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ix
o
f
lin
ea
r
an
d
n
o
n
-
lin
ea
r
co
n
tr
o
l.
Dif
f
er
e
n
t
f
ast
ch
ar
g
er
to
p
o
lo
g
ies
a
r
e
av
ailab
le
d
ep
en
d
in
g
o
n
th
eir
ap
p
licatio
n
s
[
7
]
.
T
h
e
n
ee
d
f
o
r
c
h
ar
g
in
g
s
tatio
n
s
h
as
b
ec
o
m
e
cr
u
cial
[
8
]
.
C
ar
d
r
iv
e
r
s
n
ee
d
ea
s
y
ac
ce
s
s
to
f
ast
ch
ar
g
in
g
s
tatio
n
s
to
r
ed
u
ce
th
e
s
tr
e
s
s
o
f
s
ea
r
ch
in
g
f
o
r
ch
ar
g
in
g
p
o
in
ts
an
d
th
eir
f
ea
r
ab
o
u
t
t
h
eir
b
atter
y
life
.
At
th
e
s
am
e
tim
e,
it
is
n
ec
ess
ar
y
to
d
ev
elo
p
m
u
ch
m
o
r
e
av
ailab
ilit
y
o
f
ch
a
r
g
in
g
p
o
in
ts
with
a
g
o
o
d
co
n
n
ec
ted
d
is
tr
ib
u
tio
n
m
ap
an
d
o
p
tim
al
co
s
t o
f
th
eir
u
s
e
[
9
]
.
C
h
ar
g
in
g
th
e
u
r
b
a
n
v
eh
icle
r
eq
u
ir
es
a
s
i
n
g
le
-
p
h
ase
ch
ar
g
e
r
with
a
p
o
wer
o
f
1
.
8
k
W
at
d
if
f
er
en
t
p
o
in
ts
in
th
e
city
,
with
a
ch
a
r
g
in
g
tim
e
o
f
3
h
o
u
r
s
.
Ho
we
v
er
,
o
u
r
p
r
o
p
o
s
al
o
f
f
er
s
a
h
ig
h
-
p
o
wer
s
ec
o
n
d
ar
y
ch
ar
g
er
th
r
o
u
g
h
a
DC
b
u
s
f
ast
ch
ar
g
in
g
s
tatio
n
with
a
p
o
w
er
o
f
3
.
6
k
W
to
r
ed
u
ce
th
e
c
h
ar
g
in
g
tim
e
an
d
th
e
o
cc
u
p
an
c
y
tim
e
o
f
th
e
city
ca
r
.
T
h
e
ch
ar
g
in
g
s
tr
u
ctu
r
es c
an
b
e
AC
an
d
DC
g
r
id
-
b
ased
[
1
0
]
,
[
1
1
]
.
C
h
ar
g
in
g
ca
n
b
e
o
f
b
o
th
ty
p
es
-
AC
an
d
DC
ch
ar
g
in
g
.
AC
ch
ar
g
in
g
g
en
er
ally
s
p
ec
if
ies
lev
el
1
a
n
d
lev
el
2
c
h
ar
g
in
g
f
o
r
o
n
-
b
o
ar
d
ch
ar
g
er
s
,
wh
ile
DC
ch
ar
g
i
n
g
is
co
n
s
id
er
ed
L
e
v
el
3
c
h
ar
g
i
n
g
t
h
at
r
eq
u
ir
es
o
f
f
-
b
o
a
r
d
c
h
ar
g
e
r
s
[
1
2
]
.
T
h
e
p
r
o
p
o
s
ed
s
ch
em
e
f
o
r
th
e
b
atter
y
r
ec
h
ar
g
in
g
s
y
s
tem
is
b
ased
o
n
th
e
s
etu
p
o
f
a
m
u
ltip
o
r
t
co
n
f
ig
u
r
atio
n
f
o
r
r
ec
h
ar
g
in
g
elec
tr
ic
ca
r
s
to
en
s
u
r
e
m
u
lti
-
u
s
e
f
o
r
o
th
er
ty
p
es
o
f
ca
r
s
.
Fas
t
ch
ar
g
in
g
v
ia
a
DC
b
u
s
ch
ar
g
er
at
4
0
0
VD
C
p
o
wer
ed
b
y
a
PV
s
o
u
r
ce
an
d
a
s
ec
o
n
d
ar
y
o
n
-
b
o
ar
d
ch
ar
g
er
o
n
th
e
u
r
b
an
ca
r
b
ased
o
n
a
f
u
ll
b
r
id
g
e
p
h
ase
s
h
if
t
DC
-
DC
co
n
v
er
ter
(
PS
FB
)
.
T
h
e
n
o
v
elty
o
f
th
is
ap
p
r
o
ac
h
is
to
u
p
g
r
ad
e
th
e
e
x
is
tin
g
c
o
n
f
ig
u
r
atio
n
o
f
ch
ar
g
in
g
m
et
h
o
d
s
.
We
p
r
o
p
o
s
e
ad
d
in
g
a
h
ig
h
-
p
o
wer
s
ec
o
n
d
ar
y
o
n
-
b
o
ar
d
ch
a
r
g
er
n
ex
t
to
th
e
f
ir
s
t
ex
is
tin
g
o
n
e.
T
h
e
n
o
v
elty
o
f
th
is
co
n
f
ig
u
r
atio
n
is
th
at
t
h
e
elec
tr
ic
ca
r
ca
n
b
e
c
h
ar
g
ed
,
in
a
d
d
it
io
n
to
t
h
e
s
in
g
le
-
p
h
ase
ch
ar
g
e
r
,
with
a
DC
s
tatio
n
f
ed
b
y
PV
p
an
els
to
m
ee
t
th
e
n
eu
tr
al
ca
r
b
o
n
ch
a
r
t
,
esp
ec
ially
in
m
o
b
ilit
y
ac
tiv
ity
.
To
d
is
cu
s
s
f
u
r
th
er
th
e
im
p
r
o
v
em
e
n
t
p
r
o
p
o
s
ed
in
th
i
s
wo
r
k
,
th
e
p
ap
er
is
d
iv
id
e
d
in
to
th
r
ee
s
ec
tio
n
s
.
T
h
e
f
ir
s
t
o
n
e
is
ab
o
u
t
th
e
o
v
er
v
iew
o
f
th
e
s
ch
em
a
o
f
th
e
p
r
o
p
o
s
al.
T
h
e
s
ec
o
n
d
is
ab
o
u
t
th
e
th
eo
r
etica
l
d
is
cu
s
s
io
n
o
f
th
e
cir
cu
it.
T
h
e
th
ir
d
o
n
e
is
ab
o
u
t
t
h
e
s
im
u
lat
io
n
in
MA
T
L
AB
/Si
m
u
lin
k
an
d
th
e
r
esu
lts
d
is
cu
s
s
io
n
.
I
n
th
e
en
d
,
we
h
a
v
e
th
e
co
n
clu
s
io
n
an
d
d
is
cu
s
s
io
n
o
f
f
u
r
th
er
p
er
s
p
ec
tiv
es in
th
e
co
m
m
o
n
wo
r
k
s
.
2.
M
E
T
H
O
D
2
.
1
.
O
v
er
v
iew
o
f
t
he
pro
po
s
it
io
n
As
in
itially
d
is
cu
s
s
ed
in
th
e
in
tr
o
d
u
ctio
n
,
th
e
m
ain
co
n
tr
i
b
u
tio
n
is
b
ased
o
n
s
ettin
g
u
p
th
e
u
r
b
a
n
elec
tr
ic
ca
r
with
a
s
ec
o
n
d
ar
y
h
ig
h
-
p
o
wer
o
n
-
b
o
ar
d
ch
ar
g
er
in
ad
d
itio
n
to
t
h
e
ex
is
tin
g
o
n
-
b
o
ar
d
ch
ar
g
er
.
T
h
is
s
ec
o
n
d
ch
a
r
g
er
ca
n
b
e
p
lu
g
g
ed
d
ir
ec
t
ly
in
to
a
h
ig
h
DC
c
h
ar
g
in
g
s
tatio
n
b
ased
o
n
a
p
h
o
to
v
o
ltaic
s
o
u
r
ce
,
wh
ich
will a
ls
o
b
e
d
ev
elo
p
ed
i
n
th
is
wo
r
k
.
I
n
f
ac
t,
as
s
h
o
wn
in
Fig
u
r
e
1
,
we
p
r
o
p
o
s
e
an
u
p
g
r
a
d
e
o
f
th
e
ex
is
tin
g
s
in
g
le
s
o
ck
et
to
a
co
n
f
ig
u
r
atio
n
o
f
m
u
lti
-
s
o
ck
et
wh
ich
co
n
tain
s
a
s
o
ck
et
f
o
r
AC
ch
ar
g
er
as c
o
n
v
en
tio
n
al
ch
ar
g
e
r
with
a
m
ax
im
u
m
p
o
wer
lev
e
l
o
f
1
.
8
k
W
an
d
an
o
th
e
r
s
o
ck
et
f
o
r
f
ast
ch
ar
g
in
g
th
r
o
u
g
h
th
e
s
ec
o
n
d
ar
y
o
n
-
b
o
ar
d
ch
a
r
g
er
wi
th
a
p
o
wer
lev
el
o
f
3
.
6
k
W
.
T
h
e
p
r
o
p
o
s
ed
co
n
f
ig
u
r
atio
n
h
as
m
an
y
ad
v
a
n
tag
e
s
to
o
v
er
c
o
m
e
th
e
ac
t
u
al
o
n
e
in
t
er
m
s
o
f
p
o
wer
lev
els ca
p
ab
ilit
y
an
d
to
m
ee
t a
r
ed
u
n
d
an
cy
r
ein
f
o
r
ce
d
b
y
a
d
d
in
g
a
s
ec
o
n
d
ch
ar
g
er
.
Fig
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
m
u
lti
-
s
o
ck
et
co
n
f
ig
u
r
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
S
et
u
p
o
f a
s
ec
o
n
d
a
r
y
o
n
-
b
o
a
r
d
ch
a
r
g
er fed
b
y
P
V
DC
s
ta
tio
n
w
ith
g
r
id
in
jectio
n
fo
r
…
(
M
o
h
a
med
A
r
r
a
ch
)
685
I
n
th
e
f
o
llo
win
g
d
escr
ip
tio
n
m
en
tio
n
ed
in
Fig
u
r
e
2
,
th
e
c
o
n
v
en
tio
n
al
ch
ar
g
i
n
g
is
f
ed
o
n
ly
b
y
AC
s
in
g
le
p
h
ase
t
h
r
o
u
g
h
th
e
lo
w
v
o
ltag
e
d
is
tr
ib
u
tio
n
g
r
id
with
a
p
o
wer
lim
itatio
n
o
f
1
.
8
k
W
.
W
h
ile
th
e
p
r
o
p
o
s
ed
co
n
f
ig
u
r
atio
n
co
n
s
is
ts
o
f
m
ain
tain
in
g
th
e
co
n
v
en
tio
n
al
ch
a
r
g
er
an
d
ad
d
in
g
a
s
ec
o
n
d
ar
y
on
-
b
o
ar
d
c
h
ar
g
er
f
ed
,
in
th
is
ca
s
e,
b
y
a
p
h
o
to
v
o
ltaic
d
ir
ec
t
cu
r
r
e
n
t
s
tatio
n
wh
ich
c
an
b
e
in
s
talled
in
d
i
f
f
er
en
t
p
o
in
ts
in
th
e
city
.
I
n
ad
d
itio
n
to
th
is
co
n
f
ig
u
r
atio
n
,
we
also
p
r
o
p
o
s
ed
a
c
o
u
p
led
in
v
er
ter
to
ev
ac
u
ate
th
e
en
er
g
y
p
r
o
d
u
ce
d
b
y
th
e
s
tatio
n
wh
en
n
o
ca
r
is
co
n
n
ec
t
ed
to
k
ee
p
th
e
p
r
o
p
o
s
itio
n
m
o
r
e
u
s
ef
u
l.
I
n
f
a
c
t
,
t
o
d
e
v
e
l
o
p
f
u
r
t
h
e
r
t
h
e
co
n
s
i
s
t
e
n
c
y
o
f
t
h
e
c
o
n
t
r
i
b
u
ti
o
n
,
t
h
e
PV
s
t
at
i
o
n
is
c
o
m
p
o
s
e
d
of
a
DC
-
DC
s
t
a
g
e
b
a
s
e
d
o
n
a
s
y
n
c
h
r
o
n
o
u
s
b
o
o
s
t
c
o
n
v
e
r
t
e
r
t
o
s
t
e
p
u
p
t
h
e
v
o
l
t
a
g
e
c
o
m
i
n
g
f
r
o
m
P
V
p
a
n
e
l
s
f
r
o
m
3
2
0
V
D
C
t
o
4
0
0
V
D
C
i
n
t
h
e
D
C
c
h
a
r
g
i
n
g
b
u
s
.
W
e
h
a
v
e
u
s
e
d
a
f
u
z
z
y
l
o
g
i
c
c
o
n
t
r
o
l
e
n
h
a
n
c
e
d
b
y
a
n
M
P
P
T
al
g
o
r
i
t
h
m
t
o
m
a
x
i
m
i
z
e
t
h
e
e
f
f
ic
i
e
n
c
y
o
f
P
V
p
a
n
e
l
s
.
T
h
e
s
e
c
o
n
d
a
r
y
o
n
-
b
o
a
r
d
c
h
a
r
g
e
r
i
s
c
o
m
p
o
s
e
d
of
a
p
h
a
s
e
s
h
i
f
t
f
u
l
l
b
r
i
d
g
e
c
o
n
v
e
r
t
e
r
(
P
SF
B
)
c
o
n
t
r
o
ll
e
d
b
y
a
c
o
n
s
t
a
n
t
c
u
r
r
e
n
t
c
o
n
s
t
a
n
t
v
o
lt
a
g
e
a
l
g
o
r
i
t
h
m
u
s
i
n
g
a
P
I
c
o
n
t
r
o
l
l
o
o
p
.
2
.
2
.
P
V
a
s
prim
a
ry
po
wer
f
o
r
a
DC
po
wer
s
t
a
t
io
n
W
e
t
h
o
u
g
h
t
a
b
o
u
t
i
n
t
r
o
d
u
c
i
n
g
a
r
e
n
e
w
a
b
l
e
s
o
u
r
c
e
t
o
a
l
i
g
n
w
it
h
n
e
w
e
n
v
i
r
o
n
m
e
n
t
a
l
r
e
q
u
i
r
em
e
n
t
s
.
F
o
r
t
h
i
s
p
u
r
p
o
s
e
,
w
e
p
r
o
p
o
s
e
a
p
h
o
t
o
v
o
l
t
a
i
c
s
o
u
r
c
e
as
t
h
e
p
r
i
m
a
r
y
v
o
l
t
a
g
e
s
o
u
r
c
e
o
f
t
h
e
h
i
g
h
-
p
o
w
e
r
DC
s
t
a
ti
o
n
.
To
h
a
v
e
t
h
e
r
e
q
u
e
s
t
e
d
p
o
w
e
r
s
o
u
r
c
e
,
a
s
e
r
ie
s
a
n
d
p
a
r
a
ll
e
l
P
V
p
a
n
e
l
s
c
o
m
b
i
n
at
i
o
n
i
s
p
o
s
s
i
b
l
e
wi
th
P
V
p
a
n
e
ls
[
1
3
]
.
Fu
r
th
e
r
m
o
r
e
,
to
b
e
ab
le
to
m
ax
im
ize
th
e
p
o
wer
e
x
tr
a
cted
f
r
o
m
p
h
o
to
v
o
ltaic
p
an
e
ls
,
s
ev
er
al
tech
n
iq
u
es
ar
e
p
o
s
s
ib
le
,
in
clu
d
in
g
th
e
p
er
t
u
r
b
an
d
o
b
s
er
v
e
(
P&
O)
alg
o
r
ith
m
,
m
e
n
tio
n
ed
in
Fig
u
r
e
3
.
An
d
as
illu
s
tr
ated
in
Fig
u
r
e
4
,
th
e
alg
o
r
ith
m
p
er
tu
r
b
s
th
e
o
p
e
r
atin
g
v
o
ltag
e
o
f
th
e
PV
m
o
d
u
le
s
lig
h
tly
an
d
o
b
s
er
v
es
th
e
ch
an
g
e
i
n
p
o
wer
o
u
tp
u
t.
I
f
th
e
p
o
wer
in
cr
ea
s
es
d
u
e
to
th
e
p
er
tu
r
b
atio
n
,
th
e
alg
o
r
ith
m
c
o
n
tin
u
es
to
p
e
r
tu
r
b
in
th
e
s
am
e
d
ir
ec
tio
n
.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
iter
ativ
ely
to
c
o
n
s
tan
tly
tr
ac
k
th
e
MPPT.
Fig
u
r
e
2
.
Ov
e
r
v
iew
o
f
th
e
p
r
o
p
o
s
ed
ch
ar
g
in
g
c
o
n
f
ig
u
r
atio
n
Fig
u
r
e
3
.
C
o
n
v
en
tio
n
n
el
P&
O
MPPT
tech
n
iq
u
e
2
.
3
.
Sy
nchro
no
us
bo
o
s
t
wit
h
P
&O
a
nd
f
uzzy
lo
g
ic
co
ntr
o
l
T
h
e
DC
s
tatio
n
,
m
en
tio
n
ed
i
n
Fig
u
r
e
5
,
is
co
m
p
o
s
ed
o
f
a
s
y
n
ch
r
o
n
o
u
s
b
o
o
s
t
co
n
v
er
ter
co
n
tr
o
lled
b
y
f
u
zz
y
l
o
g
ic
to
s
tep
u
p
th
e
v
o
ltag
e
f
r
o
m
3
2
0
VDC
to
4
0
0
V
DC
.
T
h
is
to
p
o
lo
g
y
o
f
t
h
e
DC
-
DC
co
n
v
er
ter
o
f
f
e
r
s
s
ev
er
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ad
v
an
ta
g
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co
m
p
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r
e
d
to
its
co
n
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en
tio
n
al
b
o
o
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t
with
a
d
io
d
e.
I
t
is
ca
lled
s
y
n
c
h
r
o
n
o
u
s
b
ec
au
s
e
th
e
co
n
tr
o
l o
f
th
e
two
s
witch
es S1
an
d
S2
is
ca
r
r
ied
o
u
t in
a
s
y
n
c
h
r
o
n
o
u
s
way
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
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8
8
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8
6
9
4
I
n
t J Po
w
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&
Dr
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Vo
l.
16
,
No
.
2
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J
u
n
e
20
25
:
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8
3
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9
4
686
Fig
u
r
e
4
.
Alg
o
r
ith
m
s
tep
s
o
f
t
h
e
P&
O
tech
n
iq
u
e
Fig
u
r
e
5
.
Fu
ll c
ir
c
u
it o
f
th
e
p
r
o
p
o
s
ed
co
n
f
ig
u
r
atio
n
2
.
3
.
1
.
I
nd
uct
o
r
s
elec
t
io
n
T
h
e
ch
o
ice
o
f
in
d
u
ctan
ce
is
cr
u
cial.
I
t
is
th
e
p
ass
iv
e
co
m
p
o
n
en
t
to
b
ac
k
u
p
e
n
er
g
y
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th
e
co
n
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ter
.
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h
e
g
r
ea
ter
th
e
in
d
u
ctan
ce
,
th
e
s
m
aller
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e
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ip
p
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is
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h
e
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alu
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o
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th
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d
u
cto
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lcu
lated
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s
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g
Kir
ch
h
o
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f
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s
law,
in
a
b
o
o
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t to
p
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y
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d
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g
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y
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×
(
1
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∆
1
=
0
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2
×
1
×
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
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8
6
9
4
S
et
u
p
o
f a
s
ec
o
n
d
a
r
y
o
n
-
b
o
a
r
d
ch
a
r
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er fed
b
y
P
V
DC
s
ta
tio
n
w
ith
g
r
id
in
jectio
n
fo
r
…
(
M
o
h
a
med
A
r
r
a
ch
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687
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h
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:
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n
d
u
cto
r
in
(
H)
,
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n
p
u
t
v
o
ltag
e
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(
V)
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DC
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u
s
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ip
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(
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d
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s
witch
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g
f
r
eq
u
e
n
cy
in
(
Hz)
2
.
3
.
2
.
DC
bu
s
ca
pa
cit
o
r
s
elec
t
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n
T
h
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u
s
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ac
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o
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ac
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it
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ip
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n
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e
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d
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r
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ce
s
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t
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ts
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e
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lated
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s
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g
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ch
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f
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an
d
g
iv
en
in
(
3
)
an
d
(
4
).
1
=
×
×
∆
(
3
)
∆
=
0
.
2
×
(
4
)
Af
ter
th
e
d
esig
n
o
f
th
e
c
o
m
p
o
n
en
ts
o
f
th
e
p
o
wer
s
tag
e,
t
h
e
p
ar
am
eter
s
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
b
o
o
s
t
co
n
v
er
ter
ar
e
m
en
tio
n
ed
i
n
T
ab
le
1
.
2
.
3
.
3
.
Desig
n o
f
t
he
f
uzzy
lo
g
ic
blo
ck
co
ntr
o
l
As
s
h
o
wn
in
Fig
u
r
e
6
,
th
e
f
u
z
zy
lo
g
ic
c
o
n
tr
o
l
is
d
esig
n
ed
to
tr
ac
k
th
e
m
ax
im
u
m
p
o
wer
f
o
r
th
e
s
o
lar
p
an
el
with
th
e
P&
O
alg
o
r
ith
m
.
It
m
ea
s
u
r
es th
e
v
alu
es o
f
th
e
v
o
ltag
e
an
d
c
u
r
r
en
t a
t th
e
o
u
tp
u
t o
f
th
e
PV a
r
r
ay
.
At
ev
er
y
d
is
cr
ete
iter
atio
n
,
i
t
ca
lcu
lates
th
e
PV
p
o
wer
to
d
er
iv
e
th
e
i
n
p
u
ts
o
f
th
e
c
o
n
tr
o
ller
[
1
5
]
.
B
y
co
m
b
in
in
g
f
u
zz
y
lo
g
ic
co
n
tr
o
l
with
th
e
P&
O
alg
o
r
ith
m
,
th
e
MPPT
s
y
s
tem
ca
n
ef
f
ec
tiv
ely
ad
ap
t
to
ch
an
g
i
n
g
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
an
d
u
n
ce
r
tain
ties
.
T
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
p
r
o
v
id
es
a
f
l
ex
ib
le
an
d
in
t
u
itiv
e
d
ec
is
io
n
-
m
ak
in
g
m
ec
h
an
is
m
,
wh
ile
th
e
P&
O
alg
o
r
ith
m
p
er
f
o
r
m
s
th
e
iter
ativ
e
ad
ju
s
tm
en
t
o
f
th
e
o
p
er
atin
g
p
o
in
t
b
ased
o
n
th
e
f
u
zz
y
co
n
t
r
o
ller
'
s
o
u
tp
u
t.
Def
u
zz
if
icatio
n
th
en
tr
an
s
lates
th
e
f
u
zz
y
o
u
tp
u
t
in
to
ac
tio
n
a
b
le
co
n
tr
o
l sig
n
als f
o
r
th
e
MPPT
s
y
s
tem
.
T
h
e
lo
g
ic
is
tr
an
s
lated
b
y
t
h
e
f
u
zz
if
icatio
n
o
f
th
e
c
o
m
p
ar
is
o
n
b
etwe
en
th
e
ev
o
lu
tio
n
s
o
f
th
e
iter
atio
n
s
b
etwe
en
th
e
s
tate
s
o
f
th
e
er
r
o
r
s
o
f
th
e
v
ar
iab
le
[
1
6
]
.
It
tak
es
a
co
m
b
in
atio
n
o
f
f
iv
e
s
tates
(
N
B
:
n
eg
ativ
e
b
ig
,
NS:
n
eg
ativ
e
s
m
all
,
Z
:
z
er
o
,
PS
:
p
o
s
itiv
e
s
m
all,
an
d
PB
:
p
o
s
itiv
e
b
ig
)
,
wh
ich
g
iv
es
a
tab
le
o
f
r
u
les
o
f
2
5
co
m
b
in
atio
n
s
o
f
s
tates
d
escr
ib
ed
in
T
ab
le
2
.
F
u
zz
y
lo
g
ic
s
tates
f
r
o
m
T
ab
le
2
ar
e
tr
an
s
lated
b
y
m
em
b
er
s
h
ip
s
d
e
p
en
d
in
g
o
n
th
e
er
r
o
r
b
etwe
en
t
h
e
iter
atio
n
s
an
d
th
e
d
if
f
er
e
n
ce
o
f
th
e
er
r
o
r
.
T
h
ese
two
s
tates
d
ef
in
e
t
h
e
o
u
tp
u
t
an
g
le.
All
o
p
er
atio
n
s
c
o
m
b
in
in
g
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
g
en
e
r
ate
n
ew
f
u
zz
y
s
tates
b
ased
o
n
lo
g
ical
r
elatio
n
s
h
ip
s
.
T
ab
le
1
.
Par
am
eter
s
o
f
s
y
n
ch
r
o
n
o
u
s
b
o
o
s
t c
o
n
v
er
ter
P
a
r
a
me
t
e
r
N
o
t
a
t
i
o
n
V
a
l
u
e
P
V
i
r
r
a
d
i
a
n
c
e
1000
W
/
m²
P
V
t
e
m
p
e
r
a
t
u
r
e
25
°C
I
n
d
u
c
t
o
r
1
0
.
6
µ
H
D
C
b
u
s
c
a
p
a
c
i
t
o
r
1
8
mF
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
1
0
k
H
z
M
a
x
i
m
a
l
r
a
t
e
d
p
o
w
e
r
3
.
6
k
W
T
ab
le
2
.
C
o
n
tr
o
l c
o
m
b
i
n
atio
n
s
o
f
f
u
z
zy
lo
g
ic
b
lo
ck
s
E
\
ΔE
NB
NS
Z
PS
PB
NB
NB
NB
NS
NS
Z
NS
NB
NB
NS
Z
PS
Z
NS
NS
Z
PS
PS
PS
NS
Z
PS
PB
PB
PB
Z
PS
PS
PB
PB
Fig
u
r
e
6
.
C
o
n
tr
o
l d
iag
r
am
o
f
s
y
n
ch
r
o
n
o
u
s
b
o
o
s
t c
o
n
v
er
ter
2
.
4
.
Desig
n o
f
s
ec
o
nd
a
ry
o
n
-
bo
a
rd
cha
rg
er
T
h
e
h
i
g
h
-
p
o
w
e
r
s
e
c
o
n
d
a
r
y
c
h
a
r
g
e
r
i
s
d
e
s
i
g
n
e
d
t
o
p
r
o
v
i
d
e
t
h
e
e
l
e
c
t
r
ic
c
a
r
w
i
t
h
a
s
e
c
o
n
d
a
r
y
a
n
d
b
a
c
k
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p
c
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
6
8
3
-
6
9
4
688
c
h
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i
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o
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s
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o
p
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l
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y
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o
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c
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o
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[
1
7
]
.
A
l
s
o
,
it
i
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e
x
t
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n
s
i
v
e
l
y
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d
i
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-
a
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it
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is
t
i
n
ct
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ea
t
u
r
e
s
,
s
u
c
h
as
h
i
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h
v
o
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o
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i
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la
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a
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s
[
1
8
]
,
[
1
9
]
.
T
o
r
ec
h
a
r
g
e
th
e
ca
r
b
atter
y
,
we
o
p
ted
,
as
m
en
tio
n
e
d
in
Fi
g
u
r
e
7
,
f
o
r
th
e
co
n
s
tan
t
v
o
lta
g
e
-
co
n
s
tan
t
cu
r
r
en
t m
eth
o
d
wid
ely
u
s
ed
in
s
u
ch
ap
p
licatio
n
s
.
I
n
f
ac
t,
th
e
co
n
v
er
ter
c
o
n
tr
o
l is p
r
o
v
id
ed
b
y
two
lo
o
p
s
b
ased
o
n
PI
b
lo
ck
s
d
ef
in
e
d
b
y
Z
ieg
l
er
-
Nich
o
ls
’
m
eth
o
d
.
An
in
n
er
cu
r
r
en
t
lo
o
p
f
o
r
cu
r
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en
t
co
n
tr
o
l
an
d
an
o
u
ter
lo
o
p
f
o
r
v
o
ltag
e
co
n
tr
o
l.
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ith
co
n
s
tan
t
cu
r
r
e
n
t
v
o
ltag
e
s
tr
ateg
y
,
t
h
e
b
atter
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is
ch
a
r
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ed
at
a
co
n
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tan
t
cu
r
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s
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ied
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ltag
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esh
o
l
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is
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ed
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d
th
en
th
e
c
h
ar
g
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g
s
witch
es
to
a
co
n
s
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t
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o
ltag
e
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til
th
e
cu
r
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en
t
d
ec
r
ea
s
es b
elo
w
th
e
th
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esh
o
ld
[
2
0
]
,
[
2
1
]
.
T
h
e
p
h
ase
s
h
if
t
f
u
ll
b
r
id
g
e
co
n
v
er
ter
,
also
k
n
o
wn
as
“PSF
B
”,
is
co
m
p
o
s
ed
of
two
leg
s
A
an
d
B
,
an
d
f
o
u
r
I
GB
T
s
witch
es.
T
h
e
v
o
lt
ag
e
f
ee
d
s
th
e
DC
b
u
s
v
o
ltag
e
o
f
4
0
0
VDC
in
to
th
e
f
ir
s
t
s
id
e
o
f
h
i
g
h
f
r
eq
u
e
n
cy
tr
an
s
f
o
r
m
er
.
I
ts
s
ec
o
n
d
s
id
e
i
s
co
n
n
ec
ted
to
a
f
u
ll
d
io
d
e
b
r
id
g
e
D1
-
D4
to
r
ec
tify
th
e
AC
wav
e
th
at
co
m
es
f
r
o
m
th
e
in
p
u
t
s
id
e.
W
h
ile
th
e
s
h
if
ted
co
n
tr
o
l
b
etwe
en
th
e
two
leg
s
an
d
o
f
th
is
co
n
v
er
t
er
is
en
s
u
r
ed
b
y
a
PW
M
co
n
tr
o
l,
at
a
f
ix
ed
f
r
eq
u
en
cy
,
co
m
p
lem
en
ta
r
y
b
et
wee
n
th
e
two
s
witch
es
o
f
t
h
e
s
am
e
leg
.
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h
e
p
ar
am
eter
s
o
f
t
h
e
s
ec
o
n
d
a
r
y
o
n
-
b
o
ar
d
ch
a
r
g
er
a
n
d
th
e
ca
r
’
s
b
atter
y
ar
e
lis
ted
r
esp
ec
tiv
ely
i
n
T
ab
les 3
an
d
4
.
Fig
u
r
e
7
.
PI
c
o
n
tr
o
l
b
lo
ck
s
o
f
th
e
s
ec
o
n
d
o
n
-
b
o
ar
d
c
h
ar
g
e
r
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ab
le
3
.
Par
am
eter
s
o
f
th
e
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ec
o
n
d
ar
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o
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b
o
a
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P
a
r
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me
t
e
r
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o
t
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t
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o
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l
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4
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t
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4
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V
Tu
r
n
s
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1
4
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w
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p
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ss
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5
mH
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6
k
W
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4
.
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am
eter
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att
er
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P
a
r
a
me
t
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1
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A
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5
1
V
C
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f
v
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3
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o
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h
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t
5
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a
l
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n
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e
0
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0
0
3
Ω
2
.
5
.
Sin
g
le
inv
er
t
er
co
up
led t
o
t
he
g
rid f
o
r
po
wer
m
a
na
g
em
ent
I
n
th
e
p
r
o
p
o
s
ed
s
ch
em
e
,
we
h
av
e
p
r
o
v
id
ed
,
in
ad
d
itio
n
to
th
e
h
ig
h
-
p
o
wer
c
h
ar
g
er
,
a
n
in
v
er
ter
co
n
n
ec
ted
t
o
an
elec
tr
ical
g
r
i
d
to
ev
ac
u
ate
th
e
elec
tr
ical
e
n
er
g
y
g
en
er
ate
d
f
r
o
m
PV
p
a
n
els
,
as
s
h
o
wn
in
F
ig
u
r
e
8
.
T
h
is
p
o
wer
is
ev
ac
u
ated
to
th
e
g
r
id
wh
en
n
o
ca
r
is
co
n
n
ec
ted
to
th
e
ch
a
r
g
in
g
s
tat
io
n
.
T
h
u
s
,
to
m
ak
e
o
u
r
in
s
tallatio
n
m
o
r
e
u
s
ef
u
l
a
n
d
p
r
o
f
itab
le.
Fo
r
t
h
is
p
u
r
p
o
s
e,
we
d
esig
n
ed
a
s
in
g
le
-
p
h
ase
i
n
v
er
ter
with
a
lev
el
o
f
p
o
wer
at
3
.
6
k
W
with
a
h
ig
h
p
o
we
r
f
ac
to
r
to
k
ee
p
a
n
o
p
tim
u
m
p
o
wer
tr
an
s
f
er
t
o
th
e
g
r
i
d
.
I
m
p
lem
en
tin
g
th
e
in
jectio
n
s
o
lu
tio
n
r
eq
u
ir
es
a
PW
M
in
v
er
ter
an
d
an
L
C
L
-
ty
p
e
lo
w
-
p
a
s
s
f
ilter
,
as
s
h
o
wn
in
Fig
u
r
e
9
.
T
h
e
r
o
le
o
f
L
C
L
is
to
f
ilter
th
e
h
ar
m
o
n
ics
to
r
ed
u
ce
t
h
e
r
ate
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
g
en
er
ated
b
y
th
e
i
n
v
er
ter
.
T
h
u
s
,
im
p
r
o
v
in
g
th
e
q
u
ality
o
f
elec
tr
ical
en
er
g
y
i
n
jecte
d
in
to
th
e
g
r
id
.
T
o
co
n
tr
o
l
th
e
in
jecte
d
p
o
wer
,
C
lar
k
-
p
ar
k
tr
a
n
s
f
o
r
m
atio
n
,
a
n
d
p
h
ase
lo
c
k
ed
lo
o
p
(
PLL
)
a
r
e
u
s
ed
to
b
e
ab
le
to
h
a
v
e
a
u
n
it
p
o
wer
f
ac
to
r
.
I
n
f
ac
t,
th
e
q
u
ad
r
ati
c
c
u
r
r
en
t
co
m
p
o
n
en
t
o
f
th
e
r
ef
e
r
en
ce
(
d
-
q
)
m
u
s
t
b
e
ca
n
ce
led
.
T
h
e
p
r
im
ar
y
r
o
le
o
f
th
e
PLL
in
th
is
g
r
id
-
tied
in
v
er
ter
s
y
s
tem
is
to
s
y
n
c
h
r
o
n
ize
t
h
e
in
v
e
r
ter
'
s
o
u
tp
u
t
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
with
th
at
o
f
th
e
u
tili
ty
g
r
id
[
2
2
]
.
T
h
is
is
cr
u
cial
f
o
r
en
s
u
r
in
g
th
at
t
h
e
p
o
wer
g
en
er
ate
d
b
y
th
e
in
v
e
r
ter
ca
n
b
e
s
af
ely
a
n
d
s
ea
m
less
ly
in
teg
r
ated
in
to
th
e
g
r
id
with
o
u
t
ca
u
s
in
g
h
ar
m
o
n
ic
p
o
llu
tio
n
.
T
h
e
co
n
tr
o
l
o
f
th
e
cu
r
r
en
t
co
m
in
g
f
r
o
m
th
e
PV
in
v
er
ter
p
ass
es
th
r
o
u
g
h
two
r
eg
u
latio
n
lo
o
p
s
,
as
s
h
o
wn
in
Fig
u
r
e
1
0
.
I
n
f
ac
t,
th
e
th
r
ee
-
p
h
ase
g
r
id
v
o
ltag
es
co
m
es
th
r
o
u
g
h
th
e
C
lar
k
an
d
Par
k
tr
an
s
f
o
r
m
atio
n
s
t
o
g
et
two
co
m
p
o
n
e
n
ts
an
d
to
f
ac
ilit
ate
th
e
co
n
tr
o
l.
T
h
e
m
ain
o
b
jectiv
e
o
f
th
is
tr
an
s
f
o
r
m
atio
n
is
to
ca
n
ce
l
r
ea
ctiv
e
p
o
wer
a
n
d
g
et
th
e
g
r
i
d
an
g
le
Ɵ
to
m
ee
t th
e
u
n
ity
o
f
p
o
wer
f
ac
to
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
S
et
u
p
o
f a
s
ec
o
n
d
a
r
y
o
n
-
b
o
a
r
d
ch
a
r
g
er fed
b
y
P
V
DC
s
ta
tio
n
w
ith
g
r
id
in
jectio
n
fo
r
…
(
M
o
h
a
med
A
r
r
a
ch
)
689
As
m
e
n
t
io
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ased
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Evaluation Warning : The document was created with Spire.PDF for Python.