Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
7
,
No
. 2,
J
une
2
0
1
6
,
pp
. 43
1~
43
9
I
S
SN
: 208
8-8
6
9
4
4
31
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
Harmonics Reduction in
a Current Source
Fed Quasi-Resonant
Invert
er Bas
e
d In
duction Heat
er
A
v
ij
it
C
h
a
k
rab
o
rt
y*
,
Tit
a
s K
u
ma
r
N
ag*
,
P
r
a
d
ip
K
u
mar
S
a
d
h
u
**
,
N
i
t
a
i
Pa
l**
* Depart
em
ent o
f
El
ectr
i
c
a
l
Engi
neering
,
Saro
j M
ohan Institute of
Techno
log
y
(Degree
Engin
eerin
g Division), a Unit of
Techno
India Gr
oup, Guptip
ara,
Hooghly
-
71251
2, India
** Electr
i
cal
En
gineer
ing Dep
a
rtment, Indian Sch
ool of Min
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 Dec 4, 2015
Rev
i
sed
Jan 18, 201
5
Accepte
d
Fe
b 2, 2016
This
paper inv
e
s
tigates
an
appr
oach to redu
ce
the inj
ect
ion of
unwanted
harmonics from the input side
power
source.
The proposed wo
rk finds an
appli
cat
ion of a suitabl
y desi
gned lo
w pass filter (LPF) for harm
onics
reduct
i
on. Th
e Low Pass
Filter
is incorporat
ed
in between th
e input power
source and
high
frequen
c
y
curr
ent source f
e
d s
i
ngle
switch
par
a
llel
quasi-
resonant inver
t
er of a domestic I
nduction Heater
. The inv
e
r
t
er has an
Insulated Gate Bipolar Junctio
n Tran
sistor (IGBT) switc
h.
Unde
sira
ble
harmonics injection to the inpu
t pow
er source makes voltage
and curren
t
waveforms non-
sinusoidal. Fa
st Fourier Transfor
m (FFT) analy
s
is has been
applied to stud
y the effect of h
a
rm
onics in frequency
dom
ain.
The ent
i
re
s
y
stem
is real
iz
ed in Power S
y
stem
Sim
u
lator (PSIM) environm
ent. It is
finally
proved
that th
e proposed filter
r
e
duces
the to
tal harmon
ic distor
tion
(THD) and th
e
distortion f
a
ctor
(DF) of the inp
u
t curr
ent. It is
also proved
that the proposed LPF can
make
the
i
nput pow
er
factor
closer to
u
n
ity
.
Keyword:
IGBT
LPF
Paral
l
e
l
q
u
asi
-
r
e
so
nant
i
nve
rt
e
r
PSIM
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
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Saro
j Moh
a
n In
stitu
te of Tech
no
log
y
(Deg
ree Eng
i
n
e
ering Div
i
si
o
n
),
G
u
p
tip
ar
a, Hoo
g
h
l
y-7
125
12
, W
e
st
Beng
al,
In
d
i
a.
Em
a
il: ab
.ch
a
kt@g
m
a
il.co
m
1.
INTRODUCTION
In
recent years, Induction heating ha
s bec
o
m
e
a
very popular tec
hni
que to
gene
rate
cont
rollable
desi
re
d hi
gh t
e
m
p
erat
ur
e q
u
i
ckl
y
for a
p
pl
i
cat
i
ons l
i
k
e
do
m
e
st
i
c
cooki
n
g
, m
e
l
t
i
ng st
ee
l
,
brazi
ng
, ha
r
d
eni
n
g
and also in s
o
me
m
e
dical applications.
It is a con
t
actless
p
o
llu
tion
free
h
eatin
g pro
cess [1
–5
].
An
y ind
u
c
tion
heater c
o
nsists
of a
‘Res
ona
n
t Inverter
’
as
a s
o
urce
of
ver
y
h
i
g
h
fr
eq
uen
c
y altern
ating
cu
rr
en
t.
I
ndu
ctio
n
heat
ers
use
di
f
f
ere
n
t
i
n
vert
er
t
o
p
o
l
o
gi
es l
i
k
e
si
ngl
e s
w
i
t
c
h
qua
si
-res
o
nant
[6
–
8
]
,
t
h
e
hal
f
b
r
i
d
ge i
n
vert
er a
n
d
fu
ll
b
r
idg
e
inverters accord
i
ng
to d
i
f
f
eren
t ap
p
li
cation
s
.
Insu
lated
Gate B
i
p
o
l
ar Jun
c
tion Tran
sistor
(
IG
BT) is
use
d
as t
h
e
po
wer
sem
i
condu
ct
or s
w
i
t
c
h i
n
t
h
i
s
a
ppl
i
cat
i
o
n
whi
c
h i
s
very
m
u
ch sui
t
a
bl
e
and
ef
fect
i
v
e
[
10]
.
A q
u
asi
-
reso
n
a
nt
i
nve
rt
er c
a
n be s
u
i
t
a
bl
y
used i
n
dom
est
i
c
i
nduct
i
o
n
heat
er. It
u
s
e
s
a Paral
l
e
l
reson
a
n
t
lo
ad
th
at h
a
s t
h
e cap
a
b
ility o
f
cu
rren
t
-
m
a
g
n
i
ficatio
n
to
produ
ce m
o
re h
eat
. An
y qu
asi-reso
nan
t
inve
rter can be
fed either from a voltage source or a cu
rr
en
t so
ur
ce.
A
t
t
h
e in
pu
t sid
e
, it
m
a
y h
a
v
e
an
y p
a
ssi
ve
o
r
activ
e filter
to
pro
v
i
d
e
less
h
a
rm
o
n
i
c inj
e
ctio
n
to th
e i
n
p
u
t sou
r
ce
[9
] from
th
e ou
tpu
t
si
d
e
.
A cu
rren
t sou
r
ce
fed
qu
asi-reso
n
a
n
t
inverter is su
itable fo
r
v
a
riab
le work
l
o
ad
co
nd
itio
ns.
Harm
oni
cs di
st
ort
i
o
ns occ
u
r d
u
e t
o
ha
rm
oni
cs i
n
ject
i
o
n at
t
h
e i
n
p
u
t
cu
rre
n
t
due t
o
hi
gh f
r
e
que
ncy
swi
t
c
hi
n
g
.
Th
e circu
it d
i
ag
ram
o
f
t
o
tal DC-link
h
i
gh
freq
u
e
n
c
y
cu
rren
t sou
r
ce
fed
qu
asi reson
a
n
t
i
n
v
e
rter
fitted
induction heater system
is given in Figure
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
431
–
4
39
43
2
Fig
u
re 1
.
Circuit
Diag
ram
o
f
DC-link
h
i
gh
frequ
e
n
c
y curren
t
so
urce
fed qu
asi reson
a
n
t
in
v
e
rter
fitted
induction heater system
2.
OPERATIONAL PRINCIPLE OF PARALLEL
QUASI-RESONANT
INVE
RTER BASED
INDUCTION HEATER
The Fi
gu
re
2
as sh
ow
n
bel
o
w re
pre
s
ent
s
s
i
m
p
l
i
f
i
e
d equi
val
e
nt
ci
rc
ui
t
of a
si
n
g
l
e
en
ded
q
u
asi
-
reso
na
nt
i
n
vert
er
based
i
n
duct
i
on
heat
i
n
g sy
s
t
em
.
Fi
gu
re
2.
Si
m
p
l
i
f
i
e
d eq
ui
val
e
nt
ci
rc
ui
t
o
f
t
h
e
q
u
asi
-
reso
na
nt
i
nve
rt
er
base
d
i
n
d
u
ct
i
o
n
h
eat
er wi
t
h
l
o
a
d
The p
r
o
p
o
se
d
quasi
-
r
es
ona
n
t
i
nvert
er ba
s
e
d In
d
u
ct
i
o
n Heat
er can
op
erat
e un
der Z
e
ro v
o
l
t
a
ge
swi
t
c
hi
n
g
(Z
V
S
) a
n
d Ze
ro
c
u
rre
nt
s
w
i
t
c
hi
n
g
(ZC
S
) c
o
ndi
t
i
ons
i
n
t
w
o m
odes i
n
e
v
ery
s
w
i
t
c
hi
n
g
peri
o
d
.
The
equi
val
e
nt
ci
rc
ui
t
s
o
f
eac
h m
ode a
r
e s
h
o
w
n i
n
t
h
e
Fi
g
u
r
e
3
and
Fi
g
u
r
e
4 re
spect
i
v
el
y
.
Fi
gu
re
3.
Si
m
p
l
i
f
i
e
d eq
ui
val
e
nt
ci
rc
ui
t
o
f
M
ode
-I
w
h
i
l
e
I
G
B
T
o
n
2.
1. M
o
de
-I
O
p
era
ti
on
In
t
h
is m
o
d
e
th
e IGBT in
itiates co
ndu
ctin
g cu
rren
t
imm
e
d
i
ately after its firing
b
y
th
e g
a
te pu
lses.
Th
e vo
ltag
e
v
C
acro
s
s th
e capacito
r C and
acro
ss th
e R-L
lo
ad
is practically co
n
s
tan
t
an
d equ
a
ls t
o
V
s.
The
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
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:
208
8-8
6
9
4
Ha
rmo
n
i
cs Red
u
c
tion
i
n
a
C
u
rren
t
Sou
rce
Fed
Qu
a
s
i
-
Reso
nan
t In
verter
Ba
sed
… (Avijit Ch
a
k
rab
o
rty)
43
3
lo
a
d
cu
rr
en
t i
L
starts in
creasin
g
exp
o
n
e
n
tially a
n
d
is eq
u
a
l
to
th
e switch
cu
rren
t i
s
.
In t
h
i
s
m
ode t
h
e i
n
duct
o
r
‘L’ receives e
n
ergy
from
the powe
r s
o
urce.
Fi
gu
re
4.
Si
m
p
l
i
f
i
e
d eq
ui
val
e
nt
ci
rc
ui
t
o
f
M
ode
-I
I
w
h
i
l
e
I
G
B
T
of
f
2.
2. M
o
de
-II Opera
ti
o
n
In
th
is m
o
d
e
, wh
en th
e
IGBT is tu
rn
ed
-OFF, re
son
a
n
c
e in
th
e p
a
rallel reson
a
n
t
circu
it produ
ces
o
s
cillatio
n
in
t
h
e lo
ad
cu
rrent wh
ich
ex
ists till v
C
reache
s
V
s
.
In th
is
m
o
d
e
, th
e indu
ctor ‘L’
o
f
t
h
e lo
ad
releases its stored e
n
ergy a
n
d
fre
que
ntly ex
ch
ang
e
s it with
t
h
e
reson
a
n
t
cap
acito
r ‘C’.
More
ove
r, t
h
e
propose
d
inverter
system
can pe
rform
under t
w
o
di
fferent operatin
g conditions
to
y
i
el
d ei
t
h
er Z
V
S co
n
d
i
t
i
on
o
r
not
w
h
i
c
h a
r
e
descri
bed
as
fo
l
l
o
ws.
2.
3. Sub
-Op
t
i
m
um
O
p
era
ti
on
In
t
h
is m
o
d
e
, t
h
e cap
acito
r
vo
ltag
e
v
C
b
e
comes eq
u
a
l to th
e su
pp
ly vo
ltag
e
V
s
, whe
n
i
L
is n
e
g
a
tive,
so t
h
at
t
o
sat
i
s
fy
Ki
rc
hh
of
f’
s
Vol
t
a
ge
Law
(
KVL
), t
h
e di
o
d
e ‘
D
’ st
a
r
t
s
con
d
u
ct
i
n
g
,
w
h
i
c
h deci
des t
h
e
end
of
m
ode-II a
nd t
h
e be
gin
n
in
g
of m
ode-
I
o
f
the ne
xt switc
h
i
ng cy
cle. The
du
ration
of t
h
e dio
d
e co
nd
u
c
tion is
v
e
ry sho
r
t.
At t
h
e ti
m
e
in
terv
al b
e
tween
th
e in
stan
t of d
i
od
e co
nd
u
c
tion
and
th
e in
stan
t wh
en
i
L
bec
o
m
e
s
zero,
th
e IGBT m
u
st b
e
trigg
e
red
so
th
at it can
tak
e
ov
er t
h
e
di
ode curre
nt. Si
nce, in this
case, th
e IGBT is tu
rn
ed
-
ON
be
fo
re i
L
reaches t
o
ze
ro, so
switchi
ng loss
occ
u
rs
.
2.
4. Op
ti
mum
Oper
ati
o
n
In
th
is m
o
d
e
, t
h
e cap
acitor (C) vo
ltag
e
v
C
reaches Vs and
the inductor curre
nt i
L
reache
s
zero at the
sam
e
in
stan
t. Th
e IGBT m
u
st b
e
turn
ed
o
n
at
th
is
in
stan
t to
yield
zero
cu
rren
t
switch
i
n
g
(ZCS) co
nd
ition
and
th
u
s
switch
i
n
g
lo
ss is n
e
g
lig
i
b
le. Th
e
n
e
x
t
cycle is in
itiat
e
d
in th
is
p
e
rio
d
. Th
e t
w
o d
i
fferen
t
con
d
itio
n
s
are
g
r
aph
i
cally sh
ow
n in
t
h
e
f
o
llow
i
ng
Fi
g
u
r
e
5
(
a)
an
d Figu
r
e
5(
b)
r
e
sp
ectiv
el
y.
Fi
gu
re 5.
(a
)
S
u
b
-
opt
i
m
u
m
and (b
) Opt
i
m
u
m
o
p
erat
i
o
ns o
f
qua
si
-res
o
nant
i
nve
rt
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
431
–
4
39
43
4
3.
GEN
E
RA
L EQUA
TION
S
OF SU
B
–
OPTIM
U
M AN
D
OPTIMUM
OPER
A
T
IONS
Th
e fo
llowing
eq
u
a
tion
s
g
i
ve th
e
m
a
th
e
m
a
tic
al expressions
of l
o
ad curre
nt
(i
L
), th
e cap
aci
to
r
v
o
ltage
(v
C
) a
nd t
h
e voltage across the IGBT (v
t
)
du
rin
g
the I
G
BT ‘O
N’
peri
od a
n
d ‘
O
FF
’ pe
rio
d
respectively
f
o
r the
sub
-
opt
i
m
u
m
operat
i
o
n of
t
h
e
i
nve
rt
er.
t
i
t
i
s
sn
n
n
Ln
n
s
Ln
2
exp
1
1
2
1
0
1
1
2
1
2
2
For
0<
ω
s
t
≤
2
π
D
(1
)
Whe
r
e: i
Ln
(0
) i
s
the
value
o
f
i
Ln
(
ω
s
t) at
ω
s
t=0, D =
Du
ty cycle o
f
th
e
IGBT
and
sn
s
Ln
n
n
sn
s
Ln
s
sn
n
s
Ln
D
t
D
i
D
t
D
i
D
t
t
i
2
sin
2
1
2
cos
2
2
exp
2
For 2
π
D <
ω
s
t
≤
2
π
(2
)
Whe
r
e: i
Ln
(2
π
D) is th
e
v
a
lu
e
o
f
i
Ln
(
ω
s
t) at
ω
s
t=2
π
D
From
Eq
uat
i
o
n
(
2
),
i
Ln
(
ω
s
t) h
a
s
d
a
m
p
ed
si
n
u
so
id
al o
s
cillatio
n
for 2
π
D <
ω
s
t
≤
2
π
1
t
v
s
Cn
F
o
r
0<
ω
s
t
≤
2
π
D
(3
)
and
sn
s
sn
n
n
n
n
sn
s
s
sn
n
s
Cn
D
2
t
sin
.
D
4
exp
1
1
2
1
D
2
t
cos
.
D
2
t
exp
t
v
For 2
π
D <
ω
s
t
≤
2
π
(4
)
and
t
v
V
t
v
s
C
s
s
t
Fo
r
0
<
ω
s
t
≤
2
π
(5
)
Whe
r
e: i
Ln
= norm
alized indu
ctor c
u
rrent, v
Cn
= norm
a
lized ca
pacitor
voltage
,
ω
sn
= norm
alized
swi
t
c
hi
n
g
f
r
e
q
uency
;
Z
0
= c
h
a
r
acteristic im
pedance
of the i
nve
rter-loa
d syste
m
;
ω
0
= resonant
fre
que
ncy
of t
h
e
paral
l
e
l
res
o
na
nt
sy
st
em
and
ω
s
= swi
t
c
hi
ng
fre
que
ncy
of
t
h
e I
G
B
T
.
The m
a
the
m
atical expressi
ons
of th
e
above
param
e
ters are a
s
follows
.
0
s
L
Ln
Z
V
i
i
(6
)
s
C
Cn
V
v
v
(7
)
L
2
R
0
n
(8
)
0
s
sn
(9
)
C
L
Z
0
(1
0)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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PED
S
I
S
SN
:
208
8-8
6
9
4
Ha
rmo
n
i
cs Red
u
c
tion
i
n
a
C
u
rren
t
Sou
rce
Fed
Qu
a
s
i
-
Reso
nan
t In
verter
Ba
sed
… (Avijit Ch
a
k
rab
o
rty)
43
5
2
2
0
L
4
R
LC
1
(1
1)
The param
e
ter
α
n
can be
su
bst
i
t
u
t
e
d by
Q
fac
t
or
of
t
h
e
res
o
n
a
nt
l
o
a
d
as
f
o
l
l
o
ws
.
2
n
1
1
2
1
R
C
L
Q
(1
2)
From
Equat
i
o
n
(11
)
, i
t
i
s
obv
i
ous
, t
h
at
v
Cn
(
ω
s
t
)
has u
nde
r
dam
p
ed osci
l
l
at
i
ons f
o
r 2
π
D <
ω
s
t
≤
2
π
an
d du
ri
n
g
th
e op
ti
m
u
m
o
p
e
ratio
n
of th
e
propo
sed ind
u
c
t
i
o
n
h
eating
sy
ste
m
, to
ach
iev
e
th
e tu
rn-ON an
d
tu
rn
-OFF and
t
h
e
fo
llowing
set o
f
equ
a
tion
s
are to b
e
satisfi
ed
.
0
2
t
d
v
d
;
0
2
v
t
t
and
0
2
i
Ln
(1
3)
So,
f
r
om
Equ
a
t
i
on
(1
3)
,
by
K
V
L t
h
e
cap
aci
t
o
r
vol
t
a
ge
v
C
reac
hes V
s
and inductor
current i
L
(t)
reaches zero at
the sam
e
insta
n
t and
the
r
efore, to
obtain t
h
e optim
u
m
op
erating c
o
nditions, the l
o
ad c
u
rrent
i
L
(t), capacito
r voltage
v
C
(t
) a
nd t
h
e
vol
t
a
g
e
v
t
(t
) ca
n be cal
cul
a
t
e
d usi
ng t
h
e eq
uat
i
o
n
s
(
1
)
-
(
5
) t
a
ki
ng i
Ln
(0
)=0
an
d th
e
relation
am
o
n
g
α
n
, D and
ω
sn
can
be
exp
r
esse
d
by
t
h
e
fol
l
o
wi
n
g
e
quat
i
o
ns
res
p
e
c
t
i
v
el
y
.
0
1
2
sin
4
exp
1
1
2
cos
4
exp
1
sn
sn
n
n
sn
sn
n
D
D
D
D
(1
4)
and
1
1
2
sin
.
4
exp
1
1
2
1
1
2
cos
1
2
exp
sn
sn
n
n
n
n
sn
sn
n
D
D
D
D
(1
5)
From
the Eq
ua
tions (
1
4) a
n
d
(1
5)
res
p
ective
l
y
,
it is
clear that the IGBT
m
u
st be controlled with a
variable duty
cycle and
variable
switching frequency, wh
ich depend on
the
qu
ality factor Q i.e.
α
n
that
determ
ined by
the circuit
co
mp
on
en
ts
.
In
cr
ea
s
e
in
α
n
cause
s increase i
n
switching fre
q
uency
ω
s
. For smaller
values of Q, the voltage v
t
c
a
nn
ot reac
h V
s
in
m
ode-I
I an
d so
ft turn
-
O
N
of the IGB
T
is not po
ssible
that
causes
hig
h
sw
itching l
o
ss.
S
o
, hi
ghe
r
value
of
Q
sh
o
u
ld
be
ch
ose
n
to
get
soft t
u
r
n
-
O
N.
4.
TOTAL HARMONIC DI
S
T
O
R
TI
ON
(
T
HD
)
It is a m
easure
of
disto
r
tio
n
of
a
no
n
-
sinus
oi
dal wa
ve
fo
rm
from
its sin
u
soi
d
al f
u
ndam
e
ntal
com
pone
nt. T
h
is is an i
nde
x t
o
visualize the
im
pact of
harm
onics
an
d t
h
e l
e
vel o
f
disto
r
tion
that they
ca
use i
n
a waveform
. It
is m
a
the
m
atica
lly
ex
p
r
essed by th
e fo
llowing equ
a
tio
n.
rms
1
n
,...
3
,
2
n
2
nrms
I
I
THD
(1
6)
Whe
r
e: I
Irm
s
= r
oot m
ean squa
red val
u
e o
f
th
e fun
d
am
ental
com
pone
nt an
d I
nrm
s
=
root m
ean
sq
uare
d
value
of the
n-
th harm
onic co
m
ponent.
Hig
h
value o
f
T
H
D
of a
n
y
wave
f
o
rm
indicates m
o
re distortio
n o
f
it
fr
om
its fun
d
a
m
ental com
ponent.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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SN:
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94
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l.
7,
No
.
2,
Ju
ne 20
16
:
431
–
4
39
43
6
5.
DISTO
R
TIO
N
F
ACT
OR
(
D
F)
A
distortio
n
f
actor i
ndicates
total am
ount
of
ha
rm
onics
that rem
a
in in
any
wave
f
o
r
m
, after the
wave
form
is subjected to
2
nd
or
de
r
atten
u
ation (i.e. divi
de
d by
n
2
)
,
whe
r
e,
n= 1,
2
,
3,
…, n. It
is
gi
v
e
n by
the
follo
win
g
e
x
pr
ession
.
rms
1
n
,....
3
,
2
n
2
2
nrms
I
n
I
DF
(1
7)
6.
TOTAL
H
A
RM
ONI
C
DI
STORTI
ON (THD
), DIST
ORTIO
N
F
A
CTOR
(
D
F)
AN
D
P
O
WE
R
FA
C
T
OR
(
P
F)
D
ETER
M
IN
A
T
ION
OF THE
PR
OPOSED
IN
DUCTION
HEA
T
ER
WITHOUT
FILTER
In
Fig
u
re
6, t
h
e
wave
f
o
rm
of
the i
n
p
u
t s
o
u
r
ce c
u
r
r
e
n
t
of
the c
u
rre
nt so
urce
fe
d
q
u
asi-
reso
na
nt
Inverter without Filter is given usi
ng PSIM and the PSIM
circuit diagram
is shown
in Figure 7. From
this
wave
f
o
rm
the R
M
S value of th
e input source curre
nt is I
irms
= 5.5
5
44
A an
d the
R
M
S value of the
fu
n
d
am
ental com
pone
nt is
I
1rm
s
= 3.90
4
A
re
spectively
.
T
h
e
Fig
u
re
8
also
represe
n
ts t
h
e FFT spectrum
of thi
s
case. From
the
FFT spectrum
the T
H
D an
d t
h
e
DF
of
the
in
put c
u
rre
nt ca
n
be
o
b
tained
w
h
ich a
r
e as
f
o
llows
.
%
22
.
43
%
100
904
.
3
40038
.
0
639
.
1
I
I
THD
2
2
rms
1
n
,...
3
,
2
n
2
nrms
(1
8)
%
67
.
4
%
100
904
.
3
5
40038
.
0
3
639
.
1
I
n
I
DF
2
2
2
2
rms
1
n
,....
3
,
2
n
2
2
nrms
(1
9)
From
the P
S
I
M
diag
ram
in Figu
re
7,
the i
n
put
p
o
we
r
factor
o
f
the
cu
rre
nt s
o
u
r
ce
fed
p
a
rallel qua
si-
resonant Invert
er
with
out Filter is
0.33183.
Figure
6. Input
Current waveform
of t
h
e current source
fed
quasi
resonant inverter without
filter
Figure
7. Sim
u
lated circuit
of
the current source fe
d
quasi-resonant i
nverter wit
h
out filter
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I
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PEDS
I
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SN:
208
8-8
6
9
4
Harmonics Reduction i
n
a
C
u
rrent
Source Fed Quasi
-
Resonant
Inverter
Based … (Avijit Chakraborty)
43
7
Figure
8. FFT
spectrum
of the input
current
of the curr
ent source
fed quasi
-resonant
i
nverter without filter
7.
TOTAL
H
A
RM
ONI
C
DI
STORTI
ON (THD
), DIST
ORTIO
N
F
A
CTOR
(
D
F)
AN
D
P
O
WE
R
FACT
OR (PF)
DETERMINATION OF
THE
PROPOSED INDUCTION
HEATER WIT
H
FILTER
In Fi
g
u
re
9, th
e wave
f
o
rm
of
inp
u
t so
urce c
u
r
r
ent
of t
h
e c
u
r
r
ent s
o
urce
f
e
d q
u
asi-
res
o
n
a
nt I
nve
rter
with Low Pass (LP)
Filter is given
usi
n
g PSIM and the circu
it diagram
is shown i
n
Figure 10. From
this
si
m
u
lated waveform
the RMS val
u
e
of t
h
e
in
pu
t sour
ce cu
rrent is
obtained as I
irm
s
= 7.
22
56
A an
d the RMS
value
of
the
f
u
n
d
am
ental com
ponent is I
1r
m
s
= 6.9
1
79
A
res
p
ectively
.
The Fi
gu
re
11 also re
present
s
the
corresponding FFT
spectrum
.
From
the FFT
spectrum
the
THD a
n
d the
DF
values
of t
h
e input c
u
rrent can be
obtaine
d
which are as follows,
%
9
.
12
%
100
9179
.
6
89262
.
0
I
I
THD
2
rms
1
n
,...
3
,
2
n
2
nrms
(2
0)
%
43
.
1
%
100
9179
.
6
3
89262
.
0
I
n
I
DF
2
2
rms
1
n
,....
3
,
2
n
2
2
nrms
(2
1)
Fr
o
m
th
e PSIM d
i
agr
a
m
as sh
own
in Figur
e 10
,
th
e input powe
r
factor
of
the curre
nt source fe
d
quasi- resona
nt Inverter
without
Filter is
0.80045.
Figure
9. Input
Current waveform
of t
h
e current source
fed
quasi
-resonant inverter with filter
Figure 10. Simulated
circuit
of
the current source
fed quasi-resonant
in
vert
er with
filter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS Vo
l.
7,
No
.
2,
Ju
ne 20
16
:
431
–
4
39
43
8
Figure
11.
FFT spectrum
of t
h
e input
current
of the cu
rrent source
fed quasi
-resona
nt i
nverter with filter
8.
SIMULATION AND RESULTS
Fr
o
m
th
e PSIM si
m
u
latio
n
s
as sho
w
n
in
Fig
u
r
e
7
and
Fig
u
r
e
1
0
of
th
e
p
r
op
o
s
ed
inductio
n
h
eatin
g
sy
stem
, two di
ffe
rent re
sults
are o
b
ta
ine
d
.
The Fi
gu
re 6
a
nd
Fig
u
re
8 s
h
ow t
h
e in
put c
u
r
r
ent
wave
f
o
r
m
and
th
e FFT
sp
ect
ru
m
o
f
th
e input cu
rr
en
t
o
f
t
h
e in
v
e
r
t
er
with
ou
t f
ilter
.
Fro
m
th
e FFT
sp
ect
ru
m
th
e 3
rd
and
the 5
th
harm
onics are
fo
u
nd t
o
be d
o
m
inant m
a
king the in
put
c
u
r
r
e
nt n
o
n
-si
nus
o
i
dal with a
relatively
highe
r
TH
D
an
d DF
v
a
lu
es. Besid
e
s th
e inp
u
t
po
wer
f
acto
r
is 0.
331
83
,
which is
quite low. As su
ch, t
o
suppress t
h
e
effects
of t
h
ese
harm
onics at an im
proved
power
factor an LC
passive filter is
used. The Fi
gure 9
shows the input
current
of the i
nverter
with
filter and Fi
gure
11 shows t
h
e FFT spect
ru
m
of the i
n
put current of t
h
e inverter
with filter. The filter circu
it used in t
h
is case is a
passive LC Lo
w
Pass Filter (LP)
w
hose param
e
te
rs are
suitably selected to
get desi
red results. From the FFT sp
e
c
trum
, the harm
onics are al
m
o
st absent in
the input
current and t
h
us the THD is relatively less and
DF is al
s
o
greatly
red
u
ce
d. B
e
side
s
the
input power factor is
quite im
proved to a
value
of
0.80045 i.e. close to
unity,
whi
c
h is t
h
e
utility
of the installed
filter.
9.
CO
NCL
USI
O
N
In the
present
work, t
h
e im
pact of
the
presence
of ha
rm
onics in th
e i
n
p
u
t cu
rre
nt is
studie
d
fo
r
a
cur
r
ent s
o
urce
fed
q
u
asi-
re
son
a
nt in
ve
rter o
p
erati
ng at
hig
h
s
w
itching
fre
q
u
e
n
cy
with a
nd
w
ithou
t
incorporating a passive
filter.
In t
h
e
first case without filter,
higher
THD and DF values
of t
h
e input current
indicate the
p
r
esence
of
hi
gh
de
gree
o
f
noi
se level.
T
h
e
low input
power fact
or indicates greate
r
re
active
power inj
ection from
the po
wer frequency input source.
In the second case, when the
LC Low Pass
Filter is
incorporate
d
, t
h
e THD and
DF val
u
es of the input cu
rrent reduce significantly
to a low value and thus
reduces t
h
e noi
s
e level of the
input
cu
rre
nt a
f
ter
harm
onics
sup
p
r
essio
n
sat
i
sfactorily
an
d
in the sec
o
nd c
a
se,
the input
powe
r fact
or is also
im
proved t
o
a l
a
rge
r
value
resulting less reactive po
wer inj
e
ction from
the input
powe
r source.
ACKNOWLE
DGE
M
ENTS
Aut
h
o
r
s a
r
e th
ank
f
ul to 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 Delhi, India
for granting
fi
nanc
ial support under Maj
o
r
Research
Proj
ect entitled
“Si
m
ulation of high
fre
que
ncy
m
i
rror i
nve
rter
fo
r
ener
gy
ef
ficien
t indu
ction
hea
t
ed co
o
k
in
g o
v
e
n” a
nd als
o
g
r
ateful t
o
the
Un
de
r
Secretary a
n
d Joint Sec
r
et
ary
of
U
G
C
,
In
dia fo
r
th
ei
r active
co-operation.
REFERE
NC
ES
[1]
A. J. Onah, “Harmonics: Generation and
Suppression in AC Sy
stem Networks”,
Nigerian Journa
l of Technolog
y,
vol
.
31
, pp
. 293–
299, 2012
.
[2]
B. Singh, K. Al-Haddad, A. C
h
a
ndra, “A Review of Active Filters for Power Qualit
y
Im
provem
e
nt”,
IEEE
Transactions on
Indus
trial Electronics,
vo
l. 46, p
p
. 960–971
, 199
9.
[3]
P. A. Dahono, A. Purwadi, Q. Am
aruzzam
an,
“
A
n LC
filter design m
e
thod for singl
e-phase P
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BIOGRAP
HI
ES OF
AUTH
ORS
Avijit Chakraborty
r
ece
ived hi
s
B.Tech and
M
.
Tech deg
r
ees
in Elctr
i
ca
l En
gineer
ing from
Calcutta univ
e
rsity
,
West Benga
l, India in 2005 and 2007 respectively
.
Curr
ently
he is working
as an Assistant Professor in E
l
ec
tric
al Eng
i
ne
ering Departm
e
nt of Saroj Mohan Institut
e
of
Techno
log
y
, G
uptipar
a, Hoog
hly
-
712512
, In
dia.
He is als
o
the Head
of
the Electrical
Engineering Department
sin
c
e
April, 2015
. He
has total 8
y
e
ars of teaching
exp
e
rien
ce and on
e
y
e
ar of Industrial exper
i
en
ce. His current ar
eas
of interest
are Power electronics applications,
Applica
tion of
h
i
gh frequ
enc
y
co
nverters
,
E
l
ec
tri
cal
M
achin
es
an
d El
ectr
i
c
Drives
.
Titas Kumar Nag
has received
his B.Tech degr
ee in
Electr
i
cal
Engineering fro
m West Bengal
University
of
Technolog
y
in
th
e
y
e
ar 2011
and
al
so r
e
ceived
h
i
s M.Tech d
e
gree in
Electrical
Engineering fro
m the same univ
e
rsity
in
the
y
ear
2014. Curr
ently
h
e
is
working
as a Techn
i
cal
Assistant in Electri
cal
Engineer
ing Departm
e
nt
at the Saro
j Mohan Institute of Technol
o
g
y
(Degree divisio
n
), Guptipara, Hooghly
-
71251
2.
His
current
areas
of inter
e
s
t
are P
o
wer
electronics and
its applications.
Pradip Kumar
Sadhu
receiv
e
d
his
Bache
l
or, P
o
s
t
-Graduate
and
P
h
.D. (Engin
eeri
ng) degre
e
s
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.
Nitai Pal
re
ce
iv
ed his
B
.
Te
ch.
a
nd M
.
Te
ch.
degr
ees
in
Electrical
Engineering fro
m University
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
blic
ations
in Jo
urnals, In
tern
ati
onal
& Na
tiona
l
conferen
ces. He is the co-inv
estig
ator of Govt f
unded project.
Hi
s current ar
eas of interest ar
e
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.
Evaluation Warning : The document was created with Spire.PDF for Python.