Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 77
4
~
78
4
I
SSN
:
208
8-8
6
9
4
, D
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10.
115
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urn
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: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Modeli
ng and simulation of
DC
to
DC
boost converter using
single phase matrix
converter topology
Fa
ja
riah
K
a
d
i
r,
S.
Z
.
M
o
h
a
mma
d
Noo
r
, Fa
ra
n
a
d
i
a
A. H.,
K.S. M
uha
mm
a
d
Facult
y
of
E
l
ec
tr
i
c
al E
ngineeri
ng,
Uni
v
e
r
siti Tekn
ologi MARA,
M
a
laysi
a
Ar
ti
cl
e Info
A
B
STRAC
T
A
r
ti
cl
e hi
st
ory:
R
ece
i
v
ed Oc
t
19
,
20
1
9
R
e
vi
sed
D
ec 1
2
, 201
9
A
c
c
e
p
ted
Jan
19
, 20
20
The main obj
e
ct
i
v
e of
this
work
is to m
ode
l a
n
d
si
mulat
e
DC
to DC
Boost
Co
nv
e
r
ter using
S
i
ng
le P
h
as
e M
a
trix
Co
nver
t
er
(S
P
M
C
) to
polog
y us
in
g
M
A
TLA
B/S
i
mulink
(MLS
)
.
Th
e
o
u
tpu
t
vo
ltag
e
is
c
o
ntrol
l
ed
b
y
us
in
g P
u
lse
Wi
dt
h Mo
du
la
tion
(PW
M
)
tec
hni
q
u
e
.
F
o
u
r
p
a
irs
of
Insul
a
te
d
G
a
t
e
B
i
p
o
la
r
Trans
i
stor
(IG
BT)
is u
s
ed
as
th
e sw
it
ching
d
e
v
i
ce
wh
ere
fo
r
ea
ch p
a
ir
, it is
loca
ted
in p
a
ral
l
el
and
op
pos
it
e
dire
ct
ion.
Saf
e
commutation techni
que
is
pe
rfo
rm
e
d
i
n
prev
e
n
t
i
n
g
v
o
lta
ge
sp
ik
e
a
t
t
h
e
ou
tput
.
T
h
ro
ug
h th
e
si
m
u
l
a
ti
on
,
at sw
itch
in
g freq
u
en
cy o
f
25
kHz
,
the
mod
e
l
is
abl
e
to
step
u
p
its
in
put v
o
lt
age
ab
ou
t tw
o
times
larger
and
all
of
the
resu
lts
a
c
hi
ev
ed
a
g
o
o
d
agr
e
emen
t
w
ith
the p
r
in
cip
l
e o
f
fou
r
q
u
adran
t
o
p
erat
io
n.
It is
al
so
reali
zed
tha
t
with
ou
t th
e
imple
m
en
tat
i
o
n
of s
a
fe co
mmu
tatio
n
t
echn
i
qu
e, sp
ik
es were
g
e
ne
r
a
ted
and
the
mo
del is
u
n
ab
le to boo
st
i
t
s
inpu
t vo
ltag
e. A
l
l
o
f
th
e s
e
lected
r
e
s
u
lts
from
th
e
a
n
a
l
ysi
s
whi
c
h in
c
l
u
d
e
s
v
a
ria
tio
n of q
u
a
dra
n
t, switc
h
i
ng fre
que
n
c
y
,
d
u
t
y
c
y
cl
e
an
d res
i
s
tive
loa
d
are
pr
ese
n
t
e
d
in thi
s
p
a
per
.
K
eyw
ords
:
MATLAB
/
Simulink
PWM
Singl
e p
h
ase ma
tri
x
c
o
n
v
e
r
t
e
r
T
h
is is
an
op
e
n
acces
s a
r
ticle
un
der
th
e
CC B
Y
-SA
l
i
cen
se
.
C
o
rre
s
pon
di
n
g
Au
th
or:
F
a
j
a
ri
a
h
Ka
di
r,
Facul
t
y
o
f
El
ec
t
r
i
c
al
En
gi
neer
ing,
U
n
i
v
e
r
s
iti
Tekn
o
l
o
g
i
MA
RA, 4
0
450
Sh
ah
Ala
m
,
S
e
l
a
ng
o
r
.
Emai
l
:
aj
a.kadi
r9
6@
gmai
l
.
c
o
m
1.
IN
TR
O
DUCTION
S
i
ngle
P
h
ase
M
a
t
r
i
x
C
onve
rt
er i
s
ap
pl
i
c
a
b
l
e
i
n
ma
ny
ap
pl
ic
at
i
ons s
u
ch a
s
fo
r
i
n
d
u
ct
i
o
n hea
t
ing
,
AC
-
AC
c
o
nve
rt
er,
re
ct
i
f
i
e
r, i
nve
rt
e
r
,
AC
v
o
l
t
a
ge
c
o
nt
rol
l
er,
fre
q
u
e
ncy
c
h
a
nge
r
(
c
ycl
o
c
o
n
v
e
r
t
e
r) a
n
d
dua
l
c
o
nv
ert
e
r.
Dual
c
o
n
v
ert
e
r
i
s
use
d
f
o
r
bi
-di
r
e
c
t
i
o
n
a
l
sp
eed
co
nt
rol
of
DC
dri
v
e
a
n
d
DC
-DC
c
o
nve
rt
er.
E
v
er
y
el
e
c
t
r
i
cal
appl
i
a
nc
e
ha
d
t
h
ei
r
ow
n rat
i
n
g.
This
rat
i
ng
us
ua
ll
y
di
spla
yed
o
n
t
h
e
st
i
c
ker
o
r
rat
i
n
g
p
l
at
e
on t
h
e el
e
c
t
r
i
cal
appl
i
a
nc
e
.
T
h
e
ra
t
i
ng
tha
t
bei
n
g
di
spl
a
y
e
d ac
t
u
a
l
ly
rep
r
ese
n
t
s
t
h
e
vol
t
a
ge
at
w
h
i
c
h
t
h
e
a
ppl
i
a
nce
i
s
de
si
g
n
e
d
to
ope
ra
t
e
a
n
d
t
h
e cu
rre
n
t
c
o
n
s
um
pt
ion
at
t
h
a
t
part
i
c
ul
a
r
vol
ta
ge. T
h
i
s
i
s
whe
r
e t
h
e
i
m
p
l
e
m
e
n
t
a
t
i
on
o
f
pow
e
r
e
l
e
c
t
r
o
n
i
cs c
onv
e
r
t
e
r is
v
e
ry im
po
r
t
an
t su
ch
a
s
D
C
-
D
C
c
onv
er
te
r, i
n
v
e
r
t
e
r
,
re
c
t
if
ie
r
an
d oth
e
r
po
w
e
r
conv
e
r
te
r.
A
DC
po
w
e
r
su
pp
ly
is u
s
ed
in
mo
st
of
t
h
e
a
p
p
l
ia
n
ces
whe
r
e
a
c
o
n
s
tan
t
v
o
lta
g
e
is
r
e
q
u
ir
ed
.
DC
-DC
po
w
e
r
con
v
e
r
te
rs
are
empl
o
y
e
d
i
n
a
vari
e
t
y
of a
p
pl
i
c
a
t
i
ons, i
n
c
l
u
d
i
n
g
p
o
we
r
su
ppl
ie
s
for p
e
rs
on
a
l
co
mput
er
, o
f
fic
e
equi
pme
n
t, sp
ace
cra
f
t
po
w
e
r syste
m
, la
pt
o
p
co
mp
ut
er, a
nd te
le
co
mmu
ni
ca
t
i
ons e
q
ui
pme
n
t, as wel
l
a
s
D
C
moto
r d
r
i
v
es
[1]
.
The
DC
-DC
c
o
n
v
e
r
t
e
r is
al
so a
n
i
m
p
o
r
t
a
nt
a
ppl
i
c
a
t
i
o
n
for
al
t
e
rnat
ive
el
e
c
t
r
i
cal
po
we
r
c
o
nd
iti
o
n
i
ng
as fo
r ex
a
m
p
l
e
p
h
o
t
ovo
lt
ai
c,
wi
nd
g
e
n
e
r
a
to
r
a
nd fu
el
c
e
l
l sy
st
em [2
].
Th
er
e ar
e
thr
e
e comm
o
n
t
ype o
f
DC
-D
C
co
nve
rt
er
w
h
i
c
h
a
r
e;
Bu
c
k
,
B
o
ost an
d B
u
c
k
B
oost
C
o
nve
rt
er.
Ma
trix
Co
nve
rt
er (MC
)
is i
n
fact
re
ga
rded
a
s
an a
d
v
a
nce
d
ci
rc
uit
t
o
p
o
l
o
g
y
whic
h
p
r
ese
n
t
s
c
o
u
n
tl
ess
a
d
v
a
n
t
ag
es w
ith
un
l
i
mi
ted
swi
t
ch
i
n
g
con
t
ro
l
,
po
ssib
l
e
'a
ll
s
ilic
o
n
so
l
u
t
i
on
s' o
r
wi
th
mi
n
i
mu
m u
s
ag
e o
f
r
e
a
c
tiv
e
devi
ce
[3]
.
It
i
s
a
f
o
rce
d
c
o
mmut
a
t
e
d
co
n
v
e
r
t
e
r
t
o
c
ont
rol
or creat
e t
h
e
v
a
ri
abl
e
out
p
u
t
volt
a
ge
a
c
ross
t
h
e
l
o
a
d
by
usin
g
c
ont
r
o
ll
e
d
bi
-direct
i
onal
s
w
i
t
c
h
es
wi
t
h
u
n
l
i
mi
te
d
fre
que
nc
y
w
h
ic
h ac
tua
l
l
y
pe
rmit
s hi
g
h
fre
q
uenc
y
o
p
e
r
a
ti
on
[4
]
.
Th
e t
o
p
o
l
o
gy of
M
C
w
a
s
a
c
tual
ly
i
n
trod
uc
ed
f
i
r
s
t by
Gy
ug
i
i
n
y
e
a
r
19
76
[5].
It of
f
e
r
s
n
u
me
r
o
u
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
on
of
DC t
o
DC
b
o
o
s
t
co
nv
ert
e
r us
i
ng si
n
g
le
p
h
a
s
e
m
a
tri
x
…
(F
a
j
aria
h Ka
di
r)
7
75
a
d
v
a
n
t
ag
es in
clu
d
i
ng
th
e c
a
p
a
b
i
lity
to
r
e
g
e
n
e
r
a
t
e
e
n
ergy
b
ack
to
th
e
u
til
ity
,
s
i
n
u
s
o
i
d
a
l inp
u
t an
d
o
u
t
p
u
t
c
u
r
r
e
n
t
and
a c
ont
roll
a
b
le
di
s
p
la
ceme
n
t
fac
t
or for
i
n
put
c
u
r
r
e
n
t
[
6
]. Mat
r
i
x
C
o
n
v
e
r
t
e
r obt
ai
ne
d s
ubst
a
nt
i
a
l
i
n
t
e
r
e
sts as
i
t
ha
s bot
h
t
o
p
o
lo
gi
ca
l a
n
d
o
p
era
t
i
o
nal
c
h
a
r
ac
t
e
ri
st
ic
s in s
a
t
i
s
fyi
n
g
t
h
e
p
r
ese
n
t
t
r
e
nds o
f
dri
v
es
[7-1
0]. It
has
al
so e
n
t
i
ced t
h
e
ind
u
st
ry
ap
pl
i
cat
i
on a
n
d
t
h
e
t
e
ch
ni
cal
i
m
pr
ove
ment
was
f
u
rt
he
r spe
d
u
p
gi
ve
n
t
h
e
pow
e
r
ful
d
e
man
d
f
o
r
ener
gy
ef
fi
ci
e
n
c
y
, p
o
w
e
r
q
u
a
li
ty a
nd r
e
d
u
c
in
g t
h
e
si
ze of th
e co
nv
er
ter
s
[1
1]
. In
on
e
of
th
e st
u
d
y
con
d
u
ct
ed
on
MC,
it
i
s
rea
l
i
z
e
d
t
h
a
t
i
ndi
re
ct
Mat
r
ix C
onv
er
te
r
(
I
M
C
) can
b
e
implem
ented for
p
e
rmanent
ma
gn
e
t
sy
n
c
h
r
o
nou
s mo
to
r
dri
v
e
[
12]
.
D
e
sp
it
e th
e
f
a
c
t
tha
t
M
a
tr
ix Conv
e
r
t
e
r of
fer
s
ma
n
y
ad
v
a
n
t
ag
es,
th
ere
are s
e
ve
ral
iss
u
es
i
n
vol
ve
d
i
n
de
al
in
g
wi
t
h
thi
s
co
n
v
erte
r s
u
ch
as
prot
e
c
t
i
o
n
i
s
sue
s
,
c
u
rrent
c
o
mmut
a
t
i
on,
harmo
n
i
c
a
nd
swi
t
c
hi
n
g
l
o
ss
e
s
a
s
wel
l
as
a
b
n
o
r
mal
i
n
p
u
t/
out
put
v
o
l
t
a
ge
[1
3].
A
m
o
n
g
t
h
ese
i
ssues
, t
h
e ma
i
n
pro
b
l
e
m i
n
e
n
gagi
ng
wi
th
Ma
trix
C
o
n
v
ert
e
r i
s
sai
d
to
be
t
h
e c
o
m
m
u
t
a
t
i
on
probl
e
m
w
h
i
c
h
rel
a
t
e
d
t
o
t
h
e
b
i
d
i
re
c
tion
a
l
sw
itc
h
e
s
imp
l
eme
n
tat
i
on
a
nd
h
e
n
c
e
le
ad
s to
th
e
o
c
c
u
rr
e
n
ce
o
f
sp
ik
e d
u
e
to
t
h
e
t
r
an
s
i
t
i
o
n
s
of
swi
t
c
h
in
g
duri
n
g
sup
p
l
y
i
n
g
t
h
e
i
n
d
u
ct
i
v
e l
o
ad
[14
]
.
T
h
erefore
,
sa
fe
comm
u
t
a
t
i
o
n st
rat
e
gy
nee
d
to
be
im
p
l
e
m
en
te
d
in
p
r
ev
en
ti
ng
t
h
e
o
ccur
r
en
c
e
of
vo
l
t
ag
e
sp
i
k
e. Th
rou
gh
a st
udy
con
d
u
c
t
e
d o
n
B
o
o
s
t I
n
v
e
r
t
e
r
u
s
i
n
g
SP
MC
t
o
pol
o
g
y
,
it
i
s
prov
en t
h
at
wi
t
h
t
h
e
im
pl
eme
n
t
a
t
i
on of
safe
commut
a
t
i
o
n
st
ra
t
e
gy
, s
p
i
k
e
s
we
re
su
c
c
e
ssfu
l
ly e
l
im
in
a
t
ed
[1
5]
.
Th
e
sing
le
ph
ase
v
e
rsi
on of
M
a
tr
ix C
onv
erte
r
is
k
n
o
w
n
a
s
Sin
g
l
e Ph
a
s
e M
a
tr
ix
Co
nv
er
ter
(
S
PM
C) w
h
ich
w
a
s
fi
rst
r
e
al
ize
d
b
y
Zu
ck
e
r
b
e
r
g
e
r
[1
6].
S.
H
.
H
o
s
e
i
n
i [17
]
a
n
d
A
bdu
ll
ah
Kh
oie
[
1
8
]
have
st
u
d
i
e
d t
h
e ot
h
e
r t
o
p
o
l
ogi
es
of
S
P
M
C
.
Si
nc
e t
h
e
n
,
mo
re
st
u
d
i
e
s o
n
co
n
v
ent
i
o
nal
ma
trix c
o
n
v
e
r
t
e
r
ha
ve
ca
rri
ed
on. It i
s
rea
l
iz
ed
t
h
at
S
P
MC
c
a
n
be
us
ed
i
n
ma
ny a
p
p
l
ic
at
i
ons s
u
ch
a
s
AC
-AC
co
n
v
e
r
t
e
r, re
ct
i
f
i
e
r, DC
-
DC
co
nve
rt
er,
i
nve
rt
e
r
a
n
d
du
al
c
o
n
v
ert
e
r
[1
9-2
0
].
A st
u
dy
i
n
2
0
1
8
s
h
o
w
s
t
h
at
S
i
ngle
P
h
a
s
e
M
a
trix
C
o
n
v
e
r
t
e
r
(SPMC)
c
a
n
al
so be
use
d
i
n
i
n
d
u
ct
i
o
n he
at
i
ng a
p
p
l
i
c
a
t
i
o
n
s
as
a
n
AC-AC
con
v
e
r
te
r i
m
pl
ement
a
t
i
o
n
[21
]
.
It
is
al
so re
al
iz
ed
t
h
at
S
P
M
C
i
s
c
a
pa
ble
t
o
ac
t
a
s
buc
k/
b
o
o
st
c
ont
roll
ed
rec
t
i
f
i
e
r wi
t
h
re
duc
ed
swi
t
c
h
c
o
u
n
t
[22
]
.
Thro
ug
h a st
u
dy ca
rri
e
d o
u
t
on gri
d
-t
o-
ve
hi
cl
e (G
2
V
) w
i
re
le
ss p
o
we
r
t
r
a
n
s
f
er usi
n
g S
P
MC
t
o
p
o
l
o
g
y
,
i
t
is
re
al
iz
ed t
h
at
t
h
e
use
of S
P
M
C
c
a
n di
re
ct
l
y
co
nve
rt
AC
t
o
A
C
, e
l
i
m
ina
t
ing
t
h
e
com
p
le
xit
y
of c
o
nve
nt
i
o
n
a
l
AC
-
DC
-AC
c
o
nve
r
t
e
r
[2
3]
. C
u
rre
ntl
y
,
the
r
e
are
man
y
re
sea
r
ch
on
t
h
ree
phase
M
a
t
r
i
x
C
o
n
v
e
r
te
r
ne
ve
rt
hel
e
s
s
a
s
fo
r
SP
MC
,
a
l
t
h
ou
gh
i
t
i
s
an
ad
va
nc
ed
ci
rc
ui
t
t
o
pol
og
y,
i
t
has
onl
y
been
see
n
for a
ve
ry li
mit
e
d
o
r
few
w
o
rk.
Thi
s
pape
r
pres
e
n
ts t
h
e
mo
del
i
n
g
a
n
d sim
u
l
a
t
i
on
o
f
D
C
t
o
D
C
Boost
C
o
nve
rte
r
usin
g S
P
M
C
top
o
l
o
g
y
.
The prima
r
y
t
a
sk
o
f
Bo
ost
C
o
n
v
e
r
t
e
r
i
s
t
o
pro
duce
a c
ont
roll
e
d
out
p
u
t
v
o
l
t
age tha
t
i
s
h
i
ghe
r
t
h
a
n
the
i
nput
vol
ta
ge
[24
]
. T
h
e mai
n
p
u
rpo
s
e
of t
h
is
re
se
a
r
c
h
i
s
to ste
p
u
p
the
s
u
p
p
l
y
v
o
l
t
age b
y
usi
n
g
S
P
MC
t
o
p
o
l
ogy a
n
d
t
h
is ope
rat
i
o
n ca
n o
n
l
y
be si
mul
a
t
e
d
in
Qu
adra
nt
1
an
d
Q
u
ad
ra
nt
3 o
n
l
y
.
T
o
s
u
ppo
rt th
e
ba
si
c
pri
n
ci
ple
o
f
fou
r
qua
d
r
a
n
t
o
p
era
t
i
on, o
p
erat
io
n
of
D
C
C
h
op
p
e
r
i
n
Q
u
a
d
ra
nt
2 a
n
d Q
u
a
d
ra
n
t
4
usi
ng SP
MC to
p
o
l
o
gy
i
s
a
l
s
o
di
sc
usse
d i
n
t
h
i
s
pa
p
e
r.
T
h
e c
i
rc
uit
i
s
co
nstr
uct
e
d a
n
d si
mul
a
t
e
d by
u
s
i
n
g
M
A
T
L
AB/
S
i
m
ul
in
k
(M
LS
) fo
r a
l
l
fo
ur q
u
a
d
ra
nt
s.
The
ci
rc
ui
t
c
o
nsist
s
of
f
o
u
r
p
a
irs
o
f
IG
BTs
wi
th
o
p
p
o
sit
e
di
rec
t
i
o
ns
w
h
ic
h
a
c
t
e
d as
t
h
e
p
o
w
e
r
swi
t
c
h
in
g
de
vi
ce.
T
h
e
o
u
t
p
ut
vol
ta
ge
ac
ross
the
l
o
a
d
is
sy
n
t
hesi
ze
d
by
usi
n
g
P
u
l
s
e
Wi
dt
h
Mo
dul
at
i
o
n (P
WM)
te
c
h
n
i
qu
e
.
A
s
fo
r
th
e
lo
ad
,
th
e l
o
ad
u
s
ed
i
s
r
e
sist
iv
e
lo
a
d
wi
th
t
h
e
imp
l
e
m
en
tat
i
o
n
o
f
LC
filte
r
t
o
e
lim
in
at
e
th
e
di
st
ort
i
o
n o
r
ri
pple
o
n
wave
f
o
rm
o
f
t
h
e
out
put
v
o
l
t
a
g
e.
O
u
t
p
ut res
u
l
t
s w
h
en
safe
c
o
mm
uta
t
ion is
impl
ement
e
d
in
th
e
c
i
r
c
u
it
wer
e
p
r
e
s
e
n
t
e
d in
th
is
p
a
p
e
r.
2.
R
E
S
E
ARC
H M
ETH
OD
In
thi
s
sec
t
i
o
n,
it
w
i
l
l
di
sc
uss
a
l
l
o
f
t
h
e
met
h
o
d
use
d
i
n
c
o
m
p
l
e
t
i
ng a
n
d
ac
hie
v
in
g t
h
e
obj
e
c
t
i
ve
s
of t
h
i
s
re
se
arc
h
.
2.1. D
C
to
D
C
b
o
ost co
nve
r
te
r
B
oost c
o
nve
rt
er i
s
use
d
t
o
s
t
ep u
p
a
D
C
v
o
lt
age
a
nd
t
h
e
arra
n
g
e
m
e
n
t for a
B
o
ost
co
nve
rte
r
i
s
as
i
l
l
u
st
rat
e
d in
Fi
gu
re
1.
T
h
e
c
o
nve
rt
er wi
ll
st
e
p
up t
h
e
DC
vo
l
t
a
g
e fro
m
Vs
t
o
V
o
.
Whe
n
t
h
e swi
t
c
h
, de
not
e
d
as
sw
,
o
r
of
te
n
kno
wn
a
s
c
hop
p
e
r
is
c
l
o
s
ed
,
th
e in
du
c
t
or
cu
rr
ent
in
c
r
e
a
s
es
and
th
e
en
er
gy
i
s
st
o
r
ed
i
n
t
h
e
in
du
ct
or,
L. T
h
i
s
p
r
oce
s
s is ca
ll
ed t
h
e i
nduc
t
o
r’s cha
r
gi
n
g
proce
s
s.
Whe
n
t
h
e
swi
t
c
h,
s
w
i
s
ope
n
e
d, t
h
e ene
r
gy t
h
at
ha
d
b
e
en
st
ore
d
in
t
h
e
in
du
ct
or
w
ill
b
e
tr
a
n
sfe
rre
d v
i
a
d
i
od
e
D
1
to
th
e
lo
ad
a
n
d
c
a
u
ses t
h
e
induc
to
r
c
u
rr
e
n
t
t
o
d
r
op.
Thi
s
pr
ocess
i
s
a
c
t
u
al
l
y
di
scha
rgi
ng p
r
ocess
o
f
t
h
e
i
n
d
u
ct
o
r
.
The
sw
it
ch
c
a
n
be
bi
p
o
la
r j
u
nc
t
i
on t
r
a
n
si
st
or (B
JT)
,
i
n
sul
a
t
e
d-gat
e
bi
p
o
l
a
r t
r
a
n
si
st
or
(I
GBT
)
, a
n
d
ot
he
rs
[2
5].
D
C
t
o
DC
B
o
ost
con
v
e
r
te
r i
s
use
d
wi
del
y
in
re
gul
at
ed
DC
p
o
w
e
r
su
ppl
i
e
s,
re
ge
ne
rat
i
ve b
r
a
k
i
n
g o
f
DC m
o
to
rs,
p
o
r
t
a
bl
e
devi
ce
a
ppli
c
a
t
io
ns et
c.
T
h
e
a
v
e
r
age
o
u
t
p
u
t
vol
ta
ge
for a
D
C
t
o
DC
Bo
ost
C
o
nve
rt
er
i
s
a
s
sh
o
w
n
i
n
(1) whe
r
e
D i
s
t
h
e
dut
y c
y
c
l
e
of
t
h
e s
w
i
t
c
h
’s op
e
n
in
g
and
cl
osi
n
g
.
T
h
e
val
u
e
o
f
dut
y
c
y
cl
e ma
y va
ry bet
w
e
e
n
0
to
1.
D
Vs
Vo
1
1
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
7
74
– 78
4
77
6
F
i
gu
re
1.
DC t
o
DC
b
o
o
st c
o
nve
r
t
er a
r
r
a
n
g
e
m
ent
2
.
2
.
Sin
g
le pha
se
mat
r
ix
conv
erter
Ba
sic
a
l
l
y
, S
P
M
C
c
o
m
p
ose
d
o
f
f
o
u
r
bidi
re
ct
iona
l
sw
it
che
s
as
sh
o
w
n
i
n
Fi
gu
re
2,
basi
c
o
p
e
r
at
i
o
n
o
f
f
o
u
r
qua
d
r
ant
as s
how
n
i
n
Fi
gu
re
3
F
o
u
r
bi
di
rec
t
i
o
nal
s
w
i
t
c
h
es a
r
e
r
e
qui
red
s
o
t
h
a
t
i
t
i
s
abl
e
t
o
bl
ock
vol
ta
ge
a
nd
c
o
nd
uct
c
u
rre
nt
i
n
b
o
t
h
di
rec
t
i
ons
. N
o
net
h
el
ess, the
r
e is
no di
scr
e
t
e
se
mi
con
d
u
ct
o
r
de
vi
ce fo
r
bi
di
re
c
t
i
ona
l
sw
itc
h
e
s a
n
d
a
n
t
i
-
p
a
r
a
lle
l I
G
BT is
th
e
r
ef
ore
u
s
ed
.
In
SPM
C
,
th
e
imp
l
e
m
en
tat
i
o
n
o
f
saf
e
comm
u
t
a
tion
sw
itc
h
i
n
g
str
a
t
e
g
i
es is v
e
ry imp
o
rt
an
t
t
o
pr
ev
en
t sw
itc
hin
g
sp
ik
e
ph
en
o
m
en
on
du
e to
t
h
e
u
s
ag
e
of
pr
a
c
t
i
ca
l d
e
v
i
ce
s [26
]
.
Fi
gu
re
2.
B
a
si
c si
n
g
l
e
p
h
ase
ma
tr
ix c
o
nve
r
t
e
r
to
po
l
o
g
y
Fi
gu
re
3.
B
a
si
c
o
p
e
r
at
i
o
n of
f
o
u
r
q
u
ad
ra
nt
2.
3.
Pr
op
osed
D
C
t
o
D
C
b
o
o
s
t
co
n
v
er
ter
u
s
i
n
g S
P
MC
t
o
p
o
l
o
gy
Th
e pr
o
p
o
s
e
d
D
C
t
o
D
C
B
oost co
nv
er
te
r
u
s
in
g S
P
M
C
t
o
po
lo
gy
a
s
d
e
p
i
c
t
e
d
in Figu
r
e
4
us
ed fo
ur
p
a
i
r
o
f
i
n
su
l
a
te
d
-
g
a
t
e
b
i
po
la
r
tran
sisto
r
(
I
G
B
T)
wh
ic
h
is
lo
c
a
te
d a
n
ti
p
a
ra
lle
l
to
e
a
c
h
o
t
h
e
r
for
e
v
ery
p
a
ir
s.
IGB
T
s
ar
e
sel
e
c
t
e
d
as t
h
e sw
i
t
ch
i
n
g
d
e
v
i
ce
s
du
e
to it
s h
i
gh
sw
it
ch
i
n
g
fr
eq
u
e
n
c
y a
n
d
its c
a
p
a
b
ility
o
f
h
a
n
d
ling
h
i
gh
c
u
r
r
e
n
t
w
h
ic
h
l
eads t
o
a
p
pli
c
at
ion
of
medi
u
m
po
we
r suc
h
as
p
o
w
e
r
su
pp
l
i
e
s, co
nt
rac
t
or
s,
s
o
l
i
d
sta
t
e
r
e
la
ys
,
mo
tor
dr
iv
es e
t
c
.
A
so
le
IG
BT ca
n
h
a
nd
le
a
c
u
r
r
e
n
t r
a
t
i
ng
u
p
to
65
00V
,
24
00A
wh
il
e c
a
n
b
e
u
p
t
o
20k
Hz
a
s
f
o
r
t
h
e s
w
it
c
h
i
n
g
f
r
e
que
nc
y [
27]
.
Be
si
des
,
I
G
BT al
so
has
a
l
o
w on
sta
t
e
p
o
we
r
di
ssipa
ti
o
n
.
The
in
d
u
ct
o
r
i
n
t
h
e
ci
rc
u
it
ac
te
d
a
s
th
e
boo
st
induc
to
r
w
h
ich
w
i
l
l
b
e
c
h
a
r
g
i
ng
d
u
r
in
g
t
h
e
sw
it
ch
i
s
o
n
and
d
i
s
c
h
a
rg
e i
t
s en
e
r
g
y
to
t
h
e l
o
a
d
w
h
e
n
t
h
e
s
w
i
t
c
h
is
of
f
.
The
o
u
t
p
ut
vo
lt
age
ac
r
o
ss t
h
e
l
o
a
d
i
s
sy
nt
he
s
i
z
e
d o
r
c
ont
r
o
ll
ed
by
i
m
ple
m
e
n
ti
ng
P
u
lse
Widt
h M
o
d
u
l
a
t
i
on
(
P
WM)
t
e
ch
ni
q
u
e
.
Fi
gu
re
4.
DC
t
o
D
C
bo
ost
c
o
nve
rt
er
usi
n
g
s
p
mc
t
o
p
o
l
o
gy
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Po
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
M
o
del
i
ng
a
n
d
si
mul
a
t
i
o
n
of
DC
to
DC
b
o
o
s
t
co
nve
r
te
r us
ing
sin
g
l
e
p
h
a
s
e
m
a
t
r
i
x
… (F
a
j
aria
h Ka
di
r)
7
77
2.
3.
1.
P
u
l
s
e w
i
d
t
h
m
o
d
u
l
a
ti
on
(PW
M
)
The l
o
ad
v
o
l
t
a
ge
or
out
put
vol
t
a
ge
ac
r
o
ss
t
h
e
l
o
ad
f
o
r
the
DC
t
o
DC
B
o
ost
c
o
n
v
e
r
te
r
u
s
i
n
g
SP
MC
t
o
p
o
l
o
g
y
i
s
c
o
nt
r
o
l
l
e
d
b
y
em
plo
y
i
n
g
P
W
M t
e
c
hniq
u
e
.
Thi
s
pa
rt
i
c
ul
a
r
te
chni
que is im
pl
ement
e
d
by co
mpa
r
i
n
g
a tr
ia
n
g
u
l
a
r
wa
v
e
sign
a
l; th
e ca
r
r
ie
r
s
i
gn
a
l
, a
n
d
a
co
n
s
t
a
nt
a
d
ju
st
ab
le
DC sig
n
a
l; th
e
re
fe
r
e
n
c
e
si
gn
al. A
s
a
r
e
sul
t
,
t
h
e
s
w
i
t
c
h
in
g
pul
se
d
u
t
y cyc
l
e
c
o
ul
d
be
var
i
ed
t
o
sy
nt
hesi
ze
t
h
e
re
qui
r
e
d
DC
to
D
C
B
o
ost c
o
n
v
ert
e
r
.
The
t
r
i
a
ngul
a
r
wa
ve si
gnal
or
car
ri
er si
gn
a
l
c
a
n
be
ei
t
h
e
r
“
M
”
s
h
a
p
e
o
r
“
W
”
s
h
a
p
e.
B
y
em
plo
y
i
n
g
P
W
M
t
e
c
hniq
u
e
,
a se
r
i
e
s
o
f
p
u
lse
t
r
ai
n i
s
ge
ne
ra
te
d t
o
t
u
rn
o
n
a
n
d
of
f
t
h
e
s
w
i
t
c
hi
n
g
devi
ce
[
2
8]
as
de
pi
ct
e
d
i
n
F
i
gu
r
e
5. T
h
e s
w
i
t
c
h
wil
l
be o
n
whe
n
t
h
e
re
fe
re
nce
si
gnal
i
s
gr
eat
e
r
t
h
a
n
the
car
ri
er si
g
n
al
a
n
d
wi
ll
be o
ff wh
en t
h
e
re
f
e
r
e
n
ce sign
al is
l
e
ss
th
an
the
c
a
r
r
i
er sign
a
l
.
F
i
gu
r
e
5.
P
u
l
s
e
wi
dt
h m
o
dula
t
ion
(P
W
M
)
2.
3.
2.
C
o
mm
ut
a
t
i
o
n pr
ob
l
e
m
Ther
e
i
s
a se
ri
ous
p
r
obl
em
w
h
e
n
de
al
i
ng
wi
th
mat
r
i
x
c
o
n
v
e
r
t
e
r
,
w
h
ic
h i
s
t
h
e
occ
u
rre
n
c
e
of
spi
k
e
due
to
th
e t
r
an
sit
i
on
s
of
swi
t
c
h
ing
du
r
i
ng
supp
ly
i
n
g
t
h
e
i
n
du
c
t
i
v
e l
o
a
d
[
1
4]
. In
SPM
C
,
th
e seq
u
e
n
ce of
sw
itc
h
i
n
g
sho
u
l
d
be
i
n
st
ant
a
ne
ous an
d s
i
mul
t
a
ne
ousl
y
,
whi
c
h i
m
possi
ble
p
r
ac
ti
ca
l
l
y,
cause
d b
y
t
h
e
tur
n
“
o
n” a
nd
“of
f
”
tim
e w
i
t
h
in the
ch
ar
ac
te
r
i
sti
c
s of
th
e IG
B
T
.
Wh
en
t
h
e
sw
itc
h
t
h
a
t
c
o
n
t
ro
ll
ed
th
e vo
l
t
ag
e
a
c
r
o
ss
l
o
ad
,
sy
n
t
h
e
siz
e
d
u
s
in
g PWM
is t
u
rn
e
d
“on
”
,
t
h
e
in
du
c
t
or
is c
h
a
r
g
e
d and th
e
ener
gy
is sto
r
e
d
in
th
e
i
ndu
ct
o
r
.
D
u
ri
n
g
tu
rn
“
o
f
f
”,
th
is is
w
h
e
r
e
th
e
co
mmu
ta
tion
pro
b
l
em a
r
ise
s
wh
e
n
t
h
e
en
e
r
g
y
sto
r
ed
i
n
t
h
e
i
n
du
ct
or
is
tr
a
n
sf
e
rre
d
to
t
h
e
l
o
a
d
. T
h
e
r
e
f
o
r
e,
a saf
e
co
m
m
u
t
a
t
i
o
n
ne
e
d
t
o
b
e
imp
l
e
m
en
t
e
d
i
n
p
r
ov
id
ing
“w
ay
” fo
r th
e
c
u
rr
en
t t
o
f
l
o
w
to
th
e
l
o
a
d
so
t
h
at
t
h
e
e
n
e
r
gy
sto
r
e
d
in
th
e
ind
u
c
t
o
r is
a
b
le
to
b
e
tran
sf
e
r
r
e
d
t
o
l
o
a
d
d
u
r
i
ng
“
o
ff
”
sta
t
e
.
Fig
u
r
e
6
sho
w
s
t
h
e
su
m
m
ar
y
f
o
r t
h
e
o
p
e
ra
ti
on
f
o
r
e
a
c
h
swi
t
c
h
dur
in
g
the
f
o
ur
q
u
ad
ra
nts
o
p
e
r
at
i
o
n
,
sw
it
c
h
i
n
g S
t
r
a
t
e
gi
es
as show
n in
Ta
b
l
e 1.
Tabl
e
1.
Sw
it
c
h
i
n
g
S
t
rat
e
gi
es
S
w
i
t
ch
Q
u
adr
a
nt
1
Qua
d
ra
nt 2
Q
u
adr
a
nt 3
Q
u
a
d
ra
nt 4
S1
a
On
O
f
f
PW
M
O
f
f
S1
b
Off
On
Off
O
f
f
S2
a
Off
O
f
f
On
O
f
f
S2
b
Off
O
f
f
Off
On
S3
a
PW
M
P
W
M
On
O
f
f
S3
b
On
O
f
f
Off
On
S4
a
On
O
f
f
Off
P
W
M
S4
b
Off
On
On
O
f
f
F
i
gu
r
e
6.
F
o
u
r
qua
d
r
ant
o
p
e
r
a
t
i
on usi
n
g SP
MC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
7
74
– 78
4
77
8
i.
Firs
t
qua
dra
n
t
(Q1)
F
o
r
th
e op
e
r
at
io
n
of
t
h
e
f
i
r
s
t
q
u
a
dr
an
t wh
ic
h
i
s
fo
rw
ard
mo
tor
i
ng
,
bo
th l
o
a
d
v
o
l
t
a
g
e
, V
L
an
d
loa
d
cu
rr
en
t
,
I
L
a
r
e
posi
t
i
ve
. T
h
e
l
o
a
d
c
u
r
r
e
nt
fl
o
w
s
o
u
t
of
the
s
o
u
r
ce
t
o
the
in
duc
t
o
r
a
n
d
i
n
or
der
t
o
ac
hi
ev
e
t
h
is
co
nd
i
tio
n,
sw
it
c
h
S1
a, S3
b,
S4
a
ar
e se
t
“on
”
w
h
i
l
e sw
i
t
ch
S3
a
emp
l
oy
s PWM
te
ch
n
i
q
u
e
to
c
o
n
t
ro
l
th
e
c
h
a
r
g
i
ng
a
n
d
di
sc
ha
rgi
ng
of
t
h
e
i
n
duc
t
o
r.
C
h
a
r
gi
ng
of
i
n
duct
o
r
d
u
r
i
n
g qua
dr
ant
1 ope
rat
i
o
n
(S
3a
P
W
M
–
O
n
)
an
d
Di
scha
rgi
n
g
O
f
I
n
duct
o
r
D
u
ri
ng
Q
u
a
d
ra
nt
1
Ope
r
at
io
n (
S
3a
P
W
M
-
Of
f)
a
r
e show
n
i
n
F
i
g
u
r
e
7
an
d F
i
g
u
r
e
8.
Fi
gu
re
7.
Cha
r
gi
n
g
of
i
nduc
t
o
r
du
ri
n
g
qua
d
r
ant
1
ope
r
a
t
i
o
n
(
S
3a
P
W
M
–
On
)
Fi
gu
re
8.
Di
sc
har
g
in
g
Of
I
n
d
u
ct
o
r
D
u
ri
ng
Q
u
ad
r
a
nt
1
Op
er
ation
(
S
3
a
PWM- Off)
ii.
Second
q
u
a
d
r
a
n
t
(Q2)
Qua
d
r
a
nt
2
is
fo
rw
a
r
d
bra
k
i
n
g,
w
h
er
e t
h
e
l
o
ad
wi
ll
bec
o
me s
u
ppl
y,
d
r
ive
n
by
volt
a
ge
E
w
h
i
c
h
i
s
b
a
t
t
e
r
y.
In th
i
s
q
u
a
d
r
a
n
t
, it
i
s
impo
ssi
b
l
e
to
s
i
mu
la
te
a
D
C
to D
C
B
o
ost conv
er
te
r.
Th
e
r
e
f
or
e
,
f
o
r
th
is
p
a
r
t
i
c
u
l
ar
qua
dr
ant
,
i
t
wi
l
l
onl
y
pe
r
f
o
r
m
the
o
p
er
at
i
o
n of
DC
C
h
o
p
p
er i
n
Qua
d
r
a
nt
2
.
D
u
r
i
n
g
t
h
is q
u
a
d
ra
nt,
t
h
e l
o
a
d
vol
t
a
ge
wi
ll
be
posi
t
i
v
e
.
As
fo
r t
h
e
l
o
a
d
c
u
rre
nt,
i
t
s
ma
g
n
it
u
d
e
wi
ll
be
ne
ga
t
i
ve
and
fl
o
w
s
out
f
r
om
the
l
o
ad.
I
n
a
c
hi
evi
n
g
t
h
i
s
c
o
n
d
it
i
o
n, s
w
i
t
c
h
S
3
a e
m
pl
oys P
W
M te
c
hni
que
w
h
ere
a
s
swit
c
h
S
1
b a
nd S
4
b
a
r
e s
e
t
as
co
n
t
inuo
usl
y
on
.
Th
e cu
rr
e
n
t t
h
rou
g
h
th
e l
o
ad
w
ill b
e
dr
iv
en
by
a
n
o
t
h
e
r sup
p
l
y
,
b
a
tt
er
y E. Wh
en sw
itc
h
S3
a
is
of
f,
t
h
e l
o
a
d
di
ssipa
te
d
i
t
s
e
n
e
r
g
y
vi
a
S1
b
an
d S
4
b
t
o
t
h
e
D
C
su
ppl
y,
C
u
rr
e
n
t
dri
v
e
n
b
y
e
t
h
r
o
ug
h
loa
d
d
u
r
i
ng
qua
dr
ant
2
o
p
e
r
a
t
i
o
n
(
S
3a
P
W
M –
O
n
)
s
h
o
w
n
in
Fi
g
u
re
9
.
V
D
C
a
s
de
pi
ct
ed in
Fi
g
u
r
e
10
.
F
i
gu
re
9.
Cu
rr
e
n
t
d
r
i
v
e
n
b
y
e
t
h
r
o
ug
h l
o
ad
d
u
r
i
n
g
qua
d
r
a
n
t 2
o
p
e
r
at
i
on
(S
3a P
W
M –
O
n
)
F
i
g
u
r
e
10
.
En
er
gy
d
i
ssip
a
t
ed
to
t
h
e
su
pp
ly
dur
ing
qua
d
r
a
n
t
2 o
p
e
r
at
ion
(S
3a P
W
M-
Of
f)
iii.
Third quad
r
a
n
t
(
Q
3
)
Ma
gni
tu
de
o
f
bot
h
l
o
ad
vol
ta
ge a
n
d c
u
r
r
e
n
t
ar
e
negat
i
ve.
T
h
e
o
p
e
r
at
i
o
n o
f
t
h
is
q
u
ad
ra
nt i
s
k
n
o
w
n
as
r
e
ve
r
s
e
mot
o
ri
ng
. T
h
e l
o
a
d
c
u
r
r
e
nt
fl
o
w
s b
y
u
s
in
g di
ffe
re
nt
r
out
e
fr
om t
h
e s
uppl
y t
o
t
h
e l
o
ad
.
Thi
s
c
o
ndi
ti
o
n
is a
c
h
i
e
v
e
d
by se
ttin
g
swi
t
c
h
S1
a to PW
M
c
o
n
t
r
o
l
wh
ere
a
s S2
a
,
S3
a
,
S4b
a
r
e
s
e
t as con
tin
uo
u
s
ly
o
n
.
Wh
en
S1
a
is on
,
th
e
c
u
rr
e
n
t
wi
ll f
l
ow
fro
m
l
o
a
d
,
d
r
iv
e
n
by
E to
the
i
n
d
u
ct
o
r
; ch
arg
i
n
g
th
e in
du
c
t
o
r
. Wh
en
sw
itc
h
S1
a
i
s
of
f
,
t
h
e e
n
er
gy
st
o
r
e
d
in t
h
e
ind
u
ct
o
r
wil
l
be t
r
a
n
s
f
er
re
d
t
o
t
h
e
l
o
a
d
;
di
schar
g
in
g
o
f
in
duc
t
o
r
.
T
h
e
fl
o
w
of
cu
rr
en
t
wh
e
n
swi
t
c
h
S1
a is on and
o
ff a
r
e
i
llu
st
ra
te
d
i
n
F
i
gu
r
e
11
a
n
d
Figu
r
e
12
r
e
sp
e
c
ti
v
e
l
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Po
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
M
o
del
i
ng
a
n
d
si
mul
a
t
i
o
n
of
DC
to
DC
b
o
o
s
t
co
nve
r
te
r us
ing
sin
g
l
e
p
h
a
s
e
m
a
t
r
i
x
… (F
a
j
aria
h Ka
di
r)
7
79
F
i
gu
r
e
1
1
.
C
h
a
r
gi
ng
o
f
i
n
d
u
ct
or
dur
i
n
g
q
u
a
d
ra
nt
3
ope
r
a
t
i
o
n
(
S
1a
P
W
M
–
On
)
F
i
gu
re
1
2
. D
i
s
c
har
g
i
n
g of
i
n
duc
t
o
r
t
o
t
h
e l
o
a
d
dur
in
g
q
u
ad
ra
n
t
3 ope
r
a
t
i
o
n (
S
1a
PWM
-
Of
f
)
iv
.
Fourth
qua
dra
n
t
(
Q
4)
The f
o
u
r
t
h
q
u
a
d
ra
nt is
a
re
ve
rse
bra
k
i
n
g q
u
a
dr
a
n
t
whe
r
e
t
h
e l
o
a
d
v
o
lt
ag
e
i
s
ne
ga
ti
ve
in
m
a
gni
t
u
de
w
h
e
r
e
a
s t
h
e
loa
d
cu
rre
n
t
is
po
si
tiv
e
.
Th
e loa
d
w
ill a
c
t
a
s
su
pp
ly
wh
ile
sup
p
l
y
w
ill
a
c
t
a
s
lo
a
d
. Th
e
lo
a
d
c
u
rr
en
t
f
l
o
w
s o
u
t
of t
h
e loa
d
. F
o
r
t
h
i
s
qu
ad
r
a
nt
,
t
h
e
si
mula
t
i
on
o
f
DC t
o
D
C
Bo
o
s
t
c
o
n
v
e
r
t
e
r
i
s
impo
ssibl
e a
n
d
he
nc
e
w
ill o
n
l
y
si
m
u
lat
e
th
e
o
p
e
r
a
t
i
o
n
o
f
D
C
Cho
p
p
e
r
fo
r
q
u
a
dr
an
t fou
r
. In
ach
ie
v
i
ng
th
i
s
co
nd
it
io
n, sw
itch
S4
a
ut
i
l
i
z
es PW
M
t
e
c
hni
que
w
h
er
e
a
s swi
t
c
h
S
2
b
and
S
3
b a
r
e
se
t
t
o
co
nt
i
n
uo
usl
y
o
n
.
W
h
en
swi
t
c
h S4a i
s
o
n
, c
u
r
r
ent
ac
r
o
ss th
e
l
o
a
d
w
ill b
e
d
r
iv
en b
y
b
a
t
t
ery
E an
d
du
r
i
n
g
S4
a
is o
f
f
,
lo
ad
d
i
ssip
a
t
e
d
its e
n
e
r
g
y
to
th
e supp
ly
as
sh
own
i
n
F
i
g
u
re
13
a
n
d
Fi
gure
14
.
Fi
gu
re
1
3
.
C
u
r
r
e
n
t
dri
v
en
b
y
e thr
oug
h l
o
a
d
du
ri
n
g
qua
d
r
a
n
t
4 o
p
e
r
at
i
on (S
4a
P
W
M
–
On)
F
i
g
u
r
e
14
.
En
er
gy
d
i
ssip
a
t
ed
to
t
h
e
su
pp
ly
dur
ing
qua
d
r
a
n
t
4 o
p
e
r
at
ion
(S
4a P
W
M-
Of
f)
2.
4.
S
i
mu
l
a
ti
o
n
mo
de
l
Th
e
c
i
r
c
u
i
t i
s
m
o
d
e
l
e
d
a
nd si
mu
la
te
d
by
u
s
in
g
MLS
.
Th
e
ci
rc
u
i
t
s
w
e
re
su
pp
lie
d
by a
D
C
v
o
l
t
a
g
e
so
ur
ce
w
i
t
h
a
m
p
lit
u
d
e
of
20V
; th
e
lo
ad
i
s
a
p
u
r
e
resist
iv
e
lo
a
d
,
R
w
h
ich i
s
2
0
Ω
;
boost
ind
u
c
t
o
r
o
f
3
m
H.
LC
fi
lte
r
is imp
l
eme
n
ted
in th
e
c
i
r
c
u
i
t as to r
e
d
u
c
e
o
u
t
p
u
t
vo
lta
g
e
ri
pp
le
;
L=3
m
H
,
C
=
5nF
.
F
o
r
op
er
a
t
i
o
n for
Qua
d
rant
2,
3 a
nd 4,
DC
su
pp
l
y
, E
r
e
p
r
e
s
e
n
t ba
c
k
em
f o
f
D
C
m
o
to
r
o
f
5
V
.
Al
l
of
t
h
e
p
a
r
a
met
e
r
s
use
d
i
n
t
h
e
si
mula
ti
on
m
o
del
i
s
su
mma
r
i
zed
as
i
n
Ta
bl
e
2
.
T
h
e
si
mul
a
t
i
on
m
odel
o
f
P
W
M s
w
i
t
c
hi
n
g
co
nt
r
o
l
i
s
as
de
pi
ct
ed
i
n
Fi
gu
re
1
5
.
I
t
i
s
obt
ai
ned
by
c
o
mpa
r
i
n
g
a
t
r
i
a
n
gul
ar
w
a
ve
ca
r
r
i
e
r
si
g
n
al
and
a
co
nst
a
nt
DC
ref
e
re
nce
s
i
gnal
.
F
i
g
u
r
e
16
,
17,
1
8
an
d
1
9
s
h
o
w
s the
si
mul
a
ti
on
model
fo
r
Qua
d
r
a
nt
1,
2,
3 a
n
d
4 re
s
p
ect
i
v
el
y usi
n
g M
L
S
.
T
h
e
swi
t
c
hi
n
g
st
rat
e
gie
s
ar
e
di
ff
e
r
e
n
t f
o
r
ea
ch
q
u
a
dra
n
t
,
de
pe
nd
i
ng o
n
i
t
s
ope
r
a
t
i
on r
e
q
u
i
r
e
d
out
put
.
Tabl
e
2. P
a
r
a
m
e
t
e
rs u
s
ed
f
o
r
s
i
mula
ti
on
C
o
m
ponent
V
a
l
u
e
Suppl
y
vol
ta
ge
,
V
in
20
V
Boost
i
nduct
o
r
,
L
4 m
H
O
u
tput r
e
sist
or,
R
20
Ω
Ba
tte
ry, E
5
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
7
74
– 78
4
78
0
Fig
u
r
e
15
. PWM
c
o
n
t
r
o
l
m
odel
F
i
g
u
r
e
16.
S
i
mul
a
t
i
on mo
del
usi
n
g ML
S f
o
r
DC
t
o
D
C
boo
st co
nver
t
e
r
u
s
i
n
g
S
P
M
C
(
Q
u
a
dr
a
n
t
1
)
F
i
gu
re
1
7
.
S
i
m
u
l
a
t
i
o
n
mode
l
usi
ng
ML
S f
o
r
DC
con
v
e
r
t
e
r
usi
n
g S
P
MC
(
Q
ua
dra
n
t
2)
F
i
g
u
r
e
18.
S
i
mul
a
t
i
on mo
del
usi
n
g ML
S f
o
r
DC
t
o
DC
b
o
o
st
c
o
n
v
e
rt
er usin
g SP
M
C
(
Q
uad
r
a
n
t 3)
F
i
gu
re
1
9
.
S
i
m
u
l
a
t
i
o
n
mode
l
usi
ng
ML
S f
o
r
DC
con
v
e
r
t
e
r
usi
n
g S
P
MC
(
Q
ua
dra
n
t
4)
3.
R
E
SU
LTS AN
D ANA
LY
SIS
S
i
mu
l
a
ti
on
o
f
t
h
e
mod
e
l w
a
s d
o
n
e
by
u
s
i
n
g M
L
S. Fi
gu
re
20
t
o
Fig
u
r
e
27 sh
ow
e
d
t
h
e
re
su
l
t
s
of
ou
t
p
u
t
vol
t
a
ge
an
d ou
t
put
cu
r
r
e
nt
f
o
r
ea
ch
qu
a
d
ra
nt
w
i
t
h
s
w
i
t
c
hi
n
g
fr
e
que
nc
y, f
s
of 2
5
k
H
z a
nd dut
y
c
y
c
l
e
,
m
a
of
0.
5.
Tab
l
e
3
sh
o
w
s
th
e
summar
y
of
th
e
v
a
lu
e ou
tp
u
t
vo
lt
ag
e
c
u
rre
n
t
fo
r e
v
ery q
u
a
dr
an
t at
th
is co
nd
i
tio
n.
From Tab
l
e
3,
t
h
e re
s
u
l
t
s
o
b
t
a
i
n
ed f
o
r
out
put
vol
ta
ge
a
n
d out
put
c
u
r
r
ent
fo
r
ea
ch q
u
ad
r
a
nt,
f
o
l
l
o
wed
t
h
e b
a
sic
fo
u
r
qua
d
r
a
n
t
ope
rat
i
o
n
a
s
s
h
ow
n i
n
F
i
g
u
re
3.
As
f
o
r
t
h
e
o
p
e
r
at
i
o
n o
f
D
C
t
o
D
C
B
o
ost
Con
v
e
r
t
e
r
usi
ng S
P
MC
t
o
p
o
l
o
g
y
i
n
Qua
d
rant
1
a
n
d
Qua
d
ra
nt
3,
the
m
o
del
si
m
u
la
te
d usi
n
g
M
L
S
ar
e
a
b
le
t
o
b
oost
i
t
s
i
n
p
u
t
v
o
lt
a
g
e
a
b
o
u
t
2
t
i
m
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
on
of
DC t
o
DC
b
o
o
s
t
co
nv
ert
e
r us
i
ng si
n
g
le
p
h
a
s
e
m
a
tri
x
…
(F
a
j
aria
h Ka
di
r)
7
81
F
i
gu
re
2
0
. O
u
t
put
v
o
l
t
a
g
e fo
r qua
d
r
ant
1,
Vin
= 20
V,
Vmean
= 35
.1V
Fi
gu
re
2
1
.
O
u
t
put c
u
rre
n
t
for
qua
d
r
ant
1,
Io
ut
=
1.7
5
5
A
F
i
gu
re
2
2
. O
u
t
put
v
o
l
t
a
g
e fo
r qua
d
r
ant
2,
Vi
n
= 2
0
V
,
Vo
ut
=
2.36
3
V
Fi
gu
re
2
3
.
O
u
t
put c
u
rre
n
t
for
qua
d
r
ant
2,
I
o
u
t
=
-
0
.118
1A
F
i
gu
re
2
4
. O
u
t
put
v
o
l
t
a
g
e fo
r qua
d
r
ant
3,
Vi
n =
2
0
V
,
V
m
e
a
n =
-
3
8V
Fi
gu
re
2
5
.
O
u
t
put c
u
rre
n
t
for
qua
d
r
ant
3,
Io
ut
=
-1
.9
A
F
i
gu
re
2
6
. O
u
t
put
v
o
l
t
a
g
e fo
r qua
d
r
ant
4,
Vi
n
= 20V
,
Vou
t
=
-
2
.
363
V
Fi
gu
re
2
7
.
O
u
t
put c
u
rre
n
t
for
qua
d
r
ant
4,
Io
u
t
=
0.
118
1A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
7
4
–
784
78
2
Tabl
e
3.
V
out
and
I
out
for eac
h
qua
d
r
ant
at
f
s
= 25
kH
z
,
ma
=
0
.
5
V
ou
t
(V
)
I
ou
t
(A
)
Q
u
adr
a
nt
1
35.
1
1.
755
Q
u
adr
a
nt
2
2.
363
-0.
1181
Q
u
adr
a
nt
3
-
38
-1.
9
Q
u
adr
a
nt
4
-
2
.
363
0.
118
1
3.1. V
a
ry
i
n
g
sw
itchi
n
g fr
eq
uen
c
y
,
f
s
To a
n
a
l
yz
e
t
h
e
perfo
rma
n
ce
of DC
t
o
DC
B
o
ost Co
n
v
e
r
t
e
r
usin
g S
P
M
C
,
t
h
e swi
t
chi
n
g
f
r
eque
nc
y
a
r
e
v
a
ri
e
d
fo
r
f
i
v
e
se
ts of
v
a
l
u
e
w
h
ich
a
r
e
5kHz
,
10k
H
z
, 15kH
z
,
25
kH
z
a
n
d
50k
Hz
. Th
e
d
u
t
y
c
y
c
l
e
,
m
a
is k
e
p
t
con
s
t
a
nt
at
0.5.
Fi
gu
re
28 a
n
d
Fi
gu
re
29 s
h
o
w
s t
h
e
w
a
vef
o
rm
o
f
o
u
t
p
ut
v
o
l
ta
ge fo
r DC
t
o
DC
B
o
ost
Co
n
v
ert
e
r
usin
g
S
M
PC
i
n
Q
u
a
d
ra
nt
1 at
swi
t
c
hi
n
g
fr
eq
uenc
y
o
f
5
k
Hz
a
nd
50
k
H
z acc
ordi
ngl
y
.
T
h
e
dut
y c
y
cl
e
ma
i
s
ke
pt
c
o
nsta
n
t
a
t
0
.
5.
Fr
om Fig
u
re
2
8
and Fig
u
re 29
, it
i
s
ob
se
rv
e
d
th
a
t
as swit
ch
i
n
g
fr
e
q
u
e
n
c
y is in
cr
ea
sed
,
t
h
e
w
a
v
e
fo
r
m
of
ou
t
p
u
t
vo
lta
g
e
be
co
m
e
smo
o
t
he
r.
W
i
t
h
i
n
c
r
e
a
se
o
f
sw
itch
i
n
g
f
r
e
qu
e
n
cy
, it
w
ill
r
e
su
lt in
de
cr
ea
se
of
v
o
l
t
a
g
e ri
pp
l
e
at
t
h
e o
u
t
p
ut si
nce
the
c
h
a
r
gi
n
g
a
nd
di
sc
h
a
rgi
ng t
i
m
e
s
o
f
the
i
n
d
u
ct
o
r
be
co
me si
gni
fi
ca
nt
ly
sh
or
te
r w
i
t
h
a
n
in
cr
e
a
s
e
in
switc
h
in
g
fr
equ
e
ncy
.
3.2. Vary
i
n
g
duty
c
y
cl
e,
m
a
Tabl
e
4 s
u
m
m
a
r
i
zed
t
h
e
va
lue
o
f
out
put
volt
a
ge
,
Vo
ut
obta
i
ne
d t
h
ro
u
g
h
si
mula
ti
o
n
of
DC
t
o
D
C
Boost
C
o
nve
rt
e
r
usin
g SP
M
C
t
o
p
o
lo
g
y
i
n
Qua
d
rant
1
a
n
d
Qu
a
d
rant
3.
It
is
obse
r
ve
d
t
h
at
as t
h
e
d
u
ty
cyc
l
e
is
i
n
cre
a
se
d,
the
out
pu
t
v
o
l
t
a
ge
is a
l
so i
n
crease
d
fo
r
b
o
t
h
q
u
ad
rant
s.
U
s
i
n
g t
h
e
for
m
ul
a
f
o
r a
v
e
r
a
g
e
o
u
t
put
vol
t
a
g
e
o
f
Boo
s
t
Conve
rt
er
as sh
own
i
n
(1
), w
i
t
h
an
i
n
c
r
ea
se o
f
t
h
e
d
u
t
y
cy
cl
e,
th
e a
v
e
r
ag
e
ou
t
p
u
t
v
o
l
t
a
g
e
wi
ll
inc
r
ea
se
to
o
.
A
s
th
e
d
u
t
y
cy
cl
e
is i
n
c
r
e
a
se
d, th
e t
i
me
fo
r t
h
e
s
w
i
t
ch
syn
t
h
e
si
zed b
y
PWM
to on
w
ill
a
l
so
i
n
cre
a
s
e
,
re
sul
t
i
ng
i
n
l
onge
r
c
h
argi
ng t
i
me.
T
h
ere
f
o
r
e
,
the
ene
r
g
y
st
o
r
ed
i
n
t
h
e i
n
d
u
c
t
o
r
wi
ll
i
n
crea
se
.
H
o
weve
r,
it
i
s
not
appl
i
cabl
e
to
Qua
d
ra
nt
3 o
p
erat
i
on
beca
use of
i
t
s re
v
e
rse
m
o
t
o
ri
n
g
pro
p
ert
y
;
t
h
e
o
u
tp
ut
v
o
l
t
a
ge
wi
ll
re
ma
in
co
ns
t
a
n
t
.
Fi
gu
re
2
8
.
Wa
ve
form of
o
u
t
p
ut v
o
lt
age
for
b
oost
c
o
n
v
e
r
t
e
r usi
ng S
P
M
C
in
q
u
a
d
ra
nt
1,
vme
a
n
=
34
.5
6
V
at
5k
H
z
F
i
gure
29. Wa
vef
o
rm of o
u
tp
ut
v
o
l
t
a
ge
for b
oost
con
v
e
r
t
e
r
usi
n
g S
P
M
C
i
n
q
u
a
d
ra
nt
1, vmea
n
=
3
4
.
33V
a
t
5
0kH
z
Tabl
e
4
.
A
v
e
r
a
g
e
out
put
v
o
l
t
a
g
e fo
r qua
d
r
ant
1 a
n
d qua
d
r
an
t
3
wi
th
respe
c
t
t
o
ma
4.
CO
NCL
U
S
I
O
N
Th
e
me
tho
d
i
n
mod
e
lli
n
g
an
d simu
la
tin
g
t
h
e
D
C
to
D
C
Boo
s
t
Con
v
e
rt
er
u
s
ing
S
P
M
C
to
po
l
ogy b
y
usin
g
MA
TL
A
B
/
S
imul
ink
(M
LS) has
bee
n
o
u
tl
i
n
ed.
F
o
r
Q
u
a
d
ra
nt
2 a
n
d
Q
u
a
d
ra
nt
4,
a
m
odel
o
f
DC
C
h
op
pe
r
fo
r t
h
e
res
p
ec
ti
ve
qua
dra
n
t
s
h
a
d
bee
n
prese
n
t
e
d. T
h
e
si
mul
a
t
i
on
res
u
l
t
s achi
e
ve
goo
d a
g
ree
m
e
n
t
w
i
t
h
t
h
e
t
h
eo
ry
of
fo
u
r
q
u
a
d
ra
nt
o
p
erat
io
n.
F
o
r
DC
t
o
DC
B
oost
C
o
n
v
e
r
te
r
usi
n
g S
P
M
C
t
o
pol
og
y, t
h
ro
ug
h t
h
e
sim
u
l
a
t
i
o
n
, t
h
e
re
sul
t
s
sho
w
e
d
tha
t
the
mode
l i
m
ple
m
e
n
te
d a
b
l
e
t
o
bo
ost i
t
in
put
vol
ta
g
e
for
abo
u
t t
w
o t
i
m
e
s
la
rge
r
at
swit
c
h
in
g
Du
t
y
cy
c
l
e,
m
a
Ave
r
a
g
e output
vo
l
t
age
,
V
mea
n
(V)
Q
u
a
d
ra
nt 1
Qua
d
ra
nt 3
0.
5 35.
1
-
38
0.
6 43.
29
-
38
0.
7 56.
17
-
38
0.
8 78.
39
-
38
0.
9 111.
1
-
38
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
on
of
DC t
o
DC
b
o
o
s
t
co
nv
ert
e
r us
i
ng si
n
g
le
p
h
a
s
e
m
a
tri
x
…
(F
a
j
aria
h Ka
di
r)
7
83
fre
que
nc
y o
f
2
5
k
H
z.
Ot
he
r
p
a
ra
me
te
rs
ha
d b
e
en va
ri
ed t
o
st
ud
y
on
it
s effec
t
to
the
out
put
vol
t
a
ge
. T
h
e se
le
ct
ed
simul
a
t
i
on re
s
u
lt
s sh
o
w
e
d
t
h
at
DC t
o
D
C
Boost
C
o
n
v
e
r
te
r u
s
i
n
g S
P
M
C
top
o
l
o
g
y
c
a
n
be im
pl
eme
n
t
e
d
fo
r
pra
c
t
i
c
a
l
use.
DC t
o
DC
B
o
ost
C
onve
rt
er
i
s
wi
del
y
be
e
n
use
d
i
n
p
o
w
e
r
e
l
e
c
t
r
oni
c a
ppl
i
a
nc
es suc
h
a
s
po
we
r
sup
p
li
es et
c.
A
C
KNOW
LE
D
G
E
M
EN
TS
Th
is re
sea
r
c
h
is sup
p
o
r
ted
by
t
h
e F
und
a
m
en
ta
l R
e
se
a
r
c
h
G
r
a
n
t
Sch
e
me
(
F
RG
S)
(F
RG
S
/
1/2
0
1
7
/
TK0
4
/U
IT
M/03/
13
)
from
t
h
e Mi
ni
st
ry
o
f
E
duca
t
i
o
n Ma
la
ysi
a
(M
OE
).
RE
FERE
NC
E
S
[1]
R.
W
.
E
r
icks
on,
“D
C-DC Power
Converte
rs
,” i
n
Wi
le
y
En
cy
c
l
oped
i
a
of Ele
c
t
ric
a
l an
d
Ele
c
tro
n
i
c
s En
gi
nee
r
i
n
g
, 200
7.
[2
]
W
.
I. Ham
e
e
d
, B.
A.
Sa
wa
d
i
,
a
nd A. Mua
y
e
d
,
“
V
ol
ta
ge
Trac
k
i
n
g
Co
n
t
ro
l of
DC-
DC Bo
ost Con
v
e
r
te
r Usi
ng
F
u
z
z
y
Neu
r
a
l
N
e
tw
ork,
”
In
tern
atio
na
l
J
o
urn
a
l o
f
Power
Elec
tr
on
ics
an
d
D
r
ive
S
y
s
t
em
s
(IJPED
S
)
,
v
o
l. 9
,
no
.
4,
p
p
. 16
57
-
16
65
, 20
18
.
[3
]
S.
Z.
M.
No
or,
N.
F.
A.
Ra
hm
an
,
a
n
d M. K.
Ham
z
a
h
,
“
S
im
ul
ation
of DC
t
o
DC
c
o
n
v
e
r
te
r usin
g
sin
g
l
e
ph
a
s
e
m
a
trix
con
v
erter
to
po
lo
gy
,”
ISIEA
20
10 – 2
0
1
0
IEEE
S
y
mp
osiu
m on
In
d
u
stria
l
El
ec
tron
ic
s a
n
d
A
p
plic
a
t
io
ns (IS
IEA
)
, pp
.
1
4
9
–
1
5
4
,
20
10.
pp
. 1
4
9
–
1
5
4
,
2010
.
[
4
]
P
.
W
.
W
h
e
e
l
e
r
,
J
.
R
o
d
r
í
g
u
e
z
,
J
.
C
.
C
l
a
r
e
,
L
.
E
m
p
r
ingh
am
, an
d
A
.
Wein
stein
,
“
M
atrix co
nv
e
r
te
rs: A
tech
nolog
y
review,”
IEEE T
r
an
sac
t
io
ns on
in
du
st
ri
al
ele
c
t
r
on
ic
s
,
vo
l.
4
9
,
no
.
2
,
pp
.
2
7
6
–28
8,
20
02.
[5]
L
.
Gyugyi
and B
.
R
.
Pell
y,
“Static
P
o
wer Ch
arger
s
,
Th
eo
ry,
P
e
rfo
r
m
anc
e
an
d App
lica
t
ion,
”
Jo
hn
Wiley
&
So
n Inc
,
19
76
.
[6]
S.
Chawda,
D
.
Ahirrao, B. Gaware
,
P
.
K
a
k
a
d
e
, and
P
.
Kh
a
r
a
d
e, “An
a
lys
i
s
o
f
S
i
ng
le
Ph
ase
M
a
trix
Co
nv
erte
r,”
Internat
ional
Jour
nal
of
E
n
gineering Research
and A
p
p
l
icati
ons www.
i
j
er
a.com ISSN
,
vo
l.
4
,
no
.
1
,
pp
.
85
6–
86
1
,
20
14
.
[
7
]
M
.
V
e
n
t
u
r
i
n
i
,
“
N
e
w
S
i
n
e
W
a
v
e
i
n
,
S
i
n
e
W
a
v
e
O
u
t
Conv
ersi
on
Te
chniqu
e
Elim
in
ates Re
ac
tive
El
em
e
n
ts
.,”
Pr
oceed
ing
s
Po
wer
c
on
7
,
pp
E3
_
1
-E3_
15,
19
80
.
[8] D.
Boroj
e
vi
ć
, “
S
p
ace Ve
ctor M
o
du
lated
Thr
ee-
P
h
as
e to
Thr
ee-
P
h
as
e M
a
trix C
o
nv
erter
w
i
th In
pu
t
Po
wer
Facto
r
Correction,
”
IEEE
t
r
a
n
s
a
c
ti
on
s on i
n
d
u
stry
ap
pli
c
at
io
ns
,
1
9
95.
[9]
F.
A
b
rahams
en et al
.
,
“L
ist
of
Contri
bu
tors,
”
i
n
C
o
nt
rol
in
P
o
wer Ele
c
troni
cs,
20
0
2
.
[10
]
S
.
Kw
ak, “Ind
ir
ect m
a
trix
co
nv
e
r
ter
d
r
iv
es
for u
n
i
t
y
d
i
sp
lac
e
m
e
nt
f
a
ct
or
and
m
i
ni
mum
sw
itch
i
n
g
lo
ss
es,”
E
l
ec
tr
ic
Power Syst
ems
Research
,
20
07
.
[11]
A.
Roth-D
ebl
on,
“Combined
DC and AC
int
e
grati
o
n
of
ener
gy s
o
urces
in
hybri
d
3-phas
e off-gri
d systems,”
Con
f
er
e
n
c
e
Re
c
o
rd
of th
e 2
006
I
E
EE
4th
W
o
rld
Confer
en
c
e
on
Ph
otovolta
ic
Ener
gy Co
nvers
i
o
n
,
WCPEC-4,
vo
l. 2
,
no
. 1
,
p
p
.
2
4
3
1
–
243
3,
20
07
.
[12]
A. M. Nori and
T. K. Has
s
an, “
M
od
eling
and
s
i
mulation
o
f
qu
as
i-Z-s
ource
in
dire
ct m
a
tr
ix
con
v
e
r
t
er
for
perm
anen
t
m
a
g
n
et
syn
c
hron
ou
s m
o
to
r d
r
iv
e,
”
In
t
e
rn
at
io
n
a
l
J
o
u
r
n
a
l
o
f
P
o
we
r E
l
ec
t
r
o
n
i
c
s and Driv
e
Sy
st
e
m
s
(IJ
P
E
DS)
, v
o
l.
1
0
,
no
. 2
,
p
p
.
8
8
2
–
8
99,
20
19
.
[13]
R. Ghoni
,
A. N.
Abdalla
,
S
.
P
.
Koh
,
H
.
F
.
Rasha
g
,
and
R. R
a
z
a
li,
“Is
s
u
e
s
of
matrix
co
nv
e
r
t
e
rs:
Te
chnic
a
l rev
i
ew,”
In
te
rna
t
io
na
l J
ourna
l
of Ph
ysica
l
Sc
ienc
es
,
vo
l.
6
,
n
o
.
15
, pp
. 3
6
2
8–3
64
0,
20
11
.
[14
]
R. Bah
a
ro
m
an
d M
.
K.
Ha
mza
h
, “A
n
e
w s
i
ng
le-p
has
e
co
ntro
l
l
ed re
ct
ifier
u
s
i
ng s
i
n
g
le-phas
e
m
a
tr
ix
conv
erter
t
o
pol
o
gy i
n
corporat
ing
active
p
o
wer filter,” in
Pro
ceed
ings
o
f
IEEE
Int
e
rna
t
io
n
a
l
Ele
c
tr
ic M
a
chines
an
d
Driv
e
s
Con
f
er
e
n
c
e
,
IE
MDC
200
7
, 2
007
.
[15
]
M
.
F.
M
o
hd
Zin,
R.
Baharo
m,
an
d
I.
M
o
hd
Y
a
ssin,
“D
eve
l
o
p
m
e
n
t
of
boo
st
inv
e
rter
using
s
i
n
g
l
e
p
h
ase
ma
trix
c
o
nv
e
r
te
r t
o
p
o
l
ogy
,
”
In
t
e
rn
atio
nal
J
o
u
r
n
a
l
of E
ngi
ne
e
r
in
g &
Tech
n
o
l
o
g
y
,
v
o
l
.
7
,
no
.
4,
pp. 2
4
1
–24
5,
20
18.
[16
]
A. Zucke
r
b
e
rger
, D. Weins
t
o
c
k
,
and
A
.
A
l
ex
andr
o
v
itz
,
“S
in
gl
e-p
h
as
e
ma
trix
co
n
v
erter
,
”
I
E
E Pr
o
ceed
ing
s
-Ele
ctr
i
c
P
o
wer App
l
ic
a
t
i
o
ns,
200
2.
[17
]
S
.
H.
Hos
s
eini
an
d E.
Bab
a
e
i
,
“
A
new
gen
e
ra
liz
e
d d
i
r
e
c
t
matr
ix
conv
erter,
”
in
IE
EE Int
e
rn
a
t
i
onal
S
y
mp
osiu
m o
n
Ind
u
s
t
rial E
l
ec
tr
on
ics
, 20
01
.
[1
8]
A.
Kh
oe
i
a
n
d S. Yu
va
ra
ja
n
,
“
S
in
gl
e
-
Pha
s
e
AC-AC Co
nv
e
r
te
rs
Usi
n
g
Po
we
r
M
o
sfe
t
’s,
”
IE
EE
Tran
sa
c
t
i
o
n
s
on
Ind
u
s
t
rial E
l
ec
tr
on
ics
,
v
o
l
.
3
5
, no.
3
,
pp.
4
4
2
–
443,
19
8
8
.
[1
9]
M.
Voro
by
ov
,
“Ov
e
rv
ie
w of Si
n
g
le
Ph
a
s
e
M
a
tri
x
Co
nv
e
r
te
r Ap
pl
ic
a
tio
n
,
”
P
ubl
ic
ati
o
n
of
Doc
t
oral
Sc
h
o
o
l
o
f
E
n
e
r
g
y
an
d G
e
ote
c
hno
lo
gy
,
v
o
l. 3, pp
.
20
1–
20
7,
20
1
1
.
[20
]
K.
Vijay
a
kuma
r
,
R. S
.
Raj,
and
S
.
K
a
nn
a
n
, “R
e
a
lization
o
f
M
a
trix co
nv
erter
as
revo
lu
tioni
zed
pow
er el
ec
t
r
on
ic
c
o
nv
e
r
te
r e
m
p
l
o
y
in
g
si
nu
so
id
a
l
pul
se
wi
dt
h
m
o
dula
t
io
n,”
i
n
20
13
IEEE In
tern
ation
a
l Con
f
er
en
ce o
n
Com
p
u
t
atio
na
l
Intell
ig
e
n
ce
an
d
Co
mp
utin
g R
e
se
ar
ch,
IEEE
ICCI
C 20
13
,
20
13.
[2
1]
R.
Ku
m
a
r,
S.
Sr
iv
a
s
t
a
va,
S.
P.
Sin
g
h
,
a
n
d N.
Si
n
g
h
,
“
S
i
m
ula
tio
n of m
a
tri
x
c
o
nve
rte
r
ba
se
d DC-DC
c
o
n
v
e
r
te
r,”
20
1
3
Stud
ents Co
n
f
er
ence
o
n
Eng
i
n
e
er
in
g a
n
d
Sys
t
em
s,
SCES
20
13
,
p
p
.
1
3
4
–
1
3
8
,
2
013.
[2
2]
R.
M.
Anu
s
uy
a
a
n
d
R.
Sa
ra
v
a
n
a
k
u
m
a
r,
“
M
o
d
e
l
ing
a
n
d
Si
m
u
l
a
tio
n
of
a Si
ng
le P
h
a
s
e
Mat
r
ix
C
onve
rt
e
r
wi
th Re
duc
e
S
w
itch
Cou
n
t
as
a Bu
ck
/
Boo
s
t
Recti
f
ier
w
i
th
Cl
ose
Lo
op
Con
t
ro
l,”
Speci
a
l Is
sue
of IJC
E
T
, pp
.
93
–9
9, 20
15
.
[2
3]
M.
Q. I. M.
Za
ma
ni
,
R.
Ba
ha
ro
m, a
n
d D. Jo
ha
ri
,
“Con
c
e
p
tu
al stud
y on
grid-to-v
e
h
i
cle (G2
V
) wir
e
le
ss
po
wer tra
n
sfer
us
in
g s
i
n
g
le-pha
s
e
matr
ix co
nv
erter,
”
Inte
rna
t
i
onal
J
o
u
r
n
a
l
o
f
Powe
r
E
l
ec
t
r
on
ic
s an
d Dri
v
e
Sy
stems
(IJ
P
E
D
S
)
, vo
l
.
10
, n
o
.
3
,
p
p
.
13
82–
13
88
, 2
019
.
[24]
J. G.
Kass
aki
a
n,
M. F. Sch
l
ech
t,
an
d G
.
C. V
e
rgh
e
se, P
r
in
cip
l
es
o
f
po
wer electron
i
cs
,
Gr
ap
his, 200
0.
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