Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
4
,
No
. 2,
J
une
2
0
1
4
,
pp
. 22
3~
23
2
I
S
SN
: 208
8-8
6
9
4
2
23
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
Simulation Investigation of SPWM,
THIPWM and SVPWM
T
e
chniques for
Thr
e
e Phase
V
o
ltage Sour
ce Inverter
Z
u
lkifil
ie
Bin
Ibra
him, Md. Lito
n Hossa
in,
Isma
d
i
Bin
B
u
gis, Nik Mu
n
a
ji Nik Mah
a
di,
Ahmad
S
h
ukri
Abu
H
a
sim
Department o
f
P
o
wer Electronics
and Driv
e,
Facu
lt
y of
El
ec
tric
al
Engine
ering,
Un
iversiti
T
e
knika
l
Mala
ysi
a
Me
lak
a
,
Me
la
ka,
Malay
s
ia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 21, 2014
Rev
i
sed
Mar
20
, 20
14
Accepte
d Apr 3, 2014
Pulse width mod
u
lation (PWM) techniqu
e is
one of the vital issues for power
electronic circu
i
t contro
l. A nu
mber
of Pulse
width modulation (PWM)
techn
i
ques ar
e increasing
l
y
app
l
ied in
ma
n
y
new industrial app
lications th
at
require super
i
or performance. Th
e most
widely
applied PWM technique for
three-ph
ase vo
ltage source
inv
e
rter
s
are Sine Pulse Width
Modulation
(SPWM), Third
Harmonic Injection
Pulse Width Modulation
(THIPWM)
and Space Vect
or Pulse W
i
dth
Modulation (SVPW
M
).
SPW
M
is the m
o
st
simple modulation techniqu
e that can
realize easily
in analog circuit.
However, it has
some drawbacks such
as high
er total harmonic distortion
(THD), lower switching frequ
ency
a
nd not capable in over
modulation
region. THIPWM and SVPWM both pr
ovide bett
er THD com
p
ared to
SPWM. SVPWM shows lower
THD in ove
r modulation
region
and in h
i
g
h
frequency
application compared to
THIP
W
M
.
Thes
e thre
e te
chniques
a
r
e
discussed, analyzed and compar
ed in
terms of
modulation index, switchin
g
frequency
and inverter
input voltag
e
in this
paper.
The modeling an
d
simulation for all PWM techniqu
es have been done b
y
using
MATLAB/S
I
MULINK and Ori
g
in 6.1
.
F
r
om
th
e sim
u
lat
i
on res
u
lts, SVPW
M
shows the best performance
and m
eet IEEE 519 standard
of current
harmonics lev
e
l.
Keyword:
SP
W
M
THIP
W
M
SVP
W
M
THD
Copyright ©
201
4 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
:
Zu
lk
ifilie Bin
Ib
rah
i
m
,
Ass
o
ciate Professor,
Depa
rt
m
e
nt
of
Po
wer
El
ect
ro
ni
cs a
n
d
D
r
i
v
e,
Facu
lty of Electrical Eng
i
n
eerin
g
,
Un
iv
ersiti Tekn
ik
al Malaysia Melak
a
,
H
a
ng
Tu
ah
Jay
a
, 761
00
Du
r
i
an
Tun
g
g
a
l, Melak
a
, Malaysia.
Em
a
il: d
r
zu
lk
ifilie@u
te
m
.
ed
u.my
1.
INTRODUCTION
Pul
s
e
W
i
dt
h M
o
d
u
l
a
t
i
on t
e
c
hni
que
pr
od
uc
es ac out
p
u
t
v
o
l
t
a
ge w
h
ere t
h
e i
n
p
u
t
of t
h
e
i
nvert
er i
s
dc
vol
t
a
ge
. It
i
s
achi
e
ve
d by
adj
u
st
i
n
g t
h
e d
u
t
y
rat
i
o
of t
h
e i
nvert
er c
o
m
ponent
s. It
gi
ves t
h
e best
resul
t
s
co
m
p
ared
t
o
an
y o
t
h
e
r ex
tern
al con
t
ro
l tech
n
i
q
u
e
s [1
].
Ou
tpu
t
wav
e
form
q
u
a
lity, syst
e
m
lo
ss and
efficien
cy
have
bee
n
dire
ctly affected
by these techniques
[2].
A
nu
mb
er of Pu
lse
wid
t
h
m
o
du
latio
n (PWM) techn
i
q
u
es
are use
d
t
o
o
b
t
a
i
n
t
h
e va
ri
at
i
on
of
o
u
t
p
ut
v
o
l
t
a
ge an
d
fre
que
ncy
.
S
P
W
M
,
THI
P
W
M
and
SV
P
W
M
are m
o
st
attractiv
e co
n
t
ro
l PW
M tech
n
i
q
u
e
s in
the real wo
rl
d
[3
]-[5
]
. SPWM is th
e si
mp
lest p
opu
lar
co
n
t
ro
l
tech
no
log
y
wh
ich
is
u
s
ed
wid
e
ly in
the in
v
e
rters
[2
]. Bu
t it h
a
s some d
r
awb
a
ck
s su
ch
as
po
or ou
tpu
t
wave
form
quality, weak m
odulation a
b
ility
on active
powe
r and rea
c
tive
powe
r,
very
narrow linea
r ra
nge
,
h
i
gh
er to
tal h
a
rm
o
n
i
c d
i
sto
r
tio
n
(THD) an
d lo
wer effec
tive u
tilizatio
n
o
f
DC v
a
lu
e [2
], [6
]. THIPWM is
widely
used s
upe
rior
performance com
p
ared t
o
SPW
M
i
n
res
p
ect
of
re
duce
d
ha
r
m
oni
c cur
r
ent
ri
p
p
l
e
,
opt
i
m
i
zed swi
t
c
hi
ng
se
que
n
ce an
d i
n
c
r
ea
sed
v
o
l
t
a
ge
tran
sfer ratio
s [7
].
SVPW
M provides
t
h
e highest
ach
iev
a
b
l
e fu
nd
am
en
tal o
u
t
pu
t vo
ltag
e
with lo
wer h
a
rm
o
n
ic d
i
sto
r
tion
o
f
th
e ou
tpu
t
cu
rren
t,
gr
eat
fl
exib
ilit
y
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
22
3
–
23
2
22
4
optimise switching waveform
an
d are
wel
l
s
u
i
t
e
d f
o
r h
a
r
d
wa
r
e
im
pl
em
ent
a
t
i
on
[
8
]
,
[
9
]
.
In
SVP
W
M
m
e
t
hods
,
a
rev
o
l
v
i
n
g
re
fe
rence
v
o
l
t
a
ge
vect
o
r
i
s
pr
ovi
ded
as
vol
t
a
ge re
fere
nce
as a re
pl
ace
m
e
nt
of t
h
ree
p
h
ase
m
odul
at
i
ng w
a
ves. T
h
e m
a
gni
t
u
de an
d f
r
eq
ue
ncy
of t
h
e fu
n
d
am
ent
a
l
co
m
pone
nt
i
n
t
h
e l
i
n
e si
de are
cont
rol
l
e
d
by
t
h
e m
a
gni
t
ude
an
d
fre
q
u
enc
y
, res
p
ect
i
v
el
y, of
t
h
e
r
e
f
e
r
e
n
ce
v
ector
. The stud
y of
SVPW
M
rev
eals t
h
at
u
tilizes DC bu
s vo
ltag
e
m
o
re effectiv
ely wh
en co
m
p
ared wit
h
SPW
M
.
SVPW
M and
THIPW
M
can
obviously
reduce t
h
e c
u
rrent ha
rm
onic c
o
m
pone
nt, c
o
m
p
aring wit
h
SP
W
M
; the
voltage utilization ca
n
be
rai
s
ed
by
1
5
.
5
% [
10]
.
S
V
P
W
M
i
s
pr
o
b
ab
l
y
t
h
e best
am
on
g al
l
t
h
e P
W
M
t
ech
ni
q
u
e
s
f
o
r
va
ri
abl
e
f
r
eq
ue
ncy
dri
v
e ap
pl
i
cat
i
o
n
[
11]
. B
eca
use
of i
t
s
s
u
pe
ri
or
pe
rf
orm
a
nce chara
c
t
e
ri
st
i
c
s, i
t
has
bee
n
fi
ndi
ng
wi
de
sprea
d
application in recent yea
r
[12].
These
three differ
e
n
t PWM techniques are
discus
s
e
d a
nd a
n
alyz
ed the
per
f
o
r
m
a
nce.
2.
GENER
A
L
T
H
EOR
Y
OF DIFFE
RENT PULS
E-WIDTH MODUL
A
TION TECHNIQUES
2.
1.
Basic Principl
e of Sin
u
soid
al Pulse width
Modulation
Si
ne
pul
se
wi
dt
h m
o
d
u
l
a
t
i
on i
s
t
h
e
si
m
p
lest
P
W
M
t
ech
ni
q
u
e a
nd
is v
e
r
y
p
opu
lar
i
n
indu
str
i
al
ap
p
lication
s
.
A l
o
w f
r
e
que
n
c
y
si
ne wa
vef
o
rm
of
desi
re
d f
r
eq
ue
ncy
i
s
com
p
ared
wi
t
h
t
h
e
hi
g
h
fre
que
nc
y
carrier t
r
iangul
ar wa
ve.
Wh
en
th
e i
n
stan
taneo
u
s v
a
l
u
e
o
f
th
e triang
le wav
e
is lesser th
an th
at of t
h
e sin
e
wav
e
, th
e
PWM o
u
t
p
u
t
si
g
n
al is in
h
i
gh
l
e
v
e
l (1
). Ot
h
e
rwise it is tu
rned
in
t
o
th
e l
o
w lev
e
l
(0). Th
e lev
e
l
swi
t
c
hi
n
g
e
dge
i
s
pr
od
uce
d
at
every
m
o
m
e
nt
of t
h
e si
ne
wav
e
i
n
t
e
rsect
s wi
t
h
t
h
e t
r
i
a
ng
ul
ar
wave
. T
h
e rat
i
o
o
f
m
odulating si
gnal am
plitude and c
a
rrier
signal am
plit
ude is called
m
odulation in
dex t
h
at controls the
am
pl
i
t
ude o
f
t
h
e ap
pl
i
e
d
out
put
vol
t
a
ge
. T
hus t
h
e di
ffe
re
nt
t
r
i
ppi
n
g
p
o
s
i
t
i
ons res
u
l
t
i
n
vari
a
b
l
e
d
u
t
y
cy
cl
e of
th
e ou
tpu
t
waveform
. The
pul
ses so
p
r
od
uce
d
are
gi
ven
t
o
t
h
e i
n
ve
rt
er c
o
n
t
rol
s
.
2.
2.
Basic Principl
e of Third-har
m
onic
-in
j
ecti
o
n Pulse wid
t
h
Modulation
Th
e sinu
so
i
d
al
PW
M is u
n
a
ble to
fu
lly u
tili
ze th
e DC b
u
s
su
pp
ly v
o
ltage an
d
THD is also
h
i
gh
er.
So,
t
h
e t
h
i
r
d h
a
rm
oni
c i
n
ject
i
o
n
p
u
l
s
e
wi
dt
h
m
odul
at
i
on
(T
HIP
W
M
)
t
ech
ni
q
u
e
was
dev
e
l
ope
d t
o
i
n
c
r
e
a
se t
h
e
in
v
e
r
t
er
p
e
rfo
rman
ce. Ph
uong
H
u
e Tran [8] co
n
s
i
d
er a
wav
e
fo
r
m
co
m
p
r
i
sin
g
of
a fund
am
en
tal co
mp
on
en
t
wi
t
h
t
h
e
acc
um
ul
at
i
on
o
f
a t
r
i
p
l
e
-f
re
que
ncy
t
e
rm
,
s
in
s
in
3
(
1
)
Whe
r
e
an
d A
i
s
a param
e
t
e
r t
o
be
o
p
t
i
m
i
zed w
h
i
l
e
kee
p
i
n
g t
h
e m
a
xim
u
m
am
pl
i
t
ude o
f
y
(t
)
un
de
r
uni
t
y
. S
o
l
v
i
n
g
equat
i
o
n
(
1
),
t
h
e re
qui
re
d
wa
v
e
fo
rm
i
s
:
s
in
1/6
s
in
3
(2
)
All trip
le h
a
rmo
n
i
cs
p
a
ss th
ro
ugh zero at the
s
e
values
of
. If
we sub
s
titu
te th
e v
a
l
u
es of
/
3
i
n
(
2
)
,
t
h
e
n
we
have
a m
a
xim
u
m
am
p
l
i
t
ude o
f
=
√
3
/2
at these a
n
gles.
It
i
s
pro
b
abl
e
t
o
i
n
crease t
h
e
am
pl
i
t
ude of t
h
e m
odul
at
i
ng
wave
f
o
rm
by
a fact
or o
f
K so
t
h
at
t
h
e ful
l
out
put
v
o
l
t
a
ge
ran
g
e
of
t
h
e i
n
vert
er
i
s
a
g
ai
n
use
d
.
If
t
h
e m
odul
at
i
n
g
wav
e
f
o
rm
i
s
exp
r
ess
e
d as:
sin
1
/6
sin
3
(3
)
Th
e v
ital
factor, K for
a
p
e
ak
v
a
lu
e of u
n
ity sh
ou
l
d
satisfy
t
h
e
limit.
2
/
√
3
(4
)
In
ject
i
n
g
one
si
xt
h
of t
h
e t
h
i
r
d ha
rm
oni
c com
pone
nt
t
o
t
h
e
f
u
n
d
am
ent
a
l
com
pone
nt
gi
ves t
h
e
fo
llowing
m
o
du
latin
g
wav
e
form
s fo
r t
h
e three-ph
ase:
2
/√3sin
1
/6
sin
3
(
5
)
2
/
√
3
s
i
n
1/6
s
in
3
(
6
)
2
/
√
3
s
i
n
1/6
s
in
3
(
7
)
The
ge
nerating PW
M tec
h
nique is t
h
e sam
e
as SPWM.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
S
i
mu
la
tion
In
vestig
a
tion
o
f
SPWM, THIPWM
and
S
VPW
M Tech
n
i
q
u
e
s
fo
r Th
ree… (Zu
l
kifilie Bin
Ibra
h
i
m)
22
5
2.
3.
Basic Principl
e of Space
Vec
t
or
Pulse width Mod
u
lation
Space
Vect
or
PW
M is a
s
p
e
c
ial switching schem
e
of
the six
powe
r transistors
of a
three
phase
po
we
r c
o
n
v
e
r
t
e
r.
A t
h
ree
-
p
h
a
se v
o
l
t
a
ge
so
urce
P
W
M
i
n
v
e
rt
er m
odel
i
s
sho
w
n i
n
Fi
gu
re
1.
S1
t
o
S
6
are t
h
e
six
po
wer switch
e
s of th
e i
n
verter th
at shape th
e ou
tpu
t
wav
e
fo
rm
.
W
h
en
an
up
p
e
r tran
sistor is switch
e
d
on,
i
.
e. S
1
,
S
3
or
S
5
i
s
1
,
t
h
e
c
o
r
r
e
sp
on
di
n
g
l
o
w
e
r t
r
a
n
si
st
o
r
i
s
swi
t
c
he
d
of
f,
i
.
e. S
2
,
S
4
or
S
6
i
s
0.
He
nce,
t
h
e
on
and
o
f
f
st
at
es o
f
t
h
e
u
p
p
er t
r
an
si
st
ors
S1
, S
3
a
n
d
S
5
ca
n
be
u
s
ed t
o
c
ont
r
o
l
t
h
e
out
put
wa
ve
fo
rm
[12]
.
Figure 1.
Thre
e-phase vo
l
t
a
g
e
so
urce
P
W
M
I
nve
rt
er
The
rel
a
t
i
ons
h
i
p bet
w
een
t
h
e swi
t
c
hi
ng
v
a
ri
abl
e
and
th
e lin
e-t
o
-line vo
ltag
e
v
e
cto
r
i
s
gi
ven
as
fol
l
ows:
1
10
01
1
1
0
1
(8
)
The rel
a
t
i
o
ns
hi
p bet
w
een t
h
e swi
t
c
hi
n
g
va
ri
abl
e
and the phase voltage
vector
is
calcu
lated
from
th
e fo
llo
wi
ng
eq
u
a
tion
:
2
1
1
12
1
1
1
2
(9
)
For eac
h s
w
itching c
o
m
b
ination a
voltage
s
p
ace vect
or
ca
n be
c
o
nstructe
d using below
e
q
uation:
∗
(1
0)
Accord
ing
to
eq
u
a
tion
s
stated ab
ov
e th
e ei
gh
t switch
i
n
g
vecto
r
s,
ou
tpu
t
lin
e to
n
e
u
t
ral
v
o
ltag
e
and
lin
e-to
-li
n
e
v
o
l
tag
e
s in term
s o
f
DC-li
n
k V
0
to
V
7
are
gi
ve
n
i
n
Ta
bl
e
1.
Tabl
e
1.
Swi
t
c
hi
n
g
Vect
o
r
s,
Phase
V
o
l
t
a
ges
an
d
Out
put
Li
ne t
o
Li
ne
V
o
l
t
a
ges i
n
t
e
rm
s o
f
V
d
c
Voltage
Vectors
Switching vector
s
L
i
ne to neutr
a
l vol
tages
Line to line voltages
A B
C
V
an
V
b
n
V
cn
V
ab
V
b
c
V
ca
V
0
0
0
0
0 0
0 0 0
0
V
1
1
0
0
2/3
-
1
/3
-
1
/3
1
0
-
1
V
2
1
1
0
1/3
1/3
-
2
/3
0
1
-
1
V
3
0
1
0
-
1
/3 2/3
-
1
/3
-
1
1
0
V
4
0
1
1
-
2
/3
1/3
1/3
-
1
0
1
V
5
0
0
1
-
1
/3
-
1
/3
2/3
0
-
1
1
V
6
1
0
1
1/3
-
2
/3 1/3
1
-
1
0
V
7
1
1
1
0 0
0 0 0
0
The switc
hing diagram
shown in Figure 2 is achie
ve
d when these s
p
ace
vectors are
plotted on a set
of real and im
a
g
ina
r
y axes. T
h
e switchi
ng s
p
ace vectors di
vide the axe
s
into 6 e
qua
lly sized sectors
.
The two
nul
l
vect
ors
V
7
(0
00
) an
d V
8
(111) are located at the origin. The
ob
jectiv
e o
f
SVPWM
is to estimate a
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. 2
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2
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3
–
23
2
22
6
refe
rence s
p
ac
e vector V s
o
mewhere
w
ith
i
n
th
e tran
scribed
circle u
s
i
n
g a co
m
b
in
atio
n o
f
th
e ei
gh
t switch
i
ng
vectors.
Fig
u
re
2
.
Determin
atio
n
of t
h
e switch
i
n
g
sequ
en
ces in th
e t
h
ree ph
ase i
n
verter
In this m
odula
tion technique
the three
pha
se
qua
n
tities can be trans
f
orm
e
d to their e
q
uivalent two-
p
h
a
se q
u
a
n
tity eith
er in
sy
n
c
hro
nou
sly ro
tatin
g
fram
e
(o
r) statio
n
a
ry fram
e
b
y
Clark
e
equ
a
tio
n. The
tran
sform
a
t
i
o
n
o
f
two
p
h
a
se qu
an
tity is rep
r
esen
ted as
[13
]
:
1
0
√
√
(1
1)
From
t
h
ese t
w
o
-
p
h
ase c
o
m
p
o
n
e
n
t
s
, t
h
e
r
e
fere
nce
vect
o
r
m
a
gni
t
ude c
a
n be
f
o
u
n
d
a
nd
use
d
f
o
r
m
odul
at
i
ng t
h
e
i
nve
rt
er
o
u
t
p
u
t
. The
m
a
gni
t
ude
of
t
h
e
refe
re
nce
vol
t
a
g
e
ve
ct
or i
s
:
.
(1
2)
Whe
r
e M
i
i
s
t
h
e m
odul
at
i
o
n
i
nde
x.
T
h
e a
ngl
e,
i
s
defi
ned
i
n
t
r
i
g
on
om
et
ri
c fu
nct
i
o
n as:
t
a
n
(1
3)
The o
p
erat
i
o
n sect
or n
u
m
b
er,
f
o
r
a
n
y
gi
ve
n refe
rence
vect
o
r
,
i
s
gi
ve
n by
[
14]
:
/
1
(1
4)
The
d
w
el
l
i
ng t
i
m
e
can be
e
v
al
uat
e
d
usi
n
g
t
h
e
eq
uat
i
o
n
s
[
1
2]
:
√
(
1
5
)
√
(
1
6
)
(
1
7
)
Wh
ere Ts is th
e switch
i
ng
period
and
Vdc is th
e inv
e
rter in
pu
t vo
ltag
e
. Calcu
l
atio
n
of switch
i
ng
time fo
r
each sect
or is
s
h
own in table
2.2
3.
MO
DELIN
G
OF CO
NTRO
L
TECH
N
IQ
UES
The s
w
i
t
c
hi
n
g
si
gnal
ge
ne
rat
i
on m
odel
f
o
r S
P
W
M
,
T
H
I
P
WM
and S
V
P
W
M
are sh
ow
n i
n
Fi
g
u
re
3,
4
and 5 res
p
ectively. The s
w
itching
dela
y
s
an
d t
h
e
f
o
r
w
ar
d
dr
o
p
o
f
t
h
e
po
wer
swi
t
c
hes
a
n
d
t
h
e
dea
d
t
i
m
e of t
h
e
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6
9
4
S
i
mu
la
tion
In
vestig
a
tion
o
f
SPWM, THIPWM
and
S
VPW
M Tech
n
i
q
u
e
s
fo
r Th
ree… (Zu
l
kifilie Bin
Ibra
h
i
m)
22
7
i
nve
rt
er a
r
e al
l
i
g
n
o
r
ed
i
n
t
h
e
s
e m
odel
i
ng.
M
y
pr
op
ose
d
H-B
r
i
d
ge i
n
ve
rt
er t
o
p
o
l
o
gy
r
e
qui
res si
x s
w
i
t
c
hi
ng
devi
ces
, si
ngl
e
DC
so
urce
of
22
0
V
;
t
h
ree
p
h
a
se R
L
-l
oad
o
f
5
0
Ω
a
n
d
20mH in eac
h
phas
e. T
h
e
fundamental
fre
que
ncy
i
s
5
0
Hz
.
Tabl
e
2.
Swi
t
c
hi
n
g
Ti
m
e
C
a
lcul
at
i
on
at
Eac
h
Sect
or
Sector
Switching
Ti
m
e
Upper
switches (S1,
S3,
S5)
L
o
wer
Switches (S2,
S4,
S6)
1
Ta
Tb
Tc
T
1
+T
2
+T
0/
2
T
2
+T
0/
2
T
0/
2
T
0/
2
T
1
+T
0/
2
T
1
+T
2
+T
0/
2
2
Ta
Tb
Tc
T
1
+T
0/
2
T
1
+T
2
+T
0/
2
T
0/
2
T
2
+T
0/
2
T
0/
2
T
1
+T
2
+T
0/
2
3
Ta
Tb
Tc
T
0/
2
T
1
+T
2
+T
0/
2
T
2
+T
0/
2
T
1
+T
2
+T
0/
2
T
0/
2
T
1
+T
0/
2
4
Ta
Tb
Tc
T
0/
2
T
1
+T
0/
2
T
1
+T
2
+T
0/
2
T
1
+T
2
+T
0/
2
T
2
+T
0/
2
T
0/
2
5
Ta
Tb
Tc
T
2
+T
0/
2
T
0/
2
T
1
+T
2
+T
0/
2
T
1
+T
0/
2
T
1
+T
2
+T
0/
2
T
0/
2
6
Ta
Tb
Tc
T
1
+T
2
+T
0/
2
T
0/
2
T
1
+T
0/
2
T
0/
2
T
1
+T
2
+T
0/
2
T
2
+T
0/
2
Fi
gu
re
3.
S
w
i
t
c
hi
n
g
si
gnal
ge
n
e
rat
i
o
n
m
odel
f
o
r
SP
W
M
Fi
gu
re
4.
S
w
i
t
c
hi
n
g
si
gnal
ge
n
e
rat
i
o
n
m
odel
f
o
r
THIP
W
M
Fi
gu
re
5.
S
w
i
t
c
hi
n
g
si
gnal
ge
n
e
rat
i
o
n
m
odel
f
o
r
SV
P
W
M
4.
RESULT AND DIS
C
USSI
ON
Three
-
P
h
ase
m
odulating signals a
r
e ge
ne
rated wh
ich a
r
e displaced
from
each other for
SP
W
M
,
TH
IPW
M
and SV
PW
M ar
e
sh
own
in
Figur
e 6, 7
and
8
respectively. T
h
eir three
phase
out
put c
u
rre
nt
wave
f
o
rm
s
are
sh
ow
n
i
n
Fi
g
u
re 9, 1
0
a
nd 11 res
p
ec
tivel
y. THD m
easurem
ent of
the corres
ponding three
p
h
a
se ou
t
p
u
t
cu
rr
en
tsar
e show
n in
Figu
r
e
12
,
13
an
d 14
resp
ectiv
ely wher
e th
e sw
itch
i
n
g
fr
equ
e
n
c
y is f
i
x
e
d
t
o
4K
Hz. T
H
I
P
W
M
sh
o
w
s t
h
e re
duce
d
TH
D by
6.
6
7
% c
o
m
p
ared t
o
SP
WM
an
d he
nc
e THIP
WM
i
s
bet
t
e
r
th
an
SPW
M.
S
V
PW
M sh
ow
s
th
e
r
e
du
ce
d TH
D
by
0.
1
8
% com
p
are
d
t
o
TH
IP
W
M
a
nd
he
nce S
V
P
W
M
i
s
b
e
tter th
an THIPW
M
. Th
e
ou
tpu
t
lin
e-li
n
e
v
o
ltag
e
s are sh
own
in Fi
g
u
re 15
, 16
and
17
respectiv
ely. THD
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8
m
easurem
ent
of t
h
e co
rres
p
on
di
n
g
out
put
l
i
n
e-l
i
n
e v
o
l
t
a
gesare
sh
o
w
n i
n
Fi
g
u
r
e 1
8
,
1
9
an
d
20
res
p
e
c
t
i
v
el
y
.
SV
PW
M shows th
e r
e
du
ced
TH
D
b
y
16
.4% th
an
SPW
M
and 1
8
.
5
1% t
h
an TH
IP
WM
.
Hence S
V
P
W
M
sho
w
s
th
e b
e
tter p
e
rform
a
n
ce i.e b
e
tter
q
u
a
lity o
f
o
u
tp
u
t
wav
e
fo
rm
th
an
an
y
o
t
h
e
rs.
Fi
gu
re
6.
Th
re
e p
h
ase m
o
d
u
l
a
t
i
ng si
gnal
f
o
r
SP
W
M
Fi
gu
re
7.
Th
re
e p
h
ase m
o
d
u
l
a
t
i
ng si
gnal
f
o
r
THIP
W
M
Fi
gu
re
8.
Th
re
e p
h
ase m
o
d
u
l
a
t
i
ng si
gnal
f
o
r
SV
P
W
M
Figure 9.
Thre
e
phase output cu
rr
en
t fo
r
SPW
M
Fig
u
r
e
10
.
Three
phase output
current for T
H
IPWM
Figure
11. T
h
ree phase
ou
tput
current for SVPW
M
0
500
100
0
1500
20
00
-1
-0.
5
0
0.
5
1
Ti
m
e
(
m
s
)
V
o
l
t
age (V
)
0
0.
5
1
1.
5
2
-1
-0.
5
0
0.
5
1
Ti
m
e
(
s
)
V
o
l
t
age (V
)
0
0.
5
1
1.
5
2
-1
-0
.
5
0
0.
5
1
Tim
e
(
s
)
Vo
l
t
a
g
e
(
V
)
0
500
1
000
150
0
20
00
-2
-1
0
1
2
Ti
m
e
(
m
s
)
C
u
rre
n
t
(
A
)
0
0.
5
1
1.
5
2
-2
-1
0
1
2
C
u
rren
t (
A
)
Tim
e
(s
)
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6
9
4
S
i
mu
la
tion
In
vestig
a
tion
o
f
SPWM, THIPWM
and
S
VPW
M Tech
n
i
q
u
e
s
fo
r Th
ree… (Zu
l
kifilie Bin
Ibra
h
i
m)
22
9
Figure
12. C
u
rrent T
H
D m
e
a
s
urem
ent for
SPW
M
Fi
gu
re
1
3
. C
u
r
r
ent T
H
D m
e
asurem
ent f
o
r
T
H
IP
WM
Figure
14. C
u
rrent T
H
D
m
e
a
s
urem
ent for
SVPW
M
Fi
gu
re 1
5
. O
u
t
put
Li
ne-
L
i
n
e vol
t
a
ge
f
o
r
SP
WM
Fi
gu
re 1
6
. O
u
t
put
Li
ne-
L
i
n
e vol
t
a
ge
f
o
r
T
H
IP
W
M
Fi
gu
re 1
7
. O
u
t
put
Li
ne-
L
i
n
e vol
t
a
ge
f
o
r
S
V
P
W
M
0
50
0
100
0
15
00
200
0
-200
-100
0
10
0
20
0
Ti
m
e
(
m
s
)
V
o
l
t
age
(
V
)
0
0.
5
1
1.5
2
-
200
-
100
0
100
200
Ti
m
e
(
s
)
Vo
l
t
a
g
e
(
V
)
0
0.
5
1
1.
5
2
-
200
-
100
0
100
200
Ti
m
e
(
s
)
Vo
l
t
a
g
e
(
V
)
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l. 4
,
No
. 2
,
Jun
e
2
014
:
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3
–
23
2
23
0
Figu
re
1
8
.
V
o
ltage T
H
D m
easurem
ent fo
r
SP
WM
Figu
re
1
9
.
V
o
ltage T
H
D m
easurem
ent fo
r T
H
IP
WM
Figure
20.
Voltage T
H
D m
eas
urem
ent for
SVPW
M
In t
h
i
s
sect
i
o
n,
o
u
t
p
ut
pe
rf
o
r
m
a
nce i
s
anal
i
zed i
n
t
e
rm
s of
m
odul
at
i
on i
n
di
ces, s
w
i
t
c
hi
n
g
fre
que
nci
e
s
and i
n
ve
rt
er i
n
put
v
o
l
t
a
ge
. V
a
ri
at
i
on o
f
T
H
D wi
t
h
m
odul
at
i
on i
n
di
ces are sh
ow
n i
n
Fi
gu
re 2
1
an
d
2
2
. T
h
e
cur
r
ent
T
H
D i
s
co
nt
i
n
u
o
u
sl
y
decrea
sed
u
p
t
o
m
odul
at
i
on
i
nde
x
1 f
o
r
SP
WM
b
u
t
i
t
sh
o
w
s i
n
c
r
easi
n
g
nat
u
re
exceedi
ng m
odulation index 1. He
nce
,
SP
WM is not
s
u
itable in ove
r
m
odulation re
gion. T
H
IP
WM and
SV
PW
M
b
o
t
h sho
w
b
e
tter THD
co
m
p
ar
ed
t
o
SPW
M. Th
e
THD is con
tin
uously d
ecr
eased up
to
m
odul
at
i
o
n
index
1.15
f
o
r
SVPW
M an
d
it sho
w
s t
h
e low
e
st
THD
th
an
o
t
her
s
.
H
e
n
ce
SVPW
M can
ru
n
in
ov
er
m
odul
at
i
on
re
gi
o
n
but
o
v
er
m
odul
at
i
on i
s
l
i
m
i
t
e
d up t
o
m
odul
at
i
o
n
i
nde
x
1.
15
be
cause T
H
D i
n
creases
exceedi
ng m
o
dulation index
1.15.Variatio
ns of T
HDs
with switching freque
ncies are s
hown in Fi
gure 23 and
24
. T
h
e
TH
D i
s
co
nt
i
n
uo
usl
y
decrease
d
u
p
t
o
s
w
i
t
c
hi
n
g
fre
que
ncy
4K
Hz
f
o
r
SP
WM
a
n
d
i
t
sho
w
s
u
n
e
x
p
ect
ed
results e
x
cee
ding 4KHz.
He
nce, SPWM is
not capa
b
le
i
n
h
i
gh s
w
i
t
c
hi
ng
a
ppl
i
cat
i
o
n. T
H
IP
W
M
an
d
SV
P
W
M
bot
h sh
o
w
co
n
t
i
nuo
us
red
u
ct
i
on
of T
H
D u
p
t
o
1
5
K
H
z b
u
t
t
h
ey
sh
ow i
n
cr
easi
ng
beh
a
vi
o
r
excee
di
n
g
1
5
KHz
.
Hence
,
they are applicable up to 15
KHz
. Va
ri
at
i
on o
f
TH
D
s
wi
t
h
i
nve
rt
er
i
n
p
u
t
vol
t
a
ges are sh
ow
n i
n
F
i
gu
re
25 a
n
d
26
. T
H
D rem
a
i
n
s co
n
s
t
a
nt
wi
t
h
t
h
e
vari
at
i
o
n o
f
i
n
vert
er
i
n
put
vo
l
t
a
ge
fo
r S
P
WM
and
TH
IP
W
M
. The
cu
rr
en
t THD
i
s
con
tin
uou
sly d
ecr
eased up
to
220
V
bu
t increased excee
ding t
h
is val
u
e
and voltage T
HD i
s
pr
o
p
o
r
t
i
onal
t
o
i
n
p
u
t
vol
t
a
g
e
for S
V
P
W
M
.
Hence, t
h
e opt
i
m
i
zed m
odul
at
i
on i
n
dex i
s
1.
1
5
, opt
i
m
i
zed
sw
itch
i
ng
f
r
e
qu
en
cy is 15K
Hz and
o
p
tim
ize
d
inv
e
r
t
er
input v
o
ltag
e
is
2
20V
.
Fi
gu
re
2
1
.
Vari
at
i
on
of
C
u
rre
n
t
TH
D wi
t
h
M
I
Fig
u
re 22
. Vari
atio
n
o
f
Vo
ltage
THD with
M
I
0.
6
0
.8
1
.
0
1
.
2
1.
4
0
2
4
6
8
10
12
14
16
18
20
T
H
D
(
%
)
M
odula
t
io
n Ind
e
x
SP
W
M
T
H
IPW
M
S
VPW
M
0
.
60
.
8
1
.
01
.
2
1
.
4
40
50
60
70
80
90
10
0
11
0
12
0
T
H
D
(
%
)
M
o
dul
ation Index
SP
W
M
THI
P
W
M
SVPW
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
S
i
mu
la
tion
In
vestig
a
tion
o
f
SPWM, THIPWM
and
S
VPW
M Tech
n
i
q
u
e
s
fo
r Th
ree… (Zu
l
kifilie Bin
Ibra
h
i
m)
23
1
Fi
gu
re
2
3
.
Vari
at
i
on
of
C
u
rre
n
t
TH
D wi
t
h
S
w
i
t
c
hi
ng
Fre
que
ncy
Fig
u
re 24
. Vari
atio
n
o
f
Vo
ltage
THD with
Switch
i
ng
Fre
que
ncy
Fi
gu
re
2
5
.
Vari
at
i
on
of
C
u
rre
n
t
TH
D wi
t
h
I
n
put
Vo
ltag
e
Fi
gu
re 2
6
. Vari
at
i
on of
V
o
l
t
a
g
e
TH
D wi
t
h
In
put
Vo
ltag
e
5.
CO
NCL
USI
O
N
In
th
is p
a
p
e
r, th
e co
m
p
arative
analysis of SPW
M
, T
H
IPWM and
SVPWM for a three phase voltage
sou
r
ce i
n
ve
rt
er i
s
per
f
o
rm
ed an
d t
h
ei
r
p
e
rf
orm
a
nce ha
s been
p
r
esen
t
e
d i
n
t
e
rm
s
of m
odul
at
i
o
n
i
nde
x
,
swi
t
c
hi
n
g
f
r
eq
uency
an
d i
n
v
e
rt
er i
n
p
u
t
v
o
l
t
a
ge. F
r
om
th
e
si
m
u
latio
n
resu
lts, SPW
M
can
n
o
t
cap
ab
le in
o
v
er
m
odul
at
i
on re
gi
o
n
an
d i
n
hi
gh s
w
i
t
c
hi
ng
f
r
eq
ue
ncy
ap
pl
i
cat
i
on. T
H
I
P
WM
an
d S
V
P
W
M
b
o
t
h
s
h
o
w
bet
t
e
r
THD up
t
o
15
KHz. THD
re
m
a
in
s con
s
tan
t
with th
e
v
a
riatio
n
o
f
inv
e
rter inpu
t vo
ltag
e
for SPWM and
THIPW
M
. T
h
e current T
H
D is continuo
usl
y
decrease
d
u
p
t
o
22
0
V
an
d v
o
l
t
a
ge TH
D i
s
pr
o
p
o
r
t
i
onal
t
o
i
npu
t
vol
t
a
ge
f
o
r
S
V
P
W
M
.
It
ca
n
be co
ncl
ude
d t
h
at
S
V
P
W
M
gi
ves e
n
ha
nced
f
u
n
d
am
ent
a
l
o
u
t
p
ut
wi
t
h
bet
t
e
r
q
u
a
lity i.e. lesser THD co
m
p
ared th
an
o
t
h
e
rs.
ACKNOWLE
DGE
M
ENTS
This work is s
u
pporte
d
by
powe
r electroni
cs and
driv
e lab
o
ratory, Faculty o
f
Electrical en
g
i
n
e
ering
(FKE),
Un
iv
ersiti Tek
n
i
k
a
l
Malaysia Me
l
a
k
a
.
We wo
u
l
d
lik
e to
th
ank
all th
e research
st
u
d
e
n
t
s
o
f
th
e
Labo
ratory for
h
e
lp
ing
u
s
in
so
lv
ing
m
a
n
y
critical p
r
ob
lem
s
.
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5
10
15
20
2
4
6
8
10
12
14
16
18
20
22
T
H
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(
%
)
Sw
itching Frequency
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W
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T
H
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(
%
)
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M
THI
P
W
M
SV
PW
M
10
0
1
50
2
0
0
250
30
0
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H
D
( %
)
Inv
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t
V
o
lt
a
g
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(
V
)
SP
W
M
THIPW
M
SV
PW
M
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S
SN
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2
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BIOGRAP
HI
ES
OF AUTH
ORS
Dr. Z
u
lkifilie B
i
n Ibrahim
received B. Sc.
in E
l
ectr
i
cal En
g
i
neering from
Universiti T
e
knologi
Malay
s
ia in 198
9 and PhD Degree from Liverpo
o
l John Moores
University
, UK, in 1999. Since
1990, he h
a
s b
een with
the S
t
andards and
In
dus
trial R
e
sear
ch Institut
e
(SIRIM Berhad),
Selangor, Malaysia. Curren
t
ly
h
e
is working as
D
ean and
an Associate Professor in Universiti
Teknik
a
l Malaysia Melak
a
. His
current r
e
sear
ch
inter
e
sts include motor control, embedded
s
y
stem
design
, fuzzy
logic
con
t
rol, biometrics
appl
ications and
power electron
ics and
drive
control.
M
d
.
Liton Hossain
was born i
n
Bangladesh, i
n
1989. He received Ba
chelor
of Science in
Electrical and
Electronic Eng
i
neering
in 201
2 from Khulna University
of
Engineering
&
Techno
log
y
, Bangladesh. He is
currently
work
i
ng as a post graduate student
in Faculty
of
Ele
c
tri
cal
Eng
i
n
eering
of Unive
r
siti T
e
knik
a
l M
a
la
ysi
a
Mel
a
ka
.
His curren
t
r
e
search
int
e
rests
includ
e power
el
ectron
i
cs
and s
o
l
a
r c
e
ll
.
Dr. Ismadi Bin Bugis
received
B. S
c
. in El
ect
rica
l P
o
wer Engineer
ing from
North S
u
m
a
tra
University
, Med
a
n, Indonesia. He received M.
Sc. in Power Electronic and Mach
ine Drive from
the Dep
a
rtm
e
nt
of El
ectr
i
c
a
l
an
d El
ectron
i
c
En
gineer
ing and
P
h
D in P
o
wer S
y
s
t
em
S
t
ab
ili
t
y
from Power Re
search Group o
f
University
of
St
rathcly
d
e, Glasgow, UK. Currently
h
e
is
working as an Associate Professor in Universiti
Teknik
a
l Mal
a
y
s
ia Melak
a
. His c
u
rrent rese
arch
inter
e
sts Power
Ele
c
troni
c
and P
o
wer S
y
st
em
.
Nik M
unaji
Nik M
a
hadi
received the Bache
l
o
r
of S
c
ience in Ele
c
tri
cal Eng
i
n
eering (Control
,
Instrum
e
ntation
& Autom
a
tion
)
from
Universiti Tekn
ikal Mal
a
y
s
i
a
Melak
a
i
n
2012 where
current
l
y
h
e
is
doing res
ear
ch toward the M
a
s
t
er of S
c
ien
ce i
n
Elec
tric
al En
gineer
ing. His
res
earch
in
teres
t
s
are
in
contro
l s
y
s
t
em
d
e
s
i
gn
an
d m
o
tor driv
e.
Ahmad
Sh
ukr
i Ab
u H
a
sim
receiv
e
d his
Diplom
a, B.S
.
and M
.
S
.
in Elec
tri
c
al Engin
eering
majoring in
Power from th
e Univ
ersiti Tekno
logi
Mara, Shah
Alam, Malay
s
ia,
in
2000, 2004
and
2008, respect
iv
el
y
.
He is a Lectur
er at the
Universiti PertahananNasional,
Kuala Lum
pur,
Malay
s
ia,
and is currently
purs
u
ing his Ph.D
.
at
the Univ
ersit
i
T
e
knika
l Ma
l
a
y
s
i
a
Me
lak
a
(UTeM), Durian Tunggal, Melaka
, Malay
s
ia.
His current res
ear
ch
interests
includ
e power
ele
c
troni
c
and dr
ive s
y
s
t
em
s
.
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