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.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 12
1
~
12
8
I
S
SN
: 208
8-8
6
9
4
1
21
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
Selection of Power Semiconductor
Switches in M.H.B.R.I. Fitted
Induction Heater for Less Harm
onic Injection in Power Line
Pradip
Kum
a
r Sadhu
*,
Pal
a
sh
Pal
*
*,
Nitai P
a
l*,
S
o
uris
h S
a
n
yal
***
* Electr
i
cal
Engineering
Depar
t
ment, Indian Scho
ol of Mi
n
e
s (und
er MHRD, Govt. of India), Dhan
bad - 82600
4, In
dia
**
Departmen
t
o
f
Electr
i
cal
Engineering
,
Saro
j M
ohan Institute of
Techno
log
y
(D
egree
Engin
eerin
g Divison), a Un
it of
Techno
India Gr
oup, Guptip
ara,
Hooghly
-
71251
2, India
*** Departmen
t
of Electron
i
cs
an
d Communicatio
n Engi
n
eering
,
Academ
y
of
Technolog
y
,
Hooghly
,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 29, 2014
Rev
i
sed
D
ec 14
, 20
14
Accepte
d Ja
n
2, 2015
Thi
s
pa
pe
r
presents a
n
a
ppr
o
a
ch
t
o
m
i
n
i
mi
z
e
t
h
e
ha
r
m
o
n
ic
s
co
n
t
a
i
ne
d
in
in
put
c
u
r
r
e
n
t
o
f
si
n
g
l
e
ph
a
s
e
Modified
Half
B
r
idg
e
R
e
s
o
n
a
n
t
I
n
v
e
r
t
e
r
(M.H.B.R.I
.) f
itted i
nduction h
e
ating equ
i
pment.
A switch
lik
e
I
G
B
T
,
G
T
O
and
MOSFET
a
r
e
use
d
f
o
r
t
h
is pur
po
se
.
It
i
s
analy
z
ed
t
h
e
h
a
r
m
o
n
ics or
n
o
i
se
c
o
n
t
e
n
t
i
n
t
h
e
sinu
so
id
a
l
input
c
u
r
r
e
nt
o
f
this inver
t
er.
F
o
u
r
i
e
r
Tra
n
sfo
r
m ha
s
b
een u
s
e
d
to
d
i
stin
guish b
e
tw
e
e
n th
e
fu
n
d
a
m
en
ta
l
a
n
d
th
e
ha
r
m
o
n
ic
s,
a
s
it
is a
bet
t
e
r
i
n
v
e
s
t
ig
a
t
i
v
e
t
o
o
l
f
o
r
a
n
unkno
w
n
si
g
n
a
l
in
t
h
e
freq
u
e
n
c
y
d
o
m
a
i
n
.
An extensive
method for the s
e
lection of
differ
e
nt
pow
er
semiconductor
sw
itch
e
s for M
o
d
i
f
i
ed
H
a
lf
B
r
idg
e
R
e
s
o
n
a
n
t
i
n
v
e
rter
f
e
d
induc
tion
he
ate
r
is
pr
e
s
e
n
te
d.
He
ating
c
o
il
of
the
induc
tion
he
ate
r
is made
of
litz
w
i
re
w
h
i
c
h
reduces
the
skin e
ffe
c
t
and proxim
ity
e
f
f
e
c
t
a
t
high
ope
r
a
ting
fr
e
quency
.
With
the
c
a
lc
ulate
d
optimum value
s
of
i
n
pu
t
c
u
r
r
e
n
t
of
the
s
y
s
t
em
at a p
a
rticu
l
ar op
era
t
in
g freq
u
e
n
c
y,
t
h
e
m
o
d
i
f
i
e
d
h
a
l
f
b
r
i
d
g
e
r
e
s
o
n
a
n
t
inverter t
o
po
l
o
gy
h
a
s
be
e
n
si
mul
a
t
e
d
usi
n
g
P-
SI
M
so
f
t
w
a
r
e
.
From
t
h
i
s
propose
d
a
n
a
l
y
s
i
s
t
h
e
se
l
e
ct
i
on of
s
u
itable
pow
e
r
s
e
m
i
c
o
nduc
tor
sw
itc
he
s like
IGBT,
GTO
and
MOSFE
T
are
made. Wavefor
m
s have been
show
n to justif
y
the feas
ibi
lit
y
for real
im
ple
m
entati
on of si
ngle
p
h
a
s
e
Modified
Half
B
r
idg
e
R
e
s
o
n
a
n
t
inve
r
t
e
r
fe
d
induc
tion
he
ate
r
in
d
o
m
e
s
t
i
c
a
p
p
l
ic
a
t
i
o
n
s
a
s
we
l
l
a
s
industr
ial applic
ations.
Keyword:
Ed
dy
cu
rre
nt
Induction heat
er
M
o
d
i
f
i
e
d
h
a
l
f
bri
dge
res
o
nan
t
In
verte
r
THD
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
:
Pra
d
ip Kum
a
r
Sadhu,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
In
di
an
Sc
ho
ol
of
M
i
nes
(u
n
d
e
r
M
H
R
D
,
G
ovt
. o
f
In
di
a)
,
D
h
anb
a
d - 8260
04
, Ind
i
a.
Em
a
il: p
r
ad
ip_sadh
u
@yaho
o
.co
.
in
1.
INTRODUCTION
In
d
u
ct
i
on
heat
er fo
r i
n
dust
r
i
a
l
appl
i
cat
i
ons [
2
]
ope
rat
e
s
at
a hi
gh
f
r
eq
ue
ncy
[4]
,
[
7
]
ra
nge
f
r
om
1
kH
z
t
o
1
0
0
k
H
z.
I
n
t
h
e ap
pl
i
cat
i
on of l
o
w
fre
que
ncy
i
n
du
ct
i
on
heat
i
ng
t
h
e
t
e
m
p
erat
ure
d
i
s
t
r
i
b
u
t
i
o
n
can
b
e
cont
r
o
l
l
e
d by
sl
owl
y
va
ry
i
n
g
m
a
gnet
i
c
fi
el
ds bel
o
w a
fr
eque
ncy
[
6
]
as
l
o
w
as
3
0
0
Hz.
F
o
r
m
e
di
um
f
r
e
q
u
e
n
c
y
ap
p
licat
io
n
,
an
au
x
iliary
v
o
ltag
e
-fed
in
v
e
rter
is
o
p
e
r
a
t
e
d
in
p
a
rallel
with
th
e
m
a
in
cu
rren
t
-fed
i
nve
r
t
e
r
, s
i
nc
e
t
h
e
c
u
r
r
e
nt
- fe
d
paral
l
e
l
i
n
v
e
rt
ers [3]
al
o
n
e
,
w
h
e
n
use
d
f
o
r
i
n
d
u
ct
i
o
n
he
a
t
i
ng, f
a
i
l
t
o
s
t
a
r
t
.
A
h
i
gh
fr
eq
u
e
n
c
y
modi
fi
ed
hal
f
bri
dge
i
n
ver
t
er
s [1
], [5
] fo
r
indu
ctio
n
heatin
g
a
n
d
m
e
l
tin
g
app
lication
s
ar
e
s
e
l
f
-
s
t
a
r
t
ed
.
Fo
r
s
e
l
f
-
c
o
m
m
u
t
a
tio
n
,
a
r
e
so
n
a
n
t
c
i
r
c
u
i
t
is
es
s
e
n
tial fo
r SC
R fitted
in
v
e
rter[8
]-[9
], [11
]
.
I
t
is
assum
e
d t
h
at
t
h
e ci
rcui
t
i
s
u
nde
r dam
p
ed;
a
m
a
ndat
o
ry
c
o
ndi
t
i
on
for t
h
e ci
rcui
t
.
T
h
e
capaci
t
o
r
requi
r
ed
for
un
de
r dam
p
i
ng can
be c
o
nn
ect
ed i
n
seri
es
or i
n
pa
ral
l
e
l
w
i
t
h
t
h
e
l
o
a
d
[
3
]
i
n
t
h
e
m
ode
r
n
t
i
m
e
s
,
I
G
B
T
s
[
1
]
,
[8]
,
GT
Os
a
n
d MOSFETs
are
pre
f
erred
to
SCRs
m
a
inly
because
they offe
r
c
o
nve
n
ient turn OFF
characte
r
istic
s
.
Som
e
a
uxi
lia
ry c
i
rc
ui
t
s
a
n
d
equi
pm
ent
are re
qui
r
e
d
t
o
m
i
nim
i
ze swi
t
c
hi
ng l
o
sses
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
12
1
–
12
8
12
2
occu
rri
ng
at
hi
gh
fre
q
u
enci
e
s
[2]
.
W
i
t
h
t
h
e
sam
e
desi
gne
d
param
e
t
e
rs of t
h
e sai
d
i
n
vert
er
ci
rc
ui
t
,
vari
o
u
s
swi
t
c
hes
s
u
ch
as IGB
T
,
GT
O
and M
O
SFE
T
ha
ve
been
u
s
ed
[1
0]
.
The requirem
ents of
i
n
duc
tion
heater a
r
e as
follows:
a)
Swi
t
c
hi
n
g
i
n
hi
gh
f
r
eq
ue
ncy
r
a
nge
b)
High e
fficienc
y
c)
Power
factor cl
ose t
o
unity
d)
W
i
de p
o
we
r ra
nge
an
d
e)
Reliab
ilit
y
Induction heat
ers a
r
e
usuall
y desi
gne
d
to operate
with
a vessel m
a
de
from
a speci
fic m
a
terial,
mainly cast ir
on
or fe
rro-m
a
gnetic stainles
s steel. The
follo
wing
is th
erefore d
e
sire ch
aracteristics fo
r t
h
e
i
nve
rt
er,
a)
No
react
i
v
e
co
m
ponent
s
ot
he
r t
h
a
n
t
h
e
heat
i
n
g
coi
l
a
n
d
t
h
e
n
o
n
-
sm
oot
h
fi
l
t
e
r i
n
d
u
ct
o
r
,
b)
No
i
n
put
o
r
m
a
t
c
hi
ng
t
r
a
n
sf
or
m
e
r,
c)
5
0
%
d
u
t
y ratio, sim
p
lifyin
g
the con
t
ro
l and
gate circu
its,
d)
C
l
am
ped swi
t
c
h
vol
t
a
ge
an
d
o
r
c
u
r
r
ent
,
e)
The use o
f
unc
ont
rol
l
e
d
v
o
l
t
a
ge
s
o
urce.
Here
th
e
co
m
p
lete
in
v
e
r
t
e
r
co
n
f
ig
u
r
a
tio
n
h
a
s
b
e
e
n
s
i
m
u
lated
u
s
in
g
P-
SIM.
I
n
th
is
p
r
es
e
n
t
p
a
p
e
r
,
r
e
spon
se
o
f
har
m
o
n
i
c in
j
ectio
n
in
inpu
t p
o
w
e
r
lin
e of
modi
fi
ed
hal
f
b
r
i
dge
re
s
o
n
a
n
t
i
n
v
e
r
t
er
i
s
t
e
st
ed
&
veri
fi
ed
wi
t
h
di
ffe
rent
po
we
r
swi
t
c
hes
a
n
d
fi
nal
l
y
ap
pr
o
p
ri
a
t
e
n
ess
of
t
h
e s
w
i
t
c
hes i
s
co
nfi
r
m
e
d.
2.
AN
ALY
S
IS
O
F
PR
OPO
S
ED
MO
DIFIE
D
H
A
LF B
R
I
D
GE
RESO
N
ANT
IN
VER
TER
Pro
p
o
se
d m
o
d
i
fi
ed
hal
f
bri
d
ge ci
rc
ui
t
i
s
n
o
rm
al
l
y
used f
o
r
hi
ghe
r
po
w
e
r
out
put
.
B
a
s
i
c ci
rcui
t
i
s
sho
w
n i
n
t
h
e Fi
gu
re 1. F
o
ur
sol
i
d
st
at
e swi
t
c
hes are use
d
an
d t
w
o s
w
i
t
c
hes are t
r
i
g
g
e
red si
m
u
l
t
a
neousl
y
.
An
ti-p
a
rallel dio
d
e
s are con
n
ected
with th
e switch
t
h
at a
llo
ws t
h
e cu
rren
t to
flow wh
en
th
e m
a
in
switch
is
tu
rn
ed
OFF.
A
ccor
d
i
n
g t
o
Fi
g
u
re
1, w
h
e
n
t
h
ere i
s
no si
gnal
at
Q
1
and Q
2
, capacitors C
1
a
nd C
2
are c
h
arged t
o
a v
o
ltage of
V
i
/2 each. The
Gate pulse appears at the
ga
te of
Q1 to turn
IGBT
ON. Ca
pacitor C
1
di
sc
har
g
es
th
ro
ugh
th
e
path
NOPTN.
At
the sam
e
tim
e capacitor
C
2
charges through the
path MNOPTSYM. The
di
scha
rgi
ng c
u
rre
nt
of C
1
and the chargi
ng c
u
rrent of C
2
si
m
u
l
t
an
eo
usly flo
w
fro
m
P to
T. In
th
e n
e
x
t
slit o
f
th
e g
a
te pu
lse,
Q
1
a
nd Q
2
remain OFF and the capacitors c
h
arge to a
voltage V
i
/2 eac
h a
g
ain. T
h
e
Gate pulse
appea
r
s at the
gate of Q
2,
so
tu
rn
ing
on
Q
2
. The ca
pacitor C
2
d
i
sch
a
rg
es th
ro
ugh
th
e
path
TPQST and
th
e
charging pat
h
for ca
pacitor C
1
i
s
M
N
TPQS
Y
M
. The di
sc
har
g
i
n
g cu
rre
nt
of
C
2
and t
h
e cha
r
gi
ng c
u
r
r
ent
o
f
C
1
sim
u
l
t
a
neousl
y
fl
o
w
fr
om
T t
o
P
.
Fi
gu
re
1.
Pr
o
p
o
se
d m
odi
fi
ed
hal
f
bri
dge
res
ona
nt
i
n
ve
rt
er
Fi
gure 2 i
n
di
cat
es a speci
al
ly desi
gne
d eddy curr
en
t h
e
at
ed
m
e
tal
lic
p
ack
ag
e wh
ich
is tig
h
tly
i
n
t
e
g
r
a
t
ed
i
n
to
t
h
e
n
o
n
-
m
e
ta
llic
v
e
ssel
o
r
t
a
n
k
in
th
e
p
i
p
e
lin
e.
Th
e
m
e
ch
an
ically
p
r
o
c
e
s
s
e
d
th
i
n
s
t
a
i
n
l
e
s
s
-
st
eel
l
a
y
e
r package
wi
t
h
m
a
ny
sp
ot
s an
d
fl
ui
d cha
n
nel
s
fo
r cy
l
i
ndri
cal
i
nduct
i
o
n-
heat
ed assem
b
l
y
i
s
dem
onst
r
at
ed i
n
Fi
gu
re
3.
W
h
en t
h
e fl
ui
d fl
o
w
s t
h
r
o
u
gh t
h
e i
n
here
n
t
packa
g
e i
n
t
h
e v
e
ssel
o
r
t
a
nk
ha
vi
n
g
a
wo
rki
ng
coi
l
connect
ed t
o
pi
pel
i
n
e, t
h
e t
u
rbul
ent fl
ui
d
i
s
heat
ed ab
r
u
pt
l
y
by
eddy
cur
r
ent
l
o
s
s
es
gene
rat
e
d i
n
si
de t
h
e
s
t
a
i
n
l
es
s
-
s
t
e
e
l
p
a
c
k
ag
e
.
In
te
rn
a
l
stru
ctur
e
of
th
is
m
e
ta
llic
p
ack
a
g
e
to
be
h
eated
b
y
e
d
d
y
cu
rr
en
t los
s
e
s
is
i
ndi
cat
ed i
n
Fi
gu
re
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
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8-8
6
9
4
S
e
lectio
n o
f
Power S
e
m
i
con
ducto
r
S
w
itch
e
s i
n
M.H
.
B.
R.I
.
Fitted
I
ndu
ctio
n
H
e
a
t
er… (Prad
i
p
K
u
m
a
r Sadh
u
)
12
3
Fi
gu
re
2.
Heat
i
n
g
pac
k
a
g
e i
n
t
h
e
vessel
a
n
d
t
a
nk
Fi
gu
re
3.
I
n
t
e
r
n
al
st
r
u
ct
u
r
e
of
fl
ui
d t
h
ro
u
g
h
m
e
t
a
l
l
a
y
e
r pac
k
i
n
g t
o
gene
rat
e
t
u
r
b
ul
ence
fl
o
w
3.
CIR
C
U
IT EQ
UATI
O
N
S
3.
1.
Instan
taneous
Curre
nt i
0
W
i
t
h
indu
ctiv
e lo
ad th
e equ
a
tio
n of i
n
stan
taneo
u
s cu
rren
t i
0
can be obt
ai
ne
d
as:
0
22
1
,
3
,
5
,
...
2
()
s
i
n
(
)
()
i
n
n
V
it
n
t
nR
n
L
Here
,
22
()
n
ZR
n
L
is th
e i
m
p
e
d
a
n
ce offered
b
y
th
e lo
ad
to
th
e n
th
harm
oni
c com
pone
nt
,
2
i
V
n
is th
e
peak am
plitude of
n
th
ha
rm
oni
c v
o
l
t
a
ge,
an
d:
1
ta
n
n
nL
R
3.
2.
Output P
o
wer
The
output power at
f
u
n
d
am
ent
a
l
fre
q
u
e
n
c
y
(n=
1
)
i
s
gi
ve
n
by
:
2
11
1
1
1
..
c
o
s
.
r
m
s
r
ms
rms
r
ms
PE
I
I
R
Whe
r
e,
1
rm
s
E
=R
M
S
val
u
e
o
f
f
u
nda
m
e
nt
al
out
put
vol
t
a
ge
.
1
rm
s
I
=R
M
S
val
u
e
o
f
f
u
ndam
e
nt
al
out
put
c
u
rre
nt
.
1
1
ta
n
L
R
Bu
t,
1
22
2
2.
.
(
)
rm
s
i
V
I
RL
2
2
11
22
2
..
.2
.
(
)
rm
s
r
m
s
i
V
PI
R
R
RL
22
22
2
2
22
2
2
4.
2.
2(
)
(
)
ii
VR
V
R
RL
RL
In
hi
gh
f
r
eq
ue
ncy
h
eat
i
n
g
ap
pl
i
cat
i
on t
h
e
f
u
n
d
am
ent
a
l
po
wer
i
s
m
o
re i
m
port
a
nt
, t
h
e
out
put
p
o
w
e
r
due
t
o
fu
n
d
am
ent
a
l
cur
r
e
n
t
i
s
ge
neral
l
y
t
h
e
usef
ul
po
wer
a
nd t
h
e
po
we
r d
u
e t
o
ha
rm
oni
c cur
r
e
n
t
i
s
di
ss
i
p
at
ed
as heat.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
12
1
–
12
8
12
4
4.
THE HARMONIC
CONT
ENT
T
h
e i
n
p
u
t
c
u
r
r
e
n
t
w
a
ve
f
o
r
m
s
o
f
a
n
id
ea
l
inve
r
t
e
r
sh
o
u
ld
b
e
si
n
u
so
id
a
l
.
B
u
t,
i
n
p
r
act
i
ce, t
h
e
inp
u
t
cu
rr
en
t w
a
v
e
f
o
r
m
s are n
o
n
-
s
i
n
u
s
o
i
d
al.
I
t
co
nt
a
i
n
s
har
m
o
n
ics
.
T
h
e
e
x
iste
nc
e
o
f
har
m
o
n
ic
s
is
vis
u
a
liz
e
d
e
i
t
h
e
r
i
n
t
h
e
ti
m
e
-d
o
m
a
i
n
o
r
in
t
h
e
f
r
eq
ue
n
c
y
d
o
m
a
i
n
e
a
s
il
y.
T
h
e
a
v
a
ila
b
ilit
y
o
f
h
i
gh s
p
ee
d
p
o
w
e
r
se
m
i
c
o
nd
u
c
to
r
d
e
vice
s
ha
s
e
n
ab
led
u
s
to
r
e
d
u
ce
t
h
e
har
m
o
n
ic
c
o
n
t
e
n
ts
i
n
t
h
e
i
n
p
u
t
v
o
lta
ge
sig
n
i
f
ic
a
n
tl
y
b
y
s
w
i
t
c
h
in
g
tec
hni
q
u
e
s
[6
].
T
o
ta
l
H
a
r
m
o
n
ic
Di
s
t
o
r
t
i
o
n (T
HD)
i
s
a
m
e
as
ure
of t
h
e
cl
o
s
en
es
s
of
a
wa
v
e
fo
r
m
wi
t
h
i
t
s
f
u
n
d
a
m
e
n
t
a
l
c
o
m
p
o
n
e
n
t
.
T
h
e
t
a
s
k
of
t
h
e d
e
s
i
g
n
e
n
g
i
n
eer i
s
t
o
re
du
ce
T
H
D.
It
i
s
acco
m
p
li
s
h
ed b
y
an LC L
o
w
P
a
ss
f
ilter
(
L
P
F
)
a
s
w
e
l
l
a
s
u
s
in
g
m
o
st su
it
ab
le h
i
gh
f
r
e
q
u
e
n
c
y
sem
i
cond
uct
o
r
swi
t
c
h.
LPF
a
p
p
e
n
d
at
t
h
e
inpu
t
pow
er
supp
ly
t
e
r
m
i
n
a
l
o
f
M
o
di
fi
e
d
Hal
f
B
r
i
dge R
e
so
nant
In
vert
e
r
f
o
r i
n
d
u
ct
i
o
n
heat
i
n
g
equi
pm
ent
.
It
p
r
ov
i
d
es
l
o
w
h
a
r
m
o
n
i
c
im
pe
da
n
c
e
t
o
g
r
o
u
n
d
.
4.
1.
An
al
yti
c
al
T
o
ol
s
T
h
e
q
u
al
i
t
y
o
f
in
pu
t
cur
r
en
t
o
f
a
M
o
di
fi
ed Hal
f
B
r
i
d
g
e
R
e
sona
nt
I
n
vert
er
i
s
ob
t
a
i
n
ed
b
y
Fa
st
Fo
u
r
ie
r
’
s
a
n
a
l
y
s
is.
I
t
i
s
a
p
o
w
e
r
f
u
l
m
a
t
h
e
m
a
tic
a
l
to
o
l
w
h
ic
h
sep
a
r
a
te
s
o
u
t
t
h
e
fun
d
a
m
e
n
ta
l
a
n
d
t
h
e
ha
r
m
o
n
ic
s.
Fo
ur
ie
r
’
s
tr
a
n
s
f
o
r
m
s
a
l
lo
w
s
u
s
to
p
e
ep
into
t
h
e
f
r
e
q
u
e
n
c
y
do
m
a
in
rep
r
esen
tatio
n
o
f
t
h
e
wavef
o
r
m
.
4.
1.
1.
T
o
t
a
l
Har
m
on
i
c
D
i
s
t
or
t
i
on
(
T
HD
)
It i
s
a
m
eas
u
r
e
of
d
i
s
t
o
r
t
i
o
n
o
f
a
w
a
v
e
f
o
r
m
.
It i
s
g
i
v
e
n
b
y
t
h
e
f
o
l
l
o
w
i
n
g
e
x
pres
s
i
on
:
2
..
2,
3
1.
.
..
nr
m
s
n
rm
s
I
TH
D
I
(
1
)
I
t
is
the
r
a
tio
o
f
the
RM
S
va
lue
o
f
all
no
n-fu
n
d
a
m
e
n
ta
l
fr
eq
ue
nc
y
c
o
m
p
o
n
e
n
t
s
to
the
RM
S
va
l
u
e
o
f
the
f
u
n
d
a
m
e
n
ta
l.
O
u
r
a
i
m
i
s
to
re
d
u
c
e
to
a
m
i
ni
m
u
m
.
Fo
r
a
r
e
c
t
a
n
g
u
la
r
w
a
ve
:
T
h
e va
lue
i
s
ver
y
la
r
g
e
.
In
q
u
a
s
i
-
r
e
c
t
a
n
g
u
la
r
f
o
rm
,
the
va
l
u
e
is
r
e
la
ti
ve
l
y
l
e
ss.
T.H
.
D C
a
l
c
ul
at
i
on
fr
om
Soft
w
a
re Si
m
u
l
a
t
i
on:
a
)
T
.
H.
D
C
a
l
c
u
l
at
i
o
n o
f
M
odi
fi
ed
Hal
f
Bri
d
g
e
R
e
s
ona
nt
In
ve
rt
er
u
s
i
n
g
M
O
S
F
E
T
.
The
R.
M
.
S
V
a
lu
e
o
f
I
n
put
C
u
r
r
e
n
t
,
4
2.21
I
A
.
2
..
2,
3
1.
.
22
22
22
1
2
..
(
1
.1
6
1
0
)
(
1
.0
7
1
0
)
(
4
.6
3
1
0
)
(
1
.0
6
1
0
)
3.
13
3.
73%
nr
m
s
n
rm
s
I
TH
D
I
A
T
.
H.
D
C
a
l
c
u
l
at
i
o
n
o
f
M
odi
f
i
ed Hal
f
B
r
i
d
g
e
R
e
so
nant
I
nve
rt
er u
s
i
n
g
G
T
O
.
T
h
e R
.
M
.
S
Val
u
e
of
In
pu
t Cu
rren
t
,
4
4.08
I
A
.
2
..
2,
3
1.
.
22
2
2
22
..
(
8
.
9
5
1
0)
(
2
.
5
6
1
0)
(
5
.
9
5
1
0)
4.
08
2.
7%
nr
m
s
n
rm
s
I
TH
D
I
A
T
.
H.
D
C
a
l
c
u
l
at
i
o
n
o
f
M
o
di
fi
ed
Hal
f
B
r
i
d
g
e
Seri
es R
e
s
ona
nt
I
n
vert
er
u
s
i
n
g
I
G
B
T
.
The R
.
M
.
S
V
a
lu
e
o
f
I
n
put
C
u
r
r
e
n
t
,
4
4.097
I
A
.
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
e
lectio
n o
f
Power S
e
m
i
con
ducto
r
S
w
itch
e
s i
n
M.H
.
B.
R.I. Fitted
Indu
ctio
n
H
e
a
t
er… (Prad
i
p
K
u
m
a
r Sadh
u
)
12
5
2
..
2,
3
1.
.
22
22
3
2
22
..
(
2
.3
8
1
0
)
(
2
.8
1
1
0
)
(7
.5
7
1
0
)
(7
.
7
6
1
0
)
4.
0
9
7
2.
1%
nr
m
s
n
rm
s
I
TH
D
I
A
4.
1.
2.
Fas
t
F
o
uri
er
T
r
ansf
orm
(F
FT
)
Anal
ysi
s
:
A Fast Fo
urier Transfo
r
m
(FFT) is an
al
gorith
m
to
co
m
pute the disc
rete Fourier t
r
ans
f
orm
(DFT
)
a
n
d
i
t
’
s
i
n
v
e
r
s
e.
I
t
is
a
li
ne
a
r
a
l
go
r
ith
m t
h
a
t
c
a
n
tr
a
n
s
f
o
r
m
a
ti
m
e
d
o
ma
i
n
si
gna
l
i
n
to
it
s
fr
eq
u
e
nc
y
d
o
m
a
i
n
e
q
uiva
le
nt
an
d b
a
c
k
.
An FFT is a way
to com
pute the sa
m
e
result
m
o
re quickly
. FFTs are of great
im
port
a
nce t
o
a wi
de
vari
et
y
of a
p
pl
i
cat
i
o
n
s
, f
r
om
di
gi
t
a
l
si
gnal
pr
ocess
i
ng a
n
d
sol
v
i
n
g pa
rt
i
a
l
di
ffe
r
e
nt
i
a
l
eq
u
a
tion
s
t
o
alg
o
rith
m
s
fo
r q
u
i
ck
m
u
ltip
licatio
n
o
f
larg
e in
teg
e
rs.
A b
e
t
t
e
r
u
n
d
e
r
s
t
a
n
d
i
n
g
o
f
a
n
unkn
own
s
i
g
n
a
l
i
s
o
b
t
a
i
n
e
d
i
n
t
h
e
f
r
e
q
u
e
n
c
y
d
o
m
a
i
n
.
P
e
a
k
n
o
i
s
e
i
n
t
h
e
i
n
p
u
t
c
u
r
r
e
n
t
o
f
M
o
d
i
f
i
e
d
H
a
l
f
B
r
i
dge R
e
s
o
n
a
nt
In
vert
e
r
usi
ng M
O
SFE
T,
GTO a
n
d IGB
T
wi
t
h
LPF fi
l
t
er i
s
det
e
rm
i
n
ed by
FFT a
n
a
l
y
s
i
s
.
The m
a
gni
t
u
de
s o
f
peak
n
o
i
s
e
s
are
gi
ve
n i
n
t
h
e
fol
l
o
wi
n
g
T
a
bl
e 1
.
Tabl
e 1. N
o
i
s
e resp
o
n
se of
di
f
f
ere
n
t
p
o
w
er
s
e
m
i
cond
uct
o
r
s
w
i
t
c
hes
Noise
Signal
Magnit
ude of
Peak
Noise Current of
Modif
i
ed H
a
lf
Bridge Resonant
Inverter
MO
SFET
G
T
O
IG
BT
1
st
Noise
2
1.16
10
2
8.95
10
2
2.38
10
2
nd
Noise
2
1.07
10
2
2.56
10
2
2.81
10
3
rd
Noise
2
4.63
10
2
5.95
10
3
7.57
10
4
th
Noise
1
1.06
10
__
2
7.76
10
4.
1.
3.
LC-Low Pas
s
Filter
An L-C
low
p
a
ss filter
(LPF)
allo
ws
wav
e
s
o
f
lower frequen
c
y to p
a
ss
ou
t m
o
re easily
co
m
p
ared
t
o
t
h
e wa
ves o
f
h
i
ghe
r f
r
eq
ue
nc
y
.
W
h
i
l
e
casca
ded
wi
t
h
a
n
i
n
vert
er
, i
t
i
s
des
i
gne
d f
o
r s
u
c
h
a cut
-
of
f fre
q
u
ency
that
the higher harm
onics face
m
o
re
im
pedan
ce an
d
get
re
d
u
ced i
n
m
a
gni
t
u
de.
5.
SIMULATION AND RESULTS
In t
h
i
s
pa
per, t
h
e p
r
o
p
o
se
d m
odi
fi
ed
hal
f
b
r
i
dge r
e
so
na
nt
i
nve
rt
er
has be
en si
m
u
l
a
t
e
d usi
ng P
-
S
I
M
wi
t
h
t
h
e
hel
p
o
f
eq
ui
val
e
nt
pa
ram
e
t
e
rs conn
e
c
t
e
d at
t
h
e inpu
t of th
e i
n
du
ctio
n
h
eated
syste
m
. Here from
th
is
t
o
p
o
l
o
gy
t
h
e
wave
f
o
rm
s ha
ve
been
obt
ai
ned
u
s
i
n
g P
-
S
I
M
s
o
ft
wa
re
u
s
i
n
g
di
f
f
ere
n
t
po
we
r sem
i
cond
uct
o
r
swi
t
c
hes u
s
i
n
g
IGB
T
, G
T
O a
nd M
O
SFET
f
r
om
m
odi
fi
ed hal
f
b
r
i
d
ge res
ona
nt
i
nve
rt
er
ci
rcui
t
and
har
m
oni
cs
can be
o
b
t
a
i
n
e
d
.
F
i
g
u
r
e
4
s
h
o
w
s
the
s
i
m
u
l
a
t
i
o
n
d
i
a
g
r
a
m
o
f
m
o
di
fi
ed hal
f
b
r
i
dge res
o
n
a
nt
i
nve
rt
er
circu
it u
s
ing
MOSFET
with Lo
w p
a
ss filter. Fi
g
u
re
5
sho
w
s
t
h
e
P
o
w
e
r
s
i
m
u
l
a
t
e
d
w
a
ve
-fo
r
m
o
f
t
h
e
i
n
p
u
t
cu
rre
nt
of t
h
e
m
odi
fi
e
d
hal
f
bri
dge
r
e
so
nant
i
nve
rt
er u
s
i
n
g
M
O
S
F
E
T
S
w
i
t
c
h
.
Fi
g
u
re
6
s
h
o
w
s t
h
e
F
F
T
wa
ve
fo
rm
of i
n
p
u
t
c
u
r
r
e
n
t
usi
ng M
O
S
F
ET s
w
i
t
c
h. I
t
m
a
y
b
e
n
o
t
e
d
t
h
at
t
h
e
ha
r
m
o
n
i
c
s are
d
o
m
i
na
nt
u
s
i
n
g
M
O
S
F
E
T
s
w
i
t
c
h
.
F
i
g
u
re
7 s
h
o
w
s the ci
r
c
ui
t
c
o
n
f
i
gurat
i
on
for
t
h
e m
odi
fi
ed
hal
f
b
r
i
d
ge
re
son
a
nt
i
nve
rt
er usi
n
g
GTO. F
i
g
u
r
e
8 s
h
o
w
s
the
w
a
v
e
-
f
o
r
m
o
f
t
h
e
i
n
p
u
t
c
u
r
r
ent
f
o
r
t
h
e
m
odi
fi
ed hal
f
bri
d
ge
reso
na
nt in
vert
er
with
G
T
O
S
w
i
t
c
h
.
Fig
u
r
e 9
s
h
o
w
s t
h
e
F
F
T
for t
h
e s
a
m
e
. It
m
a
y
b
e
n
o
t
e
d t
h
at
h
e
re also
t
h
e
ha
r
m
o
n
i
c
s are
do
m
i
na
nt
. F
i
gu
re
10
show
s t
h
e ci
rcui
t
co
nfi
g
u
r
at
i
o
n
f
o
r
t
h
e m
odi
fi
ed
hal
f
bri
d
ge
res
ona
n
t
i
nve
rt
er
usi
n
g
IGB
T
. F
i
g
u
r
e
11
s
h
o
w
s
the
w
a
ve-f
or
m
o
f
t
h
e
i
n
p
u
t
c
u
r
r
e
nt
f
o
r
t
h
e
pr
op
ose
d
i
nve
rt
e
r
usi
n
g
I
G
B
T
S
w
i
t
c
h
e
s
.
Figure
12
s
how
s t
h
e
FFT
fo
r
t
h
e s
a
m
e
.
Here also the
ha
r
m
o
n
i
c
s are
dom
i
n
a
n
t
.
I
t
is
o
b
s
er
ved
t
h
a
t
fro
m
t
h
e
p
o
w
e
r
s
i
m
u
l
a
t
e
d
w
a
ve
-
s
hap
e
s
an
d
math
e
m
atica
l
an
al
ysis
t
h
e
n
o
ise
in
t
h
e
i
n
p
u
t
c
u
r
r
e
nt
is
m
u
c
h
le
ss
a
f
te
r
usi
n
g
t
h
e
IGB
T
s
w
i
t
c
hes fro
m
the pro
posed t
o
pol
ogy
.
It i
s
exp
o
se
d
f
r
o
m
t
h
e
FFT
t
h
at
t
h
e
h
a
r
m
o
n
i
c
co
n
t
en
t
s
are
al
m
o
s
t
ab
s
e
n
t
i
n
I
G
B
T
s
w
i
t
c
h us
i
n
g
P
-
S
I
M
s
o
f
t
w
a
r
e
apart
from
o
t
her p
o
w
e
r
s
e
m
i
c
o
n
d
u
c
t
o
r
s
w
i
t
c
h
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
12
1
–
12
8
12
6
Fig
u
re
4
.
Mod
i
fied
Half B
r
idge Reson
a
n
t
In
verter circu
it usin
g MOSFET
with
LPF
filter
Fi
gu
re
5.
I
n
p
u
t
cur
r
en
t
wave
f
o
rm
of M
o
di
fi
ed
Hal
f
B
r
i
dge
R
e
so
na
nt
I
n
vert
er
usi
n
g M
O
SFET
wi
t
h
LP
F
filter
Fi
g
u
re
6.
F
F
T
of
i
n
p
u
t
cu
r
r
en
t
of
t
h
e M
odi
fi
ed
Hal
f
B
r
i
dge
R
e
so
na
nt
I
n
vert
er
usi
n
g M
O
SFET
wi
t
h
LP
F
filter
Fi
gu
re 7.
Mod
i
fied
Half B
r
idge Reson
a
n
t
In
verter circu
it usin
g GTO
with
LPF
filter
Fi
gu
re
8.
I
n
p
u
t
cur
r
en
t
wave
f
o
rm
of M
o
di
fi
ed
Hal
f
Brid
g
e
Reson
a
n
t
Inv
e
rter u
s
i
n
g
GTO wit
h
LPF filter
F
i
gu
re
9.
FFT
of
in
p
u
t
cu
r
r
en
t
of
t
h
e M
odi
fi
ed
Hal
f
Brid
g
e
Reson
a
n
t
Inv
e
rter u
s
i
n
g
GTO wit
h
LPF filter
Fig
u
re
10
. M
o
d
i
fied Half Bri
d
g
e
Reson
a
n
t
In
v
e
rter ci
rcu
it
u
s
ing
IGBT wi
th
LPF filter
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
e
lectio
n o
f
Power S
e
m
i
con
ducto
r
S
w
itch
e
s i
n
M.H
.
B.
R.I. Fitted
Indu
ctio
n
H
e
a
t
er… (Prad
i
p
K
u
m
a
r Sadh
u
)
12
7
Figu
re 1
1
. I
n
p
u
t
cur
r
en
t wav
e
fo
rm
of
M
o
di
fied Half
Brid
g
e
Reson
a
n
t
Inv
e
rter
u
s
i
n
g
IGBT with LPF filter
Fi
g
u
r
e
12
.
FFT
o
f
i
n
put
cu
r
r
e
n
t
o
f
t
h
e M
o
di
f
i
ed Hal
f
Brid
g
e
Reson
a
n
t
Inv
e
rter
u
s
i
n
g
IGBT with LPF filter
6.
LABORATORY TEST BENCH
Fi
g
u
r
e
13
. P
h
o
t
og
rap
h
of
E
x
p
e
ri
m
e
nt
al
Set
-
up
7.
CO
NCL
USI
O
N
Hence fr
om
t
h
e pro
pose
d
t
o
pol
o
g
y
i
t
can be concl
u
de t
h
at
t
h
e d
i
f
f
e
r
e
n
t
f
a
m
i
l
i
e
s
o
f
p
o
w
e
r
sem
i
conduct
o
r
s
w
i
t
c
h
e
s
l
i
k
e
G
T
O
,
I
G
B
T
a
n
d
M
O
S
F
E
T
a
r
e
t
e
s
t
e
d
i
n
m
o
d
i
f
i
e
d
h
a
l
f
b
r
i
d
g
e
r
e
s
o
n
a
n
t
i
n
v
e
r
t
e
r
fitted
i
n
du
ctio
n
h
eater.
T
o
g
e
t
mi
n
i
mu
m
h
a
r
m
o
n
i
c
s
i
n
j
e
c
t
i
o
n
i
n
t
h
e
s
u
p
p
l
y
a
n
d
to
improve th
e
e
f
f
i
c
i
e
n
c
y
o
f
t
h
e
i
n
v
e
r
t
e
r
t
h
e
p
r
o
p
o
s
e
d s
c
he
m
e
can
be
em
pl
oy
e
d
i
n
hi
g
h
fr
e
q
ue
n
c
y
i
n
d
u
ct
i
o
n
he
at
i
n
g sy
st
e
m
.
A
f
t
e
r
com
p
aring the
wa
ve-form
s
analysis
of PSIM si
m
u
latio
n
,
it is qu
ite obv
iou
s
t
h
at th
e selectio
n
of
p
o
wer
semico
n
d
u
c
tor lik
ely IGBT will b
e
m
o
re su
itab
l
e po
we
r
semico
n
d
u
c
tor switch
in
h
i
gh
frequ
e
n
c
y
mo
d
i
fied
hal
f
b
r
i
d
ge r
e
son
a
nt
i
n
vert
e
r
. It
has ad
va
nt
age
o
u
s
f
o
r
r
e
duce
d
harm
oni
c i
n
ject
i
on i
n
p
o
w
er s
u
pp
l
y
of
i
n
d
u
c
t
i
o
n
h
e
a
t
e
r
.
A
g
a
i
n
T
H
D
a
n
a
l
y
s
i
s
i
s
p
r
o
v
e
n
t
h
a
t
s
e
l
e
c
t
i
o
n
o
f
I
G
B
T
se
m
i
conduct
o
r
swi
t
ch
i
s
t
h
e
b
e
s
t
for indu
ctio
n heatin
g
ap
p
licatio
n
s
.
ACKNOWLE
DGE
M
ENTS
Aut
h
o
r
s a
r
e t
h
ank
f
ul
t
o
t
h
e
UN
IV
ER
SIT
Y
GR
A
N
T
S
C
O
M
M
I
SS
I
O
N
,
B
a
ha
du
rsh
a
h
Zafar
M
a
r
g
,
New
Delh
i,
Ind
i
a fo
r
g
r
an
ting
fi
n
a
n
c
ial su
pp
ort und
er
Maj
o
r Research
Proj
ect en
titled
“Si
m
u
l
atio
n
of h
i
gh
-
fre
que
ncy
m
i
rror i
nve
rt
er
fo
r
ener
gy
ef
fi
ci
en
t
i
ndu
ct
i
on
hea
t
ed co
o
k
i
n
g o
v
e
n” a
nd al
s
o
g
r
at
eful
t
o
t
h
e
Un
de
r
Secretary a
n
d J
o
int Sec
r
etary
of UGC,
India for
thei
r
active co-operation.
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:
2
088
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94
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No
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March
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imatsu,
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BIOGRAP
HI
ES
OF AUTH
ORS
Pradip Kumar Sadhu received h
i
s Bachelor
, Post
-Graduate
and Ph.D. (Engin
eer
in
g) degrees in
1997,
1999 and 2002
respectively
in Electrical
Engg.
from Jadav
pur Univer
sity
, West
Bengal,
India. Curr
ently
,
he is working as a Professor
in Electrical Eng
i
neer
ing Department of Indian
School of Mines, Dhanbad,
India. He has total ex
perien
ce of
18
y
ears in teaching
and industr
y
.
He has four Paten
t
s. He has
several journ
a
l
and conferen
ce publications in national and
intern
ation
a
l lev
e
l. He is prin
cip
a
l investigat
or o
f
few Govt. funded projects. He has guided a
large no
. of do
ctoral
candid
a
tes and M. Tech st
udents
.
His
curr
ent ar
eas
of
inte
res
t
are
power
electronics applications, app
l
ic
ation of high fr
equency
conver
t
er, energ
y
efficien
t
devices
,
energ
y
efficient drives,
computer aid
e
d power
s
y
stem analy
s
is, condition monitoring,
lighting
and communication s
y
stems for
underground co
al mines.
Palash Pal completed Diploma in Electrical
En
gineer
ing from
West Bengal State Council of
Techn
i
cal Education, West Beng
al, India in 2003
.
He received his B.Tech
Degr
ee in Electr
i
cal
Engineering fro
m West
Bengal University
o
f
Techno
log
y
, W
e
st Beng
al, India in 2006
and
M.Tech
. (Gold Medalist) in 200
9 from same
Un
iver
s
i
t
y
. He has
total exp
e
ri
ence
of s
i
x y
e
ars
in
teaching. He is
currently
work
ing as an Assist
ant Professor and Head in
the department of
Electri
cal
Engin
eering
,
Saroj M
ohan Institut
e
of
Techno
log
y
(SMIT-TIG), Gupt
ipara, Hooghl
y
-
712512, West Bengal, India.
He is presently
pur
suing Ph.D. programme at the
Department of
Electrical Engin
eering
,
Indian S
c
hool of Min
e
s,
Dhanbad-82600
4, India. His r
e
s
earch
interests
includ
e power electron
i
cs,
inducti
on heating, high
frequen
c
y
conv
er
ters, high fr
eq
uency
heatin
g,
control s
y
stems and power
s
y
stems.
Nitai P
a
l r
ece
ive
d
his
B.Tech
. an
d M
.
Tech
. degre
e
s
in Ele
c
tri
cal
Engine
ering fro
m
Univers
i
t
y
of
Calcutta, West Bengal,
India. He received his
Ph.D. (Engi
neering) from Jadavpur University
,
West Bengal, In
dia. He h
a
s
tot
a
l
experi
enc
e
of t
w
elve
ye
ars
in t
e
aching
.
He is
cu
rrentl
y
working
as an Assistant Professor in the
Department of
Electrical Eng
i
n
eering
,
Indian School of Mines,
Dhanbad, Jhark
h
and, Ind
i
a. He
has sev
e
ral pu
blications
in Jo
urnals, In
tern
ational
& National
conferen
ces. He is th
e co-
i
nvestigator
of Govt f
unded project.
His current ar
eas of interest
are
P
o
wer elec
tronic
s
applic
ation
,
ap
plic
ation of h
i
gh
frequenc
y
conv
erters
,
energ
y
eff
i
ci
ent dev
i
ces
,
energ
y
efficien
t drives, light
ing
and communication s
y
stems
for u
nderground co
al
mines.
Sourish Sany
al received his
Bachelor
of
Technolog
y
degree
in Electronics and
Tel
ecom
m
unicat
ion Engineerin
g in the
y
ear
2000 from
I
n
stitute of En
gineer
ing and
Management, Salt
Lak
e
under
Univer
sity
of
Kaly
ani. He h
a
s r
eceived bo
th
his Master of
Engineering in
Electronics and
Telecommunication in 2002
and
Doct
oral D
e
gree in Engin
eer
ing
in 2012 from Ja
davpur University
. He has also re
ceiv
e
d an MBA
(Finance) degr
ee from Jadavur
University
. He
is presently
wo
rking as an As
sociate Professor at Academ
y
of Technolog
y
,
Adisaptagram,
Hooghly
,
West Benga
l, India. He has a no. of p
ublished papers in National and
Interna
tiona
l jou
r
nals to his cred
it. He has part
ic
ipated and pr
esented resear
ch papers in several
Nationa
l and In
terna
tiona
l Conf
erenc
e
s. His cu
rrent ar
eas of I
n
terest
are Int
e
l
ligent Con
t
rol
S
y
stem based o
n
soft-computin
g,
Digit
a
l Im
age
and S
p
ee
ch P
r
oces
s
i
ng, P
a
t
t
ern
Clas
s
i
fic
a
tion
,
Application of Soft Computing in Power Electr
onics
Applica
t
i
on like energ
y
effic
i
ent driv
es
,
P
L
C bas
e
d
contr
o
l and
en
erg
y
eff
i
ci
ent h
i
gh fr
equ
e
nc
y Inv
e
rt
er
etc
.
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