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.
5, N
o
. 3
,
Febr
u
a
r
y
201
5,
pp
. 38
3
~
39
2
I
S
SN
: 208
8-8
6
9
4
3
83
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
A Tactical Chaos based PWM Technique for Distortion
Restraint and Power Spectrum Shaping in Induction Motor
Dri
v
es
V.
Mo
ha
n
1
, N.Sta
lin
2
,
S.
Jee
v
an
ant
h
a
n
3
1
Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectron
i
cs Eng
i
ne
ering,
E
.
G.S.Pil
l
a
y Eng
i
nee
r
ing
College
, N
a
gapa
ttinam
,
Indi
a
2
Department of Petroche
mical Technolog
y
,
Ann
a
University
BI
T Campus, Tiruch
irappalli, Ind
i
a
3
Department of Electrical
and
Elect
ron
i
cs Eng
i
neering, Pondich
er
r
y
E
ngin
eerin
g
College, Puduch
e
rr
y
,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 14, 2014
Rev
i
sed
D
ec 24
, 20
14
Accepte
d
Ja
n 16, 2015
The pu
lse width
modulated vo
ltage sour
ce inv
e
rters (PWM
-VSI) dominate
in
the modern industrial env
i
ron
m
ent.
The conv
ention
a
l PWM
methods are
designed to hav
e
higher fundamental vol
tag
e
, easy
filter
i
ng and r
e
duced total
harmonic distortion (THD).
Th
er
e are num
ber of
clus
ter
e
d harmonics aroun
d
the m
u
ltipl
e
s of switching frequency
in
the outpu
t of convention
a
l sinusoidal
pulse width m
odulation (SPW
M) and
space v
ector puls
e
widt
h m
odulation
(SVPW
M
) inverters.
This is du
e
to th
eir f
i
xed sw
itching
frequ
ency
while th
e
variab
le switching frequency
makes th
e filterin
g ver
y
complex
.
Random
carrier PWM (RCPWM)
methods are
th
e host of
PWM methods, which use
randomized carr
ier frequ
ency
and resu
lt in a
harmonic profile with well
distributed
harm
onic power
(no
harm
onic posse
sse
s signifi
cant magnitude
and hence no filtering is requ
ired).
This paper proposes a chaos-based PWM
(CP
W
M
)
s
t
rateg
y
,
which ut
ili
zes
a chao
tic
al
l
y
ch
anging s
w
itch
i
n
g
frequen
c
y
to spread
th
e harmonics continu
ously
to
a wid
e
band and
to
red
u
ce
the peak
harmonics
to a great
exte
nt. Th
is can b
e
an
eff
ective way
to s
uppress the
current harmonics and
tor
que rip
p
le
in indu
ction
motor drives. Th
e proposed
CPWM
sc
he
me
is simu
lated using MATLAB / SIMULINK so
ftware and
im
plem
ented in
three ph
as
e v
o
ltag
e
s
ource
i
nverter (VS
I)
us
ing field
programmable g
a
te arr
a
y
(FPGA).
Keyword:
Harm
onic s
p
re
ad
factor
Indu
ctio
n m
o
to
r
d
r
iv
e
Power
sp
ect
ral d
e
n
s
ity
Pu
lse wid
t
h
mo
du
latio
n
Tactical Chaos
Tot
a
l
ha
rm
oni
c di
st
o
r
t
i
o
n
Vol
t
a
ge
s
o
u
r
ce
i
nve
rt
er
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
:
V.Moha
n, Ass
o
ciate
Profe
ssor
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
EGS
Pillay Eng
i
n
e
ering
Co
ll
eg
e,
Nag
a
p
a
ttin
am
–
6
110
02
, Ind
i
a.
Em
a
il: v
eerasamy.
m
o
h
a
n
@
yah
o
o
.
co
m
1.
INTRODUCTION
The m
o
t
i
on co
nt
r
o
l
i
n
t
oday
’
s
i
ndu
st
ri
al
pr
oc
ess depe
n
d
s l
a
r
g
el
y
on ac d
r
i
v
es. The
basi
c r
e
qui
rem
e
nt
o
f
an
y
A
C
dr
i
v
e is a
po
w
e
r
co
nv
er
sion
syste
m
w
h
ich
supp
or
ts
v
a
r
i
ab
le
v
o
ltag
e
v
a
r
i
ab
l
e
f
r
e
qu
en
cy
(V
VV
F)
p
o
wer with
h
i
g
h
q
u
a
lity. The ac d
r
iv
es can
b
e
an
y
o
n
e
fro
m
th
e well-kn
own
cho
i
ces v
i
z. ac chop
p
e
r,
cy
cl
ocon
ve
rt
er
, m
a
t
r
i
x
conv
e
r
t
e
r, a
n
d rect
i
f
i
e
r an
d v
o
l
t
a
g
e
so
urce i
nve
rt
er (
V
S
I) c
o
m
b
i
n
at
i
on.
D
u
e t
o
t
h
ei
r
merits, VSIs are d
o
m
in
an
tly u
s
ed
no
t o
n
l
y as d
r
iv
es
b
u
t
also
in
app
licatio
n
s
lik
e in
du
ctio
n
h
eatin
g, stan
d-b
y
aircraft power
su
pp
lies, un
in
t
e
rru
p
tib
le power sup
p
lies fo
r
com
put
ers, hi
g
h
v
o
l
t
a
ge dc t
r
ansm
i
ssi
on l
i
n
es et
c.
Pul
s
e wi
dt
h m
odul
at
i
on (P
WM
) co
nt
r
o
l
st
rat
e
gi
es ha
ve
been t
h
e su
b
j
ect
of i
n
t
e
nsi
v
e resear
ch si
nce i
t
s
devel
opm
ent
b
y
pro
f
ess
o
r
Da
vi
d P
r
i
n
ce i
n
t
h
e y
ear 1
9
2
5
,
part
i
c
ul
a
r
l
y
i
n
dc-ac
po
we
r con
v
e
r
si
o
n
. Pas
t
fou
r
decade
s
, the industry has se
en
the develo
pment of num
erous
PWM p
a
tter
ns with a
ssocia
t
ed
th
eo
ries
fo
r
improving the perfo
rman
ce
of the VSIs [1
]-[4].
It
i
s
desi
rabl
e f
o
r a P
W
M
i
n
vert
er a
ppl
i
cat
i
o
n t
o
e
m
pl
oy
PW
M switch
i
ng
strateg
y
th
at n
o
t
on
ly ad
dresses th
e p
r
im
ary issu
es v
i
z, less to
tal h
a
rm
o
n
ic d
i
sto
r
tion
(THD),
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
83 –
39
2
38
4
effectiv
e d
c
bu
s
u
tilizatio
n
etc. bu
t also t
a
k
e
cares
o
f
seco
nd
ary issu
es lik
e electromag
n
e
tic in
terferen
ce
redu
ction
,
switch
i
ng
lo
ss,
b
e
t
t
er spread
i
n
g of
h
a
rm
onic powe
r
ove
r the
spectrum
etc [
1
]-
[8
].
A
lth
oug
h th
e
b
a
sic in
v
e
rter
is si
m
p
le, th
e
m
o
d
e
o
f
switch
i
ng
is ch
alleng
ing
in
con
t
rollin
g
th
em to
ward
s im
p
r
ov
ing
th
e
perform
a
nce indices.
From
the literature s
u
rvey,
it is underst
o
od that
e
n
orm
ous
am
ount
of ef
fort has been put
i
n
im
pro
v
i
n
g t
h
e
VSI
’
s per
f
o
r
m
ance i
n
t
e
rm
s of fu
ndam
e
nt
al
fort
i
f
i
cat
i
on, T
HD m
i
nim
i
zati
on, ha
r
m
oni
cs
el
im
i
n
at
i
on et
c
.
O
n
t
h
e
ot
he
r
si
de
issu
es like electro
m
a
g
n
etic in
terferen
c
e (EM
I
),
ha
rm
oni
c
di
st
ri
but
i
o
n
et
c.
need
f
u
rt
her
i
nve
st
i
g
at
i
o
n
a
n
d
rem
e
di
es.
The
ra
nd
om
pul
se
wi
dt
h
m
o
d
u
l
a
t
i
o
n
(R
P
W
M
)
t
e
c
h
ni
q
u
e
s are
becom
i
ng
popular a
n
d well accepted i
n
industrial m
o
tor
drives a
n
d electric ve
hicl
es. T
h
e RPWM tec
hni
que
s
effectively re
duce the
acoustic noise, ra
dio interfe
re
n
ce a
n
d m
echanical vibration
caus
e
d
by
ha
rm
oni
cs wi
t
h
l
o
w s
w
i
t
c
hi
n
g
fre
que
ncy
[
9
]
.
A ne
w
ran
d
o
m
po
si
t
i
on s
p
ace
vect
o
r
P
W
M
(R
PS
VP
W
M
)
schem
e
wi
t
h
C
1
6
7
m
i
croco
n
t
r
ol
l
e
r t
o
re
duce a
u
di
bl
e swi
t
c
hi
n
g
n
o
i
s
e has
be
en p
r
ese
n
t
e
d [
10]
.
As re
po
rt
ed i
n
[
11]
, t
h
e
po
wer
spect
ra
of a
r
a
nd
om
i
zed pul
se po
si
t
i
on P
W
M
(R
PP
-P
WM
) ca
n be
pre
d
i
c
t
e
d a
nd
opt
i
m
i
zed by
sui
t
a
bl
y
p
o
s
ition
i
ng
th
e switch
i
ng
p
u
l
se. A
h
ybrid
R
P
W
M
sch
e
m
e
wh
ich
g
e
n
e
rates th
e rand
o
m
p
u
l
se
po
sitio
n
PWM
si
gnal
s
wi
t
h
a ran
d
o
m
i
zed freque
ncy
t
r
i
a
n
g
u
l
a
r car
ri
er fo
r
im
provi
ng t
h
e
harm
oni
c spe
c
t
r
a sprea
d
i
n
g effect
has bee
n
re
p
o
r
t
ed [1
2]
. A ra
nd
om
i
zat
i
on t
e
chni
que
fo
r co
nd
uct
e
d EM
I r
e
duct
i
o
n i
n
fl
y
b
ack c
o
n
v
e
r
t
e
r
has
been
pr
op
ose
d
[13]
. Pse
u
do
-
r
an
d
o
m
seque
nce ge
nerat
o
r
(PR
S
G) i
s
us
ed t
o
pr
o
v
i
d
e
aut
o
m
a
ti
c dynam
i
c
di
t
h
eri
ng
fo
r r
e
m
ovi
n
g
u
n
d
es
i
r
ed i
d
l
e
t
o
nes
i
n
t
h
e o
u
t
p
ut
o
f
t
h
e si
gm
a del
t
a
m
odul
at
o
r
(
S
DM
)
.
Per
f
o
r
m
ance
en
h
a
n
cem
en
t o
f
ev
o
l
u
tio
nar
y
alg
o
r
ith
m
s
(
E
A
s
)
has b
e
en
rev
ealed
thr
ough
ch
ao
tic seq
u
en
ce [
1
4
]
. Numer
i
cal
exam
pl
es i
ndi
cat
i
ng t
h
e pe
rf
o
r
m
a
nce co
m
p
ari
s
o
n
o
f
t
h
e EA usi
n
g ra
n
d
o
m
and chaot
i
c
gene
rat
o
r
s
ha
s bee
n
prese
n
ted. The
chaos tim
e
series anal
ysis has been involved to capt
u
re
characte
r
istics of c
o
m
p
licated
load
beha
vior a
n
d
devel
ope
d a
new s
h
ort term
powe
r l
o
ad
forecasting m
odel ba
sed on c
h
aos the
o
ry
[15]. T
h
e
ran
d
o
m
PW
M
usi
n
g ran
d
o
m
carri
er
an
d ra
n
dom
po
si
t
i
on h
a
s
bee
n
di
scu
s
s
e
d [1
6]
-[
1
8
]
.
The e
x
isting R
P
W
M
m
e
thods
can im
prove t
h
e
harm
onic s
p
rea
d
ing a
b
ility of t
h
e
VSI undoubte
d
ly
wh
ile th
eir
p
e
rform
a
n
ce is n
o
t ap
preciab
le.
Hen
ce it is
un
der
s
too
d
t
h
at the r
a
ndo
m
n
e
ss created
by the
existing
ran
d
o
m
carri
er
P
W
M
an
d
ra
n
dom
po
si
t
i
on
P
W
M
i
s
not
ef
fi
ci
ent
.
F
u
rt
her
i
m
provi
n
g
t
h
e s
p
rea
d
i
n
g e
ffect
, t
h
e
ran
d
o
m
n
ess can be
gene
rat
e
d
t
h
ro
u
gh t
r
i
u
m
ph c
h
aot
i
c
seq
u
ence
s. T
h
e pr
op
ose
d
cha
o
s
-
base
d P
W
M
(
C
P
W
M
)
strateg
y
,
wh
ich u
tilizes a ch
aotically ch
an
g
i
ng
switch
i
ng
freq
u
e
n
c
y to
spread
th
e
h
a
rm
o
n
i
cs con
tin
uou
sl
y an
d
per
f
o
r
m
s
sui
t
a
bl
y
fo
r ac
dri
v
es.
The
p
r
o
p
o
se
d C
P
W
M
s
c
hem
e
i
s
sim
u
l
a
t
e
d usi
n
g M
A
TL
AB
/
S
IM
U
L
IN
K
soft
ware
an
d i
m
pl
em
ent
e
d i
n
t
h
e
desi
g
n
e
d
t
h
ree
p
h
ase
VS
I
t
h
r
o
ug
h a
SP
A
R
TAN
-
6
FP
G
A
(
X
C
6
SL
X4
5
)
ki
t
.
1.
1. Ch
aotic S
e
quence an
d Rand
omness
C
h
aos
,
ap
pa
re
nt
l
y
di
sor
d
e
r
e
d
be
ha
vi
o
r
w
h
i
c
h i
s
n
o
n
e
th
e less d
e
t
e
rm
in
ist
i
c, is a un
iv
ersal
phe
nom
e
non
whic
h
occurs i
n
m
a
ny system
s
in all areas
of science a
n
d e
ngi
neering.
For it to take
place the
equat
i
o
ns
de
sc
ri
bi
n
g
t
h
e si
t
u
at
i
on m
u
st
be
no
nl
i
n
ea
r a
n
d
,
th
erefo
r
e th
ey
are rarely so
l
v
ab
le in
cl
o
s
ed
form
.
Ch
ao
s is bou
nd
ed,
n
o
i
se-lik
e
o
s
cillatio
n
with
an
infin
ite
p
e
riod
,
foun
d in
n
o
n
lin
ear
d
e
termin
istic syste
m
s. It is
characte
r
ized
by extrem
e se
nsitivity to initial conditions
that is an infi
nitesim
a
l
perturbation to the
initial
co
nd
itio
ns can g
i
v
e
rise to
macro
s
cop
i
cally d
i
v
e
rg
i
n
g
so
lu
tion
s
.
Th
e
b
e
h
a
v
i
or
o
f
a ch
ao
tic system
is
a
collection of m
a
ny
orderly beha
vi
ors, none of
which
dom
i
nates unde
r
ordi
nary circum
stances. Chaotic
syste
m
s are more
flexi
b
le than
non-c
h
a
o
tic ones si
n
ce the
attractor s
p
a
n
s a larg
e
vol
ume of the
state space
and
wi
t
h
pr
op
er c
ont
r
o
l
,
o
n
e
can
ra
pi
dl
y
swi
t
c
h am
on
g
m
a
ny
di
ffere
nt
be
ha
vi
o
r
s.
Thi
s
gi
ves
a
cl
ue t
o
im
proving the
response as
we
ll as the
dom
ain
of operat
i
o
n
in
system
s th
at
exh
i
b
it ch
ao
s
for so
m
e
p
a
rameter
val
u
es
.
Ch
ao
s th
eory is a field
o
f
stud
y in
m
a
th
e
m
atics, with
ap
plicatio
n
s
in
sev
e
ral d
i
scip
li
nes in
clu
d
i
n
g
m
e
t
e
orol
o
g
y
,
s
o
ci
ol
o
g
y
,
phy
s
i
cs, engi
neeri
n
g, eco
n
o
m
i
cs,
bi
ol
o
g
y
,
a
nd
p
h
i
l
o
s
o
p
h
y
.
C
h
a
o
t
i
c
seque
nces
have
good correlation properties and they can be
use
d
as
addres
s seque
nces in Sprea
d
Spectrum
Co
mm
unic
a
tion.
Chaotic functi
ons a
r
e highly sensitive
to ini
tial condition a
nd e
xhi
bit non-
linear be
ha
vior. In Cha
o
tic sprea
d
spect
r
u
m
co
m
m
uni
cat
i
on sy
st
em
s, di
ffe
re
nt
use
r
m
a
y
be assi
gne
d
d
i
ffere
nt
se
que
nces
gene
rat
e
d wi
t
h
d
i
fferen
t
in
itial con
d
ition
s
.
Meth
od
s to imp
l
em
en
t th
e idea of ch
aos in
th
e fiel
d of
power electronic
circuits a
n
d syste
m
s have
b
een
d
e
tailed [19
]
-[2
1
]
. Bifurcatio
n
d
i
agram
is th
e
mo
st po
werfu
l
to
o
l
to
inv
e
stig
ate th
e ch
ao
s and
bi
f
u
rcat
i
o
n be
h
a
vi
o
r
. I
n
a bi
fu
rcat
i
on
di
agra
m
,
a peri
odi
c s
t
eady
st
at
e of the sy
st
em
i
s
represe
n
t
e
d as a si
ngl
e
poi
nt
or se
ver
a
l
poi
nt
s eq
ual
t
o
t
h
e peri
o
d
i
c
i
t
y
of t
h
e sy
st
em
for a fi
xed param
e
t
e
r. For cha
o
s
,
n
u
m
e
ro
u
s
poi
nts are pl
ot
ted in the dia
g
ram
because chaos m
eans pe
riod infi
nity and t
h
e points
neve
r fall at the sa
m
e
p
o
s
ition
.
Th
erefore, t
h
e ch
an
ge
of
b
e
h
a
v
i
or
o
f
a system
is clearly sho
w
n
as a
p
a
ram
e
ter is v
a
ried. So
we can
u
tilize th
e b
i
furcatio
n d
i
ag
ram
to
v
i
su
alize th
e
rou
t
e to ch
ao
s.
One i
s
s
u
e wi
t
h
rand
om
or cha
o
t
i
c
ope
rat
i
on i
s
t
h
at
t
h
e
m
a
xim
a
l
t
i
m
e
excur
s
i
ons
of wa
ve
f
o
rm
s of t
h
e
syste
m
’s state varia
b
les incre
a
se. T
hus
, ra
n
d
o
m
and cha
o
t
i
c
op
erat
i
o
n m
a
y
have s
u
peri
o
r
spect
ral
(
fre
q
u
ency
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A T
a
ctical Chaos
based PWM
Technique f
o
r
Distortio
n Rest
raint
and Pow
e
r Spectrum
Shapi
ng…
(V.Mohan)
38
5
dom
ai
n) b
u
t
i
n
feri
o
r
ri
ppl
e (t
i
m
e dom
ai
n) perf
orm
a
nce wi
t
h
res
p
ect
t
o
pe
ri
o
d
i
c
op
erat
i
o
n o
f
p
o
w
er el
e
c
t
r
o
n
i
c
co
nv
erters. A co
mm
o
n
an
d si
m
p
le ch
ao
tic fu
n
c
tion
,
th
e log
i
stic equ
a
tio
n
is:
n+
1
n
n
X =
X
(
1
-
X
)
(1)
The p
r
ope
rt
i
e
s of t
h
e l
ogi
st
i
c
fu
nct
i
o
n are w
e
l
l
kno
w
n
, b
u
t
we b
r
i
e
fl
y
di
sc
uss t
h
em
here.
For
val
u
e
s
of
λ
in (0,
3),
Equation (1) will c
onve
rge
to som
e
value x. For
λ
bet
w
ee
n
t
h
ree a
n
d a
b
o
u
t
3.
56
t
h
e s
o
l
u
t
i
on t
o
(1) b
i
fu
rcates i
n
to
two
,
th
en
fo
ur, th
en
eigh
t (an
d
so
on
)
period
ic so
lu
tion
s
. Fo
r
λ
bet
w
een 3.56 and four the
sol
u
t
i
o
ns t
o
(
1
) bec
o
m
e
ful
l
y
chaot
i
c
nei
t
her co
n
v
er
ge
n
t
nor pe
ri
o
d
i
c
,
but
vari
a
b
l
e
wi
t
h
n
o
di
scer
ni
bl
e
p
a
ttern. As
λ
a
p
proaches
four, the
va
riation i
n
s
o
lu
tions t
o
(1) appears inc
r
easingly ra
ndom
.
Th
us cha
o
t
i
c
s
e
que
nces a
r
e
hi
g
h
l
y
un
p
r
edi
c
t
a
bl
e ran
d
o
m
fu
nct
i
o
ns,
w
h
i
c
h can
hel
p
i
n
ge
ne
rat
i
n
g
ran
d
o
m
num
bers. T
h
ese
n
u
m
b
ers
can
pa
ve
a way
t
o
ge
ner
a
t
e
ran
d
o
m
freque
ncy
ca
rri
e
r
s
f
o
r
P
W
M
sc
hem
e
s.
Thi
s
ca
n be
e
x
pl
ai
ned
wi
t
h
t
h
e hel
p
o
f
Fi
g
u
re
1
.
T
h
e ra
n
dom
si
gnal
n
s
(
t
) va
ri
es
bet
w
e
e
n t
h
e
up
per
a
n
d
t
h
e
lo
wer bou
nd
aries. Its sam
p
les
are ind
i
cated
at three
poi
nts
A, B a
n
d C.
T
h
ese
values
are taken as
gui
delines
o
f
t
h
e carrier trian
g
u
l
ar
wav
e
s g
e
n
e
rated
.
The sam
p
lin
g
A is a n
e
g
a
tiv
e v
a
lu
e, B is a zero and
C is a po
sitiv
e
num
ber.
Thei
r
res
p
ect
i
v
e
fre
que
nci
e
s a
r
e l
o
w
,
m
e
di
um
and
hi
gh
. M
o
re
n
u
m
b
er o
f
sa
m
p
l
e
s needs t
o
be
co
nsid
ered
wh
ile
u
s
ed
in a PWM technique
.
Fi
gu
re
1.
R
a
n
d
o
m
si
gnal
,
n
s
(t
)
g
u
i
d
e
d
gene
ra
t
i
on of
t
r
i
a
n
g
u
l
a
r wave
car
ri
er
The
basi
c t
ool
avai
l
a
bl
e
fo
r
qua
nt
i
f
y
i
n
g
t
h
e m
e
ri
t
of any
P
W
M
t
ech
ni
q
u
e i
n
i
t
s
ha
rm
oni
c
p
o
w
e
r
sprea
d
in
g e
ffec
t
is harm
onic s
p
rea
d
in
g
facto
r
(H
SF
).
2
()
N
1
HS
F
=
Hj
Ho
N
j>
1
(2)
Whe
r
e,
N de
n
o
t
e
s t
h
e t
o
t
a
l
num
ber o
f
f
r
e
que
ncy
com
p
o
n
ent
s
c
onsi
d
er
ed,
H
j
is th
e
a
m
p
litu
d
e
o
f
t
h
e j
th
com
pone
nt
a
n
d
H
0
i
s
t
h
e a
v
era
g
e
val
u
e
o
f
al
l
com
pone
nt
s.
It
i
s
gi
ven
by
t
h
e
eq
uat
i
on:
1
H=
0
1
N
H
j
N
j
(
3
)
Th
e HSF
q
u
a
n
t
ifies th
e sp
read sp
ectra effect o
f
th
e
rando
m
PW
M schem
e
an
d
it shou
ld
be s
m
all. Fo
r ideally
flat spectra
of
white
noise
, the HSF
would be zero.
2.
PROP
OSE
D
METHOD
Th
e
b
a
sic i
d
ea of th
e pro
p
o
s
ed
CPWM is i
n
tow
fo
ld
. First a ch
ao
tically freq
u
e
n
c
y m
o
du
lated-
fi
xe
d m
a
gni
t
ude t
r
i
a
n
g
u
l
a
r c
a
rri
er
(C
FM
F
M
TC
) i
s
ge
ne
rated
.
Th
en
the CFMFMTC is co
m
p
ared
with
th
e
trad
itio
n
a
l si
n
u
so
id
al referen
c
e for pu
lse
g
e
neratio
n. Th
e co
m
p
lete sch
e
me is d
e
scri
b
e
d
in
th
e Fi
g
u
re 2. The
ch
ao
tic seq
u
e
nce is g
e
n
e
rated
and
p
a
ssed
to
th
e tria
ngu
lar o
s
cillato
r.
Th
e triangu
lar o
s
cillato
r generates
C
F
M
F
M
T
C
.
T
h
e m
odul
at
i
on
i
nde
x co
rrect
e
d
t
h
ree
p
h
ase s
i
nus
oi
dal
re
fer
e
nces are c
o
m
p
are
d
wi
t
h
t
r
i
a
ng
ul
a
r
wave
s. T
h
e
pulses obtained a
n
d their invert
ed
form
s ar
e
f
e
d
t
o
t
h
e VS
I aft
e
r dri
v
i
n
g u
n
i
t
.
T
h
e
se
que
nce of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
83 –
39
2
38
6
ran
d
o
m
nu
m
b
ers ge
nerat
e
d b
y
chaot
i
c
seq
u
e
nce d
o
es
not
exhi
bi
t
t
h
e l
i
m
i
t
a
t
i
on of
ot
he
r
ran
dom
carri
er P
W
M
(RCPW
M
)
m
e
th
od
s i.e. restri
cted
rep
e
titio
n
rate (li
m
ited
n
u
m
b
er o
f
d
i
sti
n
ct p
a
ttern
s). Th
e wo
rd
“th
e
ran
d
o
m
carrier” will get its flawless m
ean
in
g
if t
h
e freq
u
e
n
c
y i
s
v
a
ried
cycle to
cycle ran
d
o
m
l
y
lik
e sh
own in
Fi
gu
re 3.
C1
C2
C3
S1
S2
S3
S4
S6
S5
S
i
nus
oi
da
l
w
ave
120
⁰
120
⁰
Tr
i
a
n
g
u
l
a
r
wa
v
e
g
e
n
e
r
a
t
o
r
Ran
d
o
m
nu
m
b
e
r
u
s
in
g
ch
a
o
tic
s
e
q
u
en
c
e
+
+
+
‐
‐
‐
f
r
e
q
ue
nc
y
v
a
l
u
e
Co
m
p
arato
r
Del
a
y
C
F
MF
MT
C
V
a
V
b
V
c
Figure 2
.
Prop
osed
Chaos ba
sed P
W
M
Fi
gu
re
3.
C
F
M
F
M
T
C
wi
t
h
cycle to cycle va
riation
2.
1. Ch
a
o
ti
c S
e
quence an
d CF
MFMT
C
The
basi
c
p
r
i
n
ci
pl
e o
f
c
h
a
o
s-
base
d P
W
M
i
s
t
o
use
a c
h
aot
i
c signal
to
va
ry the s
w
itching
or carrier
fre
que
ncy
.
The
cha
o
t
i
c
seq
u
e
n
ce
descri
bed
i
n
t
h
e
E
quat
i
o
n
(4
) i
s
em
pl
oy
ed i
n
t
h
i
s
pa
per.
)
1
5
(
5
.
0
)
(
)
1
(
c
low
high
low
n
n
x
f
f
f
f
(4)
2(
)
(
)
0
(
)
5
(1
)
52
(
)
c
c
xn
i
f
xn
a
n
d
x
n
xn
xn
e
l
s
e
Whe
r
e,
f
n
is the
n
th
s
w
itching fre
quency
of
chao
tic PWM,
chaotic se
quences
x
n
m
a
y
be
gene
rat
e
d
si
m
p
l
y
by
i
t
e
rat
i
on. T
h
u
s
t
h
e swi
t
c
hi
n
g
fre
que
ncy
m
a
y
be vari
e
d
f
r
o
m
f
lo
w
to
f
hig
h
. Arb
itrary
p
e
riod
ic o
r
b
it can
b
e
obt
ai
ne
d
by
usi
n
g
di
f
f
e
r
ent
va
l
u
e o
f
c.
T
h
e fl
ow
cha
r
t
f
o
r
ge
nerat
i
o
n
of
cha
o
t
i
c
seq
u
e
n
ce i
s
sh
o
w
n i
n
Fi
g
u
re
4
an
d on
e
o
f
t
h
e
p
o
s
itiv
e i
n
teg
e
r seq
u
e
n
ces
g
e
n
e
rated
b
y
iteratio
n
in
M
A
TLAB env
i
ron
m
e
n
t correspo
n
d
s
to
c
=
6 i
s
s
h
ow
n i
n
F
i
gu
re
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
A T
a
ctical Chaos
based PWM
Technique f
o
r
Distortio
n Rest
raint
and Pow
e
r Spectrum
Shapi
ng…
(V.Mohan)
38
7
Fi
gu
re 4.
Fl
o
w
chart
fo
r ge
ner
a
t
i
on of
cha
o
t
i
c
seq
u
e
n
ce
Fig
u
re
5
.
Gen
e
ratio
n of
p
o
sitiv
e in
teg
e
r sequen
ces
with
un
ifo
r
m
d
i
stribu
tion
for c=
6
3.
RESULTS
A
N
D
DI
SC
US
S
I
ON
Si
m
u
latio
n
s
are carried
ou
t
usin
g
M
A
TLAB so
ft
ware
. The ch
ao
tic sequ
en
ce is co
d
e
d
in
m
-file wh
ile
th
e VSI sch
e
matized
in
Sim
u
l
i
n
k
m
o
d
e
l (.m
d
l) file.
Th
e m
a
in
ai
m o
f
th
is sectio
n
is co
m
p
aring
th
e
per
f
o
r
m
a
nces of S
P
W
M
a
n
d
t
h
e devel
ope
d C
P
W
M
. T
h
e i
n
p
u
t
dc v
o
l
t
a
ge (V
dc
) i
s
41
5
V
an
d t
h
e
out
p
u
t
fre
que
ncy
i
s
t
a
ken a
s
5
0
Hz
. T
h
e swi
t
c
hi
n
g
f
r
e
que
ncy
o
f
SP
WM
i
s
3
KHz
whi
l
e
f
o
r c
h
a
o
s base
d P
W
M
carri
e
r
f
r
e
q
u
e
n
c
y is
var
i
ed
f
o
r
m
2
K
H
z
to 4KH
z
.
Th
e l
o
ad is 3H
P
,
2
20V
,
3
ph
ase squ
i
r
r
e
l cag
e
indu
ction
m
o
to
r
.
Si
m
u
latio
n
resu
lts su
ch
as fu
nd
am
en
tal
mag
n
itud
e
,
THD and
HSF are con
s
id
ered for stud
y
.
Fi
g
u
re
6
represen
ts ou
tp
u
t
lin
e
v
o
ltag
e
s wh
ile Figu
re
7
ind
i
cates lin
e cu
rren
ts. Figu
re
8
illu
strates th
e h
a
rm
o
n
i
c
spect
r
u
m
of l
i
n
e v
o
l
t
a
ge a
n
d F
i
gu
re
9 s
h
o
w
s
t
h
e P
o
wer
spect
ral
de
nsi
t
y
f
o
r
SP
W
M
.
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.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
83 –
39
2
38
8
Figure 6
.
Si
m
u
lated
lin
e-lin
e
v
o
ltag
e
wav
e
form
s o
f
SPW
M
fo
r
Ma = 0.8
Figure 7
.
Sim
u
l
a
t
e
d cu
rre
nt
w
a
vef
o
rm
s of
S
P
W
M
fo
r M
a
=
0
.
8
Figure 8
.
Sim
u
l
a
t
e
d ha
rm
oni
c spect
r
u
m
of
S
P
W
M
fo
r M
a
=
0
.
8
Figure 9
.
Pow
e
r s
p
ectral
den
s
ity
(PSD
)
of
S
P
W
M
fo
r M
a
=
0
.
8
Harm
oni
c s
p
e
c
t
r
um
of C
P
WM
at
M
a
=0
.
8
a
nd M
a
=
1
.
2
are
prese
n
t
e
d
i
n
Fi
g
u
r
e
10
and
Fi
g
u
re
1
1
r
e
sp
ectiv
ely. In
th
e pr
opo
sed
CPW
M
sch
e
m
e
t
h
e cl
ust
e
r o
f
harm
oni
c
spect
ra
pea
k
appea
r
s at
s
w
i
t
chi
n
g
fre
que
ncy
(f
s
)
an
d t
h
e
resi
dual
d
o
m
i
nant
ha
rm
oni
cs o
ccur
at
m
u
l
t
i
pl
es
of
swi
t
c
hi
n
g
fre
q
u
enc
y
are
con
s
i
d
era
b
l
y
r
e
duce
d
at
t
h
e swi
t
c
hi
n
g
fr
eq
u
e
ncy
and
o
dd
m
u
l
tip
les o
f
it. In
g
e
n
e
ral, th
e
1
-
10
kHz range is th
e
regi
on of the greatest annoy
ance for human listeners.
Un
fortun
ately, th
is reg
i
o
n
may co
in
cid
e
with
th
e
switch
i
ng
frequ
e
n
c
y
o
f
the po
wer conv
erters. Hen
ce it is
im
p
o
r
tan
t
th
at th
e acou
s
tic no
i
s
e with
a frequen
c
y
below
10 kHz shoul
d
be re
duced.
T
h
eir ha
rm
onic
spect
rum is shape
d
a
half ci
rcle a
p
pear around f
s
a
nd
pea
k
cluster a
ppe
ars
at 2f
s
and
its
m
u
l
tip
les.
Figure 10.
Simul
a
t
e
d
harm
oni
c spect
r
u
m
of
C
P
W
M
fo
r M
a
=
0
.
8
Figure 11.
Simul
a
t
e
d
harm
oni
c spect
r
u
m
of
C
P
W
M
fo
r M
a
=
1.
2
0
0.
0
0
5
0.
0
1
0.
01
5
0.
0
2
0.
0
2
5
0.
03
0.
0
3
5
0.
0
4
0
.
045
0.
0
5
-5
00
0
50
0
Va
b
(
V)
0
0.
0
0
5
0.
0
1
0.
01
5
0.
0
2
0.
0
2
5
0.
03
0.
0
3
5
0.
0
4
0
.
045
0.
0
5
-5
00
0
50
0
Vb
c
(
V
)
0
0.
0
0
5
0.
0
1
0.
01
5
0.
0
2
0.
0
2
5
0.
03
0.
0
3
5
0.
0
4
0
.
045
0.
0
5
-5
00
0
50
0
V
ca(
V
)
Ti
m
e
(se
c
)
0.
2
0.
21
0.
22
0.
23
0.
24
0.
25
0.
26
0.
27
0.
28
0.
2
9
0.
3
-2
0
0
20
ia
(A
)
0.
2
0.
21
0.
22
0.
23
0.
24
0.
25
0.
26
0.
27
0.
28
0.
2
9
0.
3
-2
0
0
20
ib
(A
)
0.
2
0.
21
0.
22
0.
23
0.
24
0.
25
0.
26
0.
27
0.
28
0.
2
9
0.
3
-2
0
0
20
ic
(A
)
Ti
m
e
(
s
e
c
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
208
8-8
6
9
4
A Ta
ctica
l
Chao
s
b
a
sed PWM Techn
i
qu
e f
o
r
D
i
sto
r
tion
Rest
ra
in
t
an
d Po
w
e
r Sp
ectrum
Sha
p
i
n
g
…
(V.Moh
an
)
38
9
Tab
l
e
1
an
d 2
p
r
ov
id
e t
h
e com
p
reh
e
n
s
iv
e
details o
f
resu
lts ob
tain
ed
fro
m bo
th
SPWM an
d CPW
M
.
The
val
u
e
o
f
t
h
e f
u
ndam
e
nt
al
com
pone
nt
(
V
01
), TH
D
a
n
d HSF o
f
t
h
e out
put
v
o
l
t
a
ge
are
l
i
s
t
e
d
at
d
i
ffere
nt
m
odul
at
i
on i
n
d
e
x val
u
e
s
(M
a
)
.
For t
h
e e
n
t
i
r
e wo
rki
ng ra
n
g
e
C
P
W
M
of
fer
s
l
e
sser HSF a
nd T
H
D, an
d h
i
ghe
r
V
01
. At Ma=0.2
abou
t 50
% redu
ctio
n
at
HSF is ob
tained
. Th
e THD redu
ctio
n
is
marg
in
al wh
ile th
e
fundam
ental e
nha
ncem
ent is
noticeable.
At higher m
odulation indices
the im
provem
e
nt gai
n
ed in
HSF is
get
t
i
ng re
duce
d
.
Tabl
e
1. R
e
s
u
l
t
s
o
f
S
P
W
M
Ma
V
01
THD
HS
F
0.
2
49.
059
257.
97
8.
312
0.
4 75.
86
164.
31
6.
142
0.
6
114.
00
121.
10
5.
880
0.
8 146.
60
98.
23
5.
566
1.
0 190.
90
68.
42
4.
952
1.
2 211.
80
62.
23
4.
243
Tabl
e
2. R
e
s
u
l
t
s
o
f
C
P
WM
Ma
V
01
THD
HS
F
0.
2 52.
28
255.
41
4.
1416
0.
4 76.
10
162.
44
3.
9262
0.
6 114.
5
120.
74
3.
8430
0.
8
149.
70
93.
76
3.
7899
1.
0
192.
10
67.
50
3.
5380
1.
2
215.
90
56.
09
3.
3225
3.
1. HA
R
D
W
ARE
IMPL
E
M
E
N
T
A
T
I
O
N
The
designe
d
CPW
M
logic i
s
incorporated
as an
a
r
c
h
i
t
ect
ure
usi
n
g
t
h
e
VH
DL l
a
ng
ua
ge. M
o
d
e
l
s
im
9.
3f i
s
em
pl
oyed as a t
ool
f
o
r per
f
o
rm
i
ng f
unct
i
o
nal
si
m
u
l
a
t
i
on whi
l
e
Xi
l
i
nx ISE
12
.1 i
s
t
h
e sy
nt
hesi
z
e
t
ool
fo
r t
h
e R
e
gi
st
e
r
Tra
n
sfe
r
Le
v
e
l
(R
TL) l
e
vel
veri
fi
cat
i
o
n an
d i
m
pl
em
ent
a
t
i
on
. The
f
unct
i
onal
veri
fi
e
d
c
ode
of
th
e arch
itectu
r
e is do
wn
load
ed
to th
e
SPARTAN-6
FP
GA (XC
6
SLX45) d
e
v
i
ce.
Th
e fl
o
w
ch
art illu
strated
i
n
Fig
u
re 12
rep
r
esen
ts th
e respo
n
s
i
b
ilities o
f
Mo
d
e
lsim
an
d
Xilin
x
.
Th
e cod
e
alg
o
rith
m
fo
llo
ws th
e concep
tu
al
diagram
presented in
Figure
12.
Fig
u
r
e
12
.
FPG
A
D
e
si
g
n
f
l
ow
for
SPW
M an
d RPW
M
sche
m
e
s
The re
gister transistor logic
(R
TL)
vi
ew o
f
t
h
e devel
ope
d
archi
t
ect
ure i
s
gi
ven i
n
Fi
g
u
r
e 1
3
. T
h
e
d
e
v
i
ce u
tilizatio
n
su
mmary is
fo
und
in
Fig
u
re 1
4
.
Th
e co
mp
lete ti
min
g
analysis is
d
i
ag
rammed
in
Fig
u
r
e 1
5
.
Rep
r
esen
tativ
e h
a
r
d
w
a
r
e
h
a
rm
o
n
i
c sp
ectr
a
ar
e
pr
esen
ted fo
r Ma=0
.8 an
d 1.2 in Figur
e
1
6
an
d Figu
r
e
17
respectively. T
h
e capt
u
re
d line volta
ge
and
current
wa
veform
s are shown at
Fi
gu
re
1
8
.
The pul
se pat
t
e
rn
i
s
rep
r
ese
n
t
e
d
i
n
Fi
gu
re 1
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
83 –
39
2
39
0
Figu
re
1
3
. RT
L Dia
g
ram
for
CP
W
M
Device Ut
iliz
a
t
i
on Summ
a
r
y (
e
stimat
ed values)
Logic Ut
iliz
a
t
i
on
Used
Available
Utili
z
a
tion
Nu
m
b
er
of Slice Register
s
325
3006
4
1
%
Nu
m
b
er
of Slice LUT
s
793
1503
2
5
%
Nu
m
b
er
of fully
used L
U
T-
FF pair
s
228
890
26%
Nu
m
b
er
of bonded
I
O
Bs
10
186
5%
Nu
m
b
e
r
of
BUFG/
B
UFGCTRLs
5
1
6
31%
Nu
m
b
er
of DSP48
A
1s
3
3
8
8
%
Fig
u
re 14
. Device
u
tilizatio
n
su
mmary
Fig
u
re
15
. C
o
m
p
le
te ti
min
g
an
alysis
Figure 16.
Harmonic sp
ectru
m fo
r
of C
P
WM
Ma =
0.8
Figure 17.
Harmonic sp
ectru
m
of C
P
WM
for
Ma =
1.2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A Ta
ctica
l
Chao
s
b
a
sed PWM Techn
i
qu
e f
o
r
D
i
sto
r
tion
Rest
ra
in
t
an
d Po
w
e
r Sp
ectrum
Sha
p
i
n
g
…
(V.Moh
an
)
39
1
Figure 18. Lin
e
voltages and
line
currents o
f
phases
a &
b
(Ma =0
.
8
)
Figure 19.
G
ating pulses
4.
CO
NCL
USI
O
N
Di
st
ri
b
u
t
i
o
n
o
f
ha
rm
oni
c p
o
w
e
r
becom
e
s
m
a
jo
r t
opi
c
of
i
n
t
e
rest
i
n
P
W
M
-
VSI
d
r
i
v
es
. R
a
nd
om
pul
se
wi
dt
h m
o
d
u
l
a
t
i
on t
ech
ni
q
u
es
aim
i
n
reduci
ng t
h
e HS
F.
H
SF i
s
t
h
e i
n
di
cat
or f
o
r
ha
rm
oni
c p
o
we
r sp
re
adi
n
g
ab
ility o
f
a PWM techn
i
qu
e. Rand
o
m
n
e
ss
ad
d
e
d
i
n
to
th
e
PW
M
wav
e
form
can
cau
se the h
a
rm
o
n
i
c
p
o
wer t
o
sprea
d
o
v
e
r
t
h
e ha
rm
oni
c spect
r
u
m
so that
no
harm
oni
c com
pone
n
t
has a si
gni
f
i
cant
m
a
gni
t
u
de. T
h
e
pr
o
pose
d
cha
o
s based P
W
M
con
f
i
r
m
s
t
h
at t
h
e ran
dom
ization o
f
carrie
r
fre
q
u
en
cy offe
rs advanta
g
eous
feat
ure
s
suc
h
as red
u
ce
d t
o
t
a
l
harm
oni
c di
st
ort
i
o
n, EM
I
em
i
ssi
on fr
om
con
v
ert
e
r eq
u
i
pm
ent
,
acoust
i
c
an
d
vi
b
r
at
i
on e
f
f
e
c
t
s and
i
m
prove
d
harm
oni
c p
o
w
er s
p
ect
r
u
m
in electronic
dri
v
e system
s. For the e
n
tire
worki
n
g
ran
g
e CP
WM
of
fers lesse
r
HSF a
n
d T
H
D, a
nd
hig
h
e
r
V
01
. A
t
Ma=0
.2
abou
t 50% r
e
du
ction
at H
SF is
o
b
t
ain
e
d
.
At
h
i
g
h
e
r m
o
du
latio
n
ind
i
ces t
h
e i
m
p
r
o
v
e
m
e
n
t
gain
ed
i
n
HSF is g
e
tting
redu
ced
.
REFERE
NC
ES
[1]
KM Cho, WS
Oh, YT Kim, HJ Ki
m. A new switching str
a
teg
y
for pu
lse width modulation (PWM) po
wer
converters.
I
E
EE Transactions
on Industrial
Electronics
. 2007; 5
4
(1): 330-337
.
[2]
T Sutikno, AJidin, NRN Idris. New approach
FP
GA-based i
m
plementation of
discontinuous SVPWM.
Tu
rk
ish
Journal of Electrical
Engi
neerin
g &
Computer
Scien
ces
. 2010; 1
8
(4): 499-514
.
[3]
Prasad N.Enjeti, Phoivos
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James F.Lindsay
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c
hniques to Elim
in
at
e Harm
onics
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al
Eva
l
ua
ti
on.
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lica
tions
. 1
990; 26(2): 302-
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[4]
AM Hava, R
Kerkman, TA Lipo.
A High-Performance Generalized
Discontinuous PWM Algorithm.
IEEE
Transactions on
Industry applica
tions
. 1998
; 5
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[5]
TG Habetler, D
M
Divan. Acoustic noise
r
e
duction in sinusoidal
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:
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[6]
T Sutikno, M Facta. An Efficient Stra
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e
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al
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e
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e
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[7]
RL Kirlin
, S Kwok, S Legowski, AM Trzy
n
a
d
l
owski. Po
wer spectr
a
of a PWM inverter
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randomized pu
lse
position.
IEEE T
r
ansactions on Power Electronics
. 1994; 9: 463–4
71.
[8]
Z Ibrahim, ML
Hossain, I Bugis
,
NMN Mahadi,
A Shukri,
A Hasim. Simulation I
nves
tigation of S
P
WM, THIPWM
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V
P
W
M
Techniques
for
Thr
ee P
h
as
e Vol
t
ag
e S
ource Inv
e
rt
e
r
.
International
Journal of
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d
Dr
ive Sys
t
em
. 20
14; 4(2): 223-23
2.
[9]
BJ Kang, CM LiawKi-Seon Ki
m, Young- Goo
k
Jung, Young-
Cheol Lim.
Ran
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BIOGRAP
HI
ES OF
AUTH
ORS
V.
Mohan
recei
ved Bach
elor’s
degree in
the ar
ea of El
ect
ric
a
l
and Ele
c
tron
ics
Engine
ering an
d
Master’s degree
in Power Electr
o
n
ics and Drives
from Bharathidasan University
in the
y
e
ar 1995
and Nov 2001 r
e
spectively
.
No
w he is pursuing
his
resear
ch in
the ar
ea of R
a
nd
om Pulse Widt
h
Modulation at A
nna University
,
Chennai, India.
He has around 1
6
y
e
ars of teach
ing experience
.
Currentl
y
h
e
is
working as
an
a
s
s
o
ciate
profes
s
o
r in th
e d
e
part
m
e
nt of El
ec
tric
al and
E
l
ec
troni
cs
Engine
ering
at
E
.
G.S.Pill
a
y
Engi
neering
Coll
ege
,
Nagapa
ttin
am
, I
ndia.
D
r
.N
.S
talin
rec
e
ived th
e Bach
elor of Te
chno
log
y
d
e
gree
in
Chem
ical Eng
i
neer
ing from
Bharath
i
dasan University
,
Trich
y
in 1999 and Mast
er of Techno
lo
g
y
in En
erg
y
En
gineer
ing from
REC (NIT),
Trich
y
in 2003
. He completed
his
Ph
.D. degree in
Energ
y
Eng
i
neering from NIT,
Trich
y
in 2007.
Since 2009, he has been with the
Department of Petroch
e
mical Technolog
y
as an
Assista
n
t Profe
ssor a
t
Anna
Unive
r
sity
,
BIT c
a
m
pus, Tiruch
irapp
a
lli, India. He h
a
s published 10
papers in variou
s referred intern
ation
a
l journa
ls and 28 publicatioons at
various
international
conferen
ces
.
Dr.S.Jeevananthan
received th
e B.E
.
degre
e
i
n
Elec
tri
cal
and
Elec
troni
cs
Engineer
ing from
MEPCO SC
HLENK Engineer
ing Colleg
e
, Siv
a
kasi
, Ind
i
a, in
1998, and th
e
M.E. d
e
gree
from
PSG College of Techno
log
y
, C
o
imbatore, Ind
i
a,
in 2000. H
e
completed his Ph.D. degr
ee from
Pondicherr
y
University
in 2007
.
Since 2001, he
has
been with th
e Depar
t
ment of
Electrical and
Electronics Engineering
,
Pondicher
r
y
Engin
eering College, Pon
d
iche
rr
y
,
India,
where he is an
associate profes
sor. He made
a significan
t
contribution
to
the PWM theory
through his
publications and
has developed
clos
e ti
es with the intern
ation
a
l
re
s
earch com
m
u
nit
y
in
the
ar
ea
.
He has author
ed more than 5
0
papers publis
hed in in
tern
ational and n
a
tio
n
al conf
eren
ce
proceed
ings
an
d profes
s
i
onal
journals
. He r
e
gularl
y
r
e
views
papers
for a
l
l m
a
jor IEE
E
Trans
a
c
tions
in his
area and AM
S
E
periodicals
(F
rance). H
e
is
an active
m
e
m
b
er of the
professional societies, I
E
(I
ndia
)
,
MIST
E
.
, SE
MCE
.
, a
n
d SSI.
Evaluation Warning : The document was created with Spire.PDF for Python.