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
)
Vo
l.
10, No.
1, March 2019,
pp.
319~329
ISSN: 2088-8694,
DOI
:
10.115
91/ijpeds.v10.i1.
pp
319-329
319
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
escore
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x.
p
hp/IJ
PED
S
D
C
transformer modeling and c
ontrol of DC
-DC
buck con
v
erter
Sa
run
S
o
ma
n
1
,
N
i
shtha
Sh
elly
2
,
Ci
j
i
P
earl
Kurian
3
, Sud
h
eer K
uma
r
T.S
4
1
, 3
,
4
F
a
c
u
l
t
y
of
El
ectri
cal an
d
E
lectro
ni
cs E
ng
inee
ri
ng
, M
a
ni
pal Ins
ti
tute
o
f
Tech
nol
og
y,
M
a
ni
pal
Acade
m
y
o
f
H
ig
her
E
d
u
catio
n,
I
ndia
2
D
e
p
a
rt
m
e
nt
o
f
E
l
ect
ri
cal
a
nd Electron
i
cs
En
g
i
n
e
e
rin
g
, M
anip
al I
n
s
t
i
t
ut
e
of
Te
c
h
no
lo
gy
,
Ind
i
a
Ar
ticle
In
fo
ABSTRACT
A
r
t
i
cl
e hi
sto
r
y:
Rec
e
ive
d Ma
y
29,
2
0
1
8
Re
vise
d O
c
t 2
6
,
201
8
Acc
e
p
t
e
d
No
v
1
0
,
2
018
S
w
itch
in
g
P
o
wer
Con
v
erters
c
o
n
v
e
rt
o
ne
f
orm
of
p
ower
t
o
an
oth
e
r
w
i
t
h
high
ef
fi
c
i
ency
a
nd
accur
a
t
e
c
on
trol.
O
n
e
o
f
t
he
m
ost
wid
e
ly
u
sed
DC
-DC
Co
nv
e
r
t
e
r
is
B
u
c
k
Conv
erter.
C
o
n
t
r
ol
i
s
inv
a
riab
ly
r
equi
red
t
o
maintai
n
t
he
o
u
t
put
v
o
ltag
e
/curren
t
i
n
spit
e
of
v
a
r
i
a
ti
on
s
in
s
ource/
load
.
I
n
ord
e
r
to
d
esign
t
h
e
con
t
roller
and
g
a
in
i
nsig
h
t
i
n
t
o
the
s
y
st
e
m
,
a
d
y
n
a
mi
c
mo
de
l
n
eeds
t
o
be
d
evel
oped
.
M
o
d
eli
n
g
t
echni
qu
es
w
id
ely
u
s
ed
are
s
t
ate-sp
ace
aver
ag
in
g
an
d
PW
M
s
w
itch
model
.
I
n
th
i
s
p
ap
er,
a
D
C
t
ran
s
f
o
rm
er
m
od
eli
n
g
tech
niq
u
e
i
s
u
s
ed
t
o
d
e
vel
op
the
av
erag
ed
m
o
d
el
o
f
th
e
con
v
erter.
O
ne
o
f
the
advan
t
ages
of
t
h
is
m
odel
i
s
tha
t
it
can
b
e
impl
em
ent
e
d in
S
p
i
c
e
simu
l
a
t
or u
s
i
ng
b
as
ic ci
r
cuit
el
emen
ts.
T
h
e
sa
m
e
mo
d
e
l
can
b
e
us
ed
f
or
time
do
m
a
in
a
s
well
a
s
f
re
q
u
en
cy
dom
a
in
a
nalys
i
s.
A
nal
o
g
t
y
pe-II
co
m
p
ensator
i
s
d
esi
g
ne
d
to
c
omp
en
sat
e
t
he
sy
st
e
m
.
S
i
mu
la
t
i
o
n
a
nd
e
xp
e
r
im
e
n
t
a
l
r
e
su
lt
s
fo
r
s
t
a
r
t
-
u
p
t
r
a
n
si
e
n
t
and
load
t
r
ansi
ent are s
h
o
w
n t
o
v
ali
d
at
e the m
o
d
e
l.
Key
w
ords:
A
n
a
l
og
co
n
t
ro
l
B
u
ck c
o
n
v
erter
DC
-DC
co
nv
ert
e
r mo
d
e
li
ng
Co
pyr
i
g
h
t
©
2019
Instit
u
t
e of Advan
ced E
n
g
i
neer
in
g a
nd Sci
ence.
All rights
reserv
e
d
.
C
o
rre
s
po
n
d
in
g Au
t
h
or:
S
a
run
S
om
a
n,
M
a
n
i
p
a
l
In
st
i
t
ut
e o
f
Te
c
hnol
og
y
D
e
partm
ent o
f
Elec
tric
a
l
and
Elec
tron
ics
E
n
g
i
ne
eri
n
g,
M
a
n
i
p
a
l
In
st
i
t
ut
e o
f
Te
c
hnol
og
y
,
M
an
ip
al
Aca
d
e
my
o
f
High
e
r
Ed
u
c
a
tio
n,
M
a
n
i
p
a
l
,
India
-
57
61
0
4
.
P
hone: +91
8904334911
Em
ail
:
s
arun.
s
o
ma
n
@
ma
n
i
pa
l
.
edu
1.
I
N
TR
OD
U
C
TI
O
N
P
o
w
er
conver
t
e
r
s
c
h
ange
e
le
ctric
a
l
p
ow
er
f
rom
one
f
or
m
t
o
a
no
t
h
er
w
i
t
h
ve
ry
h
i
gh
e
f
fic
ie
n
c
y
a
nd
ac
cura
t
e
co
n
t
rol.D
C-D
C
c
onve
rsi
on
is
a
c
o
m
m
on
func
t
i
on
per
f
orm
e
d
by
pow
e
r
c
on
ve
rters,
in
w
h
i
ch
t
h
e
vo
lta
ge
o
f
D
C
is
cha
nge
d
an
d
poss
i
bly
re
gul
a
t
e
d
.
To
r
eg
ula
te
t
h
e
outp
u
t
vo
lta
ge
o
r
c
u
r
r
ent
a
contr
o
ll
e
r
is
requ
ire
d
t
ha
t
adj
u
s
t
s
t
h
e
con
t
rol
in
put
t
o
re
gu
l
a
te
t
he
d
e
s
i
r
e
d
quan
t
ity.
In
or
der
to
de
sig
n
a
c
ontr
ol
l
e
r
,
a
ma
them
at
i
c
al
m
odel
o
f
t
h
e
s
y
s
te
m
is
r
equire
d.
A
goo
d
m
o
d
e
l
i
n
c
o
rp
orates
the
d
om
i
n
a
n
t
be
hav
i
or
o
f
t
h
e
sys
tem
,
ig
nor
e
the
i
n
s
i
gn
i
f
ica
n
t
phe
nom
ena
.
O
nce
basic
ins
igh
t
is
g
a
ine
d
the
m
o
d
el
ca
n
be
r
efi
n
e
d
t
o
inc
o
rp
ora
t
e
some
of
t
he
pre
v
i
o
u
s
l
y ne
g
l
e
c
t
ed p
h
e
nome
n
a [
1
].
P
r
e
vio
u
sly,
m
a
ny
tec
h
ni
q
u
es
h
ave
bee
n
p
ro
pos
ed
f
or
m
od
e
l
i
n
g
of
a
conv
e
r
ter.
L
ar
ge
s
ignal
m
o
d
e
l
i
n
g
pro
duce
s
a
non
-li
n
ea
r
model
of
t
he
co
nver
t
e
r
[
2].
S
i
nc
e
si
m
u
lat
i
o
n
s
s
h
o
w
n
i
n
t
h
i
s
p
a
p
e
r
a
r
e
c
a
r
r
i
e
d
o
u
t
u
s
i
n
g
LTSP
I
CE,
t
h
e
r
efore
a
line
a
ri
ze
d
sm
all
s
i
g
n
a
l
m
ode
l
wa
s
use
d
.
Re
f
[3]
di
sc
usse
s
t
h
e
aver
age
d
s
ma
l
l
s
i
g
n
a
l
mode
l
ing
for
a
buc
k
co
nv
e
r
te
r
w
ith
a
vera
ge
cur
rent
m
ode
c
ontr
o
l
.
I
n
[
4
]
a
n
a
v
e
r
a
g
e
d
s
m
a
l
l
s
i
g
n
a
l
m
o
d
e
l
i
s
use
d
w
hic
h
r
equ
ires
a
n
ad
d
i
t
i
o
n
a
l
corr
ecti
o
n
fa
ct
or
to
be
i
nc
lu
de
d
t
o
m
a
tc
h
t
he
o
u
t
pu
t
v
o
l
tage
of
a
ve
r-a
ged
mode
l
w
i
t
h
t
ha
t
of
t
he
a
ct
ua
l
circ
u
i
t.
I
n
[5],
a
n
o
n
-
l
i
n
e
ar
co
n
tr
ol
ler
is
u
se
d
w
h
ere
as
i
n
[
6],
both
non-
line
a
r
as
w
e
ll
a
s
l
i
n
e
a
r
con
t
ro
lle
rs
a
r
e
i
m
p
lem
e
n
t
ed
o
n
buc
k
c
o
n
v
e
r
t
e
r.
I
n
[7],
[
8]
D
C
transf
orme
r
m
odel
i
ng
ap
pr
oach
is
use
d
w
hich
i
s
a
gra
phi
c
a
l
a
p
p
r
o
ac
h
w
i
t
h
m
in
imum
u
se
o
f
equa
ti
on
s.
T
h
i
s
m
a
ke
s
it
e
a
s
ie
r
to
d
er
i
v
e
tr
ansfe
r
f
u
n
c
t
i
o
n
s
f
r
o
m
a
f
i
n
a
l
c
a
n
o
n
i
c
a
l
m
o
d
e
l
o
f
t
h
e
b
u
c
k
c
o
n
v
e
r
t
e
r
a
n
d
any
ki
n
d
o
f
co
n
t
ro
ll
e
r
d
es
ig
n
bec
o
m
es
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
:
31
9 –
32
9
32
0
ea
sy.
R
e
f
[
9],
[1
0]
d
isc
u
sses
differ
ent
c
o
n
t
r
o
l
tec
h
n
i
ques
and
i
t
s
a
n
a
lysi
s.
D
i
g
it
al
c
on
t
r
o
l
t
e
c
hn
i
ques
a
r
e
di
sc
usse
d i
n
[11]
,
[12].
1n
[
1
3
]
s
t
a
te
s
p
a
c
e
a
ve
ragi
n
g
i
s
use
d
t
o
mode
l
the
pla
n
t
dis
t
ur
bance
due
t
o
lo
ad
v
ar
i
a
tio
n.
I
n
[14]
l
a
r
g
e
signa
l
n
on-
ide
a
l
a
ver
a
ge
d
m
o
d
e
l
of
t
he
D
C-D
C
buc
k
co
nv
e
r
te
r
is
i
m
plem
ent
e
d
usi
n
g
S
-
f
unc
tio
n.
T
he
p
rop
o
se
d
mode
l
i
s
v
a
l
i
d
ated
by
c
o
mpa
r
in
g
t
h
e
ope
n
l
oop
r
e
sp
onse
o
f
M
A
TLA
B
wit
h
S
abe
r
.
The
con
t
ro
l
l
er
i
n
a
B
u
c
k
Con
v
e
r
ter
m
u
st
m
ana
g
e
the
trans
i
en
ts.
Loa
d
t
ra
ns
i
e
n
t
s
a
r
e
m
a
na
g
e
d
b
y
con
t
ro
lle
rs
a
nd
inr
u
sh
c
urre
nt
dur
in
g
pow
er
-up
is
m
a
n
age
d
by
so
ft
s
t
a
rt
c
ircu
it
[1
5]
.In
[16]
a
ddi
t
i
on
a
l
f
e
e
d
b
ac
k
is
u
se
d
usi
ng
a
c
a
pac
itor
m
u
lti
pl
i
e
r
f
r
o
m
t
h
e
out
p
u
t
of
t
h
e
c
on
v
e
rt
e
r
t
o
t
h
e
i
nput
o
f
th
e
erro
r
a
m
p
l
if
i
e
r.
I
t
he
l
p
s
to
c
o
n
t
rol
t
h
e
c
o
nver
t
er
out
p
u
t
ram
p
in
g spee
d
dur
in
g p
o
w
e
r up.
D
i
ffere
n
t
type
s
of
m
ode
li
ng
te
c
hni
que
s
a
r
e
use
d
t
o
m
odel
t
h
e
dy
nam
i
c
be
h
a
vi
o
r
o
f
the
buc
k
c
o
n
v
erter
.
D
C
t
ra
ns
form
er
m
odeli
n
g
t
e
c
h
n
i
qu
e
w
h
i
c
h
i
s
a
g
ra
p
h
i
c
a
l
appr
oa
ch
i
s
le
ss
exp
l
ored.
Mode
ls
d
e
v
e
l
ope
d
in
prev
io
us
w
ork
doe
s
n
'
t
t
ake
i
n
to
a
cc
o
unt
d
y
n
a
m
ics
d
u
r
i
ng
the
sta
rt-up.
T
his
pap
e
r
discusses
DC
t
ra
nsformer
mode
l
i
ng
of
a
v
o
l
ta
ge
m
od
e
con
t
rol
l
e
d
D
C-D
C
b
uck
co
nve
r
t
e
r
.
The
d
e
v
e
l
o
p
e
d
m
o
d
e
l
i
s
i
m
p
l
e
m
e
n
t
e
d
i
n
LTS
pice
s
i
m
u
l
ator.
The
uni
q
u
e
ne
ss
o
f
t
h
is
m
ode
l
is
t
hat
n
o
n
-
ide
a
l
i
t
i
es
can
b
e
e
a
sil
y
i
ncor
po
r
a
ted
us
i
n
g
r
e
sistors
and
vo
l
t
age
s
s
ource
s,
f
or
e
xa
mple
,
di
ode
volta
ge
d
r
op,
M
O
S
F
ET
o
n-r
e
sista
n
ce
etc.
S
ta
rt-up
tra
n
sien
t
an
d
l
o
ad
trans
i
en
t
ar
e
a
n
a
l
yze
d
u
s
i
ng
a
ty
pe-
II
c
ont
r
o
ll
er
.
F
i
nally,
sim
u
l
ati
o
n
re
sul
t
s
a
r
e
c
o
mp
a
r
ed
w
i
t
h
h
ard
w
are
re
su
lt
s
to va
l
ida
t
e
the
m
odel.
S
e
c
t
io
n
2
de
scribe
s
the
sm
all
sig
n
a
l
D
C
transfor
me
r
m
odel
of
B
u
c
k
C
o
n
v
er
te
r
a
nd
i
t
s
im
pl
e
m
e
n
ta
t
i
o
n
in
LTSp
i
ce
.
C
o
n
t
ro
l
l
e
r
d
e
s
ig
n
is
p
r
e
sen
t
ed
i
n
se
ctio
n
3.Fina
ll
y
e
xper
i
m
e
ntal
r
e
s
ult
s
o
f
t
h
e
pro
t
o
t
ype
a
r
e
pro
v
i
d
e
d
a
nd c
o
m
p
ar
ed w
it
h t
h
e
simu
lat
i
on re
sults.
2.
SM
AL
L S
I
G
N
AL
M
ODE
L
ING OF BUCK CONVERT
ER
S
m
a
l
l
mode
lin
g
of a
co
nve
rte
r
i
s
require
d t
o
r
eprese
nt
t
he p
hys
i
c
al
b
eh
a
v
io
r b
y
ma
t
h
e
m
at
i
c
al
mea
n
s
.
F
o
r
exa
m
ple how
do ac
va
r
ia
tio
ns in so
u
r
ce vo
l
t
a
g
e
,
l
o
a
d
or duty cyc
l
e
affec
t
t
h
e ou
t
p
ut v
o
l
t
a
ge
.
Whi
l
e de
ve
lo
pin
g
a
m
ode
l,
o
n
l
y
d
o
min
a
n
t
b
eha
v
ior
of t
he
s
yste
m n
eed
s to
b
e ta
k
e
n
int
o
a
cc
o
unt
. Fi
g
u
r
e
1
sh
ow
s
a
B
u
ck
c
o
n
v
e
rter
a
nd
(1)
a
n
d
(2)
show
s
t
h
e
s
t
e
a
dy
s
t
a
t
e
i
nductor
current
a
nd
c
a
p
a
ci
to
r
vo
lt
ag
e
re
sp
ec
ti
v
e
ly
.
S
w
i
t
c
h
i
n
posit
i
o
n
'
1'
Ind
u
ct
or
v
o
l
t
a
g
e
is show
n
in
(
1)
(
1
)
Ca
pac
i
t
o
r
current i
s show
n in
(
2)
(
2
)
U
s
ing
sm
all
ri
pp
l
e
a
p
p
ro
xim
a
t
i
o
n
s
w
i
t
c
h
i
ng
r
i
p
p
le
i
s
ne
g
l
ecte
d
a
n
d
sw
it
chi
n
g
harm
on
i
c
s
ca
n
be
r
e
m
oved
b
y
ave
r
ag
in
g a
ll
w
a
vef
o
rms
over
one sw
itch
i
n
g
pe
r
i
od
[
7
]
.
Mo
vi
ng
aver
ag
e
of a
va
r
iab
l
e
over
a
t
i
m
e
p
e
r
io
d
is show
n
in (
3)
(
3
)
F
i
gur
e 1.
Buc
k
Co
nver
t
e
r
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
DC t
r
an
sfo
r
me
r
mo
d
e
lin
g
and c
o
n
t
rol
of
DC-DC b
u
c
k
con
v
ert
e
r
(S
a
r
un
S
o
ma
n
)
32
1
A
ll t
h
e va
ria
b
l
e
s in
(
1)
a
nd (
2
) are repla
ced
w
ith
i
t
s
m
ovi
n
g
a
ve
rage
va
l
u
e
s
yie
l
d
i
ng
(4)
and (
5
)
(
4
)
(
5
)
S
w
i
t
c
h
in
p
o
s
i
t
io
n
‘
2
’
(
6
)
(
7
)
U
s
ing
sma
l
l
ri
pp
l
e
a
ppr
o
x
i
m
ati
o
n
(
8
)
(
9
)
A
v
er
agi
n
g
in
d
u
c
t
or vo
l
tage
(
4)
a
nd (
8
)
(
10)
A
v
er
agi
n
g
ca
p
acit
o
r c
u
rre
nt
(
5)
a
nd
(9) ove
r one
sw
itc
h
i
n
g
per
i
od.
(
11)
The
so
ur
ce
curr
ent of b
uc
k
co
nver
t
er
is disc
o
n
t
i
n
u
o
u
s
an
d n
e
eds
t
o be
ave
rage
d.
(
12)
2
.
1
.
Per
t
urba
tio
n
a
nd Linea
r
iza
t
io
n
C
ons
ide
r
t
he
t
w
o
i
n
d
e
p
e
n
d
e
nt
i
n
p
u
t
s
,
so
urce
v
o
l
t
a
ge
and
du
t
y
c
yc
le
o
f
b
uc
k
con
v
er
t
e
r.
P
e
r
t
ur
bing
the
in
p
u
ts
w
i
t
h
low
fre
que
nc
y
ac
variati
o
n
s
w
hich
a
re
s
ma
l
l
i
n
ma
gni
tu
d
e
w
h
en
c
om
pare
d
to
s
t
e
a
d
y
sta
t
e
D
C
v
al
ues
a
nd
.
A
ppl
y
i
ng
a
nd
as
i
npu
t
s
t
o
the c
o
n
v
erter
p
e
r
t
ur
bs
t
he i
nd
uct
o
r
curr
ent and
o
u
t
p
u
t
vo
l
ta
ge
as
s
how
n
i
n
(
13)
a
nd
(14) respec
t
i
v
e
l
y.
̂
(
13)
(
14)
Fr
om
(
10), (11)
a
nd
(12)
can now
b
e
re
w
r
itte
n as
s
h
o
w
n
i
n
(15),
(
16) a
nd (17)
r
espe
cti
v
e
l
y.
̂
(
15)
̂
(
16)
̂
̂
(
17)
F
r
om
(
15), (16)
a
nd
(17)
a
re no
n
-
l
i
n
ear
equ
a
t
i
o
ns,
and c
a
n
be l
inea
r
i
zed
b
y assum
i
ng
≪
,
≪
,
̂
≪
,
≪
.
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
:
31
9 –
32
9
32
2
In t
he
se e
q
u
at
ions,
ave
r
ag
e
v
a
l
u
e
of D
C ter
m
s is z
ero and
se
co
n
d
o
r
der te
rm
s c
a
n be
ne
g
le
cte
d
due
it
s
sm
a
ll
e
r
m
a
g
n
i
t
u
d
e
a
n
d
r
e
m
a
i
n
i
n
g
f
i
r
s
t
o
r
d
e
r
t
e
r
m
s
a
r
e
s
h
o
w
n
i
n
(
1
7
)
,
(
1
8
)
and
(19)
r
espe
ctive
l
y.
The
thre
e
e
q
u
a
tio
ns
com
p
le
te
l
y
des
c
r
ibe t
h
e
dy
na
m
i
c be
hav
i
or of buc
k
co
nver
t
e
r
.
̂
(18)
̂
(
19)
̂
̂
(
20)
3.
DC TRA
N
S
F
ORMER M
O
DEL OF BUC
K CONVERT
ER
D
C
t
ransfor
m
e
r
m
o
d
e
l
ing
i
s
a
t
he
ore
tica
l
c
on
cept
w
h
ic
h
is
u
se
d
to
o
b
t
a
i
n
t
h
e
contr
o
l-
to-o
u
t
pu
t
trans
f
er
fu
nc
ti
o
n
.
The
system
c
an
b
e
mode
l
e
d
us
i
ng
i
n
depe
nde
n
t
,
depen
d
e
n
t
s
ource
s
an
d
pas
s
i
v
e
elem
ents.
F
i
gure
2
de
p
i
c
t
s
t
h
e
in
d
u
c
t
or
l
oo
p
m
o
d
e
l
us
i
ng
(1
8).
F
rom
(19)
sh
ow
s
t
h
a
t
i
n
d
u
c
t
or
c
urren
t
i
s
e
qua
l
to
t
he
s
um
of
t
he
capa
c
i
t
o
r
a
nd
loa
d
c
urre
nt
.
We
c
a
n
r
e
p
lac
e
t
he
v
ol
ta
ge
s
ourc
e
w
i
t
h
the
capa
c
i
tor
loo
p
a
s
dep
i
ct
e
d
in Fig
ure
3.
I
nput
v
o
l
t
a
ge
s
ource
i
s
n
o
t
prese
n
t
i
n
t
he
m
ode
l
s
how
n
in
F
ig
ure
3.
I
npu
t
si
d
e
m
od
e
l
c
a
n
be
deve
l
ope
d
us
in
g
(20)
a
s
sho
w
n
in
F
ig
ure
4.
C
irc
u
it
mod
e
ls
i
n
Fi
gures
3
a
nd
4
c
a
n
b
e
c
om
bi
ned
t
o
g
e
t
t
he
com
p
le
te
s
yste
m
m
odel
as
s
how
n
in
F
ig
ure
5.
T
he
d
e
p
e
n
d
e
nt
c
ur
re
n
t
s
ource
̂
a
nd
de
pe
n
d
en
t
v
o
lta
ge
source
c
an
b
e r
e
place
d w
i
t
h
a
D
C tra
n
sform
e
r
w
i
th
c
on
ver
s
i
on r
a
ti
o
1:
a
s
show
n in F
i
g
ur
e
6.
F
i
gur
e 2.
I
n
duc
to
r
l
o
o
p
m
ode
l
F
i
gure
3. Mo
d
e
l
w
ith
capa
c
i
t
o
r lo
op i
n
serte
d
The
ex
pr
ess
i
o
n
f
or
c
on
tro
l
t
o
o
u
t
p
u
t
t
r
a
ns
fer
func
tio
n
c
a
n
b
e
ob
ta
ine
d
b
y
ass
u
mi
ng
sourc
e
di
st
urba
nce
i
s
z
e
ro
a
nd
then
pus
h
i
ng
a
ll
the
e
l
e
m
e
n
t
s
i
n
th
e
prim
ary
side
t
o
t
h
e
s
ec
onda
ry
s
i
d
e
o
f
D
C
trans
f
or
me
r.
S
i
m
pli
f
yi
n
g
t
he
c
irc
u
i
t
r
e
m
ove
s
t
h
e
D
C
t
r
a
ns
fo
rm
e
r
f
r
o
m
t
h
e
m
o
d
e
l
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
7
a
n
d
n
o
w
it
c
a
n
be
mo
de
le
d in LTS
P
I
CE
u
si
ng
be
ha
vi
oral
v
olta
ge
so
u
rce
a
n
d bas
i
c
circ
uit e
l
em
en
t
s
.
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
DC t
r
an
sfo
r
me
r
mo
d
e
lin
g
and c
o
n
t
rol
of
DC-DC b
u
c
k
con
v
ert
e
r
(S
a
r
un
S
o
ma
n
)
32
3
S
y
st
e
m
p
ara
m
eters
unde
r
co
ns
i
d
e
r
at
i
on
a
r
e
d
e
p
i
cte
d
i
n
T
a
ble
1.
Th
e
spe
c
i
f
i
cat
io
n
s
a
re
t
a
k
e
n
f
ro
m
Buc
k
C
on
ver
t
e
r
a
va
ila
b
l
e
on
A
S
LK
P
RO
K
it
[17].
F
i
gure
8
show
s
t
he
unc
o
m
pensa
t
ed
s
ys
te
m
r
e
sponse
re
ali
z
e
d
in
LTS
P
I
CE.
In
o
rde
r
t
o
ob
t
a
in
t
he
f
re
q
u
enc
y
r
e
s
po
nse
of
t
he
s
y
s
t
em
,
an
A
C
sourc
e
i
s
p
l
ac
ed
b
e
t
ween ou
t
p
u
t
and
fee
d
b
a
ck
n
etwork.
Tab
l
e
1. S
yst
e
m
par
a
m
e
ters
D
e
s
c
ription
Pa
r
a
m
e
t
e
r
V
a
lue
Inp
u
t Volta
g
e
10V
O
u
tput
V
olta
g
e
5V
I
n
du
ct
an
ce
33µH
Cap
aci
t
a
n
c
e
660µF
Cap
aci
t
o
r
ES
R
0.
1Ω
S
w
it
c
h
i
n
g
F
r
e
que
n
c
y
400K
Hz
R
e
f
e
re
n
c
e
V
o
lt
a
g
e
0.
7V
F
i
gure
4. I
nput
s
ide
m
ode
l
F
i
gure
5. Com
bine
d sys
t
e
m
m
odel
F
i
gure
6.
B
u
c
k
c
o
ve
rter
D
C transf
orme
r model
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
:
31
9 –
32
9
32
4
F
i
gure
7.
S
im
pl
i
f
ie
d
D
C
trans
forme
r
model
Fi
g
u
re
8
. Un
comp
en
s
a
t
e
d
syste
m
r
esp
o
n
s
e
F
i
gure
9.
Type
-I
I Com
p
ensa
t
o
r
4.
COMPENSA
TOR DESIGN
The
u
n
com
p
e
n
sate
d
sys
t
em
r
esp
onse
i
n
F
ig
ure
8
show
s
a
phase
t
ra
ns
iti
on
o
f
90
at
t
he
c
or
ner
fre
que
nc
y
of 3
K
H
z
. A
t
ype-II
c
ompensa
t
or
as
sho
w
n i
n
F
i
g
ure
9
i
s
s
uita
bl
e
for
such t
ype
o
f
syst
em
.
(
21)
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
DC t
r
an
sfo
r
me
r
mo
d
e
lin
g
and c
o
n
t
rol
of
DC-DC b
u
c
k
con
v
ert
e
r
(S
a
r
un
S
o
ma
n
)
32
5
F
r
om
21
de
pic
t
s
t
h
e
tra
n
s
f
er
f
u
n
c
tio
n
of
t
he
c
ompe
nsa
t
or
,
w
h
er
e
,
a
nd
.
The
c
o
mpe
n
sa
tor
is
d
es
i
gne
d
fo
r
a
gain
c
ross
o
ver
frequency
4
a
nd
P
h
ase
M
a
rgi
n
=
60
.
The
zer
o of
t
he
c
ompe
nsa
t
or
i
s plac
e
d
a
t
3
4
0
a
nd po
le
a
t
4
8
.
The
si
m
u
lat
i
o
n
m
odel
uses
LT1
01
3
o
p
-a
mp
t
o
re
ali
z
e
t
h
e
c
o
mpe
n
sa
t
o
r
as
s
how
n
i
n
F
ig
ure
10.
T
he
gai
n
-ba
n
dw
i
d
t
h
p
rod
u
c
t
o
f
LT1
01
3
i
s
1
.5M
H
z
w
h
i
c
h
is
s
am
e
as
t
he
i
nt
egra
t
e
d
o
p
-
a
m
p
av
a
i
l
a
b
l
e
i
n
TP
S
4
0
200
con
t
ro
l
l
er
c
hip
[1
8].
TP
S
4020
0
is
u
sed
for
har
d
w
a
re
r
e
a
li
z
a
t
i
o
n
o
f
t
h
e
com
p
en
sat
o
r.
T
he
o
u
t
pu
t
v
o
l
t
a
g
e
i
s
scale
d
d
ow
n
us
i
n
g
t
h
e
vo
l
t
age
div
i
der
ne
tw
or
k
c
o
mpris
i
ng
o
f
t
w
o
r
e
s
is
t
o
rs
i
n
para
l
l
e
l
t
ha
t
m
a
ke
up
.
T
h
e
refere
nce
vol
ta
ge
0
.
7
,
r
e
a
l
i
z
e
d
u
s
i
n
g
v
o
l
t
a
g
e
s
o
u
r
c
e
a
nd
m
o
d
u
l
a
tor
ga
i
n
.
i
s
the
ou
tpu
t
of the
c
ompe
nsa
t
or
, w
h
ich in tur
n
w
i
l
l
co
n
t
ro
l
t
h
e
va
lue of b
eh
a
v
io
ral
vol
t
a
g
e
s
ou
rc
e
.
F
i
gur
e
11 sh
ow
s
t
h
e
com
p
ensated
system
f
re
quenc
y
respo
n
se.
F
i
gur
e 10.
Compensated system
F
i
gure
1
1
.
Co
m
p
ensa
te
d sy
ste
m
f
re
quency
resp
onse
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
:
31
9 –
32
9
32
6
5.
EXPE
RIMENTAL
R
ESULT
S
O
n
c
e
t
he
c
om
pen
s
a
t
or
i
s
desig
n
e
d
its
e
ffe
c
t
i
v
e
n
ess
nee
d
s
to
b
e
tes
t
e
d
.
Tw
o
stan
dar
d
t
e
s
ts
t
ha
t
ar
e
ca
rried
o
u
t
f
or
pow
er
c
on
ver
t
e
r
s a
r
e
st
a
r
t-up
tra
nsi
e
nt
t
est a
n
d
loa
d
tra
nsie
nt
t
e
s
t
.
5.1.
Star
t-u
p Tr
an
sien
t
Test
D
u
r
i
n
g
t
urn-o
n
,
there
w
il
l
be i
nrus
h
c
u
rren
t
w
hi
c
h
c
an dam
age t
h
e
s
w
i
tc
h
e
s and ind
u
c
t
or
.
TP
S
402
00
con
t
ro
l
l
er
c
hi
p
ha
s
a
progr
am
ma
bl
e
so
ft-s
tar
t
p
in.
The
ca
pa
cit
o
r
con
n
e
ct
ed
t
o
th
e
sof
t
s
ta
rt
p
in
d
e
t
ermi
n
e
s
th
e
st
a
r
t-u
p
tra
nsi
e
nt
t
i
m
e
.
The si
m
u
l
a
ti
on
mo
de
l
in
F
ig.
5
is u
s
e
d
to
d
e
t
erm
i
n
e
t
he
a
ppr
o
pri
a
te
.
So
f
t
s
t
a
r
t
i
s
implem
e
n
te
d i
n
s
imu
l
a
t
i
o
n
m
ode
l u
s
i
n
g
P
W
L vo
lta
ge
s
o
u
rc
e,
w
hich
ram
ps
u
p t
h
e
r
e
fe
r
e
nc
e v
o
lta
ge
f
r
o
m 0
t
o
0.7V
i
n
t
h
e spe
c
ifie
d tim
e.
F
igur
e
12 sh
ow
s
the
in
d
u
ct
or c
urre
n
t
an
d ou
t
p
u
t
vol
ta
ge
f
or
d
i
f
fer
e
nt
.
S
i
mulat
i
o
n
re
sults c
lear
ly i
ndic
a
te
10
gi
v
es the
m
i
n
im
um i
nru
s
h
cur
r
en
t an
d ou
t
p
u
t
v
o
l
t
a
ge
overs
ho
o
t
.
To
o
b
t
a
i
n
the
sa
me
r
esult
in
h
a
r
d
w
ar
e,
i
s
pr
ogra
m
me
d
to
10
by
co
nnec
tin
g
a
470
ca
p
acit
o
r
to s
oft star
t
p
i
n
of TP
S
4020
0.
F
igure
1
3
s
ho
w
s
h
ardw
a
r
e resu
lts
for
start-up
t
r
ans
i
ent.
5.2.
Load
Tra
n
s
ien
t
T
e
s
t
F
i
gure
15
sho
w
s
t
h
e
simula
ti
on
re
sult
for
a
ste
p
c
han
g
e
in
l
oa
d
f
rom
0.
5
A
t
o
1
A
.
The
out
pu
t
vo
l
t
a
g
e
rec
overs
s
m
oothl
y
w
ith
ou
t
an
y
rin
g
i
n
g.
T
he
r
e
c
ove
ry
tim
e
is
2
6
0
.
F
i
gure
1
0
s
how
s
the
hard
w
a
re
r
esult
for
l
o
a
d
t
rans
i
e
nt
t
e
s
t.
R
e
c
o
v
e
ry
t
im
e
is
c
o
n
side
rab
l
y
less
f
or
h
a
r
d
w
a
r
e
res
u
lt
b
e
cau
se
a
d
d
it
ion
a
l
t
w
o
10
ce
ram
i
c c
a
pa
cit
o
r
s
ar
e
use
d al
on
g w
i
t
h
t
he
o
utp
u
t
capa
c
i
t
or
to
sh
ap
e t
h
e
recove
r
y
.
F
i
gure
1
2
.
S
i
mul
a
tio
n
of start
up
t
r
a
n
si
e
n
t
w
ith s
oft start
Fi
g
u
r
e 13
. St
ar
t
-
up
t
ran
s
i
e
n
t
, CH1:
Ou
t
pu
t
vo
l
t
a
g
e
CH2:
S
o
ft
st
a
r
t
ca
p
acit
o
r vo
lt
a
g
e
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
DC t
r
an
sfo
r
me
r
mo
d
e
lin
g
and c
o
n
t
rol
of
DC-DC b
u
c
k
con
v
ert
e
r
(S
a
r
un
S
o
ma
n
)
32
7
F
i
gure
1
4
. S
imula
t
io
n o
f
trans
ien
t
r
espo
nse
w
h
e
n
l
oad
cha
nge
s
f
rom
0.
5A
to 1A
F
i
gure
1
5
. T
ra
ns
ien
t
re
s
po
nse
w
h
e
n
loa
d c
h
a
nge
s
from
0.
5
A
to 1A
,
CH
1: O
ut
pu
t v
o
l
t
a
g
e
,
C
H
2
:
Load
c
urre
nt
6.
CONCL
U
S
ION
Th
is
p
a
p
er
r
e
p
resen
t
s
a
grap
h
i
cal
m
eth
od
for
sm
all
s
i
g
n
a
l
m
ode
l
in
g
of
D
C-
D
C
c
o
nver
t
er
s.
T
he
m
ain
adva
n
t
a
g
e
of
t
h
i
s
m
ode
l
is
i
t
c
a
n
be
i
m
p
lem
e
nte
d
i
n
S
P
ICE
sim
u
l
at
o
r
u
si
ng
b
asi
c
c
i
r
cui
t
el
eme
n
t
s
,
i
n
d
e
p
e
nde
n
t
and
de
pen
d
e
n
t
source
s.
S
tar
t
-
up
tra
n
sie
n
t
dy
nam
i
c
s
a
lso
ca
n
be
dete
rm
ine
d
u
s
i
ng
th
is
m
ode
l,
w
hic
h
i
n
tur
n
i
s
use
d
t
o
des
i
gn
the
sof
t
-
s
ta
r
t
c
a
p
aci
t
o
r
for
t
h
e
a
n
al
o
g
c
o
n
t
rol
l
er
I
C
.
F
ur
t
h
e
r
,
the
s
i
mu
lat
i
on
re
sul
t
s
ar
e
c
o
mpa
r
e
d
and
i
t
i
s
o
b
se
rv
ed
t
ha
t
the
ha
rd
w
a
r
e
r
e
s
ul
ts
a
r
e
a
s
e
xpec
t
e
d
f
r
om
s
imula
t
i
o
n
w
h
ich
affirm
s
t
h
e
de
vel
o
ped
mode
l
is
v
a
l
i
d
an
d
r
eliab
l
e.
REFE
RENCES
[1]
Ch
ri
s
t
op
he P
. Ba
s
so.
S
w
itc
h-
Mo
d
e
Po
we
r Su
pp
lie
s
. M
c
Graw
-H
ill Edu
cati
o
n
,
20
14.
[2]
P.
C
h
r
i
n
,
C
.
Bunl
aks
ana
nu
so
rn
,
"Large-S
i
g
n
a
l
Av
erage
M
o
deli
ng
a
nd
S
im
u
l
ation
of
D
C-DC
C
o
n
v
e
r
te
r
s
w
i
t
h
SIMU
LINK
," i
n
P
o
wer Conversion Confer
e
n
ce -
Nagoy
a
, 2007
.
P
CC '0
7,
pp
.
2
7-
3
2
,
2
00
7.
[3]
P
. Co
oke "
M
o
deli
ng av
erag
e curren
t
mo
d
e co
nt
ro
l o
f
po
w
er con
ver
t
o
rs
,"
in
A
p
p
lied
Po
wer
Electroni
cs Co
n
f
er
ence
and
E
x
pos
ition
,
2000. APEC
2000. Fifteenth
Ann
u
al
I
E
EE
,
20
00
,
v
o
l
.
1,
pp
.
25
6
-2
62
.
[4]
A.
K
.
Jh
a,
e
t
al
.,
"
Com
p
ens
a
t
e
d
average
m
odel
i
n
g
f
or
a
b
u
c
k
co
n
verter
c
o
n
t
r
ol,
"
i
n
20
14
Inn
o
va
ti
ve Ap
p
lication
s
of
Computa
t
iona
l
Int
e
lli
g
en
ce
on Power
,
E
n
ergy
an
d
Co
ntrols
wi
th th
eir
impact
on Hu
mani
ty
(
C
IPE
C
H)
,
pp
.
1
54-1
5
8
,
2
0
1
4,
[5]
J.
M
ah
davi
,
et
a
l.,
"
A
pp
li
c
a
t
i
o
n
o
f
s
t
ate
s
p
ace
avera
g
i
n
g
met
h
o
d
to
s
l
i
ding
m
ode
c
o
n
tro
l
o
f
PW
M
D
C
/D
C
co
nvert
ers,
"
in
In
du
str
y
A
ppli
c
ation
s
Conferen
ce,
1
9
9
7
. T
h
i
r
ty-Seco
nd IA
S
A
n
n
ual M
eeti
ng,
IAS
'9
7.
, Co
n
f
erence
Reco
rd
o
f
t
h
e
19
97
IEE
E
, vo
l
.
2
, pp
.
82
0
-8
27
,
1
9
9
7
.
[6]
A.
K
um
ar,
et
a
l.,
"M
odel
i
n
g
a
nd
c
o
n
t
r
o
l
o
f
DC-D
C
b
u
ck
c
o
nvert
er
u
s
i
n
g
S
M
C
,
"
i
n
Indu
s
t
ri
a
l
Inst
rument
a
t
ion
a
n
d
Con
t
rol (
I
CIC),
20
15
Int
e
r
nati
onal
Conferen
ce on
,
p
p.
1
40
6-1
411,
2
01
5.
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
:
31
9 –
32
9
32
8
[7]
Ro
be
rt
W
.
Er
ic
kson
a
n
d
D
ra
g
a
n
Ma
k
s
imo
v
ic
.
F
u
n
dam
ent
a
ls o
f
Po
wer El
ectr
onics
.
K
l
uwer
A
cad
em
ic
P
ubli
s
h
e
rs,
20
04
.
[8]
M
.
S
.
B.
R
anjan
a
,
et
a
l.
,
"DC-D
C
c
urrent
b
u
c
k
co
nvert
er
t
h
r
oug
h
d
u
a
l
i
t
y
a
p
p
r
o
a
c
h
a
n
d
i
t
s
D
C
t
r
a
n
s
f
o
r
m
e
r
m
o
d
e
l
l
i
n
g
f
o
r
cu
rrent
b
ased
l
o
a
ds
,"
i
n
Cir
c
u
it, P
o
wer
and Co
m
p
u
t
i
n
g
Tech
no
lo
gies
(
I
CCPCT)
,
2
0
1
6
Intern
ationa
l Co
nfer
ence
on
, pp
.
1-5
, 2
01
6.
[9]
Ta
nm
oy
R
o
y
C
h
ou
dh
u
r
y
a
n
d
Bya
m
a
k
e
s
h
Na
yak
,
"
Mod
e
lin
g
a
n
d
A
n
a
lys
i
s
o
f
a
N
ov
el
A
dap
t
i
v
e
H
y
steri
s
is
B
and
Controller
f
o
r
B
o
ost
a
n
d
Buck
C
onvert
er"
,
Inter
n
a
t
i
onal
Jo
ur
na
l o
f
Po
wer Elect
ro
n
i
cs
an
d
D
r
ive
Syst
ems
(IJ
P
E
D
S
)
,
vo
l.
8,
p
p
.
3
0
5
-
315,
2
01
7.
[10]
P
.
S
r
iram
alak
shm
i
,
et
a
l
.,
"
C
o
n
t
r
ol
o
f
Ch
aos
i
n
a
C
u
rrent
M
o
d
e
C
on
tro
l
led
Buck
B
oo
st
C
o
nvert
er
Usi
ng
W
e
a
k
Periodic
P
erturb
ati
o
n
Me
t
hod,"
In
tern
atio
nal J
o
ur
na
l o
f
Po
wer
Elect
ro
n
i
cs and
D
r
i
ve
Sys
t
em
s
(
I
JPED
S
)
,
vo
l.
8,
p
p
.1
46
7-1
4
8
0
,
2
01
7.
[11]
S
a
run
S
o
m
a
n,
e
t
al
.
,
"
Devel
opm
ent
o
f
D
igita
l
Co
n
t
ro
ll
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g
,
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p
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t
r
o
l(
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,
pp.
30
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,
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0
15.
[12]
S
u
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.
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ech
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.
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[13]
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ni
cs a
nd Drive S
y
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ems (
I
JPED
S
)
,
vol.
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,
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[14]
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Al-Ba
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Electroni
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Letters}
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l
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2
, p
p.
1
88
3-1
885
, 2
01
6.
[17]
Te
xa
s
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stru
m
e
nts.
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na
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Sy
ste
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a
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a
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a
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va
ila
ble
f
r
om:
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t
tp
://www.digikey.com/
e
n
/
pdf/t
/
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lab-kit-asl
k
-pro-
m
anual.
[18]
Tex
a
s
Instrum
e
n
t
s.
W
id
e
In
pu
t
Range
N
o
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ynchro
n
o
u
s
V
o
lta
ge
M
od
e
Cont
r
o
ll
er
:
TP
S40200
.
A
va
il
ab
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e
f
rom:
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tp:
/
/
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ww
.ti
.
com/
lit/ds
/
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l
ink
/
tps40200.pd
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