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C
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[
1
]
.
T
h
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h
a
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f
f
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t
g
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at
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c
a
p
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c
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t
y
[
2
]
.
Sev
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al
r
esear
ch
ef
f
o
r
ts
h
a
v
e
aim
ed
to
m
i
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n
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ts
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o
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s
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ested
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3
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ir
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Po
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[
3
]
.
T
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f
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T
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1
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2
5
A
[
4
]
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Fo
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r
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DC
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s
h
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r
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tr
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,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4
I
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Dr
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Vo
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1
7
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No
.
3
,
Sep
tem
b
er
20
2
6
:
1859
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1
8
7
2
1860
o
f
f
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cu
r
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ch
ar
ac
ter
is
tics
[
5
]
.
C
o
m
p
ac
t
an
d
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f
icien
t
u
n
i
d
ir
ec
tio
n
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n
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DC
co
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v
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ter
s
with
r
e
d
u
ce
d
c
ir
cu
it
elem
en
ts
h
av
e
also
b
ee
n
r
ep
o
r
ted
,
ca
p
a
b
le
o
f
o
p
er
atin
g
in
m
u
ltip
le
m
o
d
es
with
m
in
im
al
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tr
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m
p
le
x
ity
u
s
in
g
a
s
in
g
le
co
n
tr
o
ller
s
et
[
6
]
.
A
f
o
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r
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p
o
r
t
co
n
v
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ter
in
teg
r
atin
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PV
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o
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le
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d
a
b
atter
y
in
to
a
b
ip
o
lar
DC
m
ic
r
o
g
r
id
(
MG
)
was
p
r
o
p
o
s
ed
,
ac
h
ie
v
in
g
s
in
g
le
-
p
h
ase
en
er
g
y
co
n
v
er
s
io
n
an
d
o
p
er
atin
g
u
n
d
er
th
r
ee
d
is
tin
ct
m
o
d
es
b
ased
o
n
e
n
er
g
y
m
an
a
g
em
en
t
r
eq
u
ir
em
e
n
ts
[
7
]
.
Hig
h
-
p
o
wer
an
d
h
i
g
h
-
g
ai
n
m
u
ltip
o
r
t
c
o
n
v
er
te
r
s
h
av
e
b
ee
n
d
ev
elo
p
ed
f
o
r
h
y
b
r
id
en
e
r
g
y
s
to
r
ag
e
ap
p
lian
ce
s
.
A
c
u
r
r
e
n
t
-
f
ed
d
u
a
l
ac
tiv
e
b
r
id
g
e
-
b
ased
m
u
ltip
o
r
t
co
n
v
e
r
ter
p
r
o
v
id
in
g
g
alv
a
n
ic
is
o
latio
n
b
etwe
en
th
e
b
atter
y
an
d
DC
b
u
s
was
v
alid
ated
u
s
in
g
a
1
k
W
p
r
o
to
ty
p
e
[
8
]
.
Similar
ly
,
a
b
i
p
o
lar
DC
–
DC
co
n
v
er
ter
co
m
b
in
in
g
a
m
u
ltip
o
r
t
d
u
al
ac
tiv
e
b
r
id
g
e
with
a
n
eu
tr
al
-
p
o
in
t
-
clam
p
e
d
to
p
o
lo
g
y
was
im
p
lem
en
ted
to
in
teg
r
ate
r
en
ewa
b
le
s
o
u
r
ce
s
o
f
v
ar
y
i
n
g
ca
p
ac
ities
in
to
a
b
i
p
o
lar
m
ed
iu
m
-
v
o
ltag
e
DC
m
icr
o
g
r
id
[
9
]
.
Par
allel
co
o
r
d
in
atio
n
co
n
tr
o
l
s
tr
ateg
ies
u
s
in
g
is
o
lated
m
u
ltip
o
r
t
co
n
v
er
te
r
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
r
ep
lace
co
n
v
en
tio
n
al
b
u
ck
–
b
o
o
s
t
cir
cu
its
,
en
ab
lin
g
elec
tr
ical
is
o
latio
n
f
o
r
en
e
r
g
y
s
to
r
ag
e
m
icr
o
-
s
o
u
r
ce
s
[
1
0
]
.
C
o
n
tr
o
ller
s
f
o
r
r
e
g
u
latin
g
b
att
er
y
v
o
ltag
e
an
d
cu
r
r
en
t
wh
ile
m
an
ag
in
g
b
i
d
ir
ec
tio
n
al
p
o
wer
f
lo
w
am
o
n
g
win
d
tu
r
b
in
es,
PV
p
an
els,
b
atter
ies,
an
d
DC
m
icr
o
g
r
i
d
s
h
av
e
also
b
ee
n
d
em
o
n
s
tr
ated
[
1
1
]
.
Ad
d
itio
n
ally
,
is
o
lated
th
r
ee
-
p
o
r
t
DC
–
DC
co
n
v
e
r
ter
s
b
ased
o
n
s
er
ies
r
eso
n
a
n
t
an
d
d
u
al
ac
tiv
e
b
r
i
d
g
e
t
o
p
o
lo
g
ies
h
av
e
b
ee
n
d
ev
elo
p
e
d
f
o
r
elec
tr
ic
v
eh
icle
ch
ar
g
in
g
s
tatio
n
s
,
s
u
p
p
o
r
tin
g
b
o
th
f
ast an
d
s
lo
w
ch
ar
g
in
g
m
o
d
es [
1
2
]
.
B
u
ck
–
b
o
o
s
t
co
n
v
er
ter
s
r
em
ai
n
a
f
u
n
d
am
e
n
tal
s
o
lu
tio
n
f
o
r
v
o
ltag
e
r
eg
u
latio
n
d
u
e
to
th
ei
r
ab
ilit
y
to
s
tep
u
p
o
r
s
tep
-
d
o
wn
o
u
tp
u
t
v
o
ltag
e.
PW
M
co
n
tr
o
l
h
as
b
e
en
d
o
n
e
u
s
in
g
m
icr
o
c
o
n
tr
o
ller
s
to
en
s
u
r
e
th
at
th
e
o
u
tp
u
t is r
eg
u
lated
[
1
3
]
.
I
n
o
r
d
er
to
en
h
a
n
ce
d
y
n
am
ic
o
p
e
r
a
tio
n
,
PID
,
f
u
zz
y
,
a
n
d
h
y
b
r
id
f
u
zz
y
-
PID
co
n
tr
o
ller
s
h
av
e
b
ee
n
e
x
p
lo
r
e
d
in
s
o
lar
-
b
atter
y
b
u
c
k
-
b
o
o
s
t
s
y
s
tem
s
,
s
u
cc
ess
f
u
lly
d
ec
r
ea
s
in
g
th
e
o
v
er
s
h
o
o
t
an
d
o
s
cillatio
n
s
[
1
4
]
.
E
x
ten
s
iv
e
a
n
aly
s
is
o
f
p
er
f
o
r
m
a
n
ce
tr
ad
e
-
o
f
f
s
b
etwe
en
co
n
tr
o
ller
tu
n
in
g
ap
p
r
o
ac
h
es
b
ased
o
n
tim
e
-
d
o
m
ain
an
d
f
r
eq
u
en
c
y
-
d
o
m
ai
n
an
aly
s
is
h
as
also
b
ee
n
p
o
in
ted
o
u
t
in
th
e
liter
atu
r
e
[
1
5
]
.
Fix
e
d
-
p
o
i
n
t
d
ig
ital
f
ilter
ar
ch
itectu
r
e
-
b
ased
d
ig
ital
co
n
tr
o
ller
s
h
av
e
also
b
ee
n
u
s
ed
(
wh
er
e
r
ep
r
o
g
r
am
m
in
g
ca
n
b
e
ac
co
m
p
lis
h
ed
with
o
u
t
d
r
asti
c
h
ar
d
war
e
ad
a
p
tati
o
n
)
.
B
u
ck
an
d
b
o
o
s
t
m
o
d
e
clo
s
ed
-
l
o
o
p
co
n
tr
o
l
h
a
v
e
b
ee
n
test
ed
o
n
MA
T
L
AB
/Si
m
u
li
n
k
with
d
if
f
e
r
en
t
o
p
er
atin
g
co
n
d
itio
n
s
[
1
6
]
.
T
h
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
u
n
id
ir
ec
tio
n
al
a
n
d
b
i
d
ir
ec
tio
n
al
b
u
ck
b
o
o
s
t
co
n
v
er
ter
s
h
as
b
ee
n
s
tu
d
ied
,
a
n
d
th
e
r
ef
in
e
d
tr
an
s
ien
t
r
esp
o
n
s
e
a
n
d
lo
w
o
v
er
s
h
o
o
t a
r
e
r
ea
lized
u
s
in
g
PID
co
n
tr
o
ller
s
[
1
7
]
.
Mo
r
e
s
o
p
h
is
ticated
m
o
d
elin
g
an
d
co
n
tr
o
l
tec
h
n
iq
u
es
h
av
e
b
ee
n
d
e
v
elo
p
ed
to
ad
d
to
co
n
v
er
ter
ef
f
icac
y
.
Gen
er
alize
d
s
tate
-
s
p
ac
e
av
er
ag
in
g
m
o
d
els
(
GSSA
M)
h
av
e
b
ee
n
u
s
ed
to
m
u
ltip
h
ase
in
ter
leav
ed
b
u
c
k
co
n
v
er
ter
s
,
esp
ec
ially
wh
e
n
th
e
s
y
s
tem
is
o
s
cillatin
g
o
r
h
as
h
ig
h
am
o
u
n
ts
o
f
r
ip
p
le
in
th
e
cu
r
r
e
n
ts
[
1
8
]
.
Gatin
g
p
u
ls
e
g
en
er
atio
n
s
tr
ate
g
ies
u
s
in
g
f
ee
d
b
ac
k
a
n
d
d
eter
m
in
in
g
t
h
e
r
an
g
e
o
f
th
e
cy
cle
o
f
d
u
t
y
h
av
e
b
ee
n
ad
o
p
ted
to
co
n
tr
o
l
t
h
e
in
p
u
t
r
esis
tan
ce
an
d
s
tab
le
o
p
e
r
atio
n
[
1
9
]
.
Activ
e
p
o
wer
f
ac
to
r
co
r
r
ec
tio
n
(
PF
C
)
h
as
also
b
ee
n
ex
ten
s
iv
ely
u
s
ed
in
b
o
o
s
t
co
n
v
e
r
ter
s
in
b
o
th
c
o
n
ti
n
u
o
u
s
an
d
d
is
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
es
[
2
0
]
.
Var
iab
le
s
witch
in
g
f
r
e
q
u
en
c
y
m
eth
o
d
s
ar
e
s
u
g
g
ested
to
d
ec
r
ea
s
e
d
is
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
at
b
o
th
lin
e
v
o
ltag
e
ze
r
o
cr
o
s
s
in
g
s
an
d
m
i
n
im
ize
s
witch
in
g
lo
s
s
in
b
o
t
h
v
o
ltag
e
p
ea
k
s
to
a
m
i
n
im
u
m
[
2
1
]
.
PID
-
c
o
n
tr
o
lled
PF
C
b
o
o
s
t
co
n
v
er
ter
s
h
av
e
b
ee
n
ap
p
lied
to
en
h
a
n
ce
th
e
DC
v
o
ltag
e
r
eg
u
latio
n
[
2
2
]
,
an
d
ad
ap
tiv
e
PW
M
-
b
ased
m
eth
o
d
s
h
av
e
b
ee
n
ap
p
l
ied
to
en
s
u
r
e
th
e
m
in
im
izatio
n
o
f
o
v
er
all
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
an
d
s
tab
le
o
p
er
atio
n
in
th
e
clo
s
ed
-
lo
o
p
[
2
3
]
.
C
lo
s
ed
-
lo
o
p
co
n
tr
o
l
s
tr
ateg
ies
h
av
e
also
s
h
o
wn
g
r
ea
t
r
ed
u
ctio
n
in
o
v
er
s
h
o
o
t
a
n
d
ef
f
icien
c
y
[
2
4
]
.
Me
ch
an
is
m
s
to
en
h
an
ce
p
o
w
er
f
ac
to
r
an
d
lo
wer
T
HD
in
AC
to
DC
co
n
v
er
ter
s
with
PID
-
co
n
tr
o
lled
b
o
o
s
t
co
n
v
er
ter
s
h
av
e
also
r
ep
o
r
te
d
[
2
5
]
.
I
n
-
d
ep
th
an
aly
s
is
o
f
PF
C
tech
n
iq
u
es
id
en
tifie
s
th
eir
ca
p
ab
ilit
ies
as
d
r
iv
in
g
in
p
u
t
cu
r
r
e
n
t
an
d
m
in
im
izi
n
g
h
a
r
m
o
n
ics,
an
d
th
e
p
er
f
o
r
m
an
ce
o
f
PF
C
tech
n
iq
u
es
h
as
b
ee
n
co
m
p
ar
ed
t
o
ea
ch
d
u
ty
r
atio
an
d
v
o
ltag
e
le
v
el
[
2
6
]
.
2.
M
E
T
H
O
D
Fig
u
r
e
1
s
h
o
ws
h
o
w
p
o
wer
in
ter
ac
ts
to
g
iv
e
th
e
p
h
o
to
v
o
ltaic
(
PV)
p
an
el
a
n
d
th
e
DC
v
o
lt
ag
e
s
o
u
r
ce
th
e
ab
ilit
y
to
f
ee
d
en
er
g
y
to
th
e
DC
g
r
id
.
I
n
o
r
d
e
r
to
s
u
p
p
ly
p
o
wer
to
th
e
DC
g
r
id
d
u
r
in
g
p
er
io
d
s
o
f
r
e
n
ewa
b
le
en
er
g
y
p
r
o
d
u
ctio
n
,
t
h
e
b
i
d
ir
e
ctio
n
al
co
n
v
er
ter
is
u
tili
ze
d
i
n
b
o
o
s
t
m
o
d
e
wh
ile
s
im
u
ltan
eo
u
s
ly
ch
a
r
g
in
g
th
e
b
atter
y
.
An
MPPT
tech
n
iq
u
e
ca
lled
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
is
u
s
ed
to
ex
tr
ac
t
th
e
P
V
p
an
el'
s
m
ax
im
u
m
p
o
wer
.
I
n
ca
s
e
o
f
a
r
ed
u
ctio
n
o
f
th
e
s
o
lar
ir
r
ad
iatio
n
an
d
t
h
e
PV
p
o
wer
is
n
o
t
en
o
u
g
h
t
o
m
ee
t
th
e
d
em
an
d
o
f
th
e
g
r
i
d
,
a
d
ef
icit
o
f
p
o
wer
w
ill
b
e
co
m
p
en
s
ated
b
y
th
e
b
at
ter
y
,
wh
ich
f
ee
d
s
th
e
DC
g
r
i
d
.
I
n
th
is
ca
s
e,
th
e
s
o
lu
tio
n
m
o
v
es
to
v
o
ltag
e
m
o
d
e
co
n
tr
o
l
as
o
p
p
o
s
ed
t
o
MP
PT.
I
n
th
e
e
v
en
t
th
at
b
o
th
th
e
PV
s
o
u
r
ce
an
d
th
e
DC
v
o
ltag
e
s
o
u
r
ce
ar
e
u
n
av
ail
ab
le,
th
e
b
atter
y
b
ec
o
m
es
th
e
s
o
le
p
o
wer
s
o
u
r
ce
f
o
r
th
e
DC
g
r
id
.
T
h
e
co
n
v
er
ter
o
p
er
ates in
b
u
ck
m
o
d
e
in
t
h
is
o
p
er
atin
g
c
o
n
d
itio
n
to
b
e
ab
le
to
co
n
tr
o
l
b
atter
y
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d
i
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at
i
c
p
l
a
n
r
e
v
ea
l
e
d
i
n
F
i
g
u
r
e
1
.
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
Desig
n
a
n
d
s
imu
la
tio
n
o
f a
fo
u
r
-
p
o
r
t b
u
ck
-
b
o
o
s
t c
o
n
ve
r
ter in
teg
r
a
ted
w
ith
…
(
M.
S
.
Mu
ku
n
d
a
s
w
a
my
)
1861
2
.
1
.
Circ
uit
dia
g
ra
m
o
f
t
he
pro
po
s
ed
s
y
s
t
em
Fig
u
r
e
2
d
is
p
la
y
s
t
h
e
ci
r
c
u
i
t
s
c
h
e
m
e
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a
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h
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te
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f
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r
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o
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r
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h
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t c
o
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ec
ts
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o
l
ar
m
o
d
u
l
es
a
n
d
a
D
C
s
o
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r
c
e
(
P
o
r
ts
1
an
d
2
)
o
n
th
e
i
n
p
u
t
s
i
d
e
,
a
b
at
te
r
y
o
n
P
o
r
t
3
,
a
n
d
a
DC
g
r
i
d
/l
o
ad
o
n
P
o
r
t
4
[
2
7
]
.
T
h
e
c
ir
cu
it
u
s
e
s
a
s
o
l
a
r
p
a
n
el
as
th
e
m
a
in
s
o
u
r
ce
o
f
en
er
g
y
,
an
d
an
a
u
x
il
ia
r
y
s
o
u
r
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o
f
DC
is
s
u
p
p
l
ie
d
t
o
al
lo
w
th
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ci
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cu
it
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o
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ti
n
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d
u
r
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n
g
p
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io
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el
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s
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PT
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iz
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la
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b
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cti
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li
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x
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m
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m
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w
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t
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lar
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ir
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ctl
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ec
t
e
d
t
o
t
h
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g
r
i
d
.
Fig
u
r
e
1
.
Pro
p
o
s
ed
s
y
s
tem
Fig
u
r
e
2
.
C
ir
cu
it d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
2
.
2
.
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ntr
o
l st
ra
t
eg
y
s
ce
na
r
io
s
o
f
t
he
pro
po
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ed
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nv
er
t
e
r
Dif
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er
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t
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f
l
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n
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itio
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s
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etwe
en
th
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b
atter
y
,
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lin
k
,
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d
r
en
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b
le
en
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g
y
s
o
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r
ce
ar
e
u
s
ed
to
ca
teg
o
r
ize
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
'
s
o
p
er
atio
n
.
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h
ese
o
p
er
atin
g
s
ce
n
ar
io
s
e
n
s
u
r
e
p
r
o
p
er
en
er
g
y
m
an
ag
em
en
t
u
n
d
er
v
ar
y
in
g
g
e
n
er
atio
n
an
d
lo
ad
co
n
d
itio
n
s
.
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u
r
d
is
tin
ct
s
ce
n
a
r
io
s
ar
e
d
ef
in
ed
to
d
escr
ib
e
th
e
co
n
v
er
ter
b
eh
a
v
io
r
an
d
co
r
r
esp
o
n
d
in
g
o
p
er
atin
g
m
o
d
es,
wh
i
ch
is
g
iv
en
as f
o
llo
ws
:
-
Scen
ar
io
1
:
<0
.
W
h
en
th
e
DC
-
lin
k
p
o
wer
is
n
eg
ativ
e,
th
e
co
n
v
e
r
ter
o
p
er
ates
in
b
u
c
k
m
o
d
e,
a
n
d
th
e
b
atter
y
is
ch
ar
g
ed
b
y
a
b
s
o
r
b
i
n
g
en
er
g
y
f
r
o
m
th
e
DC
lin
k
(
Mo
d
e
1
)
.
I
f
r
en
ewa
b
le
en
er
g
y
p
o
wer
>0
,
th
e
co
n
v
e
r
ter
tr
an
s
itio
n
s
to
M
o
d
e
2
.
-
Scen
ar
io
2
:
>
>
0
.
I
n
th
is
co
n
d
itio
n
,
r
en
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b
le
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g
y
g
en
e
r
atio
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ex
ce
ed
s
th
e
DC
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lin
k
p
o
wer
d
em
an
d
.
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h
e
ex
ce
s
s
r
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n
ewa
b
le
en
er
g
y
is
d
ir
ec
ted
to
c
h
ar
g
e
th
e
b
atter
y
,
en
a
b
lin
g
en
er
g
y
s
to
r
ag
e.
C
o
n
s
eq
u
en
tly
,
th
e
c
o
n
v
e
r
ter
o
p
er
ates in
Mo
d
es 2
a
n
d
3
.
-
Scen
ar
io
3
:
>
.
W
h
en
th
e
av
ailab
le
r
en
ewa
b
le
en
er
g
y
is
in
s
u
f
f
icien
t
to
m
ee
t
th
e
DC
-
lin
k
l
o
ad
d
em
an
d
,
t
h
e
b
atter
y
s
u
p
p
lies
th
e
p
o
wer
d
ef
icit.
Un
d
e
r
th
is
s
ce
n
ar
io
,
th
e
c
o
n
v
e
r
ter
o
p
er
ates in
Mo
d
es 3
an
d
4
to
en
s
u
r
e
u
n
in
ter
r
u
p
te
d
p
o
w
er
d
eliv
er
y
.
-
Scen
ar
io
4
:
>
0
an
d
>
0
.
I
n
th
e
ab
s
en
ce
o
f
r
en
ewa
b
le
en
er
g
y
g
en
e
r
atio
n
,
th
e
b
atter
y
b
ec
o
m
es
th
e
s
o
le
en
er
g
y
s
o
u
r
ce
s
u
p
p
ly
i
n
g
th
e
DC
lin
k
.
I
n
th
is
o
p
e
r
atin
g
co
n
d
itio
n
,
o
n
ly
M
o
d
e
4
is
ac
tiv
e.
T
h
e
DC
b
u
s
v
o
ltag
e
co
n
tr
o
l
l
o
o
p
g
e
n
er
ates
th
e
r
ef
e
r
en
ce
c
u
r
r
en
t
f
o
r
th
e
i
n
n
er
c
u
r
r
en
t
c
o
n
tr
o
l
lo
o
p
,
wh
ic
h
s
u
b
s
eq
u
en
tly
d
eter
m
in
es
th
e
d
u
ty
r
atio
D
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
.
B
ased
o
n
th
e
d
u
ty
r
atio
an
d
th
e
DC
V
o
l
t
ag
e
S
o
u
r
c
e
V
d
c
,
P
d
c
V
pv
I
pv
MPP
T
/V
o
l
t
ag
e
Mo
d
e
Co
n
tr
o
l
Pul
s
e
s
Vo
DC G
ri
d
Ba
t
t
e
r
y
Bid
i
r
e
c
t
i
o
n
al
Buck
Bo
o
s
t
Co
n
v
e
rt
e
r
P
V
P
A
N
E
L
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1859
-
1
8
7
2
1862
av
ailab
ilit
y
o
f
s
o
lar
ir
r
ad
iatio
n
,
th
e
co
r
r
esp
o
n
d
in
g
d
elay
an
g
le
is
g
en
er
ated
to
r
eg
u
late
p
o
wer
f
lo
w.
Fu
r
th
er
m
o
r
e
,
a
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
-
b
ased
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
i
n
g
(
M
PP
T
)
alg
o
r
ith
m
is
em
p
lo
y
ed
to
en
s
u
r
e
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
f
r
o
m
th
e
s
o
lar
s
o
u
r
ce
u
n
d
er
v
ar
y
i
n
g
ir
r
a
d
i
atio
n
co
n
d
itio
n
s
.
Fig
u
r
e
3
.
C
o
n
tr
o
l stra
teg
y
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
v
er
te
r
3.
M
AXI
M
U
M
P
O
WE
R
P
O
I
N
T
T
RA
CK
I
NG
T
h
is
s
ec
tio
n
d
escr
ib
es
th
e
M
PP
T
an
d
co
n
tr
o
l
f
r
a
m
ewo
r
k
i
m
p
lem
en
ted
i
n
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
s
y
s
tem
to
ac
h
iev
e
ef
f
icien
t
p
o
wer
ex
tr
ac
tio
n
an
d
s
tab
le
o
p
er
atio
n
.
T
h
e
P&
O
alg
o
r
ith
m
ad
o
p
ted
f
o
r
MPPT
is
illu
s
tr
ated
th
r
o
u
g
h
th
e
f
lo
wch
ar
t
s
h
o
wn
in
Fig
u
r
e
4
.
T
h
e
d
e
s
ig
n
o
f
th
e
p
ar
a
m
eter
s
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
,
th
e
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
co
n
tr
o
lled
b
o
o
s
t
co
n
v
er
ter
,
an
d
th
e
PI
co
n
tr
o
ller
s
em
p
l
o
y
ed
f
o
r
v
o
ltag
e
a
n
d
c
u
r
r
en
t
r
eg
u
latio
n
a
r
e
p
r
esen
ted
an
d
d
is
cu
s
s
ed
as f
o
llo
ws:
3
.
1
.
Desig
n t
he
pa
ra
m
et
er
s
o
f
t
he
pro
po
s
ed
co
nv
er
t
er
T
h
e
d
esig
n
o
f
th
e
f
o
u
r
-
p
o
r
t
b
i
d
ir
ec
tio
n
al
b
u
ck
–
b
o
o
s
t
c
o
n
v
er
ter
is
ca
r
r
ied
o
u
t
t
o
m
ee
t
b
o
th
p
o
r
t
-
lev
el
v
o
ltag
e
r
e
q
u
ir
em
e
n
ts
an
d
th
e
DC
b
u
s
/lo
ad
r
ef
e
r
en
ce
v
o
ltag
e
o
f
th
e
s
y
s
tem
[
2
8
]
.
T
h
e
co
n
v
er
ter
in
p
u
t
v
o
ltag
e
is
V
in
=
36
,
an
d
th
e
p
o
r
t
-
le
v
el
o
u
tp
u
t v
o
ltag
e
is
V
o
=
90
.
T
h
e
s
witch
in
g
f
r
e
q
u
en
cy
is
s
et
to
=
50
,
an
d
th
e
r
ated
o
u
tp
u
t
p
o
wer
i
s
=
100
T
h
e
s
y
s
tem
-
lev
el
DC
b
u
s
v
o
ltag
e,
m
ain
tain
ed
b
y
th
e
PID
co
n
tr
o
ller
,
is
d
ef
in
ed
as
V
∗
=
180
.
I
t
s
h
o
u
ld
b
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n
o
ted
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at
Vd
c*
is
th
e
s
y
s
tem
-
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el
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e
r
en
ce
v
o
ltag
e,
wh
er
ea
s
Vo
is
u
tili
ze
d
f
o
r
p
o
r
t
-
lev
el
co
m
p
u
tatio
n
s
.
T
h
e
d
u
ty
r
atio
f
o
r
th
e
b
u
ck
-
b
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o
s
t c
o
n
v
er
ter
is
ca
lcu
lated
as (
1
)
.
=
(
−
)
(
1
)
T
h
e
i
n
d
u
c
t
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r
i
s
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e
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i
g
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t
o
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m
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r
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r
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t
,
w
h
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c
h
i
s
c
h
o
s
e
n
a
s
2
0
%
o
f
t
h
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o
u
t
p
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t
c
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t
,
a
s
g
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v
e
n
i
n
(
2
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.
Δ
=
0
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2
×
(
)
×
0
(
2
)
W
h
er
e
th
e
o
u
tp
u
t
cu
r
r
e
n
t
0
is
ass
u
m
ed
to
b
e
0
.
5
6
A
(
co
r
r
e
s
p
o
n
d
in
g
to
1
0
0
W
at
th
e
p
o
r
t
-
lev
el
v
o
ltag
e)
.
Usi
n
g
th
is
r
ip
p
le
cu
r
r
e
n
t,
th
e
i
n
d
u
cto
r
v
alu
e
is
co
m
p
u
ted
as (
3
)
.
I
n
d
u
cto
r
=
(
−
Δ
−
)
(
3
)
T
h
e
o
u
t
p
u
t
c
a
p
a
c
i
t
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r
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s
e
l
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ct
ed
t
o
l
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m
i
t
v
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lt
a
g
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p
p
l
e
,
w
h
i
c
h
i
s
s
e
t
t
o
2
%
o
f
t
h
e
DC
b
u
s
r
e
f
er
e
n
c
e
v
o
l
t
a
g
e
(
4
)
.
Δ
=
0
.
02
×
V
∗
(
4
)
T
h
e
r
eq
u
ir
ed
ca
p
ac
ita
n
ce
is
th
en
ca
lcu
lated
as (
5
)
.
=
Δ
8
×
×
Δ
=
0
.
28
8
.
50
×
10
3
×
3
.
6
≈
3
.
375
(
5
)
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
Desig
n
a
n
d
s
imu
la
tio
n
o
f a
fo
u
r
-
p
o
r
t b
u
ck
-
b
o
o
s
t c
o
n
ve
r
ter in
teg
r
a
ted
w
ith
…
(
M.
S
.
Mu
ku
n
d
a
s
w
a
my
)
1863
T
h
e
d
esig
n
e
d
p
ar
am
eter
s
o
f
th
e
co
n
v
er
ter
ar
e
s
u
m
m
ar
ize
d
as
f
o
llo
ws:
d
u
ty
r
atio
=
0
.
6
,
in
d
u
cto
r
=
0
.
54
,
in
d
u
cto
r
r
ip
p
le
c
u
r
r
e
n
t
Δ
=
0
.
28
,
o
u
tp
u
t
ca
p
ac
ito
r
=
3
.
375
μ
F
,
ca
p
ac
ito
r
r
i
p
p
le
v
o
ltag
e
Δ
=
3
.
6
,
an
d
s
y
s
tem
-
lev
el
DC
b
u
s
r
ef
er
en
ce
v
o
ltag
e
V
∗
=
180
.
T
h
is
d
esig
n
en
s
u
r
es
th
e
c
o
n
v
e
r
ter
m
ee
ts
b
o
th
co
m
p
o
n
en
t
-
le
v
el
an
d
s
y
s
tem
-
le
v
el
p
e
r
f
o
r
m
an
ce
r
eq
u
i
r
em
en
ts
,
p
r
o
v
i
d
in
g
s
tab
le
an
d
ef
f
icien
t
o
p
er
atio
n
u
n
d
e
r
v
ar
y
in
g
l
o
ad
a
n
d
r
en
ewa
b
le
s
o
u
r
ce
c
o
n
d
itio
n
s
.
3
.
2
.
P
r
o
po
rt
io
na
l
-
inte
g
ra
l
co
ntr
o
lled wit
h a
bo
o
s
t
co
nv
er
t
er
I
n
th
is
s
y
s
tem
,
g
atin
g
p
u
ls
es
f
o
r
th
e
b
o
o
s
t
co
n
v
er
ter
s
witch
Q
ar
e
g
en
e
r
ated
u
s
in
g
a
p
r
o
p
o
r
tio
n
al
–
in
teg
r
al
(
PI)
co
n
tr
o
ller
[
2
9
]
.
T
h
e
v
o
ltag
e
tr
ac
k
in
g
r
elatio
n
s
h
ip
is
em
p
lo
y
ed
with
in
th
e
v
o
lt
ag
e
co
n
tr
o
l
l
o
o
p
to
r
eg
u
late
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
,
as
illu
s
tr
ated
in
Fig
u
r
e
4
.
T
h
e
r
ef
er
e
n
ce
DC
v
o
ltag
e
(
∗
)
s
er
v
es
as
th
e
d
esire
d
s
etp
o
in
t
f
o
r
th
e
co
n
v
er
ter
o
u
tp
u
t.
T
h
e
d
if
f
er
en
ce
b
etwe
en
th
is
r
ef
er
e
n
ce
v
o
ltag
e
an
d
th
e
ac
tu
al
o
u
tp
u
t
v
o
ltag
e
g
e
n
er
ates
th
e
v
o
ltag
e
er
r
o
r
,
w
h
ich
is
th
en
p
r
o
ce
s
s
ed
b
y
t
h
e
PI
co
n
tr
o
ller
to
p
r
o
d
u
ce
th
e
r
e
f
er
en
ce
c
o
n
tr
o
l
v
o
ltag
e,
as sh
o
wn
in
(
6
)
.
∗
=
×
ω
∗
(
6
)
T
h
e
v
o
ltag
e
er
r
o
r
is
m
ath
em
atica
lly
d
ef
in
ed
as
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
r
ef
er
e
n
ce
an
d
m
ea
s
u
r
ed
DC
v
o
ltag
es
(
)
.
T
h
is
er
r
o
r
s
ig
n
al
is
co
n
tin
u
o
u
s
ly
ev
alu
ated
to
d
eter
m
in
e
th
e
c
o
r
r
ec
tiv
e
ac
t
io
n
r
e
q
u
ir
ed
b
y
t
h
e
co
n
tr
o
ller
.
T
h
e
v
o
ltag
e
er
r
o
r
(
)
eq
u
atio
n
is
g
iv
en
as (
7
)
.
=
∗
−
(
7
)
Fig
u
r
e
4
.
Flo
wch
ar
t
f
o
r
t
h
e
P&
O
alg
o
r
ith
m
o
f
MPPT
T
h
e
PI
c
o
n
tr
o
ller
p
r
o
ce
s
s
es
th
e
v
o
ltag
e
er
r
o
r
to
g
e
n
er
ate
th
e
r
ef
er
e
n
ce
-
co
n
tr
o
lled
v
o
ltag
e
,
wh
ich
g
o
v
er
n
s
th
e
s
witch
in
g
b
eh
av
io
r
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
.
T
h
e
d
is
cr
ete
-
tim
e
PI
co
n
tr
o
l
la
w
in
co
r
p
o
r
ates
b
o
t
h
p
r
o
p
o
r
tio
n
al
an
d
in
te
g
r
al
ac
tio
n
s
to
r
ed
u
ce
s
tead
y
-
s
tate
er
r
o
r
an
d
im
p
r
o
v
e
v
o
ltag
e
r
e
g
u
l
atio
n
.
T
h
e
co
n
tr
o
ller
eq
u
atio
n
s
ar
e
e
x
p
r
ess
ed
as (
8
)
an
d
(
9
)
:
(
)
=
(
−
1
)
+
(
8
)
{
(
)
−
(
−
1
)
}
+
(
)
(
9
)
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1859
-
1
8
7
2
1864
Her
e,
k
d
e
n
o
tes
th
e
c
u
r
r
en
t
s
am
p
lin
g
in
s
tan
t,
wh
ile
K
P
an
d
K
I
r
ep
r
esen
ts
th
e
p
r
o
p
o
r
tio
n
al
an
d
i
n
teg
r
al
g
ain
s
,
r
esp
ec
tiv
ely
.
T
h
e
o
u
t
p
u
t o
f
th
e
PI
co
n
tr
o
ller
is
co
m
p
ar
ed
wit
h
a
h
ig
h
-
f
r
eq
u
e
n
cy
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
al
M
C
to
g
en
er
ate
th
e
g
atin
g
p
u
ls
es
f
o
r
th
e
b
o
o
s
t
co
n
v
er
ter
s
witch
Q
.
W
h
en
<
,
th
e
s
witch
is
tu
r
n
e
d
ON
(
p
u
ls
e
HI
GH)
,
an
d
w
h
en
≥
,
th
e
s
witch
is
tu
r
n
e
d
OFF
(
p
u
ls
e
L
OW
)
,
th
er
e
b
y
r
eg
u
latin
g
th
e
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e
ef
f
ec
tiv
el
y
.
3
.
3
.
P
I
c
o
ntr
o
llers
Pro
p
o
r
ti
o
n
al
-
i
n
t
eg
r
al
(
PI
)
c
o
n
t
r
o
lle
r
s
f
i
n
d
b
r
o
a
d
u
s
e
i
n
co
n
t
r
o
l
s
y
s
te
m
s
i
n
w
h
i
c
h
v
e
r
y
f
as
t
d
y
n
am
ic
r
es
p
o
n
s
e
is
n
o
t
a
k
e
y
c
o
n
s
id
er
ati
o
n
.
T
h
ese
c
o
n
t
r
o
lle
r
s
ar
e
a
ls
o
t
h
e
m
o
s
t
a
p
p
r
o
p
r
iat
e
w
h
e
n
d
ea
li
n
g
w
it
h
s
y
s
te
m
s
th
a
t
h
a
v
e
d
is
tu
r
b
a
n
c
es,
n
o
is
e,
an
d
p
a
r
a
m
e
te
r
c
h
an
g
es
.
A
ls
o
,
PI
c
o
n
t
r
o
lle
r
s
ar
e
e
f
f
e
cti
v
e
i
n
s
y
s
te
m
s
w
h
er
e
t
h
e
r
e
is
a
l
ar
g
e
s
t
o
r
a
g
e
o
f
e
n
e
r
g
y
,
li
k
e
i
n
d
u
ct
o
r
s
an
d
c
a
p
ac
i
to
r
s
,
an
d
d
y
n
a
m
i
c
b
e
h
a
v
i
o
r
is
in
h
e
r
en
tl
y
s
lo
we
r
.
T
h
e
o
m
is
s
io
n
o
f
th
e
d
er
iv
ati
v
e
(
D)
ter
m
r
em
o
v
es
th
e
co
m
p
lex
ity
o
f
th
e
co
n
tr
o
ller
s
tr
u
ctu
r
e
an
d
en
h
an
ce
s
r
o
b
u
s
tn
ess
in
n
o
is
y
en
v
ir
o
n
m
en
ts
.
W
ith
th
ese
s
y
s
t
em
s
,
th
e
n
ee
d
f
o
r
r
ap
id
tr
an
s
i
en
t
r
esp
o
n
s
e
is
n
o
t
alwa
y
s
n
ec
ess
ar
y
,
an
d
to
ler
ab
le
d
elay
s
o
f
s
y
s
tem
r
esp
o
n
s
e
ca
n
b
e
ac
ce
p
ted
.
C
o
n
s
eq
u
en
tl
y
,
PI
co
n
tr
o
ller
s
ar
e
o
f
ten
u
s
ed
in
p
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
s
in
s
tead
y
o
p
er
a
tin
g
o
r
s
lo
wly
v
ar
y
in
g
c
o
n
d
i
tio
n
s
.
T
h
e
p
r
im
a
r
y
b
en
ef
it
o
f
a
PI
co
n
tr
o
ller
is
th
at
it
allo
ws
th
e
r
em
o
v
al
o
f
s
tead
y
-
s
tate
er
r
o
r
,
wh
ich
ca
n
n
o
t
b
e
co
m
p
letely
r
em
o
v
ed
with
a
p
r
o
p
o
r
tio
n
al
co
n
tr
o
ller
alo
n
e.
T
h
is
,
h
o
wev
er
,
co
m
es
at
th
e
e
x
p
en
s
e
o
f
lo
wer
r
esp
o
n
s
e
s
p
ee
d
an
d
p
o
s
s
ib
le
s
tab
ilit
y
co
n
s
tr
ain
ts
.
Sin
ce
it
lack
s
p
r
ed
ict
iv
e
ca
p
ab
ilit
y
,
PI
c
o
n
tr
o
ller
s
ca
n
n
o
t
s
u
p
p
r
ess
o
s
cillatio
n
s
,
n
o
r
ca
n
th
e
y
r
e
d
u
ce
th
e
r
is
e
tim
e
th
at
ca
n
ca
u
s
e
an
o
v
er
s
h
o
o
t a
b
o
u
t th
e
r
ef
er
en
ce
s
et
p
o
in
t.
T
h
e
o
u
tp
u
t
o
f
t
h
e
p
r
o
p
o
r
tio
n
a
l
co
n
tr
o
ller
is
d
ir
ec
tly
r
elate
d
to
th
e
in
s
tan
tan
eo
u
s
er
r
o
r
s
ig
n
al
an
d
is
ex
p
r
ess
ed
as (
1
0
)
.
(
P)
C
o
n
tr
o
ller
o
u
tp
u
t
=
(
)
×
100
/
(
)
(
1
0
)
W
h
er
e,
(
)
is
th
e
in
s
tan
tan
eo
u
s
v
o
ltag
e
o
r
cu
r
r
e
n
t
er
r
o
r
(
i.e
.
,
th
e
d
if
f
er
e
n
ce
b
etwe
en
th
e
r
ef
er
e
n
ce
an
d
m
ea
s
u
r
ed
s
ig
n
al)
a
n
d
is
th
e
p
r
o
p
o
r
tio
n
al
g
ain
th
at
s
ca
les th
e
co
n
tr
o
ller
r
esp
o
n
s
e
to
th
e
e
r
r
o
r
m
a
g
n
itu
d
e.
T
h
e
in
teg
r
al
c
o
n
tr
o
ller
o
u
tp
u
t
is
ex
p
r
ess
ed
as (
1
1
)
.
C
o
n
tr
o
ller
o
u
tp
u
t =
1
C
r
i
t
i
cal
t
i
m
e
∗
(
cr
itical
o
f
e
(
t
)
)
(
1
1
)
Her
e,
th
e
in
teg
r
al
ter
m
ac
c
u
m
u
lates
th
e
er
r
o
r
o
v
e
r
tim
e,
c
o
r
r
ec
tin
g
s
tead
y
-
s
tate
d
ev
iatio
n
s
.
T
h
e
cr
itical
tim
e
d
eter
m
in
es
th
e
s
p
ee
d
o
f
th
e
in
teg
r
al
ac
tio
n
,
co
n
tr
o
llin
g
h
o
w
q
u
ick
ly
th
e
ac
cu
m
u
lated
e
r
r
o
r
in
f
lu
e
n
ce
s
th
e
co
n
tr
o
ller
o
u
tp
u
t.
T
o
g
eth
er
,
t
h
ese
ac
tio
n
s
en
ab
le
th
e
PI
c
o
n
tr
o
ller
to
m
ain
tain
s
tab
le
DC
b
u
s
v
o
ltag
e
o
r
o
u
tp
u
t
cu
r
r
en
t
u
n
d
er
v
ar
y
in
g
o
p
er
atin
g
co
n
d
itio
n
s
.
4.
SI
M
UL
A
T
I
O
N
M
O
D
E
L
O
F
P
RO
P
O
SE
D
SYS
T
E
M
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
'
s
im
itati
o
n
m
eth
o
d
is
p
o
r
t
r
ay
ed
in
Fig
u
r
e
5
.
I
n
th
is
s
etu
p
,
th
e
DC
s
o
u
r
ce
an
d
th
e
p
h
o
to
v
o
ltaic
(
PV)
p
an
el
ar
e
co
n
n
ec
te
d
to
th
e
s
y
s
tem
f
o
r
t
=
1
.
5
s
b
ef
o
r
e
b
ein
g
d
is
co
n
n
ec
ted
.
Fro
m
t=0
to
t
=
1
s
,
th
e
PV
p
r
o
v
i
d
es
p
o
wer
to
th
e
lo
a
d
at
a
n
ir
r
a
d
iatio
n
lev
el
o
f
1
0
0
0
W
/m
2
,
w
h
ich
is
lo
wer
ed
t
o
4
0
0
W
/m
2
b
etwe
en
t
=
1
s
an
d
t
=
1
.
5
s
b
ef
o
r
e
d
is
co
n
n
ec
ti
o
n
.
PV
p
o
wer
is
u
s
ed
to
f
ir
s
t
ch
ar
g
e
th
e
b
atter
y
.
T
h
e
b
atter
y
en
ter
s
d
is
ch
ar
g
e
m
o
d
e
an
d
g
iv
es
p
o
wer
to
th
e
lo
ad
at
t
=
1
.
5
s
af
ter
th
e
PV
s
o
u
r
ce
is
cu
t
o
f
f
.
T
h
e
MPPT
co
n
tr
o
l
ap
p
r
o
ac
h
p
r
o
d
u
ce
s
g
atin
g
p
u
ls
es
f
o
r
th
e
co
n
v
er
ter
d
u
r
i
n
g
t
h
e
PV
-
co
n
n
ec
ted
in
ter
v
al.
Fo
llo
win
g
PV
d
is
co
n
n
ec
tio
n
,
th
e
co
n
v
er
ter
r
ec
ei
v
es
th
e
n
ec
ess
ar
y
p
u
ls
es
f
r
o
m
t
=
1
.
5
to
t
=
2
s
u
s
in
g
a
s
o
lo
co
n
tr
o
l sch
em
e.
Du
r
in
g
o
p
er
atio
n
,
th
e
s
ix
s
witch
es
(
S1
-
S6
)
co
o
r
d
in
ate
t
h
e
p
o
wer
f
lo
w
b
etwe
en
th
e
PV
p
an
el,
au
x
iliar
y
DC
s
o
u
r
ce
,
b
atter
y
,
an
d
lo
ad
.
W
h
en
S1
is
ON,
en
er
g
y
f
r
o
m
th
e
PV
p
an
el
is
s
to
r
e
d
in
th
e
in
d
u
cto
r
,
en
ab
lin
g
th
e
b
u
ck
o
p
er
atio
n
a
n
d
ch
ar
g
in
g
th
e
b
atter
y
if
its
v
o
ltag
e
is
b
elo
w
th
e
s
u
p
p
ly
v
o
ltag
e.
W
h
en
S4
is
ON,
th
e
s
to
r
ed
en
er
g
y
in
th
e
in
d
u
cto
r
is
r
elea
s
ed
,
ac
tin
g
as
a
s
o
u
r
ce
an
d
p
r
o
v
id
in
g
f
ee
d
b
ac
k
to
th
e
b
atter
y
th
r
o
u
g
h
th
e
b
o
d
y
d
io
d
e
wh
ile
s
im
u
ltan
eo
u
s
ly
s
u
p
p
ly
in
g
th
e
lo
ad
.
I
f
S1
is
OFF,
S3
is
O
N,
an
d
S4
is
OFF,
en
er
g
y
f
lo
ws
f
r
o
m
th
e
PV
p
an
el
an
d
in
d
u
cto
r
to
th
e
b
atter
y
,
wh
ile
th
e
tr
an
s
f
o
r
m
er
s
ec
o
n
d
ar
y
is
en
er
g
ized
,
tr
an
s
f
er
r
in
g
p
o
wer
to
th
e
lo
ad
.
S2
c
o
n
tr
o
ls
th
e
au
x
iliar
y
DC
s
o
u
r
ce
,
allo
win
g
it
to
s
u
p
p
ly
p
o
wer
wh
en
th
e
PV
s
o
u
r
ce
is
in
s
u
f
f
icien
t
,
an
d
S5
an
d
S6
m
a
n
ag
e
b
id
ir
ec
tio
n
al
o
p
er
atio
n
with
th
e
tr
an
s
f
o
r
m
er
,
en
s
u
r
in
g
en
er
g
y
ca
n
f
lo
w
f
r
o
m
th
e
c
o
n
v
e
r
ter
to
th
e
lo
ad
o
r
f
r
o
m
th
e
lo
ad
b
ac
k
to
th
e
b
atter
y
as
n
ee
d
ed
.
T
h
is
co
o
r
d
in
ated
s
witch
in
g
s
eq
u
en
ce
en
s
u
r
es
e
f
f
icien
t
en
er
g
y
tr
an
s
f
er
f
r
o
m
all
s
o
u
r
ce
s
to
th
e
b
atter
y
an
d
lo
ad
,
m
ain
tain
in
g
p
r
o
p
er
b
u
c
k
-
b
o
o
s
t o
p
er
atio
n
a
n
d
co
n
ti
n
u
o
u
s
p
o
wer
d
eliv
er
y
u
n
d
er
v
ar
y
i
n
g
o
p
er
atin
g
c
o
n
d
i
tio
n
s
.
I
n
th
e
f
u
ll
-
b
r
id
g
e
h
alf
-
co
n
tr
o
lled
co
n
v
er
ter
,
a
v
o
ltag
e
-
c
o
n
tr
o
lled
s
tr
ateg
y
is
em
p
lo
y
e
d
.
T
h
e
r
ef
er
e
n
ce
DC
v
o
ltag
e
is
s
et
to
1
8
0
V
an
d
is
co
m
p
ar
e
d
with
th
e
m
ea
s
u
r
ed
lo
ad
v
o
ltag
e.
B
o
th
s
ig
n
als
ar
e
co
n
v
er
ted
t
o
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
Desig
n
a
n
d
s
imu
la
tio
n
o
f a
fo
u
r
-
p
o
r
t b
u
ck
-
b
o
o
s
t c
o
n
ve
r
ter in
teg
r
a
ted
w
ith
…
(
M.
S
.
Mu
ku
n
d
a
s
w
a
my
)
1865
p
er
-
u
n
it
v
alu
es
an
d
a
p
p
lied
t
o
th
e
PID
c
o
n
tr
o
ller
.
B
ased
o
n
th
e
r
esu
ltin
g
v
o
ltag
e
er
r
o
r
,
th
e
PID
c
o
n
tr
o
ller
g
en
er
ates
th
e
d
u
ty
r
atio
,
wh
ic
h
is
s
u
p
p
lied
to
th
e
p
u
ls
e
g
e
n
e
r
ato
r
to
p
r
o
d
u
ce
t
h
e
g
atin
g
s
ig
n
als.
A
v
o
ltag
e
co
n
tr
o
l
lo
o
p
is
u
s
ed
to
lim
it
th
e
b
atter
y
v
o
ltag
e.
W
h
en
th
e
b
atter
y
v
o
ltag
e
e
x
ce
ed
s
th
e
r
e
f
er
en
ce
v
alu
e
,
th
e
lo
ad
-
b
ased
PID
co
n
tr
o
ller
r
eg
u
lates
th
e
d
u
ty
r
atio
with
in
p
r
ed
ef
in
ed
u
p
p
er
an
d
lo
wer
li
m
its
.
I
f
t
h
e
b
atter
y
v
o
ltag
e
is
b
elo
w
th
e
r
ef
er
en
c
e
v
alu
e,
th
e
d
u
ty
r
atio
is
ad
ju
s
ted
ac
co
r
d
in
g
ly
to
m
ain
tain
v
o
ltag
e
r
eg
u
latio
n
.
T
h
is
ap
p
r
o
ac
h
f
o
r
m
s
a
d
u
al
co
n
d
itio
n
al
co
n
tr
o
l
l
o
o
p
in
wh
ich
th
e
d
u
ty
r
atio
s
elec
tio
n
d
e
p
en
d
s
o
n
th
e
o
p
er
atin
g
v
o
ltag
e
c
o
n
d
itio
n
s
.
T
h
e
d
u
ty
r
atio
lim
its
ar
e
d
ef
i
n
ed
b
ased
o
n
th
e
b
atter
y
o
p
e
r
atin
g
v
o
ltag
e
r
an
g
e,
with
a
lo
wer
lim
it
co
r
r
esp
o
n
d
in
g
to
2
4
V
an
d
an
u
p
p
e
r
lim
it
co
r
r
esp
o
n
d
i
n
g
to
3
8
V.
I
n
ad
d
itio
n
,
a
b
atter
y
-
b
a
s
ed
cu
r
r
en
t
c
o
n
tr
o
l
lo
o
p
is
im
p
lem
en
ted
to
g
e
n
er
ate
th
e
r
ef
er
en
ce
cu
r
r
en
t.
T
h
e
r
ef
er
en
ce
b
atter
y
cu
r
r
e
n
t
is
co
m
p
ar
ed
with
th
e
m
ea
s
u
r
ed
b
atter
y
c
u
r
r
en
t,
a
n
d
th
e
r
esu
ltin
g
er
r
o
r
is
p
r
o
ce
s
s
ed
b
y
a
PID
co
n
tr
o
ller
to
g
e
n
er
ate
a
d
u
ty
r
atio
.
T
h
is
d
u
ty
r
atio
is
th
e
n
c
o
m
p
ar
ed
with
th
e
d
u
t
y
r
atio
o
b
tain
e
d
f
r
o
m
th
e
MPPT
alg
o
r
it
h
m
,
a
n
d
th
e
m
i
n
im
u
m
o
f
th
e
two
is
s
elec
ted
to
en
s
u
r
e
s
af
e
an
d
s
tab
le
o
p
er
atio
n
.
T
h
e
s
elec
ted
d
u
ty
r
atio
is
f
i
n
ally
a
p
p
lied
to
th
e
p
u
ls
e
g
en
er
ato
r
to
p
r
o
d
u
ce
th
e
g
ati
n
g
s
ig
n
als
f
o
r
th
e
c
o
n
v
e
r
ter
s
witch
es.
T
h
e
d
u
ty
r
atio
f
o
r
So
u
r
ce
1
is
s
h
o
wn
in
Fig
u
r
e
8
,
wh
ile
th
e
d
u
ty
r
ati
o
at
th
e
s
ec
o
n
d
ar
y
s
id
e
o
f
S
o
u
r
ce
2
,
wh
e
r
e
th
e
s
ec
o
n
d
ar
y
v
o
ltag
e
v
ar
ies,
is
p
r
esen
ted
in
Fig
u
r
e
9
.
Fig
u
r
e
5
.
Simu
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
4
.
1
.
Ca
lcula
t
ed
t
he
RL
lo
a
d
v
a
lues
f
o
r
diff
er
ent
po
wer
f
a
ct
o
rs
T
h
e
R
L
lo
ad
p
ar
am
eter
s
we
r
e
ca
lcu
lated
f
o
r
d
if
f
er
e
n
t
p
o
wer
f
ac
to
r
s
ce
n
ar
io
s
to
ev
alu
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th
e
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er
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m
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itio
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h
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id
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ctiv
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PP
P
an
d
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Q
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wh
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eter
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iv
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esis
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ce
R
a
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o
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th
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ad
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h
e
v
o
ltag
e
ac
r
o
s
s
t
h
e
lo
ad
is
ass
u
m
ed
to
b
e
co
n
s
t
an
t
at
th
e
s
y
s
tem
n
o
m
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al
v
alu
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V
,
an
d
th
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u
p
p
ly
f
r
eq
u
e
n
cy
is
f
.
T
h
e
f
o
r
m
u
las u
s
ed
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o
r
th
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lc
u
latio
n
s
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g
iv
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(
1
2
)
a
n
d
(
1
3
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.
(
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(
1
2
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(
)
=
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∗
2
∗
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1
3
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-
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ase
(
a)
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ac
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r
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0
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9
Fo
r
an
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tiv
e
p
o
wer
o
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an
d
a
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ctiv
e
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th
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eq
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iv
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n
t
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esis
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ce
an
d
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d
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ctan
ce
ar
e
ca
lcu
lated
u
s
in
g
th
e
a
b
o
v
e
ex
p
r
ess
io
n
s
.
T
h
e
r
esu
ltin
g
v
alu
es
ar
e:
=
7
.
2
Ω
,
=
0
.
2
T
h
is
co
n
f
ig
u
r
atio
n
r
e
p
r
esen
ts
a
p
r
ed
o
m
in
an
tly
r
esis
tiv
e
lo
ad
with
m
in
im
al
r
ea
ctiv
e
co
m
p
o
n
en
t.
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1859
-
1
8
7
2
1866
-
C
ase
(
b
)
: Po
wer
f
ac
to
r
=
0
.
8
Fo
r
a
lo
ad
with
=
4000
an
d
=
1000
,
th
e
ca
lc
u
lated
r
esis
tan
ce
an
d
in
d
u
ctan
ce
ar
e:
=
8
.
1
Ω
,
=
0
.
1
I
n
th
is
s
ce
n
a
r
io
,
t
h
e
r
ea
ctiv
e
c
o
m
p
o
n
en
t
is
h
ig
h
er
th
a
n
in
C
ase
(
a)
,
r
esu
ltin
g
i
n
a
lo
wer
in
d
u
ctan
ce
to
m
ain
tai
n
th
e
r
eq
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ase
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to
r
=
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7
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r
a
m
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r
e
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ea
ctiv
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with
=
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an
d
=
1500
,
th
e
co
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r
esp
o
n
d
in
g
lo
ad
p
ar
am
eter
s
ar
e:
=
9
.
26
Ω
,
=
0
.
069
T
h
is
ca
s
e
r
ep
r
esen
ts
a
h
i
g
h
ly
in
d
u
ctiv
e
lo
ad
,
wh
ich
is
im
p
o
r
tan
t
f
o
r
e
v
alu
atin
g
co
n
v
er
te
r
p
er
f
o
r
m
an
ce
u
n
d
er
lo
w
p
o
wer
f
ac
to
r
co
n
d
itio
n
s
.
T
h
ese
ca
lcu
latio
n
s
p
r
o
v
id
e
a
b
asis
f
o
r
s
im
u
latin
g
a
n
d
a
n
al
y
zin
g
th
e
d
y
n
am
ic
an
d
s
tead
y
-
s
tate
b
eh
a
v
io
r
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
v
er
ter
with
d
i
f
f
er
en
t
lo
ad
ch
ar
ac
ter
is
tics
.
T
h
ey
e
n
s
u
r
e
t
h
at
b
o
th
r
esis
tiv
e
an
d
in
d
u
ct
iv
e
e
f
f
ec
ts
ar
e
p
r
o
p
er
ly
co
n
s
id
er
e
d
,
en
a
b
lin
g
ac
cu
r
ate
ass
ess
m
en
t
o
f
v
o
ltag
e
r
eg
u
latio
n
,
cu
r
r
en
t sh
ar
i
n
g
,
a
n
d
ef
f
icien
cy
u
n
d
er
r
ea
lis
tic
o
p
er
atin
g
c
o
n
d
itio
n
s
.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
eg
m
en
t
d
em
o
n
s
tr
ates
t
h
e
o
u
tp
u
t
r
esp
o
n
s
e
o
f
th
e
PID
-
co
n
tr
o
lled
b
i
d
i
r
ec
tio
n
al
b
u
ck
–
b
o
o
s
t
co
n
v
er
ter
(
B
B
C
)
.
T
h
e
B
B
C
o
p
er
ates
in
two
m
o
d
es,
n
am
ely
b
u
ck
m
o
d
e
an
d
b
o
o
s
t
m
o
d
e
.
T
h
e
ex
p
er
im
en
ta
l
o
u
tco
m
es
ar
e
attain
ed
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
o
u
tp
u
t
r
esp
o
n
s
es
o
f
d
if
f
e
r
en
t
s
y
s
tem
m
o
d
els
ar
e
an
aly
ze
d
an
d
p
r
esen
te
d
b
elo
w.
Fig
u
r
e
6
p
r
esen
ts
th
e
lo
ad
v
o
ltag
e
an
d
cu
r
r
en
t
u
n
d
er
d
if
f
er
en
t
o
p
er
atin
g
m
o
d
es.
I
t
illu
s
tr
ates
th
e
v
o
ltag
e
r
esp
o
n
s
e
d
u
r
i
n
g
PV
p
o
wer
g
en
e
r
atio
n
at
v
ar
io
u
s
ir
r
ad
iatio
n
lev
els,
in
clu
d
i
n
g
b
o
t
h
b
atter
y
c
h
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
c
o
n
d
itio
n
s
.
T
h
e
v
o
ltag
e
wa
v
ef
o
r
m
s
ettles
at
ap
p
r
o
x
im
ately
0
.
0
4
1
5
s
,
r
ea
ch
in
g
a
s
tead
y
-
s
tate
v
alu
e
o
f
1
7
8
.
3
V.
T
h
e
co
r
r
esp
o
n
d
in
g
b
atter
y
c
h
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
p
e
r
f
o
r
m
an
ce
is
f
u
r
t
h
er
r
ep
r
esen
ted
b
y
th
e
s
tate
-
of
-
ch
ar
g
e
(
%S
o
C
)
wav
ef
o
r
m
s
.
Fig
u
r
e
7
d
is
p
lay
s
th
e
s
tate
o
f
ch
ar
g
e
(
So
C
)
c
o
r
r
esp
o
n
d
in
g
t
o
th
e
PV
-
g
en
e
r
ated
v
o
ltag
e
a
n
d
cu
r
r
en
t.
I
n
itially
,
wh
en
th
e
PV
s
y
s
te
m
g
en
er
ates
p
o
wer
,
th
e
b
atter
y
o
p
er
ates
in
ch
ar
g
in
g
m
o
d
e,
r
esu
ltin
g
in
an
in
cr
ea
s
e
in
th
e
%S
o
C
.
W
h
en
th
e
PV
s
o
u
r
ce
is
d
is
co
n
n
ec
ted
,
th
e
b
atter
y
b
eg
in
s
to
d
is
ch
ar
g
e,
lead
in
g
to
a
d
ec
r
ea
s
e
in
th
e
%S
o
C
.
T
h
e
ch
a
n
g
es
in
th
e
d
u
ty
r
atio
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
d
u
e
to
ch
a
n
g
es
in
ir
r
ad
iatio
n
o
f
t
h
e
PV
ar
e
p
r
o
v
id
e
d
in
Fig
u
r
e
8
.
PV
is
o
f
f
,
p
o
wer
to
b
o
th
b
atter
y
an
d
lo
ad
.
I
n
th
is
,
u
n
til
t
=
0
.
3
s
,
P
V
i
s
s
u
p
p
ly
in
g
p
o
wer
to
b
o
th
th
e
b
att
er
y
as
well
as
lo
ad
.
Af
ter
t
=
0
.
3
s
,
th
e
ir
r
ad
iatio
n
is
r
ed
u
ce
d
,
b
u
t
s
till
,
PV
is
p
r
o
v
id
in
g
a
s
u
p
p
ly
to
th
e
b
atter
y
as we
ll a
s
th
e
lo
ad
.
At
t
=
0
.
5
s
,
th
e
b
atter
y
s
tar
ts
to
d
is
ch
ar
g
e
.
T
h
e
p
o
wer
cu
r
v
es,
lik
e
I
n
p
u
t
p
o
wer
,
b
atter
y
p
o
wer
,
a
n
d
l
o
ad
p
o
wer
is
p
r
o
v
id
ed
i
n
Fig
u
r
e
9
,
th
e
p
o
wer
cu
r
v
es
o
f
b
atter
y
an
d
l
o
ad
.
I
n
th
is
in
itially
b
atter
y
was
ch
ar
g
in
g
with
b
atter
y
p
o
we
r
o
f
ar
o
u
n
d
3
5
0
W
,
an
d
at
t
=
0
.
5
s
,
th
e
b
atter
y
b
eg
an
to
d
is
ch
ar
g
e
an
d
p
r
o
v
id
e
en
er
g
y
to
th
e
lo
ad
.
T
h
e
lo
ad
is
ch
an
g
ed
f
r
o
m
2
k
W
to
5
k
W
al
o
n
g
with
th
e
s
o
u
r
ce
,
an
d
th
e
b
atter
y
o
f
2
4
V
is
r
ep
lace
d
with
4
8
V.
T
h
e
lo
ad
v
o
ltag
e
a
n
d
cu
r
r
en
t
wav
ef
o
r
m
s
ar
e
p
r
o
v
id
ed
in
Fig
u
r
e
1
0
.
Fig
u
r
e
1
0
g
i
v
es
th
e
d
is
cu
s
s
io
n
o
f
th
e
lo
ad
v
o
ltag
e
an
d
cu
r
r
en
t
d
ep
en
d
i
n
g
o
n
t
h
e
lo
ad
co
n
d
itio
n
.
T
h
e
lo
a
d
p
o
wer
is
v
a
r
ied
t
o
5
k
W
in
s
tead
o
f
2
k
W
,
an
d
th
e
b
atter
y
v
o
ltag
e
is
v
ar
ied
to
4
8
V
i
n
s
tead
o
f
2
4
V.
I
n
s
p
ite
o
f
th
ese
d
if
f
e
r
en
ce
s
,
th
e
lo
ad
v
o
ltag
e
is
r
eg
u
lated
v
er
y
well
in
r
elatio
n
to
th
e
r
ef
er
en
ce
v
alu
e
an
d
s
h
o
ws s
tr
o
n
g
d
y
n
a
m
ic
p
er
f
o
r
m
an
ce
.
T
h
e
r
esu
lts
o
f
th
e
an
aly
s
is
o
f
b
atter
y
v
o
ltag
e
an
d
cu
r
r
e
n
t
at
th
e
tim
e
o
f
ch
ar
g
e
an
d
d
is
ch
ar
g
e
ar
e
p
r
esen
ted
in
Fig
u
r
e
1
1
.
W
h
e
n
ch
ar
g
i
n
g
,
t
h
e
b
atter
y
v
o
lta
g
e
is
k
ep
t
with
in
th
e
s
p
ec
if
ied
o
p
er
ati
n
g
r
a
n
g
e
o
f
2
4
V
to
3
8
V
,
a
n
d
th
e
c
u
r
r
en
t
ch
an
g
es
g
r
ad
u
ally
wh
en
d
is
ch
ar
g
in
g
to
aid
th
e
lo
a
d
,
wh
ich
p
r
o
v
es
th
at
b
atter
y
o
p
er
atio
n
s
ar
e
s
af
e
an
d
s
tab
le.
T
h
e
a
n
aly
s
is
o
f
t
h
e
c
o
n
v
er
ter
ef
f
icien
c
y
wh
en
o
n
v
ar
io
u
s
lo
ad
s
ca
n
b
e
o
b
s
er
v
ed
in
Fig
u
r
e
1
2
.
T
h
e
d
ata
d
is
p
lay
s
th
at
th
e
ef
f
icien
c
y
is
h
ig
h
an
d
th
e
o
p
er
atin
g
r
an
g
e
is
lar
g
e
,
b
o
th
wh
en
ch
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
th
e
b
atter
y
.
Fig
u
r
e
1
3
s
h
o
ws
th
e
DC
-
lin
k
v
o
ltag
e
r
esp
o
n
s
e
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
W
ith
a
r
ef
e
r
en
c
e
DC
-
lin
k
v
o
ltag
e
o
f
1
8
0
V,
th
e
o
u
tp
u
t
v
o
ltag
e
r
ea
ch
es
ap
p
r
o
x
im
ately
1
9
5
V
u
n
d
er
s
tead
y
-
s
tate
co
n
d
itio
n
s
,
r
esu
ltin
g
in
a
1
5
V
s
tead
y
-
s
tate
er
r
o
r
.
T
h
is
r
esp
o
n
s
e
is
u
s
ed
to
ev
al
u
ate
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