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I
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Vo
l.
15
,
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.
3
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J
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20
25
,
p
p
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2769
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2
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2
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2769
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M
a
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m
p
o
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r
p
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t
trac
k
i
n
g
(M
P
P
T)
e
n
h
a
n
c
e
s
th
e
e
fficie
n
c
y
o
f
s
o
lar
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h
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o
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ic
(P
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sy
ste
m
s
b
y
e
n
su
rin
g
o
p
ti
m
a
l
p
o
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r
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ti
o
n
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d
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v
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ry
in
g
c
o
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d
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ti
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n
s.
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P
P
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is
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m
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lem
e
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ted
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s
o
lar
c
h
a
rg
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o
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tro
ll
e
rs
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r
h
y
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rid
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n
v
e
rters
c
o
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n
e
c
ted
to
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V
a
rra
y
s.
T
h
e
c
u
rre
n
t
-
v
o
lt
a
g
e
(I
V)
c
u
rv
e
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e
n
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e
d
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p
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ra
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m
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a
n
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c
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it
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d
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r
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st
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g
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re
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wo
rld
P
V ap
p
li
c
a
ti
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s.
K
ey
w
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r
d
s
:
Ar
ch
im
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p
tim
izatio
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alg
o
r
ith
m
E
m
b
ed
d
e
d
s
y
s
tem
Ma
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
Ph
o
to
v
o
ltaic
R
en
ewa
b
le
en
er
g
y
So
lar
en
er
g
y
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
:
Prism
a
Me
g
an
to
r
o
Facu
lty
o
f
Ad
v
a
n
ce
d
T
ec
h
n
o
l
o
g
y
an
d
Mu
ltid
is
cip
lin
e,
Un
iv
er
s
itas
Air
lan
g
g
a
6
0
1
1
5
Su
r
ab
a
y
a,
I
n
d
o
n
esia
E
m
ail:
p
r
is
m
a.
m
eg
an
to
r
o
@
f
tm
m
.
u
n
air
.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
g
lo
b
al
en
er
g
y
lan
d
s
ca
p
e
is
r
ap
id
ly
s
h
if
tin
g
to
war
d
s
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
,
with
s
o
lar
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
p
lay
in
g
a
cr
u
cial
r
o
le
in
th
is
tr
an
s
itio
n
d
u
e
to
th
eir
p
o
ten
t
ial
f
o
r
lar
g
e
-
s
ca
le
d
ep
lo
y
m
e
n
t a
n
d
s
u
s
tain
ab
ilit
y
[
1
]
.
H
o
wev
er
,
th
e
e
f
f
icien
cy
o
f
PV sy
s
tem
s
is
s
ig
n
if
ican
tly
h
am
p
er
ed
b
y
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
wh
ich
ca
u
s
e
m
u
ltip
le
lo
ca
l
m
ax
im
a
o
n
th
e
p
o
wer
-
v
o
ltag
e
(
P
-
V)
cu
r
v
e,
co
m
p
licatin
g
th
e
p
r
o
ce
s
s
o
f
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
an
d
lea
d
in
g
t
o
s
u
b
o
p
tim
al
e
n
e
r
g
y
ex
t
r
ac
tio
n
[
2
]
,
[
3
]
.
T
h
e
d
ev
elo
p
m
e
n
t
an
d
im
p
lem
en
ta
tio
n
o
f
a
d
v
an
ce
d
MPPT
alg
o
r
ith
m
s
ar
e
th
er
ef
o
r
e
ess
en
tial
to
en
s
u
r
e
th
at
PV
s
y
s
tem
s
o
p
er
ate
at
th
eir
m
ax
i
m
u
m
p
o
ten
tial u
n
d
e
r
v
ar
y
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
[
4
]
–
[
6
]
.
T
r
ad
itio
n
al
MPPT
alg
o
r
ith
m
s
,
s
u
ch
as
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
an
d
in
c
r
em
en
tal
c
o
n
d
u
ctan
ce
(
I
NC
)
,
h
av
e
b
ee
n
wid
ely
ad
o
p
ted
d
u
e
to
th
eir
s
im
p
licity
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
[
7
]
,
[
8
]
.
So
m
e
r
esear
ch
er
s
u
s
ed
f
u
zz
y
-
b
ased
o
p
tim
izatio
n
f
o
r
th
e
MPPT
im
p
lem
en
tatio
n
[
9
]
–
[
1
3
]
.
Ho
wev
er
,
th
ese
m
eth
o
d
s
o
f
ten
s
u
f
f
e
r
f
r
o
m
d
r
awb
ac
k
s
s
u
ch
as
o
s
cillatio
n
s
ar
o
u
n
d
t
h
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
(
MPP)
an
d
r
ed
u
c
ed
ac
cu
r
ac
y
u
n
d
e
r
r
ap
id
ly
ch
an
g
in
g
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
,
p
ar
ticu
lar
ly
in
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
[
1
4
]
–
[
1
6
]
.
Mo
r
e
o
v
er
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
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8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
6
9
-
2
7
8
5
2770
wh
ile
th
ese
tech
n
iq
u
es
p
er
f
o
r
m
ad
e
q
u
ately
u
n
d
er
u
n
if
o
r
m
ir
r
ad
iatio
n
,
th
eir
ef
f
ec
ti
v
en
ess
s
ig
n
if
ican
tly
d
im
in
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h
es
in
n
o
n
-
u
n
if
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m
co
n
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itio
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to
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n
cr
ea
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ed
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s
es
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d
in
ef
f
icien
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in
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g
y
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ar
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esti
n
g
[
1
7
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–
[
2
0
]
.
T
o
o
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er
co
m
e
th
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ch
allen
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s
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ec
en
t
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m
e
n
ts
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e
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ee
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th
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tr
o
d
u
ctio
n
o
f
b
i
o
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i
n
s
p
ir
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an
d
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
,
s
u
ch
as
th
e
cu
ck
o
o
s
ea
r
ch
(
C
S)
[
2
1
]
,
s
ea
g
u
ll
o
p
tim
izer
(
SO)
[
2
2
]
,
an
d
s
p
o
tted
h
y
en
a
o
p
tim
izer
(
SHO)
[
2
3
]
,
s
q
u
ir
r
el
s
ea
r
ch
alg
o
r
ith
m
(
SS
A)
[
2
4
]
,
m
u
tan
t
p
ar
ticle
s
war
m
o
p
tim
iz
atio
n
(
MPSO)
[
2
5
]
,
m
o
d
if
ied
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
[
2
6
]
,
f
u
s
io
n
f
ir
ef
ly
alg
o
r
ith
m
(
FF
A)
[
2
7
]
,
an
im
m
u
n
e
f
ir
ef
l
y
alg
o
r
ith
m
(
I
FA)
[
2
8
]
,
g
r
ey
wo
lf
o
p
tim
izatio
n
(
GW
O)
[
2
9
]
,
Har
r
is
h
awk
o
p
tim
izatio
n
(
HH
O)
[
3
0
]
,
m
o
th
f
lam
e
o
p
tim
izatio
n
(
MFO)
[
3
1
]
,
g
r
a
s
s
h
o
p
p
er
o
p
tim
izatio
n
(
GHO)
[
3
2
]
,
an
d
an
t
co
lo
n
y
o
p
tim
iz
atio
n
(
AC
O)
[
3
3
]
.
T
h
ese
alg
o
r
ith
m
s
o
f
f
er
im
p
r
o
v
ed
tr
ac
k
i
n
g
p
er
f
o
r
m
a
n
ce
b
y
m
o
r
e
ef
f
ec
tiv
el
y
n
av
ig
atin
g
th
e
co
m
p
lex
P
-
V
lan
d
s
ca
p
es
ca
u
s
ed
b
y
p
ar
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
(
PS
C
s
)
also
Z
af
ar
et
a
l.
[
3
4
]
wr
o
te
a
n
o
v
el
ab
o
u
t
MPPT
co
n
tr
o
l
tech
n
iq
u
es f
o
r
PV sy
s
tem
s
u
n
d
er
p
ar
tial sh
ad
in
g
co
n
d
itio
n
s
u
s
in
g
th
e
m
etah
e
u
r
is
tic
alg
o
r
it
h
m
.
Me
g
an
to
r
o
et
a
l.
[
3
5
]
co
n
d
u
ct
ed
r
esear
ch
to
co
m
p
ar
e
s
o
m
e
e
v
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
(
E
A)
,
s
u
ch
as
th
e
g
en
etic
alg
o
r
ith
m
(
GA)
,
f
ir
ef
l
y
alg
o
r
ith
m
(
FA)
,
f
r
u
itfly
alg
o
r
ith
m
(
FOA)
,
an
d
PS
O,
wh
ich
ar
e
also
u
s
ed
f
o
r
s
o
lv
in
g
th
e
MPPT
p
r
o
b
lem
in
p
ar
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
.
T
h
ese
alg
o
r
ith
m
s
h
a
v
e
d
e
m
o
n
s
tr
ated
s
u
p
er
io
r
co
n
v
er
g
en
ce
s
p
ee
d
,
ac
c
u
r
ac
y
,
an
d
r
o
b
u
s
tn
ess
co
m
p
ar
ed
t
o
co
n
v
e
n
tio
n
al
m
eth
o
d
s
,
m
a
k
in
g
th
em
h
i
g
h
ly
p
r
o
m
is
in
g
f
o
r
r
ea
l
-
wo
r
ld
a
p
p
li
ca
tio
n
s
[
3
6
]
.
R
ec
en
t
ad
v
an
ce
m
e
n
ts
in
o
p
tim
izatio
n
alg
o
r
ith
m
s
h
a
v
e
o
p
en
e
d
n
ew
av
en
u
es
f
o
r
tack
lin
g
th
e
ch
allen
g
es
o
f
p
ar
tial
s
h
ad
in
g
i
n
p
h
o
to
v
o
lt
aic
(
PV)
s
y
s
tem
s
.
T
h
e
ar
c
h
im
ed
es
o
p
tim
izatio
n
alg
o
r
ith
m
(
AOA)
h
as
em
er
g
ed
as
a
p
r
o
m
is
in
g
m
etah
eu
r
is
tic
m
eth
o
d
d
u
e
to
its
d
y
n
am
ic
b
al
an
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
,
ef
f
icie
n
t
co
n
v
er
g
en
ce
ca
p
ab
ilit
ies,
an
d
ad
ap
tab
ilit
y
to
co
m
p
le
x
o
p
tim
izatio
n
p
r
o
b
lem
s
.
AOA'
s
v
er
s
atility
h
as
b
ee
n
d
em
o
n
s
tr
ated
in
v
ar
io
u
s
d
o
m
ain
s
,
in
clu
d
in
g
o
p
tical
s
y
s
tem
d
esig
n
,
wh
er
e
it
ac
h
iev
e
d
s
u
p
er
io
r
o
p
tim
izatio
n
o
u
tco
m
es
in
in
tr
icate
task
s
[
3
7
]
.
I
t
h
as
also
b
ee
n
s
u
cc
ess
f
u
l
ly
ap
p
lied
to
o
p
tim
ize
v
a
r
iab
l
e
p
itch
win
d
tu
r
b
in
e
co
n
tr
o
l,
h
an
d
lin
g
m
u
ltifa
ce
ted
en
g
in
ee
r
in
g
ch
allen
g
es
[
3
8
]
.
I
n
th
e
r
e
n
ewa
b
le
en
e
r
g
y
s
ec
to
r
,
AOA
h
as
s
h
o
wn
ex
ce
llen
t
p
er
f
o
r
m
a
n
ce
in
MPPT
u
n
d
er
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
d
eliv
e
r
in
g
h
ig
h
e
r
ef
f
icien
cy
an
d
f
aste
r
co
n
v
er
g
en
ce
th
a
n
tr
ad
itio
n
al
m
eth
o
d
s
[
3
9
]
.
Ad
d
itio
n
ally
,
AOA
h
as
b
ee
n
u
tili
ze
d
i
n
p
o
wer
s
y
s
tem
s
o
p
tim
izatio
n
,
s
u
c
h
as
PID
tu
n
in
g
o
f
a
DC
-
DC
b
u
c
k
co
n
v
er
ter
[
4
0
]
a
n
d
o
p
tim
izin
g
p
o
we
r
f
lo
w
i
n
elec
tr
ical
s
y
s
tem
s
f
r
o
m
o
p
tim
al
elec
tr
ic
v
eh
icle
ch
ar
g
in
g
s
tatio
n
p
lace
m
en
t
[
4
1
]
.
T
h
ese
ap
p
licatio
n
s
u
n
d
er
s
co
r
e
AOA'
s
r
o
b
u
s
tn
ess
an
d
ef
f
icien
c
y
,
ju
s
tify
in
g
its
u
s
e
in
t
h
is
s
tu
d
y
t
o
ad
d
r
ess
th
e
c
o
m
p
lex
,
n
o
n
li
n
ea
r
p
o
wer
-
v
o
ltag
e
lan
d
s
ca
p
es o
f
PV sy
s
tem
s
af
f
e
cted
b
y
p
a
r
tial sh
ad
in
g
.
T
h
is
r
esear
ch
aim
s
to
b
u
ild
u
p
o
n
th
e
s
e
p
r
o
v
e
n
s
tr
en
g
th
s
o
f
AOA
to
en
h
an
ce
MPPT
p
er
f
o
r
m
an
ce
an
d
en
s
u
r
e
o
p
tim
al
en
er
g
y
h
ar
v
esti
n
g
u
n
d
er
ch
allen
g
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
th
e
A
OA
as
an
ap
p
r
o
ac
h
to
MPPT
in
PV
s
y
s
tem
s
u
n
d
e
r
p
ar
ti
al
s
h
ad
in
g
co
n
d
itio
n
s
,
ad
d
r
ess
in
g
th
e
ch
a
llen
g
es o
f
co
m
p
lex
p
o
wer
-
v
o
lt
ag
e
lan
d
s
ca
p
es.
I
n
teg
r
atin
g
A
OA
in
to
a
r
ea
l
-
tim
e
em
b
ed
d
e
d
s
y
s
tem
with
a
DC
/DC
b
u
ck
c
o
n
v
er
te
r
h
i
g
h
lig
h
ts
its
p
r
ac
tical
ap
p
licab
ilit
y
an
d
s
ca
lab
ilit
y
f
o
r
lo
w
-
co
s
t
PV
s
o
lu
tio
n
s
.
T
h
e
s
tu
d
y
co
m
b
in
es
r
ig
o
r
o
u
s
s
im
u
latio
n
an
d
r
ea
l
-
wo
r
ld
v
alid
atio
n
s
to
estab
lis
h
th
e
alg
o
r
ith
m
'
s
r
eliab
ilit
y
an
d
ad
ap
tab
ilit
y
.
Fu
r
th
er
m
o
r
e,
th
is
r
esear
ch
lay
s
th
e
f
o
u
n
d
atio
n
f
o
r
ex
ten
d
in
g
AOA
to
b
r
o
ad
e
r
r
en
ewa
b
le
en
e
r
g
y
ap
p
licatio
n
s
,
o
f
f
e
r
in
g
a
cu
tt
in
g
-
ed
g
e
s
o
lu
ti
o
n
f
o
r
d
y
n
a
m
ic
an
d
n
o
n
lin
ea
r
o
p
tim
izatio
n
p
r
o
b
lem
s
.
2.
M
E
T
H
O
D
T
h
is
s
ec
tio
n
ex
p
lain
s
t
h
e
m
eth
o
d
s
u
s
ed
i
n
th
e
r
esear
ch
.
T
h
e
d
esig
n
ed
MPPT
d
e
v
ice
u
s
ed
a
s
im
u
lated
m
o
d
el
o
f
a
PV
m
o
d
u
le
in
d
if
f
e
r
en
t
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
th
at
ac
t
as
th
e
p
o
wer
s
u
p
p
ly
f
o
r
th
e
wh
o
le
s
y
s
tem
.
At
th
e
s
am
e
t
im
e,
th
e
MPPT
its
elf
i
s
a
co
m
b
in
atio
n
o
f
an
SC
C
D
C
/D
C
b
u
ck
co
n
v
er
ter
co
n
tr
o
lled
with
a
m
icr
o
co
n
tr
o
ller
in
jecte
d
with
t
h
e
AOA.
2
.
1
.
P
a
rt
ia
l sh
a
din
g
P
V
s
im
ula
t
io
n m
o
del
Par
tial
s
h
ad
in
g
in
PV
m
o
d
u
le
s
s
ig
n
if
ican
tly
af
f
ec
ts
th
e
p
er
f
o
r
m
an
ce
an
d
ef
f
icien
c
y
o
f
s
o
l
ar
en
er
g
y
s
y
s
tem
s
.
W
h
en
a
PV
m
o
d
u
le
is
p
ar
tially
s
h
ad
ed
,
th
e
o
u
tp
u
t
p
o
wer
o
f
th
e
en
tire
s
tr
in
g
o
f
PV
m
o
d
u
les
ca
n
b
e
s
ig
n
if
ican
tly
r
ed
u
ce
d
.
Par
tial
s
h
ad
in
g
also
cr
ea
tes
m
u
ltip
le
p
ea
k
s
in
th
e
p
o
wer
-
v
o
ltag
e
(
P
-
V)
ch
ar
ac
ter
is
tic
cu
r
v
e
o
f
th
e
PV sy
s
tem
,
co
m
p
licatin
g
th
e
task
o
f
MPPT
[
4
2
]
.
Simu
latio
n
to
o
ls
lik
e
MA
T
L
AB
an
d
PS
I
M
h
av
e
b
ee
n
u
s
ed
to
m
o
d
el
an
d
an
aly
ze
th
e
ef
f
ec
ts
o
f
p
ar
tial sh
ad
in
g
to
h
elp
u
n
d
er
s
tan
d
th
e
I
-
V
(
cu
r
r
en
t
-
v
o
ltag
e)
an
d
P
-
V
ch
ar
ac
ter
is
tics
o
f
s
o
lar
m
o
d
u
les u
n
d
er
n
o
n
-
u
n
if
o
r
m
ir
r
a
d
iatio
n
[
4
3
]
,
[
4
4
]
.
T
h
e
p
h
o
to
v
o
ltaics
m
o
d
u
le
in
th
is
r
esear
ch
s
im
u
lated
f
o
u
r
v
ar
iatio
n
s
o
f
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
:
f
u
ll
ir
r
ad
ian
ce
,
q
u
ar
ter
-
s
h
a
d
ed
,
h
al
f
-
s
h
ad
ed
,
a
n
d
q
u
ar
ter
-
ir
r
ad
ian
ce
.
T
h
e
s
im
u
latio
n
was
co
n
d
u
c
ted
with
th
e
h
elp
o
f
IT
-
M3
6
2
2
B
i
-
Dir
ec
tio
n
al
Po
wer
Su
p
p
l
y
an
d
SAS1
0
0
0
So
f
twar
e,
b
o
t
h
o
f
wh
ic
h
ar
e
m
an
u
f
ac
tu
r
ed
b
y
I
T
E
C
H.
T
h
e
I
T
-
M
3
6
2
2
s
u
p
p
lies
p
h
y
s
ical
v
o
ltag
es a
n
d
cu
r
r
en
t a
s
an
ac
tu
al
PV m
o
d
u
le,
p
air
ed
with
SAS1
0
0
0
th
at
r
u
n
s
th
e
PV
m
o
d
u
le
s
p
ec
if
icatio
n
s
,
s
h
ad
o
w
q
u
a
n
titi
es
an
d
m
o
v
e
m
en
t
v
a
r
iatio
n
s
,
an
d
d
ata
ac
q
u
is
iti
o
n
.
T
h
e
I
T
E
C
H
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Th
e
imp
leme
n
ta
tio
n
o
f A
r
ch
i
med
es o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
s
o
la
r
ch
a
r
g
e
…
(
S
ig
it Da
n
i P
erka
s
a
)
2771
IT
-
M3
6
2
2
p
o
wer
s
u
p
p
l
y
s
im
u
lates
an
8
0
W
p
PV
m
o
d
u
le
in
d
if
f
er
en
t
s
ce
n
ar
io
s
o
f
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
f
r
o
m
th
e
s
h
ad
o
w
m
o
d
e
o
f
SAS1
0
0
0
s
o
f
twar
e
with
t
h
e
s
h
ad
i
n
g
co
n
f
ig
u
r
atio
n
illu
s
tr
ated
in
Fig
u
r
e
1
.
2
.
2
.
M
P
P
T
t
ec
hn
iqu
e
MPPT
i
s
a
cr
u
cial
tech
n
iq
u
e
u
s
ed
in
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
to
o
p
tim
ize
p
o
wer
ex
tr
a
ctio
n
f
r
o
m
s
o
lar
p
an
els
b
y
en
s
u
r
in
g
th
e
y
o
p
er
ate
at
th
eir
MPP.
Sin
ce
e
n
v
ir
o
n
m
en
tal
f
ac
to
r
s
s
u
ch
as
s
o
lar
ir
r
ad
iatio
n
an
d
tem
p
er
atu
r
e
co
n
tin
u
o
u
s
ly
f
lu
ct
u
ate,
th
e
MPP
v
a
r
ies.
I
t
is
r
e
q
u
ir
in
g
d
y
n
am
ic
ad
ju
s
tm
en
ts
to
m
ain
tain
m
ax
im
u
m
ef
f
icien
cy
.
MPPT
alg
o
r
ith
m
s
co
n
tin
u
o
u
s
ly
tr
ac
k
t
h
ese
ch
an
g
es
an
d
a
d
ju
s
t
th
e
o
p
er
atin
g
v
o
ltag
e
o
r
cu
r
r
e
n
t
to
en
s
u
r
e
o
p
tim
al
p
o
wer
o
u
tp
u
t
.
T
h
e
s
im
u
lated
p
ar
tial
s
h
ad
i
n
g
co
n
f
ig
u
r
atio
n
i
n
Fig
u
r
e
1
co
n
s
is
ted
o
f
4
s
h
ad
o
w
co
n
d
itio
n
s
co
v
er
in
g
d
if
f
er
en
t
ar
ea
s
o
f
t
h
e
s
im
u
late
d
3
6
ce
lls
'
PV
m
o
d
u
le,
r
e
p
r
es
en
tin
g
ei
g
h
t
s
m
all
r
ec
tan
g
les
o
f
4
.
5
ce
lls
ea
ch
.
I
n
Fig
u
r
e
1
(
a)
,
th
e
PV
ce
lls
a
r
e
co
m
p
letely
ir
r
ad
iated
,
wh
ile
i
n
Fig
u
r
e
1
(
b
)
,
2
5
%
o
f
th
e
u
p
p
er
-
lef
t
PV
ce
lls
a
r
e
s
h
ad
ed
,
an
d
o
n
ly
2
7
ce
lls
ar
e
ir
r
ad
iated
.
I
n
Fig
u
r
e
1
(
c)
,
t
h
e
h
alf
-
lef
t
o
f
th
e
PV
ce
lls
war
e
co
v
er
ed
,
an
d
o
n
ly
1
8
ce
lls
wer
e
ir
r
ad
iated
,
an
d
i
n
Fig
u
r
e
1
(
d
)
,
o
n
ly
n
in
e
ce
lls
i
n
th
e
lo
wer
-
r
ig
h
t
ar
e
ir
r
ad
iated
o
r
7
5
% sh
ad
ed
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
.
PV m
o
d
u
le
s
h
ad
in
g
co
n
f
ig
u
r
atio
n
;
(
a
)
1
0
0
% ir
r
ad
i
an
ce
,
(
b
)
7
5
% ir
r
a
d
ian
ce
,
(
c)
5
0
% ir
r
ad
ian
ce
,
an
d
(
d
)
2
5
% ir
r
ad
ian
ce
2
.
3
.
Arc
him
edes o
ptim
iza
t
io
n a
lg
o
rit
hm
T
h
e
AOA
is
a
n
o
v
el
m
etah
eu
r
i
s
tic
alg
o
r
ith
m
in
s
p
ir
e
d
b
y
Ar
c
h
im
ed
es'
p
r
in
cip
le
[
4
2
]
,
[
4
3
]
.
T
h
e
AOA’
s
ag
en
ts
s
ig
n
if
ican
tly
ad
v
an
ce
o
p
tim
izatio
n
,
lev
er
ag
in
g
p
h
y
s
ical
p
r
in
cip
les to
en
h
an
ce
co
m
p
u
tatio
n
al
ef
f
icien
cy
an
d
s
o
lu
tio
n
q
u
ality
[
4
4
]
,
[
4
5
]
.
T
h
e
AOA
is
cla
s
s
if
ied
in
to
s
ix
m
ath
em
atica
l
s
tep
s
in
th
is
r
esear
ch
,
wh
ich
ar
e
ex
p
lain
ed
in
th
e
f
o
llo
win
g
s
ec
tio
n
.
T
h
e
AOA
was
ch
o
s
en
f
o
r
th
is
s
tu
d
y
d
u
e
to
its
ab
ilit
y
t
o
o
p
tim
ize
co
m
p
lex
,
n
o
n
lin
e
ar
s
y
s
tem
s
ef
f
ec
tiv
ely
.
Un
lik
e
tr
ad
itio
n
al
alg
o
r
ith
m
s
s
u
ch
as
PS
O
o
r
G
A,
AOA'
s
d
y
n
am
ic
b
ala
n
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
e
x
p
lo
itatio
n
en
a
b
les
it
to
c
o
n
v
er
g
e
f
aster
wh
ile
a
v
o
id
in
g
lo
ca
l
o
p
tim
a.
R
ec
en
t
a
p
p
licatio
n
s
o
f
AOA
f
u
r
th
er
u
n
d
er
s
co
r
e
its
v
er
s
atility
an
d
ef
f
icien
cy
.
Fo
r
in
s
tan
ce
,
AOA
h
as
b
ee
n
em
p
lo
y
ed
in
r
en
ewa
b
le
en
er
g
y
o
p
tim
izatio
n
an
d
p
o
wer
s
y
s
tem
s
en
g
in
ee
r
in
g
,
ac
h
iev
in
g
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
m
etr
ic
s
[
3
7
]
,
[
3
9
]
–
[
4
1
]
,
[
4
5
]
–
[
4
9
]
.
T
h
ese
m
e
r
its
m
ak
e
AOA
a
co
m
p
ellin
g
ch
o
ice
f
o
r
ad
d
r
ess
in
g
th
e
ch
alle
n
g
es
o
f
MPPT
u
n
d
er
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
2
.
3
.
1
.
I
nitia
liza
t
io
n
I
n
th
is
s
tep
,
o
b
ject
p
o
s
itio
n
s
ar
e
in
itialized
u
s
in
g
(
1
)
.
W
h
er
e
r
ep
r
esen
ts
th
e
i
-
th
o
b
ject
in
a
p
o
p
u
latio
n
o
f
N
.
an
d
d
en
o
te
th
e
lo
wer
an
d
u
p
p
er
b
o
u
n
d
s
o
f
t
h
e
s
ea
r
ch
r
an
g
e,
r
esp
e
ctiv
ely
.
T
h
e
in
itializatio
n
o
f
v
o
l
u
m
e
(
vo
l
)
a
n
d
d
en
s
ity
(
d
en
)
f
o
r
ea
ch
o
b
je
ct
i
f
o
llo
ws (
2
)
.
=
+
×
(
−
)
;
=
1
,
2
,
…
,
(
1
)
w
ith
r
a
n
d
is
a
d
im
en
s
io
n
al
v
ec
to
r
D
r
a
n
d
o
m
ly
g
e
n
er
atin
g
n
u
m
b
er
s
b
etwe
en
0
an
d
1
.
T
h
e
v
elo
city
(
a
cc
)
is
in
itialized
u
s
in
g
(
3
)
.
I
n
th
is
s
te
p
,
th
e
i
n
itial
p
o
p
u
latio
n
is
ev
al
u
ated
,
an
d
th
e
o
b
ject
with
th
e
b
est
f
itn
ess
v
alu
e
is
ch
o
s
en
an
d
ad
d
e
d
to
,
,
,
v
ar
iab
les.
=
;
=
(
2
)
=
+
×
(
−
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
6
9
-
2
7
8
5
2772
2
.
3
.
2
.
Upda
t
ing
dens
it
y
a
nd
v
o
lum
e
T
h
e
d
en
s
ity
an
d
v
o
lu
m
e
o
f
th
e
i
-
th
o
b
ject
f
o
r
iter
atio
n
n
u
m
b
er
t
+
1
wer
e
u
p
d
ated
u
s
in
g
(
4
)
an
d
(
5
)
.
W
h
er
e
an
d
is
th
e
d
en
s
ity
an
d
v
o
lu
m
e
o
f
th
e
b
est o
b
ject
f
o
u
n
d
with
u
n
i
f
o
r
m
r
a
n
d
.
+
1
=
+
1
+
×
(
−
1
)
(
4
)
+
=
+
+
×
(
−
)
(
5
)
2
.
3
.
3
.
T
ra
ns
f
er
o
pera
t
o
r
a
nd
dens
it
y
f
a
ct
o
r
C
o
llis
io
n
s
am
o
n
g
o
b
jects
o
cc
u
r
,
an
d
o
v
er
tim
e,
t
h
ese
o
b
jec
ts
attem
p
t
to
r
ea
ch
a
n
eq
u
ilib
r
iu
m
p
o
in
t.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
(
T
F)
r
eq
u
ir
ed
f
o
r
tr
an
s
f
o
r
m
in
g
th
e
s
ea
r
ch
f
r
o
m
ex
p
lo
r
atio
n
to
e
x
p
lo
i
tatio
n
is
d
ef
in
e
d
in
(
6
)
.
TF
in
cr
ea
s
es
with
tim
e
u
n
t
il
r
ea
ch
es
1
,
wh
ile
t
an
d
is
iter
a
tio
n
n
u
m
b
er
an
d
m
ax
im
u
m
iter
atio
n
.
Den
s
ity
d
ec
r
ea
s
in
g
f
ac
t
o
r
(
d)
h
elp
s
AO
A
move
f
r
o
m
g
lo
b
al
s
ea
r
ch
to
l
o
ca
l
s
ea
r
ch
,
w
h
ich
d
ec
r
ea
s
es
with
tim
e
ac
co
r
d
in
g
to
(
7
)
.
=
e
xp
(
−
)
(
6
)
+
1
=
e
xp
(
−
)
−
(
)
(
7
)
2
.
3
.
4
.
E
x
plo
ra
t
io
n a
nd
ex
plo
i
t
a
t
io
n
a
.
E
x
p
lo
r
atio
n
p
h
ase
(
o
b
ject
c
o
llis
io
n
s
)
If
TF
≤
0
.
5
,
co
llis
io
n
s
b
etwe
en
o
b
jects
h
ap
p
e
n
,
an
d
r
an
d
o
m
m
ater
ial
(
mr)
is
s
elec
ted
,
a
n
d
o
b
ject
ac
ce
ler
atio
n
is
u
p
d
ated
u
s
in
g
(
8
)
.
W
h
er
e
,
,
an
d
is
th
e
d
en
s
ity
,
v
o
lu
m
e,
an
d
v
elo
city
o
f
th
e
i
-
th
o
b
ject.
W
h
ile
,
an
d
is
th
e
d
en
s
ity
,
v
o
lu
m
e
,
an
d
v
elo
city
of
th
e
r
an
d
o
m
ly
s
elec
ted
o
b
ject.
+
1
=
+
×
+
1
×
+
1
(
8
)
b
.
E
x
p
l
o
itatio
n
p
h
ase
(
n
o
o
b
je
ct
co
llis
io
n
s
)
Su
p
p
o
s
e
TF
>
0
.
5
;
co
llis
io
n
s
b
etwe
en
o
b
jects
do
n
o
t
h
ap
p
en
.
Ob
ject
v
elo
city
at
t
+
1
i
s
u
p
d
ated
u
s
in
g
(
9
)
.
W
h
er
e
is
th
e
v
elo
city
o
f
th
e
b
est o
b
ject
.
+
1
=
+
×
+
1
×
+
1
(
9
)
2
.
3
.
5
.
No
rma
lizing
a
cc
eler
a
t
i
o
n
Velo
city
is
n
o
r
m
alize
d
to
co
m
p
u
te
p
er
ce
n
tag
e
ch
a
n
g
e
u
s
in
g
(
1
0
)
.
W
h
er
e
u
a
n
d
l
ar
e
th
e
n
o
r
m
aliza
tio
n
r
an
g
e
s
et
to
0
.
9
an
d
0
.
1
,
r
esp
ec
tiv
ely
.
−
+
1
d
eter
m
in
es
th
e
s
tep
p
er
ce
n
tag
e
ch
an
g
e
f
o
r
ea
c
h
a
g
en
t.
Ob
jects
f
ar
f
r
o
m
th
e
g
lo
b
al
o
p
tim
al
v
al
u
e
will
h
av
e
h
ig
h
er
v
elo
city
v
a
lu
es,
in
d
icatin
g
th
e
tr
an
s
itio
n
f
r
o
m
th
e
ex
p
lo
r
atio
n
p
h
ase
to
th
e
ex
p
lo
itatio
n
p
h
ase.
−
+
1
=
×
+
1
−
m
i
n
(
)
m
ax
(
)
−
m
i
n
(
)
+
(
1
0
)
2
.
3
.
6
.
P
o
s
it
io
n upd
a
t
e
I
n
th
e
e
x
p
l
o
r
a
t
i
o
n
p
h
a
s
e
,
t
h
e
p
o
s
i
t
i
o
n
o
f
t
h
e
i
-
t
h
o
b
j
e
c
t
i
n
i
t
e
r
a
t
i
o
n
n
u
m
b
e
r
t
+
1
i
s
u
p
d
a
te
d
u
s
i
n
g
(
1
1
)
.
W
h
e
r
e
1
i
s
a
c
o
n
s
t
a
n
t
e
q
u
a
l
t
o
2
,
i
n
t
h
e
e
x
p
l
o
i
t
at
i
o
n
p
h
a
s
e
(
T
F
>
0
.
5
)
,
t
h
e
o
b
j
e
c
t
p
o
s
i
t
i
o
n
is
u
p
d
a
t
e
d
u
s
i
n
g
(
1
2
)
.
+
1
=
+
1
×
×
−
+
1
×
×
(
−
)
(
1
1
)
+
1
=
+
×
2
×
×
−
+
1
×
×
(
×
−
)
(
1
2
)
w
h
er
e
2
is
eq
u
al
t
o
6
,
T
in
cr
ea
s
e
s
lin
ea
r
ly
with
tim
e
an
d
is
p
r
o
p
o
r
tio
n
al
with
T
F
an
d
d
e
f
in
ed
with
=
1
×
with
a
r
an
g
e
o
f
3
×
0
.
3
to
1
.
Ob
ject
m
o
v
em
en
t
d
ir
ec
tio
n
ch
an
g
es
ar
e
r
ep
r
esen
ted
as
F
in
(
1
3
)
.
W
h
er
e
=
2
×
−
4
=
{
+
1
≤
0
.
5
−
1
>
0
.
5
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Th
e
imp
leme
n
ta
tio
n
o
f A
r
ch
i
med
es o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
s
o
la
r
ch
a
r
g
e
…
(
S
ig
it Da
n
i P
erka
s
a
)
2773
2
.
3
.
7
.
O
bje
ct
iv
e
f
un
ct
io
n
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
aim
s
t
o
o
p
tim
ize
th
e
d
u
ty
cy
cle
(
D
)
,
r
ep
r
e
s
en
tin
g
th
e
p
o
p
u
latio
n
(
X
)
in
AOA,
to
m
a
x
im
ize
th
e
p
o
wer
o
u
tp
u
t
(
P
out
)
.
E
ac
h
ca
n
d
id
ate
d
u
ty
cy
cle
co
r
r
esp
o
n
d
s
to
a
PW
M
v
alu
e
co
n
t
r
o
llin
g
th
e
DC
/DC
b
u
ck
c
o
n
v
er
te
r
,
an
d
th
e
AOA
iter
ativ
ely
ad
ju
s
ts
th
ese
v
alu
e
s
to
f
in
d
th
e
g
lo
b
al
MPP u
n
d
er
p
ar
tial sh
ad
in
g
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
r
ep
r
es
en
ted
b
y
(
1
4
)
.
(
)
=
∙
(
1
4
)
w
h
er
e
X
=
D
(
d
u
ty
cy
cle
)
,
V
out
is
th
e
MPPT
o
u
tp
u
t
v
o
ltag
e
,
a
n
d
I
is
th
e
MPPT
o
u
tp
u
t
cu
r
r
e
n
t
.
B
y
d
y
n
am
ically
ev
alu
atin
g
a
n
d
r
ef
in
in
g
th
e
d
u
ty
cy
cle,
th
e
AOA
en
s
u
r
es
th
e
PV
s
y
s
tem
o
p
er
ates
ef
f
icien
tly
,
ad
ap
tin
g
to
co
m
p
lex
a
n
d
ch
a
n
g
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
2
.
3
.
8
.
AO
A
pa
ra
m
et
er
s
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
AO
A
in
MPPT
ap
p
licatio
n
s
d
ep
en
d
s
h
ea
v
ily
o
n
ad
e
q
u
ately
tu
n
in
g
its
p
ar
am
eter
s
.
T
h
ese
p
a
r
am
eter
s
g
o
v
er
n
th
e
alg
o
r
ith
m
'
s
ab
ilit
y
to
b
alan
ce
ex
p
lo
r
atio
n
an
d
e
x
p
lo
itatio
n
,
e
n
s
u
r
in
g
ef
f
icien
t
an
d
ac
cu
r
ate
co
n
v
er
g
en
ce
to
t
h
e
g
lo
b
al
MPP
f
o
r
M
PP
T
in
p
h
o
t
o
v
o
ltaic
PV
s
y
s
tem
s
,
th
e
p
a
r
am
eter
s
h
av
e
b
ee
n
tu
n
ed
t
o
s
u
it
d
y
n
a
m
ic
an
d
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
as
d
etailed
in
T
ab
le
1
.
B
y
s
ettin
g
th
ese
p
ar
am
eter
s
ap
p
r
o
p
r
iately
,
th
e
AOA
ca
n
d
y
n
am
ically
a
d
ap
t
t
o
ch
an
g
es
in
ir
r
ad
ian
ce
an
d
s
h
ad
in
g
c
o
n
d
itio
n
s
,
en
s
u
r
in
g
r
o
b
u
s
t
MPPT
p
er
f
o
r
m
an
ce
.
T
h
e
ch
o
s
en
v
alu
es
b
a
lan
ce
co
m
p
u
tatio
n
al
ef
f
icien
c
y
an
d
o
p
tim
izatio
n
p
r
ec
is
io
n
,
m
ak
i
n
g
th
e
AOA
s
u
itab
le
f
o
r
r
ea
l
-
tim
e
e
m
b
ed
d
ed
ap
p
licatio
n
s
in
PV sy
s
tem
s
.
T
ab
le
1
.
AOA
tu
n
in
g
p
ar
a
m
et
er
s
P
a
r
a
me
t
e
r
V
a
l
u
e
P
o
p
u
l
a
t
i
o
n
S
i
z
e
(
N
)
20
M
a
x
i
m
u
m
I
t
e
r
a
t
i
o
n
s (
T
m
ax
)
50
–
1
0
0
I
n
i
t
i
a
l
D
e
n
s
i
t
y
(
d
e
n
i
n
i
t
)
0
.
1
–
0
.
9
I
n
i
t
i
a
l
V
o
l
u
me
(
Vo
l
i
n
i
t
)
0
.
1
–
0
.
9
Tr
a
n
sf
e
r
F
u
n
c
t
i
o
n
(
TF
)
0
t
o
1
A
c
c
e
l
e
r
a
t
i
o
n
C
o
e
f
f
i
c
i
e
n
t
s (
C
1
,
C
2
)
C
1
=
2
.
0
,
C
2
=
1
.
0
N
o
r
mal
i
z
a
t
i
o
n
R
a
n
g
e
(
u
,
l
)
u=
0
.
9
,
l
=
0
.
1
2
.
4
.
SCC
DC/DC
bu
ck
co
nv
er
t
er
T
h
e
d
esig
n
an
d
im
p
lem
en
tati
o
n
o
f
s
o
lar
ch
ar
g
e
co
n
tr
o
ller
(
SC
C
)
u
til
izin
g
DC
/D
C
b
u
ck
co
n
v
er
ter
s
p
lay
a
c
r
u
cial
r
o
le
in
e
f
f
icien
t
m
an
ag
em
en
t
an
d
s
to
r
ag
e
o
f
s
o
lar
en
er
g
y
.
T
h
e
co
n
f
ig
u
r
atio
n
o
f
th
e
DC
/DC
b
u
ck
co
n
v
er
ter
in
cl
u
d
es;
MO
SF
E
T
s
,
d
io
d
es,
in
d
u
cto
r
s
,
an
d
ca
p
a
ci
to
r
s
.
T
h
e
co
n
f
ig
u
r
atio
n
o
f
th
e
co
m
p
o
n
en
ts
allo
w
ef
f
icien
t
en
er
g
y
co
n
v
er
s
io
n
b
y
r
ed
u
cin
g
th
e
h
i
g
h
er
an
d
f
lu
ctu
atin
g
in
p
u
t
v
o
ltag
es
to
lo
w
er
an
d
s
tab
le
o
u
tp
u
t
v
o
ltag
e
s
u
ited
f
o
r
ch
a
r
g
in
g
b
at
ter
ies o
r
p
o
wer
in
g
lo
ad
s
[
5
0
]
.
3.
I
M
P
L
E
M
E
NT
A
T
I
O
N
T
h
e
m
eth
o
d
o
lo
g
y
d
escr
ib
ed
i
n
th
e
p
r
ev
io
u
s
s
u
b
s
ec
tio
n
was
im
p
lem
en
ted
o
n
a
h
ar
d
war
e
p
latf
o
r
m
t
o
v
alid
ate
its
p
r
ac
tical
f
ea
s
ib
ilit
y
.
T
h
is
im
p
lem
en
tatio
n
in
clu
d
es
th
e
d
esig
n
o
f
a
SC
C
to
en
h
an
c
e
p
o
wer
c
o
n
v
e
r
s
io
n
ef
f
icien
cy
.
T
h
e
im
p
lem
en
tatio
n
co
n
d
u
cted
alo
n
g
with
th
e
in
teg
r
atio
n
o
f
a
MPPT
alg
o
r
ith
m
ca
p
ab
le
o
f
h
a
n
d
lin
g
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
Ad
d
itio
n
ally
,
th
e
ap
p
r
o
ac
h
f
o
r
em
b
ed
d
in
g
th
e
AOA
in
to
th
e
MPPT
h
ar
d
war
e
is
d
is
cu
s
s
ed
in
th
e
f
o
llo
win
g
s
u
b
s
ec
tio
n
.
I
t is en
s
u
r
in
g
r
ea
l
-
tim
e
ad
ap
tab
ilit
y
an
d
ef
f
icien
t
p
o
wer
ex
tr
ac
tio
n
.
3
.
1
.
M
P
P
T
in pa
rt
ia
l sh
a
din
g
Dete
ctin
g
p
ar
tial
s
h
a
d
i
n
g
o
c
c
u
r
r
e
n
c
e
s
a
c
c
u
r
a
t
e
l
y
is
e
s
s
e
n
ti
a
l
f
o
r
i
n
i
t
i
a
ti
n
g
t
h
e
a
p
p
r
o
p
r
i
a
t
e
M
PP
T
r
e
s
p
o
n
s
e
.
T
h
e
s
y
s
t
e
m
i
n
t
e
g
r
a
t
es
t
h
e
s
e
l
ec
t
e
d
M
PP
T
a
l
g
o
r
i
t
h
m
(
i
n
t
h
i
s
c
a
s
e
,
AO
A
)
,
a
n
d
t
h
e
i
r
p
e
r
f
o
r
m
a
n
c
e
i
s
t
e
s
t
e
d
u
n
d
e
r
c
o
n
t
r
o
l
l
e
d
p
a
r
t
i
al
s
h
a
d
in
g
s
c
e
n
a
r
i
o
s
.
D
at
a
f
r
o
m
t
h
e
ex
p
e
r
i
m
e
n
t
s
a
r
e
a
n
a
l
y
z
e
d
t
o
v
e
r
i
f
y
t
h
e
s
i
m
u
l
a
ti
o
n
o
u
t
c
o
m
e
s
,
e
n
s
u
r
i
n
g
t
h
a
t
t
h
e
MP
P
T
s
t
r
a
t
e
g
i
e
s
a
r
e
e
f
f
ec
t
i
v
e
i
n
r
e
a
l
-
w
o
r
l
d
a
p
p
l
i
c
at
i
o
n
s
.
P
V
o
u
t
p
u
t
u
n
d
e
r
p
a
r
t
i
a
l
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s
i
m
u
l
a
ti
o
n
s
is
r
e
p
r
e
s
e
n
te
d
i
n
a
s
e
t
o
f
P
-
V
a
n
d
I
-
V
c
u
r
v
e
s
illu
s
tr
ated
in
Fig
u
r
e
s
2
(
a)
to
2
(
d
)
.
T
h
e
I
-
V
a
n
d
P
-
V
cu
r
v
es
f
o
r
th
e
s
im
u
lated
PV
m
o
d
u
le
u
n
d
er
d
if
f
er
en
t
s
h
a
d
in
g
co
n
d
itio
n
s
i
n
Fig
u
r
e
2
d
em
o
n
s
tr
ate
th
e
c
h
allen
g
es
an
d
im
p
o
r
tan
ce
o
f
MPPT
in
p
a
r
tial
s
h
ad
in
g
s
ce
n
ar
io
s
.
As
s
h
ad
in
g
in
cr
ea
s
es
(
f
r
o
m
1
0
0
%
to
2
5
%
i
r
r
a
d
i
a
t
i
o
n
)
in
Fig
u
r
e
2
(
a)
s
h
o
ws
th
e
PV
r
esp
o
n
s
e
in
u
n
if
o
r
m
in
s
o
latio
n
,
Fig
u
r
e
2
(
b
)
s
h
o
ws
th
e
PV
r
esp
o
n
s
e
at
7
5
%
s
h
a
d
in
g
,
Fig
u
r
e
2
(
c
)
s
h
o
ws
th
e
PV
r
esp
o
n
s
e
at
5
0
%
s
h
ad
i
n
g
,
an
d
Fig
u
r
e
2
(
d
)
s
h
o
ws
th
e
PV
r
esp
o
n
s
e
at
2
5
%
s
h
ad
in
g
.
T
h
e
cu
r
v
es
s
h
o
w
a
r
ed
u
ct
io
n
in
b
o
th
cu
r
r
en
t
an
d
p
o
wer
o
u
tp
u
t,
wit
h
th
e
in
tr
o
d
u
ctio
n
o
f
m
u
ltip
le
lo
ca
l
m
ax
im
a.
T
h
is
co
m
p
lex
ity
r
e
q
u
ir
es
ad
v
a
n
ce
d
MPPT
alg
o
r
ith
m
s
to
ac
cu
r
atel
y
d
is
tin
g
u
is
h
an
d
tr
ac
k
th
e
tr
u
e
MPP a
m
o
n
g
th
ese
lo
ca
l p
ea
k
s
,
en
s
u
r
in
g
o
p
tim
al
en
er
g
y
h
ar
v
esti
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
6
9
-
2
7
8
5
2774
(a
)
(b
)
(c
)
(d
)
Fig
u
r
e
2
.
I
-
V
an
d
P
-
V
cu
r
v
es
o
f
s
im
u
lated
PV m
o
d
u
le
o
u
t
p
u
t u
n
d
er
d
if
f
er
e
n
t sh
ad
in
g
co
n
d
itio
n
s
.
(
a)
1
0
0
%
ir
r
ad
ian
ce
,
(
b
)
7
5
% ir
r
ad
ian
ce
,
(
c)
5
0
% ir
r
ad
ian
ce
,
a
n
d
(
d
)
2
5
% ir
r
ad
ian
ce
3
.
2
.
M
P
P
T
-
AO
A
a
pp
ro
a
ch
I
n
th
e
f
lo
wch
a
r
t
in
Fig
u
r
e
3
,
v
o
ltag
e
an
d
cu
r
r
e
n
t
f
r
o
m
th
e
PV
p
an
els
ar
e
m
ea
s
u
r
ed
an
d
f
ed
in
to
th
e
MPPT
alg
o
r
ith
m
.
T
h
e
A
O
A
w
a
s
i
m
p
l
e
m
e
n
t
e
d
t
o
p
e
r
f
o
r
m
a
m
a
x
i
m
u
m
o
f
5
0
i
t
e
r
a
t
i
o
n
s
,
g
e
n
e
r
a
t
i
n
g
f
o
u
r
m
a
t
e
r
i
a
l
s
w
i
t
h
i
n
a
s
e
a
r
c
h
r
a
n
g
e
o
f
0
t
o
1
0
0
,
w
i
t
h
a
c
c
e
l
e
r
a
t
i
o
n
c
o
e
f
f
i
c
ie
n
t
s
C
3
=
2
a
n
d
C
4
=
1
,
a
n
d
f
o
l
l
o
w
s
t
h
e
f
l
o
w
c
h
a
r
t
i
n
F
i
g
u
r
e
3
.
T
h
e
AOA
o
p
tim
izes
th
e
co
n
v
er
te
r
'
s
d
u
ty
cy
cle,
g
e
n
er
atin
g
a
PW
M
s
ig
n
al.
T
h
is
PW
M
s
ig
n
al
is
th
en
u
s
ed
to
e
v
alu
ate
th
e
MPP.
I
f
t
h
e
o
p
tim
al
MPP
is
ac
h
iev
ed
,
t
h
e
p
r
o
ce
s
s
o
u
tp
u
ts
it;
o
th
er
wi
s
e,
it
lo
o
p
s
b
ac
k
to
o
p
tim
ize
th
e
tr
ac
k
i
n
g
f
u
r
th
er
.
T
h
e
m
ater
ial
g
en
er
atio
n
p
r
o
ce
s
s
was
ev
alu
ated
,
an
d
Fig
u
r
e
4
(
a)
s
h
o
ws
s
ig
n
if
ican
t
ch
an
g
es
i
n
m
ater
ial
g
en
er
atio
n
s
f
r
o
m
in
itializatio
n
to
th
e
5
0
th
iter
atio
n
,
in
d
icati
n
g
AOA'
s
d
y
n
am
ic
an
d
n
o
n
lin
ea
r
b
eh
a
v
io
r
.
T
h
is
b
eh
av
io
r
lea
d
s
to
v
ar
iatio
n
s
in
m
ater
ial
p
r
o
p
e
r
ties
as
AOA
e
x
p
lo
r
es
d
if
f
e
r
en
t
r
eg
i
o
n
s
o
f
th
e
p
ar
am
eter
s
p
ac
e.
Fo
llo
win
g
m
ater
ial
g
e
n
er
atio
n
,
AOA
u
p
d
ated
t
h
e
b
est
m
at
er
ial
at
ea
ch
iter
atio
n
,
with
th
e
r
esu
lts
s
h
o
wn
i
n
Fig
u
r
e
4
(
a
)
in
d
icatin
g
co
n
v
er
g
en
ce
m
ar
k
ed
b
y
s
tab
le
PW
M
v
alu
es.
T
h
e
u
p
d
ated
m
ater
i
al
i
n
d
ices
wer
e
in
p
u
t
in
to
th
e
o
b
jectiv
e
f
u
n
ctio
n
to
f
ac
ilit
ate
MPP
d
etec
tio
n
,
as
s
h
o
wn
in
Fig
u
r
e
4
(
b
)
.
E
ac
h
o
b
ject
iv
e
v
alu
e
in
cr
ea
s
ed
u
n
til
s
tab
ilizin
g
,
s
ig
n
if
y
in
g
o
p
tim
al
o
b
jectiv
e
v
alu
es
ac
h
ie
v
ed
in
th
e
m
ain
lo
o
p
.
T
h
e
c
o
n
v
er
g
e
n
ce
p
r
o
ce
s
s
,
illu
s
tr
ated
in
Fig
u
r
e
4
(
c)
,
s
h
o
ws
th
e
AOA
f
u
n
ctio
n
test
r
esu
lts
,
with
th
e
alg
o
r
ith
m
ac
h
ie
v
in
g
c
o
n
v
e
r
g
en
ce
b
y
th
e
1
9
th
iter
atio
n
u
s
in
g
th
e
s
p
ec
if
ied
p
ar
am
eter
s
.
T
h
e
s
tep
s
d
em
o
n
s
tr
ated
in
Fig
u
r
e
s
3
an
d
4
s
h
o
w
th
e
MPPT
-
AOA
f
u
n
ctio
n
'
s
ef
f
ec
tiv
en
ess
in
tr
ac
k
in
g
th
e
MPP
in
th
e
s
o
l
ar
p
o
wer
s
y
s
tem
,
co
n
f
ir
m
in
g
AOA
'
s
ca
p
ab
ilit
y
in
o
p
tim
izin
g
PV m
o
d
u
le
p
er
f
o
r
m
an
ce
u
n
d
er
v
a
r
y
in
g
co
n
d
itio
n
s
.
Fig
u
r
e
3
.
MPPT
im
p
lem
en
tati
o
n
f
lo
wch
a
r
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Th
e
imp
leme
n
ta
tio
n
o
f A
r
ch
i
med
es o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
s
o
la
r
ch
a
r
g
e
…
(
S
ig
it Da
n
i P
erka
s
a
)
2775
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
AOA
p
r
o
g
r
ess
io
n
o
f
g
en
er
atin
g
t
h
e
b
est s
o
lu
tio
n
f
o
r
ea
ch
iter
atio
n
.
(
a)
m
ate
r
ial
(
PW
M)
g
en
er
atio
n
,
(
b
)
o
b
je
ctiv
e
v
alu
e
(
MPP)
,
an
d
(
c)
AOA
co
n
v
er
g
e
n
ce
cu
r
v
e
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
4
.
1
.
Dev
is
ing
t
he
M
P
P
T
-
AO
A
T
h
e
d
ev
elo
p
m
en
t
o
f
th
e
s
y
s
te
m
r
eq
u
ir
es
a
co
m
p
r
eh
en
s
iv
e
a
p
p
r
o
ac
h
th
at
in
teg
r
ates
b
o
th
h
ar
d
war
e
an
d
f
ir
m
war
e
to
ac
h
iev
e
o
p
tim
al
p
er
f
o
r
m
a
n
ce
an
d
ef
f
icien
cy
.
T
h
e
h
ar
d
war
e
d
esig
n
f
o
cu
s
es
o
n
im
p
lem
en
tin
g
k
e
y
co
m
p
o
n
en
ts
s
u
ch
as
p
o
wer
c
o
n
v
er
ter
s
an
d
co
n
t
r
o
l
cir
cu
i
ts
.
Simu
ltan
eo
u
s
ly
,
th
e
f
ir
m
wa
r
e
d
esig
n
in
v
o
lv
es
d
ev
elo
p
in
g
alg
o
r
ith
m
s
f
o
r
MP
PT
u
s
in
g
th
e
AOA
to
en
h
a
n
ce
it
with
r
ea
l
-
tim
e
a
d
ap
tab
ilit
y
an
d
p
r
ec
is
io
n
.
T
h
e
f
o
llo
win
g
s
u
b
s
ec
tio
n
s
p
r
o
v
i
d
e
a
d
etailed
ex
p
lan
atio
n
o
f
th
e
m
eth
o
d
o
l
o
g
ies
u
s
ed
in
d
esig
n
in
g
b
o
t
h
h
ar
d
war
e
an
d
f
ir
m
war
e
.
4
.
1
.
1
.
H
a
rdwa
re
des
ig
n
T
h
e
h
ar
d
war
e
d
esig
n
,
as
s
h
o
w
n
in
Fig
u
r
e
5
,
r
ev
o
l
v
es
ar
o
u
n
d
a
Nu
cleo
-
F4
4
6
R
E
m
icr
o
c
o
n
tr
o
ller
th
at
in
ter
f
ac
es
with
ess
en
tial
co
m
p
o
n
en
ts
s
u
ch
as
a
v
o
ltag
e
s
en
s
o
r
(
W
C
S1
8
0
0
Mo
d
u
le)
,
a
n
L
C
D
s
cr
ee
n
(
HD4
4
7
8
0
)
,
an
d
a
p
o
wer
m
an
ag
e
m
en
t
cir
cu
it
u
s
in
g
a
n
MP1
5
8
4
b
u
ck
co
n
v
er
ter
.
T
h
is
d
esig
n
f
ac
ilit
ates
r
ea
l
-
tim
e
d
ata
ac
q
u
is
itio
n
,
allo
win
g
t
h
e
m
icr
o
co
n
tr
o
ller
to
ad
j
u
s
t th
e
PW
M
s
ig
n
al
f
o
r
o
p
tim
al
p
o
wer
o
u
tp
u
t.
T
h
e
s
y
s
tem
also
in
clu
d
es p
r
o
tectio
n
cir
cu
its
to
p
r
ev
en
t
o
v
er
c
u
r
r
en
t a
n
d
o
v
er
v
o
ltag
e,
en
s
u
r
in
g
r
eliab
le
o
p
er
a
tio
n
.
4
.
1
.
2
.
F
irm
wa
re
des
ig
n
T
h
e
f
ir
m
war
e
d
esig
n
o
f
th
e
d
ev
ice
is
illu
s
tr
ated
in
th
e
f
lo
w
ch
ar
t
in
Fig
u
r
e
6.
T
h
e
p
r
o
ce
s
s
s
h
o
wed
in
Fig
u
r
e
6
s
tar
ts
with
th
e
co
n
f
i
g
u
r
atio
n
o
f
p
er
ip
h
e
r
als,
f
o
llo
wed
b
y
o
b
tain
in
g
th
e
PV
p
ar
am
eter
s
.
T
h
e
s
y
s
tem
th
en
s
ets
th
e
PW
M
b
ased
o
n
th
e
in
itial
co
n
d
itio
n
s
an
d
ca
l
cu
lates
AOA.
I
f
co
n
v
er
g
en
ce
to
th
e
M
P
P
is
n
o
t
ac
h
iev
ed
,
th
e
o
b
ject
is
r
eg
en
er
ated
,
an
d
th
e
p
r
o
ce
s
s
lo
o
p
s
u
n
til
co
n
v
er
g
en
ce
is
r
ea
ch
ed
.
On
ce
th
e
MPP
is
attain
ed
,
th
e
PW
M
is
ad
ju
s
ted
to
m
ain
tain
th
e
s
y
s
tem
at
th
is
o
p
tim
al
p
o
in
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
6
9
-
2
7
8
5
2776
Fig
u
r
e
5
.
Har
d
war
e
s
ch
em
atic
Fig
u
r
e
6
.
Flo
wch
ar
t
o
f
th
e
d
esig
n
ed
f
ir
m
war
e
4
.
2
.
M
P
P
T
-
AO
A
perf
o
rma
nce
a
na
ly
s
is
T
h
i
s
s
e
ct
i
o
n
p
r
es
e
n
t
s
a
d
e
t
a
il
e
d
a
n
a
l
y
s
i
s
o
f
t
h
e
MP
P
T
u
s
i
n
g
t
h
e
A
OA
u
n
d
e
r
d
i
f
f
e
r
e
n
t
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s
t
o
a
s
s
es
s
i
ts
a
d
a
p
t
a
b
i
li
t
y
a
n
d
e
f
f
i
c
i
e
n
c
y
.
T
h
e
s
t
u
d
y
e
x
a
m
i
n
es
k
e
y
p
e
r
f
o
r
m
a
n
c
e
a
s
p
ec
ts
,
i
n
cl
u
d
i
n
g
t
h
e
al
g
o
r
i
t
h
m
’
s
c
o
n
v
e
r
g
e
n
c
e
s
p
e
e
d
,
t
r
a
c
k
i
n
g
a
c
c
u
r
a
c
y
,
a
n
d
p
o
w
e
r
h
a
r
v
e
s
tin
g
e
f
f
i
c
i
e
n
c
y
.
T
h
e
a
n
a
l
y
s
is
ai
m
s
t
o
e
v
a
l
u
at
e
t
h
e
r
o
b
u
s
t
n
e
s
s
o
f
M
PP
T
-
A
OA
i
n
m
a
i
n
t
a
i
n
i
n
g
o
p
t
i
m
al
PV
p
o
w
e
r
o
u
t
p
u
t
d
e
s
p
i
t
e
i
n
p
a
r
t
i
a
l
s
h
a
d
i
n
g
e
f
f
e
c
t
s
.
4
.
2
.
1
.
Co
nv
er
g
ence
a
na
ly
s
is
C
o
n
v
er
g
en
ce
an
al
y
s
is
is
cr
it
ic
al
in
d
eter
m
in
in
g
h
o
w
q
u
ick
ly
an
d
ac
cu
r
ately
th
e
MPPT
-
AOA
ca
n
r
ea
ch
th
e
MPP u
n
d
er
d
if
f
er
e
n
t sh
ad
i
n
g
c
o
n
d
itio
n
s
.
Fig
u
r
e
7
illu
s
tr
ates th
e
co
n
v
er
g
e
n
ce
b
eh
av
i
o
r
at
d
i
f
f
er
en
t
s
h
ad
in
g
lev
els:
0
%,
2
5
%,
5
0
%,
an
d
7
5
%.
Un
d
er
0
% sh
ad
in
g
,
as sh
o
wn
in
Fig
u
r
e
7
(
a)
,
t
h
e
alg
o
r
ith
m
ex
h
ib
its
a
s
m
o
o
t
h
an
d
r
ap
id
co
n
v
er
g
en
ce
to
th
e
MPP,
in
d
icativ
e
o
f
its
ab
ili
ty
t
o
tr
ac
k
th
e
o
p
tim
al
p
o
wer
p
o
in
t
in
id
ea
l
co
n
d
itio
n
s
ef
f
icien
tly
.
W
h
en
s
h
ad
in
g
is
in
tr
o
d
u
ce
d
at
2
5
%,
as
s
h
o
wn
i
n
Fig
u
r
e
7
(
b
)
,
th
e
c
o
n
v
e
r
g
en
ce
p
r
o
ce
s
s
s
h
o
ws
m
in
o
r
f
lu
ctu
atio
n
s
b
u
t
s
till
m
an
ag
es
to
s
tab
ilize
q
u
ick
ly
,
d
em
o
n
s
tr
atin
g
th
e
alg
o
r
it
h
m
'
s
ad
ap
tab
ilit
y
to
ch
an
g
e
s
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Th
e
imp
leme
n
ta
tio
n
o
f A
r
ch
i
med
es o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
s
o
la
r
ch
a
r
g
e
…
(
S
ig
it Da
n
i P
erka
s
a
)
2777
ir
r
ad
iatio
n
.
As
s
h
ad
in
g
in
cr
ea
s
es
to
5
0
%
in
Fig
u
r
e
7
(
c)
,
th
e
co
n
v
er
g
en
ce
p
r
o
ce
s
s
en
co
u
n
ter
s
m
o
r
e
p
r
o
n
o
u
n
ce
d
o
s
cillatio
n
s
b
ef
o
r
e
s
tab
ilizin
g
,
r
ef
lectin
g
th
e
alg
o
r
ith
m
'
s
ch
all
en
g
e
in
n
av
ig
atin
g
th
r
o
u
g
h
m
u
ltip
le
lo
ca
l
m
ax
im
a
in
tr
o
d
u
ce
d
b
y
p
a
r
tial
s
h
ad
in
g
.
Un
d
er
7
5
%
s
h
ad
in
g
in
Fig
u
r
e
7
(
d
)
,
th
e
c
o
n
v
e
r
g
en
ce
b
ec
o
m
e
s
s
lo
wer
an
d
m
o
r
e
er
r
atic,
with
m
o
r
e
s
ig
n
if
ican
t
f
lu
ctu
atio
n
s
,
y
et
th
e
alg
o
r
ith
m
ev
en
tu
ally
s
tab
ilizes,
alb
eit
with
r
ed
u
ce
d
s
p
ee
d
an
d
ef
f
icien
cy
.
T
h
is
an
aly
s
is
h
ig
h
lig
h
ts
th
e
MPPT
-
AOA
'
s
ca
p
ab
ilit
y
to
ad
a
p
t
ac
r
o
s
s
v
ar
y
in
g
s
h
ad
in
g
s
ce
n
ar
io
s
,
th
o
u
g
h
with
a
tr
ad
e
-
o
f
f
in
co
n
v
er
g
en
ce
s
p
ee
d
an
d
s
tab
ilit
y
as sh
ad
in
g
b
ec
o
m
es m
o
r
e
in
te
n
s
e
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
7
.
C
o
n
v
er
g
e
n
ce
u
n
d
er
d
if
f
er
en
t sh
a
d
in
g
.
(
a)
0
% sh
ad
in
g
,
(
b
)
2
5
% sh
ad
i
n
g
,
(
c)
5
0
% sh
ad
in
g
,
an
d
(
d
)
7
5
% sh
ad
i
n
g
4
.
2
.
2
T
ra
c
k
ing
a
na
ly
s
is
T
r
ac
k
in
g
an
al
y
s
is
is
cr
u
cial
t
o
en
s
u
r
e
th
e
MPPT
-
AOA
co
n
s
is
ten
tly
o
p
er
ates
clo
s
e
to
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
T
h
e
tr
ac
k
in
g
p
e
r
f
o
r
m
a
n
ce
,
as
s
h
o
wn
i
n
Fig
u
r
e
8
,
r
e
v
ea
ls
h
o
w
th
e
alg
o
r
it
h
m
b
eh
a
v
es
u
n
d
er
d
if
f
er
en
t
s
h
ad
in
g
co
n
d
itio
n
s
.
W
ith
n
o
s
h
ad
in
g
,
as
s
h
o
wn
in
Fig
u
r
e
8
(
a)
,
th
e
MPPT
-
AOA
m
ain
tain
s
a
s
tab
le
o
p
er
atio
n
n
ea
r
th
e
MPP,
with
m
in
im
al
d
e
v
iatio
n
s
,
in
d
ica
tin
g
ex
ce
llen
t
tr
ac
k
i
n
g
ac
c
u
r
ac
y
u
n
d
er
o
p
tim
al
co
n
d
itio
n
s
.
W
h
en
s
h
ad
in
g
is
in
tr
o
d
u
ce
d
at
2
5
%,
as
s
h
o
wn
in
Fig
u
r
e
8
(
b
)
,
th
e
s
y
s
tem
'
s
tr
ac
k
in
g
r
em
ai
n
s
r
o
b
u
s
t,
with
o
n
ly
s
lig
h
t
d
ev
iatio
n
s
th
a
t
ar
e
q
u
ick
ly
co
r
r
ec
ted
,
m
in
im
izin
g
p
o
ten
tial
p
o
wer
l
o
s
s
.
Ho
wev
er
,
as
s
h
a
d
in
g
in
cr
ea
s
es to
5
0
% in
Fig
u
r
e
8
(
c
)
.
T
h
e
tr
ac
k
in
g
ac
cu
r
ac
y
b
eg
i
n
s
to
s
u
f
f
er
,
with
m
o
r
e
er
r
atic
b
e
h
av
io
r
d
u
e
to
th
e
co
m
p
le
x
p
o
wer
cu
r
v
e.
Desp
ite
th
ese
ch
allen
g
es,
th
e
a
lg
o
r
ith
m
k
ee
p
s
th
e
p
o
wer
o
u
tp
u
t
with
in
a
r
ea
s
o
n
ab
le
r
an
g
e.
I
n
Fig
u
r
e
8
(
d
)
,
u
n
d
e
r
s
ev
er
e
s
h
ad
in
g
at
7
5
%,
tr
ac
k
i
n
g
p
er
f
o
r
m
an
ce
d
ec
lin
es
f
u
r
th
er
,
with
m
o
r
e
f
r
e
q
u
en
t
an
d
s
i
g
n
if
ican
t
d
ev
iatio
n
s
f
r
o
m
th
e
MPP.
No
n
eth
eless
,
t
h
e
s
y
s
tem
r
ec
o
v
er
s
an
d
tr
ac
k
s
th
e
MPP
r
ea
s
o
n
ab
ly
,
s
h
o
wca
s
in
g
th
e
alg
o
r
ith
m
'
s
r
esil
ien
ce
ev
en
u
n
d
e
r
h
ar
s
h
co
n
d
itio
n
s
.
T
h
is
an
aly
s
is
s
u
g
g
ests
th
at
wh
ile
th
e
MPPT
-
AOA
is
h
ig
h
ly
ef
f
ec
tiv
e
in
m
ain
tain
in
g
o
p
tim
al
o
p
e
r
atio
n
u
n
d
er
lo
w
to
m
o
d
e
r
ate
s
h
a
d
in
g
,
its
tr
ac
k
in
g
ac
cu
r
ac
y
d
i
m
in
is
h
es
as
s
h
ad
in
g
s
ev
er
ity
in
cr
ea
s
es,
th
o
u
g
h
it p
er
f
o
r
m
s
s
u
f
f
icien
tly
well
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
6
9
-
2
7
8
5
2778
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
T
r
ac
k
in
g
u
n
d
er
d
if
f
e
r
en
t sh
ad
in
g
.
(
a)
0
% sh
ad
in
g
,
(
b
)
2
5
% sh
ad
in
g
,
(
c)
5
0
% sh
ad
in
g
,
a
n
d
(
d
)
7
5
%
s
h
ad
in
g
4
.
2
.
3
.
E
f
f
iciency
a
na
ly
s
is
E
f
f
icien
cy
a
n
aly
s
is
is
cr
itical
f
o
r
ass
ess
in
g
th
e
MPPT
-
AOA'
s
ab
ilit
y
to
ef
f
ec
tiv
ely
co
n
v
er
t
av
ailab
le
s
o
lar
en
er
g
y
in
to
elec
tr
ical
p
o
wer
.
As
illu
s
tr
ated
in
Fig
u
r
e
9
,
th
e
s
y
s
tem
'
s
ef
f
icien
cy
r
ef
le
cts
it
s
p
er
f
o
r
m
an
ce
ac
r
o
s
s
v
ar
y
in
g
s
h
ad
in
g
co
n
d
it
io
n
s
.
It
s
h
o
wed
b
y
Fig
u
r
e
s
9
(
a)
to
9
(
d
)
,
u
n
d
er
0
%
s
h
ad
in
g
,
t
h
e
s
y
s
tem
ac
h
iev
es
n
ea
r
-
o
p
tim
al
en
er
g
y
co
n
v
er
s
io
n
with
an
av
er
ag
e
ef
f
icien
c
y
o
f
9
3
.
9
2
%.
As
s
h
ad
in
g
in
cr
ea
s
es
to
2
5
%,
th
er
e
is
a
s
lig
h
t
d
ec
r
ea
s
e
in
ef
f
icien
cy
t
o
9
3
.
4
8
%,
wh
ich
is
ex
p
ec
te
d
as
p
ar
tial
s
h
ad
in
g
b
e
g
i
n
s
to
im
p
ac
t
th
e
s
y
s
tem
'
s
p
o
wer
o
u
tp
u
t.
At
5
0
%
s
h
ad
in
g
,
th
e
ef
f
icien
cy
d
r
o
p
s
to
9
2
.
4
6
%,
in
d
icatin
g
th
e
alg
o
r
ith
m
'
s
in
cr
ea
s
in
g
d
if
f
icu
lty
in
m
ain
tain
in
g
o
p
tim
al
e
n
er
g
y
co
n
v
er
s
io
n
,
as
s
h
ad
i
n
g
cr
ea
tes
m
o
r
e
v
ar
iab
ilit
y
i
n
th
e
p
o
wer
c
u
r
v
e.
Su
r
p
r
is
in
g
l
y
,
ev
en
u
n
d
er
7
5
%
s
h
ad
in
g
,
th
e
s
y
s
tem
m
ain
tain
s
an
ef
f
icien
cy
o
f
9
2
.
8
3
%,
d
em
o
n
s
tr
atin
g
th
e
MPPT
-
AOA'
s
ef
f
ec
tiv
en
ess
an
d
r
o
b
u
s
tn
ess
ev
en
u
n
d
er
s
ig
n
if
ican
t
ad
v
e
r
s
e
c
o
n
d
itio
n
s
.
T
h
e
s
y
s
tem
p
er
f
o
r
m
an
ce
also
d
escr
ib
ed
in
T
ab
le
2
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
9
.
E
f
f
icien
cy
u
n
d
e
r
d
if
f
er
en
t sh
ad
in
g
.
(
a)
0
% sh
ad
in
g
,
(
b
)
2
5
% sh
ad
in
g
,
(
c)
5
0
% sh
a
d
in
g
,
an
d
(
d
)
7
5
% sh
ad
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.