In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
11, N
o.
1, Mar
ch 20
20,
p
p.
178~
1
8
8
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
1
78-
18
8
1
78
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Design and imple
m
entation of hi
gh frequency induction heating
with LLC resonan
t load
m
atching usi
n
g ELTA
Su
g
a
n
t
h
i Ka
ru
p
pusa
m
y
1
,
S
u
na
nd
h
i
tha
V
2
,
Sura
j
R
3
,
R
o
j
a
T S
4
,
Sun
da
ra
ra
ma
n
K
5
1,
2
,
3,
4
Dep
artm
ent
o
f
El
e
c
t
rical
an
d
El
ectro
nics E
n
g
i
n
eeri
ng,
S
ri Venk
a
t
e
s
wa
ra
Co
l
le
ge
o
f En
g
i
ne
e
r
in
g,
Ind
ia
5
D
epartm
ent of
El
ectri
cal an
d
E
l
ectro
ni
cs E
ng
inee
ri
ng
, Raja
l
aks
h
m
i Insti
t
u
t
e of Techn
o
l
o
g
y
,
In
di
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
ug
5,
201
8
Re
vise
d Mar
1,
201
9
Ac
ce
p
t
ed
Au
g
2
0
,
2
019
Ind
u
ct
ion
h
eating
is
a
n
on
-cont
a
c
t
met
h
o
d
o
f
p
r
od
ucin
g
heat
w
h
i
ch
can
b
e
us
ed
t
o
perf
orm
vari
ous
p
ro
c
e
sses
lik
e
h
ard
e
n
i
n
g
,
an
neali
n
g
,
t
e
m
p
eri
ng,
w
e
ld
in
g
,
b
r
a
z
i
ng
,
me
l
t
in
g,
f
o
r
g
i
n
g
,
e
tc
.
T
h
i
s
p
a
p
e
r
d
is
c
u
s
s
e
s
t
he
d
e
s
ig
n
a
n
d
im
plem
en
t
a
ti
on
o
f
in
du
c
tio
n
heati
n
g
o
n
a
g
i
v
en
w
o
r
k-p
i
ece,
u
s
i
n
g
a
n
L
LC
reso
nan
t
c
i
r
cuit
a
n
d
a
trans
f
o
rm
e
r
f
o
r
i
m
p
edan
c
e
m
atchi
ng,
s
o
a
s
to
t
ransf
e
r
a
m
a
xim
u
m
pow
e
r
o
f
5KW
to
t
h
e
l
o
a
d.
T
he
l
o
a
d
param
e
ters
a
re
f
ou
nd
o
u
t
us
in
g
E
L
T
A
s
o
f
tware
w
h
i
c
h
cal
cul
a
tes
th
e
val
u
es
b
as
ed
o
n the di
men
s
i
ons
o
f
th
e
w
o
rk
p
iece,
o
p
e
ra
t
i
n
g
f
requ
e
n
cy
a
nd
t
em
peratu
re.
T
h
e
in
vert
er
u
s
e
d
i
s
bas
e
d
on
S
i
C
M
OS
FE
Ts
w
h
i
ch
m
i
n
im
izes
t
h
e
l
o
s
ses
at
h
igh
freq
u
en
cies
a
nd
hi
gh
t
em
peratu
res.
T
he
t
h
e
oreti
cal
a
nd
s
im
u
l
a
t
ed
r
esu
lts
f
rom
M
ATL
A
B
are
anal
ys
ed
a
n
d
v
er
if
i
e
d.
T
h
e
h
ard
w
are
is
i
m
p
le
m
e
nted
f
or
t
he
L
L
C
circui
t
w
i
th
trans
f
or
m
e
r and the
re
s
u
lts are pres
e
nt
ed.
K
eyw
ord
s
:
ELTA
Im
pedanc
e
ma
t
c
hin
g
Ind
u
ct
i
on hea
t
ing
LLC
res
on
ant
c
o
nv
e
r
t
e
r
SiC MOSF
ET
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
S
uga
n
t
hi K
,
Depa
rtem
ent o
f
E
lectr
i
c
a
l a
n
d
Electro
n
i
cs
E
n
g
ine
e
ri
n
g
,
S
r
i
V
e
nka
t
e
sw
ara
Colle
ge
of En
gi
neer
ing,
S
r
i
p
e
r
um
b
u
dur
, Chen
n
a
i
6
0
2
11
7
,
Tam
i
l
N
a
du.
Em
ail:su
g
a
n
th
i
@
sv
c
e
.
ac.
in
1.
I
N
TR
OD
U
C
TI
O
N
I
nduc
t
i
on
heat
in
g
i
s
t
he
m
o
s
t
c
l
e
a
n
,
effic
i
ent,
c
os
t-e
f
fec
tive
,
p
re
ci
se,
a
n
d
re
p
eat
ab
le
m
et
h
o
d
of
ma
terial
h
ea
ti
ng
a
va
i
l
a
b
le
t
o
t
h
e
i
n
d
u
str
y
,
toda
y
.
I
t
w
o
r
k
s
on
th
e
p
r
in
ci
pl
e
of
F
a
r
ad
a
y
’s
l
aw
o
f
elec
tr
oma
gne
t
i
c
i
n
d
u
c
tio
n.
T
he
p
ur
p
o
se
o
f
in
d
u
ct
i
o
n
hea
t
i
n
g
m
a
y
b
e
t
o
h
a
r
d
e
n
a
p
a
r
t
t
o
p
r
e
v
e
n
t
w
e
a
r
;
m
a
k
e
the m
e
ta
l
pl
a
s
ti
c
for
forgi
n
g; b
ra
ze
or
s
ol
der
tw
o pa
rts to
ge
t
h
er;
or for a
ny num
ber
of o
t
h
e
r
a
ppl
icat
i
o
n
s
[1]
.
Res
ona
n
t
p
ow
er
c
on
ve
rters
a
r
e
w
i
de
l
y
u
sed
for
i
n
d
u
c
t
i
o
n
he
ati
n
g
a
nd
the
y
u
sua
l
ly
o
p
e
ra
te
a
t
seve
ra
l
ten
s
o
f
K
H
z
t
o
t
h
e
MH
z
ra
nge.
The
se
l
e
cti
on
of
i
dea
l
f
r
e
que
nc
y
for
in
duc
t
i
o
n
h
e
a
t
i
n
g
of
a
p
a
r
tic
ular
app
l
ica
t
i
o
n
is
d
i
s
cuss
ed
i
n
[2
]
.
T
he
p
ow
er
r
ange
v
a
r
ies
fr
o
m
k
i
l
o
w
a
t
t
s
in
dom
est
i
c
a
nd
m
e
dica
l
a
p
plic
atio
ns
t
o
s
ev
era
l
m
eg
awa
t
t
s
i
n
i
n
d
u
s
t
r
i
a
l
ap
pli
cat
ion
s
.Th
e
s
e
d
es
ig
n
s
i
m
p
l
y
c
ha
lle
ng
e
s
p
er
t
a
in
in
g
to
b
l
o
c
k
in
g
vo
lta
ge
s,
s
w
itc
hi
n
g
l
osse
s,
a
nd
opera
ti
on
i
n
h
ar
sh
e
n
v
i
ro
nme
n
ts
t
ha
t
pe
rfe
c
tl
y
ma
tch
the
fea
t
ure
s
o
f
S
i
C
dev
i
ce
s,
o
pe
ni
ng
t
h
e
desi
g
n
w
i
n
dow
t
o
h
i
g
h
p
e
rfor
m
a
n
ce
c
o
nverte
r
s
a
nd
i
n
no
va
tiv
e
ind
u
s
t
ria
l
h
ea
t
i
n
g
a
p
pli
c
at
ion
s
.
S
i
li
c
o
n
ca
rbid
e
(Si
C
)
p
o
w
e
r
d
ev
i
c
e
s
h
a
v
e
b
een
i
n
v
e
s
ti
gate
d exte
ns
i
v
el
y
in the
p
a
s
t
tw
o
de
cade
s
.
A
re
vi
e
w
o
f
the
vari
ou
s
tec
h
n
o
l
o
g
i
cal
p
ro
gr
ess
of
S
iC
pow
e
r
d
ev
i
c
es
a
n
d
th
ei
r
em
erg
i
n
g
a
ppli
cat
ion
s
i
s
prese
n
t
e
d
in
[
3
]
.S
iC
M
osfe
t
d
e
vi
c
e
s
a
l
s
o
ha
ve
t
h
e
c
a
p
ab
i
l
i
t
y
t
o
s
i
g
nif
i
c
a
n
t
l
y
e
x
pan
d
t
h
e
v
ol
t
a
ge
r
a
n
g
e
o
ver
what
i
s
alre
a
d
y
ava
ila
b
l
e
w
ith
S
i
power
d
ev
ices.
S
iC
s
w
i
tc
he
s
wo
ul
d
o
p
erat
e
ov
e
r
h
igh
e
r
v
o
l
t
a
ge
a
n
d
tem
p
era
t
ur
e
r
a
nge
s,
a
nd
ye
t
have
s
ize
s
n
ea
r
l
y
20
t
i
me
s
sma
l
l
e
r
t
h
an
t
ha
t
o
f
S
i-ba
se
d
dev
i
ce
s.The
y
a
re
a
l
s
o
con
s
i
d
ere
d
t
o
b
e
s
upe
ri
or
i
n
t
e
rm
s
of
h
ig
h
te
mper
ature
sta
b
il
it
y,
l
ow
l
oss
in
o
pera
ti
on
a
n
d
fas
t
s
w
itc
h
i
n
g
tim
e
over
t
h
e c
o
n
v
e
n
t
i
ona
l
S
i
sw
i
t
c
he
s
[4,
5].
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
si
g
n
a
nd im
plem
e
n
t
a
ti
on
o
f
hi
g
h
fre
que
nc
y
ind
u
c
t
i
o
n he
at
i
ng
wit
h
L
L
C …
(Sug
an
thi
Karu
p
pusam
y)
17
9
Th
e
coi
l
u
se
d
f
o
r
i
n
du
c
t
ion
hea
t
i
n
g
h
a
s
ap
art
fro
m
rea
c
t
an
ce
,
a
s
mal
l
r
e
s
i
s
t
a
n
c
e
al
so
.
A
ch
ang
e
i
n
coi
l
r
esis
t
a
nce
a
nd
r
eac
ta
nce
r
e
sults
i
n
a
chan
ge
i
n
p
o
we
r
fac
t
or
(
Cos
Ф
)
and
qu
al
i
t
y
f
actor,
Q
.
W
he
n
w
e
ana
l
yse
t
h
e
ou
tp
u
t
pow
e
r
c
h
a
ra
cterist
i
c
ve
rsus
t
he
c
irc
u
i
t
ope
r
a
t
i
n
g
fr
eq
uenc
y
for
a
g
i
ve
n
l
o
a
d
c
irc
u
it,
i
t
is
seen
t
ha
t
t
h
e
o
u
t
p
u
t
p
ower
v
ar
i
e
s
wi
del
y
w
i
t
h
the
o
p
e
r
at
i
n
g
fre
q
u
e
n
c
y
.
The
goa
l
is
t
o
de
live
r
t
he
r
e
q
u
i
red
pow
er
t
o
hea
t
t
he
w
ork
p
i
ec
e
w
itho
u
t
e
xc
eed
in
g
a
ny
o
f
t
he
pow
er
sou
r
ce
p
a
r
amet
ers.
T
h
e
v
ario
u
s
a
dv
an
t
a
g
e
s
a
n
d
d
i
s
a
dv
a
n
ta
g
e
s
of
u
si
ng
a
n
LLC
r
e
s
on
a
n
t
c
onv
e
r
t
e
r
i
s
d
i
s
cu
ss
e
d
i
n
[6]
a
nd
a
n
e
qu
i
v
a
l
e
n
t
m
ode
l
i
s
prese
n
t
e
d
i
n
[
7].
The
LL
C
c
o
n
f
ig
urat
io
n
o
f
fer
s
a
b
e
t
ter
pe
rform
anc
e
t
ha
n
t
h
e
co
n
v
e
n
ti
ona
l
ser
i
es
r
eso
n
an
t
in
verter
(S
R
I
)
, due
to
it’s sh
or
t-circ
ui
t im
m
uni
t
y
a
nd l
o
w
tra
n
sf
orm
e
r seco
ndar
y
c
u
r
ren
t
. A
n op
tim
i
z
e
d
de
s
i
g
n
for
a
LL
C
reso
na
nt
c
o
nver
t
er
f
or
t
he
r
eq
uire
d
ou
t
p
u
t
p
ow
er
c
apa
ci
ty
i
s
pre
s
en
ted
i
n
[
8].
Whe
n
c
om
p
a
r
e
d
to
the
S
R
I,
t
he
LLC
c
o
n
fi
gur
a
t
i
o
n
in
v
o
l
v
es
t
he
i
nc
l
u
s
i
o
n
of
a
n
ew
rea
c
ti
ve
e
lem
e
n
t
L
s
a
n
d
the
ove
r-
dime
n
s
i
o
ni
n
g
o
f
t
h
e
ca
pa
ci
ta
nc
e.
B
ut
t
hese
d
ra
wbacks
ar
e
overc
o
me
a
t
hi
g
h
fre
que
nc
ies
as
L
s
c
o
u
l
d
be
a
para
sitic
i
n
d
u
c
t
a
n
ce
and
the
c
u
r
r
ent ga
in va
l
ue
m
inim
iz
es t
he
c
a
p
ac
ita
nce
incr
em
en
t.
Th
e
op
t
i
m
u
m
s
el
ec
ti
on
o
f
res
o
n
a
nt
t
a
n
k
c
i
rc
ui
t
an
d
a
mo
d
i
fi
ed
L
LC
l
oa
d
r
e
sona
n
t
c
irc
u
it
con
f
ig
ura
tio
n
of
a
f
ul
l
bridg
e
i
nv
e
r
ter
for
i
n
d
u
c
t
i
on
he
at
i
ng
a
ppl
i
cati
ons
a
re
d
i
s
cu
ssed
i
n
[
9
]
.
Th
e
th
ree
t
a
n
k
circ
u
i
ts
-
s
erie
s,
p
ara
l
le
l
a
nd
LLC
t
a
nk
c
i
rc
u
i
ts
a
re
c
om
pa
red
ba
se
d
on
t
h
e
i
r
pe
rfor
ma
nc
e
and
c
h
ara
c
t
erist
i
c
s
.
Th
e
se
ri
es
t
ank
ci
rcui
t
requ
i
r
e
s
a
m
a
t
c
h
in
g
t
r
an
sfo
r
me
r
wh
en
u
s
e
d
f
or
i
nd
uc
t
i
o
n
h
ea
ti
n
g
.
In
t
he
c
a
s
e
o
f
a
para
l
l
e
l
r
es
ona
nt
c
ircu
i
t
,
effic
i
enc
y
i
s
r
e
d
u
ce
d
a
t
l
ig
h
t
l
oa
ds
.
LLC
r
eso
n
an
t
circ
uit
res
u
l
t
s
in
i
nc
rea
s
ed
s
ystem
e
ffi
c
i
en
cy
w
i
t
h
l
e
ss
w
eig
h
t
a
n
d
si
ze
o
f
th
e
p
o
w
er
s
u
ppl
y
an
d
is
g
ener
ally
p
referred
ove
r
a
series
o
r
parallel
resona
nt
c
o
n
v
e
r
te
r.
Whe
n
L
L
C
r
eso
n
an
t
c
i
rc
u
it
is
u
se
d
w
i
th
a
t
rans
for
m
e
r
,
the
m
a
g
n
e
t
i
z
i
ng
i
n
duc
ta
nce
of
t
he
trans
f
or
me
r
is
a
l
s
o
co
ns
ider
e
d
a
s
o
n
e
of
t
h
e
i
n
d
u
cta
n
ce
s.
T
hi
s
n
eed
s
t
o
b
e
s
m
a
l
l
,
r
e
q
u
i
ri
ng
l
a
r
g
e
r
cu
rre
nt
thr
o
u
g
h
t
he
s
w
itc
he
s
a
n
d
c
ons
eq
ue
nt
l
o
sse
s.
I
n
[10]
i
s
sug
g
es
te
d
an
a
l
t
e
r
nat
i
v
e
co
nfig
ura
t
i
on
s
u
it
a
b
l
e
f
or
wi
d
e
i
npu
t
vol
t
a
g
e
a
nd
l
o
a
d
rang
e
s
but
t
hi
s
requi
re
s
two
re
so
n
a
nt
t
an
ks
a
nd
a
u
x
il
i
a
r
y
s
wit
c
h
e
s.
A
n
asym
me
t
r
i
c
al
v
o
l
tage
c
a
n
ce
l
l
at
i
o
n
tec
h
n
i
q
u
e
with
a
n
L
L
C
re
so
na
n
t
con
v
e
r
ter
for
in
d
u
ct
i
on
hea
t
i
n
g
is
sug
g
es
t
e
d
i
n
[
11]
w
her
e
t
he
d
u
t
y
cyc
l
e
is
v
a
r
ie
d
w
ith
P
LL
con
t
r
ol
t
ra
c
k
in
g
t
h
e
re
so
na
nt
f
req
u
e
nc
y
.
A
com
p
le
te
p
roc
e
dure
f
o
r
simu
lat
i
on,
a
n
a
l
y
sis
and
de
si
gn
cr
iter
i
a
f
o
r
a
L
L
C
r
e
s
o
n
a
n
t
c
o
n
v
e
r
t
e
r
i
s
d
i
s
c
u
s
s
e
d
i
n
[1
2]
a
nd [
13].
Th
e
lo
ad
mat
ch
in
g
t
e
ch
niq
u
e
wh
i
c
h
h
as
t
o
be
d
on
e
f
o
r hi
gh f
r
eq
u
e
n
cy
i
n
d
u
c
t
i
on he
at
i
ng ca
n be
d
o
n
e
b
y
v
a
riou
s
me
t
hod
s
as
d
isc
u
sse
d
i
n
[
1
4
-16].
Th
e
c
o
nv
ent
i
on
a
l
m
e
th
od
o
f
us
ing
a
tra
n
sf
orm
e
r
for
lo
a
d
m
a
t
c
h
i
n
g
c
a
n
b
e
r
e
p
l
a
c
e
d
b
y
a
n
L
L
C
c
i
r
c
u
i
t
.
T
h
e
u
s
a
g
e
o
f
t
r
a
n
s
f
orm
e
r
fo
r
loa
d
m
atch
i
n
g
has
i
t
s
a
dva
n
t
age
s
a
n
d
di
sadv
a
n
t
a
g
e
s
.
A
r
es
on
a
n
t
conv
e
r
t
e
r
us
in
g
Si
C
M
o
sfe
t
s
i
n
a
ha
lf-b
rid
g
e
c
o
n
f
i
g
urati
o
n
but
a
t
a
l
o
w
e
r
pow
er
leve
l
o
f 65
0
W
is
d
i
s
c
us
s
e
d i
n
[
1
7
]
.
A
S
iC bas
e
d
c
o
n
v
e
r
ter
w
ith soft
sw
itch
i
n
g
a
nd
usin
g an i
n
t
erl
e
aved
bo
ost
co
nver
t
e
r
is pr
opose
d
i
n [18]
.
A
n
appr
oach
t
o
ide
n
tif
y th
e
reso
nan
t
t
ank
elem
e
n
ts i
s sug
g
est
e
d
in
[
1
9
].
Th
is
p
a
p
er
s
t
u
die
s
a
c
o
n
fi
gu
rati
on
w
h
ic
h
i
s
a
c
om
bina
ti
on
of
a
n
L
L
C
c
i
r
c
u
i
t
i
n
a
d
d
i
t
i
o
n
t
o
a
trans
f
or
me
r.
I
n
a
n
i
nd
us
tria
l
e
n
v
i
ro
nme
n
t,
a
p
a
r
t
from
the
c
o
nve
r
t
er
a
n
d
t
he
m
a
t
c
h
i
n
g
tra
n
sform
e
r,
t
he
d
e
s
ig
n
of
t
h
e
i
nd
uc
t
i
on
c
o
il
a
n
d
i
t
s
p
rofi
l
e
i
tse
l
f
is
c
ri
ti
c
a
l
t
o
ob
t
a
i
n
the
be
s
t
p
er
form
ance
.
A
system
at
ic
d
e
s
ig
n
proce
dure
for
the
c
o
i
l
i
s
e
s
se
ntia
l
for
pro
p
e
r
m
a
t
chi
ng
of
t
he
c
o
nve
r
t
er
w
ith
t
he
c
oil.
I
nd
uc
ti
o
n
c
oi
l
de
sig
n
us
i
n
g
ELTA and 2DEL
TA
s
oftware is ill
us
trat
e
d
in [
2
0-
23] with a
n
d
w
it
hou
t
con
v
erte
r
s
.
The
m
a
in
obj
e
c
tiv
e
o
f
this
p
aper
i
s
to
p
erform
s
ur
f
a
ce
h
ardeni
n
g
o
n
t
h
e
g
i
v
en
w
ork-
piec
e
w
i
t
h
a
5K
W
re
sona
n
t
i
n
v
erter
w
h
ic
h
uses
S
i
C
s
w
itc
he
s
in
a
c
om
b
i
na
ti
on
o
f
L
L
C
r
e
s
o
n
a
n
t
c
i
r
c
u
i
t
w
i
t
h
a
t
r
a
n
s
f
o
r
m
e
r
and
using ELTA
softwar
e for coil
des
i
gn
.
2.
COI
L
D
E
S
IGN
U
S
ING
ELT
A
ELTA
(
Electr
o
Therm
a
l
Ana
l
ys
is)
so
ftware
i
s
used
t
o
sim
u
late
t
h
e
i
n
duc
ti
on
hea
t
i
ng
s
y
stem
[
24]
.
The
e
l
e
c
t
rica
l
pa
ram
e
ter
s
o
f
the
c
o
nver
t
e
r
a
r
e
s
elec
te
d
us
i
n
g
t
his
s
o
ftware.
The
type
o
f
m
a
ter
i
al
u
s
e
d
for
the
w
o
rkp
i
ec
e,
t
he
g
eom
e
tr
y
of
t
he
c
o
i
l
a
n
d
t
h
e
geom
etr
y
o
f
t
h
e
w
o
r
kpie
c
e
ar
e
spe
c
ifie
d
in
t
he
s
of
tw
are
.
T
he
cha
r
ac
t
e
ris
tics
of
t
he
l
oa
d
o
n
t
he
i
n
v
e
r
ter
i
s
e
val
u
a
t
e
d
u
si
n
g
EL
TA
s
oftw
are
a
nd
the
w
a
vef
o
rm
s
a
r
e
ob
tai
n
e
d
for
p
o
w
e
r,
v
o
l
t
a
ge,
im
pe
da
nc
e,
i
n
d
u
cta
n
c
e
,
tem
p
er
ature
a
nd
p
o
w
e
r
fac
t
o
r
w
it
h
respe
c
t
to
t
ime
.
T
he
equ
i
vale
n
t
i
n
duc
ta
nce
a
n
d
e
q
u
i
vale
n
t
r
esi
s
tance
va
l
u
es
a
re
f
o
u
n
d
ou
t
fr
om
t
h
i
s
sof
t
w
a
re
a
nd
are
use
d
f
or
furt
her
c
a
lcu
l
a
t
ions
i
n
des
i
g
n
i
ng
the
c
i
r
c
u
i
t
s
.
The
w
o
rk
p
i
ec
e
pa
ram
e
ter
s
s
uc
h
a
s
s
iz
e
of
t
he
w
or
k
pi
e
c
e
,
m
ater
i
a
l
u
se
d
a
nd
t
h
e
proc
ess
i
n
g
para
me
ters
l
i
k
e
t
e
mpe
r
at
ure
,
l
e
n
g
t
h
of
t
he
s
y
s
tem
,
e
tc
a
re
e
nt
e
red
in
t
he
d
ia
l
og
bo
x
s
h
ow
n
in
F
i
gure
1
an
d
F
i
gure
2
re
spe
c
ti
ve
ly.
EL
TA
d
oes
the
sim
u
l
a
ti
on
a
n
d
g
i
v
e
s
t
he
g
raph
i
cal
a
nd
n
u
m
e
r
i
c
al
o
u
t
pu
t
s
o
f
t
h
e
lo
a
d
and
co
i
l
p
ara
m
e
t
ers.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
17
8 –
188
18
0
Fi
g
u
r
e 1
.
Wo
rkp
i
e
c
e
di
a
lo
g
box
F
i
gure
2.
M
a
t
e
r
ial pa
ram
e
te
rs dial
o
g bo
x
2.1
Coi
l
p
ar
amet
ers
F
i
gure
3
s
how
s
t
h
e
i
n
d
u
c
t
or
d
ia
l
o
g
bo
x
a
nd
us
in
g
th
is,
the
c
o
il
s
p
e
ci
fi
ca
ti
o
n
su
ch
a
s
t
h
e
ra
diu
s
,
n
u
m
b
e
r
of
t
u
r
ns,
re
si
st
iv
it
y
a
n
d
l
e
ngt
h
of
t
he
c
oil
a
r
e
sp
eci
fi
e
d
.
The
t
h
er
m
a
l
i
n
s
u
la
t
i
on
o
n
the
c
o
il
if
n
ee
ded
ca
n als
o
be
m
e
nt
i
one
d.
T
he tu
b
e
profi
l
e
dia
l
o
g
b
o
x
ca
n
be
u
s
ed
to
s
p
e
ci
fy
t
he
sha
pe
and
siz
e
o
f the
co
i
l
.
F
i
gure
3.
I
nduc
tor
dia
l
o
g
box
C
i
rcui
t
dia
l
o
g
b
o
x
s
how
n
in
F
igure
4
c
a
n
b
e
u
se
d
to
c
ho
o
s
e
the
circ
u
it
type
i
.e
.
se
ries
o
r
par
a
l
l
el,
numbe
r
of
l
ea
ds
a
n
d
g
eome
t
r
y
of
t
he
l
ea
d.
A
lso
the
pr
oc
essi
ng
d
ia
lo
g
bo
x
s
how
n
in
F
ig
ur
e
5
is
u
s
e
d
to
spec
ify
t
h
e
t
y
p
e
o
f
proc
ess
i
n
g
s
uch
a
s
h
e
a
t
ing
or
c
o
o
l
i
n
g
and
w
het
h
er
t
h
e
s
u
p
p
l
y
co
ns
t
itu
tes
c
u
rr
ent,
v
ol
t
a
ge
or pow
er,
the w
o
rki
n
g fr
eque
nc
y
,
c
urre
nt
,
dura
tio
n
of t
he
p
roce
s
s
,
t
y
p
e
of
co
ol
i
n
g
,
e
t
c
.
F
i
gure
4.
C
irc
u
i
t
d
i
a
l
o
g
b
o
x
F
i
gur
e 5.
P
roce
ss
d
ia
lo
g
b
o
x
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
D
e
sig
n
a
nd i
m
plem
e
n
t
a
t
i
o
n
o
f
h
i
g
h
f
r
e
que
nc
y ind
u
c
tio
n he
at
ing
w
i
t
h
L
L
C
…
(
Sug
ant
hi K
a
ru
p
pusam
y
)
18
1
2.
2
Re
sults obtaine
d from
ELT
A
Har
d
ware
d
esign
is
b
ase
d
o
n
re
sults
obta
i
ne
d
fr
om
ELTA.
In
t
his
s
oftwa
r
e,
t
he
t
ota
l
h
ea
tin
g
time
is
di
v
i
de
d
i
n
to
a
l
ar
ge
numbe
r
of
s
m
a
l
l
i
nc
r
e
m
e
nts
in
t
i
m
e.
A
fter
ea
ch
s
te
p,
t
he
m
a
t
e
r
ia
l
cha
r
ac
t
e
ris
tic
s,
w
hich
de
pe
n
d
u
p
o
n
t
he
t
em
per
a
t
u
r
e
ach
ie
ve
d,
a
r
e
e
val
u
a
t
e
d
.
The
ca
l
c
u
l
a
t
i
o
n
is
e
xte
n
ded
t
i
l
l
t
he
e
nd
o
f
t
h
e
ta
r
g
et
time
.
T
he
s
of
tw
a
r
e
pr
ovide
s
us
w
ith
w
ave
f
o
r
m
s
o
f
dif
f
er
en
t
pa
r
a
me
t
e
rs
.
F
i
gur
e
6
be
l
o
w
show
s
t
h
e
gr
a
p
h
of
t
he
i
m
p
eda
n
ce
v
s
t
i
me
c
har
act
e
r
i
s
t
i
cs.
The
imp
e
dance
pea
k
s
w
h
e
n
t
he
m
ate
r
ial
i
s
m
agne
ti
c
and
w
h
e
n
t
he
r
e
s
i
s
t
i
v
ity
i
s
hi
g
h
.
A
s
the
m
a
te
r
i
al
b
ec
o
m
e
s
non-
m
a
g
n
e
tic,
t
h
e
im
peda
nc
e
dr
o
p
s.
I
nduc
ta
nc
e
vs
time
w
a
v
e
for
m
i
s
show
n
in
F
igur
e
7
.
T
h
e
i
ndu
c
t
ance
p
e
a
k
s
w
h
e
n
th
e
m
a
ter
i
al
i
s
m
a
gne
t
i
c
a
nd
w
h
en
t
he
r
e
s
i
s
ti
v
ity
i
s
h
i
g
h
.
Als
o
,
th
e
m
a
ter
i
a
l
b
e
c
o
m
e
s
no
n
-
ma
gnet
i
c
w
h
e
n
t
he
in
d
u
cta
n
c
e
d
r
o
ps.
T
hus,
fr
om
t
he
r
esu
lts
o
b
t
a
i
ne
d,
t
he
c
o
i
l
i
n
d
uc
tanc
e
is
t
a
k
en
t
o
be
1
80
n
H
.
F
i
gur
e
8
r
e
pr
e
s
en
ts
t
he
g
r
a
p
h
o
f
v
o
l
t
a
g
e
v
s
t
i
m
e
.
T
he
v
ol
ta
ge
a
ls
o
pe
a
k
s
whe
n
t
he
m
a
t
e
r
ial
is
m
a
gne
tic
a
nd
w
h
e
n
t
he
r
e
s
i
s
t
i
v
ity
i
s
h
i
gh.
A
s
t
h
e
m
a
te
r
i
a
l
b
eco
m
e
s
n
o
n
-
m
agnet
i
c
the
v
o
lta
ge
d
r
o
ps.
Fig
u
r
e
9
r
e
pr
e
s
e
n
ts
t
he
c
ur
ve
b
e
t
w
e
e
n
pow
e
r
a
n
d
tim
e.
L
ike
t
h
e
imp
e
dance
,
i
nduc
ta
nce
a
n
d
vo
l
t
a
g
e,
p
ow
er
a
ls
o
peak
s
w
h
e
n
t
he
m
ate
r
ia
l
is
m
ag
ne
ti
c,
a
nd
r
e
sist
i
v
i
t
y
is
h
ig
h.
W
h
e
n
th
e
m
a
ter
i
a
l
b
ec
om
es
n
on-
m
a
gne
tic
,
t
h
e
pow
e
r
dr
ops.
A
ll t
h
es
e
pr
o
j
e
c
t
i
on
s a
r
e
ba
se
d o
n
the
a
ssum
p
tio
n
tha
t
t
he c
ur
r
e
nt t
hr
o
u
g
h
the
c
o
i
l
is c
ons
t
a
n
t
.
I
t
i
s
a
l
s
o
pos
si
b
l
e
to
e
va
lua
t
e
the
l
o
ad
w
i
t
h
con
s
ta
n
t
a
pp
l
i
ed
v
o
l
t
a
ge
t
o
t
h
e
co
i
l
o
r
c
ons
ta
n
t
pow
er
.
F
i
gur
e
6.
I
m
p
eda
n
ce
w
a
v
e
f
or
m
F
i
g
u
r
e
7
.
I
nduc
tance
w
a
ve
for
m
F
i
gur
e
8.
V
olta
ge
w
ave
f
or
m
Fi
g
u
re
9
.
P
o
w
e
r
w
av
e
f
o
r
m
3.
DESIGN
O
F POWER
CI
RCUIT
The
t
o
p
o
l
o
gy
show
n
in
F
i
g
u
r
e
10
i
s
t
ha
t
of
a
n
LL
C
c
i
r
c
ui
t
w
ith
t
r
a
n
s
f
o
r
m
e
r
.
A
t
r
a
n
s
f
o
r
m
e
r
i
s
c
o
n
n
ec
ted
bet
w
ee
n
t
h
e
ser
i
e
s
i
nduc
tor
a
n
d
c
a
p
ac
it
or
.
A
D
C
b
loc
k
i
n
g
c
a
p
aci
to
r i
s
u
sed
t
o
f
ilt
er
h
ig
h
f
r
equ
e
ncy
c
o
mpo
n
e
n
t
s
p
a
ssing t
h
r
o
ug
h
t
h
e
tr
a
n
sf
or
me
r
.
F
r
o
m
the
ELT
A
sof
t
w
are
,
t
he
v
al
u
e
o
f
lo
ad
i
ndu
ct
a
n
ce
i
s
fo
und
to
b
e
1
8
0
n
H
.
T
he
qua
lit
y
fac
t
or
a
cc
or
d
i
n
g
t
o
the
ind
u
s
t
r
y
s
t
a
nd
ar
d
s
i
s
i
n
t
he
r
ange
o
f
3
to
1
0
a
nd
i
s
a
s
s
um
ed
to
b
e 5
.
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
17
8 –
188
18
2
Figure
10.
LLC
c
ircuit w
i
th transform
er
The
desi
gn
c
a
lcu
l
a
t
io
ns
a
re
a
s
fol
l
ow
s
:
P
=5K
W
,
Q
=
5.
4,
L
1
8
0
n
H
,
f=
150
k
Hz,
3
5
°
,
V
=
40
0
V
Va
lue o
f
the
f
irst
h
ar
mon
i
c,
1
.
3
∗
4
00
5
20
(
1
)
∗
∗
.
=
∗
∗.
= 662.
0
85
V
(
2
)
The
rati
o
of
t
he
l
oa
d
in
d
u
ct
anc
e
t
o
t
h
e
se
ries
i
n
d
u
c
t
a
n
c
e
i
n
a
LLC
c
i
r
cui
t
i
s
de
f
i
ne
d
as
β
a
nd
i
s
gi
ve
n by
∗
t
a
n
1
= 5.4
*
tan
(
35
)
– 1 = 2.
781
(
3)
Loa
d
Res
ista
nc
e,
2
=
2
∗
1
50
000
∗
∗
.
=
0
.03
1
4
16
= 31.
41
6
m
(
4
)
LLC
c
i
r
cu
it
p
a
r
amet
ers
a
r
e
c
a
l
cu
l
a
t
e
d
u
s
i
n
g
t
h
e
equi
val
e
nt
s
eri
es
r
eso
n
an
t
c
i
rc
ui
t
pr
oce
d
ure
di
sc
usse
d i
n
[6]
.
The
c
a
lc
ula
t
ions
f
rom
S
R
I
ci
r
c
ui
t
to LL
C
re
s
ona
n
t
c
irc
u
it
(Figu
re 11)
a
re
c
arried
out as
f
o
llow
s
:
ca
paci
ta
nce
of
t
he
s
e
r
ies osc
i
l
l
at
or,
=
∗
∗
∗
=
6
.
254
F
(
5
)
ca
paci
ta
nce
of
LLC osc
i
lla
t
o
r,
C
=
=
.
.
∗
.
= 8.
497
F
(
6
)
trans
f
or
ma
t
i
o
n
r
ati
o
of
SRI,
∗
∗
=
.
√
∗
∗.
=
3
7
.
354
(7
)
trans
f
or
ma
t
i
o
n
r
ati
o
of
LL
C
,
=
.
.
=
1
3
.
431
(8
)
series
i
nductance
in prim
a
ry,
∗
=
9
0.37
6
(
9
)
resona
nt
f
re
q
u
e
ncy,
∗
∗
= 1
49.
7
27
H
z
=
150 kH
z
(
10
)
ma
ximum
vo
lt
age
ac
ross
t
he
c
apa
c
i
t
or
,
∗
∗
= 95.71
9
V
(
1
1
)
pea
k
cur
ren
t
i
n
the
in
verter
,
∗
= 1
8.
438
A
(
1
2
)
F
i
g
u
r
e
12
s
hows
t
h
e
M
A
TLAB
s
i
m
ul
at
io
n
a
n
d
F
i
gu
res
13
a
nd
1
4
sho
w
the
sim
u
l
a
t
i
o
n
re
sults
o
f
o
f
LLC
w
it
h
transfor
me
r
i
nve
rter
o
u
t
p
u
t
vol
ta
ge
a
n
d
l
o
a
d
curre
n
t
w
a
v
e
f
o
r
ms
r
esp
e
c
t
iv
ely
.
D
es
i
g
n
and
si
m
u
lat
i
on
is
a
ls
o
c
a
rr
i
e
d
out
w
it
hou
t
a
trans
f
orme
r
w
i
t
h
o
n
l
y
a
n
LLC
c
irc
u
i
t
.
Wh
i
l
e
us
in
g
a
transfor
me
r,
t
he
β
va
lue
is
2
.7
81
an
d
the
p
o
w
e
r
fac
t
or
w
a
0.
81
w
h
e
r
ea
s
the
pow
er
f
a
c
t
o
r
o
f
L
L
C
c
i
r
c
u
i
t
w
i
t
h
o
u
t
t
h
e
trans
f
or
me
r
is
0
.1
w
i
t
h
the
β
va
lue
of
2
2.
47
.
By
u
si
n
g
t
ransfor
me
r,
t
he
v
al
ue
o
f
β
dec
r
e
a
ses
and
t
h
e
p
o
w
e
r
fa
ct
or incr
ease
s
w
hich i
n
tur
n
i
ncre
ases
t
he
e
fficie
n
c
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
D
e
sig
n
a
nd i
m
plem
e
n
t
a
t
i
o
n
o
f
h
i
g
h
f
r
e
que
nc
y ind
u
c
tio
n he
at
ing
w
i
t
h
L
L
C
…
(
Sug
ant
hi K
a
ru
p
pusam
y
)
18
3
Figure
1
1
.
SRI to
LLC
r
eso
n
a
n
t
circ
ui
t c
o
nv
ersio
n
F
i
gur
e
1
2
.
S
imul
a
tio
n
of
LLC
c
i
r
cui
t
w
it
h
tr
ansf
or
me
r
u
s
in
g
MA
TL
AB
F
i
gur
e
1
3
.
I
nve
r
t
er
outpu
t
vo
lt
age
F
i
gur
e
1
4
.
Load
o
u
t
pu
t
c
u
r
r
e
n
t
w
ave
f
or
m
4.
H
A
R
D
WARE
I
MPLE
MENTATION
Tab
l
e
1
show
s
the
s
p
eci
fi
c
a
t
i
o
n
s
use
d
f
or
t
he
r
equ
i
r
e
d
loa
d
.
Tab
l
e
1.
H
a
r
dw
are
spec
i
f
i
c
a
t
io
ns
S.
No
.
D
es
cr
ip
t
i
o
n
V
a
l
u
e
1.
L
ine
Volta
g
e
415
V
2.
S
uppl
y
F
r
e
que
n
c
y
50
H
z
3.
O
pe
r
a
t
i
ng
Fre
q
u
e
ncy
150
H
z
4.
C
oil
c
u
rr
e
n
t
(a
ssu
m
e
d)
240
A
5.
Q
ua
li
t
y
F
a
c
tor
5.
4
6.
P
ha
s
e
A
ngle
35
7.
O
utput
pow
e
r
r
e
quire
d
5
kW
8.
L
oa
d
induc
t
a
nce
180
nH
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
17
8 –
188
18
4
I
n
v
e
rt
er
p
o
w
e
r
=
5
K
W
Typical inver
t
e
r
ef
f
i
ci
e
n
cy (
η)
=
0
.9
Typ
i
c
a
l
po
wer f
a
ct
o
r
a
t
i
npu
t
=
0
.
93
K
V
A
d
em
and a
t
in
p
u
t
=
Inve
rte
r
pow
e
r
/ (η
*pow
er
f
ac
tor
)
=
.
∗
.
=
5
9
73.
7 V
A
(
1
3
)
Li
ne vo
l
tage
=
41
5
V
,
3
-phase
Li
ne c
urre
nt
=
.
√
∗
= 8.
3
1
A
(
14
)
4.1
Ha
rdwa
re
c
omp
o
nents
F
i
gure
15
s
h
o
w
s
the
i
n
d
u
c
t
i
o
n
hea
t
in
g
of
l
oad
us
i
n
g
ha
r
d
w
a
r
e
s
e
tup.
I
t
m
a
y
be
n
ote
d
t
ha
t
for
t
h
e
expe
r
i
me
n
t
a
l
s
e
t
u
p
,
var
i
ous
h
ar
dw
are
it
e
m
s
w
e
re
p
rovi
ded
by
M
/
s
G
H
In
duc
t
i
o
n
I
n
d
ia
P
rivate
L
im
it
e
d
[
25]
f
r
o
m
t
h
e
i
r
g
ene
r
al
s
t
o
ck
s
an
d
t
h
es
e
it
ems
ma
y
h
a
v
e
n
o
rel
a
t
i
o
n
t
o
t
he
a
ct
ual
w
o
rk
i
ng
c
o
nd
i
tio
ns.Li
n
e
cho
k
e
w
ith
t
he
i
n
duc
ta
nce
va
l
u
e
o
f
3
.2m
H
,
10A
w
as
u
se
d.
A
r
ecti
f
ier
m
o
d
u
l
e
S
KKD
1
0
1
/
1
6
rat
e
d
fo
r
1
600
V,
1
00
A
w
a
s
u
s
e
d
.
D
C
l
i
n
k
c
a
p
a
c
i
t
o
r
s
o
f
f
i
l
m
a
n
d
f
o
i
l
c
o
n
s
t
r
u
c
t
i
o
n
w
a
s
use
d
s
o
t
h
at
t
he
e
qui
va
l
e
nt
s
e
r
ie
s
r
e
sistanc
e
(ES
R
)
w
ill
be
l
ow
.
F
our
n
u
m
be
rs
o
f
3µ
F
c
a
pac
i
tors
w
ere
used.
Re
s
i
s
t
or
s
enc
a
ps
u
l
a
t
ed
i
n
a
l
um
in
iu
m
heat
sinks
w
ere
use
d
f
or
i
n
i
t
i
a
l
c
h
a
rgi
ng
of
t
he
D
C
l
i
n
k
c
a
p
ac
it
ors
a
nd
d
i
sc
h
a
rgi
ng
the
c
a
p
ac
itor
s
w
he
n
t
h
e
u
n
i
t
w
a
s
sw
itc
hed
off.
F
our
r
esistor
s
w
it
h
rat
i
ng
330
Ω,
2
5W
a
nd
S
i
C
M
osfe
t
s
C
A
S
30
0
M
1
2
B
M
2
w
e
re
u
se
d.
A
i
r
coo
l
in
g
w
a
s
u
s
ed
i
n
t
h
e
des
i
gn
t
o
a
v
o
i
d
w
a
te
r
c
o
o
l
i
ng.
E
xtr
ude
d
a
l
u
m
i
n
i
u
m
h
e
a
t
s
i
n
k
w
i
t
h
t
w
o
s
m
a
l
l
f
a
n
s
moun
te
d
at o
n
e
end
w
a
s
u
s
e
d
for
cool
i
ng t
h
e
M
O
SF
ET
s.
The
D
C
b
l
o
c
k
ing
ca
paci
t
o
rs
a
t
t
h
e
ou
t
p
ut
o
f
the
i
n
ve
rter
a
r
e
s
u
ppos
e
d
t
o
ha
ve
a
l
ow
r
eac
t
a
nce
a
t
t
he
opera
tin
g
freq
u
e
n
c
y
a
n
d
a
t
t
h
e
sa
me
time
,
p
r
e
ve
nt
t
he
s
hor
t
cir
c
u
it
of
t
he
i
n
v
erte
r
vo
l
t
age
by
the
l
o
a
d
.
The
DC
b
lo
ck
i
ng
ca
paci
t
o
r
i
s
a
l
s
o
ex
pe
c
t
e
d
t
o
c
a
rr
y
the
i
n
v
e
rter
c
u
rr
ent
a
t
h
igh
fre
que
n
c
y.
A
D
C
blo
c
kin
g
ca
paci
t
o
r of 6
0
µ
F was used.
F
r
om
t
he
c
a
l
c
u
l
a
tio
ns,
a
fe
rrite
c
ore
m
a
tch
i
n
g
tra
n
sf
orme
r
w
ith
a
t
ur
ns
r
ati
o
o
f
1
5
:
1
w
a
s
use
d
f
or
opera
tin
g
a
t
a
f
re
q
u
e
n
c
y
o
f
15
0
kH
z
,
t
h
e
p
rima
ry
v
o
l
tage
a
n
d
c
u
rrent
r
at
i
ng
be
i
ng
56
0
V
an
d
1
1
A
respe
c
t
i
ve
l
y
.
T
h
e
in
d
u
ct
anc
e
of
t
he
l
oad
co
il
w
h
i
c
h
w
as
e
st
ima
t
e
d
a
s
1
8
0
nH
i
n
t
h
e
simu
lat
i
on
s
o
f
tw
are
,
tur
n
ed
o
ut
t
ob
e
26
0
n
H
i
n
t
h
e
p
ra
ct
ical
r
e
a
liza
t
i
on.
T
he
c
a
p
aci
t
or
r
e
q
u
i
r
e
d
for
resona
n
c
e
w
a
s
8.5µ
F
.
T
h
e
c
a
p
a
c
ito
r
was
s
e
l
e
ct
ed
b
ase
d
o
n
cu
rre
nt
c
a
r
ry
i
n
g
cap
a
c
i
t
y
a
t
t
h
e
o
p
era
t
in
g
freque
nc
y.
F
rom
the
S
R
I
to
L
LC
des
i
g
n
c
a
l
cu
la
t
i
o
n
,
t
h
e
val
u
e
of
t
he
s
eries
i
n
d
u
c
t
or
s
e
l
ec
t
e
d
w
a
s
9
0µ
H
.
T
o
m
a
ke
t
he
u
n
it
c
o
m
p
ac
t
,
i
t
w
a
s
dec
i
de
d to
e
mp
lo
y ferr
i
t
e
c
o
r
e
s
t
o
assem
b
l
e
t
he in
duc
tor
.
S
tand
ard
av
ail
a
bl
e
c
o
re
s
we
re
u
sed
t
h
u
s
l
e
a
d
i
ng
t
o
a
d
i
s
p
rop
o
r
t
i
o
n
a
te
l
y
l
arg
e
l
ooki
n
g
s
e
r
i
e
s
re
ac
to
r.
A
n
i
m
ag
e
of
t
h
e
wo
rk
p
i
ece
g
e
tt
ing
i
ndu
ct
i
o
n
h
e
a
t
ed
i
s
sh
o
w
n
in F
ig
ure
15.
The
im
pe
da
nc
e
c
u
rve
of
t
he
LLC
i
nver
t
er
h
as
t
w
o
r
e
s
o
n
a
n
t
fre
q
ue
nci
e
s.
O
ne
h
ig
he
r
fre
quenc
y
wher
e
t
h
e
ser
i
e
s
r
e
s
on
a
n
ce
t
akes
p
lace
,
an
d
a
n
o
t
he
r
l
o
we
r
frequ
e
n
c
y
w
h
e
re
p
ar
al
lel
re
sona
nce
ta
k
e
s
p
l
ace
.
The
LL
C
in
ve
r
t
e
r
g
e
n
era
l
l
y
ope
ra
tes
at
a
fre
que
ncy
a
b
ov
e
the
se
ries
r
es
ona
n
t
f
r
e
q
u
e
n
c
y
,
in
t
he
“
in
du
ctive
”
mode
.
A
t
t
he
s
erie
s
re
sona
nt
f
r
e
q
u
e
n
c
y
,
the
im
peda
n
c
e
is
t
he
l
o
we
st
a
nd
t
h
e
p
o
w
er
i
s
t
h
e
hi
gh
e
s
t
.
The
p
o
w
e
r
is
c
on
tro
l
led
by
sw
ee
pin
g
t
he
f
r
e
que
nc
y
fr
o
m
a
h
i
gh
v
al
u
e
t
o
a
low
va
lue
a
ppr
oa
ch
i
n
g
t
h
e
resona
nt
f
re
q
u
e
ncy.
The
co
n
t
r
o
l
c
a
r
d
implem
e
n
ts
t
h
e
f
o
l
l
o
w
i
n
g
l
oo
ps
:
(i)
To
s
w
e
ep
t
he
s
w
itc
hi
n
g
f
re
q
u
e
n
cy
t
ow
ar
d
s
t
he
resona
nt
frequ
e
n
c
y
a
s
re
q
u
i
r
ed
t
o
me
et
t
h
e
t
arge
t
pow
e
r
.
A
P
LL
a
n
d
a
VCO
are
use
d
f
or
f
re
q
u
e
n
cy
corr
ecti
on.
(
i
i
)
To
e
nsure
t
h
a
t
t
he
s
w
i
t
c
h
i
ng
of
t
h
e
M
O
S
F
ETs
w
o
u
l
d
be
d
one
o
nl
y
a
t
t
he
zer
o
c
r
ossin
g
o
f
th
e
in
verter
c
urre
nt
o
r
cl
ose
to
t
h
e
z
e
r
o
crossi
ng
,
(iii
)
To
m
ai
nta
in
a
d
e
a
d
tim
e
betw
e
e
n
t
he
d
r
i
vi
n
g
pul
ses
for
t
h
e
tw
o cha
nne
ls p
rov
i
d
i
ng
s
afe
t
y
aga
i
n
s
t sh
ort c
i
rcu
it.
The
c
o
ntr
o
l
b
l
oc
k
dia
g
ra
m
is
s
how
n
in
F
ig
ure
s
16,
F
ig
ure
17
an
d
F
i
gur
e
18.
F
or
t
he
c
on
tro
l
o
f
a
S
R
I,
t
he
phase
a
ng
l
e
b
e
t
w
een
t
he
i
n
v
erter
vo
l
t
age
a
n
d
th
e
in
ver
ter
c
u
rre
nt
i
s
e
m
pl
oye
d.
H
ow
ever
,
f
o
r
th
e
LLC
i
n
v
erter
t
h
e
a
n
g
l
e be
twee
n
the
i
n
verter
v
o
l
tage
a
n
d
the
c
ap
ac
i
t
or vo
l
ta
ge i
s
a
l
s
o
m
ea
su
r
e
d for
a
p
pl
y
i
n
g
a
li
m
i
t.
T
hi
s
a
n
gl
e
i
s
d
ef
i
n
e
d
a
s
α.
I
n
o
u
r
pro
j
ec
t
the
s
t
an
dar
d
c
ont
rol
ca
rd
o
f
a
S
R
I
was
e
m
pl
o
y
e
d
,
sup
p
le
me
n
t
e
d
by a
n
o
t
he
r c
a
rd
t
o m
easure
th
e
angle
a
l
p
h
a.
The
p
o
w
e
r
con
t
ro
l
o
f
b
ot
h
t
h
e
S
R
I
and
the
L
L
C
i
n
ve
rter
a
r
e
i
mpl
em
en
te
d
by
fre
q
u
e
nc
y
modu
la
ti
o
n
.
The
pu
lses
r
e
p
rese
ntin
g
t
h
e
i
nver
t
e
r
v
ol
ta
ge
a
re
t
a
k
e
n
f
r
o
m
the
d
ri
ver
s
e
ctio
n
of
t
he
m
ain
c
o
n
t
ro
l
c
a
rd.
The
p
u
l
s
es
r
e
p
re
sen
tin
g
t
h
e
c
a
pac
i
to
r
v
o
lt
ag
e
are
re
ce
i
v
ed
t
h
r
o
ugh
a
fibre
optic
l
ink
from
t
h
e
card
o
ne
m
ounted
clo
s
e
t
o
t
he
c
apac
it
or.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
si
g
n
a
nd im
plem
e
n
t
a
ti
on
o
f
hi
g
h
fre
que
nc
y
ind
u
c
t
i
o
n he
at
i
ng
wit
h
L
L
C …
(Sug
an
thi
Karu
p
pusam
y)
18
5
F
i
gure
1
5
.
Induct
i
on hea
t
ing
of l
oa
d
usi
n
g h
a
rdw
a
r
e
4.2
Hardwar
e
resu
l
t
s
F
i
gures
1
9
a
n
d
2
0
s
how
t
he
4
15V
,
5
0
H
z
A
C
s
u
p
p
l
y
vo
l
t
a
g
e
w
a
ve
fo
rm
a
n
d
6
00
V
inv
e
rte
r
i
npu
t
D
C
vo
lta
ge
r
espec
tive
l
y.
F
i
g
ur
e
21
s
how
s
th
at th
e
i
n
v
er
t
e
r
ou
t
p
ut
v
o
lta
ge
w
h
i
ch
i
s
o
b
t
a
i
ne
d
a
s
5
60V
.T
he
i
nver
t
e
r
curr
ent
w
a
ve
fo
rm
obta
i
ne
d
in
F
igure
2
2
i
s
t
a
k
e
n
a
t
h
i
g
her
loa
d
c
o
n
d
i
t
i
o
n
.
I
n
F
i
gur
e
23,
t
he
t
w
o
a
rms
of
t
he
bri
dge are
no
t
“
O
N
”
sim
ul
t
a
n
e
ou
sly.
The
dea
d
t
i
m
e w
h
e
n
b
oth
t
h
e
MO
S
F
ETs a
re off
i
s
m
easure
d
t
o be
24
0
ns
as i
n F
i
gure
2
4
. The t
a
n
k v
o
l
t
a
g
e w
a
ve
form
a
cross t
h
e ca
pa
cit
o
r
sh
o
w
i
ng bo
t
h
t
he
fr
e
q
u
e
n
c
y
a
nd am
p
lit
ude
i
s
show
n in F
igur
e 25
(a) and
(b) respe
c
t
i
ve
l
y
.
F
i
gure
1
6
. Blo
ck
d
i
a
gram
of m
a
in c
ontro
l
car
d
F
i
gure
1
7
.
Bl
o
c
k dia
g
ra
m
of
p
o
w
er
calc
u
la
t
i
on
F
i
g
u
r
e
18.
Blo
ck dia
gr
am
of
fre
que
ncy
co
n
t
rol
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
17
8 –
188
18
6
F
i
g
u
r
e
1
9.
Line
vol
ta
ge
w
ave
f
orm
F
i
g
u
r
e
20
. DC
v
olt
a
g
e
wa
v
e
f
orm
F
i
gure
2
1
.Inve
rter
volta
g
e
w
a
v
efor
m
F
i
gure
2
2
.
Inver
t
e
r
c
urre
nt w
av
e
f
orm
F
i
gure
2
3
.D
r
i
ve
pul
ses –
tw
o in
st
a
n
ces
F
i
gure
2
4
.
D
e
a
d
t
i
m
e
(a)
(b)
F
i
gur
e 2
5
.
Ta
nk vo
l
t
a
g
e
w
a
ve
form
d
ispla
y
in
g
t
h
e
(a
) freque
ncy (
b) a
mpli
tude
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
si
g
n
a
nd im
plem
e
n
t
a
ti
on
o
f
hi
g
h
fre
que
nc
y
ind
u
c
t
i
o
n he
at
i
ng
wit
h
L
L
C …
(Sug
an
thi
Karu
p
pusam
y)
18
7
Me
as
urem
ent of
pha
se
a
ng
le
i
s
show
n
in
F
i
gure
2
6
a
an
d
b.
The
cur
r
e
nt
w
avef
o
r
m
loo
k
s tria
ng
u
l
ar
a
s
t
h
e
lo
ad
i
s
smal
l
.
(a)
(b)
Fi
g
u
r
e 26
. Ph
a
s
e
an
gl
e me
as
u
r
e
m
e
n
t
wi
t
h
(a)
(b)
t
1
=
1
.
6
µs
,
t
2
=
6
.4
µ
s
;
ɸ
=
x
360
=
.
.
x
360
=
90
°
(
1
5
)
5.
COMPARIS
I
O
N
O
F TH
EORETICAL, S
IMULAT
ION AND
EX
P
ERIMENT
A
L
VA
L
U
E
A
com
p
arison
of t
he
ore
t
i
c
al,
sim
u
late
d a
n
d ha
rdw
a
re
r
esul
ts
i
n
Table
2 sh
ow
s broa
d agr
e
em
ent.
Tab
l
e
2.
C
om
p
a
risi
on o
f
t
he
or
etica
l
,
simula
ti
on a
n
d ex
pe
ri
me
nt
a
l v
a
l
u
es
Pa
r
a
mete
r
The
o
r
e
ti
c
a
l
v
a
l
u
e
S
im
ul
a
t
ion va
lu
e
Ha
rdwa
r
e
v
a
l
u
e
Inve
rte
r
output
c
ur
re
nt
18.
44A
13A
14.
8A
Inve
rte
r
output
vol
ta
g
e
520V
580V
560V
I
nve
rte
r
output
p
o
w
e
r
5kW
4
.
32kW
4
.
75k
W
L
o
a
d
output
vol
ta
g
e
95.
719V
92V
91.
2V
6.
CONCLUSION
The
pro
pose
d
m
e
t
ho
d
of
l
oa
d
ma
tc
hi
n
g
u
s
i
n
g
a
c
omb
i
na
ti
o
n
o
f
a
n
LL
C
reso
na
nt
c
ir
cui
t
a
n
d
a
t
r
a
n
sf
o
r
mer
me
et
s
th
e
hi
gh
fre
qu
e
n
c
y
i
nd
u
c
ti
on
h
e
at
t
rea
t
men
t
r
e
q
u
i
re
me
nt
s.
T
he
l
oa
d
para
me
t
e
rs
a
r
e
evalua
t
e
d
using
ELTA
s
oft
w
are.
T
he
power
f
actor
o
f
L
L
C
c
i
r
cuit
w
i
t
h
ou
t
a
tra
n
sf
orm
e
r
i
s
f
o
u
nd
t
o
b
e
0.
1
w
h
er
eas
t
ha
t
w
i
t
h
a
t
rans
for
m
er
i
s
0.8
1
.
Th
us,
this
m
e
t
ho
d
i
m
pr
o
v
e
s
t
he
pow
er
f
a
c
t
or
a
nd
i
n
t
u
r
n,
t
h
e
efficie
n
c
y
.
A
l
so,
t
h
e
use
of
S
iC
s
w
i
tc
hes
i
n
p
l
a
ce
o
f
c
o
nve
nt
i
o
na
l
Si
s
w
i
tc
hes
e
n
a
b
le
s
t
o
c
a
rry
o
u
t
i
nd
u
c
t
i
o
n
hea
t
i
ng a
t
hi
g
he
r
freque
nc
ies
and i
n
c
ircu
i
t
s
w
ith
h
i
ghe
r op
e
r
a
ti
ng v
o
lta
ge
s.
ACKNOW
LEDG
E
MEN
T
S
Th
is
w
ork
is
s
po
ns
ored
b
y
M/S
G
H
Induc
ti
on
I
ndia
P
v
t.
L
td
a
n
d
i
s
do
ne
a
s
a
fina
l
yea
r
p
ro
ject.
We
w
i
sh
t
o
rec
o
rd
our
d
eep
g
ra
ti
t
ude
t
o
the
com
p
an
y
a
n
d
t
o
i
ts
V
i
c
e
C
h
a
i
rman,
Mr.V
.R.Chari
f
o
r
a
l
l
t
h
e
s
u
p
p
o
r
t
and
ass
i
s
t
anc
e
.
REFE
RENCES
[1]
O.
L
ucía,
P
.
M
au
ssi
o
n
,
E
.
Ded
e
,
and
J.
M
.
Bu
rd
í
o
,
"
I
nd
ucti
o
n
h
e
at
ing
t
echno
lo
gy
a
nd
i
ts
a
pplications:
Past
dev
e
lo
pm
ent
s
,
cu
rrent
t
echn
o
l
ogy,
f
uture
ch
all
e
n
g
es,
"
IEE
E
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Ind. El
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s
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ra
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zp
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e
w
of
S
i
l
i
c
on
Carbi
d
e
P
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wer
D
e
vi
cs
a
n
d
t
h
e
ir
Ap
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ons,
"
IE
EE T
r
ansa
c
ti
o
n
s o
n
In
dustrial Elect
ro
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i
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v
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n
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Jo
se
ph
C
arr,
J
uan
B
a
ld
a,
a
n
d
A
l
a
n
M
a
nto
o
t
h
,
"A
C
om
pa
ri
son
o
f
S
il
i
c
on
a
nd
S
ilicon
C
arbide
M
OSF
E
T
Switchi
ng Charact
eristics,"
20
07
IEEE R
e
gio
n
5 Tech
nica
l
Co
nf
eren
ce,
2
00
7.
[5]
Hel
ong
Li
an
d
S
tig
M
unk
-Ni
e
lsen
"
Det
a
il
S
tud
y
o
f
S
i
C
MO
S
F
ET
Swi
t
c
h
in
g
Ch
aracteri
s
ti
cs
,"
20
14
IEEE 5
t
h
In
te
rn
at
io
na
l S
y
mp
osiu
m on
Po
we
r E
l
e
c
t
ro
n
i
c
s
for
Distr
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d
Ge
ne
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