace
v
ect
o
r
m
eth
od
a
n
d
Mult
icar
rier
m
odu
la
tio
n
te
c
hni
que
s.
I
n
select
i
v
e
harm
on
ic
e
lim
ina
tio
n
me
tho
d
i
s
req
u
i
re
d
a
d
d
iti
o
n
al
p
rec
i
se
iter
at
i
v
e
proce
s
s
t
h
ro
ug
h
so
l
v
i
n
g
its
n
o
n
li
nea
r
equa
t
i
o
n
to pr
o
duce
op
tim
al s
w
itc
hi
n
g
a
n
g
le
. I
n
w
hich t
he S
pac
e
ve
c
t
o
r me
t
h
o
d
i
s mor
e
comple
x
an
d
i
t
nee
d
s
f
u
rth
e
r ca
l
c
ul
ati
o
n
s
, f
u
rt
h
e
r i
s
d
if
fi
cu
lt
y
t
o
b
e ex
t
e
nd
ed
wh
e
n
the
le
v
e
l
o
f t
h
e
con
v
er
t
e
r c
h
an
ges
[5].
The
Mu
lt
i
c
arr
i
e
r
t
echn
i
ques
ar
e
t
h
e
p
o
p
u
l
a
r
m
ethod
used
f
or
M
Cs
c
an
b
e
com
m
on
ly
cate
g
orize
d
i
n
t
o
t
wo
g
roups:
Ph
ase
Sh
ift
e
d
C
a
rri
e
r
(
PS
C
)
a
n
d
L
e
v
e
l
S
hi
ft
ed
Car
r
ier
(
L
SC)
m
o
d
u
l
a
ti
on
t
ec
h
n
iq
ues.
B
o
t
h
modu
la
ti
o
n
t
e
c
hn
i
que
s
ar
e
app
l
ied
for
ca
sc
ade
d
a
n
d
F
LC
c
on
ver
t
e
rs
,
w
h
e
r
e
onl
y
the
LS
C
m
o
d
u
l
a
t
i
o
n
tech
n
i
q
u
es
a
re
app
l
i
ed
f
or N
PC co
nve
rter.
4.1.
1.
Ph
a
s
e s
h
ifted
c
a
rrier m
o
d
ula
t
io
n
tech
n
i
q
u
e
G
e
nera
lly,
a
M
C
w
i
t
h
k
′
v
o
l
t
a
g
e
l
ev
el
s
n
eed
s
k
′
-
1 t
r
i
a
n
g
u
l
a
r
car
riers w
i
t
h
t
he
i
de
nt
ica
l
fr
e
que
nc
y a
n
d
the
i
d
e
n
t
i
c
a
l
p
e
a
k-t
o
-pe
a
k
a
m
pl
i
t
ude,
b
u
t
the
r
e
is
a
p
ha
se
s
hi
f
t
equa
l
to
36
0°
′
1
betw
e
e
n
e
ver
y
t
w
o
adjac
e
n
t
ca
rrie
r
w
a
v
es,
gi
ve
n
by
Th
us
f
or
s
eve
n
l
eve
l
m
ult
ile
ve
l
i
nve
rter
s
i
x
carrier
w
ave
s
a
re
r
equ
i
red
(
V
,V
,V
,V
,V
,V
)
w
i
th
a
60
°
pha
se
d
isp
l
a
c
e
m
e
n
t
s
b
e
t
ween
a
ny
two
ad
jac
e
n
t
ca
rrier
s
as
prese
n
t
e
d
in
F
i
gure
2
(
a
)
.
The
refe
renc
e
w
a
ve
form
V
i
s
pla
c
e
d
a
t
zer
o
r
e
fe
renc
e
and
alw
a
ys
c
om
par
e
d
w
ith
e
a
c
h
o
f
th
e
carri
er
w
a
v
es.
If
t
h
e
ref
e
re
n
c
e
wa
v
e
i
s
g
r
ea
te
r
t
h
a
n
a
car
rier
s
ig
nal,
t
he
n
the
ac
t
i
ve
s
w
itc
hes
corr
espo
n
d
in
g
t
o
t
ha
t ca
rrie
r
are
t
ur
ned O
N
. El
se
,
t
h
e
p
o
w
e
r
sw
itch is sw
i
t
c
he
d O
F
F
[8,
12].
S
i
mulat
i
o
n
of
P
S
C
m
o
d
u
l
a
tio
n
tec
hni
q
u
es
f
or
s
eve
n
l
e
v
el
c
on
ve
rt
e
r
c
a
r
r
i
e
d
o
u
t
u
s
i
n
g
M
a
t
l
a
b
/S
imul
i
n
k
sof
t
w
a
re
i
s
de
pic
t
e
d
i
n
F
i
gure2
(b).
S
ix
c
arrier
w
ave
s
ar
e
re
qu
i
r
ed
t
h
u
s
o
n
e
c
a
rr
i
e
r
wave
u
s
e
d
an
d
t
h
e
n
s
h
i
f
t
e
d
f
i
v
e
t
i
m
e
s
b
y
u
s
i
n
g
T
r
a
n
s
p
o
r
t
D
e
l
a
y
B
l
o
c
k
.
S
w
i
t
c
h
i
ng
f
re
que
n
c
y
of
t
he
c
ar
rier
w
ave
i
s
s
e
t
t
o
9
5
0
H
z
, a
nd 1 K
H
z
.
(a)
(b)
F
i
gure
2.
P
S
C
modu
la
ti
o
n
tec
h
n
i
que.
(
a
)
Princ
i
p
l
e
opera
t
i
o
n
of
th
e
t
ech
niq
u
e
,
(
b
)
S
i
mulation block diagr
am
4.1.
2.
Level
shi
fted
ca
rri
er m
o
d
u
l
a
ti
o
n
tech
niq
u
e
A
s
i
n
pre
v
i
o
u
s
t
e
c
h
ni
q
u
e
fo
r
k
′
l
e
v
e
l
inv
e
rt
er,
k
′
-
1
ca
rri
e
r
w
aves
w
it
h
the
sa
me
f
r
e
que
nc
y
a
n
d
am
plit
ud
e
a
r
e
re
qu
ired.
B
u
t
h
e
re
t
he
se
c
a
rri
er
w
aves
a
re
v
er
t
i
c
a
lly
d
is
p
o
s
e
d
suc
h
t
ha
t
th
e
ban
d
s
t
h
e
y
o
ccup
y
are
cont
i
g
u
ous
i
ns
tea
d
o
f
h
o
r
i
z
o
n
t
a
lly
d
i
s
p
o
se
d
as
i
n
p
h
a
s
e
shi
fted
t
ec
hni
q
u
e.
T
hi
s
m
ode
h
a
s
t
hr
ee
ty
pes
according to the
a
rrangem
e
nt
o
f
carr
i
e
r wave
s
[
9
]:
a)
Wi
t
h
pha
se
a
rray
(In-
phase
D
i
s
pos
i
t
i
o
n I
P
D)
In
t
hi
s t
y
p
e
, al
l t
h
e ca
rri
er
w
a
v
e
s
are t
h
e
sam
e p
h
a
s
e
as
sh
own
in F
i
gur
e3 (
a).
b)
P
h
a
s
e O
ppo
s
i
tion
D
i
s
posi
t
ion
P
O
D
Th
is
t
ec
hn
iq
ue
i
s
als
o
n
a
m
e
d
a
s
"A
nt
i-pha
se
a
rra
n
g
e
m
e
n
t"
b
e
cau
s
e
e
ach
o
f
t
h
e
p
o
sit
i
v
e
c
a
rriers
(c
a
r
r
i
e
r
wav
e
s
ab
ov
e
ze
ro
r
e
f
ere
n
ce)
a
re
i
n
p
h
a
se
,
b
u
t
with
a
p
h
a
se
s
hi
f
t
o
f
1
80
º
re
gar
d
i
n
g
to
t
he
n
e
g
a
t
iv
e
ca
rrier
s (c
arr
i
e
r
waves
b
el
ow z
er
o
refere
nce) as
sh
ow
in F
i
g
u
r
e
3 (
b
).
c)
A
lterna
tive
P
h
a
s
e O
ppos
i
tio
n
D
i
spos
i
tio
n
A
P
O
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
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I
nt
J
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ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
2, June
2
019
: 66
2
–
6
71
66
6
Thi
s
t
echni
qu
e
i
s
a
l
s
o
call
e
d
as
"
Al
t
e
rn
at
ely
re
v
e
rs
e
p
h
a
se
a
rr
ay"
sinc
e
ea
c
h
c
arr
i
e
r
h
as
a
pha
se
s
h
i
ft
o
f
1
80º
f
ro
m t
h
e a
d
j
a
cen
t
ca
rri
e
rs as
p
r
es
en
t
e
d
i
n
Fi
g
u
r
e
3
(c
)
.
(a)
(b)
(c)
F
i
gure
3. L
S
C
m
odu
l
a
t
i
o
n
te
c
h
n
i
qu
e
s
F
o
r P
S
C
m
odu
lat
i
on t
ech
n
i
q
u
e
s,
t
he a
mpli
tu
de of m
o
d
u
l
a
t
i
on
in
de
x
is gi
ven
b
y
m
0
m
1
(
2
)
Where
i
s
t
h
e
grea
t
e
s
t
a
mpli
tude
o
f
refere
nc
e
signa
l
,
and
i
s
the
gre
a
tes
t
a
m
p
l
i
t
u
d
e
o
f
ea
ch
ca
rrier
s
ig
na
l.
I
n
L
S
C
m
o
d
u
l
a
ti
on
tec
h
n
i
qu
e
,
t
he
a
m
p
l
itu
d
e
o
f
m
o
d
u
l
a
tio
n
in
de
x
is
d
iffe
rs
f
rom
PS
C
a
n
d
ca
n
be
d
efi
n
ed
a
s:
∗
0
1
(
3
)
The
a
m
pl
itu
de
of
the
freq
u
enc
y
m
odu
l
a
tio
n
express
i
on (
m
f
) c
a
n be
expr
ess
e
d a
s
:
m
(
4
)
wher
e
f
cr
, and
f
m
ar
e
the
fr
e
qu
enc
y
a
m
p
l
i
t
ude
o
f c
a
rr
i
e
r
and m
odu
la
tio
n
sig
n
a
l
r
e
s
p
ecti
v
e
l
y
[
8
].
S
i
mulat
i
o
n
o
f
L
S
C
m
od
ula
t
i
on
te
c
h
niq
u
e
s
f
or
s
e
v
en
l
e
v
el
c
on
ve
rt
er
i
s
dep
i
c
t
e
d
i
n
F
i
g
u
re4.
S
ix
ca
rrier
wave
s
are require
d to g
ene
r
ate
twel
ve
g
at
i
ng s
i
gna
l
s
.
F
i
gure
4. S
imulat
i
on d
i
a
g
ra
m of
I
P
D
-LS
C
,
PO
D
-
LS
C, A
PO
D
-
LS
C m
odu
la
ti
on
tech
n
i
ques
P
e
rc
entage
o
f
the
TH
D
w
h
ic
h
i
s
a
d
e
g
ree
of
c
l
o
se
ness
in
o
utl
i
ne
b
e
t
w
een
a
w
avefor
m
and
it
s
fu
n
d
am
enta
l
c
o
m
p
o
n
e
n
t,
i
s
use
d
a
s
a
per
f
orm
a
nce
fac
t
o
r
f
or
c
omp
a
r
ison
s
tu
dy
in
t
h
i
s
w
o
rk.
for
a
vo
l
t
ag
e
signa
l
,
the
T
H
D
can
b
e de
fi
n
e
d
as [8,
9]
:
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
Co
mp
ressio
n
of
mu
l
t
i
pl
e mo
du
lat
i
o
n
t
ech
niqu
e
s
fo
r va
ri
ou
s t
o
pol
og
i
e
s
of
…
(La
i
t
h
M.
A
k
ra
m
Al
sa
qal
)
66
7
∑
(
5
)
wher
e
V
h
is the
rm
s
of
h
arm
onic w
h
ic
h
has
o
r
der
h,
a
nd
V
1
is the
rms
valu
e
of t
he
f
u
n
d
am
enta
l
com
p
one
n
t
.
5.
SIMU
L
A
TION
R
ESULT
S
T
h
e
s
y
m
m
e
t
r
y
o
f
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
w
a
v
e
f
o
r
m
s
o
f
m
u
l
t
i
l
e
v
e
l
a
n
d
i
t
s
h
armo
ni
c
c
o
n
t
en
t
a
r
e
re
l
i
a
nt
o
n
m
f
w
h
e
t
h
e
r
i
f
i
t
i
s
o
d
d
o
r
e
v
e
n
.
T
h
e
r
e
f
o
r
i
n
t
h
i
s
s
t
u
d
y
,
t
h
e
e
f
f
e
c
ts
o
f
differ
ent
m
f
v
a
l
ue
s
o
n
t
he
o
u
t
pu
t
v
o
l
t
a
g
e
w
a
ve
form
a
nd har
m
on
ic
c
on
t
e
nt
s have
be
e
n
in
v
es
t
i
ga
te
d fo
r the
L
SC an
d
P
S
C
mo
d
u
l
a
t
i
ng
t
ec
hni
qu
e
s
.
I
n
o
r
d
e
r
t
o
c
l
a
r
ify
the
an
d
rec
ogn
iz
in
g
t
h
e
ty
pe
o
f
the
s
y
m
m
e
t
r
y
of
t
he
o
ut
p
u
t
vo
l
t
a
g
e
o
f
M
C
an
d
its
effec
t
i
n
g
o
n
t
he
s
pec
t
ra
a
na
l
y
s
i
s,
F
igure5
t
o
F
i
g
u
re
8
sh
o
w
t
he
o
u
t
p
u
t
v
olta
ge
w
a
v
efor
m
of
t
he
s
e
v
e
n
l
e
v
el
ca
sc
ade
d
c
onv
e
r
ter
w
i
t
h
d
i
f
fe
re
nt
t
ypes
o
f
m
od
u
l
at
i
o
n
t
e
c
h
ni
q
u
e
s.
F
ig
ure
9
t
o
F
i
g
u
re
1
2
s
how
t
h
e
l
oa
d
c
u
rre
nt
w
ith
c
orre
sp
o
n
d
i
n
g
t
h
e
har
m
on
ic
s
pec
t
rum
a
n
al
ys
i
s
.
The
con
v
e
r
te
r
o
p
e
r
at
ed
w
it
h
sw
i
t
c
h
ing
freq
u
e
n
cy
e
qu
a
l
to 950 Hz (i.
e
.
odd
m
f
=
19) fir
st
t
im
e
t
h
e
n
w
it
h sw
i
t
ch
i
n
g
fr
e
que
nc
y
equa
l
t
o
1
0
0
0
H
z
(i.e.
even
m
f
= 20).
Due
t
o
l
imi
t
e
d
s
pac
e
,
this
p
a
p
er
g
i
v
es
s
eve
n
l
e
v
el
casc
a
d
ed
s
im
ulation
waveform
,
the
remaining
si
m
u
lat
i
on re
su
lt
s of
N
P
C
-MC
is nea
rly t
h
e
sim
ilar
as c
asca
ded
sim
u
l
a
tion
result
s.
(a
)
(
b
)
F
i
gure
5.
T
he
casc
a
de
d-
MC o
ut
p
u
t v
o
l
t
a
ge
u
si
ng I
P
D-L
S
C m
e
tho
d
w
it
h i
t
s
corr
espon
d
i
n
g
f
re
que
nc
y
spe
c
t
rum
:
(a
)
odd
m
f
,
(
b
) even
m
f
(a
)
(
b
)
F
i
gure
6.
T
he
casc
a
de
d-
MC o
ut
p
u
t v
o
l
t
a
ge
u
si
ng P
O
D
-
LS
C
m
e
thod w
i
t
h
its
c
orr
e
spon
d
i
n
g
f
re
que
nc
y
spe
c
t
rum
:
(a
)
odd
m
f
,
(
b
) even
m
f
(a
)
(
b
)
F
i
g
u
r
e
7
. The
c
asca
d
e
d-M
C
o
utp
u
t
vo
lta
ge
u
sing
A
P
O
D
-
LSC m
e
t
h
od
wi
t
h
i
t
s
co
rres
p
ondi
ng
fre
qu
e
n
c
y
spe
c
t
rum
:
(a
)
odd
m
f
,
(
b
) even
m
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
2, June
2
019
: 66
2
–
6
71
66
8
(a
)
(
b
)
F
i
gure
8.
The
c
a
s
c
a
de
d-
MC
out
p
u
t v
o
lta
ge
u
si
ng
P
S
C
m
ethod
w
ith
i
t
s
co
rres
p
o
ndi
ng
fre
qu
e
n
c
y
sp
e
c
t
rum:
(
a
)
odd
m
f
, (b) even
m
f
(a
)
(
b
)
F
i
gure
9.
T
he
casc
a
de
d-M
C
lo
a
d
cu
rr
ent us
i
n
g IPD
-
LS
C
metho
d
w
it
h
its
c
orre
spon
di
n
g
freque
ncy spe
c
t
rum:
(
a
)
odd
m
f
, (b) even
m
f
(a
)
(
b
)
F
i
gure
1
0
.
The
ca
sc
aded-
M
C
l
o
a
d
cur
rent u
s
i
n
g
P
O
D
-LS
C
me
t
hod
w
i
th
i
ts
c
orre
spond
in
g freque
nc
y
spe
c
t
rum
:
(a
)
odd
m
f
,
(
b
) even
m
f
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
Co
mp
ressio
n
of
mu
l
t
i
pl
e mo
du
lat
i
o
n
t
ech
niqu
e
s
fo
r va
ri
ou
s t
o
pol
og
i
e
s
of
…
(La
i
t
h
M.
A
k
ra
m
Al
sa
qal
)
66
9
(a
)
(
b
)
F
i
gure
1
1
. The
c
asca
ded-M
C
loa
d c
u
rre
nt
u
s
i
n
g
A
P
O
D-
LSC m
e
th
od w
it
h i
t
s
co
r
re
sp
ondi
ng
f
re
qu
e
n
c
y
spe
c
t
rum
:
(a
)
odd
m
f
,
(
b
) even
m
f
(a
)
(
b
)
F
i
gure
1
2
. T
h
e
c
asca
ded-M
C
loa
d c
u
rre
nt
u
s
i
n
g
P
S
C
m
e
t
ho
d
w
ith
i
t
s
c
orre
spon
d
i
n
g
freq
u
e
nc
y s
p
ec
trum
:
(
a
)
od
d
m
f
,
(b)
even
m
f
I
t
observe
d
t
h
e
foll
ow
i
n
g
:
1-
In
I
P
D
-LS
C
m
od
u
l
at
ion
tec
h
niq
u
e
,
t
he
o
u
t
p
u
t
vo
ltage
w
av
e
f
orm
is
h
al
f
w
a
ve
s
ymm
e
try
for
o
d
d
m
f
a
nd
odd
s
y
m
m
e
t
r
y
f
or
e
ve
n
m
f
,
th
us
o
n
l
y
od
d
ha
rm
oni
c
s
a
re
a
p
p
e
a
r
in
t
he
h
a
r
m
oni
c
s
s
pec
t
ra
a
t
o
dd
m
f
w
h
i
l
e
even
p
lus
o
dd
ha
rm
on
i
c
s
are
a
p
p
e
ar
a
t
o
p
er
ati
n
g
o
n
e
ve
n
m
f
,
t
hus
its
p
re
f
e
r
to
o
perat
e
t
he
c
onverter
at
odd
m
f
w
hen
us
ing
th
is
t
ec
h
n
i
q
ue.
The
si
g
n
if
i
c
an
t
har
m
o
n
ic
e
nerg
y
i
n
t
h
i
s
t
e
c
h
n
i
q
u
e
i
s
f
o
c
u
s
a
t
t
h
e
car
rier
f
re
quen
c
y
(95
0
H
z
,
1000
H
z
)
.
2-
In
P
OD-LS
C
m
odu
la
ti
o
n
t
ec
hn
i
que,
t
h
e
m
o
s
t
s
ign
i
fica
n
t
h
arm
o
n
i
cs
a
r
e
f
o
u
n
d
i
n
t
w
o
s
i
d
e
b
a
n
d
s
n
e
a
r
b
y
t
h
e
ca
rrier
f
re
que
nc
y
a
s
s
h
o
w
n
i
n
t
h
e
har
m
onic
spec
tra
w
i
t
h
no
har
m
on
ic
a
p
p
ea
r
at
m
ul
t
i
p
l
e
c
a
rr
ier
fre
q
u
e
nc
y.
F
or in
s
t
a
nce,
a
t
=
950 the significant
harm
onics
18
th
a
nd 2
0
th
harmo
n
i
cs.
3-
In
A
P
O
D-LS
C
mod
u
la
t
i
o
n
t
e
c
hni
que,
the
o
u
tp
ut
v
o
lta
ge
w
avef
orm
h
as
o
n
l
y
od
d
sym
m
e
try
f
o
r
o
d
d
m
f
and
ha
s
od
d
q
u
a
r
ter-
w
a
ve
s
y
m
me
try
for
e
v
e
n
m
f
.
Thu
s
onl
y
odd
h
armo
ni
cs
a
re
a
pp
e
a
r
s
in
t
he
f
re
q
u
e
nc
y
s
p
ect
ru
m
wh
en
t
h
e
m
f
i
s
e
v
e
n
,
w
h
il
e
od
d
p
l
u
s
e
ve
n
harm
on
ics
a
r
e
appe
a
r
f
o
r
odd
m
f
i
n
a
d
dit
i
o
n
t
o
t
h
e
TH
D
am
pli
t
ud
e
bec
a
m
e
h
i
g
h
e
r;
s
o,
t
he
m
f
val
u
e
in
t
h
i
s
t
ech
ni
q
u
e
s
houl
d
a
l
wa
y
s
b
e
ev
en
t
o
o
b
t
a
in
b
e
s
t
out
pu
t
vo
l
t
age
qua
l
ity.
T
h
e
m
a
i
n
harm
o
n
ic
s
oc
c
u
r
at
t
he
s
i
d
eb
a
n
d
.
C
ompar
i
ng
the
a
b
ove
t
hre
e
t
e
ch
n
i
q
u
es,
t
h
e
AP
O
D
-LS
C
m
etho
d has
be
t
t
e
r
ou
t
p
u
t
vo
l
ta
ge
qua
l
i
ty
.
4-
In P
S
C
out
p
u
t
vo
l
t
a
g
e w
a
ve
for
m
h
as odd
q
u
a
r
ter
-
w
a
ve
symme
t
r
i
c
f
or bo
t
h
odd
an
d e
v
e
n
m
f
.
I
n
s
eve
n
l
e
v
e
l
M
Cs
w
he
n
em
pl
o
y
in
g
LS
C
m
odu
la
ti
on
tec
h
n
i
que
s,
i
f
t
h
e
m
a
d
ecr
ease
s
d
own
to
0
.66
6
the
n
u
m
b
er
o
f
le
vel
w
i
l
l
d
e
c
r
e
a
se
a
lso
t
o
f
i
v
e
a
nd
s
o
on
for
m
a
l
ow
er
t
h
a
n
0.
33
3
the
n
u
mbe
r
o
f
le
ve
l
w
ill
three
.
F
ig
ure1
3
sh
ow
s
t
h
e
e
f
fe
ct of varia
t
io
n
of
a
m
p
l
itu
de o
f
m
a
o
n
the
n
u
m
be
r
of
l
e
v
e
l
s of the
o
u
t
pu
t
v
o
l
t
a
g
e
of
t
he
M
Cs
w
ith
A
P
O
D
-
LSC
m
o
du
la
tio
n
tec
h
n
i
q
u
e.
A
t
be
g
i
nn
i
n
g
the
m
a
e
qua
l
t
o
0
.
9
t
h
u
s
se
ve
n
o
u
t
p
u
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
2, June
2
019
: 66
2
–
6
71
67
0
vo
lta
ge
w
il
l
p
r
od
uced
,
t
hen
from
0.04
t
o
0
.
08
sec
the
m
a
e
qua
l
t
o
0
.6
t
h
u
s
five
l
e
v
el
o
ut
put
v
o
l
tage
i
s
gene
ra
ted,
fi
n
a
l
l
y
from
0.08
to
0
.12s
ec
,
m
a
equa
l
to
0
.3,
th
ree
leve
l
v
o
lta
ge is a
p
pear
at
t
h
e
o
u
t
p
u
t
.
F
i
gure
1
3
. E
ffe
ct of
mod
u
l
at
i
o
n in
de
x
o
n
t
he num
ber
of
l
e
v
e
l
s o
f
t
h
e o
u
t
p
ut
vol
t
a
ge of M
C
In
t
hi
s
stu
d
y
,
w
e
i
n
v
e
sti
g
at
ed
t
he
e
ffe
ct
s
of
d
i
f
f
e
re
nt
m
f
a
n
d
m
a
va
lue
s
o
n
th
e
ha
rmon
ic
s
co
n
t
en
t
an
d
the
Vrms
of
s
ev
en
l
ev
el
c
a
s
c
a
d
e
d
a
n
d
NPC-M
C
f
o
r
d
if
f
e
re
n
t
t
yp
e
s
o
f
mo
dul
a
t
i
o
n
t
e
chn
i
qu
es
w
h
i
c
h
i
s
giv
e
n
in ta
b
le
2
, a
nd tab
l
e
3.
Tab
l
e
2.
V
a
r
i
a
tio
n
of
THD
v
,
a
nd TH
D
i
b
elo
n
g
to va
r
i
an
t t
h
e
m
f
a
nd
m
a
v
al
ues f
o
r d
i
ff
ere
n
t
modu
la
ti
o
n
tec
hni
que
s
T
y
p
e
s
of c
onve
r
t
e
r
F
re
que
n
c
y
m
o
d
u
la
ti
o
n
inde
x
(m
f
)
M
odula
tion
inde
x
(m
a
)
L
S
C
PS
C
I
P
D
P
O
D
AP
OD
HD
v
HD
i
HD
v
HD
i
HD
v
HD
i
HD
v
HD
i
C
a
s
c
a
d
e
d
-
M
C
1
9
0
.
6
8
.
8
6
0.
01
8
.
3
0
9.
45
28.27
9
.
0
2
.
75
.
95
0.
8
0.
6
0
.
56
0.
4
8
9
.
8
7
0.
6
4
8
.
7
7
.
51
.
15
1
3.
8
1
.
78
4.
8
9
.
46
5.
0
2
.
73
.
44
.
3
2
0
0
.
6
8
9
.
4
1
7.
14
7.
70
8
.
4
2
7.
49
.
94
.
45
0.
8
0
.
36
0
0
.
1
0
7.
55
2
.
2
6
7.
98
.
59
.
39
1
4
.
66
.
26
3.
7
5
.
90
3.
4
5
.
43
.
45
.
21
N
P
C
-
MC
1
9
0.
6
8
.
95
9
.
9
3
8.
3
5
9
.
4
2
8.
3
0
8
.
9
1
.
75
.
88
0.
8
0
.
64
0
.
9
2
0.
5
0
0
.
3
4
0.
6
4
9
.
0
7
.
56
.
16
1
3
.
79
.
72
4.
9
3
.
38
5.
0
8
.
73
.
46
.
27
2
0
0
.
6
7
.
9
9
9.
42
7
.
1
3
7.
62
8
.
4
1
7.
44
.
95
.
41
0.
8
0
.
37
0
.
5
9
0.
1
1
8
.
1
3
2.
2
6
8
.
6
6
.
60
.
17
1
4
.
67
.
26
3.
7
6
.
90
3.
4
5
.
43
.
47
.
22
I
t
i
s
obse
r
ved
t
h
at
t
he
b
e
s
t
TH
D
va
lue
s
a
re
o
b
t
a
i
ne
d
a
t
m
a
=
1,
a
n
d
w
hen
its
d
e
c
re
a
s
e,
a
g
r
eat
nega
t
i
ve
a
ffe
c
t
s
o
cc
urred
o
n
t
he
h
arm
oni
cs
c
on
te
nt
o
f
t
h
e
w
a
ve
f
orm
of
t
he
M
Cs
e
s
p
e
c
i
a
ll
y
w
h
en
e
m
p
lo
ye
d
LS
C te
ch
ni
que
bec
ause
t
he nu
m
ber
of
t
he
ou
t
pu
t
v
o
lta
ge le
v
e
l
w
i
ll
d
e
c
re
ase a
l
so
.
Ta
b
l
e
3.
V
ariat
i
on
o
f
Vr
m
s
belo
n
g
to va
r
i
an
t the
m
a
va
l
ue
s for
diffe
r
en
t m
odu
la
ti
on
tec
h
n
i
que
s
Ty
p
e
s
of
c
onve
rt
e
r
M
odula
t
ion
inde
x
(m
a
)
L
S
C
PS
C
I
P
D
PO
D
AP
OD
Vr
ms
(V
)
Vr
m
s
(V
)
Vr
ms
(
V
)
V
r
m
s
(V
)
Ca
s
c
a
d
e
d
-MC
0.
6
135.
9
136.
3
136.
3
136.
2
0.
8
182.
1
181.
6
181.
6
181.
5
1
228.
6
227
227
226.
8
N
P
C
-
MC
0
.
6
133.
1
133.
5
133.
5
133.
6
0.
8
178.
6
178.
1
178.
1
1777.
9
1
224.
3
222.
5
222.
5
222.
5
I
t
i
s
s
e
e
n
t
h
a
t
t
h
e
D
C
-
b
u
s
u
t
i
l
i
z
a
t
i
o
n
i
n
c
a
s
c
a
d
e
d
-
M
C
i
s
g
r
e
a
t
e
r
tha
n
i
n
c
a
se
o
f
us
i
ng
N
P
C-MC
f
or
motor
drive.
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
Co
mp
ressio
n
of
mu
l
t
i
pl
e mo
du
lat
i
o
n
t
ech
niqu
e
s
fo
r va
ri
ou
s t
o
pol
og
i
e
s
of
…
(La
i
t
h
M.
A
k
ra
m
Al
sa
qal
)
67
1
6.
CONCL
U
S
ION
G
e
nera
lly,
t
h
e
ca
scade
d
-M
C
has
su
pe
ri
or
a
d
v
an
ta
ge
o
ver
o
t
her
t
y
p
e
s,
a
s
i
t
r
eq
ui
re
d
l
o
we
r
a
m
o
u
n
t
of
com
p
o
n
e
n
t
i
n
a
dd
i
t
i
o
n
to
i
t
has
l
e
s
s
h
ar
monic
c
o
nte
n
t
i
n
t
he
o
u
t
p
ut
v
o
l
tage
w
a
v
e
f
orm
.
T
he
h
ar
monic
s
con
t
e
n
t
s
o
f
t
h
e
out
pu
t
vo
l
t
a
g
e
of
t
he
M
C
c
a
n
be
r
e
duc
e
d
by
e
m
p
l
oy
i
ng
mult
icar
rier
m
od
u
l
at
ion
t
e
c
h
ni
q
u
e
s
.
The
P
S
C
m
odu
la
tio
n
t
e
ch
n
i
q
u
e
i
s
t
he
b
e
s
t
m
e
tho
d
c
o
m
pa
r
e
d
w
i
t
h
t
h
e
o
t
h
e
r
a
s
i
t
i
s
o
f
f
e
r
o
u
t
p
u
t
w
i
t
h
v
e
r
y
l
o
w
THD
a
m
p
l
i
t
ude
.
It
i
s
ob
s
e
rv
ed
t
h
e
a
mpli
tude
o
f
th
e
THD
v
a
lu
e
s
o
f
PO
D
an
d
APOD
sch
e
mes
are
l
o
w
e
r
at
m
f
is
e
v
e
n
(
a
t
f
cr
=
1
000
)
c
o
mp
a
r
ed
t
o
t
h
e
THD
v
a
l
u
es
a
t
th
e
m
f
is
o
d
d
(
a
t
f
cr
=
9
5
0
).
I
t
is
s
e
e
n
t
he
A
P
O
D
-
LS
C
modu
la
ti
o
n
t
e
c
hn
i
que
i
s
f
o
u
nd
to
p
erfo
r
m
b
e
t
t
e
r
c
o
mpa
r
ed
w
it
h
t
he
o
t
h
e
r
L
S
C
t
e
c
h
n
i
que
s
a
s
i
t
has
o
d
d
quar
t
e
r
w
a
v
e sym
m
e
try,
t
hus
i
t
pr
ov
i
d
es re
l
ati
v
e
l
y l
o
w
TH
D
valu
e.
REFE
RENCES
[1]
Kh
ou
kh
a
Im
arazene,
E
l
M.
B
erk
o
uk
,
H
achem
i
Chek
ireb
,
"New
d
c-li
n
k
ba
l
a
nci
n
g
al
gorithm
f
o
r
mult
ilevel
inverter
in
p
hotovol
tai
c
s
yste
m",
IEEE
In
tern
atio
nal Co
nf
eren
ce
o
n
Ind
u
s
t
r
i
a
l T
echn
o
l
o
g
y
,
T
o
ronto
,
Cana
da
,
20
17
,
p
p
.
15
9-1
6
4
.
[2]
N.
S
u
s
heel,
Kumar
P
.
S
atis
h
,
"
P
e
rf
orm
a
nce
a
n
al
ysis
o
f
F
P
G
A
b
a
se
d
diode
cl
amped
multile
vel
inverter
f
ed
induct
i
o
n
mo
t
o
r
drive
usi
ng
ph
ase
opposition
di
sposi
tion
mu
ltic
arri
er
b
as
ed
m
odu
latio
n
S
t
rategy",
In
ter
nat
io
nal
Jou
r
n
a
l
o
f
Po
we
r Elect
ronics
and
Dri
ve Sys
t
em
(
I
JPED
S
)
,
vol.
8
,
n
o.
4
,
p
p
.
1
5
1
2
-
152
3,
2
0
17.
[3]
Kel
a
m
B.
M
.
Redd
y,
S
wapn
aji
t
P
at
tna
i
k,
"
N
ovel
sy
mm
etric
an
d
as
y
m
m
e
tri
c
t
o
polog
y
of
m
u
l
til
evel
i
n
v
erter
w
i
t
h
redu
ced
n
um
ber
o
f
s
w
i
tch
e
s",
IEEE Inter
natio
n
a
l Co
n
f
erence o
n
In
dus
tr
ial T
echn
o
l
o
g
y
,
T
o
r
onto
,
Can
ada
,
2
0
1
7
,
pp
.
1
65
-170
.
[4]
M.
E
.
Kathar,
S
.
M
.
Kulkarni,
"
C
omparati
ve
s
tu
dy
o
f
mu
ltilev
e
l
in
ve
rte
r
t
op
o
l
og
ie
s"
,
In
ter
natio
na
l Jou
r
n
a
l
of
En
gi
neer
ing S
c
iences
&
Res
e
ar
c
h
T
echn
o
l
o
g
y
z
,
v
o
l
.
6
,
n
o
.
4,
p
p.
2
2
1
-22
4
,
20
17.
[5]
S
.
U
s
h
a,
C
.
Subram
an
i,
A
.
Ge
et
ha,
"P
erf
o
rm
ance
An
aly
s
is
o
f
H
-
br
idge
a
nd
T
-Bri
dge
M
ul
tilevel
Inverters
for
Harm
o
n
i
c
s
Redu
ct
io
n",
Int
e
rnation
a
l
Jo
ur
nal
of
P
o
wer
Electr
onics
a
n
d
D
r
i
ve S
y
st
em (
I
JPED
S
)
,
v
ol
.
9,
n
o
.
1
,
pp.
2
3
1
-
23
9, 2
01
8.
[6]
M.Ma
d
h
u
Sh
ob
in
i,
J
.
Ka
mala,
R.Rathna,
"
A
na
lysis
and
si
mula
tion
o
f
f
l
y
i
n
g
capac
i
t
or
m
ulti
level
inverter
u
sing
PDPW
M
st
ra
tegy",
International IE
EE
C
onference on Innovati
ve
Mechanisms for
In
dustry A
ppli
c
ati
ons,
India
,
pp.
91
-95
,
2
017
.
[7]
S
o
u
r
abh
K
u
n
d
u
,
S
antu
K
r.
G
iri, S
arban
i
M
uk
herjee,
S
ub
rat
a
B
ane
r
jee,
"
P
e
rf
orm
a
nce
an
al
ys
is
o
f
thre
e-p
h
as
e
f
i
ve-
lev
e
l
N
P
C
in
vert
e
r
by
usi
ng
tri
a
ng
ul
a
r
a
nd
trapezo
id
al
t
riang
u
l
ar
carrier-bas
ed
m
o
d
u
l
ati
o
n
tech
niques
"
,
4
th
IEEE
Int
e
rn
ation
a
l
Co
n
f
er
ence o
n
P
o
wer,
Contr
o
l
&
E
m
bed
d
ed
Syst
ems
,
Al
la
ha
ba
d
,
Indi
a
,
pp.
1
-6
,
2
017.
[8]
P
eg
a
h
H
a
m
ed
a
n
i
,
A
b
b
as
S
ho
u
l
ai
e,
"
A
co
m
p
arati
v
e
stu
d
y
o
f
h
arm
o
n
ic
d
istortion
i
n
m
ul
t
i
carrier
b
ased
P
W
M
sw
it
chi
ng
tech
niqu
es
f
o
r
cas
c
a
d
e
d
H-bri
d
g
e
i
nvert
ers",
A
d
va
nces in
Elect
r
i
ca
l
an
d
Co
mp
ut
er
E
ngineeri
n
g
,
vol.
16
,
no
.
3
,
p
p
.
1
5
-2
4,
2
0
16.
[9]
B
.
V
.
L
.
K
a
l
a
B
h
a
r
a
t
h
i
,
V
.
S
r
i
n
i
v
a
s
a
R
a
o
,
"
C
o
m
p
a
r
a
t
i
v
e
a
n
a
l
y
s
i
s
o
f
mu
lti
carrier
P
W
M
e
leven
le
vel
inver
t
er
w
i
t
h
tw
o
m
o
d
u
l
a
ti
on
w
av
es",
IEE
E
Inter
nati
onal Con
f
er
ence
on
P
o
wer,
Co
n
t
rol
,
Si
gnals a
nd In
stru
ment
a
tion
En
gi
neer
ing,
In
d
i
a
,
2
0
1
7
,
pp.
2
5
6
4-25
72
.
[10]
Has
h
im
H
as
abel
rasul,
X
ian
g
w
u
Y
an,
"Com
pari
son
o
f
M
u
l
ti
carrier
P
W
M
T
ech
ni
qu
es
f
o
r
C
asc
a
d
e
d
H-Brid
ge
Multilevel
Invert
er
",
Int
e
rna
t
i
onal
Jou
r
n
a
l
of Power
El
ectr
onic
s
an
d
Dri
ve S
y
stem
(
I
J
P
EDS),
v
o
l
.
8
,
n
o
.
2,
pp.
8
6
1
-
86
8, 2
01
7.
[11]
Ma
h
m
ou
d
M.
E
lk
ho
ly,
"
O
p
tima
l
e
n
e
rgy
sa
ving
f
or
v
a
r
ia
ble
sp
e
e
d
s
in
g
l
e
p
h
ase
in
du
cti
on
m
o
t
o
r
drives
"
,
19
th
IEE
E
Int
e
rn
ation
a
l
Midd
le E
a
s
t
P
o
wer Sys
t
ems Conference,
Ca
ir
o,
Egypt
,
2
0
1
7
.
p
p
.
7
53
–
764
.
[12]
Bin
W
u
,
a
n
d
Meh
d
i
N
a
rim
a
n
i
,
"
H
ig
h
po
wer
con
v
ert
e
rs
a
nd
A
C
driv
e
s"
,
Se
c
o
nd
E
di
tion
,
P
u
b
l
i
sh
e
d
2
01
7
b
y
Jo
hn
Wiley &
So
ns, I
n
c
.
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