Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
6
,
No
. 2,
J
une
2
0
1
5
,
pp
. 35
6~
36
1
I
S
SN
: 208
8-8
6
9
4
3
56
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Multi Carrier based Multile
vel I
n
vert
er with Mi
nimal
Harmonic Distortion
V
.
Ja
muna
, J. Gaya
thri Monicka
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectron
i
cs
Eng
i
ne
ering,
J
e
rusalem
College of
Engineerin
g
,
C
e
ntre f
o
r Collaborative
Res
earch
with
Anna Univers
i
t
y
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 15, 2014
Rev
i
sed
Mar
14
, 20
15
Accepted Apr 12, 2015
This
paper pr
es
ents
perform
ance fe
atur
es
of As
y
m
m
e
tric
Cas
caded
Multilev
e
l inver
t
er. Multi
lev
e
l i
nverters are co
m
m
only
m
odulated b
y
using
multicarr
i
er puls
e
width modulation
(MCPWM)
techn
i
ques such as phase-
shifted m
u
lticar
rier m
odulation
and le
vel-shift
e
d m
u
lticarrier
m
odulation
.
Am
ongst these,
level-shifted
m
u
lticarri
er m
odulation t
echn
i
que p
r
oduces th
e
best harm
onic p
e
rform
ance. Th
i
s
work st
udies about m
u
ltil
evel
i
nverter
with
unequal DC sources using level
shifting MCPWM technique. Th
e
P
e
rform
ances
indices
like To
ta
l
Ha
rmonic Dist
ortion (THD), number of
s
w
itches
and DC S
ources
are cons
idered
.
A procedure to
achiev
e
an
appropria
te
lev
e
l
shifting
is
al
so presented
is this paper.
Keyword:
Asymmetric
Cascade
Multicarrier PWM
Mu
ltilev
e
l in
v
e
rter
Tot
a
l
ha
rm
oni
c di
st
o
r
t
i
o
n
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
J. Gayat
h
ri M
o
nicka,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Jerus
a
l
e
m
C
o
l
l
ege
of
En
gi
ne
e
r
i
n
g,
A
nna
U
n
i
v
ersi
t
y
,
N
a
r
a
yan
a
pu
r
a
m
,
Pall
ik
ar
an
ai
, Ch
enn
a
i 600
10
0,
I
n
d
i
a.
Em
a
il: m
o
n
i
g
a
ya2
0
0
2
@yahoo
.co
m
1.
INTRODUCTION
Th
e m
u
lti
lev
e
l in
v
e
rter
h
a
s in
tro
d
u
c
ed
th
e so
lu
tion
to
in
crease th
e con
v
erter ou
tpu
t
v
o
ltag
e
ab
ove
th
e vo
ltag
e
limits o
f
classical
semico
n
d
u
c
tors.
I
t
f
i
n
d
s
it
s
ap
p
licatio
n
m
a
i
n
ly i
n
i
n
d
u
stri
e
s
s
u
c
h
as
AC
p
o
w
e
r
sup
p
lies,
sta
tic
V
A
R
co
m
p
en
s
a
to
r
s
,
d
r
ive
s
y
ste
m
s
,
etc. A
n
e
w h
ybrid
asy
m
m
e
tric
m
u
ltilev
e
l
in
v
e
rter was
i
n
t
r
o
d
u
ced
wh
ere 2
7
l
e
vel
s
i
s
obt
ai
ne
d wi
t
h
m
i
nim
u
m
num
ber
of swi
t
c
he
s. Thi
s
achi
e
ve
s a bet
t
e
r si
nus
oi
dal
o
u
t
p
u
t
[1
]. On
e of th
e sign
i
f
ican
t adv
a
n
t
ag
es of m
u
ltile
v
e
l con
f
i
g
uratio
n
is th
e
h
a
rm
o
n
i
c redu
ction in
th
e
out
put
wa
vef
o
rm
wi
t
hout
i
n
c
r
easi
n
g s
w
i
t
c
h
i
ng
fre
q
u
ency
or
dec
r
easi
n
g t
h
e i
n
ve
rt
er
po
wer
o
u
t
p
ut
[
2
]
.
Th
e
out
put
v
o
l
t
a
ge
wave
f
o
rm
of a
m
u
l
t
i
l
e
vel
i
nvert
er i
s
com
posed o
f
t
h
e num
ber o
f
l
e
vel
s
o
f
vol
t
a
g
e
s, t
y
pi
cal
l
y
o
b
t
ain
e
d
fro
m
cap
acito
r
v
o
ltag
e
sou
r
ces. The so
-called
m
u
ltilev
e
l starts f
r
o
m
th
ree lev
e
ls. As th
e nu
mb
er
of
lev
e
ls reach
infin
ity, th
e ou
t
p
u
t
THD app
r
o
ach
es zero
[3]. Th
e m
u
ltile
v
e
l in
v
e
rters are b
a
sically classified
in
to
th
r
ee topolo
g
i
es, th
ey are as f
o
llo
w
s
, th
e f
l
yin
g
capacito
r
in
v
e
r
t
er
,
th
e d
i
od
e cla
m
p
e
d
inv
e
r
t
er
an
d
th
e
cascade
d
H-
b
r
i
dge i
n
vert
e
r
.
Al
l
t
h
e t
o
p
o
l
o
gi
es ha
ve sam
e
pro
p
ert
y
of re
d
u
ci
n
g
t
h
e ha
rm
oni
cs [4]
-
[
6
]
.
Cascaded inve
rter
has t
h
e
di
sadvanta
ge tha
t
it needs se
p
a
rate DC
sources bu
t the circu
it layo
u
t
is co
m
p
act
and
vol
t
a
ge
s
h
ari
n
g
pr
o
b
l
e
m
i
s
abse
nt
.
D
u
e
t
o
t
h
ese
a
dva
nt
ages,
t
h
e
casca
ded
i
n
vert
e
r
br
i
dge
has
been
wi
del
y
applied to s
u
c
h
applications
as HVDC, S
V
C, stabilizer
, high power
m
o
tor drive a
nd s
o
on [7],
[8]. The
vari
ous m
odul
ation strategies
have bee
n
int
r
oduced fo
r the cascaded m
u
lti
level invert
ers inorder to
reduce
th
e h
a
rm
o
n
i
c co
n
t
en
ts [9
]. M
u
ltilev
e
l in
v
e
rt
ers
w
ith
t
h
eir t
o
po
log
i
es
w
e
re in
tro
d
u
c
ed
.
O
f
all th
e topolo
g
i
es
cascade
d
has
many adva
nta
g
es whe
n
c
o
m
p
ared with di
od
e cl
am
ped a
n
d
capaci
t
o
r
cl
am
ped
i
n
vert
er
[
1
0]
[
11]
.
A
fu
rt
h
e
r study o
n
cascad
e
d
m
u
l
tilev
e
l in
v
e
rters w
a
s p
e
rform
e
d
in
o
r
d
e
r t
o
h
i
g
h
ligh
t
th
e ad
v
a
n
t
ag
e
o
f
cascad
ed
m
u
ltilev
e
l in
v
e
rter
wh
en
co
m
p
ared with th
e
o
t
h
e
r topo
log
i
es and
t
h
e switch
i
n
g
ch
aract
eristics
sare anal
y
s
ed
.
The co
ncept
of si
n
u
s
o
i
d
al
P
W
M
m
odul
at
i
on wa
s i
n
t
r
o
d
u
ced i
n
a
n
at
t
e
m
p
t
t
o
reduc
e t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
356
–
3
61
3
57
harm
oni
c co
nt
ent
s
at
t
h
e o
u
t
put
vol
t
a
g
e
. L
e
vel
shi
f
t
e
d m
o
d
u
l
a
t
i
on t
e
c
h
ni
q
u
e gi
ves
be
t
t
e
r resul
t
com
p
are
d
with
th
e ph
ase sh
ifted
.
Lev
e
l
sh
ifting
is
don
e to redu
ce t
h
e
harm
onics
at the outp
ut
v
o
l
t
a
ge [1
2]
-[
1
4
]
.
Thi
s
p
a
p
e
r
will in
v
e
stig
ate a con
t
ro
l techn
i
qu
e ap
p
lied to
t
h
e
Hyb
r
i
d
asymmetric cascad
ed
m
u
l
ti-lev
e
l in
verter i
n
o
r
d
e
r to
en
su
re an
efficien
t vo
ltag
e
u
tilizatio
n
an
d better
h
a
rm
o
n
i
c sp
ectru
m
.
Lev
e
l sh
ifting
is a well-
est
a
bl
i
s
hed em
ergi
ng m
odul
at
i
on a
nd c
ont
rol
t
echni
q
u
es
ha
s been
desi
g
n
e
d
an
d di
sc
usse
d. T
h
e l
e
vel
sh
i
f
t
i
n
g
m
e
t
hods
ha
ve
been
i
n
t
r
o
duce
d
a
n
d
res
u
l
t
s
w
e
re
prese
n
t
e
d
.
2.
HYBRID MULTILEVEL INVE
RTER
Th
e stru
cture in
tro
d
u
c
ed
in
t
h
is wo
rk
is an As
ymmetric
cascad
ed
m
u
lti
lev
e
l in
v
e
rter,
wh
ich
u
s
es
u
n
e
qu
al DC So
urces. Th
e
g
e
n
e
ral fun
c
tio
n
o
f
th
is m
u
ltile
v
e
l in
v
e
rter is
th
e sam
e
as
th
at o
f
th
e
o
t
h
e
r two
in
v
e
rters. Th
e
m
u
l
tilev
e
l in
v
e
rter u
s
i
n
g
Asy
mmetric
casc
a
d
e
d-inv
e
rter p
r
ov
id
es a larg
e nu
m
b
er o
f
o
u
t
p
u
t
v
o
ltag
e
lev
e
ls
with
ou
t in
creasin
g
th
e nu
m
b
er o
f
fu
ll b
r
i
d
g
e
uni
t
s
. Thi
s
c
o
n
f
i
g
urat
i
o
n p
r
ovi
des hi
ghe
r vol
t
a
g
e
at
hi
g
h
er m
o
d
u
l
at
i
on f
r
eq
ue
nc
y
due t
o
whi
c
h
t
h
e t
o
pol
ogy
c
a
n
be em
pl
oy
ed f
o
r hi
gh
p
o
w
er ap
pl
i
cat
i
ons
.
Du
e
t
o
t
h
e red
u
ct
i
o
n i
n
t
h
e n
u
m
b
er of DC
S
o
urc
e
s em
pl
oy
ed, t
h
e st
ruct
ure be
com
e
s
m
o
re rel
i
a
bl
e and t
h
e out
pu
t
vol
t
a
ge
has hi
ghe
r res
o
l
u
t
i
o
n d
u
e t
o
i
n
cre
a
sed n
u
m
b
er
of steps. T
h
is configura
tion
recen
tly b
eco
m
e
s v
e
ry
po
p
u
l
a
r i
n
AC
po
we
r su
ppl
y
and a
d
just
a
b
l
e
spee
d dri
v
e ap
pl
i
cat
i
ons. T
h
i
s
i
nvert
e
r
can
avoi
d ext
r
a cl
a
m
pi
ng
di
o
d
es or
v
o
l
t
a
ge bal
a
nci
n
g
capaci
t
o
rs
[
4
]
.
A
n
Asy
m
m
e
tric cascade
d
H-bridge inve
rter circu
it is shown in
Fi
gu
re 1.
Fig
u
re
1
.
Stru
ctu
r
e
o
f
tern
ary
v
o
ltag
e
cascaded
m
u
ltilev
e
l i
n
v
e
rter
Tab
l
e 1
.
Switch
i
ng
state
for po
sitiv
e v
o
ltag
e
V
S1
S2 S3 S4
S5
S6
S7 S8
S9
S10 S11
S12
1
1
1
0
0
0
1 0
1 0 1
0
1
2
0
0
1
1
1
1 0
0 0 1
0
1
3
0
1
0
1
1
1 0
0 0 1
0
1
4
1
1
0
0
1
1 0
0 0 1
0
1
5
0
0
1
1
0
0 1
1 1 1
0
0
6
0
1
0
1
0
0 1
1 1 1
0
0
7
1
1
0
0
0
0 1
1 1 1
0
0
8
0
0
1
1
0
1 0
1 1 1
0
0
9
0
1
0
1
0
1 0
1 1 1
0
0
10
1
1
0
0
0
1 0
1 1 1
0
0
11
0
0
1
1
1
1 0
0 1 1
0
0
12
0
1
0
1
1
1 0
0 1 1
0
0
13
1
1
0
0
1
1 0
0 1 1
0
0
DC S
u
p
p
ly
Co
n
t
ro
ller
Loa
d
H
-
Br
idg
e
-I
H
-
Br
idg
e
-I
I
H
-
Br
idg
e
-I
II
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Multi Carrier
based Multilevel Inverter
with Mi
nimal Harm
onic Distortion
(J. Gay
a
thri
Monicka)
35
8
In t
h
i
s
p
r
o
p
o
s
e
d m
odel
t
r
i
n
a
r
y
DC
v
o
l
t
a
ge
s pr
o
g
ressi
on
s
of
u
n
eq
ual
D
C
sou
r
ces
of
AC
M
L
I a
r
e
use
d
. Thi
s
i
s
m
o
st
popul
a
r
of
une
q
u
al
vo
l
t
a
ge pr
og
ressi
on
wi
t
h
am
pl
it
ude o
f
DC
v
o
l
t
a
ge ha
vi
n
g
rat
i
o
1:
3:
9:
27;
81
...
.
3
N a
n
d t
h
e m
a
xi
m
u
m
out
put
vol
t
a
ge
reac
h t
o
(
(
3
N
-
1
)/
2)
V
dc
. A
C
H
B
co
nsist o
f
3-b
r
idges is
use
d
t
o
gene
rat
e
2
7
l
e
vel
out
p
u
t
f
o
r t
h
e
DC
So
urces
of
9:
3:
1
rat
i
o
.
The
ou
t
put
wa
vef
o
rm
27
l
e
vel
s
as
+
13
Vdc
…. +
1Vdc and zero. By diffe
rent com
b
inations
of the 12
s
w
itches, S1-S12, each inverte
r
level can generate
t
h
ree di
f
f
ere
n
t
vol
t
a
ge o
u
t
p
u
t
s, +
V
dc
, -
V
dc
and zer
o. Let
t
h
e o
u
t
p
ut
of
H bri
dge
-
1
i
s
den
o
t
e
d as V
1
(t), the
out
put
o
f
H
b
r
i
dge
-
2
i
s
den
o
t
e
d as
V
2
(t
) a
nd
H
bri
d
ge
-3
i
s
d
e
not
e
d
as
V
3
(t
)
.
He
nce t
h
e
out
put
v
o
l
t
a
ge i
s
g
i
ven
by
V (t
) =
V
1
(t)
+
V
2
(t)
+
V
3
(
t
)
(
1
)
Switch
i
ng
stat
es are d
e
v
e
loped
fo
r
po
sitiv
e, n
e
g
a
tiv
e and
zero
vo
ltag
e
s as p
e
r t
h
e p
a
ttern
s g
i
v
e
n
in
the switching
Table 1.
The
generate
d gate pulses ar
e
give
n to each switc
h in acco
rda
n
ce
with the devel
ope
d
pat
t
e
rn
an
d t
h
u
s
t
h
e
o
u
t
p
ut
i
s
obt
ai
ne
d.
3.
MULTICARRIER
BASE
D MODULATION MET
H
ODS
Pu
l
s
e
W
i
d
t
h
Mod
u
l
a
t
i
o
n
r
e
f
e
r
s
t
o
a m
e
tho
d
o
f
carr
y
i
ng
inf
o
r
m
at
ion
on
a
tr
ai
n
o
f
p
u
l
s
es
,
th
e
i
n
f
o
rm
a
t
i
o
n
i
s
en
c
o
d
e
d
i
n
t
h
e
w
i
d
t
h
o
f
each
pu
l
s
e
.
T
h
i
s
t
e
ch
n
i
q
u
e
h
e
l
p
s
i
n
m
a
i
n
t
a
i
n
i
n
g
a
c
o
n
s
t
a
n
t
v
o
l
t
ag
e
.
A
m
o
d
u
lat
i
o
n
s
t
rateg
y
f
o
r
m
u
ltile
vel
i
n
verters
is
gi
v
e
n
in
Figu
re 2
.
In
the
carrier-b
ased
m
u
lt
ilev
e
l
m
o
d
u
latio
n, each
level i
n
a
p
h
a
s
e
req
u
ires
a c
a
r
r
i
e
r
o
f
its o
w
n
.
C
a
rri
e
r- b
a
sed
m
o
d
u
latio
n
sch
e
m
e
s
a
r
e
m
a
in
l
y
d
i
vi
d
e
d
into
t
w
o
catego
r
ies:
leve
l
-
sh
if
ted
(LSP
W
M
) and
p
h
ase-shi
f
ted
(
P
SP
W
M
) m
e
t
h
o
d
s
. B
o
th
o
f
these
have
se
v
e
r
a
l
var
i
at
i
o
ns,
w
h
ic
h d
i
f
f
e
r
b
y
th
e a
l
l
o
c
a
t
i
o
n
o
f
m
o
d
u
l
e
ca
r
r
i
e
r
s
w
i
t
h
r
e
s
p
e
c
t
to
ea
c
h
o
t
her.
Fig
u
r
e
2
.
Modu
latio
n
s
t
r
a
t
e
g
i
e
s
f
o
r
m
u
l
t
i
l
e
ve
l
i
nve
r
t
er
s
In al
l
l
e
vel
-
shi
f
t
e
d P
W
M
m
e
t
h
o
d
s, t
h
e ca
rr
i
e
rs of t
h
e m
odul
es
have a f
r
eq
ue
ncy
of
f
car = 1
/T
sw
whe
r
e t
h
e
fre
quency
of the
c
a
rrier signal is
inve
rsely
p
r
o
p
o
rt
i
o
nal
t
o
t
h
e
swi
t
c
hi
n
g
pe
ri
od
o
f
t
h
e
de
vi
ce (T
he
r
a
ng
e of
th
e
f
car i
s
sel
ect
ed b
e
t
w
een
10
kHz
t
o
10
0
k
Hz
). T
h
e re
fere
nce v
o
l
t
a
ge,
on t
h
e
ot
he
r ha
nd
, ca
n ha
v
e
val
u
es
of t
h
e r
a
nge
−
M
V
dc and M
V
dc. T
o
co
ver t
h
e w
hol
e v
o
l
t
a
ge r
a
nge
, t
h
e carri
ers are t
h
e t
r
i
a
ng
ul
a
r
wave
s wi
t
h
sa
m
e
phase a
nd
peak t
o
pea
k
a
m
pli
t
ude an
d
arra
nge
d
vertic
ally, so that the carrier
of t
h
e first
m
odul
e co
ver
s
t
h
e
ra
nge
f
r
om
zero
t
o
Vdc
,
whi
l
e
t
h
e seco
nd
co
ve
r
s
t
h
e
ran
g
e
fr
o
m
Vdc t
o
2
V
d
c
. Th
e
l
a
st
m
odul
e covers t
h
e v
o
l
t
a
g
e
from
(M
−
1)
Vdc t
o
M
V
dc.
T
hi
s m
e
t
hod ar
e gener
a
l
l
y
used i
n
C
M
LI as it
gi
ve
s
reduce
d T
H
D.
There
f
ore, an i
nve
rter
with
M
- m
odul
es i
n
s
e
ri
es i
s
usual
l
y
refe
rre
d t
o
as
an
n
-le
v
el in
ve
rter
and
t
h
e
n
u
m
b
er
of l
e
vel
s
ca
n
be cal
cul
a
t
e
d a
s
gi
ven
i
n
E
q
u
a
t
i
on
(2
).
n
=
2
M
+
1
(
2
)
T
h
e
r
e a
r
e
t
h
r
e
e
k
i
n
d
s
o
f
l
e
ve
l
s
h
i
f
t
e
d
m
o
d
u
l
a
t
i
o
n
t
ech
n
i
qu
e
s
n
a
m
e
l
y
;
P
h
as
e
Oppo
s
ition
D
i
s
p
o
s
it
i
on
(
P
OD
),
A
lte
r
n
ati
v
e
P
h
as
e
Oppos
ition
Dis
pos
ition (A
P
OD),
P
h
ase
Dis
p
o
s
itio
n
(PD).
I
n
the p
h
as
e
opp
os
ition
di
sp
os
i
t
i
o
n
(
P
O
D
)
t
h
e
ca
r
r
i
e
rs
a
b
o
v
e
t
h
e
r
e
f
e
r
e
n
c
e
p
o
i
n
t
,
are
ou
t
o
f
p
h
a
s
e
w
i
th
t
h
os
e
bel
o
w
zer
o
,
b
y
18
0
d
e
gree. In
t
h
e
altern
at
iv
e
ph
as
e
oppo
s
ition
d
i
s
p
o
s
iti
on
(A
P
OD), t
h
e
carriers of
adj
a
cen
t
b
a
n
d
s are
p
h
as
e
s
h
i
f
ted
b
y
180
d
e
gr
e
e
.
In
t
h
e
p
h
a
s
e
d
i
spo
s
ition
(P
D),
all
th
e
carriers
are i
n
p
h
ase
ac
ros
s
all
the
b
a
n
d
s
.
T
h
is
gi
ves rise
to
t
h
e
lo
w
e
st har
m
o
n
ic in
the hi
g
h
er m
o
d
u
latio
n
in
d
i
ces, w
h
e
n
co
m
p
a
r
ed
to the
o
t
her
d
i
s
p
o
s
it
io
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
356
–
3
61
3
59
m
e
t
h
o
d
s
.
T
h
e level s
h
i
f
ted
m
u
l
ticarrier
m
o
d
u
latio
n
o
f
f
e
rs
b
e
tter
har
m
o
n
ic
atte
n
u
atio
n
,
b
u
t also offers
a
n
u
n
e
q
u
a
l
d
e
vice
co
n
d
itio
n.
4.
RESULT AND DIS
C
USSI
ONS
T
h
e f
easib
ilit
y o
f
the
p
r
o
p
osed
P
W
M st
rateg
y
has b
e
e
n
inv
e
sti
g
a
t
ed
a
n
d
v
e
r
i
fied
t
h
ro
u
g
h si
m
u
lat
i
o
n
res
u
lt
s,
f
o
r
b
o
t
h
m
u
lti
le
vel
i
n
verter an
d
m
u
lti
carrier PW
M in
verter,
f
o
r
a
t
w
e
n
t
y
s
e
v
e
n
l
e
vel ca
scad
ed
asy
m
m
e
tric H-B
r
id
ge
in
ver
t
er
.
Th
e pro
p
o
s
ed
techn
i
qu
e
for a twen
ty seven
lev
e
ls
inv
e
rter with
asymmetric
DC
s
o
u
r
ces i
n
vol
ves t
h
e
usa
g
e
of
o
n
l
y
t
h
re
e DC
cel
l
s
.
Th
e v
o
l
t
a
ges a
r
e
gi
ve
n i
n
t
h
e
rat
i
o o
f
9:
3:
1
wi
t
h
whi
c
h
a t
w
ent
y
seve
n l
e
vel
ca
n be
achi
e
ve
d wi
t
h
onl
y
t
h
ree D
C
sou
r
ces.
Th
e sim
u
l
i
nk m
odel
f
o
r a t
w
ent
y
seven
lev
e
l MLI is sh
own
in
Figure 3
th
ey
are created with a se
parate s
ubsyste
m
.
The pul
ses
are ge
nerat
e
d
wi
t
h
t
h
e
devel
ope
d
pat
t
e
rn a
n
d gi
ve
n t
o
t
h
e c
o
r
r
es
p
o
ndi
ng
swi
t
c
he
s
vi
a t
h
e s
u
bsy
s
t
e
m
s
. The 2
7
l
e
vel
o
u
t
p
ut
v
o
l
t
age i
s
sho
w
n i
n
Fi
g
u
re
4(a
)
. Hi
gh
er t
h
e l
e
vel
,
t
h
e ha
rm
oni
cs are re
duce
d
t
o
great
er e
x
t
e
n
t
. To det
e
rm
ine t
h
e
harm
oni
cs i
n
t
h
e
pr
o
pose
d
ci
rcui
t
,
t
h
e F
F
T
anal
y
s
i
s
i
s
pe
rf
orm
e
d w
h
i
c
h
i
s
sh
o
w
n
i
n
Fi
g
u
re
4
(
b
)
.
T
h
is is
the
l
o
g
i
cal
e
x
te
nsio
n
o
f
t
h
e
si
ne trian
g
le
P
W
M m
u
ltile
vel i
nverter,
i
n
w
h
ich
n-
1
carriers
are
need
e
d
f
o
r
an n-
level
in
ve
rter. T
h
e
p
r
ef
e
rre
d ty
p
e
is
P
h
as
e
d
i
spo
s
it
ion.
T
h
e
c
a
rriers are
arra
nge
d in
vertical
s
h
i
f
ts
i
n
conti
n
uo
us
b
a
n
d
s
d
e
fi
ned
b
y
the
leve
ls
o
f
t
h
e
i
n
ver
t
er
.
E
a
c
h
car
r
i
er
has
t
h
e
s
a
m
e
f
r
e
q
u
e
n
c
y
and
a
m
p
l
i
t
u
d
e
.
An n
-
lev
e
l
inv
e
rt
er u
s
i
n
g
l
e
v
e
l sh
ifted
m
u
l
t
i
c
ar
rier
m
o
du
l
a
ti
on
sch
e
m
e
re
q
u
ires
(n
-
1
) t
r
ia
ng
u
l
ar
ca
rr
i
e
r
s
,
a
l
l
h
a
vi
n
g
s
a
m
e
fr
eq
u
e
nc
y
a
n
d
p
e
a
k
t
o
p
e
a
k
a
m
pli
t
ude
, he
nce
for
2
7
-
l
e
v
e
l
i
n
vert
er
, 2
6
ca
rri
ers are
use
d
. M
o
d
u
l
a
t
i
o
n
i
s
gene
ral
l
y
pe
rf
orm
e
d i
n
any
ci
rc
ui
t
t
o
r
e
duce
t
h
e
ha
r
m
oni
c cont
e
n
t
at
t
h
e
out
put
v
o
l
t
a
ge.
The
harm
oni
c
co
nt
ent
aft
e
r
m
odul
at
i
on i
s
anal
y
s
ed
by
t
h
e FFT s
p
ect
r
u
m
shown
i
n
F
i
gu
re 5
(
a)
, a
n
d
5(
b)
respectively.
It is clear from the
FFT analysis that the harm
onics are
reduce
d to
a greate
r
exte
nt after
m
odul
at
i
on. T
h
e va
ri
at
i
o
n
s
o
f
t
h
e
harm
oni
c
cont
e
n
t
p
r
es
e
n
t
at
t
h
e out
put
vol
t
a
ge
be
fo
re
and a
f
t
e
r m
o
d
u
l
at
i
o
n
are clearly see
n
from
the FFT
spectrum
.
Fig
u
r
e
3
.
Sim
u
l
i
nk
m
odel
of
Asym
m
e
t
r
ic
m
u
l
t
i
carri
er PWM
i
nvert
er
W
i
t
h
t
h
e
sam
e
ci
rcui
t
t
h
e
ot
he
r m
odul
at
i
ons
are al
s
o
per
f
o
r
m
e
d. Va
ri
at
i
ons a
r
e
o
n
l
y
wi
t
h
t
h
e
m
u
lt
i
carri
er t
h
at
has
bee
n
ge
nerat
e
d.
O
n
l
y
di
ffe
re
nce i
s
w
i
t
h
t
h
e ca
rri
e
r
s
t
h
at
has
bee
n
gene
rat
e
d
i
n
si
de t
h
e
su
bsystem
s
fo
r b
o
t
h
po
sitiv
e
an
d
n
e
g
a
tiv
e cycles. Th
e m
a
i
n
circu
it
m
o
d
e
l rem
a
in
s th
e same fo
r th
e
o
t
her two
m
odul
at
i
ons.
Al
so t
h
ei
r FFT
anal
y
s
i
s
i
s
per
f
o
r
m
e
d t
o
anal
y
s
e t
h
e harm
oni
cs. A c
o
m
p
arat
i
v
e st
u
d
y
ha
s bee
n
mad
e
to
d
e
m
o
n
s
trate th
e superio
r
ity of th
e
Asymmetr
ic c
a
scad
ed
m
u
lti
lev
e
l in
v
e
rter
o
v
e
r symmetri
c
MLI
and
p
r
ese
n
t
e
d
i
n
Ta
bl
e 2.
F
r
om
t
h
e t
a
bl
e i
t
i
s
obser
ve
d
t
h
at
f
o
r t
h
e s
a
m
e
num
ber o
f
b
r
i
d
ges,
swi
t
ches,
asy
m
m
e
tric M
L
I prov
id
es
m
o
re n
u
m
b
e
r o
f
lev
e
ls. From th
e FFT an
alysis i
t
is o
b
s
erv
e
d
th
at the to
tal
harm
oni
c di
st
o
r
t
i
on c
o
nt
ent
at
out
p
u
t
wa
vef
o
rm
for 2
7
l
e
vel
i
nve
rt
er i
s
fo
u
nd t
o
be
qui
t
e
hi
g
h
a
nd i
t
doe
s n
o
t
meet to international IEEE standa
rd. So t
o
reduce t
h
e THD c
onte
n
t furt
her, m
u
lticarrier PWM technique i
s
in
trodu
ced Ay
mme
tric Cascad
ed MLI.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Multi Carrier
based Multilevel Inverter
with Mi
nimal Harm
onic Distortion
(J. Gay
a
thri
Monicka)
36
0
It
i
s
fo
un
d t
h
at
THD i
s
co
nsi
d
e
r
abl
y
re
d
u
ced a
f
t
e
r m
odul
at
i
o
n i
s
be
i
ng
per
f
o
r
m
e
d. Fr
om
t
h
e
pre
v
i
o
us
w
o
r
k
i
t
i
s
kn
o
w
n
t
h
a
t
t
h
e P
D
t
e
c
hni
que
p
r
od
uces
f
e
wer
ha
rm
oni
c o
n
a
l
i
n
e-t
o
-l
i
n
e
basi
s c
o
m
p
ared
t
o
t
h
e
ot
her
t
w
o t
echni
que
s
bec
a
use i
t
p
u
t
s
ha
rm
oni
c ene
r
gy
di
rect
l
y
i
n
t
o
a
com
m
on m
ode car
ri
er c
o
m
pone
nt
whi
c
h cancel
s
acros
s t
h
e l
i
n
e-t
o
-l
i
n
e
o
u
t
p
ut
s [2]
.
TH
D co
nt
ent
i
s
red
u
ce
d by
ap
pl
y
i
ng
m
odul
at
i
on sc
hem
e
.
From
t
h
e c
o
m
p
ari
s
on
m
a
de bet
w
ee
n
di
f
f
er
ent
m
odul
at
i
o
n sc
hem
e
s, P
D
Tec
h
ni
q
u
e
pr
o
v
ed
t
o
be
t
h
e
bes
t
m
odul
at
i
on t
e
c
hni
que
s c
o
m
p
ared
t
o
t
h
e
ot
he
r
m
odul
at
i
o
n
t
echni
que
s.
(a)
(b
)
Fig
u
re
4
.
(a) Si
m
u
la
ted
ou
tpu
t
wav
e
fo
rm
s o
f
Asymmetric M
u
ltilev
e
l in
v
e
rter
(b
) Harm
oni
cs Spect
r
u
m
of o
u
t
p
ut
v
o
l
t
a
ge
wave
f
o
rm
(a)
(b
)
Fi
gu
re
5.
(a
)
O
u
t
p
ut
v
o
l
t
a
ge
o
f
P
D
m
o
d
u
l
a
t
i
on;
(
b
)
Ha
rm
oni
c s
p
ect
rum
o
f
O
u
t
put
v
o
l
t
a
g
e
(P
D)
Table
2. C
o
m
p
arison
of Asy
m
m
e
tric Multilev
el inverte
r
with and
without
m
odulation
Para
m
e
ters
Sy
mm
et
ric ML
I
Asy
m
m
e
t
r
ic ML
I
W
ithout
M
odulation
Level Shifted
M
odulation
W
ithout
M
odulation
Level Shifted
M
odulation
Nu
m
b
er
of switches
12
12
12
12
Nu
m
b
er
of DC
Sour
ces
3
3
3
3
Fundam
e
ntal voltage
42.
47
50.
12
44.
18
51.
69
h3
9.
24
6.
41
11.
18
0.
17
h5
2.
04
1.
03
4.
07
0.
24
h
7
3.
79
1.
60
2.
12
0.
23
h9
3.
83
0.
17
1.
31
0.
83
Distor
tion factor
(
D
F
1
)
0.
1224
32
0.
0128
43
0.
0596
0.
0128
35
Distor
tion factor
(
D
F
2
)
0.
0232
49
0.
0180
15
0.
0122
0.
0013
7
THD%
25.
09
18.
89
9.
66
4.
8
5.
CO
NCL
USI
O
N
Opt
i
m
al
swi
t
c
hi
n
g
st
rat
e
gy
of m
u
lt
ic
a
r
r
i
e
r
for
Hybri
d
Asymmetric Multi Le
v
e
l Inv
e
rter
has
bee
n
prese
n
t
e
d
.
Si
m
u
li
nk m
odel
s
for
vari
ous
l
e
vel
shi
f
t
i
ng
m
e
t
hods l
i
k
e
PD an
d A
P
O
D
are p
r
esent
e
d. T
h
e
b
e
h
a
v
i
our of hyb
rid
m
u
lti le
v
e
l in
v
e
rter is
p
r
esen
ted
with an
d
witho
u
t
i
m
p
l
e
m
en
tin
g
Mu
lticarrier st
rateg
y
.
Asy
m
m
e
t
r
i
c
MLI To
p
o
l
o
gy
u
s
es red
u
ce
d n
u
m
ber of DC
so
urces t
h
us d
ecr
easi
ng t
h
e c
o
m
p
l
e
xi
t
y
and t
h
e
cost
of t
h
e ci
rcui
t
.
M
o
re
ove
r, t
h
i
s
app
r
oach e
n
a
b
l
e
s t
o
obt
ai
n
a t
w
ent
y
seve
n
-
l
e
vel
co
n
v
ersi
on
wi
t
h
onl
y
t
h
ree
d
c
bus
l
e
vel
s
. T
h
i
s
red
u
ces t
h
e c
o
st
an
d
of
fers
t
h
e m
o
re num
ber
of
l
e
vel
s
a
t
t
h
e o
u
t
p
ut
wi
t
h
a l
east
n
u
m
b
er
of
0
0.
02
0.
04
0.
0
6
-1
0
0
-5
0
0
50
10
0
Ti
m
e
V
o
l
t
ag
e(
V
)
0
10
20
0
5
x 10
-3
H
a
r
m
oni
c
o
r
der
F
unda
m
e
n
t
a
l
(
50
H
z
)
=
51.
69
,
T
H
D
=
4.
8
%
M
a
g (
%
o
f
Fu
ndam
e
n
t
a
l
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
356
–
3
61
3
61
pri
m
ary
devi
ces and
DC
v
o
l
t
a
ge so
urc
e
s. T
h
e res
u
l
t
s
for bot
h of the techni
que
s are then com
p
ared a
g
ains
t
v
a
ri
o
u
s
p
e
rfo
r
man
ce in
d
i
ces. Fro
m
th
e co
mp
ariso
n
, it is ob
serv
ed
th
e THD
ob
tain
ed
with
MCPW
M
Inv
e
rt
er
is lesser th
an
th
e MLI. By increasing
th
e num
b
e
r o
f
step
s,
wave
f
o
rm
appr
oache
s
t
h
e desi
red si
n
u
s
o
i
d
al
sha
p
e
and T
HD i
s
re
duce
d
t
o
IEE
E
st
andar
d
. P
r
o
pos
ed w
o
rk ca
n be ext
e
nde
d
t
o
t
h
ree p
h
ase
and t
h
e sam
e
can be
realised
in hard
ware t
o
d
r
iv
e
h
i
gh
p
o
wer
m
o
tors s
u
c
h
as
P
M
BLDC m
o
tors a
n
d so on.
REFERE
NC
ES
[1]
K.
Ramani,
et a
l
., “New h
y
brid
27 level m
u
ltil
evel inver
t
er fed
induction m
o
tor
drive”,
International Journal of
Recent Trends
in
Engin
eering
, vo
l. 2
,
2009
.
[2]
Carrara
et al
., “
A
new m
u
ltilev
e
l PWM m
e
thod: A theoretical
anal
y
s
is”,
I
EEE T
r
ans.Power
Electron
,
v
o
l
.
7,
pp
.
497–505, 1992
.
[3]
Thoegersen
et a
l
., “Improved modulation
techniques for PWM-
drives”,
I
E
EE Trans. Ind. Electr
o
n
, V
o
l. 44
, pp
.
87–95, 1997
.
[4]
Loh
et al
.,
“
I
m
p
lem
e
nta
tion and
control of distr
i
b
u
ted PW
M
cascaded m
u
ltil
eve
l
i
nverters with m
i
n
im
al harm
onic
distortion and co
mmon-
mode
voltage”,
IEE
E
T
r
a
n
s. Power
El
ectr
o
n
, vol. 20
, pp
. 9
0–99, 2005
.
[5]
Chetan
ya Gupt
a
et al.,
“
H
arm
onic Anal
y
s
is of Seven and Nine
Level Casc
ade
Multilev
e
l Inver
t
er using Multi-
Carrier
PWM Technique”,
Intern
ational Journal of
Pow
e
r Electronics
and Drive
System
, Vol 5
,
N
o
1, 2014.
[6]
Gnana P
r
akas
h
et
al
.,
“
A
New Multilev
e
l Inv
e
r
t
er with Redu
ce
d Num
b
er of Switches”
,
Intern
ational Journal
of
Power Electronics
and Drive Sys
t
em
, Vol 5, No 1
,
2014
[7]
Czarkows
k
i
et al.
,
“
M
ultilev
e
l
sele
ctiv
eharm
onic e
lim
ina
tion
PW
M techniq
u
e in ser
i
es-co
nnect
ed vol
tag
e
inverters”, in
Pr
oc. Industry App
licat
ions Annu
.
Meeting,
pp. 145
4-1461, 1998
.
[8]
Grath
et al
., “
M
ultic
arri
er PW
M strategi
es for m
u
ltil
evel
invert
er
s”,
IEEE Trans. Ind. Electron
, v
o
l. 49, pp
. 858–
867, 2002
.
[9]
J. Rodr´
ı
guez
et al
., “Multilev
e
l
inverters: A survey
of t
opolog
i
e
s, controls and
applications”,
IEEE T
r
ans. Ind.
Electron,
vol. 49
, pp
. 724–738
, 2
002.
[10]
M.
Ma
linowski
et a
l
.
,
“
A
surve
y
on c
a
scad
ed m
u
ltil
evel
inv
e
rte
r
s”,
I
E
EE Trans. I
nd. Electron
, vo
l. 57
, pp
. 2197–
2206, 2010
.
[11]
R. Gupta
et al
.
,
“
S
witching char
act
eriz
ation of c
a
scaded m
u
ltil
ev
el-inv
erter-
contr
o
lled s
y
st
em
s”,
IEEE T
r
ans. Ind.
Ele
c
tron
, vol. 55
, pp
. 1047–1058
, 2008.
[12]
M.
S.
A.
Dahidah
et al.
,
“Single carrier
sinusoi
dal PWM equivalent selective h
a
r
m
onic elimination for a five lev
e
l
voltag
e
source inverter
”,
El
ec
tr. Power
Syst
. Res
., vol. 78
, pp
. 182
6–1836, 2008
.
[13]
R. Naderi
et a
l
., “Phase shifted carrier PWM techni
qu
e for general cascad
ed inverters”,
IE
EE Trans.
P
o
we
r
Ele
c
tron
, vol. 23
, pp
. 1257–1269
, 2008.
[14]
B.P. McGrath
et
al
., “
O
ptim
ized
space vector s
w
itching sequen
ces for m
u
ltilev
e
l inver
t
ers”
,
IE
EE T
r
ans. Power
Electron,
vol. 18
, pp
. 1293–1301
, 2003.
BIBLIOGRAPHIES
OF AUTHO
R
S
V. Jamuna
is
P
r
ofes
s
o
r in Electr
i
ca
l and E
l
ectron
i
cs
Engin
eering Dep
a
rtm
e
nt, J
e
rus
a
lem
College of Eng
i
neer
ing, Indi
a.
S
h
e received
her B.E. d
e
gre
e
in Ele
c
tri
cal
& Ele
c
troni
cs
Engineering in 1
999, M.E. d
e
gree in Power El
ectronics and Drives in 2005 and Ph
D from Anna
University
in 20
10. She has secured fifth univ
e
rsity
r
a
nk in P.G degree. She h
a
s 15
y
e
ars of
teaching
exper
i
ence. She h
a
s pu
blished ov
er 90
technical paper
s
in na
tiona
l an
d
int
e
rnat
ional
conferen
ces
pro
c
eedings
/jou
r
nals
.
Her r
e
s
ear
ch in
t
e
res
t
includ
es
Dr
ives
and
Neura
l
Networks
.
E.Mail: jamuna_
22@
y
a
hoo
.com
J.
Ga
yath
ri
Mo
n
i
ck
a
is curren
t
l
y
pursuing
her P
h
.D in E
l
e
c
tri
cal
& E
l
ec
troni
cs
E
ngineer
ing,
at
Jerusalem college of Eng
i
neer
ing, Anna univ
e
r
s
ity
,
Chenn
a
i.
She receiv
ed her
B.E. degree in
Electrical & Electronics Engine
ering in 2002, M.E. degr
ee in Power Electronics
and Drives in
2007. She h
a
s
8
y
ears of
teaching exp
e
rien
ce.
She has pub
lis
hed over
8
tech
nical pap
e
rs in
nation
a
l and inte
rnation
a
l confer
e
n
ces
proc
eed
ing
s
/
journ
a
ls.
E.Mail: monig
a
ya2002@
y
a
hoo.com
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