I
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n J
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l En
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5
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.
67
~
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5
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40
.i
1
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pp
67
-
77
67
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a
2
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t
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with
m
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l
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h
a
rm
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.
S
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su
lt
s
in
d
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te
th
a
t
t
h
e
m
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h
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%
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rm
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to
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o
m
m
e
rc
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ti
o
n
s
,
th
e
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p
o
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d
d
e
s
ig
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e
n
h
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n
c
e
s
e
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y
wh
i
le
in
teg
ra
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n
g
k
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y
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o
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ts.
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d
d
it
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o
n
a
l
ly
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th
e
sy
ste
m
m
a
in
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s
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ffe
c
ti
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e
ss
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n
d
d
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o
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l
to
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s
e
n
e
rg
y
e
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m
a
k
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g
it
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v
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d
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e
ffe
c
ti
v
e
so
lu
ti
o
n
fo
r
PV
e
n
e
r
g
y
c
o
n
v
e
rsio
n
.
K
ey
w
o
r
d
s
:
E
f
f
icien
cy
Mic
r
o
in
v
er
ter
MPPT
Pu
r
e
wav
e
R
eg
u
lato
r
So
lar
p
an
el
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
W
alter
Nar
an
jo
L
o
u
r
id
o
E
n
g
in
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r
in
g
Sch
o
o
l,
Facu
lty
o
f
B
asic Scie
n
ce
s
an
d
E
n
g
in
ee
r
in
g
,
Un
iv
er
s
id
ad
d
e
lo
s
L
lan
o
s
Km
1
2
Via
Pu
er
to
L
o
p
ez
.
Ve
r
ed
a
B
ar
ce
lo
n
a,
Villav
icen
cio
,
C
o
lo
m
b
ia
E
m
ail: w
n
ar
an
jo
@
u
n
illan
o
s
.
e
d
u
.
co
1.
I
NT
RO
D
UCT
I
O
N
E
lectr
icity
is
f
u
n
d
am
en
tal
to
m
o
d
er
n
i
n
f
r
astru
ctu
r
e,
p
o
wer
i
n
g
in
d
u
s
tr
ies,
h
ea
lth
ca
r
e
,
ed
u
ca
tio
n
,
an
d
d
aily
life
.
A
r
eliab
le
en
er
g
y
s
u
p
p
ly
is
ess
en
tial
f
o
r
ec
o
n
o
m
i
c
g
r
o
wth
,
tech
n
o
lo
g
ical
ad
v
an
ce
m
en
t,
an
d
s
y
s
tem
s
tab
ilit
y
.
W
ith
o
u
t
it,
p
r
o
d
u
ctiv
ity
ce
ases
,
d
is
r
u
p
tin
g
c
r
itical
s
er
v
ices
an
d
in
d
u
s
tr
ial
o
p
e
r
atio
n
s
.
As
g
lo
b
al
en
er
g
y
d
e
m
an
d
co
n
tin
u
es
to
r
is
e,
o
p
tim
izin
g
co
n
s
u
m
p
tio
n
an
d
in
teg
r
atin
g
s
u
s
tain
ab
le
en
er
g
y
s
o
u
r
ce
s
i
s
im
p
er
ativ
e
f
o
r
b
o
t
h
ef
f
icien
c
y
an
d
en
v
ir
o
n
m
e
n
tal
s
u
s
tain
ab
ilit
y
[
1
]
.
Po
wer
g
en
er
atio
n
r
elies
o
n
r
en
ewa
b
le
an
d
n
o
n
-
r
en
ewa
b
le
s
o
u
r
ce
s
,
with
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ir
ec
tly
r
ef
lectin
g
en
er
g
y
d
e
m
an
d
.
C
o
al,
n
at
u
r
al
g
as,
a
n
d
o
il
r
em
ain
d
o
m
in
an
t
b
u
t
ar
e
f
in
it
e
,
co
s
tly
to
ex
tr
ac
t,
an
d
e
n
v
ir
o
n
m
en
tally
d
am
ag
i
n
g
.
T
h
eir
c
o
n
tin
u
e
d
u
s
e
ac
c
eler
ates
r
eso
u
r
ce
d
ep
letio
n
a
n
d
clim
ate
c
h
an
g
e
,
r
ein
f
o
r
cin
g
th
e
u
r
g
e
n
cy
o
f
tr
an
s
itio
n
in
g
to
clea
n
er
,
m
o
r
e
s
u
s
t
ain
ab
le
alter
n
ativ
es [
2
]
,
[
3
]
.
R
en
ewa
b
le
en
er
g
y
tech
n
o
lo
g
i
es
p
r
o
v
id
e
a
clea
n
,
ab
u
n
d
an
t
,
an
d
s
u
s
tain
ab
le
s
o
lu
tio
n
,
m
in
im
izin
g
en
v
ir
o
n
m
en
tal
im
p
ac
t
wh
ile
en
h
an
cin
g
en
e
r
g
y
s
ec
u
r
ity
a
n
d
lo
n
g
-
ter
m
ec
o
n
o
m
ic
r
esil
ien
ce
.
L
ar
g
e
-
s
ca
le
ad
o
p
tio
n
o
f
r
en
ewa
b
les r
ed
u
ce
s
d
ep
en
d
en
ce
o
n
f
o
s
s
il f
u
els estab
lis
h
in
g
a
m
o
r
e
r
esil
ien
t e
n
er
g
y
s
y
s
tem
[
4
]
.
A
v
ar
iety
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
s
er
v
e
as
v
iab
le
alte
r
n
ativ
es
to
f
o
s
s
il
f
u
els
[
5
]
,
[
6
]
.
Un
lik
e
ce
n
tr
alize
d
p
o
wer
g
r
id
s
,
th
ese
s
o
u
r
ce
s
ca
n
b
e
in
teg
r
ated
in
to
lo
ca
lized
m
icr
o
g
r
id
s
y
s
tem
s
,
r
ed
u
cin
g
in
f
r
astru
ctu
r
e
r
eq
u
i
r
em
en
ts
an
d
ex
p
a
n
d
in
g
elec
tr
i
city
ac
ce
s
s
to
r
em
o
te
ar
ea
s
.
S
elec
tin
g
th
e
o
p
tim
al
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
d
e
p
en
d
s
o
n
r
e
g
io
n
al
r
eso
u
r
ce
av
ailab
ilit
y
,
en
s
u
r
in
g
ef
f
icien
t
an
d
co
s
t
-
ef
f
ec
tiv
e
im
p
lem
en
tatio
n
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
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4
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5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
40
,
No
.
1
,
Octo
b
er
20
25
:
67
-
77
68
Desp
ite
tech
n
o
lo
g
ical
ad
v
an
c
em
en
t,
8
6
0
m
illi
o
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p
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p
le
will
s
till
lack
elec
tr
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it
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b
y
2
0
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if
th
er
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is
n
o
r
am
p
-
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p
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o
f
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y
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T
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ap
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f
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x
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in
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r
astru
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is
ess
en
tial
to
u
n
iv
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s
al
elec
tr
ici
ty
ac
ce
s
s
[
8
]
,
[
9
]
,
wh
ile
r
e
d
u
cin
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f
o
s
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f
u
el
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ep
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en
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as e
m
is
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s
[
1
0
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,
[
1
1
]
.
Use
o
f
Ph
o
to
v
o
ltaic
s
y
s
tem
s
(
PVS)
allo
ws
f
o
r
th
e
h
ar
v
esti
n
g
o
f
s
o
lar
e
n
er
g
y
an
d
its
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n
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er
s
io
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in
to
u
s
ab
le
elec
tr
ical
p
o
we
r
,
o
f
f
er
i
n
g
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v
iab
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m
ea
n
s
o
f
p
o
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r
in
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d
if
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e
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en
t
a
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licatio
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s
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id
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co
n
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ted
PVS
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d
s
tan
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-
alo
n
e
PV
p
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e
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er
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tio
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av
e
b
ee
n
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tu
d
ie
d
f
o
r
th
eir
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b
ilit
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to
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e
im
p
le
m
en
ted
f
o
r
d
iv
er
s
e
en
er
g
y
n
ee
d
s
[
1
2
]
m
icr
o
in
v
e
r
ter
s
y
s
tem
s
(
MI
S)
h
a
v
e
f
u
r
th
er
d
ev
el
o
p
ed
in
th
e
ar
ea
o
f
e
n
er
g
y
ef
f
icien
c
y
b
y
in
co
r
p
o
r
atin
g
b
o
o
s
t
-
h
alf
-
b
r
id
g
e
DC
-
DC
co
n
v
er
ter
s
an
d
f
u
ll
-
b
r
id
g
e
p
u
ls
e
-
wid
th
m
o
d
u
lated
in
v
er
ter
s
to
ac
h
iev
e
m
a
x
im
u
m
p
o
wer
co
n
v
er
s
io
n
[
1
3
]
.
R
ec
en
t
in
n
o
v
ati
o
n
s
in
m
icr
o
in
v
er
ter
tec
h
n
o
lo
g
y
h
av
e
i
n
tr
o
d
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ce
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ac
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clam
p
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n
v
er
ter
s
with
s
er
ies
-
r
es
o
n
an
t
v
o
ltag
e
d
o
u
b
ler
s
,
co
m
b
in
ed
with
h
ig
h
-
ef
f
icien
cy
in
v
e
r
ter
s
f
ea
tu
r
in
g
s
in
g
le
-
s
witch
-
m
o
d
u
latio
n
s
t
ep
-
d
o
wn
c
o
n
v
e
r
ter
s
[
1
4
]
.
T
h
ese
ad
v
an
ce
m
e
n
ts
en
h
an
ce
en
er
g
y
ef
f
icien
c
y
,
im
p
r
o
v
e
v
o
ltag
e
r
eg
u
latio
n
,
an
d
r
ed
u
ce
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
m
ak
in
g
s
o
lar
en
er
g
y
s
y
s
tem
s
m
o
r
e
r
eliab
le
an
d
ef
f
ec
tiv
e.
Ad
d
itio
n
ally
,
m
ass
p
r
o
d
u
ctio
n
a
n
d
tech
n
o
lo
g
ical
p
r
o
g
r
ess
h
av
e
lo
wer
ed
m
an
u
f
ac
tu
r
in
g
c
o
s
ts
,
in
cr
ea
s
in
g
ac
ce
s
s
ib
ilit
y
an
d
af
f
o
r
d
ab
ilit
y
f
o
r
b
r
o
a
d
er
ad
o
p
tio
n
.
T
h
is
p
r
o
ject
aim
s
to
d
ev
elo
p
a
m
o
d
u
lar
p
u
r
e
s
in
e
wav
e
m
icr
o
in
v
er
ter
with
a
n
in
te
g
r
ated
h
ig
h
-
ef
f
icien
cy
,
lo
w
-
co
s
t
m
a
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
co
n
tr
o
ller
to
m
ax
im
ize
p
o
wer
ex
tr
ac
tio
n
a
n
d
im
p
r
o
v
e
e
n
er
g
y
co
n
v
er
s
io
n
[
1
5
]
-
[
1
8
]
.
T
h
e
s
y
s
tem
is
b
u
ilt
f
o
r
co
s
t
ef
f
icien
c
y
,
s
ca
lab
le,
an
d
ad
ap
ta
b
le
to
d
if
f
er
en
t
PV
ap
p
licatio
n
s
,
en
s
u
r
in
g
h
ig
h
er
ef
f
icien
cy
an
d
s
e
am
less
g
r
id
in
teg
r
atio
n
.
T
o
o
p
tim
ize
p
o
wer
o
u
tp
u
t,
th
i
s
s
tu
d
y
em
p
l
o
y
s
th
e
d
is
tu
r
b
a
n
d
o
b
s
e
r
v
e
(
D&
O)
alg
o
r
ith
m
f
o
r
MPPT.
T
h
is
m
eth
o
d
d
y
n
am
ically
ad
j
u
s
ts
th
e
o
p
er
atin
g
v
o
ltag
e
(
V
p
)
b
ased
o
n
p
o
wer
f
lu
ctu
atio
n
s
.
I
f
p
o
wer
o
u
tp
u
t
in
cr
ea
s
es
af
ter
a
v
o
ltag
e
ch
an
g
e,
th
e
s
y
s
tem
k
ee
p
s
ad
ju
s
tin
g
in
th
e
s
am
e
d
ir
ec
tio
n
,
b
u
t
if
p
o
wer
d
ec
r
ea
s
es,
it
r
ev
er
s
es
th
e
v
o
ltag
e
p
er
tu
r
b
a
tio
n
to
s
u
s
tain
o
p
er
atio
n
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
.
T
h
is
iter
ativ
e
p
r
o
ce
s
s
en
s
u
r
es
o
p
tim
al
e
n
er
g
y
tr
an
s
f
er
u
n
d
er
v
a
r
y
in
g
s
o
lar
co
n
d
itio
n
s
[
1
9
]
.
Fig
u
r
e
1
s
h
o
w
s
th
e
D&
O
-
b
ase
d
MPPT
im
p
lem
en
tatio
n
th
at
estab
lis
h
es
th
e
co
n
tr
o
l
lo
g
ic
th
at
in
cr
ea
s
es
th
e
m
icr
o
i
n
v
er
ter
ef
f
icien
cy
a
n
d
r
esp
o
n
s
iv
en
ess
to
im
m
ed
iate
c
h
an
g
es in
s
o
lar
in
p
u
t c
o
n
d
itio
n
s
.
E
n
v
ir
o
n
m
en
tal
r
eg
u
latio
n
s
ar
o
u
n
d
th
e
g
lo
b
e
in
cr
ea
s
in
g
l
y
p
r
o
m
o
te
th
e
u
tili
za
tio
n
o
f
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
th
r
o
u
g
h
tax
in
ce
n
tiv
es
an
d
r
eg
u
lato
r
y
p
o
licy
.
I
n
C
o
lo
m
b
ia,
th
e
n
atio
n
al
g
o
v
er
n
m
e
n
t
en
ac
ted
Dec
r
ee
8
2
9
o
f
2
0
2
0
,
w
h
ich
m
o
d
if
ies
an
d
co
m
p
lem
en
ts
r
eg
u
latio
n
s
s
u
ch
as
L
aw
1
7
1
5
o
f
2
0
1
4
,
Dec
r
ee
6
2
5
o
f
2
0
1
6
,
an
d
Dec
r
ee
1
0
7
3
,
to
s
tim
u
late
in
v
estme
n
t
in
n
o
n
-
co
n
v
en
tio
n
al
en
er
g
y
p
r
o
jects
[
2
0
]
.
T
h
e
in
ce
n
tiv
es
ar
e
aim
ed
at
ac
ce
ler
atin
g
th
e
tr
an
s
itio
n
to
s
u
s
tain
ab
le
en
er
g
y
s
o
lu
tio
n
s
,
f
ac
ilit
atin
g
th
e
u
s
e
o
f
s
o
lar
PV
s
y
s
tem
s
an
d
o
th
e
r
clea
n
en
e
r
g
y
tech
n
o
l
o
g
ies.
T
h
is
r
esear
ch
aim
s
to
p
r
o
v
id
e
tech
n
ical
in
s
ig
h
ts
in
to
d
esig
n
in
g
m
o
r
e
ef
f
icien
t
m
icr
o
in
v
er
ter
s
with
lo
wer
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
I
t
f
o
cu
s
es
o
n
d
ev
el
o
p
in
g
a
m
icr
o
in
v
er
ter
f
o
r
s
o
lar
p
a
n
els
th
at
o
p
tim
ally
h
ar
n
ess
s
o
lar
r
ad
iatio
n
.
T
h
e
p
r
o
p
o
s
ed
d
esig
n
o
f
f
er
s
s
ev
er
al
co
m
p
ar
ativ
e
tech
n
ical
a
d
v
an
tag
es
,
en
h
an
ci
n
g
en
e
r
g
y
ef
f
icien
cy
.
T
h
e
ar
ticle
is
d
iv
id
ed
in
to
f
o
u
r
s
ec
tio
n
s
.
T
h
e
in
tr
o
d
u
ctio
n
o
u
tlin
es
th
e
s
tate
o
f
t
h
e
ar
t
an
d
r
esear
ch
o
b
jectiv
e.
T
h
e
m
eth
o
d
o
lo
g
y
d
escr
ib
es
th
e
d
esig
n
ch
ar
ac
ter
is
tics
.
T
h
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
s
ec
tio
n
ex
am
in
es
s
y
s
tem
p
er
f
o
r
m
a
n
ce
,
s
im
u
lati
o
n
s
,
an
d
m
u
ltil
ev
el
in
v
er
ter
f
ea
tu
r
es.
L
astl
y
,
th
e
co
n
cl
u
s
io
n
s
h
ig
h
lig
h
t
k
e
y
f
in
d
in
g
s
.
Fig
u
r
e
1
.
D&
O
d
iag
r
am
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Desig
n
o
f
h
ig
h
-
efficien
cy
micr
o
in
ve
r
ter fo
r
a
p
h
o
to
v
o
lta
ic
s
ystem
w
ith
lo
w
…
(
Wa
lter
N
a
r
a
n
jo
Lo
u
r
id
o
)
69
2.
M
E
T
H
O
D
T
h
e
p
r
o
p
o
s
ed
d
esig
n
m
icr
o
in
v
er
ter
s
y
s
tem
c
o
n
s
is
ts
o
f
th
r
ee
k
ey
co
m
p
o
n
e
n
ts
:
a
DC
b
o
o
s
ter
,
an
HFL
in
v
er
ter
,
a
n
d
a
m
u
ltil
ev
el
in
v
er
ter
.
T
h
e
to
p
o
l
o
g
y
is
d
esig
n
e
d
f
o
r
m
ax
im
u
m
p
o
wer
r
etr
iev
al,
h
ig
h
co
n
v
er
s
io
n
ef
f
icac
y
,
an
d
l
o
w
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
f
o
r
PV
ap
p
licatio
n
.
T
h
e
d
esig
n
i
n
g
p
r
o
ce
s
s
f
o
llo
ws
a
f
o
r
m
alize
d
d
esig
n
p
r
o
ce
s
s
wit
h
o
p
tim
izatio
n
o
f
th
e
p
er
f
o
r
m
an
ce
o
f
ea
c
h
co
m
p
o
n
en
t
,
m
in
i
m
izatio
n
o
f
p
o
wer
lo
s
s
es,
an
d
g
r
id
in
teg
r
atio
n
wi
th
n
o
c
o
m
p
atib
ilit
y
p
r
o
b
lem
s
.
T
h
e
f
ir
s
t
s
tag
e
o
f
th
e
s
y
s
tem
is
a
D
C
b
o
o
s
ter
co
n
v
er
ter
th
at
d
o
es
im
p
ed
an
ce
m
atch
in
g
as
well
a
s
v
o
ltag
e
r
eg
u
latio
n
.
T
h
e
b
o
o
s
t
er
is
d
esig
n
e
d
to
ch
a
n
g
e
th
e
im
p
ed
an
ce
p
r
o
v
id
ed
to
th
e
s
o
lar
p
an
el
s
o
th
at
it
allo
ws
MPPT
th
r
o
u
g
h
an
ad
ap
tiv
e
co
n
tr
o
l
al
g
o
r
ith
m
s
u
c
h
as
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
.
I
n
ad
d
itio
n
,
it
in
cr
ea
s
es
th
e
p
a
n
el
v
o
ltag
e
t
o
th
e
r
eq
u
ir
e
d
le
v
el,
d
eli
v
er
in
g
s
tab
le
an
d
ef
f
icien
t
p
o
wer
t
o
th
e
i
n
v
er
ter
.
Hig
h
-
f
r
eq
u
e
n
cy
m
o
s
f
et
s
ar
e
u
s
ed
in
o
r
d
er
to
m
in
im
ize
p
o
we
r
lo
s
s
es
b
y
r
ed
u
cin
g
co
n
d
u
ctio
n
an
d
s
witch
in
g
lo
s
s
es
.
T
h
e
MPPT
alg
o
r
ith
m
co
n
tr
o
ls
th
e
b
o
o
s
t
co
n
v
er
ter
,
co
n
tin
u
o
u
s
ly
ad
ju
s
tin
g
th
e
d
u
ty
cy
cle
b
ased
o
n
r
ea
l
-
tim
e
v
o
ltag
e
an
d
cu
r
r
e
n
t
m
ea
s
u
r
em
en
ts
to
m
ax
im
ize
p
o
wer
ex
tr
a
ctio
n
f
r
o
m
th
e
PV
p
an
el
u
n
d
er
v
ar
y
in
g
ir
r
ad
ia
n
ce
co
n
d
itio
n
s
.
Af
ter
v
o
ltag
e
r
eg
u
latio
n
,
th
e
am
p
lifie
d
DC
v
o
ltag
e
is
s
u
p
p
lied
to
a
2
0
k
Hz
h
ig
h
-
f
r
e
q
u
en
cy
lin
k
(
HFL)
in
v
er
ter
,
wh
ich
en
h
a
n
c
es
en
er
g
y
co
n
v
er
s
io
n
e
f
f
icien
c
y
an
d
o
f
f
er
s
g
alv
a
n
ic
is
o
latio
n
b
etwe
en
in
p
u
t
a
n
d
o
u
tp
u
t.
T
h
e
HFL
to
p
o
lo
g
y
is
ex
tr
em
ely
u
s
ef
u
l
to
o
v
e
r
all
s
y
s
tem
p
er
f
o
r
m
a
n
ce
b
y
r
ed
u
ci
n
g
th
e
s
ize
o
f
p
ass
iv
e
co
m
p
o
n
en
ts
a
n
d
co
r
e
lo
s
s
es,
th
u
s
m
ak
in
g
it
a
p
r
o
m
in
e
n
t
d
esig
n
f
ea
tu
r
e
in
co
m
p
ac
t
h
ig
h
-
ef
f
icien
cy
p
o
wer
s
y
s
tem
s
.
A
h
ig
h
-
f
r
eq
u
en
cy
to
r
o
id
al
tr
an
s
f
o
r
m
er
is
u
s
ed
d
u
e
to
its
lo
w
h
y
s
ter
esis
lo
s
s
e
s
an
d
h
ig
h
ef
f
icien
c
y
r
ate
(
m
o
r
e
th
an
9
5
%),
with
lo
w
en
er
g
y
d
is
s
ip
atio
n
[
2
1
]
,
[
2
2
]
.
T
h
e
AC
v
o
ltag
es
at
s
o
m
e
r
atio
s
(
1
:3
a
n
d
1
:9
)
ar
e
g
en
e
r
ated
b
y
th
is
tr
an
s
f
o
r
m
er
,
wh
ich
ar
e
u
tili
ze
d
f
o
r
r
e
ctif
icatio
n
b
y
Sch
o
ttk
y
o
r
SiC
d
io
d
es,
with
ad
d
ed
ef
f
icien
cy
a
n
d
r
ed
u
cin
g
s
witch
in
g
lo
s
s
es.
T
h
e
to
r
o
id
al
tr
an
s
f
o
r
m
er
o
f
f
er
s
b
etter
tec
h
n
ical
ad
v
an
tag
es
as
well,
in
clu
d
in
g
v
o
ltag
e
f
le
x
ib
ilit
y
,
r
ed
u
ce
d
ed
d
y
c
u
r
r
en
t
lo
s
s
,
an
d
elec
tr
ical
is
o
latio
n
[
2
1
]
,
[
2
2
]
.
Ho
wev
er
,
t
o
en
s
u
r
e
o
p
tim
al
ef
f
icien
c
y
,
co
p
p
er
a
n
d
co
r
e
lo
s
s
es
m
u
s
t
b
e
co
n
tr
o
lled
with
ca
u
tio
n
[
2
3
]
.
T
o
en
s
u
r
e
o
p
tim
al
p
er
f
o
r
m
an
ce
,
is
o
lated
s
u
p
p
li
es
ar
e
in
clu
d
ed
in
th
e
cir
cu
it,
with
elec
tr
ical
is
o
latio
n
f
r
o
m
th
e
r
est
o
f
th
e
s
y
s
tem
[
2
4
]
.
T
h
is
is
ac
h
iev
ed
b
y
s
u
m
m
in
g
th
e
v
o
ltag
e
in
th
e
m
ain
an
d
au
x
iliar
y
s
ec
tio
n
s
in
th
e
m
u
ltil
ev
el
in
v
er
ter
,
th
u
s
en
s
u
r
in
g
p
o
wer
d
is
tr
ib
u
tio
n
,
v
o
ltag
e
r
eg
u
latio
n
o
p
tim
iz
e
d
,
an
d
a
g
en
e
r
al
co
m
p
ac
t
an
d
ef
f
icien
t stru
ctu
r
e.
T
h
is
m
eth
o
d
g
iv
es
a
s
tep
-
by
-
s
tep
p
r
o
ce
s
s
o
f
d
esig
n
a
n
d
im
p
lem
en
tatio
n
o
f
a
h
ig
h
-
ef
f
icien
cy
m
icr
o
in
v
er
ter
with
DC
b
o
o
s
ter
,
HFL
,
a
n
d
m
u
ltil
ev
el
in
v
er
ter
.
C
o
m
b
in
in
g
MPPT
al
g
o
r
ith
m
s
,
e
n
h
an
ce
d
m
o
d
u
latio
n
s
ch
em
es
,
an
d
o
p
tim
ized
s
witch
in
g
o
f
s
em
ico
n
d
u
cto
r
s
,
t
h
e
s
y
s
tem
is
ca
p
ab
le
o
f
d
eliv
er
in
g
en
h
an
ce
d
en
er
g
y
c
o
n
v
e
r
s
io
n
,
lo
w
T
HD,
an
d
ef
f
icien
t
g
r
id
in
teg
r
atio
n
.
Fu
r
th
er
im
p
r
o
v
em
en
ts
,
s
u
ch
as
s
o
f
t
-
s
witch
in
g
tech
n
iq
u
es,
tr
a
n
s
f
o
r
m
er
co
r
e
d
esig
n
o
p
tim
izatio
n
,
an
d
r
ea
l
-
ti
m
e
ad
ap
tiv
e
co
n
tr
o
l
,
ca
n
f
u
r
th
er
r
ef
in
e
o
v
er
all
p
er
f
o
r
m
an
ce
,
an
d
th
is
m
icr
o
in
v
er
ter
s
y
s
tem
is
th
u
s
a
n
ex
t
-
g
en
e
r
atio
n
tech
n
o
lo
g
y
f
o
r
d
is
tr
ib
u
ted
PV
en
er
g
y
a
p
p
licatio
n
s
.
2
.
1
.
Desig
n pa
ra
m
et
er
s
T
h
e
d
esig
n
p
r
in
cip
les
f
o
r
th
i
s
p
r
o
ject
ar
e
p
r
esen
ted
in
T
ab
le
1
.
I
t
is
MPPT
r
eg
u
lato
r
d
i
s
tu
r
b
an
d
o
b
s
er
v
e
.
Fo
r
o
p
tim
al
ef
f
icien
cy
,
ea
ch
s
o
lar
p
an
el
with
in
t
h
e
s
y
s
tem
p
o
s
s
ess
e
s
a
u
n
iq
u
e
m
icr
o
in
v
er
ter
s
u
ch
th
at
th
er
e
is
m
a
x
im
u
m
p
o
wer
tr
an
s
f
er
with
m
in
i
m
u
m
l
o
s
s
d
u
e
to
m
is
m
atch
in
g
o
r
s
h
ad
i
n
g
ef
f
ec
t.
T
h
is
s
y
s
tem
en
h
an
ce
s
th
e
o
v
e
r
all
en
er
g
y
e
f
f
icien
cy
o
f
t
h
e
PV
s
y
s
te
m
s
in
ce
it
f
ac
ilit
ates
m
o
d
u
le
-
lev
el
p
o
wer
c
o
n
v
er
s
io
n
an
d
s
tan
d
-
alo
n
e
MPPT.
T
h
e
p
r
o
p
o
s
ed
m
icr
o
in
v
er
ter
to
p
o
l
o
g
y
is
d
esig
n
ed
t
o
o
p
tim
ize
en
er
g
y
h
ar
v
esti
n
g
,
im
p
r
o
v
e
g
r
i
d
c
o
m
p
atib
ilit
y
,
an
d
r
e
d
u
ce
p
o
wer
lo
s
s
,
th
u
s
in
cr
ea
s
in
g
th
e
s
y
s
tem
ef
f
icien
c
y
.
E
lectr
ical
c
ir
cu
it
o
f
th
e
p
r
o
p
o
s
ed
m
icr
o
in
v
er
ter
s
y
s
tem
,
d
escr
ib
in
g
its
p
r
im
ar
y
f
u
n
ctio
n
al
c
o
m
p
o
n
en
ts
an
d
p
o
wer
co
n
v
er
s
io
n
s
tag
es
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
p
r
im
ar
y
DC
p
o
wer
s
o
u
r
c
e
o
f
th
e
s
y
s
tem
is
a
6
0
0
W
s
o
l
ar
p
an
el.
B
ased
o
n
th
e
esti
m
ated
an
n
u
al
av
er
ag
e
s
o
lar
ir
r
a
d
i
an
ce
o
f
6
5
0
-
7
5
0
W
/m
²
in
Villav
icen
cio
,
th
e
p
an
el
will
s
u
p
p
l
y
a
n
o
u
tp
u
t
o
f
u
p
to
4
0
0
W
in
r
ea
l
o
p
er
atio
n
co
n
d
itio
n
s
.
Ho
wev
er
,
s
o
lar
r
ad
iatio
n
is
n
o
t
c
o
n
s
tan
t
o
v
er
a
d
ay
,
s
ig
n
if
ican
t
ly
af
f
ec
tin
g
e
n
er
g
y
g
en
er
atio
n
.
T
h
ese
v
ar
iatio
n
s
s
h
if
t
th
e
MPP,
p
r
ev
en
tin
g
t
h
e
p
an
el
f
r
o
m
b
ein
g
at
its
n
o
m
i
n
al
ca
p
ac
ity
all
th
e
tim
e,
r
esu
ltin
g
in
ef
f
icien
cy
lo
s
s
es
an
d
th
e
n
ee
d
f
o
r
d
y
n
am
ic
MPPT
ad
ju
s
tm
en
ts
to
o
p
tim
ize
p
o
wer
ex
tr
ac
tio
n
.
T
h
e
d
esig
n
e
d
s
y
s
tem
i
n
co
r
p
o
r
ates
a
s
tep
-
u
p
DC
/DC
v
o
ltag
e
r
eg
u
lato
r
with
MPPT
to
d
eliv
e
r
a
s
tab
l
e
an
d
o
p
tim
ized
o
u
tp
u
t
to
th
e
D
C
/A
C
co
n
v
er
ter
.
T
h
e
MPPT
c
o
n
tr
o
ller
,
im
p
lem
en
tin
g
th
e
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
alg
o
r
ith
m
,
d
y
n
am
ical
ly
ad
ju
s
ts
th
e
d
u
ty
cy
cle
in
o
r
d
er
to
tr
ac
k
th
e
MPP,
m
ax
im
izin
g
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
th
e
s
o
lar
p
a
n
el
an
d
en
h
an
ci
n
g
s
y
s
tem
e
f
f
ic
ien
cy
.
T
h
is
ap
p
r
o
ac
h
co
n
tin
u
o
u
s
ly
co
m
p
e
n
s
ates
f
o
r
ir
r
ad
ian
ce
v
ar
iatio
n
s
,
e
n
s
u
r
in
g
o
p
tim
al
p
er
f
o
r
m
a
n
ce
.
T
h
e
f
o
llo
win
g
s
ec
tio
n
s
p
r
o
v
id
e
t
h
e
ass
u
m
p
tio
n
s
an
d
ca
lcu
latio
n
s
f
o
r
th
e
r
eg
u
lato
r
d
esig
n
.
A
ca
p
ab
ilit
y
o
f
s
u
p
p
o
r
tin
g
an
in
p
u
t
cu
r
r
e
n
t
o
f
1
4
A
is
r
eq
u
i
r
ed
in
o
r
d
er
to
m
ax
im
ize
en
er
g
y
tr
an
s
f
er
wh
en
th
e
s
o
lar
ir
r
ad
ian
ce
is
ty
p
ical.
T
o
r
ea
lize
a
MPP
v
o
ltag
e
o
f
3
6
VDC,
a
b
o
o
s
t
r
eg
u
lato
r
m
u
s
t
b
e
em
p
lo
y
ed
in
o
r
d
er
to
in
cr
ea
s
e
th
e
v
o
ltag
e
to
s
u
p
p
o
r
t
e
f
f
e
ctiv
e
p
o
wer
c
o
n
v
e
r
s
io
n
.
T
h
e
r
eg
u
lato
r
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
f
ac
ilit
atin
g
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
f
r
o
m
th
e
PV
p
an
el
a
n
d
m
ain
tain
in
g
s
tab
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
40
,
No
.
1
,
Octo
b
er
20
25
:
67
-
77
70
o
u
tp
u
t
v
o
ltag
e
.
Fig
u
r
e
3
s
h
o
w
s
th
e
to
p
o
lo
g
y
o
f
th
e
b
o
o
s
t
r
eg
u
lato
r
,
wh
ich
d
ep
icts
its
r
o
le
in
b
o
o
s
tin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
ab
le
1
.
D
esig
n
b
ases
C
h
a
r
a
c
t
e
r
i
s
t
i
c
s
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
5
0
0
W
O
u
t
p
u
t
1
2
0
V
A
C
/
4
.
1
A
(
p
u
r
e
w
a
v
e
2
7
st
e
p
s
)
I
n
p
u
t
15
-
3
6
V
D
C
/
1
4
A
Fig
u
r
e
2
.
Hig
h
-
ef
f
icien
c
y
m
o
d
u
lar
m
icr
o
in
v
er
ter
d
esig
n
Fig
u
r
e
3
.
DC
-
DC
b
o
o
s
t r
eg
u
lato
r
B
y
ap
p
ly
in
g
(
1
-
7
)
f
r
o
m
[
2
5
]
-
[
2
6
]
,
th
e
r
ef
er
e
n
ce
v
alu
es f
o
r
o
p
tim
al
MPPT
o
p
er
atio
n
ar
e
d
e
ter
m
in
ed
.
=
1
1
−
(
1
)
=
(
2
)
=
(
1
−
)
2
2
(
3
)
=
1
−
(
4
)
=
(
1
−
)
2
(
5
)
=
(
6
)
á
=
+
2
=
(
1
−
)
2
+
2
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Desig
n
o
f
h
ig
h
-
efficien
cy
micr
o
in
ve
r
ter fo
r
a
p
h
o
to
v
o
lta
ic
s
ystem
w
ith
lo
w
…
(
Wa
lter
N
a
r
a
n
jo
Lo
u
r
id
o
)
71
A
2
0
k
Hz
s
witch
in
g
f
r
eq
u
e
n
cy
is
u
s
ed
to
ac
h
iev
e
s
m
aller
,
lo
w
-
co
s
t
co
m
p
o
n
e
n
ts
.
T
h
e
s
y
s
tem
em
p
lo
y
s
MO
SF
E
T
-
b
ased
s
wi
tch
in
g
elem
en
ts
.
T
o
g
en
e
r
ate
is
o
lated
DC
s
o
u
r
ce
s
,
a
tr
an
s
f
o
r
m
er
r
eq
u
ir
in
g
a
n
AC
s
ig
n
al
is
n
ec
es
s
ar
y
.
T
h
is
i
s
ac
co
m
p
lis
h
ed
th
r
o
u
g
h
a
HFL
DC
/A
C
c
o
n
v
er
ter
; it
s
wi
tch
es th
e
DC
lev
el
at
2
0
k
Hz
to
g
en
er
ate
a
s
q
u
ar
e
-
wav
e
AC
s
ig
n
al.
T
h
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
is
p
er
f
o
r
m
ed
b
y
an
H
-
b
r
id
g
e
(
HB
)
an
d
a
m
icr
o
co
n
tr
o
ller
th
at
p
r
o
d
u
ce
s
th
e
n
ec
ess
ar
y
b
in
ar
y
s
witch
in
g
s
eq
u
en
ce
.
Op
er
atin
g
at
a
h
ig
h
f
r
eq
u
en
cy
r
ed
u
ce
s
tr
a
n
s
f
o
r
m
er
s
ize
an
d
e
n
h
an
ce
s
ef
f
icien
cy
c
o
m
p
ar
e
d
t
o
lo
w
-
f
r
e
q
u
en
cy
tr
a
n
s
f
o
r
m
e
r
s
.
L
ik
ewise,
p
ass
iv
e
co
m
p
o
n
en
ts
s
u
ch
as in
d
u
ct
o
r
s
an
d
ca
p
ac
ito
r
s
ar
e
m
in
im
ized
A
k
ey
co
m
p
o
n
en
t o
f
th
is
d
esig
n
is
th
e
to
r
o
id
al
tr
an
s
f
o
r
m
e
r
,
wh
ich
g
en
er
ates th
r
ee
AC
o
u
t
p
u
ts
.
T
h
ese
ou
tp
u
ts
ar
e
co
m
b
in
ed
t
h
r
o
u
g
h
ad
d
itio
n
a
n
d
s
u
b
tr
ac
tio
n
to
f
o
r
m
a
s
in
e
wav
e.
T
o
d
eter
m
in
e
th
e
d
if
f
e
r
en
t
v
o
ltag
e
lev
els,
th
e
p
r
im
ar
y
win
d
in
g
’
s
tu
r
n
s
ar
e
ca
lcu
late
d
b
ased
o
n
p
o
wer
an
d
v
o
lta
g
e.
T
h
e
s
ec
o
n
d
a
r
y
win
d
in
g
s
’
tu
r
n
s
ar
e
th
e
n
c
o
m
p
u
ted
,
f
o
llo
we
d
b
y
r
ec
tific
atio
n
u
s
in
g
Sch
o
ttk
y
d
io
d
es
f
o
r
h
ig
h
-
f
r
eq
u
en
cy
o
p
er
atio
n
.
Fin
ally
,
th
e
ca
p
ac
ito
r
is
s
ized
to
en
s
u
r
e
an
ac
ce
p
tab
le
v
o
ltag
e
r
ip
p
le.
I
n
(
8
)
an
d
(
9
)
d
ef
in
e
th
e
t
u
r
n
ca
lcu
latio
n
s
.
=
4
,
44
∗
∗
∅
(
tu
r
n
s
)
(
8
)
=
1
2
Δ
Vo
Vm
(
9
)
Her
e,
Es
r
ep
r
esen
ts
th
e
v
o
lt
ag
e
in
d
u
ce
d
i
n
th
e
s
ec
o
n
d
ar
y
wi
n
d
in
g
(
V)
,
an
d
ff
f
d
en
o
tes
th
e
f
r
eq
u
e
n
c
y
(
Hz)
.
Ad
d
itio
n
ally
,
(
1
0
)
an
d
(
1
1
)
ar
e
u
s
ed
to
d
eter
m
in
e
th
e
win
d
in
g
ar
ea
s
:
=
∗
(
2
)
(
10
)
W
h
er
e,
=
(
f
o
r
p
r
im
a
r
y
)
,
a
n
d
is
th
e
win
d
in
g
s
p
ac
in
g
f
ac
to
r
.
=
∗
∗
(
2
)
(
1
1
)
Similar
ly
,
th
e
n
ex
t
cir
cu
it
co
m
p
o
n
e
n
t
is
th
e
r
ec
tifie
r
b
r
id
g
e
an
d
ca
p
ac
ito
r
,
wh
ic
h
co
n
v
e
r
t
alter
n
atin
g
cu
r
r
en
t
in
to
d
ir
ec
t
cu
r
r
e
n
t
to
s
u
p
p
ly
ea
ch
HB
o
f
th
e
m
u
ltil
ev
el
in
v
er
ter
.
T
h
e
in
p
u
t
v
o
lta
g
e
wav
ef
o
r
m
in
th
e
tim
e
d
o
m
ain
is
ex
p
r
ess
ed
b
y
(
1
2
)
[
2
7
]:
=
√
2
1
(
)
(
1
2
)
Fin
ally
,
to
ac
h
iev
e
a
s
in
g
le
-
p
h
ase
s
in
u
s
o
id
al
o
u
tp
u
t
o
f
1
2
0
VAC
R
MS
at
6
0
Hz,
a
m
u
ltil
ev
el
in
v
er
ter
was
im
p
lem
en
ted
.
T
h
is
in
v
er
ter
g
en
er
ates
m
u
ltip
le
v
o
ltag
e
lev
els
th
r
o
u
g
h
b
i
n
ar
y
co
m
b
in
atio
n
.
Fig
u
r
e
4
s
h
o
ws th
e
s
in
u
s
o
id
al
wav
ef
o
r
m
f
o
r
m
e
d
b
y
th
e
2
7
g
en
er
ated
lev
els
:
T
h
e
m
u
ltil
ev
el
in
v
er
s
io
n
tech
n
iq
u
e
c
o
n
s
tr
u
cts
th
e
s
in
e
wav
e
b
y
s
tack
in
g
v
o
ltag
e
lev
els
h
o
r
izo
n
tally
.
Mu
ltil
ev
el
in
v
er
ter
s
u
s
e
m
u
ltip
le
p
o
we
r
s
witch
es
ar
r
an
g
ed
t
o
ad
d
o
r
s
u
b
tr
ac
t
v
o
ltag
es.
Gen
er
atin
g
th
e
wav
e
r
eq
u
ir
es d
eter
m
i
n
in
g
th
e
p
ea
k
v
alu
e,
wh
ich
is
ca
lcu
lated
u
s
in
g
(
1
3
)
an
d
(
1
4
)
[
2
8
]
:
=
/
√
2
(
1
3
)
=
√
2
=
170
(
1
4
)
T
h
e
co
n
f
ig
u
r
atio
n
o
f
th
r
ee
HB
en
ab
les
th
e
g
en
er
atio
n
o
f
2
7
v
o
ltag
e
lev
els,
f
o
llo
win
g
th
e
f
o
r
m
u
la
3
N
+
1
,
wh
er
e
N
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
a
u
x
iliar
y
HB
.
E
ac
h
HB
r
eq
u
ir
es
an
is
o
lated
D
C
v
o
ltag
e
s
o
u
r
ce
to
allo
w
f
o
r
v
o
ltag
e
ad
d
itio
n
an
d
s
u
b
tr
ac
tio
n
.
B
y
s
o
lv
i
n
g
(
1
5
)
an
d
(
1
6
)
f
o
r
t
h
is
s
p
ec
if
ic
ca
s
e,
th
e
f
o
llo
win
g
r
esu
lts
ar
e
o
b
tain
ed
:
=
+
3
+
9
(
1
5
)
Vn
=11
8,
9
=
13
VDC
(
1
6
)
Vn
/9
r
ep
r
esen
ts
th
e
s
m
allest
v
o
ltag
e
lev
el
u
s
ed
t
o
co
n
s
tr
u
ct
th
e
s
tep
p
ed
s
in
e
wav
e,
m
in
im
i
zin
g
T
HD
an
d
elim
in
atin
g
t
h
e
n
ee
d
f
o
r
o
u
tp
u
t
f
ilter
s
.
T
h
e
im
p
lem
en
ted
ar
ch
itectu
r
e
f
ea
t
u
r
es
a
s
er
ies
co
n
n
ec
tio
n
o
f
th
r
ee
HB
with
d
if
f
er
en
t
DC
v
o
ltag
e
lev
els,
g
en
er
atin
g
an
AC
o
u
tp
u
t,
as
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
is
co
n
f
ig
u
r
atio
n
em
p
lo
y
s
an
alg
o
r
ith
m
to
c
o
n
tr
o
l
th
e
b
in
ar
y
s
witch
in
g
o
f
tr
an
s
i
s
to
r
s
,
p
r
o
d
u
cin
g
2
7
v
o
ltag
e
lev
els,
ea
ch
d
if
f
er
in
g
b
y
1
3
v
o
lts
.
B
y
u
tili
zin
g
a
6
0
Hz
s
in
u
s
o
id
al
r
e
f
er
en
ce
s
ig
n
al,
t
h
e
s
y
s
tem
e
f
f
ec
tiv
e
ly
r
ep
licates
a
s
in
e
wav
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
40
,
No
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1
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er
20
25
:
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Fig
u
r
e
4
.
Mu
ltil
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el
s
ig
n
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g
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n
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ated
b
y
th
e
co
m
b
in
atio
n
o
f
v
o
ltag
es o
f
ea
c
h
HB
Fig
u
r
e
5
.
HB
co
n
f
ig
u
r
atio
n
f
o
r
m
u
ltil
ev
el
v
o
ltag
e
g
en
er
atio
n
o
f
2
7
s
tep
s
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Fig
u
r
e
6
s
h
o
ws
th
e
o
p
er
atio
n
o
f
th
e
DC
-
DC
b
o
o
s
t
r
eg
u
lato
r
,
m
ain
tain
in
g
a
s
tead
y
3
6
V
DC
o
u
tp
u
t
wh
ile
d
y
n
am
ically
ad
ju
s
tin
g
cu
r
r
en
t
th
r
o
u
g
h
MO
SF
E
T
tr
ig
g
er
co
n
tr
o
l.
T
h
e
MPPT
alg
o
r
ith
m
,
u
tili
zin
g
th
e
P&
O
m
eth
o
d
,
co
n
tin
u
o
u
s
ly
m
o
n
ito
r
s
p
o
we
r
v
ar
iatio
n
s
to
m
ax
im
i
ze
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
th
e
s
o
lar
p
an
el.
T
h
e
b
o
o
s
t
co
n
v
e
r
ter
’
s
d
u
t
y
cy
cle
is
ad
ju
s
ted
with
a
d
is
tu
r
b
a
n
ce
s
tep
s
ize
o
f
1
0
m
W
to
e
n
s
u
r
e
o
p
tim
al
p
o
wer
tr
an
s
f
er
.
MA
T
L
AB
s
im
u
latio
n
s
esti
m
ate
an
ef
f
icien
c
y
o
f
9
5
%
b
y
co
m
p
ar
in
g
th
e
s
o
lar
p
an
el'
s
in
p
u
t
p
o
wer
with
th
e
r
eg
u
lato
r
’
s
o
u
tp
u
t p
o
wer
.
HB
in
v
er
ter
p
e
r
f
o
r
m
an
ce
,
co
n
v
er
tin
g
DC
v
o
ltag
e
i
n
to
a
p
r
e
-
s
elec
ted
f
r
eq
u
e
n
cy
2
0
k
Hz
s
q
u
ar
e
-
wav
e
AC
s
ig
n
al
is
s
h
o
wn
in
Fig
u
r
e
7
.
Hig
h
-
f
r
eq
u
en
cy
s
witch
in
g
is
th
e
m
ain
f
ea
t
u
r
e
o
f
th
e
HFL
tr
an
s
f
o
r
m
er
ap
p
licatio
n
to
p
r
o
v
id
e
m
u
ltip
l
e
is
o
lated
AC
v
o
ltag
e
lev
els.
Fig
u
r
e
8
co
n
f
ir
m
s
r
ec
tifie
d
D
C
v
o
ltag
e
o
u
tp
u
ts
ac
h
iev
ed
u
s
in
g
th
e
t
o
r
o
id
al
tr
an
s
f
o
r
m
er
a
n
d
h
as
a
9
7
%
ef
f
i
cien
cy
lev
el
with
f
er
r
ite
co
r
e
an
d
lo
w
-
im
p
e
d
an
c
e
SiC
s
witch
es.
T
h
e
m
u
ltil
ev
e
l
in
v
er
ter
o
u
tp
u
t
wav
ef
o
r
m
with
a
2
7
-
lev
el
s
in
u
s
o
id
al
s
ig
n
al
o
f
T
HD
o
f
ap
p
r
o
x
im
ately
3
%,
s
ig
n
if
ican
t
ly
lo
wer
th
an
in
c
o
n
v
e
n
tio
n
al
in
v
er
ter
s
is
s
h
o
wn
in
Fig
u
r
e
9
.
On
e
o
f
t
h
e
k
ey
co
n
tr
ib
u
tio
n
s
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
is
p
o
wer
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u
ality
im
p
r
o
v
e
m
en
t
a
n
d
h
ar
m
o
n
ic
r
ed
u
ctio
n
,
wh
ich
h
as
ex
ce
llen
t p
o
ten
tial f
o
r
f
u
tu
r
e
s
tu
d
ies an
d
h
ig
h
-
en
d
PV in
v
er
t
er
ap
p
licatio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Desig
n
o
f
h
ig
h
-
efficien
cy
micr
o
in
ve
r
ter fo
r
a
p
h
o
to
v
o
lta
ic
s
ystem
w
ith
lo
w
…
(
Wa
lter
N
a
r
a
n
jo
Lo
u
r
id
o
)
73
Fig
u
r
e
6
.
MPPT
s
o
lar
p
a
n
el
r
e
g
u
lato
r
o
u
tp
u
t
Fig
u
r
e
7
.
I
n
v
er
te
r
DC
-
AC
HF
L
Fig
u
r
e
8
.
I
s
o
lated
s
o
u
r
ce
s
o
u
t
p
u
t
Fig
u
r
e
9
.
Mu
lti
-
lev
el
i
n
v
er
ter
o
u
tp
u
t
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
g
en
e
r
ates
a
m
u
ltil
ev
el
s
in
u
s
o
id
al
s
ig
n
al
b
y
u
s
in
g
a
r
ef
er
e
n
ce
s
ig
n
al
an
d
a
v
o
ltag
e
lev
el
co
m
p
ar
ato
r
[
2
9
]
-
[
3
0
]
,
en
a
b
lin
g
th
e
cr
ea
tio
n
o
f
2
7
d
is
cr
ete
v
o
ltag
e
lev
els
f
o
r
th
e
m
u
ltil
ev
el
s
in
g
le
-
p
h
ase
in
v
er
ter
.
T
h
e
s
y
s
tem
is
d
esig
n
ed
f
o
r
9
7
%
ef
f
icien
cy
b
y
in
c
o
r
p
o
r
atin
g
Sil
ico
n
C
ar
b
id
e
(
SiC
)
MO
SF
E
T
s
,
wh
ich
o
f
f
er
lo
w
im
p
ed
an
ce
in
cu
r
r
e
n
t
s
atu
r
atio
n
(
~5
m
Ω
)
an
d
m
i
n
im
al
s
witch
in
g
lo
s
s
e
s
.
Ad
d
itio
n
ally
,
p
ar
allel
o
p
e
r
atio
n
o
f
SiC
MO
SF
E
T
s
ca
n
f
u
r
th
er
en
h
an
ce
p
er
f
o
r
m
an
ce
an
d
ef
f
icien
cy
.
W
h
ile
th
ese
co
m
p
o
n
en
ts
ar
e
h
ig
h
ly
r
eliab
le
-
m
ak
i
n
g
th
em
i
d
ea
l
f
o
r
a
p
p
licatio
n
s
in
m
ilit
ar
y
,
ae
r
o
s
p
ac
e,
elec
tr
ic
v
eh
icles,
UPS,
an
d
s
o
lar
co
n
v
er
ter
s
-
th
eir
h
ig
h
co
s
t r
em
ain
s
a
lim
itin
g
f
ac
to
r
f
o
r
wid
esp
r
ea
d
ad
o
p
ti
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
40
,
No
.
1
,
Octo
b
er
20
25
:
67
-
77
74
Fig
u
r
e
1
0
s
h
o
ws
o
n
e
o
f
th
e
k
e
y
f
in
d
in
g
s
o
f
th
is
wo
r
k
,
wh
er
e
p
o
wer
lev
els
at
t
h
e
m
icr
o
in
v
e
r
ter
in
p
u
t
an
d
o
u
tp
u
t
ar
e
d
em
o
n
s
tr
ated
.
E
f
f
icien
cy
ca
lc
u
latio
n
in
d
icate
s
th
at
th
e
s
y
s
tem
ac
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ie
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er
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icien
c
y
o
f
9
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r
ep
r
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te
d
b
y
th
e
r
atio
o
f
3
3
0
W
o
u
tp
u
t
p
o
wer
to
3
7
0
W
in
p
u
t
p
o
wer
.
T
h
is
r
esu
lt
v
alid
ates
th
e
ex
ce
llen
ce
o
f
th
e
p
r
o
p
o
s
ed
d
esig
n
in
en
er
g
y
co
n
v
er
s
io
n
o
p
tim
izatio
n
an
d
lo
s
s
m
in
im
izatio
n
,
s
ig
n
if
y
in
g
its
h
ig
h
-
p
e
r
f
o
r
m
an
ce
PV
ap
p
licat
io
n
p
o
te
n
tial
.
Fig
u
r
e
1
1
s
h
o
ws
th
e
r
elatio
n
s
h
ip
b
etwe
en
m
u
ltil
ev
el
t
o
p
o
lo
g
y
a
n
d
wav
ef
o
r
m
q
u
ality
,
i
n
wh
ich
a
s
m
aller
n
u
m
b
er
o
f
lev
els
r
esu
lts
in
in
cr
ea
s
ed
T
HD,
d
eter
io
r
atin
g
p
o
wer
q
u
ality
.
C
o
n
v
er
s
ely
,
th
e
r
is
e
in
th
e
n
u
m
b
er
o
f
v
o
ltag
e
le
v
els
s
ig
n
i
f
ican
tly
en
h
an
ce
s
th
e
p
r
ec
is
io
n
o
f
th
e
wav
ef
o
r
m
an
d
r
ed
u
ce
s
T
HD,
r
esu
ltin
g
in
im
p
r
o
v
e
d
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
o
b
s
er
v
atio
n
d
is
tin
ctly
s
h
o
ws
th
e
lin
ea
r
d
ep
en
d
en
ce
o
f
m
u
ltil
ev
e
l
in
v
er
ter
s
tr
u
ct
u
r
e
o
n
h
ar
m
o
n
i
c
elim
in
atio
n
,
ju
s
tify
in
g
th
e
r
eq
u
ir
em
e
n
t
f
o
r
i
n
v
er
ter
s
wit
h
h
ig
h
er
lev
els
f
o
r
ac
h
iev
in
g
im
p
r
o
v
e
d
p
o
wer
q
u
ality
an
d
ef
f
icien
c
y
o
f
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
s
.
Fig
u
r
e
1
0
.
Mic
r
o
iv
er
s
o
r
p
o
we
r
in
p
u
t a
n
d
o
u
tp
u
t
Fig
u
r
e
11
.
E
x
p
e
r
im
en
tal
T
HD
o
f
th
e
v
o
ltag
e
as a
f
u
n
ctio
n
o
f
th
e
n
u
m
b
er
o
f
lev
els
4.
CO
NCLU
SI
O
N
T
h
e
p
r
o
p
o
s
ed
h
i
g
h
-
ef
f
icien
cy
m
icr
o
in
v
er
te
r
s
y
s
tem
s
u
cc
ess
f
u
lly
in
teg
r
ates
MPPT
-
co
n
tr
o
lled
DC
-
DC
co
n
v
er
s
io
n
,
HFL
in
v
er
te
r
,
an
d
m
u
ltil
ev
el
in
v
er
ter
a
n
d
h
as
a
o
v
er
all
ef
f
icien
c
y
o
f
9
0
%
with
an
o
u
tp
u
t
wav
ef
o
r
m
o
f
3
%
T
HD.
Sy
n
er
g
y
b
etwe
en
MPPT
al
g
o
r
ith
m
s
,
em
er
g
i
n
g
s
em
ico
n
d
u
ct
o
r
tech
n
o
l
o
g
ies,
a
n
d
o
p
tim
al
p
o
wer
elec
tr
o
n
ics
to
p
o
lo
g
y
s
u
cc
ess
f
u
lly
en
h
an
ce
s
th
e
s
o
lar
en
er
g
y
co
n
v
er
s
io
n
,
d
em
o
n
s
tr
atin
g
th
e
ad
v
an
tag
es
o
f
h
ig
h
-
f
r
eq
u
en
cy
s
witch
in
g
,
v
o
ltag
e
r
eg
u
latio
n
,
an
d
elim
in
atio
n
o
f
h
ar
m
o
n
ics,
wh
at
co
u
l
d
b
e
tak
en
in
to
ac
co
u
n
t in
th
e
d
if
f
e
r
en
t p
h
ases
o
f
s
cien
tific
r
esear
ch
r
elate
d
to
m
icr
o
in
v
e
r
ter
.
T
h
ese
r
esu
lts
v
alid
at
e
th
e
ef
f
ec
tiv
e
n
ess
o
f
m
u
ltil
ev
e
l
in
v
er
ter
s
a
n
d
h
ig
h
-
f
r
eq
u
en
c
y
co
n
v
er
s
io
n
in
im
p
r
o
v
in
g
th
e
p
o
wer
q
u
ality
an
d
s
y
s
tem
p
er
f
o
r
m
a
n
ce
.
Sil
ico
n
C
ar
b
id
e
(
SiC
)
tr
an
s
is
to
r
s
'
ap
p
licatio
n
r
esu
lts
in
im
p
r
o
v
e
d
s
witch
in
g
ef
f
icien
cy
,
lo
wer
co
n
d
u
ctio
n
l
o
s
s
es,
an
d
im
p
r
o
v
ed
th
er
m
al
p
er
f
o
r
m
an
ce
an
d
h
en
ce
r
e
n
d
er
th
em
a
cr
itical
co
m
p
o
n
en
t
i
n
h
ig
h
-
p
o
wer
-
d
e
n
s
ity
ap
p
licatio
n
s
.
H
o
wev
er
,
SiC
d
ev
ice
co
s
t
r
em
ai
n
s
a
lim
itin
g
f
ac
to
r
f
o
r
m
ass
d
ep
lo
y
m
en
t.
H
y
b
r
id
s
o
lu
tio
n
s
th
at
ar
e
co
s
t
-
ef
f
ec
tiv
e,
wh
er
ein
Si
-
b
ased
an
d
SiC
-
b
ased
s
witch
es
ar
e
co
m
b
in
ed
,
c
o
u
ld
b
e
co
n
ce
i
v
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Desig
n
o
f
h
ig
h
-
efficien
cy
micr
o
in
ve
r
ter fo
r
a
p
h
o
to
v
o
lta
ic
s
ystem
w
ith
lo
w
…
(
Wa
lter
N
a
r
a
n
jo
Lo
u
r
id
o
)
75
in
th
e
f
u
tu
r
e
to
m
ar
r
y
ef
f
i
cien
cy
with
co
s
t
-
ef
f
ec
tiv
en
e
s
s
an
d
r
en
d
er
h
ig
h
-
p
er
f
o
r
m
an
ce
PV
in
v
er
ter
s
ec
o
n
o
m
ically
v
iab
le.
Hig
h
-
f
r
eq
u
en
cy
c
o
n
v
er
s
io
n
p
l
ay
s
a
cr
u
cial
r
o
le
in
m
in
im
izin
g
th
e
s
ize
o
f
p
ass
iv
e
co
m
p
o
n
en
ts
s
u
ch
as
tr
an
s
f
o
r
m
er
s
,
in
d
u
ct
o
r
s
,
an
d
ca
p
ac
ito
r
s
,
w
h
er
e
it
is
co
n
c
lu
d
ed
t
h
at
th
e
d
esig
n
p
r
in
cip
l
es
o
f
u
s
ab
ilit
y
an
d
u
s
er
ex
p
er
ien
ce
.
T
h
is
r
ed
u
cti
o
n
lead
s
to
a
m
o
r
e
co
m
p
ac
t
an
d
co
s
t
-
ef
f
ec
tiv
e
d
esig
n
.
B
y
o
p
er
atin
g
at
h
ig
h
er
f
r
eq
u
e
n
cies,
th
e
s
y
s
tem
en
h
an
ce
s
ef
f
icien
cy
wh
ile
d
ec
r
ea
s
in
g
m
ater
ial
u
s
ag
e,
m
a
k
in
g
it
a
n
o
p
tim
al
s
o
lu
tio
n
f
o
r
m
o
d
er
n
p
o
wer
c
o
n
v
e
r
s
io
n
ap
p
licatio
n
s
.
B
y
o
p
er
atin
g
at
h
ig
h
f
r
eq
u
e
n
c
ies,
th
e
s
y
s
tem
g
i
v
es
lo
w
e
n
er
g
y
lo
s
s
es,
r
ed
u
ce
d
co
m
p
o
n
e
n
t
s
ize,
an
d
im
p
r
o
v
e
d
o
v
er
all
p
o
wer
d
en
s
ity
,
an
d
as
s
u
c
h
,
t
h
e
s
y
s
tem
is
well
s
u
ited
f
o
r
PV
d
is
tr
ib
u
ted
a
p
p
licatio
n
s
.
Mo
r
eo
v
er
,
with
th
e
im
p
lem
en
tatio
n
o
f
ad
v
an
ce
d
m
o
d
u
latio
n
tech
n
iq
u
es,
f
o
r
ex
am
p
le,
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SV
M)
o
r
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
(
SHE)
,
wav
ef
o
r
m
s
y
n
th
esis
an
d
s
witch
in
g
ef
f
icien
c
y
m
ay
b
e
en
h
a
n
ce
d
e
v
en
f
u
r
t
h
er
.
T
h
e
s
tu
d
y
also
i
d
en
tifie
s
m
o
d
u
le
-
lev
el
MPPT
co
n
tr
o
l
as
a
r
eq
u
ir
em
e
n
t,
wh
ich
ca
n
o
p
tim
ize
in
d
iv
i
d
u
al
p
an
el
p
er
f
o
r
m
a
n
ce
in
d
e
p
en
d
e
n
tly
an
d
m
i
tig
ate
m
is
m
atch
lo
s
s
es
d
u
e
to
p
ar
tial
s
h
ad
o
win
g
o
r
n
o
n
-
u
n
if
o
r
m
p
a
n
el
ag
in
g
.
Mic
r
o
in
v
e
r
ter
s
p
r
o
v
id
e
b
etter
f
au
lt
d
etec
tio
n
,
im
p
r
o
v
e
d
m
o
n
ito
r
in
g
,
an
d
im
p
r
o
v
e
d
s
ca
lab
ilit
y
th
a
n
ce
n
tr
alize
d
in
v
er
te
r
ar
c
h
itectu
r
es.
Mic
r
o
in
v
e
r
ter
s
ar
e
t
h
er
ef
o
r
e
a
s
u
p
er
i
o
r
o
p
tio
n
f
o
r
r
esid
e
n
tial,
co
m
m
er
cial,
an
d
in
d
u
s
tr
ial
s
o
lar
ap
p
li
ca
tio
n
s
.
Fu
tu
r
e
r
esear
ch
will
f
o
cu
s
o
n
in
teg
r
atin
g
r
ea
l
-
tim
e
ad
a
p
tiv
e
co
n
tr
o
l
tec
h
n
iq
u
es
an
d
m
ac
h
in
e
lear
n
in
g
-
b
ased
MPPT
alg
o
r
ith
m
s
to
im
p
r
o
v
e
d
y
n
am
ic
tr
ac
k
in
g
ca
p
a
b
ilit
y
u
n
d
e
r
s
u
d
d
en
en
v
i
r
o
n
m
e
n
tal
va
r
iatio
n
.
A
d
d
itio
n
ally
,
th
e
u
s
e
o
f
s
o
f
t
-
s
witch
in
g
tech
n
iq
u
es
an
d
o
p
tim
ized
tr
a
n
s
f
o
r
m
e
r
co
r
e
m
ater
ials
will
lead
to
h
ig
h
er
e
f
f
icien
cy
a
n
d
life
tim
e.
All
th
e
im
p
r
o
v
em
en
t
s
m
ak
e
th
e
p
r
o
p
o
s
ed
m
icr
o
in
v
er
ter
an
ad
v
an
ce
d
tech
n
o
lo
g
y
f
o
r
ef
f
icien
t,
s
ca
lab
le,
an
d
h
ig
h
-
p
er
f
o
r
m
an
ce
s
o
lar
en
er
g
y
co
n
v
er
s
io
n
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
s
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