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.
10, N
o.
1, Mar
ch 20
19,
p
p.
514~
5
2
1
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
5
14-
52
1
514
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Op
timization of PFC cuk conv
erter p
a
rameters d
esign for
minimization of THD
and volt
a
ge ripple
M. A
.
Z
.
A
. R
ashid,
A
. Ponniran
, M.
K.
R.
Noor,
J.
N
. Jumad
ril,
M
.
H
.
Y
a
ti
m,
A
.
N
.
K
a
s
i
ra
n
Faculty of E
l
ectr
i
cal
a
nd
E
l
ectron
i
c
Engin
eering,
Uni
versiti
T
u
n
H
u
s
s
e
in
O
n
n
M
a
l
a
ys
ia
,
M
a
l
a
ys
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
1
7
,
2
018
Re
vise
d N
ov
2
9
,
201
8
A
c
c
e
pte
d
D
ec 14,
2
0
1
8
Th
is
p
aper
p
rese
n
t
s
t
h
e
o
p
tim
i
zatio
n
o
f
P
F
C
C
u
k
c
onv
erter
par
a
m
eter
d
esi
gn
f
o
r
th
e
m
i
nim
i
zat
io
n
o
f
T
HD
and
vo
lt
age
rip
p
le.
In
t
h
i
s
s
t
u
dy,
the
PFC
Cuk
c
o
nv
e
r
te
r
is
d
e
s
ign
e
d
to
o
p
e
ra
te
i
n
d
i
sc
on
tin
uo
us
c
o
n
d
u
c
tion
m
o
d
e
(
D
C
M
)
i
n
ord
e
r
t
o
achi
e
ve
a
lm
ost
u
n
ity
p
ow
er
f
act
or.
T
h
e
pas
s
i
v
e
com
p
o
n
e
nts,
i
.e
.
,
in
du
ctor
a
nd
capacit
o
r
are
d
e
si
gn
ed
b
ased
on
switch
i
n
g
f
req
u
enc
y
a
n
d
re
son
a
nt
f
re
q
u
e
n
c
y
.
Ne
v
e
rthe
le
ss,
th
e
ra
ng
e
s
o
f
du
ty
c
yc
le
f
or
bu
ck
a
nd
bo
ost
op
erati
ons
a
re
0
<D
<0.
5
a
nd
0
.
5
<D<1
,
resp
ec
t
i
vely
f
or
t
h
e
output
voltage
vari
ati
on
o
f
t
h
e
c
o
n
v
e
rt
er.
T
h
e
p
r
in
c
i
pl
e
of
t
he
p
aram
eters
des
ign
op
timizati
o
n
is
b
as
ed
o
n
t
h
e
b
a
l
a
nci
n
g
energy
c
om
p
e
nsat
io
n
b
e
tw
ee
n
t
h
e
in
pu
t
cap
acito
r
and
o
u
tp
ut
i
n
ducto
r
f
o
r
mi
nimizati
o
n
of
T
HD
c
ur
rent.
In
addition,
t
he
s
electio
n
of
h
igh
output
cap
aci
tance
wi
l
l
m
ini
m
i
z
e
th
e
o
u
tp
ut
vo
lt
age
ri
pp
le
s
i
gnif
i
can
tl
y.
A
6
5
W
P
F
C
Cu
k
co
nv
erter
p
r
ot
ot
yp
e
is
dev
e
lo
ped
and
ex
peri
men
t
ally
t
ested
t
o
c
on
firm
t
h
e
p
aram
et
ers
d
esi
g
n
op
timizati
o
n
princi
ple.
T
h
e
e
xperi
m
e
ntal
r
esult
s
s
ho
w
th
at
t
he
T
H
D
current
is
r
ed
uced
t
o
4.
5%
f
rom
61
.
3
%
a
n
d
t
h
e
ou
tp
ut
v
o
l
tage
r
ip
pl
e
is
redu
ced
t
o
7
V
f
r
o
m
1
8
V
after
param
e
ters
o
p
timizati
o
n
are
rea
l
ized
.
F
u
rth
e
r
more,
it
is
con
f
irm
e
d
th
a
t
t
he
o
u
t
pu
t
vo
lt
ag
e
ri
pp
le
f
req
u
en
c
y
i
s
a
l
way
s
d
o
ubl
e
of
t
h
e
in
pu
t
li
ne
f
requen
c
y,
5
0
Hz
a
n
d
t
h
e
o
ut
put
voltag
e
r
i
p
p
l
e
is
a
l
ways
l
o
w
er
th
an
t
he m
ax
im
um
i
n
put
v
o
l
t
a
ge
r
i
p
p
l
e.
K
eyw
ord
s
:
Cuk
co
n
v
er
t
e
r
Opt
i
m
i
za
t
i
o
n
p
ar
am
eter
d
esi
g
n
P
o
w
e
r fac
t
or
cor
rec
t
i
o
n
O
u
t
p
u
t
v
olta
ge
ripp
l
e
P
F
C
cuk
con
v
e
r
ter
To
tal ha
rmo
n
ic
d
istort
i
on
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
s
ma
rashid P
onn
iran,
Fa
cult
y
o
f
E
l
e
c
t
rica
l
and
E
l
e
c
t
r
on
ic E
n
g
i
n
ee
rin
g
,
U
n
i
v
ersi
ti
T
un
H
u
ssei
n
O
nn
Ma
lays
ia (
U
T
H
M
),
86
4
00 Pa
rit Ra
ja,
Bat
u
P
ahat,
Joh
o
r,
M
ala
y
si
a.
Em
ail:
asma
r@u
t
hm.
e
du.
my
1.
I
N
TR
OD
U
C
TI
O
N
In
r
e
c
e
n
t
y
ea
rs,
p
o
rt
abl
e
e
l
ect
ron
i
c
eq
ui
pme
n
t
h
a
s
a
d
v
a
n
c
e
d
f
r
o
m
a
pow
e
r
c
onve
r
t
e
r
a
nd
has
t
h
e
adva
n
t
a
g
e
s
o
f
hi
g
h
e
ffic
i
enc
y
,
sm
all
in
s
iz
e
a
nd
p
o
sse
s
s
a
w
i
de
i
np
ut
a
nd
out
put
v
ol
t
a
ge
r
an
g
e
s
[1
]-[
3
].
O
n
the
o
t
her
ha
n
d
,
the
c
onve
n
tio
nal
p
o
w
e
r
con
v
er
ter
is
n
ot
a
ble
t
o
o
pera
te
i
n
a
w
i
de
o
pe
rati
o
n
r
an
ge
a
n
d
a
t
t
h
e
sam
e
t
im
e ma
inta
i
n
i
n
g hi
g
h
e
fficie
nc
y
;
es
p
e
c
i
a
l
ly w
he
n t
h
e
ste
p
up
an
d s
t
ep
dow
n vo
l
t
a
g
e c
o
n
v
ersi
o
n
ne
e
d
t
o
be
ach
ie
ve
d
[4]
-
[6].
B
esi
d
e
s
,
batt
ery
v
o
l
t
a
ge
d
e
c
re
ases
a
s
the
ba
tt
e
r
y
d
i
sc
ha
rges
a
nd
lea
d
t
o
v
a
r
i
o
u
s
di
ffic
ul
t
i
e
s
i
f the
r
e is n
o v
o
l
t
age co
ntr
o
l. Th
e
re
fore
, t
he
m
os
t
effec
t
i
v
e me
th
od o
f
regu
l
at
in
g v
o
lta
ge thr
oug
h a
circ
u
i
t i
s
b
y
us
in
g
a
D
C
/D
C c
o
n
v
er
t
e
r. Cu
k
con
ve
rter ca
n
be use
d as
a
D
C vo
lta
ge
r
e
g
u
l
a
t
or
d
ue
t
o
t
h
e
abi
lit
y
of
t
he
c
o
n
v
e
r
t
e
r
to
s
t
e
pp
ing
-
up
or
s
te
pp
i
n
g-d
o
w
n
t
he
v
ol
t
a
ge
w
i
t
h
n
e
g
at
ive
p
o
l
a
r
ity
d
e
p
en
d
i
ng
on
th
e
app
l
ica
t
i
o
n
re
q
u
i
r
em
en
t.
I
n
a
d
d
i
ti
on,
t
he
t
r
a
di
tio
na
l
te
l
e
co
m
m
u
nica
t
i
o
n
s
e
qui
pm
ent
re
q
u
ires
a
n
i
n
put
p
ow
er
D
C
o
f
-4
8
V
[7]
and
c
o
nta
i
n
s
num
er
ous
p
a
r
a
l
le
l
-
redu
nda
n
t
r
ecti
f
i
e
r
s
w
hi
ch
c
o
nver
t
t
he
i
n
p
u
t
A
C
p
o
w
e
r
t
o
ou
tpu
t
D
C
p
o
w
e
r
.
Be
si
de
s,
t
he
t
e
l
e
c
o
m
m
unic
a
t
i
o
ns
n
e
t
w
o
r
k
s
an
d
i
nform
a
tio
n
tec
h
n
o
lo
g
y
e
q
u
i
p
m
e
nt
h
a
s
con
v
er
ge
d
ca
u
s
i
ng
the p
o
w
e
r
equ
i
pm
ent
ne
e
d
t
o have
a
v
ar
i
o
us in
put
power
requirements
[
8
]
.
T
herefore,
it
is
a
cha
l
l
e
n
g
e
to
t
ele
c
o
m
m
un
ica
t
i
o
ns
f
ac
i
l
i
t
i
e
s
de
s
i
g
n
e
r
t
o
c
o
nstr
u
c
t
a
re
li
abl
e
a
n
d
eco
no
mi
c
a
l
p
o
w
er
c
onv
ert
e
r
so t
hat i
t
a
b
l
e
t
o
suppor
t
var
i
o
u
s
in
p
u
t
p
ow
er
re
q
u
i
rem
e
nts [9
]
-
[11].
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Optimiz
a
tion of PFC c
u
k
conve
r
te
r
par
a
meters de
sign for
mi
nimiz
a
t
i
on of T
H
D
and ... (M.
A
.
Z. A. Rashid)
51
5
I
n
o
rder
t
o
c
o
nver
t
t
he
a
va
i
l
a
b
l
e
i
n
p
u
t
A
C
s
ourc
e
from
gri
d
t
o
D
C
s
o
u
rce
-48
V
,
a
f
u
ll-br
id
ge
re
ct
i
f
i
e
r i
s
r
e
qui
red
to
r
e
c
t
i
f
y
t
h
e
i
npu
t
AC
t
o
ou
tpu
t
D
C
whi
l
e
Cu
k c
o
nver
t
e
r
i
s
a
s
u
ita
b
l
e
co
nve
ter
to
b
e
use
d
to
c
on
vert
t
he
o
u
t
put
p
os
iti
ve
p
ol
arit
y
t
o
n
e
g
at
i
v
e
p
o
l
a
r
i
t
y
[
1
2].
The
Cu
k
co
nv
er
t
e
r
i
s
a
m
odi
fied
b
o
o
s
t
-buc
k
con
v
er
t
e
r
a
n
d
ca
n
be
u
se
d
e
i
ther
t
o
st
e
p
u
p
or
s
t
e
p
d
o
w
n
t
he
o
u
tp
ut
v
olt
a
g
e
w
i
t
h
re
sp
ect
t
o
t
h
e
dut
y
c
y
cl
e.
The
in
te
gra
tio
n
o
f
t
hese
t
w
o
c
on
verter
s
w
h
i
c
h
are
the
ful
l
-
b
ri
d
g
e
r
e
c
t
i
fi
e
r
a
nd
t
h
e
C
u
k
c
o
n
v
er
t
e
r
nam
e
l
y
t
he
P
F
C
C
u
k
c
o
n
v
e
r
t
e
r
.
N
e
v
e
r
t
h
e
l
e
s
s
,
t
h
e
u
s
e
o
f
b
r
i
d
g
e
r
e
c
t
i
f
i
e
r
,
t
ransf
o
r
m
e
r
,
i
n
d
u
c
t
or,
and
c
a
p
ac
i
t
or
c
a
n
pro
duce
t
h
e
D
C
o
ut
p
u
t
vo
l
t
a
g
e
w
ith
ou
t
an
y
dis
t
or
tio
n
ho
w
e
ver
w
i
l
l
c
au
se
t
he
i
n
p
u
t
c
ur
rent
t
o
be
e
xt
rem
e
ly
di
st
orte
d.
H
enc
e
,
a
re
ctifier
i
.
e.,
A
C
/D
C
c
o
nvers
io
n
i
s
t
ot
all
y
r
eq
uire
d
in
P
F
C
c
on
ve
rte
r
s
truct
u
re
s
t
o
e
nsur
e
t
h
e
in
pu
t
v
o
lt
ag
e
and
i
nput
c
u
r
re
n
t
a
re
p
u
r
el
y
sin
u
s
oid
a
l
.
S
e
v
e
ra
l
c
i
rcui
t
t
opo
l
o
g
i
es;
boo
st
,
b
u
c
k
-
bo
ost
,
C
u
k
,
and
SEP
I
C
co
nve
r
t
er
h
ave
b
een
d
e
v
e
l
o
p
e
d
f
or
P
F
C
a
pp
l
i
cat
i
o
n
s
.
H
ow
ever
,
t
h
e
P
F
C
Cu
k
c
o
n
v
e
r
te
r
has
sever
a
l
dr
awbacks
i.e., high
THD
curr
ent
at
the
i
nput
s
ide as
w
e
l
l
as hig
h vo
ltage
ri
p
ple
at t
he o
utp
u
t si
de d
ue
to t
he
out
p
u
t
v
ol
ta
ge
f
rom
the
ful
l
-bri
d
g
e r
ecti
f
ier
prod
uce
d
i
nco
n
s
t
a
n
t D
C
.
T
h
i
s
p
a
p
e
r
p
r
e
s
e
n
t
s
t
h
e
o
p
t
i
m
i
z
a
t
i
o
n
o
f
P
F
C
C
u
k
c
o
n
v
e
r
t
e
r
p
a
r
a
m
e
t
ers
des
i
g
n
f
or
t
he
m
inimi
z
a
t
ion
of
T
H
D
a
n
d
v
o
l
t
a
g
e
rip
p
le
i
n
or
der
to
o
ve
rc
ome
its
d
ra
w
b
acks.
B
es
i
d
es,
t
o
r
e
duce
the
THD
cur
r
e
n
t
a
t
t
he
in
put
s
ide
,
t
he
p
rinc
i
p
le
o
f
bala
nc
in
g
e
n
er
gy
c
o
mpe
n
sa
ti
on
be
tw
ee
n
t
h
e
in
p
u
t
c
a
p
ac
itor,
C
1
a
nd
outp
u
t
in
duc
t
o
r
,
L
o
i
s
c
oncer
ne
d.
M
ea
nw
h
i
l
e
,
t
h
e
ou
t
p
u
t
v
o
l
tage
r
i
p
p
l
e
c
a
n
b
e
r
e
du
ce
d
b
y
o
pt
imiz
i
ng
the
ou
t
p
ut
ca
paci
ta
nce
,
C
o
.
Ther
efore
,
t
he
e
ner
g
y
fro
m
the
o
u
tp
ut
f
ul
l
-
bri
d
g
e
r
ec
t
i
fie
r
m
ust
be
t
r
a
nsferr
ed
t
o
th
e
Cu
k
c
o
nv
e
r
t
e
r
e
f
f
ect
iv
e
l
y
wit
h
out
a
n
y
"
ex
tra
"
e
n
e
r
gy.
I
f
the
e
n
er
gy
is
n
o
t
e
ffe
c
ti
ve
l
y
t
ransfe
rred,
t
he
i
np
u
t
T
H
D
c
u
rre
n
t
i
s
a
ff
e
c
t
e
d
at
t
h
e
i
npu
t
si
d
e
a
n
d
i
ncre
ase
s
t
h
e
out
put
volt
a
g
e
ripple.
Th
e
parameters
a
r
e
d
es
igned
base
d
o
n
t
he
s
tan
d
a
r
d
o
f
I
EC
6
1
0
00-
3-2,
w
hic
h
i
s
c
l
ass
D
i.e.
,
ma
ximu
m
of
T
H
D
curre
nt
i
s
5%
[
1
3
]
-[15]
.
T
h
e
P
W
M
s
i
g
n
a
l
f
o
r
t
h
e
s
w
i
t
c
h
i
s
r
e
a
l
i
z
e
d
u
s
i
n
g
A
l
t
e
r
a
D
E
2
a
s
i
n
[1
6],
[1
7].
The
resu
l
t
s
of
t
he
o
p
t
imiza
t
ion
pro
duce
d
a
n
o
u
tp
ut
o
f
-48
V
w
i
t
h
t
he
T
H
D
curr
ent
i
s
dow
n
t
o
4
.5
%
an
d
the
m
a
x
i
m
u
m
ou
t
p
u
t
v
o
lta
ge
r
ip
ple
is
a
p
p
rox
i
m
a
te
ly 2
0%
o
f
t
h
e
ou
t
p
u
t
v
olta
ge
.
2.
CONVE
N
T
IONAL
PFC
C
UK
C
ONVER
TER
A
c
o
n
v
e
n
t
i
o
n
a
l
P
F
C
C
uk
is
a
t
y
p
e
of
c
on
ve
nt
i
o
na
l
P
F
C
conver
t
e
r
wi
t
h
t
h
e
i
nt
e
g
rat
i
o
n
of
f
ull
-
b
r
id
ge
rec
t
i
f
i
e
r
a
n
d
Cuk
c
o
nver
t
er
t
hat
a
l
low
s
t
he
s
te
p-up
a
n
d
st
ep-d
o
w
n
o
f
ou
tpu
t
v
o
lta
ge
b
y
co
n
t
ro
lli
ng
t
h
e
d
u
ty
cyc
l
e
.
F
igur
e
1
show
s
t
h
e
f
u
ll
-brid
g
e
rec
t
i
f
ie
r
part
t
ha
t
r
e
qu
i
res
fo
ur
s
ta
nd
ard-
diode
a
s
a
bri
d
ge
,
w
h
i
l
e
l
a
rge
in
put
in
duc
t
a
n
ce
L
1
a
nd large
ou
t
p
u
t
ca
p
ac
it
anc
e
C
o
a
re
r
equired
for
the
Cuk
part
.
The
operation
of
Cuk
is
the
sam
e
a
s
t
h
e
c
onve
n
t
i
o
nal
b
u
c
k
-
boos
t
c
o
nver
t
e
r
w
it
h
c
o
ns
t
a
nt
D
C
s
o
urce
,
w
h
ic
h
the
o
u
t
p
u
t
v
o
lta
ge
i
s
a
l
w
a
ys
i
n
n
eg
a
t
iv
e
pol
ari
t
y
.
G
e
nera
lly,
the
char
acte
r
istic
s
of
t
he
c
o
n
v
e
nt
i
ona
l
P
F
C
C
uk
c
o
n
v
e
r
ter
and
Cu
k
c
o
nver
t
er
a
r
e
di
ffe
re
nt,
w
h
i
c
h
t
h
e
Cu
k
co
nver
t
e
r
r
ec
eiv
e
s
a
c
onsta
nt
D
C
as
t
h
e
s
u
p
p
l
y
w
h
i
l
e
t
h
e
P
F
C
C
u
k
c
o
n
v
e
r
t
e
r
rec
e
ives
a
no
t
con
sta
n
t
D
C
s
our
ce.
T
here
for
e
,
a
la
rge
inp
u
t
i
n
d
uc
t
a
nce
a
n
d
o
u
p
u
t
c
a
p
aci
t
a
nc
e
are
re
qu
i
r
ed
f
or
the
s
t
ruc
t
ur
e of
P
F
C
C
uk
c
o
nve
rter.
N
e
ver
t
h
e
l
e
ss,
t
h
e o
u
t
put
v
o
l
t
a
g
e
c
a
n
be
s
te
ppe
d-
u
p
or st
e
p
ped-
do
w
n
w
i
t
h
appr
opr
i
a
t
e
c
o
m
pone
n
t
s
de
si
gn
for
b
o
t
h
s
tr
uct
u
res.
W
he
n
the
sam
e
spec
ifica
t
io
ns
a
n
d
p
a
r
am
ete
r
s
of
t
he
C
u
k
con
v
er
t
e
r
ar
e
app
l
ied
in
t
he
c
on
ve
nt
i
o
na
l
P
F
C
Cu
k
c
o
nve
rter
,
th
e
THD
cur
r
ent
an
d
o
u
t
p
u
t
v
ol
ta
ge
r
i
p
p
l
e
bec
o
me
hi
g
h. There
fore,
the
in
d
u
cta
n
ce
a
n
d
ca
p
ac
ita
nc
e of
t
he o
ut
p
u
t
i
ndu
ct
o
r
a
nd
c
a
p
ac
i
t
o
r
,
res
p
ec
tiv
el
y
a
r
e
requ
ire
d
to be
o
p
t
i
m
ize
d
in or
de
r to
r
educe
t
h
e
TH
D
c
u
rre
n
t
a
nd
ou
t
put
v
ol
t
a
g
e
ri
ppl
e.
2.1.
Basic
Pri
n
c
i
p
l
e of
PFC cu
k
c
on
ve
rte
r
The
o
reti
ca
ll
y,
w
hen
a
du
t
y
c
ycle
a
p
p
roa
c
h
e
s
u
n
i
ty,
the
D
C
g
a
i
n
towards
zero
[
14].
T
h
e
s
wi
t
c
hi
ng
fre
que
nc
y
nee
d
t
o
be
c
o
n
s
i
der
e
d
f
o
r
par
a
m
e
ters
optim
i
z
at
i
on
p
u
r
p
o
s
e
.
When
t
he
s
w
i
t
c
h
i
ng
fre
q
u
e
nc
y
incre
a
ses,
t
he
r
ip
p
l
e
c
u
rre
t
o
n
t
h
e
in
duc
tor
d
e
cre
a
ses.
F
i
gur
e
2
s
h
ows
the
D
C
g
a
i
n
c
h
ar
acter
i
s
ti
cs
f
or
t
h
e
P
F
C
C
u
k
co
nv
ert
e
r.
B
e
s
id
e
s
,
th
e
stru
c
t
u
r
e
as
d
epi
c
t
e
d
i
n
F
ig
u
r
e
1
c
o
n
s
i
sts
of
b
uck
a
nd
bo
ost
opera
tio
ns
w
he
re
f
o
r
the
b
u
c
k
oper
a
t
i
o
n
,
t
h
e
du
t
y
c
ycle
i
s
le
ss
t
h
a
n
0
.5
a
nd
t
he
dut
y
cyc
l
e
i
s
g
rea
t
e
r
t
ha
n
0.5
for
t
h
e
bo
ost
o
p
era
t
i
o
n.
F
i
gure
1.
P
F
C
Cuk
co
n
v
erte
r c
i
r
c
u
i
t
L
o
i
Lo
L
1
C
1
C
o
R
V
AC
i
AC
i
L1
D
p
D
n
D
n
D
p
S
V
ou
t
D
o
V
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
51
4 –
52
1
51
6
F
i
gur
e 2.
D
C ga
in
c
ha
rac
t
e
r
is
tics
for
P
F
C
Cu
k
con
v
erte
r
2.2.
O
p
erat
i
o
n
of PFC
c
u
k
c
on
ve
rte
r
The
P
F
C
Cu
k
c
o
n
v
erter
c
i
r
c
u
it
w
i
th
s
in
g
l
e
-
sw
itc
h
is
c
o
n
tro
l
l
e
d
b
y
dut
y
c
y
cle
s
i
gna
l.
T
h
i
s
circ
u
it
c
a
n
b
e
d
i
v
i
d
ed
i
nt
o si
x
op
era
t
ing
m
odes a
n
d con
s
is
t of
p
osit
i
v
e a
n
d
nega
t
ive
half
c
ycles
,
r
ef
erring F
i
gur
e
1.
M
o
d
e
-
1
a
n
d
M
od
e-
4:
M
od
e
-
1
is
pos
i
tive
ha
lf
c
ycle
w
hi
l
e
m
ode
-4
i
s
ne
gat
i
ve
h
a
l
f
cy
cl
e.
W
h
e
n
the
sw
it
c
h
S
i
s
tur
n
e
d
-
on,
t
he
e
n
e
rgy
from
s
ou
r
ce
is
s
t
o
r
e
d
i
n
i
n
d
u
ct
or
L
1
.
A
t
the
sam
e
t
ime
,
c
a
p
aci
t
o
r
C
1
i
s
di
sc
harg
i
n
g
to
i
nd
uc
t
o
r
L
o
a
n
d
c
a
p
a
c
i
t
o
r
C
o
.
D
u
ring
t
h
i
s
in
terva
l
,
t
h
e
d
i
ode
D
o
i
s
t
u
r
n
e
d
-
o
f
f
a
n
d
t
h
e
p
o
w
e
r
su
pp
li
e
d
t
o
th
e
l
o
ad
.
M
o
d
e
-
2
a
n
d
M
od
e-5:
M
o
d
e
-
2
i
s
pos
i
tive
ha
lf
c
yc
le
w
he
r
e
m
ode
-5
i
s
n
e
gat
i
v
e
ha
lf
c
y
cl
e.
W
h
e
n
t
h
e
sw
it
c
h
S
i
s
tur
n
e
d
-
o
ff,
the
i
nduc
tor
L
1
r
e
c
har
g
es
t
he
c
a
p
a
c
it
or
C
1
,
and
i
n
d
u
c
t
or
L
o
r
echarge
s
t
h
e
c
a
p
a
c
i
t
o
r
C
o
thr
o
u
g
h
the
f
re
e
w
hee
lin
g d
i
od
es
D
o
a
nd su
pp
li
e
s
pow
er
to t
h
e
l
o
a
d
s.
M
o
d
e
-
3
a
n
d
M
o
d
e
-
6
:
Mode
-3 i
s posi
t
i
v
e h
a
l
f
c
ycle w
h
i
le
m
ode-6 i
s ne
ga
ti
ve ha
l
f cy
c
l
e
.
D
urin
g
t
h
e
sam
e
s
t
a
t
e
w
he
n
t
h
e
swi
t
ch
S
i
s
turned-o
ff,
the
ca
pa
ci
t
o
r
C
1
a
nd
i
n
d
u
c
t
or
L
o
s
tore
e
nergy
thro
u
gh
th
e
di
sc
harg
i
n
g
i
n
duc
t
o
rs
L
1
.
Th
e
c
a
p
a
cit
o
r
C
o
a
re
d
ischa
r
gin
g
.
D
u
r
i
ng
th
is
i
n
t
er
v
a
l,
t
he
d
i
ode
D
o
i
s
turned-
o
ff
and
the
p
o
w
e
r
sup
p
l
i
e
d t
o
t
he
l
o
a
ds.
2.3.
Paramet
ers
d
e
s
ign
of
P
FC
c
u
k
c
on
ve
r
t
er
Ta
b
l
e
1
sh
ow
s
th
e
spec
ifica
t
i
ons
t
o
de
s
i
g
n
t
he
p
assive
e
le
m
e
nts
.
Ba
se
d
on
t
h
e
oper
a
tion
mo
de
,
t
h
e
pass
ive e
l
em
e
n
ts
a
re
e
stim
ate
d
b
ase
d
on
t
h
e DCM c
o
n
d
i
t
i
o
n
.
Ta
b
l
e
1.
S
pe
cifica
ti
on
s
Pa
r
a
m
e
te
rs
V
alue
s
Inp
u
t
Volt
a
g
e
,
V
AC
(50
-
100)
V
F
r
e
que
n
c
y
lin
e
,
f
L
50
H
z
Pe
r
i
od
of
line
volta
g
e
,
T
L
0
.
02
s
O
u
tput
V
olta
g
e
(
D
C
)
,
V
o
-4
8 V
Out
put
P
ow
e
r
,
P
ou
t
65
W
Sw
it
c
h
ing
Fre
que
n
c
y
,
f
s
50
kH
z
Ma
xi
m
u
m
input
c
u
r
re
nt
r
ippl
e
,
Δ
i
L1
<
25%
o
f
f
u
nda
m
e
nta
l
c
ur
re
nt
Output
V
olta
g
e
r
ipple
,
Δ
V
o
<
20
%
of
V
o
2
.
3
.
1
D
esig
n o
f
in
put induct
o
r
The
i
npu
t
in
d
u
ct
ors
L
1
a
re
e
xpr
esse
d
i
n
(
1)
w
i
t
h
i
n
p
u
t
v
o
l
tage
(
V
AC
)
i
s
i
n
po
si
t
i
v
e
a
n
d
n
eg
at
ive
h
al
f cy
c
l
e
s
.
1
1
AC
L
s
Vt
D
L
If
(1)
2.3.
2 D
esign
of
ou
t
pu
t
i
n
du
c
t
or
The
vo
lta
ge
c
o
nve
rs
i
o
n
r
a
t
i
o
M
i
n
term
s
o
f
t
he
r
ecti
f
ier
pa
ra
me
t
e
r
c
a
n
be
o
b
t
a
i
ned
by
a
p
p
l
yi
n
g
the
pow
er
-bala
n
c
e
pr
i
nc
ip
le
[
1
3
]:
2
o
AC
V
M
V
(2)
-12
0
0
-7
00
-2
00
0
0
.2
0.
4
0
.6
0
.
8
1
Outp
ut
V
o
ltag
e
G
ain
(
V
)
D
u
ty
C
y
c
le
,
D
Bo
o
s
t
Bu
c
k
V
1
=
50
V
DC
g
ain
to
w
a
rd
s ze
r
o
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Optimiz
a
tion of PFC c
u
k
conve
r
te
r
par
a
meters de
sign for
mi
nimiz
a
t
i
on of T
H
D
and ... (M.
A
.
Z. A. Rashid)
51
7
The
va
lue o
f
K
e-cr
iti
cal
can
b
e
e
v
al
ua
te
d b
y
:
2
1
2(
2)
e
e
c
r
itica
l
KK
M
(3)
To e
nsur
e the
oper
a
tio
n
i
s
i
n
D
C
M
,
the
f
o
llo
w
i
n
g
v
al
ue o
f
K
e
is selec
t
ed:
0.85
e
e
c
r
itica
l
KK
(4)
Th
us, by
eva
l
u
a
t
i
n
g
the
p
ara
m
e
t
er
K
e
g
i
v
e
s
a
n
equ
i
val
e
n
t
i
nd
uc
tanc
e
L
e
val
ue of
2
eL
e
s
K
R
L
f
(5)
The
va
lue o
f
L
o
c
an be
e
xpressed
as foll
o
w
s
:
1
1
2
e
o
e
LL
L
LL
(6)
2.3.
3 D
esign
of
ou
t
pu
t
i
n
du
c
t
or
The
ca
pac
itor
C
1
w
ill
no
t
ca
use
low
-
fre
que
ncy
osc
illa
ti
o
n
s
w
it
h
t
h
e
c
o
n
v
erter
i
n
d
u
c
t
or
s.
T
hus,
the
energy
t
ransfer
f
r
om
capacitor
s
C
1
i
s determ
i
n
ed base
d
o
n
t
h
e ind
u
c
t
or
L
1
, and
L
o
such th
a
t
t
he
l
i
n
e fre
q
uen
c
y
(
f
L
)
s
h
o
u
l
d
be
l
ow
er
t
ha
n
t
h
e
sw
itch
i
ng
fre
que
nc
y
(
f
s
)
.
T
h
u
s,
a
b
et
t
e
r
in
i
t
i
a
l
ap
pro
x
ima
tio
n
for
c
h
o
o
s
i
ng
t
he
resona
nt
f
re
q
u
e
ncy
(
f
r
)
is given by
[5]:
L
rs
f
ff
(7)
11
1
2
r
o
f
CL
L
(8)
2
.
3.
4 S
e
l
ec
tion
o
f ou
tp
u
t
c
ap
a
c
ito
r
The
ou
tp
u
t
v
o
l
tage
r
ip
p
l
e
fr
eque
nc
y
o
f
t
he
c
on
ve
rter
i
s
t
w
o
t
i
m
es
o
f
th
e
in
put
f
re
qu
en
cy.
Th
e
r
ef
o
r
e,
C
o
can be obtained as f
o
llows
:
4
o
o
L
oo
P
C
f
VV
(9)
2.4.
O
p
timiza
tion
p
ar
amet
ers
d
esign
of PFC
c
u
k
con
ve
rt
er
F
i
gure
3
sh
ow
s
the
o
p
t
i
m
i
za
tio
n
para
me
ters
o
f
L
o
a
n
d
C
1
w
ith
T
H
D
c
urre
nt,
h
o
w
e
ve
r
t
h
e
al
l
o
w
a
b
l
e
TH
D
cur
r
ent
ra
nge
m
ust
be
w
it
hi
n
1.
8%
t
o
4%
i
n
or
der
to
e
s
t
i
m
at
e
L
o
a
nd
C
1
f
or
o
ptim
iza
t
io
n
p
u
r
pose
.
Energies
o
f
L
o
a
nd
C
1
m
ust
be
c
om
pe
nsa
t
i
ng
ea
c
h
o
t
h
er.
O
t
herw
ise,
t
h
e
r
e
m
a
i
ni
ng
e
n
er
gy
o
f
L
o
w
i
l
l
b
e
trans
f
e
rre
d
to
t
he
s
o
u
rce
and
conse
q
ue
nt
ly
t
he
qua
l
ity
o
f
in
p
u
t
c
urre
nt
l
ine
wi
l
l
b
e
a
f
fe
cted.
As
h
a
s
b
e
e
n
me
ntio
ne
d, the
T
H
D
cur
r
ent
of 2% is use
d as
a
r
efe
r
enc
e
t
o ens
u
re
t
h
e
e
ffi
c
i
en
c
y
o
f
t
h
e
p
r
op
o
s
ed
c
onve
rt
er
i
s
hi
gh
and
TH
D
c
u
rrent
i
s
low
,
a
cc
ord
i
n
g
t
o
th
e stan
da
rd of IEC 6
1
000
-3
-2
.
F
i
gure
3.
O
pt
i
m
izat
io
n par
a
m
e
ter
of
L
o
a
nd
C
1
w
i
t
h
T
H
D
cu
r
r
e
n
t
0
10
20
30
40
50
60
1.
8
3
4
C
1
(µ
F)
a
nd
L
o
(µ
H
)
THD
c
ur
rent
(
%
)
L
o
C
1
f
L
<
f
r
<
f
sw
R
e
fe
re
nce
of
T
H
D
c
u
rrent
Re
si
dual
ener
g
y
of
L
o
C
om
pens
ati
o
n
of
e
n
e
rg
y
,
C
1
Not
al
lowed
re
g
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
51
4
–
521
51
8
The
o
u
t
p
u
t
c
a
p
ac
it
or
r
ip
ple
cur
r
ent,
Δ
i
c
1
a
nd
c
a
p
ac
i
t
or
v
ol
ta
ge
r
ip
p
l
e,
Δ
V
c1
a
r
e
e
x
p
r
e
s
s
e
d
b
y
(
1
0
)
a
nd
(
1
1)
.
I
n
a
ddi
t
i
on,
t
he
o
u
t
p
u
t
v
o
lta
ge
r
ip
p
l
e
i
s
e
xpr
e
s
se
d
b
y
(
1
3)
.
1
L
cL
s
o
V
ii
D
T
L
(
10)
11
1
1
cc
Vi
d
t
C
(
11)
1
ESR
c
Vi
E
S
R
(
12)
1
oc
E
S
R
VV
i
(
13)
B
a
se
d
o
n
(
9)
,
the
o
u
t
p
ut
v
o
l
ta
ge
r
i
p
pl
e
i
s
r
e
d
u
ced
w
h
e
n
c
a
p
ac
it
a
n
ce
i
n
c
re
ase
s
.
Af
t
e
r
al
l
th
e
pa
ram
e
ter
s
a
re
o
p
timiz
e
d
b
y
c
onsi
d
er
ing
a
v
a
i
l
a
b
ili
t
y
i
n
the
mar
k
e
t
,
t
h
e
P
F
C
C
u
k
c
o
n
v
e
r
t
e
r
s
p
e
c
i
f
i
c
a
t
i
o
n
s
a
r
e
list
e
d
as
sh
o
w
n in
Tabl
e
2
.
Tab
l
e
2.
O
p
tim
i
z
at
i
on
p
a
r
a
m
e
ter
desi
gn
o
f
p
assi
ve
e
lem
e
n
t
Pa
r
a
m
e
t
e
rs
v
a
l
u
e
s
Inp
u
t
induc
t
o
r
,
L
1
2.
2 m
H
O
u
tput
I
n
duc
tor,
L
o
22
µH
I
n
pu
t
cap
aci
t
o
r
,
C
1
1
µ
F
Output Ca
p
ac
itor, C
o
3300
µF
3.
RESU
L
T
S
A
ND ANALY
S
IS
R
e
fe
r
r
i
ng
t
o
t
h
e
T
a
b
l
e
2
,
t
h
e
sim
u
la
ti
on
a
n
d
exper
i
m
e
n
t
a
l
r
esul
t
s
a
re
d
i
s
cu
ssed
b
y
fo
cu
si
ng
o
n
th
e
m
i
ni
m
i
za
ti
on
of
T
H
D
cur
r
ent
a
n
d
ou
t
p
ut
v
o
lta
ge
r
ipp
l
e.
T
o
r
e
d
u
c
e
th
e
T
HD
c
u
rren
t
,
t
h
e
indu
c
t
an
ce
o
f
t
he
o
u
tp
ut
i
ndu
c
t
ors
are
se
t
t
o
2
.2
m
H
an
d
22
µ
H
wh
i
l
e
t
h
e
cap
a
c
it
a
nce
o
f
the
o
u
t
pu
t
c
a
p
ac
i
t
or
s
ar
e
se
t
t
o
4
7
0
µ
F
a
nd
3
3
0
0
µ
F
i
n
o
r
d
er
to
ob
se
r
v
e
t
h
e
o
u
t
p
ut
v
o
l
tage
r
ip
p
l
e
r
e
duc
t
i
o
n
w
it
h
the
sw
i
t
ch
i
n
g
f
r
e
que
nc
ies
of
1
0
kH
z
a
nd
5
0
k
H
z
.
3.
1.
Min
i
m
i
z
a
tion of
THD
c
u
rr
ent
D
u
r
i
n
g
t
he
s
i
m
ula
t
i
on
of
t
he
c
o
nver
t
e
r
c
i
r
cu
it
,
al
l
th
e
sw
itch
i
ng
de
vice
s
and
c
o
m
pone
n
t
s
ar
e
a
s
sum
e
d
idea
l
w
i
t
h
n
o
l
o
sses.
F
igur
e
4(
a
)
a
nd
F
i
gur
e
4(
b)
s
how
t
h
e
inp
u
t
so
ur
ce
vo
l
t
a
g
e
an
d
i
n
pu
t
s
our
c
e
c
u
r
r
e
nt
,
r
e
specti
v
e
l
y
f
o
r
the
P
F
C
C
u
k
con
v
er
t
e
r
.
T
he
qual
i
t
y
of
t
he
i
n
put
c
u
r
r
e
nt
i
s
po
or
.
(a)
(b
)
F
i
gur
e
4.
I
npu
t
sour
ce
(
a)
volt
a
ge
,
(
b
)
cur
r
ent
Th
is
m
e
a
ns
t
ha
t
t
h
e
TH
D
c
u
r
r
ent
is
v
er
y
po
or
i
n
t
h
is
c
on
d
iti
on
an
d
t
h
e
perc
en
tage
o
f
the
THD
c
u
r
r
e
nt
o
f
the
i
n
p
u
t
li
ne
c
ur
r
e
nt
i
s
6
1
.
3
%.
F
igur
e
5
s
h
ow
s
t
h
e
fr
equ
e
nc
y
s
p
e
c
t
r
u
m
o
f
T
H
D
c
u
r
r
e
nt
b
efor
e
op
t
i
miza
tio
n.
I
n
o
t
her
w
o
r
d
s,
t
he
i
np
u
t
l
i
n
e
cur
r
ent
is
n
o
t
a
p
u
r
e
si
nu
so
i
d
al
a
s
t
h
e
i
n
put
l
i
n
e
v
o
l
t
a
g
e
b
eca
u
s
e
t
h
e
i
npu
t
lin
e
c
u
rren
t
c
ont
a
i
ns
s
ing
l
e
h
a
r
m
o
n
i
c
di
sto
r
ti
on
.
Th
e
o
p
t
i
m
i
z
e
d
p
a
r
a
m
e
t
e
r
i
s
n
e
e
d
e
d
t
o
e
n
s
u
r
e
t
h
e
ha
r
m
onic
l
i
m
i
t
s
i
s
a
l
w
a
ys
w
i
t
h
i
n
t
h
e
r
a
n
g
e
of
I
E
C
6
1
0
0
0
-
3-
2
sta
n
d
a
r
ds.
The
par
a
m
e
ter
s
f
or
t
he
h
a
r
d
w
ar
e
e
xper
i
m
e
nt
lis
te
d
i
n
T
a
b
l
e
s
1
and
2
ar
e
c
o
n
s
t
r
uc
ted
to
e
va
lua
t
e
t
he
p
er
f
o
r
m
a
n
ce
of
t
h
e
p
r
opose
d
c
ir
c
u
it
a
s
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
Opti
miz
a
tion
of
PFC cuk
c
o
nv
erter pa
r
a
me
te
rs design
for mi
nimization of T
H
D and
... (M.
A
.
Z.
A
.
Rashid)
51
9
show
n
in
F
ig
u
r
e
1.
T
he
T
H
D
c
u
r
r
e
nt
i
s
m
e
a
s
ur
ed
by
us
i
n
g
pow
er
a
na
l
y
se
r
a
nd
a
ll
da
ta
a
r
e
t
a
b
ul
a
t
e
d
i
n
o
n
e
gr
ap
h.
I
n
add
i
tio
n,
t
he
i
n
d
u
c
t
anc
e
o
f
the
o
u
t
p
ut
i
nd
uc
t
o
r
s
,
L
o
u
sed
ar
e
2.
2
mH
a
nd
22
µ
H
with
a
f
ix
ed
c
a
pac
i
t
a
nce
of
t
he
o
ut
p
u
t
c
a
p
ac
itor
,
C
o
w
hic
h
i
s
33
0
0
µ
F
a
nd
t
h
e
sw
i
t
c
h
ing
fr
eq
ue
nc
y
i
s
50
kH
z
to
o
b
s
e
rv
e
the
THD
cur
r
ent
i
n
t
erm
s
o
f
t
h
e
rip
p
l
e
c
u
rre
nt
a
s
s
h
own
i
n
Figu
r
e
6
.
F
r
om
F
igur
e
6(
a)
,
th
e
TH
D
cur
r
ent
of
L
o
=
2.
2
m
H
i
s
us
ed
a
nd
t
he
r
e
s
u
l
t
o
f
t
he
i
n
p
u
t
TH
D
cur
r
ent
is
h
i
g
h
a
t
t
he
i
n
p
u
t
l
i
n
e
c
u
r
r
e
nt
w
it
h
TH
D
i
o
f
6
1
.
3
%
w
i
t
h
p
ea
k-
pea
k
c
ur
r
e
nt
i
s
1
0
A
an
d
pea
k
-
p
ea
k
vo
ltage
i
s
160
V
.
In
F
ig
u
r
e
6
(
b
)
,
t
h
e
L
o
=
2
2
µ
H
i
s
u
s
e
d
and
pr
oduc
es
t
he
T
H
D
i
o
f
4.
5%
w
i
t
h
pea
k
-
p
ea
k
c
u
r
r
e
nt
i
s
7.
4
A
and
p
ea
k-
p
e
a
k
v
ol
ta
ge
i
s
160
V
.
I
n
a
ddit
i
o
n
,
th
e
pos
i
tio
n
o
f
t
h
e
s
ine
w
a
ve
i
s
in
pha
se.
F
r
om
F
igur
e
6,
w
he
n
lar
g
e
i
n
duc
ta
nc
e
o
f
t
h
e
o
u
t
pu
t
i
n
du
ctor
i
s
co
ns
id
e
r
e
d
,
t
h
e
THD
c
u
rre
n
t
i
s
poo
r
a
n
d
t
h
e
out
put
v
o
l
t
a
g
e
r
i
p
p
l
e
f
r
e
que
ncy
is
d
ou
b
l
e
fr
om
t
h
e
l
i
n
e
f
r
e
que
n
c
y
f
o
r
one
c
yc
l
e
a
s
sh
ow
n
i
n
(
14
)
.
F
i
g
u
r
e
5
. Freq
u
e
n
c
y
sp
ectrum o
f THD
i
b
e
f
or
e
pa
r
a
m
e
ter
s
opt
i
m
iza
tio
n
(a)
(b
)
F
i
g
u
r
e
6
. THD cu
r
r
en
t
o
f
ou
t
p
u
t in
du
ctan
ce (a)
2
.2
mH, (b
)
2
2
µ
H
The
ou
t
p
u
t
D
C
is
d
e
p
e
n
d
i
n
g
o
n
ha
lf
-
w
av
e
and
f
u
l
l
-
w
a
v
e
br
i
dge
r
e
c
t
i
f
ier
s
i
s
s
h
ow
n
in
F
i
g
ur
e
7.
Howe
ver,
t
he
o
u
t
put
v
o
l
tage
r
ipp
l
e
is
d
ecr
ease
d
w
h
i
c
h
w
ill
be
d
isc
u
s
s
ed
i
n
the
ne
x
t
s
ec
ti
o
n
.
Mea
n
wh
i
l
e
,
F
i
g
u
r
e
8
s
how
s
the
fr
e
que
nc
y
spe
c
t
r
u
m
w
i
t
h
v
a
r
i
ous
f
r
e
q
u
e
n
c
i
es
a
nd
ou
tp
u
t
c
apa
c
i
t
o
r
val
u
es.
The
ha
r
m
oni
c
co
mp
on
en
ts
a
re
c
ol
l
e
ct
ed
from
t
h
e
fu
nd
a
m
e
n
t
a
l
h
a
rmo
n
i
c
t
o
11
th
h
a
r
m
o
n
i
c
s
b
y
usi
n
g
pow
er
a
nal
y
se
r
.
T
he
sw
itc
h
i
n
g
f
r
e
que
nc
y
of
50
kH
z
an
d
t
h
e
ou
t
p
u
t
c
a
p
ac
it
anc
e
o
f
4
7
0
µ
F
pr
oduce
th
e
3
rd
a
nd
5
th
h
i
g
h
e
s
t
ha
r
m
onic
s
w
h
i
c
h
r
esul
ts
i
n
a
hi
gh
TH
D
c
u
r
r
e
nt
.
H
o
w
e
ve
r
,
f
or
t
he
7
th
a
nd
9
th
h
a
r
mon
i
c
s
c
om
po
ne
n
t
,
the
c
u
r
r
e
nt
i
s
l
o
w
com
p
ar
e
d
t
o
th
e
o
t
her
har
m
onic
com
p
o
n
en
t
s
m
a
g
n
i
t
ud
e
.
I
t
mea
n
s
th
at
t
o
re
d
u
c
e
T
HD
cu
rre
n
t
w
i
t
h
r
ega
r
d
t
o
s
ta
ndar
d
s
I
E
C
61
0
0
0-
3-
2
w
h
ic
h
is
l
ess
t
h
a
n
5
%,
t
he
3
rd
a
n
d
5
th
s
ho
uld
b
e
m
i
n
i
m
iz
ed
a
s
lo
w
a
s
pos
si
b
l
e
.
F
igur
e
9
show
s
the
f
r
e
que
nc
y
spec
t
r
um
o
f
TH
D
c
u
r
r
ent
a
f
ter
op
t
i
m
i
za
ti
o
n
w
hic
h
i
s
4.
5%
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
51
4
–
521
52
0
F
i
g
u
r
e
7
. Freq
u
e
n
c
y
lin
e
an
d
freq
u
e
n
c
y
o
u
tpu
t
DC
F
i
gur
e
8.
F
r
eque
nc
y
spe
c
t
r
u
m
w
ith
v
a
r
ious
fr
eque
nc
y
and
ou
tpu
t
c
apa
c
i
t
o
r
F
i
gur
e
9.
F
r
eque
n
c
y
spec
tr
u
m
o
f
TH
D
i
a
ft
e
r
p
a
r
a
m
et
ers o
p
t
i
m
i
zati
o
n
3.
1.
Min
i
m
i
z
a
t
i
on
o
f
ou
tpu
t
volt
age
r
i
p
p
l
e
F
i
gur
e
s
1
0
s
h
ow
s
the
c
o
m
p
ar
i
s
on
o
f
the
o
u
t
p
u
t
v
o
lta
ge
a
n
d
r
ip
pl
e
cu
rren
t
w
he
n
th
e
c
a
p
ac
i
t
a
n
c
e
of
the ou
t
put
c
a
p
acit
o
r
use
d
a
r
e
4
7
0
µ
F
a
nd
3
3
00
µF
w
ith
a
f
i
x
ed
s
w
itc
hi
n
g
f
r
e
que
nc
y
of
5
0
kH
z.
I
t
c
a
n
be
s
e
e
n
tha
t
t
he
out
pu
t
vo
l
t
a
g
e
r
i
p
p
le
i
s
r
e
duce
d
f
r
o
m
18
V
to
7
V
w
hen
t
he
c
a
p
aci
ta
nc
e
o
f
outp
u
t
c
a
p
ac
itor
i
s
incr
ease
d
.
Fur
t
he
rm
o
r
e,
t
he
o
ut
p
u
t
c
u
rre
nt
r
i
p
p
l
e
als
o
d
ecr
e
a
se
s
f
r
o
m
0.
6
0
A
t
o
0
.
1
6
A
w
h
en
t
he
c
a
p
ac
i
t
a
nc
e
is
i
ncr
ease
d
.
B
e
si
des,
t
he
o
u
t
pu
t
r
i
p
p
l
e
fr
e
q
uenc
y
o
f
t
he
s
t
r
uc
t
u
r
e
i
s
tw
o
t
i
m
e
s
of
t
he
i
n
p
u
t
f
r
e
q
u
e
n
c
y
.
F
i
gur
e
1
0
(
a
)
show
s
t
h
e
o
u
t
p
u
t
vo
lta
ge
r
ipp
l
e
w
i
t
h
t
he
o
utpu
t
c
a
p
a
c
i
t
o
r
o
f
4
7
0
µ
F
.
I
n
t
h
i
s
c
a
s
e
,
t
h
e
ou
t
p
u
t
v
ol
ta
ge
r
ip
p
l
e
is
18
V
and
the
o
u
t
p
u
t
c
ur
r
e
nt
r
i
p
pl
e
i
s
0.
60
A
.
I
t
ca
n
be
s
e
e
n
t
h
a
t
t
he
e
x
p
er
im
enta
l
r
e
sults
i
s
a
ppr
ox
ima
t
e
l
y
agr
e
e
w
i
t
h
t
he
s
i
m
ulat
i
on
r
e
su
lts.
The
s
p
i
ke
o
f
t
h
e
o
u
t
pu
t
vol
tage
w
a
v
e
f
or
m
is
de
pe
n
d
i
ng
o
n
t
he
p
ar
asi
tic
e
l
e
m
e
nts.
W
he
n
the
o
u
tp
ut
c
a
p
a
c
i
t
a
n
c
e
is
3
30
0
µF
,
the
out
p
u
t
v
o
l
t
a
g
e
rip
p
l
e
is
r
e
duce
d
t
o
7
V
a
nd
o
u
tp
ut
c
u
r
r
e
nt
r
ip
p
l
e
be
c
o
me
s
0.
1
6
A
.
Th
is
i
s
beca
use
when
t
he
c
a
p
ac
it
a
n
ce
is
h
i
g
h,
t
h
e
ou
t
p
u
t
vol
ta
ge
r
ip
pl
e
i
s
r
ed
uc
e
d
.
Th
us,
the
f
unc
t
i
o
n
o
f
t
h
e
c
a
p
a
c
i
t
or
i
s
t
o
r
e
duce
the
o
u
t
p
u
t
v
o
ltage
r
ip
pl
e
a
s
show
n
i
n
F
i
gur
e
10(
b)
.
(a)
(b
)
F
i
gur
e
1
0
.
O
u
tpu
t
v
ol
t
a
ge
r
i
p
ple
w
i
th
o
u
t
p
u
t
capa
c
i
t
ance
(
a
)
4
7
0
µ
F
,
(
b
)
330
0
µ
F
0.
4
3
0.
1
6
0.
0
7
0.
01
0.0
9
0.
06
0.
45
0.
13
0.
05
0.
02
0.0
9
0.
0
5
0.
41
0.2
2
0.
09
0.0
1
0.
02
0.0
1
0.
4
4
0.
2
0
0.
0
8
0.
0
2
0.
02
0.
01
0.
00
0.
10
0.
20
0.
30
0.
40
0.
50
0.
60
135
79
1
1
C
u
rr
ent
Sourc
e
, I
s
Ha
rm
on
ic
s,
n
th
10kHz,
4
7
0
u
F
, 48.0%
10kHz,
2
4
0
0
u
F
, 40.6
%
50kHz,
4
7
0
u
F
, 66.1%
50kHz,
2
4
0
0
u
F
, 56.9
%
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Optimiz
a
tion of PFC c
u
k
conve
r
te
r
par
a
meters de
sign for
mi
nimiz
a
t
i
on of T
H
D
and ... (M.
A
.
Z. A. Rashid)
52
1
4.
CONCL
U
S
ION
Th
is
p
aper
h
a
s
p
re
se
nt
e
d
t
he
o
p
t
i
m
iza
t
i
o
n
of
P
F
C
C
u
k
c
on
ver
t
e
r
paramet
e
rs
d
esign
for
the
minim
i
z
a
t
i
on
o
f
t
he
T
H
D
cur
r
ent
ri
pp
l
e
a
n
d
t
he
o
u
t
pu
t
v
o
lta
ge
r
i
p
ple.
A
p
rot
o
ty
pe
o
f
t
h
e
P
F
C
Cu
k
c
o
nv
e
r
ter
with
o
p
tim
iz
ed
p
ar
am
eters
ha
s
bee
n
p
r
o
p
o
se
d
an
d
e
x
pe
r
i
me
nta
l
l
y
c
o
nfir
m
e
d.
T
he
e
x
p
e
r
ime
n
t
a
l
resu
lt
s
ha
ve
show
n
a
g
o
o
d
a
gre
e
m
e
nt
w
ith
t
he
d
e
s
i
gne
d
para
me
te
rs.
The
TH
D
cu
r
r
ent
i
s
4
.5%
a
f
ter
pa
r
a
m
e
ters
op
tim
iza
t
i
o
n.
S
atisfac
tio
n
o
f
I
EC
6
1
0
00-3-
2
l
e
ss
t
h
a
n
5
%
re
qui
r
em
en
t
h
a
ve
b
ee
n
a
c
h
i
e
v
ed
b
y
b
a
la
nc
i
ng
the
ene
r
g
y
c
om
pe
nsa
t
i
o
n
o
f
p
ass
i
ve
e
l
e
me
n
t
s.
M
ore
ove
r,
t
he
o
u
t
pu
t
v
o
lta
g
e
r
ip
ple
7
V
i
s
r
e
duce
d
s
ig
n
i
fi
ca
ntl
y
w
ith
t
h
e
o
u
t
pu
t
freque
nc
y
is
t
w
o
t
i
m
es
o
f
t
h
e
li
ne
f
r
e
q
u
e
n
c
y
.
O
t
h
er
t
ha
n
tha
t
,
w
i
t
h
h
i
gher
p
o
w
e
r
fa
c
t
o
r
a
n
d
efficie
n
c
y
,
t
h
e
struc
t
ur
e
c
a
n
be
u
sed
to
m
o
s
t
of
t
he
c
ons
u
m
er
e
lec
t
r
o
n
i
c
ap
pl
ia
nce
s
.
T
h
i
s
t
o
p
o
l
ogy
u
s
es
t
he
com
b
i
n
a
t
i
o
n
o
f
f
u
ll-br
idge
r
e
c
tif
i
e
r
and
C
uk
c
o
n
v
e
r
ter
s
t
r
u
c
t
ur
e
s
w
i
t
h
s
i
ngl
e
-
swi
t
c
h
(M
OS
F
ET).
A
h
i
gh
pow
er
fa
c
t
o
r c
a
n
be a
chi
e
ve
d
by a
p
p
l
yi
n
g
a
pp
r
opria
te
P
WM
s
w
i
tc
h
in
g sc
hem
e
s.
ACKNOW
LEDG
E
MEN
T
S
The
a
u
t
h
ors
w
oul
d
l
i
ke
t
o
sh
ow
g
ra
ti
tu
de
t
o
U
n
ive
r
sit
i
T
u
n
H
uss
e
i
n
O
n
n
Ma
lays
ia
(
U
T
H
M
)
for
the
fi
na
nc
i
a
l
su
ppo
r
t
by TIE
R
1
V
ot U
8
58.
REFE
RENCES
[1]
A.
B
in
P
o
nni
ran
et
a
l.
,
“
F
un
dament
al
O
p
e
rat
i
o
n
o
f
M
a
rx
T
opology
f
o
r
H
i
g
h
B
o
o
s
t
R
a
t
i
o
D
C
-
D
C
C
o
n
v
e
r
t
e
r
,
”
IE
E
J
J.
In
d. A
ppl
.,
vol.
5,
no.
4
,
p
p
.
329–
33
8,
201
6.
[2]
A
.
B
i
n
P
o
n
n
i
r
a
n
,
S
.
M
e
m
b
e
r
,
K
.
O
r
i
k
a
w
a
,
a
n
d
M
.
J
u
n
-
i
c
h
i
I
t
o
h
,
“
Minimizat
ion
of
P
as
siv
e
C
omp
onen
t
s
in
M
ulti-
lev
e
l
Fl
y
i
ng
Cap
acit
o
r
D
C
-DC
Co
nv
e
r
t
e
r,
”
IEE
J
J. Ind. App
l
., vo
l
. 5
, n
o.
1,
p
p
.
10
–1
1, 2
01
5.
[3]
H.
T
.
Y
a
ng
and
H
.
W
.
Ch
i
a
ng,
“
Im
pl
em
en
t
a
tion
of
b
ri
dg
e
l
ess
Cu
k
po
wer
fact
or
c
orrecto
r
w
ith
po
sitiv
e
o
ut
put
vo
lt
age,”
in
20
14
In
tern
at
io
nal
Power
E
l
ectr
o
n
i
cs
Con
f
er
ence
(
I
PEC-H
i
ro
shim
a 2
0
1
4
- E
C
CE
A
S
IA)
,
2
014
,
pp
.
2
100
–2
10
7.
[4]
A
.
P
onn
iran
,
K.
O
rik
a
wa,
an
d
J
.
I
to
h,
“
F
u
nd
ame
n
tal
Op
e
r
atio
n
o
f
M
a
rx
T
o
polo
g
y
f
o
r
Hi
gh
B
o
o
st
R
atio
D
C-DC
Converter,
”
IE
EJ J. Ind.
A
ppl
.
,
v
ol.
5
,
no
. 4
,
p
p
. 3
29
–3
38
, 20
1
6
.
[5]
A
.
B
i
n
P
o
n
n
i
r
a
n
,
K
.
O
r
i
k
a
w
a
,
a
n
d
J
.
I
t
o
h
,
“
M
i
n
i
m
i
z
a
t
i
o
n
o
f
P
a
s
s
iv
e
Com
p
o
n
ents
i
n
Mu
lti-l
e
vel
F
l
y
i
ng
C
ap
acit
o
r
DC-D
C
Convert
e
r,”
IE
EJ J.
Ind
.
A
ppl
.,
v
o
l
. 5
, no
.
1
, pp
.
1
0–
1
1
, 20
1
6
.
[6]
H.
T
.
Y
a
ng,
H
.
W
.
C
hian
g,
a
nd
C
.
Y.
C
hen
,
“
Im
p
l
e
m
ent
a
ti
on
o
f
Br
id
ge
l
e
ss
Cuk
P
o
wer
F
a
c
t
or
C
orrecto
r
W
ith
Posi
tive
Ou
t
put Voltage,”
IE
E
E
Tr
ans
.
Ind
.
Appl
.
, vo
l
.
51
,
no
. 4
,
p
p
. 3
32
5–
33
3
3
,
2
0
1
5
.
[7]
T. Babasak
i, T. Tanak
a
, Y
.
No
zak
i
,
T
.
Aok
i
,
and
F. Ku
r
ok
awa,
“
D
ev
elo
p
in
g of
hig
her v
o
lt
age direct
-current
po
w
er
-
f
eedi
ng
p
r
ot
o
t
yp
e
s
y
s
t
em,
”
i
n
T
e
leco
mmu
ni
cations E
n
er
gy Con
f
er
ence
,
20
0
9
.
INTELEC
2
00
9.
3
1st
I
n
te
rna
t
io
n
a
l,
p
p
. 1–
5
, 2
00
9.
[8]
F
.
G
oetzi
n
g
e
r,
T
.
Li
lj
a
,
a
nd
M
.
Gerl
ach,
“E
ne
rg
y
m
a
n
a
gem
e
nt
s
ys
t
e
ms
i
n
t
h
e
n
e
w
d
a
tacom
w
o
rl
d
,
”
i
n
2
001
Tw
enty-T
hir
d
Inter
n
a
t
io
nal
T
e
l
ecom
m
un
ica
t
i
ons
E
n
erg
y
Con
f
er
e
n
ce INT
E
LE
C 2
0
01
,
p
p
.
5
82
–586,
2
0
0
1
.
[9]
A
.
N
.
K
.
a
n
d
A
.
P
.
a
n
d
M
.
A
.
H
.
a
n
d
H
.
H
.
H
a
m
z
a
h
,
“
A
S
t
u
d
y
o
f
4
-l
evel
D
C-DC
B
oo
st
I
nv
erter
w
i
t
h
P
as
s
i
v
e
Com
p
o
n
en
t
Reduct
i
on
C
onsi
d
era
t
ion,
”
J. Ph
ys. Co
nf
. S
e
r
.,
v
o
l
.
9
9
5
,
n
o.
1
,
p
.
1
2062,
2
0
1
8
.
[10]
A.
B
.
P
o
nniran
an
d
M
.
A
.
N
.
B
.
Kasi
ran,
“
P
a
ram
e
ters
d
esign
e
v
al
u
a
ti
on
in
3
-l
evel
f
l
y
i
ng
ca
p
acit
o
r
bo
os
t
con
v
erter,
”
in
2
0
1
7
IEEE
Sym
p
o
s
i
u
m
on Com
p
u
t
er
Appl
icati
o
n
s
&
Indu
st
ri
a
l
El
ectr
o
n
i
cs (
I
SCA
I
E)
,
pp
.
1
95–
19
9,
2017.
[11]
M
.
H
.
Y
a
t
i
m
e
t
a
l
.
,
“
S
y
m
m
e
t
r
i
c
a
l
a
n
d
a
s
y
m
m
e
t
r
i
c
a
l
m
u
l
t
i
l
e
v
e
l
i
n
v
e
rter
s
t
r
uct
u
res
w
i
t
h
r
edu
ced
n
u
m
ber
of
sw
it
chin
g
d
e
vi
ces,”
In
do
nes
i
an Jou
r
n
a
l
o
f
Electr
i
cal En
g
i
ngeeri
ng
and
Co
m
p
u
t
er
Sc
i
e
n
c
e
,
v
o
l
.
1
1
,
n
o
.
1
,
pp
.
1
44–
15
1,
2018.
[12]
M
.
S
.
Ali,
S
.
K
.
K
amaru
d
i
n
,
M
.
S
.
M
a
sd
ar,
a
n
d
A.
M
oh
am
ed,
“An
O
vervi
e
w
o
f
P
ower
E
l
ectro
nics
A
pp
li
ca
t
i
o
n
s
in
F
u
el
Cell S
y
ste
m
s
:
D
C
and
A
C
Co
nvert
ers,”
Sci.
W
o
rl
d
J
.,
vol.
2
0
14,
p
p
.
1
–9,
2014
.
[13]
E.
H
. I
sma
il,
“
Br
i
dgel
e
ss
S
EPIC
R
ect
ifier
With U
nity
P
ower
F
act
or
a
n
d
R
e
d
uc
e
d
Con
du
c
t
io
n
Los
s
e
s
,”
IEEE Tr
ans.
Ind
.
El
ectr
o
n
.
,
vol
.
5
6
,
n
o
.
4
,
pp.
11
4
7
–
1
157
,
2
009.
[14]
R.
B
al
am
uru
g
an,
S
.
H
ari
p
rasat
h
,
an
d
R.
N
it
hya,
“
P
ow
er
F
act
or
C
o
rrecti
o
n
u
s
in
g
Val
l
ey
-Fill
SE
P
I
C
T
opo
lo
gy
w
ith
Fu
z
z
y
L
og
ic
C
on
tr
ol
,
”
TELK
OM
NIKA
,
Ind
o
n
e
si
a
n
Jou
r
n
a
l
o
f
Ele
c
t
r
i
c
a
l
En
gi
ng
ee
ri
ng an
d Com
p
u
t
er Sci
e
nce
,
v
o
l.
12
,
n
o.
1
1,
p
p
.
7622
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63
0,
2
01
4.
[15]
A.
P
rud
e
nzi,
U
.
G
r
assel
l
i,
a
n
d
R
.
L
a
m
e
dica,
“
IEC
Std
.
6
10
00
-3-2
h
arm
o
nic
curren
t
e
m
i
ss
io
n
limi
ts
i
n
practi
c
al
sy
st
e
m
s:
n
eed
o
f
con
s
i
d
erin
g
l
o
ad
in
g
l
e
vel
and
atten
u
at
ion
e
f
f
e
cts,”
in
2
0
0
1
Power E
n
g
i
neer
in
g
S
o
ci
ety Su
mm
er
M
eet
ing
.
C
o
n
f
e
rence
Pro
c
e
e
di
ngs
(
Cat.
N
o.
01
CH37
26
2),
200
1,
v
o
l
.
1,
p
p.
2
77
–2
8
2
vo
l
.
1
.
,
2
00
1
.
[16]
Y.
I
shizuka,
S
.
Nagat
a
,
M.
T
a
k
as
ak
i,
a
nd
T
.
Hiro
se,
“S
ta
t
i
c
Ch
a
racteri
s
t
i
c
Analys
is
o
f
P
r
op
o
s
ed
B
i-Directi
o
n
a
l
Du
al A
c
t
i
v
e Bridge
D
C-DC Co
n
v
e
rter,”
IE
EJ
J.
Ind.
Ap
pl
.
,
v
ol.
4
,
n
o
.
5
,
pp.
6
02
–610,
2
0
1
5
.
[17]
A
.
B
a
k
a
r
,
W
.
M
u
l
y
o
U
t
o
m
o
,
T
.
T
a
u
f
i
k
,
S
.
A
i
z
a
m
,
a
n
d
Y
.
m
.
Y
.
B
u
s
wi
g
,
"
Des
i
g
n
o
f
A
n
al
og
t
o
D
ig
i
t
a
l
C
onv
erter
f
o
r D
C
to
DC
B
oos
t
Co
nv
erter w
i
t
h
C
o
n
st
ant
Ou
tp
ut
V
olt
a
ge".
2
0
1
4.
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