Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
44
7
~
45
7
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.8
034
4
47
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
/
IJECE
Behaviour of a High Frequenc
y Parall
el Quasi Res
o
nant
Invert
er Fitted In
duction Heat
er with Diff
erent Switching
Frequencies
A
v
ij
it
C
h
a
k
rab
o
rt
y*
, P
r
ad
ip
K
u
ma
r Sa
dh
u
*
*
,
Ka
llo
l B
h
a
u
mik*
, Pa
la
sh
Pa
l
*
,
Nitai Pa
l**
* Depart
em
ent o
f
El
ectr
i
cal
Engi
neering
,
Saro
j M
ohon In
stitu
te of
Technolog
y
(A
Unit of
Techno-I
ndia group)
,
Guptipara, Hoog
hly
-
712512
, Ind
i
a
** Electr
i
cal
En
gineer
ing Dep
a
rtment, Indian Sch
ool of Mi
n
e
s (un
d
er MHRD, Gov
t
. of
India), Dhanbad - 8260
04, I
ndia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 9, 2015
Rev
i
sed
No
v
23
, 20
15
Accepted Dec 16, 2015
This paper investigates th
e beh
a
vior
of a high
frequency
par
a
llel qu
asi-
resonant inver
t
er fitted dom
esti
c induc
tion heat
er with differen
t
switching
frequencies.
Th
e power semiconducto
r switch Insulated
Gate Bipo
lar
Junction Tr
ansis
t
or (IGBT)
is incorporat
ed in
this high fr
equency
inv
e
rter
that
can op
erate under ZVS
and ZC
S conditions during th
e switchin
g
operations at certain switch
i
ng freque
ncy
to r
e
duce switching
losses.The
proposed induction heating s
y
s
t
em re
sponds to three d
i
ffer
e
n
t
switchin
g
frequencies with providing dif
f
erent
re
sults.
An Insulated G
a
te B
i
polar
Junction Transis
t
or (IGBT) provides bett
er effi
c
i
enc
y
and f
a
s
t
er
s
w
itching
operations. After the complete study
of the
proposed induction heating
s
y
s
t
em
at the s
e
l
ect
ed s
w
itching frequenc
ies
,
th
e res
u
lts
are com
p
ared and i
t
is
decided th
at
m
o
s
t
reliable
,
e
ffici
ent and eff
ect
ive oper
a
tion
s
from
the
proposed induction heater
can
be obtai
ned
if
the switch
i
ng fr
equency
is
selected sligh
t
ly above
the r
e
sonant
frequ
ency
of the tank circuit of th
e
resonant
inverter. Th
e proposed
scheme
is
analy
z
ed using
Power S
y
stem
Simulator (PSIM) environment.
Keyword:
Hi
g
h
F
r
e
que
nc
y
In
vert
e
r
IGBT
PFM
PSIM
Quasi
-
Reso
na
n
t
THD
Copyright ©
201
6 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
:
Avi
j
it Cha
k
ra
b
o
rty
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Saro
j Moh
o
n
In
stitu
te of Tech
no
log
y
(A Unit o
f
Techn
o
-Ind
ia gro
u
p
)
.
Gu
pt
i
p
a
r
a, H
o
og
hl
y
-
71
2
5
1
2
,
In
di
a.
Em
a
il: a.ch
ak
t@g
m
ail.co
m
1.
INTRODUCTION
In
d
u
ct
i
on
heat
i
ng t
e
c
h
nol
ogy
i
s
wi
del
y
use
d
i
n
i
n
duct
i
o
n
ba
sed c
o
o
k
e
r
s f
o
r
i
t
s
cl
eanl
i
n
ess,
pol
l
u
t
i
o
n
-
free,
ve
ry
fa
st
heating
,
hig
h
e
fficiency
a
n
d
s
a
fety
[1
-
3
]. It
is a con
t
actless h
eating
p
r
o
c
ess, in wh
ich
a v
e
ry
hi
g
h
fre
q
u
ency
curre
nt
i
s
sent
t
o
a worki
ng
coi
l
t
h
ro
ug
h p
o
we
r sem
i
conduct
o
r s
w
i
t
c
he
s, whi
c
h pr
o
d
u
ces an
ed
d
y
em
f in
the wo
rk
ing
co
il [3
].
Th
is em
f
p
r
od
u
ces a
v
e
ry h
i
gh
freq
u
e
ncy altern
atin
g
mag
n
e
tic field
in
th
e
co
il and
suffici
en
t heat will be g
e
n
e
rated
i
n
th
e work
p
i
ece. Th
e
freq
u
e
n
c
y o
f
th
e i
n
d
u
c
t
o
r curren
t
d
e
p
e
n
d
s
on
th
e size o
f
th
e
h
eatin
g
co
il, pen
e
tr
ation
d
e
p
t
h
and
th
e electr
o
m
a
g
n
e
tic cou
p
ling
.
I
n
inductio
n
h
eating
pr
o
cess
a pot
i
s
di
rect
l
y
heat
ed by
t
h
e i
n
d
u
ce
d ed
dy
cur
r
ent
pr
o
duce
d
by
t
h
i
s
m
a
gnet
i
c
fi
el
d. I
n
duct
i
o
n h
eat
i
ng
process is ve
ry
m
u
ch suitable
for
dom
estic
cooking,
m
e
lting, surface
hardeni
n
g, br
azing and sol
d
ering [6-9,
15]
.
No
w a
da
y
,
i
t
i
s
al
so appl
i
e
d t
o
hy
pe
rt
herm
i
a
t
r
eatm
e
nt
an
d bl
oo
d r
e
heat
i
ng
u
nde
r
m
e
di
cal
appl
i
cat
i
o
n
[3, 9]
.
In
t
h
i
s
pa
per
an
IGB
T
ba
se
d
paral
l
e
l
q
u
a
s
i
res
ona
nt
i
n
vert
er
i
s
pr
o
p
o
se
d a
n
d
i
m
plem
ent
e
d f
o
r
i
n
d
u
ct
i
o
n
h
eat
i
ng a
p
pl
i
cat
i
on a
n
d
i
t
s
pe
r
f
o
r
m
a
nce an
d
be
havi
ou
r a
r
e anal
y
zed
us
i
ng
PS
IM
so
f
t
ware
si
m
u
latio
n
under
thr
ee
d
i
f
f
e
r
e
n
t
sw
itch
i
n
g
freq
u
e
n
c
ies,
wh
i
c
h
ar
e 15k
H
z
,
3
2kH
z an
d
45
kH
z r
e
sp
ectiv
el
y. Th
e
i
n
co
rp
orat
e
d
re
son
a
nt
i
n
ve
rt
er
has t
h
e re
so
na
nt
f
r
eq
ue
ncy
o
f
3
0
k
H
z.
It
i
s
f
o
un
d t
h
at
m
a
xim
u
m
energy
t
r
ansfe
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
44
7 – 4
5
7
44
8
to the
work
piece from
the worki
ng c
o
il occ
u
rs
whe
n
e
v
er
t
h
e switching
fre
que
ncy is set c
l
oser t
o
the
res
ona
nt
fre
que
ncy
.
T
h
e
pr
op
ose
d
q
u
a
s
i
reso
nant
i
n
vert
er c
o
nt
ro
l
schem
e
i
s
based o
n
va
ri
abl
e
freq
u
e
n
cy
or
Pul
s
e
Fre
que
ncy
M
o
dul
at
i
o
n (
PFM
) co
nt
r
o
l
m
e
t
h
od
. A t
y
pi
cal
i
n
d
u
ct
i
o
n
heat
i
ng
sy
st
em
i
s
sho
w
n i
n
t
h
e f
o
l
l
o
wi
n
g
fig
u
re.
Fi
gu
re 1.
B
a
si
c
I
n
d
u
ct
i
o
n heat
i
ng sy
st
em
2.
MERITS OF IGBT OVER OTHER
POWER
SE
MI-SEMICONDUCTO
R SWITC
H
ES
I
N
QU
ASI
-
RES
O
N
ANT IN
V
E
RTER
The
p
o
we
r se
m
i
cond
uct
o
r s
w
i
t
c
h l
i
k
e
I
G
B
T
i
s
p
r
efe
r
a
b
l
e
o
v
er
ot
her
p
o
w
er
sem
i
condu
ct
or s
w
i
t
c
he
s
in
p
a
rallel qu
asi reson
a
n
t
inv
e
rter
d
u
e
to
t
h
e
fo
llowing
reaso
n
s
[4
-5
, 14-18]:
•
IGBT
has
less
switching l
o
ss
[10-13].
•
I
t
pr
ov
id
es f
a
ster
sw
itch
i
ng
speed
.
•
It
has
l
e
ss
ON
st
at
e dr
op
.
•
It
i
s
a
bet
t
e
r
vo
l
t
a
ge co
nt
r
o
l
l
e
d
devi
ce.
•
It prov
id
es
b
e
tter en
erg
y
efficien
t op
eratio
n.
3.
PARALLEL QUASI-RESONANT
CONVERTER TOPOLOGY
The
fol
l
o
wi
n
g
fi
g
u
re
2
de
pi
ct
s a cert
a
i
n
t
o
p
o
l
o
gy
o
f
a
pa
r
a
l
l
e
l
quasi
re
s
ona
nt
i
n
ve
rt
er
usi
n
g si
ngl
e
IGBT
.
Fi
gu
re
2.
I
G
B
T
base
d
pa
ral
l
e
l
qua
si
res
o
nan
t
i
nve
rt
er
Quasi
-
R
e
so
na
n
t
(QR
)
c
o
n
v
e
r
t
e
rs are
wi
del
y
use
d
as hi
gh
fr
eque
ncy
AC
p
o
we
r s
o
u
r
ces i
n
i
n
duct
i
o
n
heating a
pplic
ations. Suc
h
conve
r
ters are very cost e
ffective for the domestic appliance
s
because it requi
re
s
onl
y
o
n
e IGB
T
, an
d o
n
l
y
one res
ona
nt
capaci
t
o
r C
.
Q
u
asi
-
R
e
so
nant
c
o
n
v
e
r
t
e
rs m
i
g
h
t
be co
nsi
d
e
r
ed as a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Beha
viou
r
o
f
a High
frequ
e
n
c
y Pa
ra
llel Qu
asi Resona
n
t
Inverter Fitted
Ind
u
c
tion
…
(Avijit Ch
a
k
rabo
rt
y)
44
9
reasona
b
le com
p
romise between c
o
st and effective pe
rf
orm
a
nce. O
n
l
y
one d
r
aw
b
ack
of th
is famil
y
o
f
co
nv
erter is that it h
a
s li
m
ite
d
regu
latio
n
ran
g
e
. Besid
e
s it is d
e
sirab
l
e to op
erate in
t
h
e
ZVS m
o
d
e
, ind
u
c
tion
heat
i
ng
base
d
coo
k
e
r
s are n
o
r
m
a
ll
y
al
l
o
wed
t
o
ope
rat
e
at
powe
r
l
e
vel
s
at
whi
c
h t
h
e res
o
nant
vol
t
a
ge
d
o
es n
o
t
qui
t
e
reac
h ze
r
o
.
At
p
o
w
e
r l
e
vel
s
l
o
wer t
h
an
t
h
i
s
, t
h
e
o
v
era
l
l
powe
r
m
odul
at
i
on i
s
p
u
l
s
e-
wi
dt
h
-
m
odul
at
ed at
a
v
e
ry low frequen
c
y to
li
m
it
t
h
e lo
sses. In
this lo
w pow
er
m
o
d
e
o
f
op
eratio
n
,
th
e
un
it may o
p
e
rate at th
e lo
w
p
o
wer lev
e
l for v
e
ry sm
a
ll
ti
me d
u
r
atio
n
an
d
th
en
it will
b
e
OFF for sm
a
ll
ti
m
e
d
u
r
ation
.
Th
is is
m
u
ch
sh
orter
t
h
an t
h
e t
h
er
m
a
l
tim
e const
a
nt
of t
h
e pa
n an
d i
t
s
co
nt
ent
s
, a
nd
has
no
ne
gat
i
v
e ef
fect
of t
h
e co
ok
i
n
g
o
p
e
ration
;
howev
er, it do
es help
to
m
a
x
i
mi
ze th
e
p
e
rfo
rmance of
the power
stage
and
li
mit th
e te
m
p
eratu
r
e
ri
se of t
h
e I
G
B
T
swi
t
c
h. Fo
r a gi
ven l
o
a
d
i
ng co
n
d
i
t
i
on
(i
.e. a cert
a
i
n
pot
), m
a
xim
u
m
power l
e
v
e
l
and
m
a
xim
u
m
suppl
y
vol
t
a
ge
, t
h
e peak
vol
t
a
ge
rat
i
ng f
o
r t
h
e
swi
t
c
h an
d re
son
a
nt
capaci
t
o
r
,
can be cal
c
u
l
a
t
e
d
fr
om
Quasi
-
R
e
so
nant
t
h
eo
ry
and can be
approxim
ated
b
y
th
e
fo
llowing
eq
u
a
tion
.
E=
C
V
(
1
)
Whe
r
e, E is the energy store
d
in
the induct
or coil duri
ng t
h
e on pe
ri
od T
o
n. C is the ca
pacitance of
t
h
e res
o
nant
c
a
p
aci
t
o
r
an
d
Vr
es i
s
t
h
e
res
ona
nt
v
o
l
t
a
ge.
Thus,
V
(
2
)
Si
m
ilarly, wh
en
th
is en
erg
y
is ex
ch
ang
e
d
to th
e reso
nant
c
a
paci
t
o
r
,
t
h
en i
t
can be repres
ented by the
equat
i
o
n
E=
L
I
(3)
An
d t
h
e
I
i
s
di
r
ect
l
y
pro
p
o
rt
i
o
nal
t
o
To
n a
n
d
dc
bu
s
vol
t
a
ge
V
b
y
th
e fo
llowin
g
equ
a
tion
I
= Ton.
(
4
)
The res
ona
nt
v
o
l
t
a
ge
V
can be
expresse
d as
V
=
αV
wh
er
e,
α
is t
h
e
duty cycle.
So, it can e
x
pressed a
s
α
=
(
5
)
An
d i
f
be t
h
e
r
e
so
nant
fre
q
u
e
n
cy
, t
h
e
n
=
=
So,
V
can
be e
x
presse
d as,
V
V
(
6
)
4.
OPERATIONAL MODES OF
PARALL
EL QUASI-RESONANT
CONVERTER
The m
a
i
n
quas
i
-res
ona
nt
po
w
e
r ci
rcui
t
cont
a
i
ns a para
llel c
o
nv
erter. It con
s
ists o
f
fu
ll b
r
idg
e
d
i
ode
rectifier, a p
a
ssiv
e LC filter a
n
d
an
an
ti-p
a
rallel d
i
o
d
e
co
nnected
acro
s
s th
e IGBT. Th
e circu
it g
e
n
e
rates h
i
gh
freq
u
e
n
c
y switch
i
ng
b
y
tu
rn
ing
ON t
h
e IGB
T
un
d
e
r ZVS
co
nd
itio
n wh
ile
th
e d
i
o
d
e
is in
th
e cond
u
c
ting state.
The re
so
na
nt
ci
rcui
t
co
nsi
s
t
s
of
res
ona
nt
i
n
d
u
ct
o
r
Lr
(c
oil inductance
and
resistan
ce)
and a resona
nt capacitor
C. Th
er
e ar
e
f
o
u
r
m
o
d
e
s of
oper
a
tio
n ex
is
t
with
in
on
e
switch
i
ng
cycle as
fo
llo
ws:
(i)
Mo
de-
1
I
G
B
T
on
,
Di
ode
o
f
f
In
th
is m
o
d
e
as sh
own
in
figu
re
3
,
switch
Q1
is switch
e
d o
n
with
su
itable g
a
te v
o
ltag
e
an
d
curren
t
flows fro
m
th
e co
llecto
r
t
o
the emitter o
f
Q1
. Th
e cu
rren
t
th
ro
ugh
th
e L
g
r
adu
a
lly rises so
th
at it is sto
r
i
ng
ener
gy
p
r
o
v
i
d
i
ng Z
V
S t
u
r
n
o
n
o
f
t
h
e
IGB
T
swi
t
c
h Q
1
fol
l
owi
ng t
h
e di
od
e con
d
u
ct
i
o
n
.
I
n
t
h
i
s
m
ode, c
u
r
r
ent
passes t
h
rough a sim
p
le R-L
circuit.
M
ode
-
1
ca
n
b
e
ex
pres
sed
by
t
h
e f
o
l
l
o
wi
n
g
e
quat
i
o
n
Ri
L
V
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
44
7 – 4
5
7
45
0
Fi
gu
re
3.
M
o
d
e
1 e
q
ui
val
e
nt
ci
rcui
t
(ii)
Mo
de-
2
IGB
T
of
f,
Di
ode
o
ff
Wh
en
th
e
swit
ch
Q1
is turn
ed
off, th
e cu
rren
t
will still b
e
in
creasi
n
g
an
d
fin
a
lly attai
n
s th
e
p
e
ak
value.
At this instant, the e
n
e
r
gy
sto
r
ed i
n
L
begi
ns to
tra
n
sfer to C. T
h
is
m
ode is a self-res
o
nating m
ode o
f
LC o
s
cillatin
g
circu
it wh
ich is shown in
figure
4
.
M
ode
-
2
ca
n
b
e
ex
pres
sed
by
t
h
e f
o
l
l
o
wi
n
g
e
quat
i
o
n
Ri
L
+
idt
0
(
8
)
Fi
gu
re
4.
M
o
d
e
2 e
q
ui
val
e
nt
ci
rcui
t
(iii)
Mo
de-
3
IGB
T
of
f,
Di
ode
o
f
f
I
n
th
is m
o
d
e
as show
n in f
i
gu
r
e
5, af
ter
t
h
e cu
rre
nt through L
becom
e
s zero,
th
e cap
acito
r C
b
e
g
i
ns
t
o
di
scha
r
g
e t
h
r
o
ug
h L an
d
a curre
nt
i
n
t
h
e re
verse
di
r
ect
i
on fl
o
w
s
.
The v
o
l
t
a
ge a
c
ross
L i
n
crea
ses a
n
d
p
o
l
arity is rev
e
rsed.
Mo
de -3
can
be exp
r
essed b
y
th
e fo
llow
i
ng
eq
u
a
tion
idt
Ri
L
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Beha
viou
r
o
f
a High
frequ
e
n
c
y Pa
ra
llel Qu
asi Resona
n
t
Inverter Fitted
Ind
u
c
tion
…
(Avijit Ch
a
k
rabo
rt
y)
45
1
Fi
gu
re
5.
M
o
d
e
3 e
q
ui
val
e
nt
ci
rcui
t
(iv)
Mo
de-
4
IGB
T
of
f,
Di
ode
o
n
In this
m
ode
as s
h
own in figure
6,
whe
n
the
reve
rse
d
pola
r
ity across
L
exceed
V
, t
h
e
di
od
e
b
eco
m
e
s fo
rward b
i
ased
and th
e curren
t
o
f
L
flows t
h
ro
ug
h th
is
d
i
od
e
u
n
til th
is curren
t
reach
e
s th
e
zero.
Aft
e
r
m
ode-
4
,
m
ode-1 st
a
r
t
s
wi
t
h
IGB
T
o
n
un
de
r ZC
S
co
n
d
i
t
i
on.
Mo
de -4
can
be exp
r
essed b
y
th
e fo
llow
i
ng
eq
u
a
tion
L
V
R
i
(
1
0
)
Fi
gu
re
6.
M
o
d
e
4 e
q
ui
val
e
nt
ci
rcui
t
At the
end m
ode-4, one cycl
e opera
tion
of
th
e qu
asi-reso
nan
t
conv
erter i
s
co
m
p
leted
.
After that th
e
ci
rcui
t
o
p
e
r
at
i
o
n
repeat
s
fr
om
m
ode-1 a
n
d s
o
on
.
In t
h
e f
o
l
l
o
wi
ng
fi
g
u
r
e 7
di
f
f
ere
n
t
v
o
l
t
a
ge,
cur
r
e
n
t
an
d G
a
t
e
si
gnal
wav
e
fo
rm
s are sh
o
w
n
f
o
r t
h
e
pr
o
pose
d
sy
st
e
m
at
di
ffe
rent
m
odes.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
44
7 – 4
5
7
45
2
Fi
gu
re
7.
Ty
pi
cal
vol
t
a
ge, c
u
r
r
ent
a
n
d
gat
e
si
gnal
s
Whe
r
e,
V
= Gate
v
o
ltag
e
of IGB
T
,
I
=
I
G
BT
co
lle
c
t
o
r
cu
rr
en
t,
I
= Inductor current,
V
= vol
t
a
ge
acros
s IGBT,
I
= Capacito
r c
u
rre
nt,
I
= Diode c
u
rrent.
The c
o
llector c
u
rrent
of the
IGBT ca
n
be e
x
press
e
d as
I
=
(
1
1
)
Whe
r
e,
T
= rise tim
e
.
An
d t
h
e c
o
l
l
ect
or
v
o
l
t
a
ge ca
n
be e
x
p
r
esse
d a
s
,
V
=
V
(1
+
)
(
1
2
)
Whe
r
e
T
= fall time.
From
t
h
e a
b
o
v
e
m
e
nt
i
oned
f
o
ur
m
odes
of
o
p
erat
i
o
ns,
t
h
e
ope
rat
i
o
n
ove
r
a s
w
i
t
c
hi
n
g
p
e
ri
o
d
ca
n
be
descri
bed
by
t
w
o
ci
rc
ui
t
m
odes.
First m
o
d
e
begin
s
wh
en
t
h
e
IGBT switch
is
tu
rn
ed on
at
ZVS con
d
ition
with
in
itial cond
itio
n
s
V
(0)
= 0 a
n
d
i
(0) =
0, the i
n
duct
or c
u
rrent iLR at
an
y in
s
t
an
t c
a
n
b
e
ex
pr
e
s
s
e
d
as
i
(t) =
1
e
(
1
3
)
Whe
r
e,
τ
=
=tim
e constant of the ci
rcuit.
Peak
value
of
the curre
nt is
at t= t2
. Th
is
m
o
d
e
co
n
tinu
e
s till t
h
e switch
is t
u
rn
ed off at t=t1
Th
e secon
d
m
o
d
e
starts at t=t1
wh
en
th
e
IGBT is tu
rned
off at t=t1. Consi
d
eri
ng t
h
e m
e
s
h
form
ed by
the s
o
urce
volt
age
V
, i
n
duct
a
nc
e
L
an
d resistan
ce R
with in
itial con
d
ition
s
(0
) =
0
an
d
i
(0)
=
I
, the
cor
r
es
po
n
d
i
n
g equat
i
o
ns
are
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Beha
viou
r
o
f
a High
frequ
e
n
c
y Pa
ra
llel Qu
asi Resona
n
t
Inverter Fitted
Ind
u
c
tion
…
(Avijit Ch
a
k
rabo
rt
y)
45
3
i
t
e
V
V
sinωt
I
co
s
ωt
θ
(
1
4
)
V
t
V
e
V
V
co
s
ωt
θ
I
sinωt
(
1
5
)
fo
r du
rin
g
t
h
e reso
na
nt cycle. where
,
α
,
ω
an
d
θ
a
r
e c
o
nst
a
nt
s a
n
d
are
gi
ven
by
α
=
,
ω
L
C
,
ω
=
ω
α
,
θ
=
tan
)
5.
TOTAL HARMONIC DI
S
T
O
R
TI
ON
(
T
HD
)
It is the
m
easure
of
ha
rm
onic presence
in a
non-si
n
u
s
o
idal
pe
rio
d
ic wa
ve
fo
rm
. It is re
pr
esented
by
th
e fo
llowing
ex
pressi
o
n
THD
∑
(
1
6
)
whe
r
e, I
0rm
s
i
s
the r
oot
m
ean squa
re
d (R
M
S
)
val
u
e of
an
y no
n-
sinu
so
id
al cu
rr
en
t and
I
1rm
s
is th
e ro
o
t
m
ean sq
uare
d
(R
M
S
)
val
u
e
of t
h
e f
u
ndam
e
nt
al
harm
oni
c
pre
s
ent
i
n
t
h
a
t
cur
r
ent
.
TH
D
gi
ves
an i
d
ea
abo
u
t
ho
w cl
ose a
n
o
n
-si
nus
oi
dal
w
a
vef
o
rm
cl
ose
t
o
i
t
s
f
u
n
d
am
ent
a
l
i
n
s
h
a
p
e.
6.
SWITCHING
LOSS
Swi
t
c
hi
n
g
o
p
er
at
i
on i
n
cl
udes
t
u
r
n
-
ON a
n
d t
u
r
n
-
O
F
F
lo
sses resp
ectiv
ely.
Gen
e
rally switch
i
ng
lo
sses
n
eed to
b
e
estimated
. Estim
a
t
in
g
t
h
e
IGBT switch
i
ng
loss as g
i
v
e
n b
e
l
o
w,
P
(
1
7
)
7.
PSIM SI
MUL
A
TIO
N
The de
vel
o
pe
d
PSIM
schem
a
t
i
c
ci
rcui
t
di
agram
i
s
show
n i
n
Fi
g
u
re
8, i
n
whi
c
h f
o
u
r
di
o
d
es are u
s
ed
i
n
a ful
l
-
bri
dge
rect
i
f
i
e
r
a
n
d
a hi
g
h
fre
que
ncy
i
nve
rt
er usi
n
g
onl
y
one
I
G
B
T
.
Figure
8. PSIM si
m
u
latio
n
of th
e propo
sed
p
a
rallel Qu
asi-reson
a
n
t
inv
e
rt
er
8.
RESULTS
A
N
D
DI
SC
US
S
I
ONS
The m
a
i
n
equi
val
e
nt
ci
rc
ui
t
of t
h
e
pr
o
p
o
s
e
d
pa
ral
l
e
l
quas
i
reso
nant
i
n
ve
rt
er i
s
sh
ow
n i
n
Fi
g
u
re
2.
Th
e
d
i
fferen
t param
e
ters are sh
own
in
Tab
l
e 1
.
Th
e fou
r
m
o
d
e
s (fro
m
m
o
d
e
-1
to m
o
d
e
-4
)
will rep
eat
o
n
th
e
basi
s o
f
speci
f
i
ed IGB
T
on t
i
m
e
and of
f t
i
m
e. The dept
h
of pe
net
r
at
i
o
n
of t
h
e h
eat
i
n
t
h
e coo
k
i
n
g p
a
n i
s
i
nve
rsel
y
pr
o
p
o
rt
i
o
nal
t
o
t
h
e
ope
rat
i
n
g f
r
eq
uency
a
nd t
h
e
ope
rat
i
n
g t
i
m
e
peri
od i
s
t
h
e
i
nve
rse o
f
ope
rat
i
n
g
fre
que
ncy
.
Th
us aft
e
r cha
n
g
i
ng t
h
e o
n
-
o
f
f
t
i
m
e
of t
h
e IGB
T
, t
h
e o
p
e
r
at
i
ng f
r
eq
ue
n
c
y
and t
h
e de
pt
h o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
44
7 – 4
5
7
45
4
penet
r
at
i
on
o
f
heat
can
be c
ont
rol
l
e
d
.
I
n
t
h
e p
r
ese
n
t
w
o
rk
, t
h
e
pr
op
os
ed pa
ral
l
e
l
qu
asi
-res
ona
nt
ci
rcui
t
i
s
t
e
st
ed un
de
r t
h
ree
di
ffe
re
nt
swi
t
c
hi
n
g
f
r
eq
uenci
e
s
whic
h are 15kHz,
32kHz and
45kHz res
p
ectivel
y. The
reso
na
nt
fre
qu
ency
of t
h
e t
a
n
k
ci
rcui
t
i
s
30
k
H
z.
Whe
n
the switching frequency is selected at 32kHz cl
ose to
t
h
e res
ona
nt
f
r
e
que
ncy
,
t
h
e
n
fr
om
Fi
gure
9 i
t
i
s
show
n t
h
a
t
swi
t
c
hi
n
g
o
p
e
rat
i
ons
f
o
l
l
o
w
t
h
e ZVS a
n
d
ZC
S
co
nd
itio
ns en
su
ri
n
g
less swit
ch
ing
lo
ss with h
i
g
h
e
r efficien
cy. Th
e switch
i
ng
frequ
en
cy
at 3
2
k
Hz also
mak
e
s
t
h
e i
n
p
u
t
cu
rr
ent
si
nu
soi
d
al
wi
t
h
l
e
ss Tot
a
l
Harm
oni
c Di
st
ort
i
o
n (T
H
D
)
as gi
ve
n i
n
Tabl
e 2. T
h
e
out
put
po
we
r fact
o
r
i
s
al
so t
h
e
m
a
xim
u
m
at
t
h
i
s
swi
t
c
hi
n
g
fre
q
u
e
ncy
,
w
h
i
c
h i
s
gi
ven i
n
Ta
bl
e 3. B
e
si
des, great
er
Tot
a
l
Ha
rm
oni
c Di
st
ort
i
o
n
(
T
HD
) at
t
h
e
out
put
c
u
r
r
e
n
t
al
so
pr
ovi
des
l
a
rge am
ou
nt
of
heat
ge
ne
art
i
o
n
.
There
f
ore, t
h
e
sel
ect
i
on o
f
t
h
e swi
t
c
hi
n
g
f
r
eq
ue
ncy
s
l
i
ght
l
y
abo
v
e
t
h
e res
ona
nt
fre
que
ncy
i
s
m
o
stly
bene
ficial.
When the s
w
itchi
ng
fre
quency
i
s
selected at 15kHz m
u
ch less th
an t
h
e res
ona
nt
f
r
eq
ue
nc
y
,
t
h
en
fro
m
Fig
u
r
e, it
is sh
own
th
at t
h
e switch
i
ng
op
eratio
n
d
o
e
s no
t fo
llo
w t
h
e ZVS an
d
ZCS co
nd
itio
ns th
at
cau
ses
h
i
gh
switch
i
ng lo
sses an
d
efficien
cy redu
ces, b
e
si
d
e
s
th
e in
v
e
rter o
p
e
rates
in
cap
acitive
m
o
d
e
. Sin
c
e,
the
THD
o
f
t
h
e i
n
put
s
o
urce c
u
r
r
ent
i
s
very
hi
gh at
t
h
i
s
swi
t
chi
n
g f
r
e
que
nc
y
,
whi
c
h m
a
kes t
h
e i
n
p
u
t
s
o
u
r
ce
cur
r
ent
n
o
n
-si
nus
oi
dal
and
t
hus t
h
e i
n
put
sou
r
ce v
o
l
t
a
ge m
a
y
cont
ai
n un
wa
nt
ed
harm
oni
cs. As
such
in
stallatio
n
o
f
an
ac filter i
s
requ
ired
at t
h
e in
pu
t si
d
e
an
d
th
is will mak
e
th
e in
d
u
ctio
n
h
eater co
stlier.
B
e
si
des, t
h
i
s
l
o
w s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
m
a
y
cause an
u
nde
s
i
rabl
e au
di
bl
e
noi
se
. The
o
u
t
put
c
u
r
r
ent
al
s
o
has a
lo
w
THD
com
p
ar
ed
to 32k
H
z
sw
itch
i
ng f
r
e
qu
en
cy as show
n in Tab
l
e
2
.
So, th
e selectio
n of
sw
itch
i
ng
fre
que
ncy
at
15k
Hz i
s
gene
ra
l
l
y
avoi
ded. T
h
e sel
ect
i
on o
f
swi
t
c
hi
ng
fre
q
u
ency
at
45
k
H
z abo
v
e t
h
e res
ona
nt
fre
que
ncy
gi
ve
s a hi
g
h
TH
D
val
u
e
of t
h
e
o
u
t
put
cu
rre
nt
an
d i
s
fr
ui
t
f
ul
fo
r
i
n
d
u
ct
i
on
heat
i
ng
pu
rp
ose
,
b
u
t
t
h
i
s
i
s
al
so avoi
de
d beca
use o
f
t
h
e swi
t
c
hi
ng
o
p
erat
i
o
ns d
o
n
o
t
fol
l
o
w t
h
e ZVS an
d ZC
S
oper
a
t
i
ons a
n
d t
h
u
s
pr
o
duce
hi
gh
s
w
i
t
c
hi
n
g
l
o
sse
s t
h
at
i
s
s
h
ow
n
Tabl
e
3.
T
h
e
po
we
r fact
ors
of
t
h
e
o
u
t
p
ut
p
o
we
r a
r
e l
e
ss
f
o
r
b
o
t
h
1
5kH
z an
d 45kH
z sw
itch
i
ng
fr
equ
e
n
c
ies com
p
ar
ed
to
sw
itch
i
ng
f
r
e
q
u
e
n
c
y 3
2kH
z as show
n in
Tab
l
e
3
.
Tabl
e
1.
Desi
g
n
param
e
t
e
rs o
f
Pa
ral
l
e
l
qu
asi
res
ona
nt
i
n
ve
r
t
er
Para
m
e
ters
Coil I
nductance(
L
r
)
=
47µH
M
a
in supply
voltage= 230Volts
Internal Resistance
of
the coil(R)=1oh
m
Oper
ating fr
equency
=
30 kHz
Capacitor(C1)=0.5
µF
Resonant capacitor
(
C
)
=
0.
6µF
I
nductor
(
L
1)
=100µH
Tabl
e
2.
In
p
u
t
C
u
r
r
ent
T
H
D a
n
d
O
u
t
p
ut
C
u
r
r
e
nt
T
H
D
vers
us S
w
i
t
c
hi
ng
f
r
e
que
ncy
Switching fr
equen
c
y
(
kHz)
I
nput Cur
r
e
nt
T
HD
va
lue (
p
ercent)
Output
Cur
r
e
nt T
HD
value (
p
er
cent)
1
5
k
H
z
3
2
.
0
0
%
3
2
k
H
z
2
.
6
6
%
4
5
k
H
z
1
.
7
6
%
93.
37%
103.
13%
146.
57%
Tabl
e 3. Swi
t
c
hi
n
g
L
o
ss
an
d Out
put
Po
we
r Fact
or
ve
rs
us Swi
t
c
hi
n
g
fre
q
u
ency
Swi
t
ch
in
g
f
r
eq
u
e
n
c
y(k
H
z)
Swi
t
ch
in
g
Lo
ss (watt)
Ou
tp
u
t
Po
wer F
acto
r
1
5
k
H
z
4
1
.
4
3
3
2
k
H
z
2
0
.
3
3
4
5
k
H
z
5
6
.
2
7
0
.
2
5
8
5
0.
3
178
0
.
2
3
3
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Beha
viou
r
o
f
a High
frequ
e
n
c
y Pa
ra
llel Qu
asi Resona
n
t
Inverter Fitted
Ind
u
c
tion
…
(Avijit Ch
a
k
rabo
rt
y)
45
5
Fi
gu
re
9.
V
o
l
t
a
ge ac
ros
s
I
G
B
T
an
d c
u
r
r
e
n
t
t
h
r
o
ug
h
IGB
T
a
t
swi
t
c
hi
n
g
fre
que
ncy
=
3
2
k
H
z
Fi
gu
re
1
0
.
V
o
l
t
a
ge ac
ros
s
I
G
B
T
an
d c
u
r
r
e
n
t
t
h
r
o
ug
h
IGB
T
a
t
swi
t
c
hi
n
g
fre
que
ncy
15
k
H
z
Fi
gu
re
1
1
.
V
o
l
t
a
ge ac
ros
s
I
G
B
T
an
d c
u
r
r
e
n
t
t
h
r
o
ug
h
IGB
T
a
t
swi
t
c
hi
n
g
fre
que
ncy
45
k
H
z
9.
CO
NCL
USI
O
N
In
th
is p
a
p
e
r, th
e circu
it o
f
a p
a
rallel q
u
a
si- re
so
nant
i
n
v
e
rt
er base
d i
n
duct
i
o
n heat
i
n
g sy
st
em
i
s
analysed m
a
the
m
atically and also its
per
f
o
r
m
a
nce i
s
veri
fi
ed usi
n
g PS
IM
soft
ware
. The
pri
n
ci
pl
e o
f
i
n
vert
e
r
ope
rat
i
o
n has
been
p
r
esent
e
d an
d
di
ffe
re
n
t
sim
u
l
a
t
e
d wavef
o
rm
s are sho
w
n at
t
h
re
e di
ffe
re
nt
sw
i
t
c
hi
n
g
fre
que
nci
e
s
1
5
k
Hz
,
32
k
H
z a
n
d
45
k
H
z re
spe
c
t
i
v
el
y
.
It
i
s
al
so s
h
ow
n t
h
at
at
swi
t
c
hi
n
g
fr
eque
ncy
32
k
H
z nea
r
t
o
t
h
e reso
na
nt
freq
u
e
n
cy
onl
y
pro
v
i
d
es Z
V
S or ZC
S
ope
r
a
t
i
on d
u
ri
ng t
u
rn
-O
N an
d t
u
r
n
-
O
FF c
o
n
d
i
t
i
ons a
n
d
p
r
ov
id
es th
e
min
i
m
u
m
swit
ch
ing
lo
sses
with
an
i
m
p
r
ov
e
d
output powe
r factor and overall pe
rform
a
nce is
im
pro
v
ed
. It
can be co
ncl
u
d
e
d t
h
at
paral
l
e
l
quasi
- res
o
n
a
nt
base
d i
nve
rt
er can be
us
ed i
n
cost
ef
f
ect
i
v
e
in
du
ctio
n heatin
g app
licatio
n
s
.
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a
ma
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ree
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BIOGRAP
HI
ES OF
AUTH
ORS
Avijit Ch
akrabo
rt
y
obtained h
i
s B.Sc degr
ee in
Ph
y
s
ics (Honours
)
from
the Cal
c
u
tta Univ
ersit
y
,
West Bengal, In
dia, in 2002 and
obtained his B.Tech degr
ee in
Electrical Eng
i
n
eering from th
e
Calcutta Univer
sity
, West Beng
al, India, in 200
5 and M
.
Tech d
e
gree in
Ele
c
tri
c
al Engin
eering
from the Calcutta University
,
We
st Bengal, I
ndia,
in 2007.
He
is presently working as an
Assistant Professor in Electrical Engin
eer
ing
at th
e Saroj Mohan Inst
itute of
Technolog
y
,
Hooghly
,
West Bengal, India. His research in
terest in
cludes
Power Electro
nics, Electr
i
cal
Machines, Power S
y
stem, Hig
h
frequen
c
y
Po
we
r Electron
i
c
converters Renewable
Energ
y
Sources. At pres
ent h
e
is enga
ged in r
e
sear
ch wo
rks on Inducti
on
based heating
ap
plications.
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 El
ectrical
Engg. From Jadavpur
University
,
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.
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