Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
No.
2
,
Jun
2021
,
pp.
94
3
~
95
6
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v12.i
2
.
pp
94
3
-
95
6
943
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Duty r
atio
control ofth
ree port
isolat
ed bidi
rectional
asymmet
rical tri
ple
ac
ti
ve bri
dge
DC
-
DC
c
onve
rter
Adarsh
S
.
,
Na
gend
r
appa
H.
Depa
rtment
o
f
E
le
c
tri
c
al a
nd
Ele
ct
roni
cs,
Na
ti
on
al
Inst
it
ut
e
of
T
e
chnol
ogy
Karn
ataka
,
Manga
lore,
India
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ja
n
2
, 20
21
Re
vised
Feb 2
5,
2021
Accepte
d
M
ar
19
, 20
21
Multi
port
conv
e
rte
rs
are
used
i
n
interfa
ci
ng
of
distri
bu
te
d
en
e
rgy
source
s
with
grid/load
.
Isolat
ed
conv
ert
ers
are
n
eeded
in
appl
i
cations
where
conve
rt
er
g
ai
n
is
high
and
th
ere
is
a
req
u
ir
em
en
t
of
isolat
ion.
Du
al
tra
nsformer
asy
mm
et
r
ic
tri
p
le
a
ct
iv
e
bridg
e
offe
rs
the
adv
antage
of
red
u
ce
d
ci
rcu
la
t
ing
cur
r
e
nt.
How
eve
r
,
th
e
oper
ating
ran
g
e
is
low
for
var
ia
t
ion
in
lo
ad
and
sourc
e
vo
lt
a
ge.
In
thi
s
p
ape
r
duty
ra
ti
o
modulati
on
t
ec
hniqu
e
i
s
proposed
to
r
egul
a
te
th
e
lo
ad
vol
ta
g
e
and
c
ontrol
the
power
flow
in
both
the
dir
ec
t
ions.
As
a
re
sult
of
t
he
new
g
ating
s
che
m
e,
the
conv
ert
er
sw
it
ch
es
o
per
ate
with
ZVS,
irre
spe
ct
i
ve
of
v
ari
a
ti
on
s
in
loa
d
powe
r
and
sourc
e
v
olt
ag
e.
The
conve
rt
er
is
desi
gned
to
ensure
h
igh
sw
itch
utilizati
on
.
The
cont
r
ol
te
chn
ique
is
val
id
at
ed
throu
gh
simul
ation
of
a
1kW
thre
e
po
rt
DC
-
DC
converte
r.
It
was
observe
rd
that
t
he
loa
d
vo
ltage
was
reg
ula
t
ed
fo
r
wide
ran
g
e
of
var
iation
in
loa
d
power
and
source
port
volta
ges.
Th
e
singl
e
i
nput
dual
outpu
t
mode
was
al
so ve
r
ifi
ed
.
Ke
yw
or
d
s
:
Bi
directi
on
al
powe
r flo
w
Du
t
y rati
o
c
on
t
ro
l
High
fr
e
qu
e
nc
y
is
olati
on
Sw
it
ch uti
li
sat
i
on
Zero v
oltage
s
witc
hing
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Ad
a
rs
h
S
Dep
a
rt
me
nt of
Ele
ct
rical
an
d
Ele
ct
ro
nics
E
nginee
rin
g
Nati
on
al
I
ns
ti
tute o
f
Tec
hnol
ogy Ka
rn
at
a
ka,
Surat
hkal
Dak
s
hi
na Kan
nad
a
D
ist
rict
,
Karnata
ka
, In
di
a
Emai
l:
ada
rsh
.s
riniv
asa
ra
gh
a
va
n@gmail
.c
om
1.
INTROD
U
CTION
M
ulti
port
c
onver
te
r
s
(
M
PC)
are
us
e
d
in
sy
ste
ms
wh
e
re
m
or
e
t
han
t
wo
s
ources
a
nd
l
oad
s
a
re
interface
d
.
T
he
m
ulti
port
c
onve
rter
has
l
ower
numb
e
r
of
c
ompone
nts
c
ompare
d
to
mu
lt
iple
tw
o
port
conve
rters;
he
nce
it
is
com
pa
ct
[1
]
-
[
3].
Mu
lt
ipo
rt
co
nvert
ers
can
be
cl
as
sifie
d
int
o
thre
e
typ
es
base
d
on
t
he
isolat
ion
of
ports.
Th
ey
a
re,
i
so
la
te
d,
non
-
is
olate
d
an
d
par
t
ia
l
ly
isolat
ed
M
PC
[
2
]
,
[
3].
In
non
-
isolat
ed
M
PC
there
is
no
galvan
ic
is
olati
on
betwee
n
an
y
ports.
Some
por
ts
of
par
ti
al
ly
isolat
ed
M
PC
a
re
isolat
ed
a
nd
al
l
the
ports a
re
galva
nical
ly isolat
ed
in
the
case
of Isola
te
d MPC
.
Iso
la
te
d
MPC
is
us
e
d
in
a
ppl
ic
at
ion
s
wh
e
re
there
is
a
re
quireme
nt
of
t
r
ansfo
rmer
isol
at
ion
.
It
ca
n
al
so
be
use
d
i
n
a
ppli
cat
ion
s
dema
nd
i
ng
high
c
onve
rter
ga
in
a
nd
high
po
wer.
Us
ually
hi
gh
f
reque
nc
y
(H
F
)
trans
forme
rs
ar
e
us
e
d
in
M
PC
,
due
to
high
s
witc
hing
f
re
quency.
T
his
re
duces
the
siz
e
of
the
tra
nsfo
rm
er
an
d
oth
e
r
ma
gnet
ic
com
pone
nts
[
2
]
-
[
4
]
.
Iso
la
te
d
MPC
to
po
l
ogie
s
ha
ve
bee
n
de
rive
d
f
r
om
c
orres
pondin
g
t
w
o
port
topolo
gies, suc
h
as
, fo
rw
a
rd c
onve
rters,
pus
h
-
pull
con
ver
te
r
s and
fly
back c
onve
rters
[2
]
,
[
3
].
A
m
o
ng
t
he
t
o
po
l
o
gi
e
s
r
e
p
or
t
e
d
i
n
t
he
l
i
t
er
a
t
ur
e
,
t
r
i
pl
e
a
c
t
i
ve
br
i
dg
e
(
T
A
B
)
ha
s
be
e
n
r
e
s
e
a
r
c
he
d
e
xt
e
ns
i
ve
l
y.
I
t
f
a
c
i
l
it
a
te
s
bi
di
r
e
c
t
i
on
a
l
po
w
e
r
f
l
ow
i
n
a
l
l
t
he
po
r
t
s
[
5
]
-
[
1
2
]
.
T
he
ph
a
s
e
s
hi
f
t
w
a
s
op
t
i
m
i
z
e
d
t
o
m
i
ni
m
i
z
e
s
w
i
tc
hi
ng
l
os
e
s
a
n
d
m
i
t
i
ga
t
e
e
l
e
ct
r
om
a
gn
e
t
i
c
i
s
s
ue
s
[
1
3
]
.
P
ow
e
r
f
l
o
w
w
a
s
c
on
t
r
ol
l
e
d
us
i
ng
ph
a
s
e
s
hi
f
t
c
on
t
r
ol
m
e
t
ho
d.
T
he
s
of
t
s
w
i
t
c
hi
ng
op
e
r
a
t
i
ng
r
e
gi
o
n
w
i
t
h
ph
a
s
e
s
hi
f
t
c
on
t
r
ol
wa
s
ve
r
y
na
r
r
o
w
,
he
nc
e
du
t
y
r
a
t
i
o
t
e
c
hn
i
qu
e
w
a
s
ut
i
l
i
z
e
d
to
i
nc
r
e
a
s
e
t
he
r
a
ng
e
of
Z
V
S
f
or
va
r
i
a
t
i
on
of
i
np
ut
v
ol
t
a
ge
a
nd
l
oa
d
[
1
4
]
-
[
1
8
]
.
I
t
a
l
s
o
he
l
pe
d
t
o
r
e
du
c
e
t
he
s
w
i
t
c
h
vo
l
t
a
ge
a
nd
c
ur
r
e
nt
s
t
r
e
s
s
e
s
.
T
he
t
op
ol
og
y
i
s
a
l
s
o
s
c
al
a
bl
e
t
o
hi
gh
e
r
po
r
t
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
94
3
–
95
6
944
[1
9
]
-
[
21
]
ha
d
d
e
m
on
s
t
r
a
t
e
d t
h
e
s
c
a
l
a
bi
li
t
y b
y
e
xt
e
nd
i
n
g t
he
nu
m
be
r
of
po
r
t
s
t
o f
o
ur
.
H
ow
e
ve
r
c
o
nt
r
ol
o
f
po
w
e
r
f
l
ow
i
n
t
he
t
op
ol
og
y
i
nv
ol
ve
d
c
r
os
s
c
ou
pl
i
ng
o
f
c
o
nt
r
ol
l
o
op
s
,
t
hi
s
pr
ob
l
e
m
w
a
s
r
e
c
t
i
f
i
e
d
b
y
t
he
de
c
o
up
l
i
ng
ne
t
w
or
k
i
m
pl
e
m
e
nt
e
d
i
n
[
1
8
]
.
L
C
,
L
L
C
a
nd
C
L
L
C
r
e
s
on
a
nt
t
a
nk
c
i
r
c
ui
t
s
r
e
s
pe
c
t
i
ve
l
y
w
e
r
e
a
dd
e
d
t
o
T
A
B
c
on
ve
r
t
e
r
,
t
he
r
e
by
r
e
d
uc
i
ng
t
he
s
w
i
t
c
hi
ng
l
os
s
e
s
a
nd
e
na
b
l
i
ng
t
he
op
e
r
a
t
i
on
a
t
10
0
kH
z
,
he
nc
e
i
nc
r
e
a
s
i
ng
t
he
po
w
e
r
de
ns
i
t
y
[
2
2
]
-
[
2
4
]
.
T
w
o
m
od
ul
e
s
of
T
A
B
w
e
r
e
us
e
d
t
o
i
nt
e
r
f
a
c
e
f
o
ur
p
or
t
s
,
c
o
ns
i
s
t
i
ng
of
t
w
o
e
ne
r
g
y
s
t
or
a
ge
de
vi
c
e
s
.
T
he
r
e
w
a
s
o
n
e
e
ne
r
gy
s
t
o
r
a
ge
de
vi
c
e
f
or
e
a
c
h
m
od
ul
e
a
nd
t
he
s
ou
r
c
e
a
nd
l
oa
ds
w
e
r
e
s
ha
r
e
d
by
bo
t
h
m
o
du
l
e
s
[
2
5
]
.
D
i
s
t
r
i
bu
t
e
d
t
r
a
ns
f
o
r
m
e
r
s
w
e
r
e
us
e
dt
o
r
e
d
uc
e
t
he
i
np
ut
c
u
r
r
e
nt
r
i
pp
l
e
s
a
nd
i
nc
l
ud
e
d
a
de
c
ou
pl
i
ng
ne
t
w
or
ki
n
t
he
c
o
nt
r
ol
s
ys
t
e
m
t
o
o
ve
r
c
om
e
t
h
e
c
r
os
s
c
ou
pl
i
ng
[
2
5
]
.
M
od
i
f
i
e
d
T
A
B
w
i
t
h
DC
M
op
e
r
a
t
i
on
e
ns
u
r
e
d
t
he
de
c
o
up
l
i
ng
op
e
r
a
t
i
on
by
a
ve
r
a
ge
c
ur
r
e
nt
c
on
t
r
ol
,
w
i
t
ho
ut
t
he
de
c
ou
pl
i
ng
ne
t
w
or
k
[
2
6
]
.
A
l
t
e
r
i
ng
t
he
ge
om
e
t
r
y
o
f
t
he
t
r
a
ns
f
or
m
e
r
c
or
e
a
nd
w
i
nd
i
n
gs
t
o
ob
t
a
i
n
f
ou
r
qu
a
dr
a
nt
i
nt
e
gr
a
t
e
d
t
r
a
ns
f
or
m
e
r
s
t
r
uc
t
ur
e
r
e
s
ul
t
e
d
i
n
de
c
o
up
l
e
d
c
o
nt
r
ol
[
2
7
].
T
he
t
o
po
l
o
gi
e
s
di
s
c
us
s
e
d
e
a
r
l
i
e
r
us
e
d
t
hr
e
e
w
i
nd
i
n
g
t
r
a
ns
f
or
m
e
r
,
w
hi
c
h
i
s
s
us
c
e
p
t
i
bl
e
t
o
m
a
gn
e
t
i
c
s
ho
r
t
c
i
r
c
ui
t
[
2
8]
.
T
o
o
ve
r
c
o
m
e
t
hi
s
pr
ob
l
e
m
,
du
a
l
t
r
a
ns
f
o
r
m
e
r
ba
s
e
d
t
o
p
ol
og
i
e
s
w
e
r
e
i
m
pl
e
m
e
nt
e
d.
T
he
y
w
e
r
e
m
ul
t
i
po
r
t
C
L
L
r
e
s
on
a
nt
c
on
ve
r
t
e
r
a
nd
D
u
a
l
t
r
a
ns
f
or
m
e
r
a
s
ym
m
e
t
r
i
c
a
l
t
r
i
pl
e
a
c
ti
ve
br
i
dg
e
(
D
T
A
T
A
B
)
.
Mu
l
t
i
po
r
t
C
L
L
r
e
s
on
a
nt
c
o
nv
e
r
t
e
r
r
e
du
c
e
d
t
he
v
ol
t
a
ge
s
t
r
e
s
s
i
n
t
he
s
w
i
t
c
he
s
;
ho
w
e
ve
r
,
t
he
l
oa
d
p
or
t
w
a
s
n
ot
bi
di
r
e
c
t
i
on
a
l
[
2
9]
.
D
T
A
T
A
B
e
ns
ur
e
d
bi
di
r
e
c
t
i
on
a
l
po
w
e
r
f
l
ow
i
n
a
l
l
i
t
s
po
r
t
s
,
ho
w
e
ve
r
i
t
s
s
w
i
t
c
h
c
ur
r
e
n
t
a
nd
vo
l
t
a
ge
s
t
r
e
s
s
w
e
r
e
hi
gh
[
2
8]
.
S
i
nc
e
o
nl
y
ph
a
s
e
s
hi
f
t
c
on
t
r
o
l
w
a
s
us
e
d
t
o
c
on
t
r
ol
t
he
p
ow
e
r
f
l
ow
,
t
he
s
w
i
t
c
he
s
di
d
no
t
op
e
r
a
t
e
w
i
t
h
Z
V
S
f
o
r
t
he
e
nt
i
r
e
r
a
n
g
e
of
l
oa
d
a
n
d
s
up
pl
y
vo
l
t
a
ge
.
H
e
nc
e
,
a
ne
w
m
od
ul
a
t
i
on
t
e
c
hn
i
q
ue
(
D
ut
y
r
a
t
i
o
c
on
t
r
ol
)
i
s
pr
op
o
s
e
d
i
n
t
hi
s
pa
pe
r
,
t
o
r
e
gu
l
a
t
e
l
oa
d
vo
l
t
a
ge
,
c
on
t
r
ol
p
ow
e
r
f
l
ow
i
n
bo
t
h
t
he
di
r
e
c
t
i
on
s
a
nd
op
e
r
a
t
e
t
he
s
w
i
t
c
he
s
w
i
t
h
Z
V
S
f
or
t
he
e
nt
i
r
e
r
a
ng
e
of
va
r
i
a
t
io
n
i
n
t
he
l
oa
d
a
nd
s
up
pl
y
v
ol
t
a
ge
.
T
he
pa
pe
r
i
s
or
ga
ni
z
e
d
a
s
f
ol
l
ow
s
:
w
or
ki
ng
pr
i
nc
i
pl
e
o
f
du
t
y
r
a
t
i
o
c
on
t
r
ol
a
p
pl
i
e
d
t
o
D
T
A
T
A
B
t
op
ol
o
gy
i
s
e
x
pl
a
i
ne
d
i
n
S
e
c
t
i
on
2
.
S
t
e
a
dy
s
t
a
t
e
a
na
l
y
s
i
s
is
e
xp
l
a
i
ne
d
i
n
S
e
c
t
i
on
3.
T
he
c
on
ve
r
t
e
r
de
s
i
gn
i
s
gi
ve
n
i
n
S
e
c
t
i
on
4
a
nd
t
he
s
i
m
ul
a
t
i
on
r
e
s
ul
t
s
a
r
e
di
s
c
us
s
e
d
i
n
S
e
c
t
i
on
5.
T
he
c
o
nc
l
us
i
on
s
a
r
e
dr
a
w
n
i
n
S
e
c
t
i
on
6.
2.
OPER
ATING
PR
I
N
CIPLE
2.1.
Circui
t descr
iption
DTATAB
i
s
a
d
ua
l
t
r
a
ns
f
o
r
m
e
r
f
ul
l
y
i
s
ol
a
t
e
d
t
hr
e
e
po
r
t
c
on
ve
r
t
e
r
.
T
hi
s
c
on
f
i
gu
r
a
t
i
on
w
a
s
i
ni
t
i
a
ll
y
i
m
pl
e
m
e
nt
e
d
b
y
J
a
k
ka
et
.
al
.
t
o
o
ve
r
c
o
m
e
t
h
e
pr
ob
l
e
m
s
o
f
m
a
gn
e
t
i
c
s
ho
r
t
c
i
r
c
ui
t
i
ng
i
n
t
he
t
r
i
pl
e
a
c
t
i
ve
br
i
d
ge
t
hr
e
e
po
r
t
c
on
v
e
r
t
e
r
[
28
]
.
I
n
t
hi
s
t
o
po
l
o
g
y
t
w
o
v
ol
t
a
ge
s
ou
r
c
e
p
or
t
s
a
r
e
c
on
ne
c
t
e
d
a
c
r
os
s
t
w
o
s
i
n
gl
e
ph
a
s
e
H
br
i
d
g
e
i
nv
e
r
t
e
r
s
.
T
he
r
e
s
i
s
t
i
ve
l
oa
d
p
or
t
i
s
c
on
n
e
c
t
e
d
a
c
r
os
s
a
t
hr
e
e
p
ha
s
e
i
nv
e
r
t
e
r
br
i
d
ge
.
T
he
t
r
a
ns
f
or
m
e
r
s
a
r
e
c
on
ne
c
t
e
d
t
o
t
he
br
i
dg
e
c
o
nF
i
g
u
r
e
ur
a
t
i
on
s
a
s
s
ho
w
n
i
n
F
i
gu
r
e
1.
T
he
s
w
i
t
c
he
s
of
t
he
i
nd
i
vi
du
a
l
i
nv
e
r
t
e
r
s
a
r
e
ga
t
e
d
i
n
s
uc
h
a
w
a
y a
s
t
o c
on
t
r
ol
t
he
ph
a
s
e
s
hi
f
t
be
t
w
e
e
n t
he
in
ve
r
t
e
r
o
ut
pu
t
vo
l
t
a
ge
s
.
B
y a
d
j
us
t
i
ng
t
he
ph
a
s
e
s
hi
f
t
be
t
w
e
en
t
he
t
r
a
ns
f
or
m
e
r
w
i
nd
i
n
g
i
np
ut
v
ol
t
a
ge
s
(
i
nv
e
r
t
e
r
ou
t
p
ut
vo
l
t
a
ge
s
)
t
he
p
ow
e
r
de
l
i
ve
r
e
d
b
y
t
he
p
or
t
s
c
a
n
b
e
c
on
t
r
ol
l
e
d
a
n
d
t
he
l
oa
d
p
or
t
v
ol
t
a
ge
V
3
c
a
n
a
l
s
o
be
r
e
gu
l
a
t
e
d.
T
hi
s
i
s
c
a
l
l
e
d
p
ha
s
e
s
hi
f
t
c
on
t
r
ol
.
T
he
pr
o
c
e
s
s
of
c
on
t
r
ol
l
i
ng
t
he
pu
l
s
e
w
i
dt
h
of
t
he
t
r
a
ns
f
or
m
e
r
w
i
nd
i
n
g
v
ol
t
a
ge
w
a
ve
f
or
m
s
(
i
nv
e
r
t
e
r
o
ut
pu
t
)
i
s
c
a
ll
e
d
du
t
y
r
a
t
i
o
c
on
t
r
ol
.
U
s
i
ng
du
t
y
r
a
t
i
o
c
o
nt
r
ol
c
om
bi
ne
d
w
i
t
h
ph
a
s
e
s
hi
f
t
c
on
t
r
ol
,
i
t
i
s
po
s
s
i
bl
e
t
o
op
e
r
a
t
e
t
he
c
on
ve
r
t
e
r
s
w
i
t
c
he
s
w
i
t
h
Z
V
S
.
H
e
nc
e
t
hi
s
w
or
k
i
s
a
i
m
e
d
a
t
a
pp
l
yi
ng
a
ga
t
i
ng
s
c
he
m
e
i
n
t
he
s
w
i
t
c
he
s
t
o
e
na
bl
e
du
t
y
r
a
t
i
o
c
on
t
r
ol
.
2.2.
Gating
schem
e
V
1
a
nd
V
2
a
r
e
DC
vo
l
t
a
ge
s
o
ur
c
e
s
c
o
nn
e
c
t
e
d
a
c
r
os
s
po
r
t
1
a
nd
po
r
t
2
r
e
s
pe
c
t
i
ve
l
y,
R
i
s
a
r
e
s
i
s
t
i
ve
l
oa
d
c
on
ne
c
t
e
d
a
c
r
os
s
po
r
t
3.
T
he
c
a
pa
c
i
t
or
C
3
i
s
a
s
s
um
e
d
to
be
l
a
r
ge
e
n
ou
gh
t
o
o
bt
a
i
n
a
DC
vo
l
t
a
ge
V
3
a
c
r
os
s
R
,
w
i
t
h
m
i
ni
m
um
r
i
p
pl
e
.
T
h
e
s
w
i
t
c
he
s
a
r
e
ga
t
e
d
a
s
s
ho
w
n
i
n
F
i
g
u
r
e
2.
T
he
w
a
ve
f
o
r
m
s
of
i
n
ve
r
t
e
r
ou
t
p
ut
vo
l
t
a
ge
s
d
ue
t
o
t
hi
s
ga
t
i
ng
s
c
h
e
m
e
a
r
e
a
s
s
h
o
w
n
i
n
F
i
gu
r
e
2
.
T
he
t
r
a
ns
f
o
r
m
e
r
w
i
n
di
ng
c
ur
r
e
nt
s
a
r
e
a
l
s
o
s
ho
w
n
i
n
F
i
gu
r
e
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Du
ty
ra
ti
o co
nt
ro
l
ofthree
por
t i
so
lated
b
i
dir
ect
i
on
al
as
y
m
metri
cal tri
ple
activ
e…
(
A
da
r
sh
S
)
945
Figure
1. Ci
rcui
t diagr
a
m
of DTAT
AB
(
a
)
(b)
(
c
)
Figure
2.
(a
) G
at
ing
si
gn
al
s
of
inv
e
rter i
nter
f
aci
ng
port,
(
b)
Gati
ng sig
nal
s
of in
ver
te
r
inte
rf
aci
ng
port,
(c
)
Gati
ng sig
nals
of in
ver
te
r
inte
rf
aci
ng
port
3
P
1
S
1
1
i
1
3
i
1
1
i
1
2
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
3
S
1
2
S
1
4
i
2
3
i
2
1
i
2
2
i
2
4
i
3
3
i
3
1
i
3
2
i
3
4
i
3
5
i
3
6
S
2
1
S
2
3
S
2
2
S
2
4
S
3
1
S
3
3
S
3
2
S
3
4
S
3
5
S
3
6
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
i
A
i
C
v
A
B
S
1
1
S
1
2
S
1
3
S
1
4
V
1
-
V
1
p
0
.
5
p
1
.
5
p
p
D
1
p
D
1
p
+
p
D
1
2
p
w
t
w
t
w
t
w
t
w
t
v
C
D
S
2
1
S
2
2
S
2
3
S
2
4
V
2
-
V
2
p
0
.
5
p
1
.
5
p
p
D
2
f
1
2
+
p
D
2
f
1
2
+
p
+
p
D
2
2
p
w
t
f
1
2
f
1
2
+
p
w
t
w
t
w
t
w
t
v
E
O
S
3
1
S
3
6
S
3
3
S
3
4
V
3
-
V
3
p
0
.
5
p
1
.
5
p
p
D
3
f
1
3
+
p
D
3
f
1
3
+
p
D
3
-
p
2
p
f
1
3
f
1
3
+
p
S
3
5
S
3
2
v
F
O
w
t
w
t
w
t
w
t
w
t
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
94
3
–
95
6
946
Figure
3.
I
nv
e
r
te
r
outp
ut
vo
lt
a
ges
a
nd tra
ns
f
ormer
w
i
nd
i
ng c
urren
ts
2.3.
Opera
tio
n m
odes
T
he
r
e
a
r
e
s
i
x
op
e
rati
ng
m
od
e
s
f
o
r
ha
l
f
t
he
s
w
i
t
c
hi
ng
c
yc
l
e
.
T
he
pr
o
po
s
e
d
m
od
ul
a
t
i
on
t
e
c
hn
i
qu
e
i
s
s
ym
m
e
t
r
i
c
.
a.
M
ode
1
:
0
w
t
1
S
11
,
S
14
,
S
22
,
S
23
,
S
33
,
S
32
,
S
36
a
r
e
t
he
s
w
i
t
c
he
s
ga
t
e
d
d
ur
i
n
g
t
hi
s
m
od
e
.
T
he
pa
t
h
of
c
u
r
r
e
nt
f
l
ow
i
s
s
ho
w
n
i
n
F
i
gu
r
e
4
(
a
)
.
T
he
v
ol
t
a
ge
a
c
r
os
s
A
a
n
d
B
i
s
(
v
AB
)
i
s
V
1
,
vo
l
t
a
ge
a
c
r
os
s
C
a
n
d
D
i
s
(
v
CD
)
i
s
V
2
,
t
he
vo
l
t
a
ge
a
c
r
os
s
E
a
nd
O
(
v
EO
)
a
nd
t
he
v
ol
t
a
ge
a
c
r
os
s
F
a
n
d
O
i
s
(
v
FO
)
i
s
V
3
.
T
he
w
i
n
di
ng
c
ur
r
e
nt
s
a
r
e
a
s
s
ho
w
n
i
n
F
i
gu
r
e
4
(
a
)
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
s
i
s11
a
nd
i
s14
a
r
e
e
qu
a
l
t
o
i
A
.
C
ur
r
e
nt
s
i
s23
a
nd
i
s22
a
r
e
e
qu
a
l
t
o
-
i
C
.
T
he
c
ur
r
e
nt
s
i
A
a
nd
i
C
a
r
e
t
r
a
ns
f
or
m
e
d
a
s
i
A
a
nd
i
C
i
n
t
he
s
e
c
on
da
r
y
s
i
de
of
t
he
t
r
a
ns
f
or
m
e
r
.
T
h
e
s
w
i
t
c
h
c
ur
r
e
n
t
i
s3
2
i
s
e
qu
a
l
t
o
i
A
,
i
s
i
s3
6
i
s
e
qu
a
l
t
o
i
C
a
nd
i
s33
i
s
e
qu
a
l
t
o
i
A’
+
i
C
.
b.
M
ode
2
1
<
w
t<
2
S
11
,
S
14
,
S
22
,
S
24
,
S
33
,
S
32
,
S
36
a
r
e
t
he
switc
hes
ga
t
e
d
du
r
i
n
g
t
hi
s
m
od
e
.
T
he
pa
t
h
of
c
u
r
r
e
nt
f
l
ow
i
s
s
ho
w
n
i
n
F
i
gu
r
e
4(
b
)
.
T
he
v
ol
t
a
ge
v
AB
i
s
V
1
,
vC
D
i
s
0,
v
EO
i
s
V
3
a
nd
v
FO
i
s
V
3
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
s
i
s11
a
nd
i
s14
a
r
e
e
q
ua
l
t
o
i
A
.
C
ur
r
e
nt
i
s22
i
s
e
qu
a
l
t
o
–
i
C
a
n
d
i
s24
i
s
e
qu
a
l
t
o
i
C
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
i
s32
i
s
e
q
ua
l
t
o
i
A
,
i
s
i
s36
i
s
e
qu
a
l
t
o
i
C’
a
nd
i
s33
i
s
e
qu
a
l
t
o
i
A’
+
i
C
.
c.
M
ode
3
:
2
<
w
t<
3
S
11
,
S
14
,
S
22
,
S
24
,
S
32
,
S
34
,
S
36
a
r
e
t
he
switc
hes
ga
t
e
d
du
r
i
n
g
t
hi
s
m
od
e
.
T
he
pa
t
h
of
c
u
r
r
e
nt
f
l
ow
i
s
s
ho
w
n
i
n
F
i
g
ur
e
4
(
c
)
.
T
he
v
ol
t
a
ge
v
AB
i
s
V
1
,
vC
D
i
s
0,
v
EO
i
s
0
a
nd
v
FO
i
s
0
.
T
he
s
w
i
t
c
h
c
u
r
r
e
nt
s
i
s11
a
nd
i
s1
4
a
r
e
e
qu
a
l
t
o
i
A
.
C
ur
r
e
nt
s
i
s22
i
s
e
qua
l
t
o
-
i
C
a
nd
i
s24
i
s
e
qu
a
l
t
o
i
C
.
T
he
s
w
i
t
c
h
c
u
r
r
e
nt
i
s32
i
s
e
qu
a
l
t
o
i
A
,
i
s36
i
s
eq
ua
l
t
o
i
C’
a
nd
i
s34
i
s
e
qu
a
l
t
o
–
(
i
A’
+
i
C’
)
.
d.
M
ode
4
:
3
<
w
t<
4
S
11
,
S
14
,
S
21
,
S
24
,
S
32
,
S
34
,
S
36
a
r
e
t
he
s
w
i
t
c
he
s
ga
t
e
d
d
ur
i
n
g
t
hi
s
m
od
e
.
T
he
pa
t
h
of
c
u
r
r
e
nt
f
l
ow
i
s
s
ho
w
n i
n F
i
gu
r
e
4(
d)
.
T
he
vo
l
t
a
ge
v
AB
i
s
V
1
,
v
CD
i
s
V
2
,
v
EO
is
0 a
nd
v
FO
i
s
0
.
T
he
s
w
i
t
c
h c
ur
r
e
nt
s
i
s11
a
nd
i
s1
4
a
r
e
e
qu
a
l
t
o
i
A
.
C
urr
e
nt
s
i
s21
a
nd
i
s
24
a
r
e
e
qu
a
l
t
o
i
B
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
i
s32
i
s
e
qu
a
l
t
o
i
A
’
,
i
s
36
i
s
e
qu
a
l
t
o
i
C
a
nd
i
s34
i
s
e
qu
a
l
t
o
–
(
i
A’
+
i
C’
)
.
e.
M
ode
5
:
4
<
w
t<
5
S
11
,
S
14
,
S
21
,
S
24
,
S
31
,
S
34
,
S
35
a
r
e
t
he
switc
hes
ga
t
e
d
du
r
i
n
g
t
hi
s
m
od
e
.
T
he
pa
t
h
of
c
u
r
r
e
nt
f
l
ow
i
s
s
ho
w
n
i
n
F
i
g
ur
e
4
(
e
)
.
T
he
vo
l
t
a
ge
v
AB
i
s
V
1
,
vC
D
i
s
V
2
,
v
EO
i
s
V
3
a
n
d
v
FO
i
s
V
3
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
s
i
s11
a
nd
i
s14
a
r
e
e
qu
a
l
t
o
i
A
.
C
ur
r
e
nt
s
i
s21
a
nd
i
s24
a
r
e
e
q
ua
l
t
o
i
C
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
i
s31
i
s
e
qu
a
l
t
o
-
i
A
,
i
s
35
i
s
e
qu
a
l
to
-
i
C’
a
nd
i
s34
i
s
e
qu
a
l
t
o
-
(
i
A’
+
i
C’
)
.
f.
M
ode
6
:
5
<
w
t<
6
S
11
,
S
13
,
S
21
,
S
24
,
S
31
,
S
34
,
S
35
a
r
e
t
he
s
w
i
t
c
he
s
ga
t
e
d
d
ur
i
n
g
t
hi
s
m
od
e
.
T
he
pa
t
h
of
c
u
r
r
e
nt
f
l
ow
i
s
s
ho
w
n i
n F
i
gu
r
e
4
(
f
)
.
T
he
vo
l
t
a
ge
v
AB
i
s
0
,
v
CD
i
s V
2
,
v
EO
i
s
V
3
a
nd
v
FO
i
s
V
3
.
T
he
s
w
i
t
c
h c
ur
r
e
nt
i
s
11
i
s
e
qua
l
t
o
i
A
a
nd
i
s
13
i
s
e
qu
a
l
t
o
-
i
A
.
C
ur
r
e
nt
s
i
s
21
a
nd
i
s
24
a
r
e
e
qu
a
l
t
o
i
C
.
T
he
s
w
i
t
c
h
c
ur
r
e
nt
i
s31
i
s
e
qu
a
l
t
o
-
i
A
,
i
s
35
i
s
e
qu
a
l
t
o
-
i
C’
a
nd
i
s34
is
e
qu
a
l
t
o
-
(
i
A’
+
i
C’
)
.
v
A
B
=
w
t
i
n
r
a
d
i
a
n
i
A
o
i
C
v
C
D
v
E
O
v
F
O
1
2
3
4
5
6
p
p
D
1
f
1
2
f
1
2
+
p
D
2
f
1
3
f
1
3
+
p
D
3
f
1
3
+
p
D
3
-
p
w
t
w
t
w
t
w
t
w
t
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Du
ty
ra
ti
o co
nt
ro
l
ofthree
por
t i
so
lated
b
i
dir
ect
i
on
al
as
y
m
metri
cal tri
ple
activ
e…
(
A
da
r
sh
S
)
947
(a)
(b)
(c)
(d)
(e)
(f)
Figure
4.
Co
nverter c
urren
t
p
a
th and
switc
hi
ng tra
ns
it
ion i
n (
a) mo
de 1 (b
) mo
de 2
(c)
mode
3 (d) m
ode
4(
e
)
mode
5 (f
)
m
ode
6
P
1
S
1
1
i
1
1
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
4
i
2
3
i
2
2
i
3
3
i
3
2
i
3
6
S
2
3
S
2
2
S
3
1
S
3
3
S
3
2
S
3
5
S
3
6
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
P
1
S
1
1
i
1
1
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
4
i
2
2
i
3
3
i
3
2
i
3
6
S
2
2
S
3
3
S
3
2
S
3
5
S
3
6
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
i
2
4
S
2
4
P
1
S
1
1
i
1
1
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
4
i
3
3
i
3
2
i
3
6
S
3
3
S
3
2
S
3
6
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
i
2
4
S
2
4
i
2
1
S
2
1
P
1
S
1
1
i
1
1
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
4
i
3
2
i
3
6
S
3
3
S
3
2
S
3
6
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
i
2
4
S
2
4
i
2
1
S
2
1
i
3
4
P
1
S
1
1
i
1
1
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
4
i
3
1
i
3
5
S
3
4
S
3
1
S
3
5
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
i
2
4
S
2
4
i
2
1
S
2
1
i
3
4
P
1
S
1
1
i
1
1
i
1
4
+
-
R
V
3
C
V
1
V
2
1
:
N
1
1
:
N
2
L
A
L
C
i
C
’
i
A
’
P
o
r
t
1
P
2
P
3
S
1
4
i
3
1
i
3
5
S
3
4
S
3
1
S
3
5
A
B
C
D
E
O
F
P
o
r
t
2
P
o
r
t
3
i
2
4
S
2
4
i
2
1
S
2
1
i
3
4
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
94
3
–
95
6
948
2.4.
Equi
va
le
nt
cir
cuit
R
e
f
e
r
r
i
ng
t
o
t
he
op
erati
on
s
t
a
ge
s
e
xp
l
a
i
ne
d
i
n
S
e
c
t
i
on
I
I
C
,
t
he
ci
r
c
ui
t
c
a
n
be
a
pp
r
ox
i
m
a
t
e
d
t
o
a
n
e
qu
i
va
l
e
nt
c
i
r
c
ui
t
a
s
s
ho
w
n
i
n
F
i
gu
r
e
5.
T
he
f
ol
l
ow
i
ng
a
s
s
u
m
pt
i
on
s
a
r
e
m
a
de
t
o
ob
t
a
i
n
t
he
e
q
ui
va
l
e
nt
c
i
r
c
ui
t
.
L
1
a
nd
L
2
a
r
e
th
e
s
um
of
t
he
l
e
a
ka
ge
i
nd
uc
t
a
nc
e
of
t
he
r
e
s
p
e
c
t
i
ve
t
r
a
ns
f
o
r
m
e
r
s
r
e
f
e
r
r
e
d
t
o
t
he
s
e
c
on
da
r
y
s
i
de
a
nd
t
he
i
n
du
c
t
o
r
s
L
A
a
nd
L
C
r
e
s
pe
c
t
i
ve
l
y.
a.
T
he
s
w
i
t
c
he
s
a
nd
di
od
e
s
a
r
e
a
s
s
um
e
d
t
o
be
i
de
a
l
b.
T
he
t
r
a
ns
f
or
m
e
r
c
a
n
be
r
e
pl
a
c
e
d
b
y
a
T
e
q
ui
va
l
e
nt
c
i
r
c
ui
t
w
i
t
h
a
l
l
qu
a
nt
i
ti
es
r
e
f
e
r
r
e
d
t
o
t
h
e
s
e
c
on
da
r
y
s
i
d
e
c.
T
he
t
r
a
ns
f
or
m
e
r
l
o
s
e
s
a
r
e
ne
gl
e
c
t
e
d
d.
T
he
m
a
g
ne
t
i
z
in
g
i
n
du
c
t
a
nc
e
of
t
he
t
r
a
ns
f
or
m
e
r
c
a
n
be
ne
gl
e
c
t
e
d
a
s
i
t
s
ef
f
e
c
t
on
t
he
c
u
r
r
e
nt
s
o
bt
a
i
ne
d
w
i
l
l
be
m
i
ni
m
um
d
ue
t
o
hi
g
h
s
w
i
t
c
hi
ng
f
r
e
q
ue
nc
y
e.
A
l
l
t
he
s
w
i
t
c
he
s
i
n
t
he
c
on
ve
r
t
e
r
a
r
e
s
w
i
t
c
he
d
a
t
t
he
s
a
m
e
s
w
i
t
c
hi
ng
f
r
e
q
ue
n
c
y.
Figure
5.
Eq
ui
valent
ci
rc
uit o
f
D
TA
TAB
3.
STE
ADY ST
ATE A
N
ALY
SIS
T
he
c
ur
r
e
nt
e
x
pr
e
s
s
i
on
s
f
or
i
A’
a
nd
i
C’
a
r
e
de
r
i
ve
d
f
r
om
t
he
e
qu
i
va
l
e
nt
c
i
r
c
ui
t
us
i
ng
s
up
e
r
po
s
i
t
i
on
t
he
or
e
m
.
T
he
r
e
a
r
e
6
op
e
r
a
t
i
ng
m
o
de
s
ba
s
e
d
on
t
he
va
l
ue
s
of
p
ha
s
e
s
hi
f
t
s
f
12
,
f
23
a
nd
d
ut
y
r
a
t
i
os
D
1
,
D
2
an
d
D
3
.
T
he
v
ol
t
a
ge
a
c
r
os
s
p
or
t
3
c
a
n
be
e
x
pr
e
s
s
e
d
a
s
s
h
ow
n
i
n
(
1
)
.
3
=
1
1
13
1
+
2
2
23
2
(1)
t
he
p
ow
e
r
a
t
t
h
e
t
hr
e
e
po
r
t
s
P
1
, P
2
a
nd
P
3
c
a
n
be
e
xp
r
e
s
s
e
d
a
s
s
ho
w
n
i
n
(
2
)
.
3
=
1
1
13
1
3
+
2
2
23
2
3
(2)
1
=
1
1
13
1
3
(3)
2
=
2
2
23
2
3
(4)
ℎ
1
=
1
1
2
=
1
2
(5)
=
2
,
W
he
re
f
is
the
switc
hing
f
requen
c
y
M
13
a
nd
M
23
de
pe
nd
o
n
t
he
phase
s
hi
f
t
s
a
nd
du
t
y
r
a
t
i
os
.
T
a
bl
e
1
a
nd
T
a
bl
e
2
s
h
ow
s
t
he
e
x
pr
e
s
s
i
on
of
M
13
a
n
d M
23
r
e
s
pe
c
t
i
v
e
l
y.
F
or
ne
ga
t
i
ve
va
l
ue
o
f
f
13
a
nd
f
23
r
e
s
pe
c
t
i
ve
l
y
M
13
a
nd
M
23
c
a
n
be
ob
t
a
i
ne
d
b
y
ne
ga
t
i
ng
t
he
c
or
r
e
s
po
n
di
ng
e
xp
r
e
s
s
i
on
s
i
n
T
a
bl
e
s
1
a
nd
2.
T
he
pl
ot
s
of
M
13
v
e
r
s
us
ph
a
s
e
s
hi
f
t
i
s
s
ho
w
n
i
n
F
i
gu
r
e
6.
I
t
c
a
n
be
ob
s
e
r
ve
d
f
r
o
m
F
i
gu
r
e
6
t
ha
t
M
13
i
s
m
a
xi
m
u
m
f
or
ph
a
s
e
s
hi
f
t
o
f
9
0
o
.
H
e
nc
e
p
ow
e
r
t
r
a
ns
f
e
r
r
e
d
i
s
m
a
xi
m
um
a
t
a
p
ha
s
e
s
hi
f
t
o
f
9
0
o
.
H
e
nc
e
t
he
ph
a
s
e
s
hi
f
t
i
s
f
i
xe
d
a
t
90
o
a
nd
t
he
po
w
e
r
f
l
o
w
i
s
c
on
t
r
ol
l
e
d
b
y
va
r
yi
n
g
t
he
du
t
y
r
a
t
i
o
D
1
,
D
2
a
nd
D
3
.
I
f
D
3
i
s
fixed
a
t
1
a
nd
ph
a
s
e
s
hi
f
t
f
13
a
n
d
f
23
a
r
e
f
i
xe
d
a
t
0.
5
p
c
,
t
he
va
l
ue
o
f
M
13
a
nd
M
23
w
i
l
l
de
pe
nd
on
D
1
a
nd
D
2
a
l
on
e
,
r
e
s
p
e
c
t
i
ve
l
y.
S
i
nc
e
P
1
i
s
pr
o
po
r
t
i
on
a
l
t
o
M
13
i
t
c
a
n
be
c
on
t
r
ol
l
e
d
us
i
n
g
D
1
a
nd
P
2
c
a
n
be
c
o
nt
r
ol
l
e
d
us
i
ng
D
2
a
s
i
t
i
s
pr
o
po
r
t
i
on
a
l
t
o
M
23
.
H
e
nc
e
t
he
t
e
c
h
ni
qu
e
i
s
e
a
s
y
t
o
i
m
pl
e
m
e
nt
.
N
1
*
V
A
B
N
2
*
V
C
D
L
1
L
2
V
E
O
i
A
’
i
C
’
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Du
ty
ra
ti
o co
nt
ro
l
ofthree
por
t i
so
lated
b
i
dir
ect
i
on
al
as
y
m
metri
cal tri
ple
activ
e…
(
A
da
r
sh
S
)
949
Table
1.
E
xpre
ssion o
f M
13
Ran
g
e of du
ty
r
atio
D
1
an
d
D
3
Exp
ressio
n
of M
13
3
+
13
≤
1
≤
1
0
≤
3
≤
1
−
13
3
2
2
+
3
13
2
−
1
3
2
13
≤
1
≤
3
+
13
0
≤
3
≤
1
−
13
−
1
2
2
+
1
13
+
1
3
2
−
13
2
2
13
≤
1
≤
1
1
−
13
≤
3
≤
1
13
(
1
+
1
−
3
)
−
13
2
−
2
{
1
2
−
1
3
+
(
1
−
3
)
2
}
0
≤
1
≤
13
+
3
−
1
1
−
13
≤
3
≤
1
1
2
2
+
1
−
1
13
−
1
3
2
0
≤
1
≤
13
0
≤
3
≤
1
−
13
1
3
2
1
−
13
≤
3
≤
1
3
+
13
−
1
≤
1
≤
13
3
+
1
3
2
−
2
−
3
2
2
−
13
2
2
−
3
13
Table
2.
E
xpre
ss
ion
of
M
23
Ran
g
e of du
ty
r
atio
D
2
an
d
D
3
Exp
ressio
n
of M
23
3
+
23
≤
2
≤
1
0
≤
3
≤
1
−
23
3
2
2
+
3
23
2
−
2
3
2
23
≤
2
≤
3
+
23
0
≤
3
≤
1
−
23
−
2
2
2
+
2
23
+
2
3
2
−
23
2
2
23
≤
2
≤
1
1
−
23
≤
3
≤
1
23
(
1
+
2
−
3
)
−
23
2
−
2
{
2
2
−
2
3
+
(
1
−
3
)
2
}
0
≤
2
≤
23
+
3
−
1
1
−
23
≤
3
≤
1
2
2
2
+
2
−
2
23
−
2
3
2
0
≤
2
≤
23
0
≤
3
≤
1
−
23
2
3
2
1
−
23
≤
3
≤
1
3
+
23
−
1
≤
2
≤
23
3
+
2
3
2
−
2
−
3
2
2
−
23
2
2
−
3
23
(a)
(b)
Figure
6.
Plot
of M1
3v
s
phas
e sh
ift
f
or
(a)
D1
=
1 (b)
D
1=
0.2
ℎ
≥
0
.
5
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
94
3
–
95
6
950
3
=
−
2
4
−
2
2
(5)
ℎ
<
0
.
5
3
=
2
2
(6)
ℎ
1
1
2
2
T
he
pl
ot
o
f
M
13
ve
r
s
us
D
1
i
s
sh
ow
n
i
n
F
i
g
ur
e
7.
T
he
gr
a
ph
o
f
M
23
ve
r
s
us
D
2
i
s
s
a
m
e
a
s
F
i
gu
r
e
7
.
Figure
7.
Gai
n vs Dut
y
Ra
ti
o at
Ph
ase
S
hift
90o
a
nd
-
90o
F
or
bo
t
h
t
he
c
a
s
e
s
t
he
e
xp
r
e
s
s
i
on
of
c
ur
r
e
nt
i
n
t
he
s
w
i
t
c
he
s
d
ur
i
ng
t
ur
n
o
n
i
s
gi
ve
n
by
(
7
)
.
(
0
)
=
−
1
[
(
2
)
]
(7)
S
i
nc
e
(
7
)
i
s
ne
ga
t
i
ve
i
r
r
e
s
pe
c
t
i
ve
of
V
x
a
nd
D
x
i
t
c
a
n
be
i
n
f
e
r
r
e
d
t
ha
t
t
he
c
on
ve
r
t
e
r
s
w
i
t
c
he
s
o
pe
r
a
t
e
w
i
t
h
Z
V
S
i
r
r
e
s
pe
c
t
i
ve
of
l
oa
d
po
w
e
r
a
n
d
s
o
ur
c
e
v
ol
t
a
ge
va
r
i
a
t
i
on
s
.
H
ow
e
ve
r
,
i
n
t
he
c
a
s
e
of
s
t
a
nd
a
l
o
ne
ph
a
s
e
s
hi
f
t
c
on
t
r
ol
,
Z
V
S
c
a
n
oc
c
u
r
on
l
y
w
he
n
t
he
c
on
di
t
i
on
s
pe
c
i
f
i
e
d
i
n
(
8
)
i
s
s
a
t
i
s
f
ie
d.
H
e
n
c
e
w
h
e
n
t
he
r
a
ng
e
o
f
Z
V
S
i
s
t
a
ke
n
i
nt
o
c
o
ns
i
de
r
a
t
i
on
,
du
t
y
r
a
t
i
o
c
on
t
r
ol
i
s
be
t
t
e
r
t
ha
n
p
ha
s
e
s
hi
f
t
c
on
t
r
ol
.
3
−
≤
0
(8)
4.
DESIG
N
I
n
t
hi
s
s
e
c
t
i
on
a
n
i
s
ol
a
t
e
d
D
T
A
T
A
B
DC
t
o
DC
C
on
ve
r
t
e
r
i
s
de
s
i
gn
e
d
f
o
r
t
he
s
pe
c
i
f
i
c
a
t
io
ns
gi
ve
n
i
n
T
a
bl
e
3,
t
he
c
o
nv
e
r
t
e
r
i
s
de
s
i
g
ne
d
f
or
w
or
s
t
c
a
s
e
op
e
r
a
t
i
ng
c
on
di
t
i
on
s
of
m
i
ni
m
um
vo
l
t
a
ge
i
n p
or
t
1,
po
r
t
2 a
n
d
m
a
xi
m
um
l
oa
d
of
1K
W
.
It
is
a
desirab
le
qual
it
y
to
desi
gn
the
co
nverte
r
in
su
c
h
a
wa
y
as
to
inc
reas
e
the
switc
h ut
il
iz
at
i
on. Swit
ch uti
li
zat
ion
def
i
ned
by
(
9
)
.
=
3
(9)
w
he
re
P
3
is t
he maxim
um
pow
er at
port 3 (L
oa
d powe
r)
a
nd
S is the
sw
it
ch
stress
giv
e
n by
(
10
)
.
=
∑
1
(
)
1
(
)
4
=
1
+
∑
2
(
)
2
(
)
4
=
1
+
∑
3
(
)
3
(
)
6
=
1
(10)
=
4
{
[
(
1
+
3
)
×
(
13
)
]
+
[
(
2
+
3
)
×
(
23
)
]
}
(11)
Fr
om
Fig
ur
e
8
(Lef
t)
it
c
an
be
unde
rst
ood
t
hat
the
switc
h
util
iz
at
ion
is
maxi
mu
m
w
he
n
P
2
=(V
2
/V
1
)*P
1
.
The
rati
o
of
powe
r
bet
wee
n
port
2
an
d
port
1
is
fixe
d
a
t
(V
2
/V
1
)
,
as
it
cannot
be
i
nc
reased
furthe
r.
S
witc
h
util
iz
at
ion
is
pl
otted
versus
n/
(
w
*L
)
f
or
dif
fer
e
nt
values
of
tra
nsfo
rme
r
tur
ns
rati
o
in
Fi
gure
8
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Du
ty
ra
ti
o co
nt
ro
l
ofthree
por
t i
so
lated
b
i
dir
ect
i
on
al
as
y
m
metri
cal tri
ple
activ
e…
(
A
da
r
sh
S
)
951
(Righ
t
).
It
is
ob
s
er
ved
in
t
he
plo
t
t
hat
uti
li
zat
ion
increa
ses
with
incre
ase
in
tra
nsfo
r
mer
t
urns
rati
o
a
nd
reducti
on
in
i
nductance
.
He
nce
n=
n
1
=n
2
is
ch
os
en
as
5
and
n/
(
w
*L
)
is
ch
os
e
n
as
0.176
8.
Henc
e
the
inducta
nce
L
1
=L
2
=L
is 45
µ
H.
In (1)
can
b
e
m
od
i
fied
as
s
hown in (
12).
Figure
8.
S
witc
h Uti
li
sat
ion
(U)
vs
n/(
2*
p
*f
*L) f
or d
i
ff
e
re
nt v
al
ues of P
2/
P1
(Le
ft)
a
nd
di
ff
ere
nt
values
of n
(Righ
t
)
Table
3.
C
onve
rter
sp
eci
ficat
ion
s
V
1
(V)
V
2
(V)
V
3
(V)
Switch
in
g
Fr
eq
u
en
cy
f
(
KHz)
P
3
(KW)
4
8
to 7
2
2
4
to 4
8
100
100
1
3
=
1
13
(
1
+
2
1
)
(12)
ℎ
,
2
1
13
=
2
×
×
10
0
×
45
10
×
48
×
(
1
+
24
48
)
=
4
(13)
Divid
i
ng
(
4
)
by
(
3
)
,
(
14
)
is
obta
ined
.
2
1
=
23
2
13
1
(14)
23
=
13
=
4
(15)
D1
an
d
D
2
a
re
deduce
d from
Figure
7.
1
=
2
=
1
(16)
T
he
c
on
ve
r
t
e
r
pa
r
a
m
e
t
e
r
de
s
i
gn
va
l
ue
s
a
r
e
d
i
s
pl
a
ye
d
i
n
T
a
b
l
e
4
Table
4.
C
onve
rter P
a
ramete
r desig
n values
R (Full Load
)
(
)
n
L (
H)
f
1
3
f
2
3
D
1
D
2
D
3
10
5
45
0
.
5
p
c
0
.
5
p
c
1
1
1
5.
RESU
LT
S
In
this
s
e
c
t
i
on
,
t
he
s
i
m
ul
a
t
i
on
r
e
s
ul
t
s
of
a
1K
W
D
T
A
T
A
B
DC
-
DC
c
on
ve
r
t
e
r
de
s
i
gn
e
d
i
n
S
e
c
t
i
on
4
i
s
s
ho
w
n.
T
he
w
or
s
t
c
a
s
e
op
e
r
a
t
i
ng
c
on
di
t
i
on
i
s
V
1
=
48
V
,
V
2
=
24
V
a
nd
t
he
l
oa
d
R
=
10
Ω
.
B
ot
h
t
he
po
r
t
s
1
a
nd
2
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
2
,
J
une
2021
:
94
3
–
95
6
952
de
l
i
ve
r
e
qu
a
l
po
w
e
r
t
o
p
or
t
3.
F
or
c
ha
ng
e
s
i
n
l
oa
d
c
on
ne
c
t
e
d
t
o
po
r
t
3,
V
3
i
s
r
e
gu
l
a
t
e
d
t
o
10
0V
by
a
dj
us
t
i
ng
t
h
e
du
t
y
r
a
t
i
os
D
1
a
nd
D
2
.
T
he
co
nverter
i
s
s
i
m
ul
a
t
e
d
in
P
S
I
Mt
o
ve
r
i
f
y
l
oa
d
v
ol
t
a
ge
r
e
gu
l
a
t
i
on
(
p
or
t
3)
a
n
d
Z
V
S
i
n
a
l
l
t
he
c
on
ve
r
t
e
r
s
w
i
t
c
he
s
f
or
di
f
f
e
r
e
nt
va
l
ue
s
of
l
oa
d
(
R
,
c
o
nn
e
c
t
e
d
a
t
po
r
t
3)
a
nd
v
ol
t
a
ge
s
a
t
po
r
t
1(
V
1
)
a
nd
p
or
t
2(V
2
)
.
T
he
va
l
ue
of
l
oa
d
v
ol
t
a
ge
,
c
a
l
c
ul
at
e
dt
he
or
i
t
i
c
al
y
(
T
h
)
a
nd
ob
t
a
i
ne
d
t
hr
ou
gh
s
i
m
ul
a
t
i
on
(
S
i
m
)
i
s
t
a
bu
l
a
t
e
d
i
n
T
a
bl
e
5
a
nd
a
ve
r
a
ge
c
ur
r
e
nt
de
l
i
ve
r
e
d
b
y
p
or
t
1
i
s
t
a
bu
l
a
t
e
d
in
T
a
bl
e
6,
f
or
v
a
r
yi
ng
va
l
ue
s
o
f
l
oa
d
a
nd
s
o
ur
c
e
vo
l
t
a
ge
s
i
n
po
r
t
1
a
nd
p
or
t
2.
T
he
a
ve
r
a
ge
c
ur
r
e
nt
de
l
i
ve
r
e
d
b
y
p
or
t
2
i
s
s
a
m
e
a
s
po
r
t
1
.
F
r
om
T
a
bl
e
5,
i
t
i
s
e
vi
de
nt
t
ha
t
t
he
l
oa
d
v
ol
t
a
ge
(
V
3
)
i
s
r
e
g
ul
a
t
e
d
a
t
10
0
V
,
i
r
r
e
s
pe
c
t
i
ve
o
f
va
r
i
a
t
i
on
s
i
n
s
ou
r
c
e
vo
l
t
a
ge
V
1
, V
2
a
nd
l
oa
d
R
.
T
h
e
r
a
t
i
o
of
P
2
t
o
P
1
i
s
m
a
i
nt
ai
n
e
d
a
t
V
2
/V
1
,
to
m
a
xi
m
i
s
e
t
he
s
w
i
tc
h
ut
i
l
i
s
a
ti
on
.
F
i
gu
r
e
9
a
nd
F
i
gu
r
e
1
0
s
h
ow
t
he
w
a
ve
f
o
r
m
s
of
s
w
i
t
c
h
c
ur
r
e
nt
s
t
hr
o
ug
h
a
l
l
t
he
c
on
ve
r
t
e
r
s
w
i
t
c
he
s
,
f
o
r
f
ul
l
l
oa
d.
I
t
c
a
n
be
ob
s
e
r
ve
d
fr
om
t
he
w
a
ve
f
o
r
m
s
t
ha
t
e
ve
r
y
s
w
i
t
c
h i
s
t
ur
ne
d
on
w
i
t
h Z
V
S
.
H
e
nc
e
,
t
he
s
w
i
t
c
hi
ng
l
os
s
e
s
a
r
e
r
e
du
c
e
d
i
n
t
he
c
on
ve
r
t
e
r
du
e
t
o
s
of
t
s
w
i
t
c
hi
ng
.
A
s
t
he
l
oa
d
r
e
du
c
e
s
,
t
he
du
t
y
r
a
t
i
o
D
1
a
nd
D
2
a
r
e
r
e
du
c
e
d
t
o
r
e
g
ul
a
t
e
t
he
l
oa
d
vo
l
t
a
ge
V
3
,
ke
e
pi
ng
D
3
,
f
1
3
a
nd
f
2
3
c
o
ns
t
a
nt
.
H
e
nc
e
t
he
c
o
nv
e
r
t
e
r
op
e
r
a
t
e
s
w
i
t
h
m
od
e
3
or
m
o
de
4.
I
n
m
o
d
e
3
o
r
m
od
e
4
t
h
e
s
w
i
t
c
h
op
e
r
a
t
e
s
w
i
t
h
Z
V
S
i
r
r
e
s
pe
c
t
i
ve
of
po
r
t
vo
l
t
a
ge
s
o
r
l
oa
d
va
l
ue
.
T
o
de
m
on
s
t
r
a
t
e
Z
V
S
a
t
a
l
ow
e
r
va
l
ue
of
l
oa
d,
t
he
s
w
i
t
c
h
c
ur
r
e
nt
w
a
ve
f
or
m
s
f
or
10
%
of
f
ul
l
l
oa
d
a
r
e
s
ho
w
n
i
n
F
i
gu
r
e
11
a
nd
F
i
gu
r
e
12
.
I
t
i
s
e
vi
d
e
nt
f
r
o
m
t
he
s
w
i
t
c
h
c
ur
r
e
nt
w
a
ve
f
or
m
s
i
n
F
i
gu
r
e
11
a
nd
F
i
gu
r
e
12
t
ha
t
a
l
l
t
he
c
on
ve
r
t
e
r
s
w
i
t
c
he
s
t
ur
n
on
w
i
t
h
Z
V
S
.
The
resu
lt
s
m
entione
d
ea
rlie
r
in
t
his
sect
io
n
c
orrespo
nd
to
the
dual
in
put
sin
gle
outp
ut
case.
T
he
wav
e
f
or
m
s
of
load
volt
age,
s
ource
c
urre
nts
and
tra
ns
f
orme
r
wi
nd
i
ng
volt
ages
at
50%
of
fu
ll
lo
ad
a
re
s
how
n
in
Fig
ur
e
13
(a
).
T
he
fig
ure
shows
t
hat
the
lo
ad
volt
age
is
r
egu
la
te
d
at
100V
a
nd
the
s
ource
c
urren
ts
I
1
and
I
2
are
e
qu
al
,
wh
i
ch
i
nd
ic
at
es
t
ha
t
the
r
at
io
of
P
2
t
o
P
1
i
s
m
a
i
nt
a
i
n
e
d
a
t
V
2
/V
1
.A
s
the
c
onve
r
te
r
ha
s
bid
irect
i
on
al
capab
il
it
y,
it
c
an
operate
i
n
s
ing
le
i
nput
dua
l
outp
ut
m
ode,
with
port
1
be
ing
the
in
pu
t
port
a
nd
port
2,
port
3
bein
g
the
loa
d
ports.T
he
sim
ul
at
ion
is
perfor
med
to
ver
if
y
wh
et
her
V
2
is
r
egu
la
te
d
at
24
V
a
nd
V
3
is
re
gu
la
te
d
at
1
00V
, when
port 3
a
nd
port
2
are
loa
de
d
to 50
0W
a
nd
100W re
sp
ect
iv
el
y.
Th
e
volt
ag
es at po
rt
2
an
d port 3
are
regulat
ed
by
a
dju
sti
ng
D
1
at
0.7
764,
D
2
a
t
0.3
873
,
f
13
at
0.5
*
p
a
nd
f
23
at
-
0.5
*
p
.
T
he
wa
vefo
rms
of
load
vo
lt
age
,
source
cu
rr
e
nts
an
d
t
ran
s
f
or
me
r
wi
nd
i
ng
vo
lt
age
s
in
the
sin
gle
i
nput
dual
ou
t
put
m
ode
a
re
show
n
in
Figure
13
(
b)
.
The fig
ur
e s
ho
ws
that t
he
v
al
ue
of
V
2
an
d V
3
are 24
V
an
d 100
V
res
pecti
ve
ly,
hen
ce t
he vo
lt
age
regulat
ion i
s
ve
rified.
The
resu
lt
s
de
monstrate
the
capab
il
it
y
of
duty
rati
o
c
on
t
r
ol
to
regulat
e
the
loa
d
volt
ag
e
eff
ect
ivel
y
for
wide
range
of
va
riat
ion
i
n
load
a
nd
s
our
ce
volt
ages.
It
is
al
so
s
how
n
that
the
c
onve
rter
s
witc
hes
operate
with
ZV
S
irre
sp
ect
ive
of
the
load
an
d
s
our
ce
vo
lt
age
val
ue.
T
he
bi
dire
ct
ion
al
opera
ti
on
is
ver
ifie
d
from
a
case o
f
si
ng
le
i
nput
du
al
outp
ut ope
rati
on.
Table
5.
Simul
at
ion
resu
lt
s: a
ver
a
ge value
of V3
Sl
No
V
1
(V)
V
2
(V)
R
(Ω)
D
1
D
2
V
3
(V)
Th
Sim
1.
48
24
10
1
1
100
1
0
0
.45
2.
48
24
20
0
.5
0
.5
100
1
0
0
.31
3.
48
24
100
0
.22
0
.22
100
1
0
0
.19
4.
72
24
10
0
.65
0
.65
100
1
0
0
.36
5.
48
48
10
0
.65
0
.65
100
1
0
0
.28
6.
72
48
10
0
.55
0
.55
100
1
0
0
.37
Table
6.
Simul
at
ion
resu
lt
s: a
ver
a
ge value
of I1
Sl
No
V
1
(V)
V
2
(V)
R
(Ω)
D
1
D
2
I
1
(A)
Th
Sim
1.
48
24
10
1
1
1
3
.89
1
3
.91
2.
48
24
20
0
.5
0
.5
6
.94
6
.94
3.
48
24
100
0
.22
0
.22
1
.39
1
.37
4.
72
24
10
0
.65
0
.65
1
0
.42
1
0
.54
5.
48
48
10
0
.65
0
.65
1
0
.42
1
0
.61
6.
72
48
10
0
.55
0
.55
8
.33
8
.40
Evaluation Warning : The document was created with Spire.PDF for Python.