Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 4
,
A
p
r
il
201
5, p
p
.
52
9
~
54
0
I
S
SN
: 208
8-8
6
9
4
5
29
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Real Coded Genetic Algorithm Based Improvement of
Effici
ency in Int
e
rleaved Boost Converter
M. Aru
n
Devi
*, K. Valarm
athi**,
R.
Mah
e
ndhr
an
*
* Depart
em
ent o
f
El
ectr
i
c
a
l
a
nd
Electronics Eng
i
neering
,
P.S.R
Engineer
ing College
** Depart
em
ent
of El
ectron
i
cs
an
d Com
m
unicatio
n Engin
eering
,
P
.
S.R Eng
i
neerin
g College
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 4, 2014
Rev
i
sed
D
ec 17
, 20
14
Accepte
d Ja
n
8, 2015
The r
e
li
abil
it
y,
e
ffici
enc
y
,
and
co
ntrollab
ili
t
y
of P
hoto Volta
ic po
wer s
y
stem
s
can be incr
eased b
y
embeddin
g
th
e components of a Boost
Converter
.
Currently
, the converter
techn
o
log
y
over
c
omes the main problems of
manufacturing cost, efficiency
and mass
production. Issue to limit the life
span of a Photo
Voltaic inverter is th
e huge electroly
tic capacitor
across the
Direct Curr
ent b
u
s for energ
y
d
ecoupli
ng. Th
is paper presen
ts a two-phase
interleav
ed boos
t conver
t
er which ensu
res 180 angle phase shift
between
the
two interleav
ed
converters. Th
e Proporti
onal In
tegral contro
ller
is used to
reshape tha
t
the
controlle
r att
e
m
p
ts to
m
i
nim
i
ze the error b
y
adjusting the
control inpu
ts an
d also real
coded
ge
netic algorith
m is proposed fo
r tuning of
controlling par
a
meters of Proportional
In
tegr
al controller.
The real cod
e
d
genetic
algorith
m
is applied in th
e
Inter
l
e
a
v
e
d Boost Conv
erter
with
Advanced Pulse Width Modulation Tec
hniqu
es
for improving th
e results of
efficiency
and r
e
duction of ripp
le curr
ent. Sim
u
lation r
e
sults il
l
u
strate th
e
improvement
of efficiency
and
th
e diminution of
r
i
pple curr
ent.
Keyword:
B
oost
C
o
nve
rt
er
Int
e
rl
ea
ve
d B
o
ost
C
o
n
v
ert
e
r
PI C
ont
rol
l
e
r
R
eal
C
ode
d
Ge
net
i
c
Al
g
o
r
i
t
h
m
Solar Ene
r
gy
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
D
r
.K
.V
alar
m
a
t
h
i,
Depa
rt
em
ent
of El
ect
r
oni
cs
a
n
d
C
o
m
m
uni
cat
i
on E
n
gi
nee
r
i
n
g
,
P.S.R
En
gi
nee
r
i
ng
C
o
l
l
e
ge,
Sev
a
lp
atti, Sivak
a
si
-62
614
0.
Em
a
il: k
r
v
a
larmath
i
@yah
oo
.co
.
in
1.
INTRODUCTION
A G
r
i
d
-sy
n
c
h
ro
ni
zed
Ph
ot
o
Vol
t
a
i
c
(P
V
)
po
we
r sy
st
em
i
s
const
r
uct
e
d f
r
om
a gr
o
up
o
f
p
o
w
e
r
conve
r
ters a DC–DC convert
e
r ens
u
ri
ng the Maxim
u
m
P
o
wer Po
in
t Track
ing
(MPP
T
)
cascade
d
by
a grid-
syn
c
hr
on
ized in
v
e
r
t
er
[1
],
[2
].
Fo
r a PV
pow
er g
e
n
e
r
a
ti
o
n
syste
m
, th
e actu
al po
wer-g
e
neratin
g d
e
v
i
ce
is th
e
sol
a
r pa
nel
,
a
nd i
t
has a l
o
nge
r l
i
f
e t
h
an
t
h
e po
we
r co
n
v
ert
e
r
s
. P
hot
o
Vol
t
a
i
c
m
odu
l
e
em
bedde
d po
we
r-
electro
n
i
cs topo
log
y
d
e
riv
e
d
fro
m
a b
a
ttery equ
a
lizer,
wh
i
c
h
elim
in
ates t
h
e m
u
ltip
le
max
i
m
u
m
p
o
w
er po
in
t
peak
s c
o
m
m
o
n
t
o
part
i
a
l
sh
adi
n
g i
n
P
V
m
odul
es [
3
]
.
I
n
part
i
c
ul
a
r
a
p
pl
i
cat
i
ons
suc
h
as m
i
li
t
a
ry
us
es i
n
a
b
a
ttlefield
o
r
i
n
ex
trem
e weath
e
r cond
itio
n
s
, rep
a
i
r
o
r
altern
ate of th
e co
nv
erter is d
i
fficu
lt, and
a hig
h
l
y
reliable PV-ba
s
ed power sys
t
e
m
, which is com
p
act and
hig
h
l
y
m
o
b
ile in
n
a
ture, is n
e
ed
ed. Ab
usaleh
M.
Im
tiaz et al [4] descri
bes t
h
e
power Metal Oxi
d
e
Sem
i
co
nd
uct
o
r Fi
el
d Effect
Tra
n
si
st
or
(M
OSFE
T)
i
s
t
o
ens
u
re t
h
at
t
h
e
uni
nt
err
u
pt
ed
ope
rat
i
o
n o
f
t
h
e i
nve
rt
er, e
v
e
n
t
h
ou
g
h
i
t
gi
v
e
s hi
g
h
er
m
a
nufact
uri
n
g c
o
st
. Thi
s
hi
g
h
c
o
st
c
oul
d
be el
i
m
i
n
at
ed usi
n
g
hi
g
h
ba
n
d
-
g
a
p
sem
i
conduct
o
rs
.
For desi
g
n
i
n
g hi
g
h
effi
ci
e
n
cy
so
lar powe
r s
y
ste
m
s, a suita
ble DC-DC conve
rter is nece
ssary. The
DC-DC Boo
s
t co
nv
erter is used
to
in
crease th
e vo
ltag
e
lev
e
l in
th
e so
lar system
. In
o
r
d
e
r t
o
im
p
r
ov
e the
efficiency
of
boost c
o
nverte
r, a two
pha
s
e
interleav
e
d
bo
ost
c
o
n
v
ert
e
r i
s
use
d
.
The
use
of a
Swi
t
ched
C
a
paci
t
o
r
(SC
)
DC
–DC
c
o
nv
ert
e
r
fo
r t
r
ac
ki
ng
t
h
e M
a
xi
m
u
m
Power
Poi
n
t
(M
PP
)
of
a
ph
ot
o
vol
t
a
i
c
ar
ra
y
wi
t
h
th
e p
o
ssib
ility o
f
p
a
rtial sh
ad
ing
is d
e
scri
b
e
d
in
[5
]. The SC co
nv
erter to
po
log
y
can
b
e
recon
f
i
g
u
r
ed
to
m
a
xim
i
ze con
v
ersi
on
ef
fi
ci
ency
de
pe
ndi
ng
o
n
t
h
e
sol
a
r r
a
di
at
i
on a
n
d l
o
ad
.
Gene
ral
l
y
spea
ki
n
g
a
b
o
u
t
hi
g
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
52
9
–
54
0
53
0
st
ep-
u
p
DC
–
D
C
co
nve
rt
ers
f
o
r
t
h
ese
ap
pl
i
cat
i
ons
ha
ve t
h
e f
o
l
l
o
wi
ng
fe
at
ures
suc
h
a
s
hi
g
h
st
e
p
-
u
p
v
o
l
t
a
ge
gain,
high effi
ciency. Naayagi et al.
[6]
expl
ai
ned t
h
e st
e
a
dy
-st
a
t
e
anal
y
s
i
s
of t
h
e bi
di
r
ect
i
onal
Dual
Act
i
v
e
B
r
i
dge
DC
–
D
C
co
nve
rt
er.
A
n
a
n
al
y
s
i
s
o
f
Z
e
ro
V
o
l
t
a
ge
S
w
i
t
c
hi
n
g
(Z
VS
)
bo
u
nda
ri
es
f
o
r
t
h
e
b
u
ck
a
n
d
bo
ost
m
odes while consideri
ng t
h
e effect of s
n
ubber ca
pacitors on the
DAB
c
o
nvert
e
r
is
also
pre
s
ented.
B
oost
co
n
v
ert
e
rs are wi
del
y
used as
po
we
r fact
o
r
co
rrec
t
ed pre
reg
u
l
a
t
o
rs
. D
u
e t
o
an
i
nduct
o
r
o
f
b
o
o
s
t co
nv
erter th
e
ripp
le curren
t is in
creased
,
h
a
rm
o
n
i
cs
als
o
in
cr
e
a
s
e
d
an
d po
we
r
f
actor
is r
e
du
ced. In h
i
gh
po
we
r ap
pl
i
cat
i
ons
, i
n
t
e
rl
eav
ed o
p
erat
i
o
n
o
f
t
w
o
or m
o
re
bo
ost
co
n
v
ert
e
rs has
bee
n
pr
op
ose
d
t
o
i
n
c
r
ease t
h
e
out
put
p
o
we
r a
n
d
t
o
re
duce
t
h
e o
u
t
p
ut
ri
ppl
e.
Ge
nc et
al
. e
x
pl
o
r
ed
[
7
]
a
no
n i
s
ol
at
ed,
hi
g
h
bo
ost
rat
i
o
h
y
b
ri
d
t
r
ans
f
o
r
m
e
r DC
–DC
co
n
v
ert
e
r wi
t
h
ap
pl
i
c
at
i
ons f
o
r l
o
w
-
v
o
l
t
a
ge re
ne
w
a
bl
e ener
gy
so
urces
. The
pr
o
pos
ed
co
nv
erter em
p
l
o
y
s a
h
ybrid
tran
sform
e
r to
tran
sfer the ind
u
ctiv
e and
cap
a
citiv
e en
erg
y
an
d th
en
ach
i
evin
g
a
hi
g
h
b
o
o
s
t
rat
i
o
wi
t
h
a sm
aller m
a
gnet
i
c
com
pone
nt
. H
o
weve
r, t
h
e
dra
w
bac
k
o
f
t
h
i
s
con
v
e
r
t
e
r i
s
t
h
at
t
h
e
v
o
ltag
e
acro
ss
th
e switch is very h
i
gh
du
ring
th
e
reso
n
a
nc
e m
ode com
p
onents
[8]. Lee
et al. [9]
descri
bed the
opt
i
m
al desi
gn
of t
h
e reso
na
nt
com
pone
nt
s and t
h
e i
n
t
e
rl
eaved m
e
t
hod
i
s
prop
ose
d
f
o
r res
o
nant
cu
rre
nt
red
u
ct
i
o
n. T
h
a
t
t
h
e i
n
t
e
rl
eave
d
m
e
t
hod di
st
r
i
but
es t
h
e i
n
p
u
t
curre
nt
t
o
ea
ch p
h
ase
,
t
h
e
cur
r
ent
rat
i
ng
of t
h
e
swi
t
c
hi
n
g
de
vi
ces can
be
dec
r
eased
by
usi
n
g i
n
t
e
rl
eave
d
m
e
t
hod.
Al
s
o
,
i
t
can re
d
u
ce t
h
e i
n
p
u
t
cu
rre
n
t
ri
p
p
l
e
,
o
u
t
p
u
t
vo
ltag
e
ripp
le, and
size o
f
th
e p
a
ssi
v
e
. Yon
g
et al. [10
]
illu
strated
an
In
terleav
ed
So
ft Switch
i
ng
Bo
o
s
t
Con
v
erte
r (IS
S
BC)
f
o
r
a PV
po
we
r gene
ration
sy
stem
.
Th
e t
o
pol
ogy
use
d
t
o
r
a
i
s
e t
h
e
e
fficiency
of the DC-
DC con
v
e
rter. Th
e conv
erter o
f
th
e PV Power C
o
nd
itio
nin
g
System
(PVPCS) and
it min
i
mizes switch
i
ng
l
o
sses
by
a
d
o
p
t
i
ng m
e
t
hods
of
so
ft
s
w
i
t
c
hi
ng
. C
h
i
e
n et
a
l
. [
11]
desc
ri
b
e
d a
ZV
S-P
W
M
Int
e
rl
eave
d
B
o
ost
Rectifier.
A
no
vel
gri
d
-c
on
nect
ed
b
o
o
st
hal
f
-
bri
dge
P
V
m
i
cro i
n
vert
er sy
st
em
and i
t
s co
nt
rol
i
m
pl
em
ent
a
t
i
ons
are
p
r
esen
ted i
n
[12
]
.
In ord
e
r to ach
iev
e
l
o
w co
st,
h
i
gh
efficien
cy,
for easy con
t
ro
l
and
h
i
gh
er reliabilit
y, a
post
-
hal
f
-
b
ri
dg
e DC
–
D
C
c
o
n
v
ert
e
r
u
s
i
n
g
m
i
nim
a
l
devi
ces
is in
trod
u
c
ed
to in
terface th
e low-vo
ltag
e
PV
m
odul
e. An
ul
t
r
a l
a
rge v
o
l
t
a
ge co
nve
rsi
o
n
rat
i
o
co
nve
rt
er
i
s
pro
p
o
s
ed
b
y
i
n
t
e
grat
i
ng a
Swi
t
c
hed C
a
p
aci
t
o
r
circuit with a
coupled inductor tech
nol
ogy
.
A
DC
-t
o-
DC
con
v
e
r
t
e
r i
s
re
qui
red
t
o
c
o
up
l
e
t
h
e el
ect
r
o
l
y
zer
t
o
the
system
DC
bus [13]. A di
rect
c
onnection
of DC
bus t
o
the electrolyzer
is
not
suitable because it lacks t
h
e
ab
ility to
co
n
t
ro
l th
e
p
o
wer flo
w
b
e
tween
t
h
e ren
e
wab
l
e i
n
pu
t so
urce and
th
e electro
lyzer.
Go
pi
nat
h
et
al
.
[14
]
and
Aru
l
m
u
ru
g
a
n
et al. [15
]
illu
trated th
e in
terl
eaved
boo
st Con
v
e
rter with PI co
n
t
ro
ller is
u
s
ed
t
o
feed
bac
k
t
h
e o
u
t
p
ut
si
gnal
t
o
t
h
e i
nput
f
o
r
t
h
e red
u
ct
i
o
n of ri
ppl
e cu
rre
nt
and i
m
prov
em
ent
of effi
c
i
ency
.
Com
p
ared to
a PID controller, PI co
ntroller has i
n
crea
s
e
d the e
fficiency
and
reduce
s the ripple c
u
rrent
.
Ahm
a
d et
al
. [1
6]
de
vel
o
pe
d t
h
e
vari
ous
pul
ses
o
r
d
u
t
y
cy
cl
e i
s
appl
i
e
d i
n
t
h
i
s
C
o
nve
rt
er
usi
n
g
P
W
M
Techniques.
Ast
r
om
[17]
has de
vel
o
pe
d
t
h
e PI co
nt
r
o
l
l
e
r pa
ram
e
t
e
rs are ch
ose
n
i
n
cor
r
ect
l
y
, t
h
e co
nt
r
o
l
l
e
d
p
r
o
cess inp
u
t
will n
o
t
b
e
stab
le. Tun
i
ng
a
co
n
t
ro
l l
o
op
is th
e ad
ju
stm
e
n
t
of its co
n
t
ro
l p
a
ram
e
ters to
the
opt
i
m
u
m
val
u
es fo
r t
h
e
desi
re
d co
nt
r
o
l
res
p
o
n
se. Zi
e
g
l
e
r-
Ni
chol
s [1
8]
has devel
ope
d
P
I
b
a
sed on o
p
en
l
o
o
p
and
cl
ose
d
l
o
o
p
t
e
st
.
It
has t
o
be
n
o
t
e
d t
h
a
t
cont
rol
l
e
rs
t
u
ned
u
s
i
n
g t
h
i
s
pr
oce
d
u
r
e a
r
e
t
une
d t
o
c
ont
r
o
l
,
not
track
ing
.
Thu
s
, con
t
ro
llers wit
h
p
a
ram
e
ters tu
n
e
d
acc
ord
i
ng
to Zieg
ler-Ni
ch
o
l
s
reco
mme
n
d
a
tion
will p
e
rfo
r
m
well
in
d
i
sturban
ce rej
ection
,
b
u
t
it will
p
e
rfo
rm
p
o
o
r
ly
i
n
t
r
ack
i
n
g reference ch
ang
e
s.
Al
so
, co
m
p
u
ting
th
e PI
cont
roller
para
m
e
ters by
Ziegler-
Nich
ols m
e
tho
d
d
o
es
no
t p
r
ov
id
e
o
p
timu
m
syste
m
response si
nce they are
depe
ndent on t
h
e exact m
a
the
m
atical
m
odel
of t
h
e
pr
ocess.
In t
h
i
s
C
o
nve
rt
er PI C
o
nt
r
o
l
l
er wi
t
h
Zi
egl
e
r an
d
Ni
ch
ol
s m
e
t
hod are
p
r
op
ose
d
.
The i
m
pro
v
e
m
ent
of e
ffi
ci
e
n
cy
i
s
n
o
t
s
u
f
f
i
c
i
e
nt
, s
o
t
h
at
t
h
e o
p
t
i
m
i
zat
i
on of
real
code
d ge
net
i
c
al
gori
t
h
m
i
s
pr
o
pose
d
.
An
d
t
h
en t
h
e co
nv
en
tion
a
l m
e
t
h
od
of PI contro
ller, wh
ich
means
Zieg
ler- Nicho
l
s, is
no
t su
itab
l
e fo
r In
terleav
ed Boo
s
t
Co
nv
erter.
So, th
at th
e GA
is id
eally su
ited
for
unc
o
n
st
rai
n
e
d
opt
i
m
i
zati
on p
r
o
b
l
e
m
s
. B
u
t
,
m
o
st
of t
h
e search a
nd
o
p
t
i
m
i
zat
i
on pro
b
l
e
m
s
are const
r
ai
ned i
n
nat
u
re. He
nce
i
t
i
s
necessary
t
o
t
r
ansfo
r
m
i
t
i
n
t
o
an un
con
s
t
r
ai
ne
d p
r
obl
em
. The bi
nary
co
ded
G
A
has
Hammin
g
cliff p
r
o
b
l
em
s [1
9], wh
ich
so
m
e
ti
m
e
s
may cau
se d
i
fficu
lties in
th
e case of co
d
i
n
g
co
n
t
i
n
u
o
u
s
v
a
riab
les. To
ov
erco
m
e
th
e ab
ov
e
d
i
fficu
lty th
is ch
ap
te
r proposes
a real
-param
eter
genet
i
c al
go
ri
t
h
m
[20]
i
n
whi
c
h t
h
e
o
p
t
i
m
i
zat
i
on vari
a
b
l
e
s are
re
pre
s
ent
e
d a
s
fl
oat
i
n
g
poi
nt
n
u
m
b
er
s.
Th
is artificial
ev
o
l
u
tio
n
p
r
o
c
ess o
f
real coded
g
e
n
e
tic alg
o
r
ith
m
is
th
e fo
und
atio
n
o
f
th
e th
ree m
a
in
di
ffe
re
nt
evol
u
t
i
onary
ba
sed
al
go
ri
t
h
m
s
:
Evol
ut
i
o
ns St
rat
e
gi
es (ES
)
[
2
1]
, Ev
ol
ut
i
o
nary
Pro
g
ram
m
i
ng (EP)
[2
2]
, a
nd
Ge
n
e
t
i
c
Al
go
ri
t
h
m
s
(G
A
)
[
2
3]
.
The
pr
o
pose
d
real
co
ded
ge
net
i
c
al
go
ri
t
h
m
approac
h
h
a
s bee
n
appl
i
e
d
fo
r co
nt
r
o
l
l
e
r t
uni
n
g
(co
n
t
r
ol
l
i
ng pa
ram
e
t
e
rs) i
n
Int
e
rl
eaved B
o
os
t
C
onve
rt
er. T
h
e sim
u
l
a
t
i
on r
e
sul
t
s
sho
w
t
h
at
t
h
e
p
r
o
p
o
sed al
g
o
ri
t
h
m
has resul
t
e
d i
n
m
i
nim
i
zi
ng ri
ppl
e c
u
r
r
e
n
t
and i
m
pro
v
i
n
g ef
fi
ci
ency
t
h
an t
h
e
conve
n
tional
m
e
thod a
nd the traditiona
l bi
nary code
d ge
netic algorithm
.
The propos
ed of real coded GA-
base
d ap
pr
oac
h
i
s
appl
i
e
d t
o
t
une t
h
e P
I
cont
rol
l
e
r i
n
t
h
e Int
e
rl
ea
ved
B
oost
C
o
n
v
ert
e
r. Al
s
o
, t
h
e
p
r
o
p
o
sed
al
go
ri
t
h
m
obt
ai
ns l
e
ss t
i
m
e for
co
nve
r
g
ence
c
o
m
p
ared t
o
t
h
e
bi
na
ry
c
ode
d
genet
i
c
al
go
ri
t
h
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Rea
l
Cod
e
d
Gen
e
tic Algo
rithm Ba
sed
Imp
r
ovemen
t
o
f
Efficien
cy in
In
terlea
ved Bo
o
s
t… (
M
.Aru
n Devi)
53
1
2.
INTERLEAVED BOOST
CONVERTER
A Boo
s
t Co
nverter is a p
o
wer con
v
e
rter
with
an
ou
tpu
t
DC vo
ltag
e
is h
i
gh
er th
an
its in
pu
t DC
vol
t
a
ge
.
It
i
s
a
set
o
f
S
w
i
t
c
hi
ng
M
o
de
Po
w
e
r S
u
ppl
y
(SM
PS)
with at least two sem
i
co
n
d
u
c
tor switches and
o
n
e
en
erg
y
stor
ag
e elem
en
t. Th
is conv
er
ter b
o
o
s
t up
th
e
v
o
ltag
e
at doub
led
th
an
th
e
o
t
h
e
r
con
v
e
r
t
er
. Th
e
filters m
a
d
e
o
f
cap
acitors
o
r
in
du
ctors are
n
o
rm
all
y
ad
d
e
d
to th
e
ou
tput o
f
t
h
e co
nv
erter to redu
ce
o
u
t
p
u
t
v
o
ltag
e
r
i
p
p
l
e. In
du
ctor
and
I
npu
t supp
ly ar
e tog
e
th
er
i
n
ser
i
es co
nn
ectio
n fo
r ad
d
i
n
g
th
e inpu
t and
sto
r
ed
ener
gy
i
n
t
h
e i
n
d
u
ct
o
r
. It
i
s
n
o
t
sui
t
a
bl
e f
o
r
hi
g
h
p
o
we
r. T
h
e o
u
t
p
ut
of t
h
e bo
ost
co
nve
r
t
er havi
ng a
n
am
ount
o
f
r
i
pp
le,
du
e t
o
r
i
pp
le cur
r
e
nt, d
i
stor
tio
n is i
n
cr
eased
.
Int
e
rl
ea
ve
d B
o
ost
C
o
n
v
e
r
t
e
r
has a n
u
m
b
er of
bo
ost
co
n
v
e
r
t
e
rs co
n
n
ect
ed
i
n
paral
l
e
l
,
w
h
i
c
h ha
ve t
h
e
sam
e
frequenc
y
and phase s
h
ift,
m
a
inly used for
rene
wa
ble energy sourc
e
s. In case of boost c
o
nve
r
ter
ripple
i
s
present
i
n
t
h
e i
nput
cu
rre
nt
due t
o
ri
se an
d fal
l
of t
h
e i
n
duct
o
r c
u
r
r
ent
.
Thi
s
pr
obl
em
can be el
im
i
n
at
ed by
u
s
ing
t
h
e In
terl
eav
ed Boo
s
t C
o
nv
erter
wh
ich is shown in
Fig
u
re
1
.
Fig
u
re
1
.
Circuit Diag
ram
o
f
In
terleav
ed
B
oost Co
nv
erter
In a
n
Interleaved Boost Converter t
w
o
b
oost co
nv
er
ters op
er
ated
in
180
˚
o
u
t
of
pha
se.
The i
n
p
u
t
current
is
the
s
u
m
of two
inductor
curre
nts
and
. Because
the two induc
t
or ri
pple c
u
rrents are out of
pha
se, t
h
ey cancel each
othe
r
and re
duce the
input ri
pple c
u
rre
nt.
Wh
en
switch
is on
and
switch
is o
ff:
(1)
(2)
Wh
en
switch
is off
and
switch
is on
:
(3)
(4)
The t
w
o induct
o
r curre
nts
will be
out of
phase an
d
ca
ncel out
the ripple of
each othe
r
i
f
:
(5)
(6)
Th
e abov
e Equ
a
tio
n
(5) and
(6) will b
e
satisfied
if and
only if L1
= L2
= 0
.
713
e
-3
H.T
h
e duty cycle
o
f
th
e system
i
s
0
.
4
.
Hen
c
e the du
ty cycle is calcu
lated
th
e
Equ
a
tio
n (7
) wh
ich
is g
i
v
e
n belo
w:
1
(7)
The ca
pacitor
value
(C = 4.79
F) i
s
cal
cul
a
t
e
d f
r
om
t
h
e Eq
u
a
t
i
on (
8
) a
n
d t
h
e swi
t
c
hi
n
g
f
r
e
que
ncy
o
f
the converte
r i
s
set at the
val
u
e
of 50
KHz.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
52
9
–
54
0
53
2
∆
(8)
The cal
cul
a
t
i
o
n o
f
basi
c pa
ram
e
t
e
r i
s
used t
o
desi
g
n
t
h
e ci
rcui
t
di
agram
of
bot
h
B
oost
a
n
d
Int
e
rl
ea
ve
d B
o
ost
C
o
n
v
ert
e
r
.
100
(9)
The
param
e
ter of e
fficie
n
cy is calculated
from
the ab
o
v
e
Eq
.
(9) also
it is
represen
ted
b
y
th
e rati
o
o
f
out
put
a
nd i
n
p
u
t
p
o
we
r. E
n
er
gy
co
nve
rsi
o
n
effi
ci
ency
(
η
) is th
e ratio
between t
h
e use
f
ul output of an
energy
co
nv
er
sion
an
d th
e inpu
t.
2.
1. Si
gn
al
Ge
nera
tors
Pu
lse Wid
t
h
Mo
du
latio
n
is th
e
sign
al g
e
nerato
rs
th
at con
f
o
r
m
s
th
e wid
t
h
of
th
e p
u
l
se
b
a
sed
on
m
odul
at
or si
g
n
a
l
i
n
fo
rm
ati
o
n
.
It
i
s
a way
of
del
i
v
eri
ng e
n
er
gy
t
h
r
o
u
g
h
a s
u
ccession
of
pulses rather than a
n
analog signal.
In t
h
is pa
per,
d
i
ffe
re
nt
t
y
pes
of
P
W
M
t
e
c
h
ni
q
u
es a
r
e exa
m
i
n
ed t
h
at
are
si
ngl
e
pul
se
wi
dt
h
m
odul
at
i
o
n
,
si
nus
oi
dal
pul
se
wi
dt
h m
odul
at
i
o
n
and
m
odi
fi
ed si
nus
oi
d
a
l
pul
se wi
dt
h
m
odul
at
i
o
n
.
In
th
is
PW
M, the s
w
itch betwee
n supply and loa
d
is turne
d
on/off at a very fast
pace so as to
cont
rol the ave
r
age
v
a
lu
e
o
f
vo
ltag
e
and
cu
rren
t fed
t
o
th
e l
o
ad
. Thu
s
th
e
switch
b
a
sically o
p
e
rates on
th
e abov
e m
e
n
tio
n
e
d
pri
n
ci
pl
e usi
n
g
P
W
M
swi
t
c
hi
ng sc
hem
e
. Th
e t
e
r
m
dut
y
cy
cl
e
ex
p
r
esses th
e ratio
of on
ti
m
e
to
th
e en
tire
peri
od
o
f
t
h
e
t
i
m
e i
n
pe
rcent
a
ge.
It
i
s
gen
e
ra
t
e
d by
c
o
m
p
aring DC
re
fere
nce signal with
a saw tooth si
gnal as
a carri
er
wa
ve.
P
W
M
s
w
i
t
c
hi
ng
schem
e
t
h
u
s
of
fe
rs a
n
ad
v
a
nt
age
of
bea
r
i
n
g
l
o
w p
o
w
er
l
o
ss i
n
t
h
e s
w
i
t
c
hi
n
g
devi
ces
.
In si
n
g
l
e
p
u
l
s
e-wi
dt
h m
odul
at
i
on co
nt
r
o
l
,
one
pul
se p
e
r
hal
f-cy
c
l
e
an
d
t
h
e wi
dt
h o
f
t
h
e pul
se i
s
v
a
ried
to
con
t
ro
l th
e ou
tpu
t
vo
ltag
e
.
I
n
m
u
l
t
i
p
l
e
-p
ul
se m
odul
at
i
on, al
l
p
u
l
s
es are t
h
e eq
ual
wi
dt
h. Va
r
y
t
h
e
pul
se
wi
dt
h
ac
cor
d
i
n
g
t
o
t
h
e
am
pl
i
t
ude of a si
ne wave
eval
uat
e
d at
t
h
e
ce
nt
er of
t
h
e
di
ff
erent
p
u
l
s
e. Fi
gu
re
2
sho
w
s
t
h
e m
o
d
i
fi
ed si
n
u
s
o
i
d
al
p
u
l
s
e m
odul
at
i
on
si
g
n
al
.
Fi
gu
re 2.
M
o
di
fi
ed Si
n
u
soi
d
al
Pul
s
e
W
i
dt
h M
o
d
u
l
a
t
i
o
n
2.
2. Desi
gn of
Co
ntr
o
l
l
ers
Th
e In
terleav
ed
Bo
ost Co
nv
erter with
PI con
t
ro
ller
i
s
pro
p
o
se
d i
n
or
de
r t
o
re
duce t
h
e ri
ppl
e cu
rre
nt
and im
proved efficiency.
A
Proportio
nal
Integ
r
al co
n
t
roller
(PI
)
is
a generic
co
ntr
o
l loo
p
fee
dbac
k
mechanism
widely use
d
in i
n
dustrial
control syste
m
s. A PI controller
calculates
an "error" value as
the
diffe
re
nce
between a m
easured
varia
b
le
an
d a
desi
re
d
set
p
o
i
n
t
.
T
h
e c
o
nt
roller efforts
to m
i
nimize the error
b
y
adju
sting
the pro
cess co
n
t
ro
l inp
u
t
s.
A bl
ock
di
ag
ra
m
of a si
m
p
l
e
cl
osed
-l
o
op
sy
st
em
consi
s
t
i
n
g o
f
a pl
a
n
t
an
d a PI c
o
nt
r
o
l
l
e
r wi
t
h
uni
t
y
feed
bac
k
i
s
sh
ow
n i
n
Fi
g
u
re
3. T
h
e p
u
r
p
o
s
e of t
h
e sy
stem is to keep the proc
e
ss o
u
t
put
(
Y
) cl
ose
t
o
t
h
e
desi
re
d o
u
t
put
(Y
d
)
i
n
s
p
i
t
e
o
f
di
st
u
r
bance
s
.
Thi
s
i
s
achi
e
v
e
d by
m
a
ni
pul
at
i
ng t
h
e
pr
oce
ss i
n
p
u
t
(
U
)
t
h
ro
u
g
h
th
e con
t
ro
ller.
Th
e p
e
rcep
tio
n o
f
th
e cl
osed l
o
o
p
sy
st
em
i
s
defi
ned
by
t
h
e
Int
e
gral
pe
rf
o
r
m
a
nce
m
easur
es and
tim
e
response specifications.
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
repr
esent
a
t
i
o
n
o
f
a
cl
osed
-l
o
o
p
sy
st
em
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Rea
l
Cod
e
d
Gen
e
tic Algo
rithm Ba
sed
Imp
r
ovemen
t
o
f
Efficien
cy in
In
terlea
ved Bo
o
s
t… (
M
.Aru
n Devi)
53
3
Th
e PI co
n
t
ro
l
l
er
m
a
k
e
s th
e p
l
an
t less sen
s
itiv
e to
ch
anges in
th
e su
rro
und
ing
env
i
ro
n
m
en
t an
d
facilitates s
m
al
l ch
ang
e
s in
t
h
e p
l
an
t. Th
e
tran
sfer fun
c
tion
o
f
th
e PI
con
t
ro
ller
is:
s
K
K
s
G
i
p
c
)
(
(10)
W
h
er
e
is t
h
e
p
r
op
or
tio
n
a
l
gain
,
is th
e i
n
teg
r
al
g
a
i
n
and
i
s
th
e
d
e
ri
v
a
tive gain
.
In th
e
PID
co
n
t
ro
ller, t
h
e p
r
op
ortio
n
a
l
part d
eals with
th
e error o
f
t
h
e syste
m
at p
r
esen
t; th
e in
teg
r
al p
a
rt tak
e
s th
e p
a
st
in
to
acco
u
n
t
that w
ill h
a
pp
en
in
th
e
fu
t
u
re. Th
e
p
r
o
por
tio
n
a
l g
a
in
o
f
th
e co
n
t
ro
ller
red
u
c
es error responses t
o
d
i
stu
r
b
a
n
ces.
Th
e in
tegral of th
e erro
r elimin
ates th
e st
ead
y state error, th
us i
m
p
r
oves th
e stab
ility
o
f
th
e
syste
m
. Th
e con
t
ro
ller h
a
s two
p
a
ram
e
ters th
at can b
e
adjusted
lik
e
p
r
op
ortio
n
a
l
g
a
in (
K
)
,
an
d In
tegr
al g
a
in
(
K
). The c
ont
rol
l
o
o
p
pe
rf
orm
s
wel
l
i
f
t
h
e p
a
ram
e
t
e
rs are cho
s
en
pr
o
p
erl
y
. It
per
f
o
r
m
s
po
o
r
l
y
ot
her
w
i
s
e.
Im
prope
r t
u
ni
n
g
m
a
y
m
a
ke t
h
e sy
st
em
beco
m
e
unst
a
bl
e.
T
h
e
pr
oced
u
r
e o
f
fi
ndi
ng t
h
e c
ont
rol
l
e
r
para
m
e
t
e
r i
s
called
tun
i
ng
.
3.
REAL
C
O
DED
GE
NE
TIC
ALGO
RI
THM
In
real world i
n
dustrial applicati
o
n
s
,
o
p
tim
i
zatio
n
algo
rithm
s
tak
e
p
a
rt in an
i
m
p
o
r
tan
t
ro
le, as th
ese
alg
o
rith
m
s
are
u
s
ed
to
au
t
o
mate sev
e
ral indu
strial p
r
ocess
e
s. The m
a
nua
l search
of a so
lu
tion
fo
r
o
p
t
i
m
iz
in
g
requ
ires a
g
r
eat d
eal
o
f
in
si
gh
t an
d p
a
tien
c
e. Fu
rt
h
e
rm
o
r
e, m
a
n
u
a
l op
timizin
g
ofte
n limits th
e scop
e of the
sear
ch
p
r
o
cess to
w
h
at th
e
hu
m
a
n
ex
p
e
r
t
is tr
ain
e
d
to
consid
er
as a good
so
l
u
tio
n. Con
v
e
r
s
ely, op
timizatio
n
alg
o
rith
m
s
au
to
m
a
te th
e sear
ch a
n
d
are
n
o
t
bi
ase
d
i
n
sco
p
e
re
gar
d
i
n
g t
h
e
sol
u
t
i
ons
. T
h
e
wi
de
ra
n
g
e
of
real
-
wo
rl
d
o
p
t
i
m
i
z
at
i
on
pr
o
b
l
e
m
s
and
t
h
e i
m
port
a
nce
of
fi
n
d
i
n
g
go
o
d
a
p
p
r
ox
im
at
e sol
u
t
i
ons
ha
ve l
ead
t
o
a
gr
ea
t
v
a
riety of
op
timizatio
n
s
. Th
is ch
ap
ter presen
ts th
e
d
e
tails of
GA,
fo
r so
lv
ing th
e
sea
r
ch and optimization
pr
o
b
l
e
m
.
In
a st
a
nda
rd
Genet
i
c
Al
g
o
ri
t
h
m
,
bi
nary
st
r
i
ngs
are
ap
pl
i
e
d t
o
re
p
r
esent
t
h
e
deci
si
o
n
var
i
abl
e
s o
f
t
h
e
o
p
tim
izat
io
n
pr
ob
lem
in
th
e g
e
n
e
tic popu
latio
n
,
irr
e
sp
ectiv
e of
th
e ch
aracter
o
f
t
h
e
d
e
cisio
n
v
a
r
i
ab
les. Th
e
use
of
fl
oat
i
n
g
poi
nt
n
u
m
b
ers
i
n
t
h
e
GA
re
p
r
esent
a
t
i
o
n
has
a n
u
m
b
er of a
dva
nt
age
s
o
v
e
r
bi
na
ry
co
di
n
g
.
The
effective
n
ess
of the
GA is i
n
creased a
s
the
r
e is no
nee
d
to co
nv
ert th
e solu
tio
n
v
a
riab
les to
th
e
b
i
n
a
ry typ
e
,
less m
e
m
o
ry is
essen
tial, th
ere is no
lo
ss in
p
r
ecision
by
di
scret
i
zat
i
on t
o
bi
na
ry
o
r
ot
her
val
u
es
, a
n
d
t
h
ere i
s
l
i
b
ert
y
t
o
use
di
ffe
re
nt
ge
net
i
c
ope
rat
o
r
s
.
W
i
t
h
fl
oat
i
ng
poi
nt
re
prese
n
t
a
t
i
on, t
h
e e
v
a
l
uat
i
on
pr
oces
s an
d
rep
r
o
d
u
ct
i
on
o
p
erat
or rem
a
i
n
t
h
e sam
e
as t
h
at
i
n
bi
nary
-c
o
d
ed
GA
, b
u
t
cr
oss
ove
r o
p
e
r
at
i
on i
s
m
a
de var
i
abl
e
by
va
ri
abl
e
.
Al
so, t
h
e
uni
f
o
r
m
m
u
t
a
t
i
on i
s
use
d
f
o
r
t
h
e
re
al
param
e
t
e
r m
u
t
a
t
i
on o
p
e
r
a
t
or.
The
det
a
i
l
s
of
t
h
e
cross
o
ver
an
d
m
u
t
a
t
i
on o
p
e
r
a
t
or a
r
e
prese
n
t
e
d i
n
t
h
e
f
o
l
l
o
wi
n
g
s
u
b
s
ect
i
o
ns.
3.
1. Cr
oss
over
Oper
ati
o
n an
d
M
u
t
a
ti
on
The c
r
os
sover
ope
rator is m
a
inly accountable for
the
global search property of the
GA. Cross
o
ve
r
basi
cal
l
y
m
e
rg
es su
bst
r
uct
u
r
e
s o
f
t
w
o
pa
r
e
nt
c
h
r
o
m
o
somes to create
ne
w st
ruct
ure
s
,
with the
preferred
p
r
ob
ab
ility typ
i
cally in
th
e ran
g
e
of 0.6
–
1
.
0
.
Th
e Blend
cro
s
sov
e
r
op
erat
o
r
(BLX-
α
)
(
D
ev
ar
aj
20
05)
is
u
tilized
in
th
is stu
d
y
. Fi
g
u
re 4 illu
strates th
e BLX-
α
cr
oss
o
ver
ope
rat
i
o
n f
o
r t
h
e
one
-dimensional case.
In the
BLX-
α
c
r
o
ss
o
v
er
t
h
e
of
f s
p
ri
ngy
i
s
sam
p
l
e
d fr
om
t
h
e space
[
]
,
2
1
e
e
as fo
llows:
y =
otherwise
sampling
repeat
u
y
u
if
e
e
r
e
:
:
max
min
1
2
1
(1
1)
Whe
r
e,
)
(
1
2
1
1
u
u
u
e
(12)
1
2
2
2
u
u
u
e
(13)
:
r
U
n
i
f
or
m
r
a
n
dom
n
u
m
b
er
1
,
0
It is to
b
e
n
o
t
ed
th
at
e
1
and
e
2
will lie
b
e
tween
min
u
and
ma
x
u
, th
e v
a
riab
le’
s
lo
w
e
r
an
d
u
p
p
e
r
bo
und
resp
ectiv
ely.
In
a
n
u
m
b
e
r
o
f
test p
r
ob
lem
s
, it is ex
a
m
in
ed
th
at
α
= 0.
5 p
r
ovi
des
go
o
d
re
sul
t
s
. T
h
e feat
ure
of
t
h
i
s
t
y
pe o
f
c
r
oss
ove
r
ope
rat
o
r i
s
t
h
at
t
h
e
creat
ed
p
o
i
n
t
depe
n
d
s
on
t
h
e l
o
cat
i
o
n
o
f
bot
h
pare
nt
s.
I
f
b
o
t
h
pare
nts are
nea
r
er to each
other, the
ne
w c
h
ild will also
be
close to the
pa
rents.
On the
other
hand, i
f
parent
s
are
distant from
each other, t
h
e sea
r
ch is si
milar to a ra
ndom
search.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
52
9
–
54
0
53
4
Fi
gu
re
4.
Sc
he
m
a
t
i
c
represe
n
t
a
t
i
on
of
B
L
X
-
α
cros
so
ver
After cross
ove
r is com
p
leted, m
u
tation take
s place.
T
h
e m
u
tation
operat
or is used t
o
int
r
oduce ne
w
g
e
n
e
tic
o
b
j
ects in
to
th
e pop
u
l
atio
n
.
M
u
tation
rand
o
m
ly ad
j
u
sted
a
v
a
riable with
a sm
all
p
r
ob
ab
ility. In
th
is
work, t
h
e
Un
ifo
r
m
Mu
tatio
n
o
p
e
rator is applied
,
wh
ich
is t
h
e
v
a
riab
le set
b
e
tween
th
e lower to
up
p
e
r limit.
4
.
GA IMPL
EMENT
A
TION
In t
h
e R
eal
-c
o
d
ed
Ge
net
i
c
Al
g
o
ri
t
h
m
im
pl
em
ent
a
t
i
on, t
h
e fol
l
owi
ng
m
odi
fi
cat
i
ons are m
a
de t
o
im
prove the
efficiency of
form
ula
ti
ng co
ntr
o
ller
param
e
ters.
With a
real
-co
d
e
d
f
o
rm
of re
pr
esentatio
n, t
h
e
sel
ect
i
on sc
he
m
e
rem
a
i
n
s t
h
e sam
e
, but
m
odi
fi
cat
i
ons
are desi
red
f
o
r cr
oss
ove
r a
n
d m
u
t
a
t
i
on o
p
e
rat
o
r
s
.
While s
o
lvi
n
g an optimization problem
us
ing
GA, each
indivi
dual
in t
h
e
population
signifie
d
a
candidate
so
lu
tion
.
Each
in
d
i
v
i
d
u
a
l
in
t
h
e
p
opu
latio
n rep
r
esen
ts t
h
e
param
e
ters o
f
t
h
e PI con
t
ro
ller. For t
h
e
In
terleav
e
d
Boost Convert
e
r the controller param
e
ters are K
p
and
K
i
. Whe
r
e
K
i
=K
c
/
τ
i.
In
th
is
work, th
e p
a
ram
e
ters o
f
the
cont
rol
l
e
r are r
e
prese
n
t
e
d as f
l
oat
i
ng p
o
i
n
t
n
u
m
b
ers. A
typ
i
cal ch
ro
m
o
some with
flo
a
tin
g
po
in
t represen
tation
i
s
gi
ve
n
bel
o
w.
Thi
s
t
y
pe
of
re
prese
n
t
a
t
i
o
n
ha
s a n
u
m
b
er of
adva
nt
age
s
o
v
e
r bi
nary
re
p
r
e
s
ent
a
t
i
o
n
.
T
h
e
effi
ci
ency
of
th
e GA is imp
r
ov
ed
as t
h
ere is n
o
n
e
ed
to
conv
ert th
e
in
pu
t v
a
riab
les to
th
e b
i
n
a
ry
typ
e
. Th
e
prop
o
s
ed
Genet
i
c
Al
go
ri
t
h
m
searches f
o
r t
h
e o
p
t
i
m
al
sol
u
t
i
o
n
by
m
a
xi
m
i
zi
ng o
r
m
i
ni
m
i
zi
ng t
h
e f
unct
i
o
n a
nd t
h
eref
ore
an
ev
alu
a
tion
fun
c
tion
wh
ich
pro
v
i
d
e
s a
measu
r
e
o
f
t
h
e qu
ality o
f
th
e
p
r
o
b
l
em
so
lu
tio
n
is
n
e
eded
. Th
e
Equation (14) i
ndicates t
h
e
objective
function.
MSE
f
f
(14)
During the
GA run, GA sea
r
ches
for a so
lu
tio
n
with
m
a
x
i
m
u
m
fitn
ess-fun
c
tion
v
a
l
u
e. Hen
c
e, the
m
i
nim
i
zat
i
on o
b
ject
i
v
e f
u
nct
i
o
n
i
s
gi
ve
n
by
(3
.4
) i
s
t
r
a
n
s
f
o
r
m
e
d as:
Fitn
ess=
(15)
K
is a co
nstant. In
the
d
e
nomin
ato
r
a v
a
l
u
e of
‘1’ is added
with
‘
f ’
i
n
o
r
de
r t
o
a
voi
d
di
vi
si
o
n
by
zero.
5.
RESULTS
A
N
D
DI
SC
US
S
I
ON
Th
is section
presen
ts th
e sim
u
latio
n
resu
lts an
d
an
alys
is o
f
DC to
DC i
n
terleav
ed
boo
st co
nv
erter.
In
clo
s
ed
loop
, th
e ou
tpu
t
is feed
b
a
ck
to
the g
a
te p
o
l
es
o
f
th
e switch
(transisto
r) th
is u
s
ing
Pu
lse W
i
d
t
h
m
odulator. T
h
e softwa
re for
the pr
opos
ed
genetic algorit
hm
is writte
n in MATLAB a
n
d exec
uted
on
a PC
wi
t
h
2.
4 M
H
Z
an
d
2
5
6
M
B
R
A
M
.
T
h
e M
A
TL
AB
Si
m
u
l
i
n
k
di
a
g
ram
o
f
t
h
e
bo
ost
c
o
nve
rt
er
i
s
s
h
o
w
n
i
n
Fi
gu
re 5
.
The
resp
o
n
se o
f
t
h
e B
oost
C
o
nve
rt
er wi
t
h
Si
n
g
l
e
Pul
s
e
W
i
dt
h
M
odul
at
i
o
n i
s
sho
w
n i
n
Fi
g
u
re
6.
From
t
h
e fi
g
u
r
e
, i
t
i
s
fou
nd t
h
at
for a
nom
i
n
al
i
nput
vol
t
a
g
e
i
s
24
V t
h
e c
o
nve
rt
er
pr
o
duc
es t
h
e o
u
t
p
ut
v
o
l
t
a
ge
47V.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Rea
l
Cod
e
d
Gen
e
tic Algo
rithm Ba
sed
Imp
r
ovemen
t
o
f
Efficien
cy in
In
terlea
ved Bo
o
s
t… (
M
.Aru
n Devi)
53
5
Fi
gu
re
5.
M
A
T
L
AB
Si
m
u
l
i
n
k
di
ag
ram
of B
o
ost
C
o
n
v
ert
e
r
Fi
gu
re
6.
R
e
sp
ons
e
of B
o
ost
C
o
n
v
ert
e
r
wi
t
h
Si
n
g
l
e
P
W
M
t
echni
que
The
res
p
o
n
se
of
a
bo
ost
c
o
n
v
ert
e
r
wi
t
h
si
n
u
soi
d
al
P
W
M
t
echni
q
u
e i
s
sh
ow
n i
n
Fi
gu
re
7.
Fr
om
t
h
e
respon
se, it is
foun
d
t
h
at th
e
o
u
t
p
u
t
settling ti
m
e
is h
i
g
h
.
W
i
t
h
n
o
m
in
al in
pu
t vo
ltag
e
i
s
24
V, th
e conv
erter
p
r
od
u
ces th
e
ou
tpu
t
vo
ltag
e
4
8
V. Th
e ou
tpu
t
curren
t
is
oscillatin
g
b
e
tween
0
to 6A.
Th
is sh
ows t
h
e h
i
gh
ri
p
p
l
e
cu
rre
nt
i
n
t
h
i
s
m
e
t
hod.
Fi
gu
re 7.
R
e
sp
ons
e of
B
o
ost
C
o
n
v
ert
e
r wi
t
h
SP
W
M
t
ech
ni
que
The res
p
o
n
se of a bo
ost
c
o
n
v
ert
e
r
wi
t
h
M
o
di
fi
ed
Sinu
so
id
al PW
M techn
i
qu
e is sho
w
n in
Fi
g
u
r
e
8.
From
the res
p
onse, it is instigate that the out
put settli
ng tim
e is high.
W
i
t
h
nom
inal input
voltage is
24V, the
co
n
t
ro
ller
produ
ces th
e ou
tpu
t
vo
ltag
e
between
4
8
V to 50V
and
th
e
ou
tpu
t
cu
rren
t is o
s
ci
llatin
g
b
e
tween
0
to
2
A
. Th
is sho
w
s th
e efficien
cy
is h
i
g
h
and
t
h
e ripp
le cu
rren
t
is less.
dc
pw
m
C
o
nt
i
n
uo
us
po
w
e
r
g
u
i
v
+
-
Vol
t
ag
e
1
v
+
-
Vol
t
ag
e
b1
T
o
W
o
r
k
s
pac
e
Subt
r
a
c
t
S
c
ope4
S
c
ope3
Sc
ope2
S
c
ope1
S
c
ope
S
a
tu
r
a
ti
o
n
R
PI
D
P
I
D
C
ont
r
o
l
l
e
r
gm
DS
Mo
s
f
e
t
L1
1
Ga
i
n
Di
o
d
e
D
C
Vol
t
ag
e
Sou
r
c
e
i
+
-
C
u
r
r
e
n
t
M
e
a
s
u
r
em
en
t
1
i
+
-
C
u
r
r
e
nt
M
e
a
s
ur
e
m
e
n
t
48
C
o
ns
t
ant
Ca
2
0
0.
5
1
1.
5
2
2.
5
3
3.
5
x 1
0
5
-2
0
0
20
40
60
80
100
120
Ti
m
e
(
s
e
c
)
V
o
l
t
ag
e(
V
)
B
oos
t
C
onv
er
t
e
r
w
i
t
h
S
i
ngl
e P
u
l
s
e W
i
dt
h M
odul
at
i
o
n
I
nput
V
o
l
t
age
I
nput
C
u
r
r
ent
Out
put
C
u
rr
ent
Out
put
V
o
l
t
age
0
1
2
3
4
5
6
7
8
9
10
x 1
0
6
-10
0
10
20
30
40
50
60
70
80
90
Ti
m
e
(
s
e
c
)
V
o
l
t
age(
V
)
B
oos
t
C
onv
ert
e
r
w
i
t
h
S
i
nus
oi
d
a
l
P
u
l
s
e
W
i
dt
h
M
odul
at
i
o
n
O
u
t
put
C
u
rren
t
I
n
pu
t
V
o
l
t
ag
e
I
n
p
u
t
C
u
r
r
ent
O
u
t
put
V
o
l
t
age
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
52
9
–
54
0
53
6
Fi
gu
re 8.
R
e
sp
ons
e of
B
o
ost
C
o
n
v
ert
e
r wi
t
h
M
S
P
W
M
t
ech
ni
q
u
e
Int
e
rl
ea
ve
d
B
o
ost
C
o
nve
rt
er r
e
duce
s
t
h
e ri
p
p
l
e
curr
ent
due
t
o
t
h
e ri
se
an
d f
a
l
l
of
i
n
duct
o
r cur
r
ent
by
t
h
e paral
l
e
l
co
nnect
i
o
n o
f
t
w
o b
o
o
s
t
con
v
er
t
e
rs. Fi
g
u
re
9 sho
w
s t
h
e Si
m
u
l
i
nk
di
ag
ram
of I
n
t
e
rl
ea
ved
B
oos
t
C
o
n
v
ert
e
rs. T
h
e resp
onse
of I
B
C
wi
t
h
si
ngl
e pul
se wi
dt
h m
o
d
u
l
a
t
i
on i
s
sh
ow
n i
n
Fi
g
u
re
10
. The res
p
on
se o
f
IB
C
wi
t
h
si
n
g
l
e
p
u
l
s
e
wi
dt
h
m
odul
at
i
on i
s
s
h
o
w
n i
n
t
h
e
Fi
gu
re
1
1
.
Fi
gu
re
9.
M
A
T
L
AB
Si
m
u
l
i
n
k
di
ag
ram
of
IB
C
wi
t
h
PI c
o
nt
r
o
l
l
e
r
Fig
u
r
e
10
.
Resp
on
se
of
I
BC w
ith
Si
n
g
l
e PW
M
techn
i
qu
e
0
1
2
3
4
5
6
7
8
9
10
x 1
0
6
-2
0
0
20
40
60
80
10
0
Ti
m
e
(
s
e
c
)
V
o
l
t
age
(
V
)
B
o
o
s
t C
o
n
v
e
r
t
e
r
w
i
th
MS
P
W
M
O
u
t
put
C
u
r
r
ent
I
n
put
V
o
l
t
age
I
n
put
C
u
r
r
ent
O
u
t
put
V
o
l
t
ag
e
dc
pw
m
C
o
nt
i
nuo
u
s
po
w
e
r
g
u
i
v
+
-
Vo
l
t
a
g
e
1
v
+
-
Vo
l
t
a
g
e
i1
T
o
W
o
r
k
s
pac
e
Subt
r
a
c
t
S
c
ope6
Sc
op
e5
Sc
ope4
Sc
ope3
S
c
ope2
Sc
op
e1
S
a
tu
r
a
ti
o
n
R
PI
D
P
I
D Co
n
t
r
o
l
l
e
r
g
m
D
S
Mo
s
f
e
t
1
g
m
D
S
Mo
s
f
e
t
L2
L1
1
Ga
i
n
Di
o
d
e
1
Di
o
d
e
DC
i
+
-
Cu
r
r
e
n
t
48
C
ons
t
ant
Ca
2
0
0.
5
1
1.
5
2
2.
5
3
3.
5
x 1
0
5
-2
0
0
20
40
60
80
10
0
12
0
Ti
m
e
(
s
e
c
)
V
o
l
t
age(
V
)
I
B
C
w
i
t
h
S
i
n
g
l
e
P
u
l
s
e W
i
dt
h M
o
dul
at
i
o
n
I
nput
C
u
r
r
en
t
I
nput
V
o
l
t
ag
e
Out
put
C
u
rr
ent
Out
put
V
o
l
t
ag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Rea
l
Cod
e
d
Gen
e
tic Algo
rithm Ba
sed
Imp
r
ovemen
t
o
f
Efficien
cy in
In
terlea
ved Bo
o
s
t… (
M
.Aru
n Devi)
53
7
Fi
gu
re
1
1
. R
e
s
p
o
n
se
o
f
IB
C
wi
t
h
S
P
W
M
t
echni
que
The res
p
onse
of a
n
interleaved boost conve
r
ter w
ith
Mod
i
fied
Sinu
so
id
al
P
W
M
t
echni
q
u
e i
s
sho
w
n
i
n
Fi
g
u
re
1
2
.
W
i
t
h
nom
i
n
al
i
n
p
u
t
vol
t
a
ge
i
s
2
4
V
,
t
h
e
c
o
nv
ert
e
r pr
od
uces
t
h
e
o
u
t
p
ut
vol
t
a
ge 50
V. The
out
put
cu
rr
en
t is less
co
m
p
ar
ed
w
ith th
e boo
st conver
t
er
.
I
t
show
s
th
e eff
i
cien
cy
o
f
t
h
e in
ter
l
eaved
b
o
o
s
t co
nv
er
ter
is
h
i
gh
du
e to
th
e red
u
c
ti
o
n
of
ripp
le cu
rren
t.
Alth
oug
h
th
e efficien
cy is h
i
gh
, th
e o
s
cillatio
n
in
ou
t
p
u
t
cu
rren
t
sho
w
s
t
h
e
ri
p
p
l
e
an
d
real
co
de
d
GA
i
s
p
r
op
os
ed t
o
t
u
ne t
h
e c
ont
rol
l
e
r
pa
ra
m
e
t
e
rs.
Fi
gu
re 1
2
.R
es
p
ons
e of IB
C
wi
t
h
M
S
P
W
M
t
e
chni
que
The cl
osed
l
o
o
p
pr
op
o
r
t
i
onal
Int
e
gral
c
o
nt
r
o
l
l
e
r casca
ded
wi
t
h
t
h
e
pr
oc
ess i
s
t
u
ned
f
o
r t
h
e
o
p
t
i
m
al
val
u
es
o
f
K
p
and
K
i
usi
n
g a
bi
nary
c
o
ded
G
A
al
go
ri
t
h
m
and
R
eal
code
d
G
A
.
Th
e
op
ti
m
a
l GA setting
s
are
Num
b
er
of
ge
n
e
rat
i
ons
:
10
Po
pul
at
i
o
n
si
ze
:
10
Cro
s
sov
e
r
probab
ility
:
0
.
8
Mu
tatio
n
p
r
obab
ility
:
0
.
06
Bo
th
GA is ap
p
lied
to
o
b
t
ain
th
e p
a
ram
e
ters o
f
th
e PI co
n
t
ro
ller for th
e Bo
o
s
t Co
nv
erter and
In
terleav
e
d
Boo
s
t Co
nv
erter.
Th
e bou
nd
aries o
f
the
optim
ization va
riable
s are taken as
0<K
p
<1
0;
0<
K
i
<5. The
opt
i
m
al cont
r
o
l
gai
n
s obt
ai
ne
d by
t
h
e pr
o
p
o
s
ed al
g
o
ri
t
h
m
along with the
efficiency an
d
ripp
le cu
rren
t
o
f
bo
th
genet
i
c
al
go
ri
t
h
m
wi
t
h
B
oost
and I
n
t
e
rl
eave
d
B
o
o
s
t
C
o
n
v
e
r
t
e
r are gi
ve
n i
n
Tabl
e 1. T
h
e
perf
orm
a
nce of t
h
e
syste
m
is fo
und
to
b
e
satisfacto
r
y with th
e con
t
ro
l
g
a
in
s
o
b
t
ain
e
d
u
s
ing th
e pro
p
o
s
ed
alg
o
rith
m
.
From
th
e
t
a
bl
e, i
t
i
s
f
o
u
n
d
t
h
at
t
h
e
pr
o
pos
ed
real
c
o
d
e
d
GA
wi
t
h
i
n
t
e
rl
eave
d
bo
ost
co
nve
rt
er
i
s
h
a
vi
n
g
m
i
nim
u
m
ri
ppl
e
current a
n
d m
a
xim
u
m
efficiency.
Also
, th
e
co
m
p
u
t
atio
n
ti
me requ
irem
en
t is min
i
m
u
m
i
n
Pro
p
o
s
ed
GA.
Th
at
all requirem
ents of real code
d
GA produce
be
tter res
u
lt compare
d
t
h
an the
bina
ry code
d
genetic algorithm
.
Fo
r an
in
terleav
e
d
boo
st conv
erter
with
sing
le PW
M Kp
and
Ki values
are 7 and 1.9, this conve
rter
produces the e
f
ficiency at 73%
and ri
p
p
l
e
cur
r
ent
at
0.
00
2
A
fo
r ge
nerat
i
o
n
si
ze of 1
0
. T
h
e K
p
a
nd K
i
valu
es o
f
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
x 1
0
6
-1
0
0
10
20
30
40
50
60
70
Ti
m
e
(
s
e
c
)
V
o
l
t
ag
e(
V
)
I
B
C
w
i
t
h
S
i
nus
oi
dal
P
u
l
s
e W
i
dt
h M
odu
l
a
t
i
on
O
u
t
put
C
u
rr
ent
I
n
put
V
o
l
t
age
I
n
put
C
u
r
r
ent
O
u
t
put
V
o
l
t
age
0
1
2
3
4
5
6
7
8
9
10
x 1
0
6
-20
0
20
40
60
80
10
0
Ti
m
e
(
s
e
c
)
V
o
l
t
age
(
V
)
I
B
C
w
i
t
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
52
9
–
54
0
53
8
an
in
terleav
e
d
b
o
o
s
t conv
erter with
Mod
i
fied
Sinu
so
id
al
PWM are 9 a
nd 2, this s
h
ows the
efficiency of 89%
and ri
ppl
e cu
rr
ent
i
s
0.0
0
0
9
A
.
From
the Table 1 com
p
arin
g th
e en
tire tech
n
i
qu
es, in
terleav
e
d
b
o
o
s
t conv
erter
with
M
o
d
i
fied Sinu
so
id
al Pu
lse
W
i
d
t
h Mo
du
latio
n techn
i
qu
e sho
w
s th
e
b
e
st resu
lt
co
m
p
ared to bo
o
s
t
conve
r
ter.
Tabl
e 1.
Com
p
arison
of
Per
f
o
rm
ance A
n
alysis
PWM
T
e
chniques
GA
Gn
Size
Pop
Size
Ti
m
e
Ir
Boost Converter w
ith
Single Pulse W
i
dth
M
odulation
BGA 5
5
7
2
1.
11e3
13.
42
0.
05
RGA 5
5
6
1
425.
53
2
4.
09
0.
009
BGA 7
7
9
0.
02
2.
18e3
18.
41
0.
05
RGA 7
7
6
1.
5
1.
09e3
2
4.
94
0.
009
BGA 10
10
9
0.
02
4.
70e3
2
7.
86
0.
05
RGA 10
10
6
1.
9
1.
88e3
2
9.
19
0.
009
Boost Converter w
ith
Sinusoidal Pulse W
i
dth
M
odulation
BGA 5
5
8
0.
3
8.
25e3
18.
22
0.
03
RGA 5
5
8
4
212.
27
2
5.
13
0.
005
BGA 7
7
9
.
6
0.
5
2.
35e4
4
0.
83
0.
03
RGA 7
7
8
4
249.
93
4
5.
44
0.
005
BGA 10
10
9
0.
5
3.
14e4
60.
69
0.
03
RGA 10
10
8
4
759.
12
65.
60
0.
005
Boost Converter w
ith
M
odified Sinusoi
d
a
l
Pulse W
i
dth M
odulation
BGA 5
5
9
2
1.
12e3
11.
77
0.
04
RGA 5
5
9
2
154.
40
10.
76
0.
004
BGA 7
7
9
0.
5
1.
15e3
2
5.
27
0.
04
RGA 7
7
9
1
195.
32
2
6.
52
0.
004
BGA 10
10
6
1
1.
12e3
7
2.
36
0.
04
RGA 10
10
6
1
503.
20
7
1.
11
0.
004
Interleaved Boost
Conver
t
er
with Sin
g
le
Pulse W
i
dth M
odulation
BGA 5
5
9
0.
5
1.
15e3
2
5
0.
05
RGA 5
5
9
1.
9
199.
15
15.
14
0.
001
BGA 7
7
9
0.
7
1.
29e3
4
9
0.
05
RGA 7
7
8
.
2
1.
9
381.
56
30.
57
0.
001
BGA 10
10
9
1.
2
5.
47e3
67
0.
05
RGA 10
10
7
1.
9
840.
46
7
1.
71
0.
001
Interleaved Boost
Conver
t
er
with
Sinusoidal Pulse W
i
dth
M
odulation
BGA 5
5
9
0.
8
5.
18e3
33
0.
04
RGA 5
5
6
1.
9
153.
29
4
5.
23
0.
002
BGA 7
7
9
1.
1
5.
23e3
61
0.
04
RGA 7
7
6
.
7
1.
9
270.
65
50.
77
0.
002
BGA 10
10
9
1.
5
5.
67e3
7
2
0.
04
RGA 10
10
7
1.
9
750.
24
7
3.
17
0.
002
Interleaved Boost
Conver
t
er
with
M
odified Sinusoi
d
a
l
Pulse W
i
dth M
odulation
BGA 5
5
9
1.
2
6.
12e3
34
0.
03
RGA 5
5
8
.
9
0.
8
120.
25
35.
50
0.
0009
BGA 7
7
9
1.
1
1.
13e4
59
0.
03
RGA 7
7
9
1
209.
20
56.
36
0.
0009
BGA 10
10
9
1.
5
1.
25e4
84
0.
03
RGA 10
10
9
2
683.
32
89.
17
0.
0009
Fi
gu
re
1
3
. R
e
a
l
C
ode
d
G
A
f
o
r IB
C
wi
t
h
M
S
P
W
M
Fi
gu
re
13
s
h
o
w
s t
h
e
co
n
v
er
gence
o
f
pr
o
p
o
se
d real
c
o
de
d
genet
i
c
al
g
o
r
i
t
h
m
and i
t
i
s
obs
er
ved
t
h
at
the fitnes
s
value inc
r
eases
ra
pidly in t
h
e
2
nd
g
e
n
e
ration
on
th
e g
e
n
e
tic alg
o
rith
m
.
Du
ri
n
g
th
is stag
e, t
h
e
GA
co
n
c
en
trates main
ly o
n
find
ing
feasib
le so
lu
t
i
o
n
s
to
th
e
p
r
ob
lem
.
Th
en
th
e v
a
lu
e in
creases slo
w
ly an
d
settles
d
o
wn
n
e
ar to
th
e op
tim
u
m
v
a
lu
e o
f
5
th
ge
n
e
rat
i
on
wi
t
h
m
o
st
of i
ndi
vi
d
u
a
l
s
i
n
t
h
e po
p
u
l
a
t
i
on reac
hi
n
g
t
h
at
poi
nt
.
1
2
3
4
5
6
7
8
9
10
5.
7
5.
8
5.
9
6
6.
1
6.
2
6.
3
x 1
0
-3
G
ene
r
a
t
i
ons
Fi
t
n
es
s
Be
s
t
A
v
er
age
Evaluation Warning : The document was created with Spire.PDF for Python.