Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
4, N
o
. 3
,
Sep
t
em
b
e
r
2014
, pp
. 30
8
~
31
3
I
S
SN
: 208
8-8
6
9
4
3
08
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
Total Harmonic Distortion of
Dodecagonal Space Vector
Modulation
Babita Nand
a
Departem
ent
of
Ele
c
tri
cal
and
E
l
ectron
i
cs
Eng
i
ne
ering,
J
N
TU, H
yderabad
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 31, 2013
Rev
i
sed
Ap
r
14
, 20
14
Accepted
May 10, 2014
Space ve
ctor m
odulation
techn
i
q
u
e is one
of the
best PW
M techniques which
have be
en im
plem
ented to th
e Multilev
e
l inv
e
r
t
er cir
c
uit
to ge
t the pur
e
l
y
sinusoidal cuurent. This is a im
porta
nt a
l
gorith
m
which is im
plem
ented i
n
open wind
indu
ction
motor.
This ty
p
e
of
I.M
h
a
s
grea
t im
pact
on
El
ectr
i
c
Drive s
y
stem. S
V
M is nothing b
u
t the techniqu
e
of switching alg
o
rithm. The
Hexagonal space vector
modulation h
a
s been
implemented
before, bu
t
elimination of
higher ord
e
r harmonics is not
possible. To
rqu
e
pulsation
arises. Speed
co
ntrol of Induct
i
on m
o
tor was n
o
t sm
ooth. So
Dodecagona
l
(12) structur
e d
e
veloped
.
A 12
side pol
ygon
al s
p
a
ce v
ector
s
t
ruc
t
u
r
e is
m
ean
t
for eliminating (
6n±1) harmonics in
the phase
current wavefo
rm throughout
the modulating
range. A high resoluti
on of PWM technique is proposed
involving multiple 12 sided p
o
ly
gon
al
(Dodecagonal) structu
r
e that
can
generate high
ly
sinusoida
l voltage at a r
e
duced
switching frequ
ency
. In th
is
paper diff
erent v
a
lues
of frequ
en
cies
ha
v
e
been taken for harmon
ic analy
s
is.
SVM method features
a high
er
level of
dc-bus v
o
ltag
e
utilizatio
n compared
to th
e
conventio
nal PWM.
Keyword:
D
S
P TMS3
20LF281
2
Harm
onic Ana
l
y
s
is
Matlab
20
12
Mu
ltilev
e
le in
verter
Space vector m
odulation
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
:
B
a
bi
t
a
Na
nda
Depa
rtem
ent of Electrical and El
ect
ro
ni
cs E
n
gi
nee
r
i
n
g, J
N
T
U
,
Hy
de
raba
d
Em
a
il: b
a
b
ita.nan
d
a
@g
m
a
i
l
.co
m
1.
INTRODUCTION
The c
once
p
t of space
vect
or is derive
d
from roat
aing
fie
l
d of ac m
odulati
ng the inve
rter output
vol
t
a
ge
. I
n
t
h
i
s
m
odul
at
i
o
n t
echni
que t
h
e t
h
r
ee phas
e
q
u
ant
i
es can be t
r
a
n
sfo
r
m
e
d t
o
t
h
ei
r eq
ui
val
e
nt
2-
pha
se
qua
nt
i
n
t
y
ei
t
h
er i
n
sy
nc
hr
ou
s
l
y
rot
a
t
i
ng f
r
a
m
e or st
at
i
ona
ry
fram
e
prese
n
t
e
d i
n
phas
o
r
di
agram
,
Fi
g
u
re
1.
From
t
h
i
s
2-p
h
ase com
p
o
n
e
n
t
t
h
e refe
re
nc
e vect
or m
a
gn
i
t
ude can
be f
o
u
n
d
an
d use
d
for m
o
d
u
l
a
t
i
ng t
h
e
inve
rter output. These switching stat
es can be represe
n
ted by active a
nd zero space ve
ctors, re
pectively.
A
typical space vector dia
g
ram
has bee
n
s
h
own in Figure 1.
In the s
p
ace
ve
ctor m
odulation technique, one leg
i
s
act
i
ong as a
swi
t
c
h,
but
w
h
en
we c
onsi
d
eri
n
g t
h
e Hi
g
h
e
r m
odul
at
i
on
ran
g
e,
we are
seen t
h
e
Harm
oni
c i
n
pha
se cu
rr
ent
a
n
d
p
h
ase
v
o
l
t
a
ge
of t
h
e sy
st
e
m
. W
e
are
n
o
t
get
t
i
ng
p
u
rel
y
si
nus
oi
dal
c
u
rr
ent
w
h
i
c
h
a I
n
duct
i
o
n
m
o
tor requi
red for its speed c
ont
rol.
T
h
ats why Dodecagonal (12 side
de)sp
ace vect
or struct
ure in the
highe
r
m
odul
at
i
on re
g
i
on cam
e
t
o
t
h
e researc
h
w
o
r
k
. T
h
e m
a
i
n
i
d
ea behi
n
d
S
V
P
W
M
i
s
t
o
di
vi
de t
h
e 2
D
-
p
l
a
n
e
i
n
t
o
tweleve equal
areas each
of them
is
called sector
In t
h
e e
x
trem
e
m
odula
tion ra
nge,
voltage vect
ors
at the
vert
i
ces o
f
t
h
e
out
er
d
odec
a
g
o
n
a
nd t
h
e v
e
rt
i
ces fr
om
t
h
e out
e
r
m
o
st
hexag
o
n
s i
s
use
d
f
o
r
P
W
M
c
ont
rol
,
resu
lting
in h
i
g
h
l
y su
ppressed
5
t
h
and
7
t
h
o
r
d
e
r h
a
rm
o
n
i
cs th
ereb
y im
p
r
ov
ing
th
e h
a
rm
o
n
i
c p
r
ofile
o
f
t
h
e
m
o
to
r cu
rren
t. Th
is lead
s to
th
e 12
-step
o
α
perat
i
o
n at
5
0
H
z
whe
r
e al
l
t
h
e
5t
h a
n
d 7t
h
or
de
r
harm
on
i
c
s are
com
p
l
e
t
e
l
y
elim
i
n
at
ed. At
t
h
e sam
e
t
i
m
e
, the l
i
n
ea
r
ran
g
e
o
f
m
odul
at
i
o
n
ext
e
n
d
s
u
p
t
o
96
.6
%
of
base
spee
d.
Because of thi
s
, and the
high de
gree of s
u
ppressi
on
of
l
o
we
r order harm
onics,
s
m
ooth acceleration
of t
h
e
m
o
to
r u
p
to
rated
sp
eed
is po
ssib
le. Ap
art from th
is, th
e switch
i
n
g
frequ
ency o
f
th
e m
u
lti
lev
e
l in
v
e
rter ou
tput
is always limit
ed
with
in 1kHz. Th
e m
i
d
d
l
e in
v
e
rter
(h
i
g
h
v
o
l
t
a
ge i
nve
rt
er
)
devi
ces
are
s
w
i
t
c
hed
l
e
ss t
h
an2
5
%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Tot
a
l
H
a
rm
o
n
i
c
Di
st
ort
i
o
n
of
Do
dec
a
g
o
nal
S
pace
Vect
or
M
o
d
u
l
a
t
i
o
n (
B
ab
i
t
a
N
a
nd
a)
30
9
of
t
h
e out
put
fu
n
d
am
ent
a
l
swi
t
c
hi
n
g
peri
o
d
.
C
o
n
s
i
s
t
s
o
f
t
h
ree cascade
d
2-l
e
vel
i
n
ve
rt
ers. The
p
r
o
pos
ed
technology is realized by casc
a
ding
t
h
ree co
nve
nt
i
o
nal
t
w
o
l
e
vel
i
nvert
e
r
s
fed
fr
om
asym
m
e
t
r
i
cal
i
s
ol
at
ed dc
v
o
ltag
e
so
ur
ces v
a
l
u
e
0
.
5
77kV
dc,
0
.
42
3kV
dc
an
d 0.155
V
dc
as show
n in
Figu
r
e
1
Fi
gu
re
1.
P
o
we
r ci
rc
ui
t
o
f
t
h
e
expe
ri
m
e
nt
al
set
up
.
The t
o
t
a
l
v
o
l
t
a
ge i
s
1.
1
5
5
V
d
c
. Eac
h
p
h
ase
can t
a
ke
fo
ur
di
ffe
re
nt
l
e
vel
.
Twel
ve s
p
ace
vect
or
ar
e
form
ed by com
b
ination
of vol
t
ag
e s
p
ace
vectors
along three
phases.
2.
R
E
SEARC
H M
ETHOD
2.
1. E
v
ol
uti
o
n
o
f
D
o
de
ca
g
o
n
a
l
Sp
ace
Vec
t
or
In
vert
e
r
ci
rc
ui
t
t
o
p
o
l
o
gy
ca
pa
bl
e o
f
ge
nerat
i
ng
m
u
l
t
i
l
e
vel
do
deca
go
nal
(
1
2
-
si
de
d
p
o
l
y
g
o
n
)
v
o
l
t
a
ge
space vect
ors
by the cascade
d
conne
cti
on
of two-level and three
-
level inve
rters
.
By the prope
r selection
of
DC-link voltages and
res
u
ltant switching stat
es for the
inverters, voltage s
p
ace vectors whose tips lie on t
h
ree
conce
n
tric dodecagons
,
are obtained. A
rect
ifier circuit for the inverter is
also propose
d
, whic
h signi
ficantly
im
pro
v
es t
h
e
p
o
we
r fact
or
. T
h
e t
o
pol
ogy
of
fers a
d
vant
a
g
e
s
suc
h
as t
h
e c
o
m
p
l
e
t
e
el
im
i
n
at
i
on o
f
t
h
e
fi
f
t
h an
d
seve
nt
h
ha
rm
oni
cs i
n
phase
v
o
l
t
a
ges a
n
d a
n
ext
e
nsi
o
n
o
f
t
h
e l
i
n
ear
m
odul
at
i
on
ran
g
e.
I
n
t
h
i
s
st
udy
,
a si
m
p
le
m
e
t
hod f
o
r t
h
e
cal
cul
a
t
i
on of
pul
se wi
dt
h m
o
d
u
l
a
t
i
on t
i
m
ing
was p
r
ese
n
t
e
d al
on
g wi
t
h
ext
e
nsi
v
e si
m
u
l
a
t
i
o
n
an
d exp
e
rim
e
n
t
al resu
lts in
ord
e
r to v
a
lid
at
e th
e
p
r
o
p
ose
d
concept. The
12-step
operation at rated vol
t
age
ope
rat
i
o
n, l
ead
i
ng t
o
t
h
e c
o
m
p
l
e
t
e
el
im
i
n
at
ion
of
6n
±1
har
m
oni
cs. (n=o
d
d
) f
r
o
m
t
h
e ph
ase vol
t
a
ge
. T
h
e t
o
t
a
l
harm
oni
c di
st
o
r
t
i
o
n
,
o
r
T
H
D,
of a
si
g
n
al
i
s
a
m
easurem
ent
of t
h
e
harm
oni
c
di
st
ort
i
o
n
rese
nt
an
d i
s
defi
n
e
d as
th
e ratio
of th
e
su
m
o
f
th
e p
o
wers
o
f
all h
a
rm
o
n
i
c co
m
p
o
n
en
ts to
th
e power o
f
t
h
e funda
m
ental frequency. By
t
a
ki
ng
t
h
e
di
f
f
e
rent
fre
q
u
enc
y
di
ffe
re
nt
p
h
a
s
e v
o
l
t
a
ge a
n
d
pha
se c
u
r
r
ent
has
bee
n
not
e
d
d
o
w
n
fo
r t
h
e a
n
al
y
s
i
s
o
f
to
tal h
a
rm
o
n
i
c d
i
stortio
n.
Th
ere sho
u
l
d
b
e
th
e m
eas
u
r
e
m
en
t o
f
THD for g
e
tting
pure sinu
so
i
d
al cu
rren
t.
SVM
al
g
o
ri
t
h
m
i
s
I
m
pl
em
ent
e
d t
h
e se
q
u
en
ce of
swi
t
c
hi
n
g
o
p
e
r
at
i
o
n
o
f
In
vert
e
r
.s
o t
h
at
wi
t
h
ove
rm
od
ual
t
i
on
ran
g
e
we ca
n
g
e
t
pu
re si
nu
soi
d
al
cu
rre
nt
.
It
’s
im
pl
em
ent
e
d
on
V/
F
co
nt
r
o
l
of
I
n
d
u
ct
i
o
n m
o
t
o
r.
Figure
2.
Dode
cagonal s
p
ace
vector m
odulat
ion
struct
ure
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
.
3
,
Sep
t
em
b
e
r
2
014
:
30
8 – 313
31
0
The swi
t
c
hi
ng
t
i
m
e
and cor
r
e
s
po
n
d
i
n
g swi
t
c
h st
at
e fo
r each
po
wer switch
is calcu
lated
in
Matlab
-
2012. T
h
e m
a
tlab code firstly identif
ies
the sector of
the re
fere
nce
volta
ge. Th
e tim
e o
f
ap
p
lication
of activ
e
and zero
vectors a
r
e the
n
calc
u
lated.
2.
2. Pro
g
r
a
m
me
f
o
r 12
-s
ec
tor Identi
ficati
on
F
u
n
c
tio
n[
s1
,s2
,
s3
,
s
4
,
s5
,s
6,
s7
,
s
8
,
s9
,
s
10
,
s
11,
s
1
2
]
=f
cn
(n
)
if
n
=
0,s1
=1
:else s1
=0
;end
.
If n=
1i
f
,s
2=1:
el
se
s2=
0
;
e
n
d
.
if
n
=
2,s3
=1
:else s3
=0
;end
.
if
n
=
3,s4
=1
:else s4
=0
;end
.
if
n
=
4,s5
=1
:else s5
=0
;end
.
if
n
=
5,s6
=1
:else s6
=0
;end
.+
if
n
=
6,s7
=1
:else s7
=0
;end
.
if
n
=
7,s8
=1
:else s8
=0
;end
.
if
n
=
8,s9
=1
:else s9
=0
;end
.
i
f
n=9
,
s1=
1
:
e
l
s
e s1
0=
0;
en
d.
i
f
n=1
0
,s
1=
1:
el
se s1
1=0;
e
n
d
.
i
f
n=1
1
,s
1=
1:
el
se s1
2=0;
e
n
d
.
:S” stands
for s
ector.
Th
ere are 12
prin
cip
a
l
vo
lta
g
e
space
vect
ors
fr
om
t
h
i
s
t
o
p
o
l
ogy
.
A
refe
re
nce vector lying in a
sector
can
be
gene
rat
e
d
by tim
e
ave
r
agi
n
g the t
w
o
pri
n
ci
pal volta
ge
s
p
ace vectors
e
n
com
p
assing the
sector.
3. RES
U
LTS AN
D A
NAL
Y
S
IS
The c
u
r
r
e
n
t cont
rollers
p
r
o
duce
the
v
o
ltage re
fe
rences
in the
d
-
q
r
o
to
r re
fere
nce
fram
e
. The
volta
g
e
refe
rences
Vd
and Vq a
r
e tra
n
sf
orm
e
d to t
h
e stator t
w
o phase
(
αβ
)
refe
rence
f
r
am
e to give
the
refe
r
e
nce
vol
t
a
ge
s V
α
and
V
β
. Th
ese
v
o
ltag
e
referen
c
es are t
h
e inpu
ts to
th
e switch
i
ng
in
terv
als.
A-
PH
AS
E
α
B-PHASE
β
C-P
H
A
S
E
Now t
o
th
e three ph
ase system
is co
nv
erted to
tw
o
phase
(d-q) system
and the
n
start
or two
phase
(
)to
m
a
in
tain
v
o
lt-tim
e ratio
co
nstan
t
.
3.1.
Switching Status
for
Different Le
vel
of P
o
le Voltage
of One Phase
A-PHA
S
E
Pole
voltage level S11
S21 S31
1.
155Vdc
3
1 1
1
1.
0kVdc
2
0
1
1
0.
577Vdc
1
1 0
1
0 Vdc
0
1
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Tot
a
l
H
a
rm
o
n
i
c
Di
st
ort
i
o
n
of
Do
dec
a
g
o
nal
S
pace
Vect
or
M
o
d
u
l
a
t
i
o
n (
B
ab
i
t
a
N
a
nd
a)
31
1
S1
1, S
2
1
,
S3
1
are t
h
e bi
di
re
ct
i
onal
sel
f
co
m
m
u
t
a
t
i
ng swi
t
c
hes an
d t
h
e unsy
m
m
e
t
r
i
cal dc vol
t
a
ge
l
e
vel
has
bee
n
sho
w
n i
n
Fi
gu
r
e
1.
3.
2. Sw
i
t
chi
n
g
Ci
rcuit Simul
a
ti
on
The A,
B,
C
are the
three
p
h
ase
vol
tage
su
pplyin
g
to the
Induc
tion
motor
and
“o”cor
respon
d
s
to th
e
pol
e
vol
ta
ge o
f
repec
ti
vep
h
a
s
e.
Here
V
a
o
,
Vb
o, Vc
o are the
di
ffe
nt pol
e
or
l
e
g vol
ta
g
e
o
f
t
h
e
In
ver
t
er.
Fi
gu
re
2.
Th
re
e p
o
l
e
v
o
l
t
a
ges
are s
h
ow
n
f
o
r
60
de
g
r
ee at
3
5
Hz
ope
rat
i
o
n
Figure 3.
Sim
u
link di
agram
of Dodeca
gonal
space vector
m
o
dulation
B
y
t
a
ki
ng t
h
e
fre
que
ncy
at
3
5
Hz
, asy
m
m
e
try
p
o
l
e
v
o
l
t
a
g
e
has
bee
n
fo
un
d
o
u
t
.
I
n
‘A
’ p
h
ase
t
h
e
vol
t
a
ge l
e
vel
f
l
uct
u
at
e bet
w
e
e
n l
e
vel
s
‘
3
’
and
‘2
’,
a
nd i
n
‘C
’
p
h
ase t
h
e vol
t
a
ge l
e
vel
fl
uct
u
at
es
bet
w
e
e
n
l
e
vel
s
‘1
’ an
d ‘
0
A
di
gi
t
a
l
si
g
n
al
pr
ocess
o
r (
D
SP
), TM
S
3
2
0
LF
2
8
1
2
i
s
us
ed f
o
r e
x
peri
m
e
nt
al
veri
fi
cat
i
o
n
.
F
o
r
di
ffe
re
nt
l
e
vel
s
of
o
u
t
put
i
n
t
h
e p
o
l
e
v
o
l
t
a
ge
,
t
h
ree
car
riers
are requ
ired
.
Ho
wev
e
r, it is
d
i
fficu
lt to syn
t
hesize
t
h
ree carri
e
r
w
a
ves i
n
t
h
e DS
P, as such
onl
y
one carri
er i
s
used an
d t
h
e
m
odul
at
i
ng w
a
ve i
s
appr
o
p
r
i
at
el
y
scaled
and
level sh
ifted
.
Th
i
s
si
m
u
latio
n
an
alysis
is d
one b
y
Sim
u
lin
k
MA
TLA
B
-
201
2.Th
e sequ
ence in
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
.
3
,
Sep
t
em
b
e
r
2
014
:
30
8 – 313
31
2
w
h
ich
the sw
itch
e
s ar
e
op
er
ated
ar
e as
fo
llo
w
s
: (2
00)
,
(21
0
)
,
(2
11)
,
(3
11
),
(32
1
)
,
(31
1
)
,
(
211
),
(2
10)
,
(
211
),
(
311
)
,
(32
1
)
,
(2
11)
,
(
221
),(32
1
)
,
(2
21)
,
(2
10
), (22
0
)
,
(22
1
)
,
(
321
),(3
31)
,
(
221
)
,
(22
0
)
,
w
h
er
eth
e
nu
mb
er
s i
n
brac
ket
s
i
ndi
c
a
t
e
t
h
el
evel
of
v
o
l
t
a
ge.
T
h
i
s
seq
u
e
n
ce co
rrespon
d
s
to
2 sam
p
les p
e
r
secto
r
.with th
e ran
g
e
bet
w
ee
n 20
Hz
-
4
0
H
z.
2 sam
p
l
e
s p
e
r sect
or.B
ey
on
d 4
0
H
z:
1 sam
p
l
e
per sect
or-e
xt
en
di
n
g
u
p
t
o
fi
nal
12
-st
e
p
m
ode.In
d
i
v
i
d
u
a
l
i
nvert
e
r
s ar
e
swi
t
c
he
d l
e
ss t
h
an
hal
f
o
f
th
e
to
tal cycleW
ith
low switch
i
ng
freq
u
e
n
c
y for h
i
gh
po
we
r dri
v
es,
t
h
e (6
n
1)
ha
rm
oni
cs i
n
t
h
e
cu
rre
nt
wa
vef
o
rm
can
p
r
o
d
u
ce t
o
rq
ue
p
u
l
s
at
i
on i
n
t
h
e
d
r
i
v
e.
The
pr
o
b
l
e
m
i
s
part
i
c
ul
a
r
l
y
severe i
n
ove
r-m
od
ul
at
i
o
n
re
gi
o
n
whe
r
e t
h
e
(
6
n
1
) h
a
rm
o
n
i
cs co
n
s
titu
te a m
a
j
o
r
po
rt
i
o
n of t
h
e
t
o
t
a
l
current
.
A 12
-si
d
e
d
p
o
l
y
go
nal
spac
e vect
or st
r
u
ct
ure f
o
r IM
d
r
i
v
e has al
rea
d
y
bee
n
pr
o
pose
d
usi
n
g
co
nv
ent
i
o
nal
2-l
e
vel
i
n
vert
e
r
s.
Thi
s
has
t
h
e ad
va
nt
age
o
f
el
im
i
n
at
i
ng al
l
(
6
n
1) harm
oni
c
s
in
th
e ph
ase cu
rr
en
t
w
a
v
e
form
th
r
o
ug
hou
t t
h
e m
o
du
latin
g r
a
n
g
e
.
Ho
w
e
ver
,
on
e
d
r
awb
a
ck
o
f
th
e sch
e
me i
s
th
e h
i
gh
dv
/d
tstress on
th
e d
e
v
i
ces,
since ea
ch inve
rter s
w
itches betwee
n
th
e v
e
r
t
ex
of
th
e 12
-
s
i
d
ed
p
o
lyg
on
and t
h
e zer
o
v
ect
or at
t
h
e ce
nt
re. T
h
us i
t
h
a
s bee
n
o
b
se
rv
ed t
h
at
wi
t
h
i
n
creased l
i
near
m
odul
at
i
on ra
n
g
e, l
e
s
s
swi
t
c
hi
n
g
f
r
eq
uency
an
d i
m
pr
o
v
ed
harm
oni
c spect
rum
,
t
h
e pr
op
ose
d
co
ncept
s
m
a
y
b
e
consi
d
ere
d
as an
in
terestin
gadd
i
tio
n
to th
e
field of m
u
ltilev
e
l i
n
v
e
rter
s fo
r h
i
g
h
/
m
e
d
i
u
m
v
o
ltag
e
h
i
g
h
power ap
p
licatio
ns.
3.
3.
Har
m
o
n
i
c
Perf
orm
a
nce
of
Ph
ase
V
o
l
t
age
a
nd
Ph
ase
Curre
nt
w
h
i
c
h i
s
Feedi
n
g
t
o
In
duc
t
i
o
n
M
o
t
o
r
Wave
f
o
rm
Fre
que
ncy
T.H.D
.
on
Vp
Ip
15
Vp=
7
5.
4%
Ip=
2
4.
49%
30
Vp=
2
7.
5%
Ip=
1
0.
59%
45
Vp=
1
3.
47
%
Ip=
1
4.
6%
50
Vp=
1
7.
54
%
Ip=
1
9.
54%
Fi
gu
re
4.
TH
D
anal
y
s
i
s
can
b
e
st
u
d
i
e
d
by
t
a
ki
n
g
di
ffe
re
nt
f
r
eq
ue
nci
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Tot
a
l
H
a
rm
o
n
i
c
Di
st
ort
i
o
n
of
Do
dec
a
g
o
nal
S
pace
Vect
or
M
o
d
u
l
a
t
i
o
n (
B
ab
i
t
a
N
a
nd
a)
31
3
Thi
s
Tot
a
l
Ha
rm
oni
c Di
st
i
on gi
ve
s t
h
e i
d
ea abo
u
t
t
h
e di
ffe
re
nt
spect
rum
and re
pre
s
t
t
h
at
out
er
envel
o
p
o
f
wa
vef
o
rm
at
l
o
w
e
r f
r
eq
ue
nci
e
s
becom
e
i
nne
r
envel
o
p o
f
at
hi
g
h
er
fre
q
u
e
n
cy
. T
h
e Ha
r
m
onic
spectrum
of phase
voltage
and phas
e c
u
rrent s
h
ows
the abse
nce
of
p
eak
y
h
a
r
m
o
n
ic th
r
oug
h out th
e
range.c
o
m
p
lete
absence
of the 6n
1(
n=
od
d
)
harm
oni
cs i
s
o
b
ser
v
e
d
. T
h
e
m
o
t
o
r curr
ent
at
rat
e
d fre
q
u
e
n
cy
ope
rat
i
o
n i
s
ne
arl
y
a p
u
re
si
n
u
soi
d
al
wa
ve
form
as the ha
rmonics
are
ve
ry low.
4. CO
N
C
L
U
S
I
ON
B
y
t
h
e pr
o
p
er
sel
ect
i
on
of
D
C
-l
i
nk
v
o
l
t
a
ge
s an
d re
sul
t
a
nt
swi
t
c
hi
n
g
st
at
es f
o
r t
h
e i
n
ve
rt
ers,
v
o
l
t
a
ge
space vectors
whose tips lie
on three conc
e
n
tric dodeca
gons, are obtaine
d
. A
rectifier c
i
rcuit for the i
nve
rter
is also
p
r
op
osed
,
wh
ich
sign
ifican
tly i
m
p
r
o
v
es th
e po
we
r f
act
or. T
h
e t
o
p
o
l
o
gy
of
fe
rs a
dva
nt
age
s
suc
h
as t
h
e
com
p
l
e
t
e
el
im
inat
i
on
o
f
t
h
e f
i
ft
h an
d se
ven
t
h ha
rm
oni
cs i
n
p
h
ase
vol
t
a
g
e
s and a
n
e
x
t
e
nsi
o
n o
f
t
h
e l
i
near
m
odul
at
i
on ra
nge
. I
n
t
h
i
s
st
udy
, a si
m
p
l
e
m
e
t
hod f
o
r t
h
e
cal
cul
a
t
i
on o
f
pul
se
wi
dt
h
m
odul
at
i
on t
i
m
i
ng wa
s
p
r
esen
ted along
with
ex
ten
s
i
v
e sim
u
latio
n
an
d exp
e
rim
e
n
t
al resu
lts in
ord
e
r t
o
v
a
lid
ate
th
e propo
sed
co
n
c
ep
t.
SVM is a po
pular ch
o
i
ce in
t
h
e in
v
e
rter con
t
ro
l.
A trad
e-
o
ff is req
u
i
red
t
o
main
tain
th
e qu
ality o
f
th
e inv
e
rter
out
put voltage
without res
o
rt
ing to
higher s
w
itching fr
equency. In this regard,
a dodec
agonal space
vector
di
ag
ram
i
s
ver
y
desi
ra
bl
e t
h
a
t
el
im
i
n
at
es al
l t
h
e
5t
h
a
n
d
7t
h
or
der
h
a
rm
onics from
the phase
voltage, l
eaving
th
e n
e
x
t
set of
h
a
rm
o
n
i
cs at (1
2n±1),
n
=
in
teg
e
r. Bu
t
th
e m
a
in
d
i
sad
v
a
n
t
ag
e is it will sho
w
m
o
re
d
v
/
d
t
stress
wh
ich
will lead
t
o
EM
I (Electro
Mag
n
e
ti
c In
terferen
ce) Prob
lem
s
. Ge
n
a
rally we are im
p
l
e
m
en
ti
n
g
on
Electric Dri
v
es
syste
m
only.
REFERE
NC
ES
[1]
Hariram, NS Marimuthu.
Spac
e
vector swit
chin
g patterns for differe
nt app
lica
t
i
ons a comparative analysis
.
Proc
.
IEEE Internation
a
l Conf
eren
ce o
n
Industrial
Technolog
y
,
Hong
Kong. 2005: 144
4-14.
[2]
AM Trzy
nadlow
ski, RL Kirlin
,
SF Legowski. S
p
ace vect
or PWM techn
i
que with mi
nimum swit
c
h
ing
losse
s a
n
d
avariable pulse r
a
te [for VSI]
.
IEEE Trans. Industr
ial Electronics
.
1997; 44(2): 173
-181.
[3]
AtifIqbal, AdoumLamine, Im
tiazAsharf, Mohibullah
.
MATLAB/SIMULINK mod
e
l of s
pace v
ect
or
pwm for thr
ee-
phase voltage source in
verter.
Pr
oc UPEC. 2006:
1096-1100.
[4]
AR Bakhshai,
HR Saligheh R
a
d G Joos. Space ve
ctor
m
odulation b
a
sed on
classific
a
t
i
on m
e
thod in thre
e-
phasem
u
lti-l
e
vel
volt
a
ge
source
i
nverters.
IEEE
. 2001.
[5]
Fei Wang, Senior Member.
Sine-Triangle versu
s Space-Vec
t
or Modula
tion for Three-Level PW
M Voltage-Sour
c
e
Inver
ter
s
.
The 2
7
th Annual Conferenc
e
of the I
EEEIndustr
ial
E
l
ec
tronics Socie
t
y
.
I
EEE tr
ansac
t
ions on industr
y
applications. 20
02; 38(2).
[6]
KVinoth Kumar, Prawin Angel Michael,
Josep
h
P John, Dr S Suresh Ku
mar. Simulation and
comparison of
spwmandsvp
wm contro
l for
thr
e
e lev
e
l inver
t
er
.
ARPN
Journal of
Engg.And
Applied Scien
ce.
2010
; 5(7).
[7]
P Tripura, YS KishoreBabu, YR Tagore
.
Space v
ector pul
se widt
h m
odulation schem
e
s
for two-level volt
a
ge sour
c
e
inverter.
ACEEE Int. J.
on c
o
ntrol sy
ste
m
and instrume
ntation
. 20
11; 02(03).
[8]
Sanjay
Lakshminaray
an
an, Gop
a
l Mondal, PN Tekwani,
KK Mohapatra, K Gopakumar
. Twelve-sided poly
g
o
n
al
voltag
e
spac
e
vector
based
m
u
lti-lev
e
l
inve
rter for
an
ind
u
ction
m
o
tor d
r
ive wi
th
com
m
on-m
ode voltage
elim
inat
ion.
IEEE Transactions
onIndustrial Electronics
. 2007; 5
4
(5): 2761-2768
.
[9]
SurinKhom
foi, Leon M
Tolb
ert. Multil
evel Power Conver
t
ers B
ook. Th
e Univ
er
sit
y
of
Tenn
essee.
BI
O
G
R
A
P
HY
OF
A
U
T
HO
R
Mrs. Babita Na
nda rece
ived th
e B.E.
in Ele
c
tri
cal Engin
eer
ing
from
KITS, Ut
kal Universit
y
,
Odisha in 2001. M.Tech
. in Power Electroni
cs a
nd Machine Drives from
the Ind
i
an Institut
e
of
Technology
Delhi,
India,
in 2008.
She is a
Life
member of ISTE.
Presently
working as HOD in
the Electrical
an
d Engineering D
e
partment. Malla
Redd
y
Colleg
e of Engin
eer
in
g for Women
,
Hy
d
e
ra
b
a
d,
An
dh
r
a
Pr
a
d
e
s
h.
Evaluation Warning : The document was created with Spire.PDF for Python.