TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 3, March 2
015,
pp. 483 ~ 49
2
DOI: 10.115
9
1
/telkomni
ka.
v
13i3.718
1
483
Re
cei
v
ed
No
vem
ber 1
2
, 2014; Re
vi
sed
De
cem
ber 3
0
,
2014; Accep
t
ed Jan
uary 1
6
, 2015
Three Phase Trinary Source MLI Using Multicarrier
SPWM Strategies
T.Sengolraja
n*
1
, B.Shanthi
2
, M.Arumugam
3
*
1
Dep
a
rtment o
f
EEE, Arunai Engi
neer
in
g C
o
lle
ge, T
i
ruvan
nama
l
ai,
T
a
milnadu, Ind
i
a, Ph ./F
ax: 04
175/2
3
7
789
2
Centralis
ed In
strumentatio
n and Serv
ices
L
abor
ator
y
,
An
n
a
mal
a
i Un
ivers
i
t
y
,
Annam
ala
i
n
a
g
a
r,
T
a
milna
du, India, Mob
ile: +
91-9
486
78
66
1
1
3
Departme
n
t of EEE, Arunai Engi
neer
in
g Col
l
ege, T
i
ruvann
a
m
alai,
T
a
milna
du, India, Ph./F
ax: 0
417
5/23
778
9
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: sengolm
a
h
a
@
gmai
l.com
1
, au_s
ha
n@
ya
h
oo.com
2
,
drmarumuga@y
ahoo.com
3
A
b
st
r
a
ct
T
h
is pap
er pr
esents a co
mpreh
ensiv
e an
alysis of
va
ri
ou
s b
i
po
la
r Mul
t
i
c
a
rri
e
r
Pu
l
s
e Wi
d
t
h
Modu
latio
n
(M
CPW
M) strategies w
i
th S
i
n
u
s
oid
a
l ref
e
renc
e for thre
e p
h
a
se N
i
n
e
lev
e
l
T
r
inary S
ourc
e
cascad
ed
inv
e
rter. A n
e
w
appr
oach
of
ni
ne l
e
ve
ls
is f
o
r medi
u
m
vo
ltage
ap
plic
atio
ns. T
he pr
op
o
s
e
d
topol
ogy uses reduc
ed nu
mb
er
of
sw
itchin
g
devic
es a
nd th
us red
u
ci
ng l
o
s
s
es an
d l
o
w
T
HD i
n
co
mp
ari
s
o
n
w
i
th the conve
n
tion
al top
o
l
o
g
y
. T
he config
ur
ation
of t
he cir
c
uit is si
mp
le a
nd e
a
sy to control. Performanc
e
factors such as
%THD, V
RMS
w
here measur
ed an
d Crest F
a
ctor (CF
)
,
Disto
rtio
n
Fa
cto
r
(DF), Fo
rm
Fa
cto
r
(F
F
)
of output
voltag
e w
e
re
calcul
ated
for
different
mo
du
l
a
tion
in
dices
a
nd the
resu
lts w
e
re co
mpar
e
d
.
VF
PW
M strate
gies pr
ovid
es
mi
ni
mu
m T
H
D
and COPW
M strategy provi
des
hi
gh
er funda
mental V
RMS
output volt
age.
Ke
y
w
ords
:
ca
scade
d multil
e
v
el inverter (C
MLI), total harmo
nic distorti
o
n
(T
HD), multi
c
arrier pu
lse w
i
dth
m
o
dulation (MCPWM),
b
ipol
a
r
, mini
mu
m sw
itches
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Multilevel inverter i
s
used
to synthesi
z
e
a near
by sin
u
soi
dal volta
ge from vari
o
u
s level
s
of DC volta
g
e
s
and
the
p
r
opo
sed
cascaded
H-b
r
idg
e
inve
rter is
use
d
to
re
du
ce th
e
numb
e
r
of
bridg
e
s
and t
he switche
s
.The p
r
op
ose
d
three
pha
se nine level t
r
inary sou
r
ce inverter
req
u
ire a
less nu
mbe
r
of com
pon
ent
s to o
b
tain
same n
u
mbe
r
of voltage lev
e
ls
whe
n
co
mpared to di
ode
clamp
ed a
n
d
flying capa
ci
tor type topol
ogie
s
.The
st
ructure requi
res le
sser
acti
ve swit
che
s
as
comp
ared wit
h
co
nvention
a
l ca
scade
d
H-b
r
id
ge top
o
logy with m
u
ch
red
u
ced
swit
chin
g losse
s
.
Due
to thi
s
, the
swit
chin
g l
o
ss g
e
ts
red
u
c
ed. Al
so
, it
g
enerally regul
arises
the
sta
i
r-ca
se volta
g
e
waveform fro
m
seve
ral DC source
s
which h
a
s
red
u
ce
d ha
rmo
n
ic
content.
Arun et al [
1
]
introdu
ce
d u
n
ipola
r
PWM
control tech
nique h
a
ving
inverted si
n
e
ca
rrie
r
for
Trina
r
y DC source
multilevel inv
e
rter. Pe
rformance eval
u
a
tion of va
rio
u
s unipol
ar
S
P
WM strategi
es of
Trin
ary DC
Source m
u
ltilevel inverter
was di
scusse
d in [2]. Bharath et al [3
] p
r
opo
se
d a
9-Level Tri
nary
DC
sou
r
ce invert
er u
s
ing Emb
edde
d Co
ntroller. Che
c
hn
ya et al [4] aims to extend
the kno
w
le
d
ge
about the p
e
rform
a
n
c
e
of different clamped m
u
ltilevel inverter throug
h harmonic
analy
s
is.
Gnan
a Pra
k
a
s
h et al [5] propo
sed a m
e
thod whi
c
h i
s
well suite
d
for a hig
h
po
wer
appli
c
ati
ons
and it
built
with th
ree
DC
sou
r
ce
s a
nd
six Swit
ches.
Gupta
e
t
al [6] a
nd [
7
] develo
ped
the
topology fo
r
multilevel inv
e
rters to
attai
n
maximu
m
n
u
mbe
r
of l
e
vels fro
m
give
n
DC source
s
a
n
d
a co
mprehe
n
s
ive review
of a re
ce
ntly propo
sed m
u
ltilevel inverte
r
. Jan
s
i
R
ani
et al [8] pre
s
e
n
ted
the impleme
n
tation of 81 level inverter usin
g Tri
nary logi
c. Mohamm
ed
Yaichi et al
[9
]
impleme
n
ted
a mechani
sm
of SVM control strat
egie
s
applied to five level cascaded multi
-
le
vel
inverter.
Sudha
ka
r et al [10] focu
ssed o
n
the d
e
sig
n
of nine
level inverte
r
topolo
g
y for three
pha
se in
du
ction moto
r d
r
ives. Yu Li
u et
al [11]
an
d [
18] su
gge
ste
d
that trina
r
y
hybrid
81
-le
v
el
multilevel inverter fo
r moto
r drive with
zero
co
mm
on-mode voltage
. Bahravar et
al [12] desig
n
ed
a ne
w
ca
sca
ded
multileve
l inverte
r
top
o
logy
with
re
duced va
riety of ma
gnitud
e
s
of DC voltage
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 3, March 2
015 : 483 – 4
9
2
484
sou
r
ces.
Cha
ttopadhyay et
al [13] disti
ngui
she
d
ca
scad
ed H-b
r
id
ge and
neut
ral point cl
am
ped
hybrid a
s
ym
metric m
u
ltile
vel inverter t
opolo
g
y fo
r g
r
id interactive
transfo
rme
r
l
e
ss photovolt
a
ic
power
plant.
Che
o
l-soo
n
K
w
on
et al
[14]
pres
ented
cascad
ed
H-bridge m
u
ltilevel inverte
r
usi
n
g
Trina
r
y DC
source
s. Miran
da et al
[15] evaluated the modulatio
n techni
que
s to multilevel trin
ary
inverter ap
pli
ed to
cu
rrent
active
filters.
Rahil
a
et
al [
16] devel
ope
d a
ne
w 8
1
l
e
vel inverte
r
with
redu
ce
d num
ber of switch
es. Won-kyu
n
Choi
et
al [17] analysed
the perfo
rma
n
ce of
ca
sca
ded
H-b
r
id
ge mult
ilevel inverter employing bi
dire
ctional
switche
s
.
This p
ape
r a
i
ms at co
mprehen
sively a
nal
ysin
g the prop
osed three pha
se ni
n
e
level
Trina
r
y so
urce H-brid
ge
ca
scade
d invert
er u
s
ing va
rio
u
s bip
o
la
r SPWM st
rategie
s
. In this pap
er,
the afore
s
aid
topology was
devel
op
ed u
s
ing MATLAB-SIMULINK.
2. Three Pha
se Nine Lev
e
l Trinar
y
Sou
r
ce Ca
sca
de
d Multile
v
e
l Inv
e
rter
The fu
ndam
e
n
tal H-Bri
dge
ca
scad
ed
to
pology i
n
cre
a
se
s th
e
nu
mber of
com
pone
nts
requi
re
d, whi
c
h in
turn
ma
ke
s the
de
sig
n
co
mplexity and in
crea
se
s the
co
st [1,
2]. It is also
to be
establi
s
hi
ng t
hat the maxi
mum outp
u
t voltage
can
not
go beyo
nd th
e su
m of voltage of in
divid
ual
sou
r
ces
which be
co
mes t
he m
o
st im
p
o
rtant
setb
ac
k of
this topo
logy. Because of the
fore
said
rea
s
on
in
an
appli
c
ation
whi
c
h
req
u
ire
s
hi
gh o
u
tput
voltage fro
m
low voltag
e level, it ne
eds
H-b
r
id
ge m
o
d
u
le in
additio
n
or ste
p
-up t
r
an
sform
e
rs.
T
o a
c
compli
sh this proble
m
a n
e
w topo
logy
prop
osed is
shown in Figu
re 1 to redu
ce
comp
one
nt count.
S
1
S
2
S
3
S
4
V
DC
HB
1
S
5
S
6
S
7
S
8
V
DC
HB
2
3
S
1
S
2
S
3
S
4
V
DC
HB
1
S
5
S
6
S
7
S
8
3V
DC
HB
2
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
3V
DC
HB
2
HB
1
A
BC
V
DC
N
+
_
+
_
+
_
+
_
+
_
+
_
•
Figure 1. Three pha
se ni
n
e
levels Tri
n
ary source Cascaded multilevel inverter
Figure 1
sh
o
w
s th
e top
o
l
ogy of the p
r
opo
sed th
re
e
pha
se
nine
level Trin
ary
sou
r
ce
ca
scade
d mu
ltilevel inverter. It views like a co
nvent
i
onal cascad
e
d
H-b
r
idg
e
m
u
ltilevel inverte
r
apart fro
m
in
put DC
so
urces. The top
o
l
ogy com
p
ri
se
s of floating i
nput
DC source
s co
nne
cte
d
throug
h po
wer switche
s
. The structu
r
e re
qui
re
s lesser
active
swit
che
s
a
s
comp
are
d
with
conve
n
tional
ca
scade
d H-bridg
e
to
polo
g
y
with
mu
ch redu
ce
d
switchi
ng l
o
sses. By u
s
in
g
V
DC
and 3V
DC
, it c
an synthe
size
nine output levels; -4V
DC
, -3V
DC
, -2V
DC
, -V
DC
, 0, V
DC
, 2V
DC
, 3V
DC
and
4V
DC
. The lo
wer inve
rter
gene
rate
s a
n
eleme
n
tary
output voltag
e with
thre
e l
e
vels
and
the
n
the
uppe
r inve
rte
r
ad
ds
or
su
btract
s o
ne l
e
vel fr
om th
e
fundam
ental
wave to
syn
t
hesi
z
e
stepp
ed
wave
s. At this point, the final output voltage leve
l be
come
s the su
m of each terminal voltage
o
f
H-b
r
id
ge [7] and it is given as:
out
H
B
1
H
B2
V=
V
+
V
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Thre
e Phase Trina
r
y So
urce MLI Usin
g Multica
rrie
r
SPWM Strateg
i
es (T.Se
ngol
rajan
)
485
In the prop
osed ci
rcuit design, sup
p
o
s
e
the
n
numb
e
r of H-b
r
idg
e
comp
one
nt h
a
s self-
governi
ng DC source
s in seque
nce of
the power of 3, a predi
ctabl
e
output voltage level is given
as:
n
n
V
=
3
,
n =1,2,3,..........
(2)
Whe
r
e; n is n
u
mbe
r
of H bridge
s
Wavefo
rms o
f
output voltage are den
oted as
(V
out
), uppe
r termi
n
al voltage is (V
HB1
) and
the lower volt
age i
s
(V
HB2
) i
n
verter in
seq
uen
ce. Th
e o
u
tput voltage
has nine
leve
ls in
clud
e
zero
level. Thoug
h
it is clo
s
e
to
a sin
u
soidal
wave,
it ha
s l
o
we
r o
r
de
r h
a
rmo
n
ics. So
it need
s mo
re H-
bridg
e
mo
dul
es o
r
o
u
tput filter to obtai
n
high q
uality o
u
tput voltage
s. Ad
vantag
e
of the propo
sed
multilevel inverter
sche
me
is the eli
m
in
ation of
tra
n
sformer in the
main po
we
r
stage. Ho
wev
e
r,
each
cell
of
the
pro
p
o
s
ed m
u
ltilevel inverte
r
req
u
ire
s
it
s o
w
n isolated
p
o
we
r
su
pply. The
provisi
on of these isol
ated
suppli
e
s i
s
the main
limit
ation in the p
o
we
r ele
c
tro
n
i
c ci
rcuit desi
gn.
So the proposed multilevel inverter i
s
suit
abl
e fo
r ph
otovoltai
c
p
o
wer
gen
erating
sy
ste
m
s
equip
ped wit
h
distrib
u
ted
power sou
r
ce
s [7].
3. Multicarri
er Sine Pulse Width Mo
d
u
lation Stra
tegies
To synthe
size multilevel output AC voltage
usi
n
g
different levels of DC inputs,
semi
con
d
u
c
tor devi
c
e
s
m
u
st be
switch
ed O
N
an
d O
FF in such a
way that de
si
red fun
dam
e
n
tal
is obtain
ed with minimum
harm
oni
c dist
ortion. Th
e
r
e
are different
types of app
roa
c
he
s for t
he
sele
ction
of switchi
ng
strat
egie
s
for th
e
Trin
a
r
y source inverte
r
s. A
m
ong all th
e
PWM meth
od
s
for Trin
ary so
urce casca
d
e
d
inverter,
ca
rrie
r
ba
se
d PWM meth
ods and spa
c
e vector
method
s
are
often
use
d
but
wh
en th
e nu
mbe
r
of
output level
s
is m
o
re
than
f
i
ve, the spa
c
e vecto
r
meth
od
will be very compli
cated with the increase of
swit
ching states. So the carri
er based P
W
M
strategy
i
s
preferred unde
r
this
conditi
on in
Trin
ary
so
urce i
n
verters. T
h
is pa
per fo
cu
se
s
on
carrie
r ba
sed
PWM strate
gies
whi
c
h h
a
ve been ext
ende
d for u
s
e in Trina
r
y source inve
rte
r
by
usin
g multipl
e
ca
rrie
r
s. Multicarrie
r
ba
sed PWM
stra
tegies h
a
ve
more th
an on
e ca
rrie
r
that
can
be trian
gula
r
wave
s or
sa
wtooth wave
s and
so
on. The carrier
waves
can b
e
either bi
pola
r
or
unipol
ar. In this pa
per, a
comp
re
hen
si
ve analysi
s
o
f
the aforeme
n
tioned top
o
l
ogy is ca
rri
ed
ou
t
usin
g bipol
ar multi-carrier
PWM st
rateg
i
es. In th
is p
aper, va
riou
s multica
rrie
r
PWM st
rateg
i
es
like Pha
s
e
Di
spo
s
ition
(PD), Phase Opp
o
sition
Disp
o
s
ition (P
OD), Alternative Phase Opp
o
siti
on
Dispo
s
ition
(APOD), Va
ri
able F
r
e
que
ncy (V
F)
an
d Carrier O
v
erlappi
ng
(COP
WM) were
prop
osed for
three ph
ase n
i
ne level Trin
ary sou
r
ce ca
scade
d invert
er.
For an
m
-level
inverter usi
n
g bipola
r
mul
t
icarrier
strat
egy,
(m-
1
)
c
a
rr
iers
w
i
th
s
a
me
freque
ncy
c
f
and same p
e
a
k
-to
-
pe
ak
am
plitude
C
A
are use
d
.
The re
feren
c
e wave
form
ha
s
amplitude
m
A
and
freque
n
c
y
m
f
are pla
c
ed at zero
referen
c
e. T
he refere
nce
wave is
contin
uou
sly
comp
ared
with ea
ch of th
e ca
rri
er
sign
als. If the ref
e
ren
c
e
wave
is mo
re tha
n
a
carrie
r si
gnal,
then the a
c
ti
ve device
s
co
rre
sp
ondi
ng
t
o
that
ca
rri
er are swit
che
d
ON.
Othe
rwise,
the device
switched O
FF. In this pa
per,
the frequ
en
cy ratio
f
m=
4
0
and m
o
dulation in
de
x
a
m
is varied from
0.8 to 1.
fc
m
m=
f
/
f
(3)
except for VF
PWM
am
C
m
= 2A
/(
m
-
1)
A
(4)
except for
COPWM
3.1. Phase Disposition (P
D) PWM Stra
teg
y
The Pri
n
ci
ple
of PDPWM
strategy i
s
to
us
e
the
sev
e
ral
ca
rri
ers
with si
ngle
m
odulatin
g
waveform. In Phase
Disp
osition all the
carrie
rs
a
r
e
in pha
se an
d
the carrie
rs
are di
spo
s
e
d
so
that the band
s they occup
y
are
contig
u
ous. The m
o
dulation wave is ce
ntere
d
in the middle of
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TELKOM
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Vol. 13, No. 3, March 2
015 : 483 – 4
9
2
486
the ca
rri
er
se
t. Figure 2
sh
ows the multi
c
arri
e
r
a
rra
ng
ement for P
D
PWM st
rateg
y
for
0
.
9
and
21.
Figure 2. Carrier a
r
rang
em
ent for PDPWM Strategy
3.2. Phase O
pposition
Disposition
(POD) PWM Strategy
With the
PO
D
P
WM m
e
thod
the
ca
rrie
r
w
a
v
e
form
s a
b
o
v
e the
ze
ro
re
feren
c
e
v
a
lue
ar
e in
pha
se. The
carri
er
wavefo
rms
belo
w
zero a
r
e al
so
in pha
se b
u
t are 1
80°
pha
se
shifted fro
m
those
above
ze
ro. Figu
re 3 sho
w
s t
he multicar
ri
er a
rra
nge
m
ent for PO
DPWM meth
o
d
for
a
m=
0
.
9
and
f
m=
4
0
.
Figure 3. Carrier a
r
rang
em
ent
for PODP
WM Strategy
3.3. Altern
ati
v
e
Phase Op
position Dis
position (AP
O
D) PWM Strategy
Figure 4. Carrier a
r
rang
em
ent for APODPWM Strateg
y
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TELKOM
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ISSN:
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046
Thre
e Phase Trina
r
y So
urce MLI Usin
g Multica
rrie
r
SPWM Strateg
i
es (T.Se
ngol
rajan
)
487
This
metho
d
req
u
ire
s
ea
ch
of the ei
g
h
t ca
rri
er
wa
ves for a
nin
e
level inve
rt
er to
be
pha
se di
spla
ced from ea
ch other by 18
0° alter
nately
.
Fig.4 sho
w
s the
multicarri
er arra
ngem
e
n
t
for APODPWM method for
a
m=
0
.
9
and
f
m=
4
0
.
3.4. Variable Freque
nc
y
(
V
F) PWM Str
a
tegy
The
numb
e
r of
swit
chin
g
s
fo
r u
ppe
r
and l
o
wer d
e
vice
s of
ch
ose
n
ni
ne l
e
vel thre
e
pha
seT
r
ina
r
y casca
ded
DC so
urce inv
e
rter i
s
mu
ch
more tha
n
that of interme
d
iate switch
e
s
in
con
s
tant freq
uen
cy ca
rri
ers. In
order to
equali
z
e th
e
numb
e
r of
sw
itchi
n
g
s
for
all the switch
es,
variable f
r
equency PWM
st
rategy is
used as illustrated in
Fi
gure
5, in which the carrier
freque
ncy of
the interme
d
iate switch
es is
p
r
op
erly increa
se
d
to balance
the number of
swit
chings for all the switches.
Figure 5. Carrier a
r
rang
em
ent for VFPWM Strategy
3.5. Carrier
Ov
erlapping
(CO) PWM S
t
rateg
y
In the Ca
rrie
r
Overlap
p
ing
strategy,
m -1
carri
e
rs
are dispo
s
ed
su
ch that
the band
s th
ey
occupy ove
r
l
ap ea
ch
oth
e
r, the ove
r
l
appin
g
vertical dista
n
ce b
e
twee
n ea
ch
ca
rrie
r
i
s
c
A/
2
c
(A
=1
)
.
The refe
ren
c
e wavefo
rm is cent
red
in
t
he
mi
ddle
of
t
he ca
rrie
r
sig
nals. The
am
plitude
modulatio
n in
dex m
a
is defined a
s
follows:
am
c
m=
A
/
(
2
.
5
×
A
)
(5)
The ve
rtical
offset of
carri
e
rs for nine
-l
evel
inverte
r
with
COPWM
strate
gy is shown in
Figure 6.
Figure 6. Carrier a
r
rang
em
ent for COP
W
M Strategy
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TELKOM
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Vol. 13, No. 3, March 2
015 : 483 – 4
9
2
488
4. Simulation Resul
t
s
The nine lev
e
l three pha
se Trina
r
y ca
scad
ed DC
so
urce multilevel inverter is
modele
d
in SIMULINK
using Po
we
r System blo
ck
set. Switching si
gnal
s
for Trin
ary cascad
ed sou
r
ce
multilevel inverter a
r
e dev
elope
d usin
g multica
rri
e
r
si
nusoidal PWM strategie
s
.
Simulations
are
perfo
rmed fo
r different values of
a
m
rangin
g
from 0.8 –1
.
Figure 7-1
7
show the si
mu
lated output volt
age of thre
e phase Trin
ary sou
r
ce ca
scade
d
inverter
with
their co
rre
sp
ondin
g
FFT
plot
s
sh
own f
o
r o
n
ly on
e
sample val
ue
of
a
m0
.
9
for
above said
PWM strateg
i
es. Figu
re 1
7
sho
w
s a g
r
aphi
cal
com
pari
s
on
of %THD fo
r vari
ous
strategi
es fo
r different mod
u
lation indi
ce
s.
The
corre
s
po
nding %T
HD
is me
asu
r
e
d
usin
g the FF
T blo
ck
and t
heir valu
es
a
r
e list
ed
in Table 1. T
able 2 sho
w
s the Disto
r
tio
n
Fact
o
r
(a
measure of close
n
e
ss in
shape b
e
twe
e
n
a
waveform an
d its fundam
ental com
p
o
nent) of
the
output voltage of cho
s
e
n
MLI. Table
3
displ
a
ys the
V
RM
S
of fundamental i
n
ve
rter
output
(a
mea
s
ure of
DC bu
s utili
zation). T
able
4
displ
a
y the correspon
ding
Cre
s
t Fa
cto
r
(u
se
d to
sp
ecify pea
k
current ratin
g
of the device
s
).
Table 5 di
spl
a
y the con
s
e
quent Fo
rm
Facto
r
(FF
)
.T
he followi
ng
para
m
eter va
lues a
r
e u
s
e
d
for
simulat
i
o
n
:
DC
1
V
=
100V
,
DC
2
V=
3
0
0
V
, load
(R
=
1
0
0
Ω
)
,
c
f=
2
0
0
0
H
z
and
m
f=
5
0
H
z
.
Figure 7. Output Voltage g
enerated by
PDPWM Strategy
Figure 8. FFT
Plot for Output Voltage of
PDPWM Strategy
Figure 9. Output Voltage g
enerated by
PODPWM Strategy
Figure 10. FF
T Plot for Output Voltage o
f
PODPWM Strategy
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TELKOM
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ISSN:
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046
Thre
e Phase Trina
r
y So
urce MLI Usin
g Multica
rrie
r
SPWM Strateg
i
es (T.Se
ngol
rajan
)
489
Figure 11. Ou
tput Voltage gene
rated by
APODPWM Strategy
Figure 12. FF
T Plot for Output Voltage o
f
APODPWM Strategy
Figure 13. Ou
tput Voltage gene
rated by
VFPWM Strategy
Figure 14. FF
T Plot for Output Voltage o
f
VFPWM Strategy
Figure 15. Ou
tput Voltage gene
rated by
COP
W
M Stra
tegy
Figure 16. FF
T Plot for Output Voltage o
f
COP
W
M Stra
tegy
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TELKOM
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Vol. 13, No. 3, March 2
015 : 483 – 4
9
2
490
Table 1. %THD for Differen
t
Modulation Indices
a
m
PDPWM PO
DPWM
A
P
ODPWM
VFPWM
CO
PWM
1
13.65
13.47
13.20
13.76
18.27
0.95
15.53
15.56
15.56
15.52
20.08
0.9
16.71
16.70
16.67
16.59
21.82
0.85
17.00
16.94
16.82
17.00
23.56
0.8
17.13
16.80
17.25
16.62
25.97
Table 2. %Di
s
tortion F
a
cto
r
for Different Modulatio
n Indice
s
a
m
PDPWM PO
DPWM
A
P
ODPWM
VFPWM
CO
PWM
1
0.02250
0.0425
5.7459
0.0587
0.1871
0.95
0.0302
0.0437
5.7609
0.0987
0.2574
0.9
0.0643
0.014
6.4549
0.2572
0.3778
0.85
0.1133
0.0571
0.0162
0.4405
0.5265
0.8
0.1219
0.0359
6.4145
0.436
0.6437
Table 3. V
RM
S
(Fun
dame
n
ta
l) for Different
Modulation I
ndices
a
m
PDPWM PO
DPWM
A
P
ODPWM
VFPWM
CO
PWM
1
282.8
283.4
282.8
282.9
290.4
0.95
268.7
269.1
268.7
268.7
278.8
0.9
254.5
254.5
254.6
254.5
266.7
0.85
240.4
239.6
240.4
240.4
253.3
0.8
226.2
226.2
226.2
226.3
238.3
Table 4. Cre
s
t Factor for
Di
fferent Modul
ation Indices
a
m
PDPWM
PODPWM
A
P
ODPWM
VFPWM
COPWM
1
1.414
1.414
1.414
1.413
1.414
0.95
1.414
1.413
1.414
1.414
1.414
0.9
1.414
1.414
1.413
1.414
1.414
0.85
1.414
1.414
1.413
1.414
1.414
0.8
1.414
1.413
1.414
1.414
1.414
Table 5. Fo
rm Facto
r
for Different Mo
d
u
lation Indi
ce
s
a
m
PDPWM PO
DPWM
A
P
ODPWM
VFPWM
CO
PWM
1
2.02E
3
INF
INF
2.3575E
3 3.63E
3
0.95
3.3587E
3 0.0134E
6
INF
0.4554E
3 0.0278E
6
0.9
2.1208E
3 0.0127E
6
INF
0.2796E
3 3.3337E
3
0.85
0.5463E
3 0.0239E
6
INF
0.2246E
3 1.6886E
3
0.8
0.9425E
3 0.0226E
6
INF
0.1985E
3 5.9575E
3
It is obse
r
ve
d from Ta
ble
1 that the harm
oni
c co
ntent is foun
d to be mini
mum in
VFPWM st
rat
egy and m
a
ximum in CO
PWM strateg
y
for cho
s
e
n
modulatio
n in
dice
s. Tabl
e
2
sho
w
s that the variation
in harmoni
c content
of the output voltage after seco
nd ord
e
r
attenuation in
dicate
d by % DF is rel
a
tively less
in P
O
DP
WM stra
tegy. From Table 3, it is found
that
the COP
W
M strategy provide
relati
vely
highe
r
DC bus utilization. It is inferred from T
abl
e 4
that CF
is al
most
sam
e
f
o
r all
the stra
tegies
of
the
simulate
d
o
u
tput
voltage. Table 5
in
dicates
that APODPWM ha
s high
er Fo
rm Fa
ctor.
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TELKOM
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ISSN:
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046
Thre
e Phase Trina
r
y So
urce MLI Usin
g Mult
ica
rrie
r
SPWM Strateg
i
es (T.Se
ngol
r
ajan
)
491
Figure 17. %THD V
S
a
m
5. Conclusio
n
In this pap
er,
variou
s mult
icarrie
r
PWM
strategi
es fo
r ch
osen nin
e
level three
phase
Trina
r
y so
urce ca
scade
d inverter h
a
ve
been d
e
velop
e
d and
simul
a
tion re
sult
s are p
r
e
s
ente
d
for
different mo
d
u
lation in
dice
s rangi
ng fro
m
0.8-1.
Va
ri
ous
pe
rform
a
nce fa
cto
r
s li
ke %T
HD,
DF
,
V
RM
S
of fundamental, CF
a
nd FF
have b
een eval
uate
d
, pre
s
e
n
ted
and a
nalysed
.
It is observe
d
that VFPWM strategy p
r
ovi
des re
latively minimum T
H
D. PODPWM
provides relatively lower DF
.
The maximu
m DC b
u
s util
ization i
s
achi
eved in CO
P
W
M st
rategy
(Tabl
e
3). CF
is almo
st sa
me
for all th
e
strategie
s
(Ta
b
le 4
)
. Hi
gh
er F
F
is obt
ained
in AP
ODP
W
M Strategy (T
able
5).
Appro
p
riate
PWM strate
gies may b
e
empl
oyed
depen
ding
on the perfo
rman
ce me
a
s
ure
requi
re
d in a particula
r app
lication.
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hant
hi B, N
a
taraj
a
n
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ar
PW
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e
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v
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ng Inv
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urce Multil
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ar SPW
M Strategies
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urce Multil
evel
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14-1
021.
0
5
10
15
20
25
30
PDPW
M
P
ODPW
M
APODPW
M
VFPW
M
C
OPW
M
%T
H
D
1
0.95
0.9
0.85
0.8
Evaluation Warning : The document was created with Spire.PDF for Python.
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NI
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