In
te
r
n
ation
a
l Jou
rn
al
of Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJPED
S
)
V
o
l.
11, N
o
.
1, Mar
c
h 20
20,
p
p
.
367~
3
7
3
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
3
67-
37
3
3
67
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Voltage tracking of bri
d
geless PFC Cuk
converter
usi
n
g PI contr
o
ller
W. M
.
Utomo
1
,
N.
A.
A
.
I
s
a
2
,
A. A.
Bak
a
r
3
,
A.
F.
H.
A.
G
a
n
i
4
, B.
E. Pr
asetyo
5
, H
.
E
l
m
u
n
s
y
a
h
5
, Y. M.
Y
Bu
sw
ig
7
1
,
2,
3,
4
Dep
a
rt
m
e
nt
of
E
l
ectri
cal P
o
wer E
ngineeri
n
g
(JEK), F
acu
lt
y
o
f
El
ectri
ca
l an
d Electro
ni
cs
E
ngin
e
eri
n
g
(FKEE),
Un
iv
e
r
s
i
t
i
Tu
n
H
u
s
s
e
in
On
n
M
a
l
a
ys
ia
,
M
a
l
a
ys
ia
5
D
e
p
a
rtm
e
n
t
o
f
El
ectrical
En
gi
n
eeri
ng,
P
o
lit
eknik
Negeri
M
a
lan
g
,
In
do
nesia.
6
D
e
p
a
rtm
e
n
t
o
f
El
ectri
ca
l
E
ngi
n
eeri
n
g
,
Univ
ersitas
Negeri
M
a
lan
g
, In
do
nesia.
7
D
e
p
a
rt
men
t
Elect
rical
and
El
ectron
i
c
E
ngin
eeri
n
g
,
F
aculty
o
f
E
n
g
i
ne
e
r
ing
,
Un
iv
e
r
sit
i
Ma
la
ys
ia
S
a
ra
wa
k,
Ma
la
ysi
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
S
e
p 8,
201
9
Re
vise
d N
ov
1
4
,
201
9
A
c
c
e
pte
d
D
ec
7, 201
9
Th
is
pap
e
r pro
p
os
es a
Pro
p
o
r
ti
o
n
al-Int
e
gral
(PI)
cont
rol vo
lt
age t
r
ac
k
i
n
g
of
Brid
geles
s
P
o
we
r F
acto
r
Correcti
o
n
(B
P
F
C)
Cu
k
co
nv
erter.
In ord
e
r to
in
ves
t
i
g
ate
t
h
e
b
e
hav
i
ou
r of diff
erent
outp
u
t
vo
ltag
e
s d
u
ri
ng overs
ho
ot,
st
eady
st
ate
and
s
t
ep resp
on
s
e
, P.I
con
t
roll
er
is
d
e
si
gn
ed
t
o
set
t
h
e
-42
V,
-48
V,
-54
V ou
tp
u
t
voltag
e
s.
The sim
u
lation resu
lt
s s
how
th
at
t
h
e prop
osed
P
I
con
t
ro
ller
abl
e
to
cont
ro
l t
h
e
outp
u
t
vo
lt
age
and achi
e
ve
f
a
s
t
st
ea
dy
state
and
st
ep resp
ons
e
of BP
F
C
Cuk
co
nv
e
r
t
e
r.
W
h
en
the valu
e
o
f
o
u
tpu
t
voltag
e
in
crease, th
e
o
v
ers
h
o
o
t v
o
ltage will
becom
e
hi
gh
er
b
u
t
t
h
e steady
s
t
ate
resp
on
d will b
e
f
a
ster.
F
u
rt
hermore,
BP
F
C
Cu
k
con
v
erter wi
th
P.
I
co
nt
ro
ll
er
h
a
ve
low ou
tp
ut
vo
lta
g
e
r
i
p
p
le
s.
K
eyw
ord
s
:
Br
idge
l
e
ss
Powe
r fac
t
or
cor
r
ec
t
i
on
Cuk co
n
v
er
t
e
r
Control sys
t
em
P
r
op
or
tio
na
l-I
n
t
e
gral
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:
Wa
hy
u M
u
ly
o U
t
om
o,
Depa
rtem
ent
o
f
Electr
i
c
a
l
a
n
d Electro
n
i
c En
gine
eri
n
g,
U
n
i
v
ersi
ti
T
un H
u
ssei
n
O
nn
Ma
lays
ia,
86
4
00, P
a
r
i
t Raja
,
Joh
o
r,
Ma
l
a
ysia
.
Em
ail: w
a
hy
u
@
u
t
hm.
e
du.my
1.
I
N
TR
OD
U
C
TI
O
N
Po
we
r el
ec
t
r
o
n
i
c
e
q
ui
p
m
ent
wi
th
an
ac
t
i
v
e p
o
w
er
f
a
ct
o
r
co
rrec
t
io
n
(PFC
)
f
o
r
t
e
l
e
co
m,
d
a
t
aco
m,
a
n
d
aut
o
m
o
ti
ve e
l
e
c
trica
l
sys
t
em
are
becom
i
n
g
nece
ssa
r
y n
o
w
a
da
y
s
[1-5].
There
are
se
vera
l type
s
of DC
-
D
C
BP
F
C
con
v
e
r
t
e
rs w
e
re
de
v
e
l
ope
d for P
F
C
app
l
ica
t
i
o
ns
su
c
h
as boost,
buck, buc
k-b
o
o
s
t,
S
E
P
I
C a
nd Cu
k
con
v
er
t
e
rs [6]
.
H
o
w
e
ver
,
for low
pow
e
r
a
ppl
ica
t
i
o
n,
BP
F
C
Cu
k co
nv
er
t
e
r is the
mos
t
re
l
i
a
b
l
e
c
o
nve
r
t
er
bec
a
u
s
e i
t
offe
rs low
TH
D
of in
pu
t cur
r
en
t,
go
od
p
o
w
e
r
fac
t
or
, e
a
sy t
o
i
m
ple
m
e
n
t
in tra
n
sform
e
r
i
s
ol
ati
o
n,
and
nat
u
ra
l
prote
c
t
i
o
n a
g
a
i
n
s
t i
n
rus
h
c
u
rre
nt
fr
om start-u
p
or o
v
e
r
l
o
a
d
curre
nt
[
7
-1
1].
This c
o
nver
t
e
r
ac
t
s
si
m
i
lar to t
h
e
buc
k-b
o
o
st c
o
nver
t
e
r
since
it
a
b
l
e
t
o
ste
p
u
p
an
d
ste
p
-
d
o
w
n the o
u
t
p
u
t
vol
tage
by co
n
t
ro
ll
in
g
the d
u
t
y c
y
c
l
e
[1
1,
12]
Bas
i
ca
ll
y,
the D
C
-D
C c
o
n
v
e
r
ter
used pow
e
r
semicon
duc
tor
device
s
t
h
a
t
opera
ted a
s
the
e
l
e
c
tron
ic
sw
it
c
h
es w
h
ic
h a
r
e
refer a
s
sw
itc
he
d m
ode pow
e
r
sup
p
l
y
[S
M
P
S
]
[13,
14].
The ope
rati
o
n
of th
is sw
it
c
h
i
n
g
dev
i
ce
s m
a
y ca
use
i
nher
e
nt
ly
n
o
n
l
i
ne
ar cha
r
ac
teris
t
i
c
of
t
h
e BP
F
C
Cu
k con
v
e
r
t
e
r [15].
P
u
lse
w
i
dth
mo
d
u
l
a
t
i
on
(PWM
) i
s
t
h
e
mo
st
p
opu
l
a
r
me
t
hod
fo
r
th
e
v
a
ri
ou
s
swi
t
c
hi
n
g
t
e
c
hni
qu
e
[1
5
,
1
6
]. Swi
t
c
h
-
mo
d
e
P
W
M
dc
–dc
con
v
erte
rs use
d
to
pr
ov
ide
a c
o
ns
t
a
nt
out
pu
t v
o
l
t
a
ge
[17]
. P
r
o
por
ti
o
n
a
l
-In
teg
r
a
l
(P
I)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
n
t
J
P
o
w
Elec
& Dr
i
S
y
st V
o
l.
11,
N
o
.
1, Ma
r 202
0
:
367
–
37
3
36
8
con
t
ro
l
l
er ofte
n to
use a
s
th
e c
o
n
t
r
o
l
me
tho
d
f
o
r P
W
M sw
itch
i
ng
d
u
e
to t
h
e
sim
p
le
desi
gn a
nd
easy t
o
implem
e
n
t [18,
1
9
]
.
The
pr
op
ose
d
sys
t
em
brid
ge
l
e
ss P
F
C Cu
k con
v
erte
r is s
h
o
w
n in F
i
g
u
re 1
w
h
er
e, a
sing
l
e
MO
S
F
ET
sw
it
c
h
r
e
p
l
aci
ng
t
h
e
tw
o
M
O
SF
ETs, w
h
ich he
lp
s t
o
r
e
d
u
ce
h
i
gh c
o
n
d
u
ct
ion
l
o
ss an
d size
of
the str
u
c
t
ure
[2
0, 21]
. In
this c
a
se,
the
struc
t
ur
e prop
ose
d
to reduc
e
t
h
e
com
p
l
e
x
i
t
y
of c
ontro
l
l
e
r
c
i
rcui
t. Basical
l
y
,
bri
dge
less P
F
C
struc
t
ure
suffe
r from the
diffic
u
l
t
y of
implem
en
ta
ti
on
of c
ont
r
o
l
circ
uit
beca
u
s
e of tw
o
sw
it
c
h
es. N
e
verthe
le
ss,
t
h
is s
t
r
u
ct
ure c
a
n re
duce c
o
nduc
tio
n
losse
s
form
brid
ge
less. In th
i
s
paper
,
the o
u
t
p
u
t
vo
lta
ge w
a
s sel
e
cted
to
-42 a
n
d -54
V
for
t
h
e
ele
c
tric
ve
hic
l
e
appl
i
c
a
t
io
n [22-
24]
.
M
e
an
w
h
i
l
e -
48 V
i
s
use
d
in
telec
o
m
m
u
n
i
c
a
t
i
on app
l
ica
t
i
o
n[7, 25].
The
re
ma
i
nde
r of thi
s
st
u
d
y
is orga
n
i
z
e
d
a
s
fol
l
ow
s: op
e
r
ati
on of BP
F
C
C
uk
co
nv
erte
r
w
ill b
e
show
n in section II
. Then the par
a
m
e
ter
design for
P
F
C
converter is present
e
d in sect
ion III.
S
ection IV
descr
i
be
a
b
out
th
e
P
.
I
c
o
n
t
r
o
l
l
er
for
BP
F
C
Cu
k con
v
e
r
t
e
r.
S
i
m
u
la
ti
o
n
re
su
l
t
an
d
a
n
al
ys
i
s
in sec
tio
n V
,
fo
l
l
ow
e
d
by
co
ncl
u
s
i
on
i
n
sec
t
i
o
n V
I
.
2.
OPE
R
A
T
ION
OF BPFC CUK
CONVE
R
T
ER
The
pr
o
pose
d
BP
F
C
Cu
k
str
u
ct
ure
a
s
show
n in F
i
gure
1
.
Whe
n
t
h
e M
O
S
F
ET
M
is turne
d
-
on d
u
r
i
n
g
pos
it
ive cyc
l
e,
D
p
, D
1
are on-state an
d
D
ou
t
is
off-state as shown in
F
i
gure 2. There
are
tw
o mode
s for
this
ope
r
a
ti
on. For the first
m
ode,
th
e ind
u
ct
ors
L
1
and
L
2
are
cha
r
g
i
ng.
Meanwh
ile,
t
h
e
capa
c
i
t
o
r
C
1
an
d ca
paci
t
o
r
C
2
a
r
e
di
sc
harg
i
ng.
The
n
out
p
u
t in
duc
t
o
r
L
o
is char
gin
g
and capa
c
i
tor
C
out
is disc
har
g
i
n
g. In
mode
2 condi
tio
n, ca
paci
t
o
r
C
1
an
d ca
paci
t
o
r
C
2
are c
h
argin
g
thro
ug
h
in
duc
t
o
r
s
L
1
and
L
1
.
T
h
e
n
,
the in
d
u
ct
or
L
ou
t
rechar
ges
t
h
e capa
c
i
t
o
r
C
out
.
Whe
n
the
MO
S
F
ET
M is
turned-
on
d
u
ri
ng ne
ga
t
i
ve
c
y
c
l
e,
D
n
, D
2
opera
te i
n
on-sta
t
e an
d D
out
is off-
st
a
t
e
a
s
show
n in F
i
g
u
re 3. There
a
r
e
tw
o
m
o
des for thi
s
op
e
r
ati
on. F
i
rst, t
h
e
in
d
u
c
t
ors
L
1
and
L
2
a
r
e ch
a
r
g
i
n
g
,
the ca
p
a
c
i
t
o
r
C
1
a
nd ca
pa
c
i
t
o
r
C
2
a
r
e disc
har
g
i
n
g,
t
h
e
o
u
t
p
ut
i
n
d
u
c
t
or
L
o
is
c
h
ar
gi
n
g
and ca
paci
t
o
r
C
ou
t
is
di
sc
harg
i
ng. F
o
r the ne
x
t
co
nd
iti
o
n
, c
a
pac
i
t
o
r
C
1
a
n
d ca
p
acit
o
r
C
2
are
c
h
a
r
gi
ng
t
h
ro
ugh
i
n
du
ct
o
r
s
L
1
a
nd
L
1
.
Th
en
, t
h
e
i
nduc
t
o
r
L
ou
t
re
charges t
h
e
ca
p
a
ci
t
o
r
C
out and
p
o
w
e
r supp
lie
d to the
load.
Whe
n
t
h
e
MO
SF
ET M is tur
n
e
d
-
o
ff, D
p
, D
1
are
o
f
f
-
st
a
t
e an
d
D
out
is
on-s
t
ate
as show
n i
n
F
i
gure 4.
There
ar
e
fo
ur
co
n
d
i
tio
ns for
t
h
is
m
ode. In the fi
r
s
t c
o
n
d
i
t
i
on,
c
a
pac
itor
C
1
a
nd ca
paci
t
o
r
C
2
are char
gin
g
.
I
nduct
o
rs
L
1
a
nd
L
2
a
r
e d
i
sc
ha
rgi
ng.
Then,
the
ou
tp
u
t
i
n
d
u
c
t
or
L
out
is di
sc
har
g
i
n
g w
h
ile
,
ca
paci
t
o
r
C
o
is c
h
arg
i
n
g
an
d
t
h
e p
o
wer
is supp
l
i
ed
t
o
the lo
a
d
. For the secon
d
co
n
d
i
tio
n, in
d
u
ct
or
L
1
, in
duc
t
o
r
L
2
and ca
pac
i
t
o
r
C
2
are dischar
g
in
g.
Then,
ind
u
c
t
or
L
1
, inductor
L
2
a
n
d ca
p
a
ci
to
r
C
2
ar
e discha
rg
in
g, w
h
i
l
e
ca
paci
t
o
r
C
1
i
s
ch
a
r
g
i
ng
.
Ou
t
p
ut
in
du
ct
o
r
L
out
i
s
discha
r
g
i
ng an
d c
a
pa
ci
tor
C
ou
t
is cha
r
g
i
n
g
an
d the
p
o
w
er
i
s
sup
p
l
i
ed
t
o
th
e loa
d
.
F
o
r the
th
i
r
d co
n
d
i
t
ion,
i
n
d
u
c
t
or
L
1
, i
n
du
c
t
o
r
L
2
a
n
d
cap
aci
t
o
r
C
2
a
r
e
di
sc
hargi
n
g.
M
e
an
whi
l
e
ca
p
a
cit
o
r
C
1
i
s
c
h
arg
i
n
g
. The
n
, ca
pacit
o
r
C
out
is disc
harg
in
g thr
o
u
g
h
outp
u
t
ind
u
ct
or
L
ou
t
a
nd t
h
e
pow
er
is sup
p
l
ied to t
h
e lo
a
d
. For
the four
th
cond
i
tio
n,
c
a
pac
itor
C
1
and
c
a
p
ac
ito
r
C
2
a
r
e
d
i
s
c
h
a
rg
ing
t
h
ro
ugh
in
duc
t
o
r
s
L
1
.
Then,
L
2
are
cha
r
g
i
n
g
an
d o
u
t
p
ut
in
duc
t
o
r
L
out
rec
h
arg
e
s ca
p
a
ci
t
o
r
C
ou
t
.
The
n
, the
p
o
w
e
r is
su
pp
li
e
d
t
o
th
e
l
o
ad
.
When the
MO
SFET M is turned-off
,
D
n
, D
2
a
r
e
in off-
st
a
t
e whi
l
e D
out
i
s
on-s
t
ate
a
s
show
n i
n
F
i
gure
5.
Ther
e
are
four
m
odes a
t
th
i
s
c
o
n
d
i
t
i
o
n
.
F
i
rst,
ca
pacit
o
r
C
1
a
nd c
a
pa
ci
t
o
r
C
2
are
c
h
argi
n
g
, at
th
e sam
e
ti
m
e
in
d
u
ct
ors
L
1
and
L
2
a
r
e disc
har
g
in
g.
The
n
, the outp
u
t
i
n
d
u
ct
or
L
out
i
s
disc
har
g
i
n
g, ca
pac
i
t
o
r
C
o
is
cha
r
g
i
ng and t
h
e pow
er is
supp
l
i
ed to the loa
d
.
In the second mode
, ind
u
c
t
or
L
1
, inductor
L
2
a
nd c
a
pa
citor
C
2
are
di
sc
harg
in
g. The
n
,
indu
c
t
or
L
1
,
in
d
u
c
to
r
L
2
an
d
ca
p
a
cit
o
r
C
2
ar
e
dischar
g
i
ng
w
h
i
l
e
capa
c
i
t
o
r
C
1
is
cha
r
g
i
ng.
O
u
tp
ut i
n
d
u
c
t
or
L
ou
t
i
s
disc
har
g
i
n
g.
Capa
ci
tor
C
out
i
s
char
g
i
n
g
and
powe
r
i
s
sup
p
l
i
ed t
o
the loa
d
.
For
the t
h
ird m
o
d
e
,
induc
t
o
r
L
1
, inductor
L
2
and capa
c
i
tor
C
2
are
dischar
g
in
g,
but c
a
pa
c
i
t
o
r
C
1
is c
h
argi
ng.
M
e
an
whi
l
e
, ca
p
a
ci
to
r
C
ou
t
is d
i
sc
ha
rgi
n
g
thro
ug
h ou
t
p
ut
i
n
d
u
ct
or
L
out
and the
pow
er
is supp
l
i
e
d
t
o
the
l
o
ad.
In
the fo
urt
h
m
o
d
e
, capa
c
it
or
C
1
a
nd c
a
pa
ci
tor
C
2
are disc
har
g
i
n
g thro
ug
h i
nduc
to
r
s
L
1
.
Th
en
,
L
2
is in
c
h
ar
g
i
n
g
mode
. H
o
w
e
ve
r, i
n
d
u
c
t
or
L
out
re
c
h
arg
e
s t
h
e
cap
a
c
i
t
o
r
C
ou
t
.
and
t
h
e p
o
w
e
r is supp
lie
d to
t
h
e
loa
d
.
F
i
gure 1. BP
FC
c
u
k
struc
t
ure
V
DC
L
ou
t
C
ou
t
R
V
AC
D
p
D
n
M
L
2
L
1
C
1
C
2
D
1
D
2
D
ou
t
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
r
i
S
y
st
IS
S
N
:
2088-
86
94
Vo
l
t
a
g
e
tra
c
ki
ng o
f
br
i
dge
les
s
PFC C
u
k
con
v
e
r
t
e
r us
ing
PI c
ont
ro
l
l
er (
W
.
M. U
t
om
o)
3
69
F
i
gure 2. M
O
SF
E
T
turned-
o
n duri
ng
pos
i
t
i
ve
c
y
c
l
e
F
i
gure 3. M
O
S
F
ET turned-o
n
duri
ng
n
e
g
a
ti
v
e
cy
cl
e
F
i
gure
4.
MO
SF
ET turne
d
-
o
ff
duri
n
g
pos
i
t
i
ve
c
y
c
l
e
F
i
gure 5. MO
SF
ET
turned-
o
ff
dur
ing
n
e
g
a
ti
v
e
cy
cl
e
3.
PARAMETER
DESIGN F
O
R BPFC
CUK CONVERT
ER
3.1.
Volta
g
e conve
r
si
on
r
a
tio, M
The
v
o
l
ta
ge
co
nver
s
io
n ra
tio
M
=
V
o
/V
m
i
n
te
rm
s of circui
t
st
r
u
ct
ure pa
ra
m
e
ter
s
c
a
n be ob
ta
ine
d
b
y
app
l
yi
ng
th
e p
o
we
r-ba
l
a
n
c
i
n
g
pri
n
ci
p
l
e
where
P
in
=
P
AC
by
assumi
ng
a l
o
ss
l
e
ss co
nve
r
t
e
r
.
⋅
(1
)
Th
e av
e
r
ag
e AC
sup
p
ly
cu
rre
n
t
i
s
g
i
v
e
n
a
s
(
2
),
(2
)
Where
t
h
e
R
e
is define
d as
t
h
e
e
ffe
ct
ive
in
p
u
t re
sis
t
a
n
ce
of
the c
o
n
v
erter
a
n
d
g
i
ven b
y
(3)
⋅
⋅
(3
)
The
D
to
n
is the
sum
m
a
t
i
on o
f
D
1T
s
and
D
2
T
s
. O
n
t
h
e
othe
r han
d
, the a
v
era
g
e ou
t
put c
u
r
r
ent of d
i
o
d
e
dur
in
g o
n
e-
l
i
ne
cyc
l
e
is e
qua
l
to t
h
e
aver
age
curr
ent,
I
o
thro
ug
h
to
the l
o
a
d
,
R
(4
)
Th
us,
it can
be
simpl
i
fie
d
b
y
eval
ua
t
i
n
g
(2) by usi
n
g (3) and ap
pl
y
i
n
g
t
h
e
pow
e
r-ba
l
a
n
c
i
ng be
t
w
ee
n
the A
C
su
p
p
l
y
a
nd D
C
o
u
t
p
u
t
,
the
vo
lta
ge
c
o
nvers
io
n ra
t
i
o
is
equa
l to
:
√
⋅
⋅
⋅
(5
)
3.2.
Gain
rat
i
o
as fu
n
c
tion
of
d
u
t
y cyc
l
e
,
D
D
C
M o
p
e
r
a
t
i
o
n mode
re
qu
ires th
a
t
the su
m
of
dut
y cyc
l
e a
nd
t
h
e n
o
rm
alize
d
MO
S
F
ET-off tim
e
len
g
t
h t
o
be
les
s
tha
n
one.
F
o
l
l
ow
i
n
g
ine
q
ua
l
ity
must be
sa
ti
sfie
d
:
1
(6
)
V
DC
L
ou
t
C
ou
t
R
V
AC
D
p
D
n
M
L
2
L
1
C
1
C
2
D
1
D
2
D
ou
t
L
ou
t
C
ou
t
R
V
AC
D
p
D
n
M
L
2
L
1
C
1
C
2
D
1
D
2
V
DC
D
ou
t
V
DC
L
out
C
out
R
V
AC
D
p
D
n
M
L
2
L
1
C
1
C
2
D
1
D
2
D
out
V
DC
L
ou
t
C
out
R
V
AC
D
p
D
n
M
L
2
L
1
C
1
C
2
D
1
D
2
D
out
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IS
S
N
: 208
8-
869
4
I
n
t
J
P
o
w
Elec
& Dr
i
S
y
st V
o
l.
11,
N
o
.
1, Ma
r 202
0
:
367
–
37
3
37
0
Wh
e
r
e t
h
e
D
toff
is the summa
t
i
o
n
of
D
3
T
s
a
nd
D
4
T
s
.
The w
o
rst si
t
u
a
t
i
on occ
u
rs at
ω
t
=
90
o
.
There
f
ore
,
t
o
opera
t
e
i
n
D
C
M
ope
rat
i
o
n
(7
)
3.3.
D
e
sign
of in
pu
t in
d
u
c
t
or
L
1
an
d
L
2
The
i
n
p
u
t
in
du
c
t
ance
is
ca
lcu
l
ated by us
ing ind
u
c
t
or
cur
r
ent
r
i
pp
le:
√
⋅
⋅
⋅
⋅
(8
)
Th
e
ma
x
i
mu
m i
ndu
ct
o
r
c
u
rre
n
t
ri
pp
l
e
c
a
l
c
ul
a
t
ed
fro
m t
h
e
p
e
a
k
i
npu
t
cu
rre
nt
i
s
gi
v
e
n
by
(9
)
,
⋅
√
⋅
,
(9
)
B
y
subs
t
itu
ti
n
g
(9) int
o
(
10),
the
i
n
p
u
t i
n
duc
t
a
nc
e
L
1
c
a
n
b
e
ca
l
c
ul
at
ed
. No
t
e
d
t
h
at
, t
h
e
L
1
is e
qua
l t
o
L
2
, thus t
h
e
sam
e
form
ula c
a
n be
use
d
.
The
val
u
e
o
f
i
n
p
u
t i
n
d
u
c
t
anc
e
ca
n
be fo
u
n
d
as:
⋅
⋅
(1
0
)
3.4.
Desig
n
o
f
o
u
t
p
u
t
induct
o
r,
L
o
F
r
om (
1
),
the a
v
era
g
e
o
u
t
p
u
t
c
u
rre
nt
of
dio
d
e
,
I
Do
dur
i
n
g
one li
ne-
c
yc
le of t
h
e
A
C
sup
p
l
y
can b
e
deter
m
i
n
ed b
y
(11)
,
⋅
⋅
⋅
⋅
(1
1
)
K
e
is d
i
m
e
ns
ionle
s
s
para
me
t
e
r
a
r
e
defi
ne
d and
ca
n be
ex
pr
e
s
se
d b
y
(
12)
⋅
(1
2
)
Th
e av
e
r
ag
e ou
tpu
t
c
u
rre
n
t
i
s
t
h
e
a
v
era
g
e dio
d
e
cu
rrent
,
L
e
fr
om can be fo
un
d
b
y
(
13)
⋅
⋅
(1
3
)
The
r
ef
ore,
the ou
tpu
t
i
n
d
u
c
t
or can be d
e
term
ined
b
y
ap
pl
y
i
n
g
(10) and
(
13)
:
⋅
(1
4
)
3.5.
D
e
sign
of in
pu
t c
a
p
a
cit
o
r
,
C
1
and
C
2
The
in
pu
t ca
p
acit
o
r,
C
1
is a
n
im
p
o
rta
n
t c
o
m
p
o
n
e
n
t
in t
h
e C
u
k t
o
p
o
l
o
gy s
i
nce i
t
ma
y d
i
stor
t t
h
e
qua
l
ity o
f
A
C
su
p
p
l
y
c
u
rre
nt
.
The
C
1
must be
des
i
g
n
e
d
pr
oper
l
y by co
ns
ider
in
g
r
e
so
na
nt
fre
que
nc
y,
f
r
no
t
clo
s
e to l
i
ne
freque
n
c
y
f
L
and
sw
i
t
ch
i
n
g
fre
q
u
e
nc
y
f
sw
. Hence
,
the
ener
g
y
transfe
r
to ca
pac
i
t
o
r
C
1
is
d
e
t
e
rmin
e
d
b
a
se
d
on
i
ndu
c
t
ors
L
1
,
L
2
, and
L
o
val
u
es.
In ad
d
i
ti
o
n
, a
bette
r ini
t
ia
l
e
s
tim
ati
o
n for c
h
o
o
si
ng t
h
e
resona
nt
fr
eq
u
e
ncy,
f
r
is g
i
ve
n
by (15).
N
o
ted tha
t
, the
C
1
is e
qua
l to
C
2
w
h
ic
h
the
sa
me
form
u
l
a
c
a
n be
use
d
,
th
us the
de
sig
n
C
1
(16) i
s
:
(1
5
)
⋅
⋅
(1
6
)
3.6.
D
e
sign
of
ou
tp
ut cap
a
citor,
C
o
S
i
nce t
h
e
in
pu
t
of c
o
n
v
e
r
ter i
s
A
C
su
pp
ly,
the
o
u
t
pu
t c
a
pa
c
i
t
o
r m
u
st
be l
a
rge
eno
u
gh
t
o
reduc
e t
h
e
ou
tpu
t
v
o
l
t
a
g
e rip
p
le. Thus, t
h
e ou
t
p
u
t
r
i
p
p
l
e
fr
equenc
y
of
t
h
e
con
v
erte
r i
s
tw
o t
i
m
e
s of the in
pu
t
freq
u
enc
y
,
gi
ve
n in
(
15).
I
n
t
h
e
w
o
rst ca
se
, the out
pu
t
c
u
rre
nt
dur
in
g hal
f
-
p
eri
o
d of the rip
p
l
e fr
equenc
y i
s
prov
i
d
ed b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
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o
w
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c
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D
r
i
S
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IS
S
N
:
2088-
86
94
Vo
l
t
a
g
e
tra
c
ki
ng o
f
br
i
dge
les
s
PFC C
u
k
con
v
e
r
t
e
r us
ing
PI c
ont
ro
l
l
er (
W
.
M. U
t
om
o)
3
71
the
ou
tp
u
t
c
a
pac
i
tor.
The
r
efore,
the
ou
t
p
ut
v
o
l
t
a
ge
ripple
m
u
s
t
be
selec
t
e
d
ba
se
d
on
t
h
e
a
p
p
l
i
c
a
tio
n
re
q
u
i
r
emen
t
a
n
d
C
o
ca
n be
ob
ta
ine
d
a
s
fo
ll
ow
s:
2
(1
7
)
⋅
⋅
⋅
(1
8
)
4.
PI CONTRO
LLE
R
FO
R
BPFC CUK
C
O
N
V
E
R
TER
F
i
gure 6 il
lus
t
r
a
te the sim
u
l
a
tio
n d
i
agra
m of pro
p
o
s
ed
des
i
g
n
of P
.
I
c
o
n
t
ro
lle
r for BP
F
C
Cu
k
c
o
nv
e
r
t
e
r
by
usin
g
M
a
lt
ab
s
o
ft
ware. Th
e re
f
e
re
n
c
e
vo
l
t
a
ge
for P
.
I c
o
ntr
o
l
l
er
is set
t
o
-48V
w
ith
2/
5
0
ga
in
val
u
e.
The
va
l
u
e of P
is 1.
0
w
h
i
l
e t
h
e val
u
e of I is 3.
3
4
.
The o
u
tp
ut
of the
P
.
I
c
ont
r
o
l
i
s
a
pow
e
r
va
l
u
e
a
nd
i
n
order
to c
o
n
v
e
r
t it
to a
q
u
a
n
t
i
t
y
t
h
a
t
is c
o
m
p
ar
ab
le
to
tha
t
of
the
co
n
t
ro
l
sig
n
a
l
,
it
g
o
es
thro
u
gh
a
p
o
w
e
r
to
P
W
M
signa
l
con
v
e
r
ter.
F
i
gure
6.
S
i
m
u
lat
i
on
d
i
a
g
ram
of pro
p
o
se
d
BP
F
C
Cuk w
i
t
h
P
I
contro
l
l
e
r
5.
SIMU
L
A
TION RESULT
The
per
f
orm
a
n
c
e
of
BP
F
C
Cuk c
onve
r
t
er
i
s
verifie
d
by th
e sim
u
l
a
ti
on r
e
su
lt
s
by
using
M
A
TL
A
B
softw
a
re
.
The con
v
erte
r is de
si
gne
d
b
y
the
fol
l
ow
i
ng s
p
e
c
i
f
ica
tio
ns
:
-
Inp
u
t v
o
lta
ge,
V
AC =
23
0 V
-
Ou
tp
ut
vo
l
t
a
g
e
,
V
DC
=
-
42 V
,
-48
V
,
-54 V
-
Ou
tp
ut
po
we
r,
P
out
= 20
0
W
-
Swi
t
c
hi
ng
fre
qu
en
cy
,
f
sw
= 5
0
H
z
-
M
a
x
i
mu
m o
u
tp
ut
vo
lt
a
g
e
ri
pp
l
e
,
∆
V
out
=
˂
2V
F
i
gure 7
show
the cha
r
ac
t
e
ri
stic of BP
F
C
Cuk con
v
e
r
ter out
pu
t
vo
l
t
a
g
e w
ith P
.
I control
l
er
w
h
en th
e
refere
nce
vo
lta
ge
is set u
p
t
o
-42V
ou
t
p
u
t
v
o
l
t
a
g
e.
The re
sult sh
ow
s t
h
e P
.
I
contro
ller f
unc
t
i
o
n
a
l
w
e
ll
sinc
e
the
BP
F
C
Cu
k
c
o
n
v
erter
pro
duc
e -4
2
V
ou
tp
u
t
v
o
l
t
a
g
e b
y
fo
l
l
ow
in
g
t
h
e refere
nce vo
lt
a
g
e com
m
a
n
d. The
overs
ho
o
t
vo
l
t
a
ge i
s
-56
V
.
A
t
0.6 se
co
nds, the
sys
t
em
ac
hie
v
ed ste
a
d
y
sta
t
e con
d
iti
o
n
.
Whe
n
t
h
e r
e
fe
renc
e vo
lta
ge
for
P.I
contro
lle
r is se
t
to -48
V,
t
h
e
BPF
C
Cuk
co
n
v
er
t
e
r w
ill pro
d
u
c
e
-
48 V
ou
tpu
t
v
o
lta
ge
a
s
show
n
i
n
F
i
gure 8. The overs
ho
o
t
v
o
l
t
age is
-59 V
.
The stea
d
y
st
a
t
e
c
o
nd
iti
o
n
a
c
hie
v
e
d
at 0.
5 sec
o
nds.
F
i
gure 9 i
llus
t
rate
the
-54 V
outp
u
t
vo
l
t
a
g
e w
ith P.
I con
t
ro
ller.
The ov
ersho
o
t v
o
lta
g
e
is -
63 V
.
F
o
r
-54
V
out
p
u
t
v
o
l
t
a
ge,
the
sys
t
em
starts t
o
achie
ve
sta
b
i
lit
y a
t
0.41
sec
o
n
d
s (
F
igure
1
0
).
F
i
gure 1 show
the re
sul
t
for
t
h
e
out
put v
o
lta
ge r
i
p
p
le va
l
u
e
w
ith P
.
I c
o
n
t
ro
l
l
e
r
. A
s
i
n
c
r
ea
se the
ou
tpu
t
vo
l
t
a
g
e
,
the
ripp
le w
i
l
l
be
incre
a
se too.
P
.
I
contro
l
is func
t
i
o
n
i
n
g
w
e
ll in or
der t
o
reduc
e
the
ou
t
put
vo
lta
ge r
i
pp
les
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
I
n
t
J
P
o
w
Elec
& Dr
i
S
y
st V
o
l.
11,
N
o
.
1, Ma
r 202
0
:
367
–
37
3
37
2
F
i
gure 1
1
.
O
u
tpu
t
v
o
l
t
a
g
e rip
p
l
e
ve
rs
us o
u
tp
ut vo
lta
ge
6.
CONCL
U
S
ION
In
t
h
i
s
p
a
p
e
r,
a
p
r
o
p
o
r
ti
on
a
l
-i
n
t
eg
ra
l
c
o
nt
rol
f
o
r
b
r
i
d
g
e
l
e
ss
P
F
C
Cu
k
c
onve
rt
er i
s
d
i
s
c
u
ssed
.
Va
ri
o
u
s
ou
tpu
t
v
o
l
t
a
g
e
w
a
s set up t
o
obser
ve the
char
ac
t
e
ristic
of
ou
tp
u
t
vo
lta
ge
d
u
r
i
ng stead
y sta
t
e a
nd ste
p
respo
n
se.
The
pr
opose
d
de
si
g
n
o
f
P
.
I contro
l
l
er able
to
c
o
n
t
rol the
o
u
t
p
u
t
vo
lta
ge of BP
F
C
C
uk co
nve
r
t
er.
A
s
incre
a
se
t
h
e
o
u
t
p
ut vo
l
t
a
g
e val
u
e,
t
h
e o
v
ersho
o
t
v
o
lta
ge
w
ill inc
r
ea
se too
bu
t
the
s
t
ea
dy
s
t
a
t
e t
i
m
e
w
i
l
l
be
fa
ste
r
. F
u
rtherm
ore
,
the per
f
orm
a
nc
e of
BP
F
C
Cu
k co
n
v
e
r
t
e
r bec
o
me
be
tter si
nce
t
h
e
o
u
tp
ut
vo
l
t
a
g
e able
to
a
c
h
i
e
v
e
fa
st
st
ea
d
y
st
at
e
co
nd
i
t
i
o
n
.
Th
e ou
tp
ut
vol
t
a
g
e
ri
pp
l
e
s
a
r
e a
f
f
e
ct
ed
to
wa
rd
t
h
e
o
u
t
p
ut
vol
t
a
g
e
v
a
l
u
e
.
Howeve
r, the
P
.
I
con
t
rol
l
er able t
o
re
duce the
ou
t
p
u
t
v
o
lta
ge
r
i
p
p
les.
ACKNOW
LEDG
E
MEN
T
S
The
a
u
t
h
or
s wou
l
d
li
ke t
o
ex
pr
ess
the
i
r dee
p
es
t
a
pprec
i
a
ti
on to t
h
e M
i
n
i
st
r
y
of
H
i
gher
Educa
tio
n
(MO
H
E
) Ma
l
a
ysia
a
n
d U
n
iv
e
r
siti Tu
n H
u
s
s
e
i
n
O
n
n
Ma
la
ysia
for su
p
por
tin
g t
h
i
s
re
sear
ch un
der r
e
sea
r
ch
fu
n
d
U
T
H
M
by
usin
g G
e
ran P
e
nye
li
d
i
k
a
n P
a
scasisw
a
z
a
h (G
P
P
S
)
V
o
t. H
3
0
9
a
n
d
P
o
w
e
r
El
e
c
tro
n
i
c
Con
v
e
r
ters F
o
c
u
s G
r
oup (P
EC)
,
D
e
par
t
me
n
t
o
f
Elec
tric
a
l
P
o
w
e
r Engi
neer
ing,
F
a
c
u
lty o
f
Ele
c
t
rica
l and
Elec
tron
ic En
g
i
ne
er
in
g,
U
T
HM
t
o
unde
rta
k
e
this resea
r
ch a
c
t
i
v
i
t
y
.
REFE
RENCES
[1]
A. A.
Fardoun, E. H. I
s
m
a
il,
M. A
.
Al-S
a
f
f
a
r, an
d A
.
J. S
a
bzal
i, "New
‘real’
brid
gel
e
ss h
i
gh
e
fficien
cy A
C
-DC
con
v
erter,
"
in
Co
nf
erence
Pr
oceed
ing
s
- IEEE App
lied
Power
Elect
ron
i
cs
Co
n
f
erence
an
d
Exp
o
s
i
ti
on - APEC
, p
p
.
31
7-3
23,
20
12
.
20
m
V
25
m
V
30
m
V
0
5
10
15
20
25
30
35
‐
42
‐
48
‐
54
O
u
t
put
vol
t
a
g
e
r
i
ppl
e
(m
V
)
O
u
t
put
vol
t
a
g
e
(V
)
F
i
gur
e 7.
The
ou
t
p
u
t
v
o
lta
ge
ve
rsus t
i
m
e
w
a
ve
form
w
h
e
n
t
h
e
refere
nce
vo
lta
ge is
-
42V
F
i
gure
8. The ou
tpu
t
v
o
l
t
a
g
e versus
t
i
m
e
w
a
vef
o
rm w
h
en
the r
e
fe
renc
e
vol
ta
ge
is -48
V
F
i
gur
e 9.
The
ou
t
p
u
t
v
o
lta
ge
ve
rsus t
i
m
e
w
a
ve
form
w
h
e
n
t
h
e
refere
nce
vo
lta
ge is
-
54V
F
i
g
u
r
e
60.
The
out
p
u
t
v
o
l
t
a
ge
ve
rsus
ti
m
e
w
a
vef
o
rm
w
h
en
the r
e
fe
renc
e
vol
ta
ge
ste
p
-d
ow
n
fr
om -42
V
to
-54 V
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
r
i
S
y
st
IS
S
N
:
2088-
86
94
Vo
l
t
a
g
e
tra
c
ki
ng o
f
br
i
dge
les
s
PFC C
u
k
con
v
e
r
t
e
r us
ing
PI c
ont
ro
l
l
er (
W
.
M. U
t
om
o)
3
73
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H.
Nen
e
,
C.
Jiang,
and
S.
Ch
ou
d
h
ury,
"Cont
rol
for
li
gh
t
l
o
ad
e
f
f
i
ci
ency
and
TH
D
im
pro
v
em
ent
s
in
P
F
C
con
v
erter,
"
pp
.
1
785
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8
8
,
2
017
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[3]
B. Ma
ng
u a
n
d B
.
G
.
Fe
rn
a
n
d
e
s,
"
E
ffic
ie
nc
y
imp
r
ov
e
m
e
n
t o
f
so
la
r
-
wind
b
a
se
d du
a
l
-in
p
u
t
Cuk
-
SEP
I
C
c
o
nv
e
r
te
r
fo
r
te
le
c
o
m po
we
r
s
u
pp
ly
,"
IECON P
r
oc.
(
I
nd
u
s
tri
a
l
El
ectr
o
n
.
Conf.
,
pp
.
9
78-9
83,
2
0
1
2
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[4]
K.
C.
L
ee and
B.
H
.
Cho, "Lo
w
co
st
p
o
wer f
act
o
r
correcti
o
n
(P
FC) co
nvert
er u
s
in
g
del
a
y co
nt
rol,"
Powe
r
Convers.
Con
f
. - Naga
oka
19
97
,
P
r
oc
.
, v
o
l.
1(S
e
p
)
, pp
. 3
35-340
,
1
9
9
7
.
[5]
A.
Cocor, A. F
.
M
e
m
b
er,
A.
P
o
p
e
s
c
u,
D
.
St
oi
che
s
c
u
, an
d
S. Op
rea, "
Power su
pply b
l
o
cks with cúk a
n
d
self
- li
ft c
ú
k
con
verter
s
f
o
r
t
e
l
ecom
m
un
ica
t
i
o
n
s
i
tes
,
"
20
14.
[6]
H.
Z.
Azazi,
S
.
M
.
A
h
m
e
d
,
and
A
.
E.
Las
h
i
n
e, "Hi
gh po
we
r factor an
d reg
u
l
a
ted
ou
tp
ut
voltag
e
for th
re
e-p
h
as
e AC-
DC c
o
nv
erter
u
s
i
n
g
s
i
ngle-s
w
i
t
c
h
CUK
con
v
ert
e
r,
"
20
17
19
th In
t.
Mid
d
l
e
-Ea
s
t Po
wer S
y
st.
Co
n
f
. M
E
PCO
N
20
17 -
Proc.
,
pp.
43
-51
,
2
018
.
[7]
H. T.
Yang
,
H
.
W. Chiang,
and C. Y.
Ch
en,
"
I
mp
lem
e
nt
atio
n
o
f
brid
gel
e
ss cuk
p
o
wer
fact
or
c
o
rrecto
r
with po
si
tive
ou
tp
ut voltag
e
,
"
IEEE T
r
an
s.
In
d
.
Ap
pl.
, v
o
l.
51,
N
o
.
4
,
p
p
.
33
25-3
3
3
3
,
201
5.
[8]
D.
S
.
L
.
S
i
mo
ne
tti
,
J.
Se
ba
stia
n,
a
n
d
J.
Uc
e
d
a
,
"
T
h
e
d
i
scon
ti
nu
o
u
s
con
d
u
c
ti
on
m
o
d
e
sepi
c and
cu
k p
o
wer
f
act
o
r
prereg
ulat
ors
:
analy
s
is
and
d
e
s
i
gn,
"
IE
E
E
Tran
s
.
Ind. E
l
ect
ron.
, vol
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4
,
No.
5,
pp
. 63
0-6
3
7
,
19
97.
[9]
M
.
Brko
v
i
c and
S
.
Cuk
,
"Inp
ut
curren
t
s
h
aper u
s
i
n
g
cuk
con
v
erter,
"
[
P
r
o
ceedi
n
g
s
]
Fo
ur
teent
h
In
t.
Tel
ecom
m
un
.
En
ergy Conf.
- INT
E
L
E
C
’9
2
,
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39,
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92
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[10]
S
.
Rak
s
hit
an
d
J. M
a
it
y
,
"
F
u
zzy lo
gic con
t
ro
ll
ed
ć
uk
c
o
nv
e
r
te
r,
"
20
18
In
t.
Con
f
.
Co
mm
un
. Sig
n
a
l
Pr
ocess,
p
p
. 77
1
-
77
5,
20
18
.
[11]
A.
H
.
Ab
e
d
in and
A
.
Cho
udhury
,
"
In
pu
t
switch
ed si
ng
le phas
e
h
i
g
h
per
f
orm
ance
b
r
id
gel
e
ss
CÛ
K AC-DC
con
verter
," 2
0
1
2
.
[12]
M. K.
R
.
No
or
et al.
, "
O
ptim
i
z
atio
n o
f
PF
C
SEP
I
C con
v
erter param
e
ters
d
e
sign f
o
r
m
i
nim
i
zat
io
n
o
f
THD
and
vo
lt
age ri
ppl
e,"
Int
.
J. Eng
.
T
ech
no
l.
,
vo
l
.
7
,
N
o
.
1, p
p
.
24
0-24
5
,
2018.
[13]
W
.
M
.
Ut
om
o
,
S.
S.
Y
i
,
Y
.
M
.
Y.
B
u
s
w
i
g
,
Z
.
A
.
H
a
r
o
n,
A.
A.
Bak
a
r
,
a
n
d M
.
Z
.
Ah
m
a
d
,
“
V
ol
t
a
ge
t
r
a
c
k
i
n
g
of
a
D
C
-
DC f
l
yb
ack
con
v
erter
us
in
g n
e
u
r
al
n
e
two
r
k
con
t
rol
,
”
Inter
n
a
t
i
onal
Jou
r
n
a
l of P
o
wer
El
ectr
o
n
i
cs an
d
Drive
Syst
em
(I
J
P
E
D
S
)
,
vol.
2
,
N
o
.
1
,
pp
.
35
-4
2
,
20
12
.
[14]
W.
A. Y.
S
a
l
a
h an
d S
.
Ta
i
b
, "Im
p
ro
vem
e
nt o
f
tran
sf
orm
e
rl
e
s
s
200W
SMP
S
usi
n
g
CUK DC-D
C con
v
erter,
"
p
p
. 49
7
-
50
0,
20
06
.
[15]
I.
En
g
i
neerin
g,
"Com
p
a
ri
ti
ve
stud
y o
f
single phase p
o
wer f
acto
r
co
rrecti
on b
a
sed
o
n
f
i
x
e
d
an
d
variab
le
PWM
tech
niq
u
es
usin
g
b
r
id
gel
e
ss cuk c
o
n
v
erter,
"
p
p
.
290-29
5,
201
8.
[16]
B.
Ab
de
l
h
am
id,
L. Rad
hou
ane, an
d A.
Bilel, "
R
e
al
time im
plem
e
n
t
a
tion
o
f
pert
u
r
b a
nd o
b
s
e
rve a
l
go
rit
h
m
and PI
con
t
r
o
ll
er for DC/
D
C co
nver
ter
,
"
201
7.
[17]
Y.
Li
u
,
Y.
S
u
n
,
an
d M
.
S
u
,
"A c
o
nt
rol
m
e
th
od f
o
r
brid
gel
e
ss cuk
/
s
e
pi
c P
F
C
rectifier
to
achi
e
ve p
o
w
e
r deco
up
lin
g,
"
IEEE
Trans. Ind
.
Elect
ron
.
, Vo
l.
6
4
, No
. 9
,
p
p
.
72
72
-72
7
6
, 20
17
.
[18]
Y.
Jan
g
an
d M.
M
.
Jo
van
ovi
ć
,
"
A
n
e
w, so
ft-swit
c
he
d
,
high
-po
w
e
r-f
acto
r
b
oost
co
nv
erter w
i
t
h
IGBTs,"
IEEE Tr
a
n
s.
Po
wer E
l
ectr
o
n
.
,
vo
l. 17
,
No
.
4
,
p
p
. 4
6
9
-
47
6,
2
0
0
2
.
[19]
Z.
Chen,
"
P
I
a
n
d
sl
id
i
n
g
m
o
d
e
co
n
t
ro
l of
a cuk
convert
er,
"
vo
l. 2
7
,
No
. 8,
pp
. 3
6
9
5
-37
0
3
,
2
012
.
[20]
A.
J
.
S
a
bzal
i, E.
H.
Ism
a
i
l
,
M
.
A
.
Al
-S
a
f
f
a
r,
and A.
A
.
F
a
rdo
un,
"
A
new b
r
id
geles
s
P
F
C
S
e
pic
an
d Cuk
rectif
i
e
rs
with
lo
w co
nd
ucti
on and
swit
c
hing
loss
es,
"
20
09
Int
.
Co
nf.
Po
wer Elect
ro
n. Dri
ve
Sys
t
.
,
pp.
5
50-5
5
6
,
2
009
.
[21]
H.
F
a
rzaneh
-Far
d
an
d M. M
a
hdavi
, "Brid
g
e
l
e
s
s
CUK po
wer
f
actor
correct
ion rect
ifi
e
r with red
u
ced
con
duct
i
o
n
losses
,"
I
E
T P
o
w
e
r E
l
e
c
t
ro
n.
,
vol
. 5,
No
. 9
,
pp
.
1
7
3
3
-1
740
,
2
012.
[22]
R. D
.
Belek
a
r,
S
.
S
u
bram
ani
a
n,
P
.
V.
P
a
n
v
alk
a
r, M
.
D
e
sa
i
,
and R. P
a
to
le
,
"Alternat
or
charg
i
n
g
s
y
stem f
o
r
e
l
ect
ric
mo
to
rc
y
c
le
s
,
"
pp
.
1
7
5
9
-
17
66
,
20
17
.
[23]
K. Wi
ll
i
a
ms
,
"
Hybr
id
vehicl
e
s
,
4
2
volt
vehi
c
le
el
ectr
i
ca
l
system
s
and
th
e
im
p
lica
t
i
o
ns
f
o
r EM
C
techn
o
l
o
g
y
,
"
20
04.
[24]
D.
Pat
il,
"
A
cuk con
verter
b
a
sed
b
r
id
gel
e
s
s
to
polo
g
y f
o
r high
p
o
wer
fa
c
t
or f
a
s
t
bat
ter
y
cha
r
g
e
r
f
o
r
electri
c vechi
c
le
ap
pl
ica
t
io
n
," 20
12
.
[25]
L.
Ahmet
h
odži
ć
, "
Ca
sc
ad
e
SMC
c
o
n
t
ro
l of
Ć
uk c
o
nverter for tele
commun
icatio
n
syst
ems
po
wer s
u
pp
ly
,"
20
14
.
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