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[
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o
r
t
to
th
e
s
y
s
tem
.
T
h
e
c
o
n
v
er
ter
s
wo
u
ld
b
e
co
n
tr
o
lled
b
y
s
h
if
ted
-
p
h
ase,
in
ter
leav
ed
s
witch
in
g
s
ig
n
als
wi
th
th
e
s
am
e
s
witch
in
g
f
r
eq
u
en
cy
.
A
s
im
p
le
b
o
o
s
t
co
n
v
er
ter
r
aises
a
DC
v
o
ltag
e
b
y
co
n
v
er
tin
g
it.
R
ed
u
ce
d
r
ip
p
le
cu
r
r
en
ts
in
b
o
th
th
e
i
n
p
u
t
an
d
o
u
tp
u
t
cir
cu
its
r
ep
r
esen
t
a
n
a
d
d
itio
n
al
b
en
ef
it
o
f
in
ter
leav
in
g
.
Sato
et
a
l.
[
1
3
]
s
ay
d
iv
i
d
in
g
th
e
o
u
tp
u
t
cu
r
r
e
n
t
in
to
two
p
ath
way
s
r
esu
lts
in
h
ig
h
e
r
ef
f
icie
n
cy
an
d
m
u
ch
lo
wer
I
2
R
a
n
d
in
d
u
cto
r
alter
n
atin
g
c
u
r
r
en
t
(
AC
)
lo
s
s
es.
T
h
e
in
ter
leav
ed
b
o
o
s
t
co
n
v
er
ter
s
tan
d
s
o
u
t
as
a
n
ex
ce
lle
n
t
o
p
tio
n
f
o
r
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
d
u
e
t
o
its
ab
ilit
y
t
o
p
r
o
v
id
e
r
ed
u
ce
d
i
n
p
u
t
an
d
o
u
tp
u
t
r
ip
p
le,
h
eig
h
ten
e
d
ef
f
i
cien
cy
,
an
d
in
c
r
ea
s
ed
p
o
wer
d
en
s
ity
.
W
ith
an
in
ter
leav
ed
c
o
n
v
e
r
ter
,
y
o
u
m
a
y
g
et
h
ig
h
er
ef
f
icien
c
y
,
l
o
wer
r
ip
p
le
v
o
ltag
e,
l
o
wer
r
ip
p
le
in
d
u
cto
r
cu
r
r
e
n
t
,
a
n
d
f
aster
s
witch
in
g
s
p
ee
d
m
en
tio
n
ed
in
th
ese
ar
ticles [
1
4
]
-
[
2
2
]
.
I
n
th
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
with
p
h
ase
an
g
le
s
h
if
t
(
PP
AS)
co
n
tr
o
l a
p
p
r
o
ac
h
,
th
e
s
witch
d
u
ty
cy
cle
an
d
p
h
ase
an
g
le
o
f
in
ter
lea
v
ed
co
n
v
er
ter
s
s
er
v
e
as
two
in
d
ep
en
d
en
t
co
n
tr
o
l
p
ar
am
ete
r
s
s
h
o
wn
in
[
2
3
]
.
L
ian
g
et
a
l.
an
d
Yad
a
v
et
a
l.
[
2
4
]
,
[
2
5
]
s
ay
th
at
en
a
b
les
th
e
attain
m
en
t
o
f
d
ec
o
u
p
led
v
o
lta
g
e
r
eg
u
latio
n
ac
r
o
s
s
m
u
ltip
le
p
o
r
ts
with
in
a
s
p
e
cif
ied
o
p
er
atio
n
al
r
an
g
e.
Ad
d
itio
n
ally
,
th
e
p
h
ase
an
g
le
ad
ju
s
tm
en
t
o
f
th
e
in
ter
leav
ed
b
u
ck
-
b
o
o
s
t
c
o
n
v
e
r
ter
en
h
a
n
ce
s
co
n
t
r
o
l
f
le
x
ib
ilit
y
,
f
ac
ilit
atin
g
p
r
ec
is
e
m
an
ag
em
en
t
o
f
s
ec
o
n
d
a
r
y
o
u
tp
u
t v
o
ltag
e
.
B
y
in
teg
r
atin
g
E
SS
,
o
n
e
m
a
y
ac
h
iev
e
a
b
r
o
ad
o
u
tp
u
t v
o
ltag
e
g
ain
,
h
i
g
h
ef
f
i
cien
cy
,
ch
ea
p
co
s
t,
s
m
all
s
ize,
an
d
h
ig
h
s
tab
ilit
y
a
b
o
u
t th
ese
tech
n
i
q
u
es we
r
e
an
aly
ze
d
in
[
2
6
]
,
[
2
7
]
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
a
f
o
u
r
-
p
o
r
t
co
n
v
er
ter
co
m
p
r
is
in
g
two
p
h
o
to
v
o
ltaic
(
PV)
in
p
u
ts
,
a
b
a
tter
y
p
o
r
t
,
an
d
a
lo
ad
p
o
r
t
f
o
r
a
n
aly
s
is
an
d
g
et
ef
f
icien
c
y
b
etter
th
an
co
m
p
ar
ed
to
t
h
e
liter
atu
r
es.
T
h
e
co
n
v
e
r
ter
s
ar
e
m
eticu
lo
u
s
ly
m
o
d
eled
a
n
d
s
im
u
lated
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
c
o
n
v
e
r
ter
'
s
p
er
f
o
r
m
an
ce
is
ev
alu
ate
d
ac
r
o
s
s
d
if
f
er
en
t
d
u
t
y
cy
cles,
an
d
th
e
f
in
d
i
n
g
s
ar
e
co
m
p
r
eh
en
s
iv
ely
s
h
o
wca
s
ed
.
Fu
r
th
er
m
o
r
e,
a
h
a
r
d
war
e
p
r
o
to
ty
p
e
o
f
th
e
f
o
u
r
-
p
o
r
t c
o
n
v
er
ter
is
d
ev
elo
p
ed
to
v
alid
ate
th
e
s
im
u
latio
n
o
u
tc
o
m
es.
2.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
p
lu
s
p
h
ase
an
g
le
s
ch
em
e
f
o
r
a
f
o
u
r
-
p
o
r
t
DC
-
DC
co
n
v
er
ter
en
h
an
ce
s
th
e
c
o
n
tr
o
l
a
n
d
e
f
f
ic
ien
cy
o
f
p
o
wer
d
is
tr
ib
u
tio
n
a
m
o
n
g
m
u
ltip
le
p
o
r
ts
.
I
n
t
h
is
s
ch
em
e,
ea
ch
p
o
r
t
ca
n
b
e
in
d
e
p
en
d
e
n
tly
c
o
n
tr
o
lle
d
to
o
p
tim
ize
p
o
wer
tr
an
s
f
er
an
d
m
in
im
ize
lo
s
s
es.
PW
M
co
n
tr
o
ls
th
e
d
u
t
y
c
y
cle
o
f
th
e
s
witch
in
g
d
ev
ices,
r
e
g
u
lat
in
g
th
e
av
er
a
g
e
v
o
ltag
e,
an
d
cu
r
r
en
t
d
eliv
er
e
d
to
ea
ch
p
o
r
t.
B
y
ad
j
u
s
tin
g
th
e
p
u
ls
e
wid
th
,
t
h
e
co
n
v
er
ter
ca
n
p
r
ec
is
ely
m
a
n
ag
e
th
e
p
o
wer
f
lo
w
to
m
atc
h
th
e
lo
ad
r
eq
u
ir
e
m
en
ts
.
Ph
a
s
e
an
g
le
co
n
tr
o
l
a
d
d
s
an
o
th
er
la
y
er
o
f
p
r
ec
is
io
n
b
y
ad
ju
s
tin
g
th
e
tim
in
g
o
f
th
e
s
witch
in
g
d
ev
ices
with
in
th
e
co
n
v
er
ter
.
B
y
s
ettin
g
th
e
p
h
ase
an
g
les
f
o
r
ea
ch
p
o
r
t,
th
e
s
ch
em
e
en
s
u
r
e
s
th
at
p
o
wer
tr
an
s
f
er
is
n
o
t
o
n
l
y
ef
f
icien
t
b
u
t
also
s
y
n
ch
r
o
n
ize
d
,
r
ed
u
ci
n
g
in
ter
f
er
en
ce
,
an
d
h
ar
m
o
n
ics.
T
h
is
co
m
b
in
ed
ap
p
r
o
ac
h
allo
ws
f
o
r
th
e
p
h
ase
-
s
h
if
ted
o
p
er
atio
n
o
f
m
u
ltip
le
p
o
r
ts
,
wh
ich
ca
n
h
elp
r
ed
u
ce
th
e
o
v
er
all
r
ip
p
le
an
d
im
p
r
o
v
e
th
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
co
n
v
e
r
ter
.
I
m
p
lem
en
tin
g
th
is
s
ch
em
e
in
a
f
o
u
r
-
p
o
r
t
DC
-
DC
co
n
v
er
te
r
in
v
o
lv
es
a
d
etail
ed
co
n
tr
o
l
s
tr
ateg
y
.
First,
th
e
p
h
ase
an
g
les
f
o
r
ea
c
h
p
o
r
t
a
r
e
ca
lcu
lated
b
ased
o
n
th
e
lo
ad
d
em
an
d
s
an
d
th
e
d
esire
d
p
o
wer
s
h
a
r
in
g
am
o
n
g
th
e
p
o
r
ts
.
T
h
ese
p
h
ase
an
g
les
d
eter
m
in
e
th
e
tim
i
n
g
o
f
th
e
s
witch
ac
tiv
atio
n
.
Nex
t
,
PW
M
is
ap
p
lie
d
wit
h
in
th
ese
p
h
ase
-
co
n
tr
o
lle
d
p
er
io
d
s
to
r
eg
u
late
th
e
p
o
wer
d
eliv
er
ed
to
ea
c
h
p
o
r
t.
T
h
is
s
y
n
ch
r
o
n
ize
d
ap
p
r
o
ac
h
e
n
s
u
r
es
th
at
th
e
c
o
n
v
er
ter
o
p
er
ates
e
f
f
icien
tly
,
p
r
o
v
id
in
g
s
tab
le
an
d
p
r
ec
is
e
p
o
w
er
to
all
co
n
n
ec
ted
lo
ad
s
.
T
h
e
PW
M
p
lu
s
p
h
ase
a
n
g
le
s
ch
em
e
is
p
ar
ti
cu
lar
l
y
b
e
n
ef
icial
in
a
p
p
licatio
n
s
w
h
er
e
m
u
ltip
le
lo
ad
s
with
d
if
f
er
en
t
p
o
wer
r
eq
u
i
r
em
en
ts
n
ee
d
t
o
b
e
m
an
ag
e
d
s
im
u
lt
an
eo
u
s
ly
,
s
u
ch
as
in
r
e
n
ewa
b
le
en
er
g
y
s
y
s
tem
s
,
elec
tr
ic
v
eh
icles,
an
d
d
is
tr
ib
u
ted
p
o
we
r
s
y
s
tem
s
.
I
t
o
f
f
e
r
s
im
p
r
o
v
e
d
co
n
tr
o
l,
r
ed
u
ce
d
elec
tr
o
m
ag
n
etic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
timiz
in
g
s
ta
n
d
a
lo
n
e
d
u
a
l P
V
s
ystems
w
ith
fo
u
r
-
p
o
r
t c
o
n
v
erter
tech
n
o
lo
g
y
(
S
h
a
r
ma
S
h
a
)
83
in
ter
f
er
en
ce
,
a
n
d
en
h
a
n
ce
d
o
v
er
all
ef
f
icien
cy
o
f
t
h
e
DC
-
DC
co
n
v
er
s
io
n
p
r
o
ce
s
s
.
Fig
u
r
e
3
d
ep
icts
th
e
f
u
ll
b
r
id
g
e
–
f
o
u
r
p
o
r
t
co
n
v
er
ter
(
F
B
-
FP
C
)
.
I
t
h
as
two
s
o
u
r
ce
p
o
r
ts
th
at
ar
e
lin
k
ed
to
th
e
PV
ar
r
ay
,
as
well
as
a
s
to
r
ag
e
p
o
r
t
a
n
d
a
lo
a
d
p
o
r
t.
T
h
e
co
n
v
er
ter
h
as
two
PV
ar
r
ay
s
ar
e
co
n
n
ec
ted
to
th
e
i
n
p
u
t
p
o
r
t
u
s
in
g
a
tr
an
s
f
o
r
m
er
with
a
tu
r
n
s
r
atio
o
f
1
:
n
.
T
h
e
p
r
im
ar
y
s
id
e
o
f
th
e
tr
an
s
f
o
r
m
er
em
p
lo
y
s
a
tr
a
d
itio
n
al
f
u
ll
b
r
i
d
g
e
co
n
v
er
ter
,
co
n
n
ec
tin
g
two
s
o
u
r
ce
s
to
th
e
m
id
p
o
in
t
o
f
ea
c
h
l
eg
,
th
u
s
estab
lis
h
in
g
two
-
s
o
u
r
ce
p
o
r
ts
.
M
o
r
eo
v
er
,
a
s
to
r
ag
e
p
o
r
t
is
also
in
teg
r
at
ed
o
n
th
e
p
r
im
ar
y
s
id
e.
On
t
h
e
s
ec
o
n
d
ar
y
s
id
e,
a
co
n
v
e
n
t
io
n
al
d
io
d
e
b
r
id
g
e
r
ec
tifie
r
is
em
p
lo
y
ed
,
co
n
n
ec
t
ed
to
th
e
lo
a
d
p
o
r
t.
W
h
en
it
is
o
b
s
er
v
ed
f
r
o
m
th
e
s
o
u
r
ce
p
o
r
t,
th
e
s
o
u
r
ce
p
o
r
t
to
th
e
b
atte
r
y
p
o
r
t
f
o
r
m
s
a
b
o
o
s
t
co
n
v
er
ter
cir
cu
it.
Hen
ce
as
a
wh
o
le
p
r
im
ar
y
s
id
e
is
co
m
p
o
s
ed
o
f
two
PV
p
o
r
ts
,
a
b
atter
y
p
o
r
t
,
an
d
f
o
u
r
s
witch
es
to
f
o
r
m
a
b
i
-
p
h
ase
b
o
o
s
t c
o
n
v
er
ter
o
r
an
i
n
ter
leav
ed
b
o
o
s
t
co
n
v
er
te
r
.
As
m
en
tio
n
ed
ea
r
lier
,
th
e
in
p
u
t
s
id
e
o
f
th
e
co
n
v
er
te
r
u
n
d
er
co
n
s
id
er
atio
n
f
ea
tu
r
es
a
f
u
ll
-
b
r
id
g
e
co
n
f
ig
u
r
atio
n
,
co
m
p
r
is
in
g
c
o
m
p
lem
en
tar
y
s
witch
es
o
n
ea
c
h
leg
.
B
ased
o
n
th
e
d
u
t
y
r
atio
ass
ig
n
ed
to
ea
c
h
leg
,
a
r
ec
tan
g
u
lar
v
o
ltag
e
wav
e
f
o
r
m
is
g
en
er
ated
f
r
o
m
th
e
m
i
d
p
o
in
t
o
f
ea
ch
leg
(
U
a
,
Ub
)
.
T
h
e
b
atter
y
p
o
r
t
is
p
ar
allel
-
co
n
n
ec
te
d
to
th
e
ca
p
a
cito
r
o
n
t
h
e
p
r
im
ar
y
s
id
e
t
o
f
a
cilitate
b
o
th
ch
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
o
p
e
r
atio
n
s
.
T
h
e
p
o
wer
f
r
o
m
th
e
s
o
u
r
ce
lik
e
d
u
al
PV
p
an
els
(
So
u
r
ce
p
o
r
t
1
,
So
u
r
ce
p
o
r
t
2
)
is
co
n
n
ec
te
d
p
ar
allelly
to
ea
ch
ca
p
ac
ito
r
co
n
n
ec
ted
with
in
d
u
cto
r
s
(L
l
,
L
2
)
.
Switch
es
S
1
,
S
2
,
S
3
,
an
d
S
4
co
n
s
titu
te
th
e
co
m
p
lete
b
r
i
d
g
e
co
n
v
er
ter
cir
cu
it.
T
o
r
eg
u
late
th
e
p
o
wer
b
alan
ce
b
etwe
en
th
e
p
h
o
t
o
v
o
ltaic
(
PV)
s
o
u
r
ce
s
a
n
d
th
e
b
atter
ies,
th
e
d
u
ty
r
atio
o
f
s
witch
es
S
1
an
d
S
3
s
er
v
es
as
two
co
n
tr
o
l
v
ar
iab
les
(
i.e
D
PV1
,
D
PV2
)
.
T
h
e
v
o
ltag
e
d
if
f
e
r
en
ce
b
etwe
en
U
a
an
d
U
b
,
d
en
o
ted
as
U
ab
,
is
ap
p
lied
to
th
e
p
r
im
ar
y
win
d
in
g
o
f
th
e
h
ig
h
-
f
r
eq
u
en
cy
tr
an
s
f
o
r
m
er
.
Fu
r
th
er
m
o
r
e
,
th
e
two
v
o
ltag
es
U
a
an
d
U
b
ar
e
p
h
ase
-
s
h
if
ted
(
ϕ
)
,
wh
ich
is
u
s
ed
as
th
e
th
ir
d
v
ar
iab
le
to
co
n
t
r
o
l
th
e
o
u
tp
u
t v
o
ltag
e.
Fig
u
r
e
3
.
Fu
ll b
r
id
g
e
f
o
u
r
p
o
r
t c
o
n
v
er
te
r
On
e
s
witch
in
g
cy
cle
o
f
p
er
i
o
d
T
S
co
m
p
r
is
es
s
ix
s
tate
s
,
as
d
ep
icted
in
Fig
u
r
e
4
.
T
o
p
r
o
d
u
ce
a
r
ec
tan
g
u
lar
v
o
ltag
e
f
r
o
m
th
e
m
id
p
o
in
t
o
f
ea
ch
leg
,
two
s
witch
es
o
n
ea
ch
leg
o
p
er
ate
in
a
co
m
p
lem
en
tar
y
m
an
n
er
.
T
h
e
d
u
ty
c
y
cles
o
f
S
2
(S
1
)
a
n
d
S
4
(S
3
)
f
u
n
ctio
n
as
a
p
air
o
f
c
o
n
tr
o
l
v
ar
ia
b
les,
g
o
v
e
r
n
in
g
th
e
elec
tr
ical
p
o
wer
ex
ch
an
g
e
am
o
n
g
PV
1
an
d
th
e
en
er
g
y
s
to
r
ag
e
u
n
it,
an
d
PV
2
an
d
th
e
b
atter
y
,
co
r
r
esp
o
n
d
in
g
ly
.
Mo
r
eo
v
er
,
th
e
two
r
ec
tan
g
u
la
r
-
wav
ef
o
r
m
v
o
ltag
es,
U
a
an
d
U
b
,
o
b
tain
ed
f
r
o
m
th
e
m
id
p
o
i
n
ts
o
f
th
e
two
leg
s
,
ar
e
p
h
ase
-
s
h
if
ted
b
y
an
an
g
le
ϕ
to
co
n
tr
o
l a
n
d
r
eg
u
late
t
h
e
o
u
tp
u
t v
o
ltag
e
U
o
.
T
h
e
tr
an
s
f
o
r
m
er
'
s
tu
r
n
s
r
atio
is
d
en
o
ted
with
a
r
atio
o
f
N
P
:
N
S
=
1
:
n
,
with
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
b
lo
ck
C
b
r
ep
r
esen
ted
as
U
Cb
.
W
ith
in
o
n
e
s
witch
in
g
o
p
er
atio
n
s
cy
cle,
th
er
e
ar
e
s
ix
s
witch
in
g
s
tates.
E
ac
h
s
tate
h
as
co
r
r
esp
o
n
d
in
g
eq
u
iv
alen
t
cir
c
u
it
an
d
s
witch
in
g
tab
le
wh
ich
is
g
iv
en
in
Fi
g
u
r
e
5
a
n
d
T
a
b
le
1
r
esp
ec
tiv
ely
.
T
h
is
s
tate
p
er
s
is
ts
u
n
til
S
1
is
d
ea
ctiv
ated
a
n
d
S
2
is
ac
tiv
ated
.
Su
b
s
eq
u
e
n
tly
,
a
n
ew
s
witch
in
g
p
er
io
d
c
o
m
m
en
ce
s
.
T
ab
le
1
.
Switch
in
g
ta
b
le
S
t
a
t
e
S
w
i
t
c
h
e
s
O
N
L1
L2
D
i
o
d
e
O
N
P
r
i
mary
v
o
l
t
a
g
e
I
S
2
, S
3
C
h
a
r
g
e
s
D
i
sch
a
r
g
e
s
A
l
l
-
(U
b
+U
cb
)
II
S
2
, S
3
C
h
a
r
g
e
s
D
i
sch
a
r
g
e
s
D
01
, D
04
-
(U
b
+U
cb
)
III
S
2
, S
4
C
h
a
r
g
e
s
C
h
a
r
g
e
s
D
01
, D
04
-
U
cb
IV
S
1
, S
4
D
i
sch
a
r
g
e
s
C
h
a
r
g
e
s
A
l
l
U
b
-
U
cb
V
S
1
, S
4
D
i
sch
a
r
g
e
s
C
h
a
r
g
e
s
D
02
, D
03
U
b
-
U
cb
VI
S
1
, S
3
D
i
sch
a
r
g
e
s
D
i
sch
a
r
g
e
s
D
02
, D
03
-
U
cb
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
81
-
89
84
Fig
u
r
e
4
.
Switch
in
g
m
o
d
es o
f
o
p
er
atio
n
o
f
FP
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
timiz
in
g
s
ta
n
d
a
lo
n
e
d
u
a
l P
V
s
ystems
w
ith
fo
u
r
-
p
o
r
t c
o
n
v
erter
tech
n
o
lo
g
y
(
S
h
a
r
ma
S
h
a
)
85
(a
)
(b
)
(c
)
(d
)
(e
)
(f)
Fig
u
r
e
5
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
FP
C
in
d
if
f
er
en
t switch
in
g
m
o
d
es
:
(
a)
t
0
-
t
1
,
(
b
)
t
1
-
t
2
,
(
c
)
t
2
-
t
3
,
(
d
)
t
3
-
t
4
,
(
e)
t
4
-
t
5
,
an
d
(
f
)
t
5
-
t
6
T
h
e
f
in
al
o
u
tp
u
t e
q
u
atio
n
d
er
i
v
ed
f
r
o
m
th
e
s
witch
in
g
m
o
d
es
o
f
th
e
s
y
s
tem
wr
itten
as (
1
)
.
=
{
[
2
(
1
−
∆
21
)
+
2
∆
21
−
2
∆
21
2
]
,
∆
21
>
0
[
2
(
1
+
∆
21
)
]
,
∆
21
<
0
[
2
]
,
∆
21
=
0
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
81
-
89
86
W
h
er
e
ΔD
PV
21
=
D
PV
2
-
D
PV
1
.
Acc
o
r
d
in
g
to
(
1
)
,
th
e
d
u
ty
c
y
cles
DPV1
an
d
DPV2
ca
n
b
e
u
tili
ze
d
to
eq
u
alize
t
h
e
p
o
wer
s
f
r
o
m
th
e
p
h
o
to
v
o
ltaic
(
PV)
s
o
u
r
ce
s
an
d
th
e
b
atter
ies,
wh
ile
th
e
p
h
ase
an
g
le
ϕ
is
ad
ju
s
tab
le
to
r
eg
u
late
th
e
o
u
tp
u
t
v
o
ltag
e
o
n
th
e
s
ec
o
n
d
ar
y
s
id
e.
T
h
ese
th
r
ee
co
n
tr
o
l
p
ar
am
eter
s
en
s
u
r
e
th
e
f
u
ll
co
n
tr
o
llab
ilit
y
o
f
th
e
f
o
u
r
-
v
ar
iab
le
s
y
s
tem
.
Ad
d
itio
n
ally
,
as
illu
s
tr
ated
i
n
Fig
u
r
e
6
,
en
s
u
r
in
g
co
n
tr
o
llab
ilit
y
o
f
th
e
p
h
ase
an
g
le
ϕ
in
v
o
lv
es
a
c
o
n
s
tr
ain
t.
I
t
ca
n
b
e
wr
itten
as
(
2
)
.
Fro
m
Fig
u
r
e
6
,
it'
s
ev
id
en
t
th
at
if
t
h
e
co
n
s
tr
ain
t
co
n
d
itio
n
is
n
'
t
m
et,
th
e
o
u
tp
u
t
v
o
ltag
e
Uo
ca
n
n
o
t
b
e
r
e
g
u
lated
s
o
lely
b
y
th
e
p
h
ase
an
g
le
ϕ
.
T
h
is
s
itu
atio
n
lead
s
to
th
e
lo
s
s
o
f
th
e
co
n
tr
o
l
v
ar
iab
le
ass
o
ciate
d
with
th
e
v
o
ltag
e
o
u
tp
u
t.
2
≤
1
2
≤
1
−
2
(
2
)
Fig
u
r
e
6
.
Prim
ar
y
v
o
ltag
e
an
d
cu
r
r
en
t w
av
e
f
o
r
m
f
o
r
2
≤
,
2
≤
(
1
−
)
3.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
s
im
u
latio
n
m
o
d
el
f
o
r
th
e
f
o
u
r
-
p
o
r
t
c
o
n
v
er
te
r
is
co
n
s
tr
u
cted
u
s
in
g
MA
T
L
A
B
/Si
m
u
lin
k
.
Switch
in
g
p
u
ls
es
ar
e
g
e
n
er
ate
d
u
s
in
g
a
p
lu
s
p
h
ase
a
n
g
le
s
h
i
f
t
(
PP
AS)
PW
M
s
ch
em
e
as
d
is
cu
s
s
ed
in
s
ec
tio
n
2
with
a
s
witch
in
g
f
r
e
q
u
en
c
y
o
f
1
0
0
k
Hz.
T
ab
le
2
g
iv
es
th
e
cir
cu
i
t
p
ar
am
eter
s
u
s
ed
f
o
r
s
im
u
latio
n
.
T
wo
m
o
d
u
les
o
f
Ky
o
ce
r
a
KD1
3
5
G
X
-
L
P
ar
e
co
n
n
ec
ted
i
n
s
er
ies
to
g
en
e
r
ate
2
7
0
W
.
A
c
o
m
p
r
e
h
en
s
iv
e
an
aly
s
is
o
f
th
e
co
n
v
er
ter
’
s
p
er
f
o
r
m
an
ce
is
co
n
d
u
cted
,
ex
a
m
in
in
g
v
ar
i
o
u
s
s
o
lar
ir
r
ad
ian
ce
s
an
d
lo
a
d
in
g
c
o
n
d
itio
n
s
in
d
etail.
T
h
e
e
f
f
ec
t
o
f
d
u
ty
r
atio
is
s
tu
d
ied
an
d
th
e
r
esu
lts
ar
e
d
is
cu
s
s
ed
.
3
.
1
.
Sim
ula
t
i
o
n r
esu
lt
s
f
o
r
v
a
rio
us
s
o
la
r
irra
dia
nces
Fig
u
r
e
7
s
h
o
ws
th
e
s
im
u
latio
n
r
esu
lts
at
a
r
ated
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
2
an
d
d
u
ty
r
ati
o
DPV1
=
DPV2
=
0
.
5
with
0
.
2
5
p
h
ase
s
h
if
t.
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RE
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NC
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S
[
1
]
M
.
R
o
u
h
a
n
i
a
n
d
G
.
J.
K
i
s
h
,
“
M
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9
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4
.
[
2
]
J.
H
o
n
g
,
J.
Y
i
n
,
Y
.
Li
u
,
J.
P
e
n
g
,
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n
d
H
.
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a
n
g
,
“
En
e
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v
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l
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/
A
C
C
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.
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3
4
5
8
.
[
3
]
G
.
Zh
a
n
g
e
t
a
l
.
,
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f
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EEE
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6
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C
C
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.
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.
[
4
]
W
.
K
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.
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g
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d
e
g
re
e
in
re
n
e
wa
b
l
e
e
n
e
rg
y
fro
m
G
a
n
d
h
ig
ra
m
Ru
ra
l
In
stit
u
te
in
t
h
e
y
e
a
r
2
0
1
9
.
Cu
rre
n
tl
y
,
h
e
p
u
rs
u
in
g
P
h
.
D.
d
e
g
re
e
fro
m
P
u
d
u
c
h
e
rry
Tec
h
n
o
l
g
ica
l
Un
i
v
e
rsity
(Er
stwh
il
e
P
o
n
d
ich
e
rry
E
n
g
i
n
e
e
rin
g
C
o
ll
e
g
e
).
His
a
re
a
s
o
f
re
se
a
rc
h
e
x
p
a
n
d
p
o
we
r
e
lec
tro
n
ics
,
re
n
e
wa
b
le
e
n
e
rg
y
sy
ste
m
s,
a
n
d
e
lec
tri
c
a
l
m
a
c
h
in
e
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
sh
a
rm
a
sh
a
3
8
@g
m
a
il
.
c
o
m
o
r
sh
a
r
m
a
.
sh
a
@p
tu
n
i
v
.
e
d
u
.
i
n
.
Ra
ja
m
b
a
l
K
a
l
a
y
a
n
a
sun
d
a
r
a
m
re
c
e
iv
e
d
h
e
r
b
a
c
h
e
lo
r
o
f
e
n
g
i
n
e
e
rin
g
d
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g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
a
n
d
m
a
ste
r
o
f
e
n
g
i
n
e
e
rin
g
d
e
g
re
e
in
p
o
we
r
e
lec
tro
n
ics
fro
m
An
n
a
Un
iv
e
rsity
,
Ch
e
n
n
a
i,
In
d
ia,
in
1
9
9
1
a
n
d
1
9
9
3
,
re
sp
e
c
ti
v
e
ly
.
S
h
e
re
c
e
iv
e
d
h
e
r
P
h
.
D.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fro
m
An
n
a
Un
iv
e
rsity
i
n
2
0
0
5
.
C
u
rre
n
tl
y
,
sh
e
is
wo
rk
in
g
a
s
a
p
ro
fe
ss
o
r
in
t
h
e
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t
o
f
EE
E
at
P
u
d
u
c
h
e
rry
Tec
h
n
o
lo
g
ica
l
Un
iv
e
rsity
(Er
stw
h
il
e
P
o
n
d
ich
e
rr
y
E
n
g
in
e
e
rin
g
C
o
ll
e
g
e
).
He
r
a
re
a
s
o
f
re
se
a
rc
h
in
c
l
u
d
e
p
o
we
r
e
lec
tro
n
ics
,
e
lec
tri
c
a
l
d
ri
v
e
s,
re
n
e
wa
b
le
e
n
e
rg
y
sy
ste
m
s,
a
n
d
e
le
c
tri
c
v
e
h
icle
s.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ra
jam
b
a
lk
@p
t
u
n
i
v
.
e
d
u
.
i
n
.
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