I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
3
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
5
,
p
p
.
1
9
2
3
~
1
937
I
SS
N:
2
5
0
2
-
4
7
5
2
,
DOI
: 1
0
.
1
1
5
9
1
/ijeecs.v
3
9
.i
3
.
pp
1
9
2
3
-
1
9
3
7
1923
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ee
cs.ia
esco
r
e.
co
m
M
o
delling
and sim
ula
tion o
f
ma
x
i
mum
power
po
int
t
ra
cking
on
pa
rtial sha
ded
P
V bas
ed
-
o
n a p
hy
sica
l phenom
eno
n
-
inspi
red
metah
euristi
c alg
o
rithm
P
rism
a
M
eg
a
nto
ro
1
,
J
o
y
Sef
ine D
o
na
Sa
y
a
1
,
M
uh
a
m
m
a
d
Ak
ba
r
Sy
a
hb
a
ni
1
,
M
a
rwa
n F
a
dh
ila
h
1
,
P
a
nd
i V
ig
nes
hwa
ra
n
2
1
F
a
c
u
l
t
y
o
f
A
d
v
a
n
c
e
d
Te
c
h
n
o
l
o
g
y
a
n
d
M
u
l
t
i
d
i
sc
i
p
l
i
n
e
,
U
n
i
v
e
r
s
i
t
a
s Air
l
a
n
g
g
a
,
S
u
r
a
b
a
y
a
,
I
n
d
o
n
e
s
i
a
2
D
e
p
a
r
t
me
n
t
o
f
C
o
m
p
u
t
e
r
S
c
i
e
n
c
e
a
n
d
E
n
g
i
n
e
e
r
i
n
g
,
A
c
h
a
r
y
a
U
n
i
v
e
r
s
i
t
y
,
K
a
r
a
k
u
l
,
U
z
b
e
k
i
st
a
n
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Sep
5
,
2
0
2
4
R
ev
is
ed
Ap
r
10
,
2
0
2
5
Acc
ep
ted
J
u
l
3
,
2
0
2
5
M
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
i
n
g
(M
P
P
T)
is
a
tec
h
n
i
q
u
e
to
o
p
t
imiz
e
th
e
p
h
o
to
v
o
lt
a
ic
(P
V)
c
u
rre
n
t
g
e
n
e
r
a
ti
o
n
,
so
i
t
c
a
n
imp
ro
v
e
t
h
e
e
fficie
n
c
y
o
f
so
lar
e
n
e
rg
y
h
a
rv
e
sti
n
g
.
M
P
P
T
wo
rk
s
b
y
se
a
rc
h
in
g
th
e
v
o
lt
a
g
e
wh
ich
g
e
n
e
ra
tes
th
e
m
a
x
imu
m
p
o
we
r,
c
a
ll
e
d
th
e
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
(M
P
P
)
.
M
P
P
v
a
lu
e
c
h
a
n
g
e
s
b
y
t
h
e
flu
c
tu
a
n
c
e
o
f
a
m
b
ie
n
t
tem
p
e
ra
tu
re
a
n
d
so
la
r
in
so
lati
o
n
lev
e
l
d
e
p
icte
d
b
y
th
e
I
-
V
c
u
rv
e
.
S
e
a
rc
h
in
g
t
h
e
M
P
P
wil
l
b
e
m
o
re
c
o
m
p
lex
if
th
e
p
a
rti
a
l
sh
a
d
in
g
is
h
a
p
p
e
n
e
d
.
T
h
e
e
ffe
c
t
o
f
p
a
rti
a
l
sh
a
d
in
g
wil
l
rise
to
m
o
re
t
h
a
n
o
n
e
lo
c
a
l
M
P
P
s.
In
th
is
re
se
a
rc
h
,
a
n
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
is
m
o
d
e
led
a
n
d
sim
u
late
d
th
e
M
P
P
T
tec
h
n
iq
u
e
in
p
a
rti
a
l
sh
a
d
in
g
.
T
h
e
o
p
ti
m
iza
ti
o
n
u
se
s
t
h
e
n
e
w
m
e
ta
h
e
u
risti
c
a
l
g
o
ri
th
m
w
h
ich
in
sp
ir
e
d
fro
m
a
p
h
y
sic
a
l
p
h
e
n
o
m
e
n
o
n
,
c
a
ll
e
d
Arc
h
ime
d
e
s
o
p
ti
m
iza
ti
o
n
a
l
g
o
ri
th
m
(AO
A).
Th
e
AO
A
u
se
s
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
li
n
g
wh
ich
h
a
s
c
o
n
v
e
rg
e
n
c
e
c
a
p
a
b
il
it
ies
,
b
a
lan
c
e
d
e
x
p
lo
ra
ti
o
n
,
a
n
d
e
x
p
l
o
i
tatio
n
a
n
d
is
su
it
a
b
le
fo
r
so
l
v
i
n
g
c
o
m
p
lex
o
p
ti
m
iza
ti
o
n
tec
h
n
i
q
u
e
,
l
ik
e
M
P
P
T.
T
h
e
re
se
a
rc
h
u
se
d
v
a
ries
p
a
rti
a
l
in
so
lati
o
n
p
e
rc
e
n
tag
e
.
T
h
e
imp
l
e
m
e
n
tatio
n
o
f
M
P
P
T
-
AO
A
c
o
m
p
a
re
d
to
o
th
e
r
m
e
tah
e
u
risti
c
a
l
g
o
rit
h
m
s
t
o
a
n
a
ly
sis
i
ts
p
e
rfo
rm
a
n
c
e
i
n
th
e
a
sp
e
c
t
o
f
P
V
sy
ste
m
p
a
ra
m
e
ters
a
n
d
trac
k
in
g
p
ro
c
e
ss
p
a
ra
m
e
ters
.
Th
e
s
imu
latio
n
re
su
lt
sh
o
ws
t
h
a
t
th
e
AO
A
c
a
n
e
n
rich
t
h
e
M
P
P
T
tec
h
n
i
q
u
e
a
n
d
i
m
p
ro
v
e
t
h
e
so
lar en
e
rg
y
h
a
rv
e
sti
n
g
w
h
ich
is su
p
e
rio
r
to
o
t
h
e
r
a
lg
o
rit
h
m
s.
K
ey
w
o
r
d
s
:
Ma
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
Me
tah
eu
r
is
tic
alg
o
r
ith
m
Op
tim
izatio
n
Ph
o
to
v
o
ltaic
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
So
lar
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
ar
e
cr
u
cial
co
m
p
o
n
en
ts
in
co
n
v
er
tin
g
s
o
lar
en
er
g
y
in
to
elec
tr
icity
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
PV
s
y
s
tem
s
d
ep
en
d
s
o
n
s
o
lar
in
s
o
latio
n
an
d
tem
p
er
atu
r
e,
wh
ich
d
ir
ec
tly
af
f
ec
t
th
e
g
en
er
ated
cu
r
r
en
t
an
d
v
o
ltag
e.
Ho
wev
er
,
th
e
co
n
s
tan
t
f
l
u
ctu
atio
n
s
in
s
o
lar
in
s
o
latio
n
p
r
esen
t
a
s
ig
n
if
ican
t
ch
allen
g
e
as
th
ey
im
p
ac
t
th
e
ef
f
icien
cy
o
f
th
e
s
o
lar
m
o
d
u
le
[
1
]
-
[
4
]
.
T
h
ese
f
lu
ctu
atio
n
s
af
f
ec
t
th
e
cu
r
r
en
t
-
v
o
ltag
e
(
I
-
V)
c
h
ar
ac
ter
is
tics
,
lead
in
g
to
is
s
u
es
s
u
ch
as
o
v
e
r
ch
ar
g
in
g
,
u
n
d
e
r
ch
ar
g
i
n
g
,
s
h
o
r
ten
ed
b
atter
y
life
,
a
n
d
c
o
m
p
r
o
m
i
s
ed
i
n
v
e
r
te
r
p
e
r
f
o
r
m
an
c
e
[
4
]
,
[
5
]
.
F
u
r
t
h
e
r
m
o
r
e,
s
h
ad
i
n
g
f
r
o
m
c
lo
u
d
s
,
t
r
e
e
s
,
an
d
n
e
ar
b
y
s
t
r
u
c
t
u
r
e
s
in
t
r
o
d
u
c
e
s
p
a
r
t
i
a
l
s
h
a
d
i
n
g
e
f
f
e
c
t
s
,
ca
u
s
i
n
g
m
i
s
m
a
t
c
h
ed
p
o
we
r
o
u
tp
u
t
an
d
e
f
f
i
c
i
e
n
cy
lo
s
s
e
s
[
6
]
-
[
9
]
.
P
a
r
t
i
a
l
s
h
ad
i
n
g
c
an
a
l
s
o
r
e
s
u
l
t
i
n
lo
c
a
l
i
z
ed
o
v
e
r
h
e
a
t
in
g
,
f
o
r
m
in
g
h
o
t
s
p
o
t
s
t
h
a
t
m
ay
d
a
m
a
g
e
th
e
P
V
m
o
d
u
l
e
s
[
1
0
]
,
[
1
1
]
.
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.
3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
9
2
3
-
1
9
3
7
1924
T
o
ad
d
r
ess
th
ese
is
s
u
es,
m
ax
i
m
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
i
n
g
(
M
PP
T
)
alg
o
r
ith
m
s
h
av
e
b
ee
n
d
e
v
elo
p
ed
to
o
p
tim
ize
PV
s
y
s
tem
p
er
f
o
r
m
a
n
ce
b
y
en
s
u
r
in
g
o
p
er
ati
o
n
at
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
u
n
d
er
v
ar
y
i
n
g
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
[
1
2
]
-
[
1
5
]
.
Ho
wev
er
,
MPPT
u
n
d
er
p
ar
tial
s
h
ad
i
n
g
co
n
d
itio
n
s
is
p
ar
ticu
la
r
ly
ch
allen
g
in
g
b
ec
au
s
e
m
u
ltip
le
lo
ca
l
m
ax
im
u
m
p
o
we
r
p
o
in
ts
(
L
MPPs
)
ca
n
f
o
r
m
,
m
ak
i
n
g
it
d
if
f
icu
lt
to
lo
ca
te
th
e
tr
u
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
[
1
6
]
-
[
1
9
]
.
Sev
er
al
tech
n
iq
u
es
h
a
v
e
b
ee
n
ex
p
lo
r
e
d
to
a
d
d
r
ess
th
is
ch
allen
g
e.
C
o
n
v
e
n
tio
n
al
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
alg
o
r
ith
m
s
[
2
0
]
,
[
2
1
]
o
f
f
er
a
s
im
p
le
an
d
wid
ely
u
s
ed
MPPT
ap
p
r
o
ac
h
b
u
t
o
f
te
n
f
ail
to
lo
ca
te
th
e
GM
PP
,
lead
in
g
to
s
u
b
o
p
tim
al
en
er
g
y
h
ar
v
esti
n
g
.
T
o
o
v
er
c
o
m
e
th
is
lim
itatio
n
,
g
en
etic
alg
o
r
ith
m
(
GA)
-
b
ased
MPPT
tech
n
iq
u
es
h
av
e
b
ee
n
p
r
o
p
o
s
e
d
[
2
2
]
,
[
2
3
]
,
wh
ich
s
u
cc
ess
f
u
lly
lo
ca
te
th
e
GM
PP
u
n
d
er
p
ar
tial
s
h
a
d
in
g
.
Ho
wev
er
,
GA
-
b
ased
m
eth
o
d
s
s
u
f
f
er
f
r
o
m
l
o
n
g
co
n
v
er
g
en
c
e
tim
es
an
d
r
eq
u
ir
e
p
r
ec
is
e
p
ar
am
eter
tu
n
in
g
f
o
r
o
p
tim
al
p
er
f
o
r
m
an
ce
.
T
h
e
d
if
f
er
en
tial
ev
o
lu
tio
n
alg
o
r
ith
m
(
DE
)
[
2
4
]
h
as
b
ee
n
i
n
tr
o
d
u
ce
d
to
im
p
r
o
v
e
co
n
v
er
g
en
ce
s
p
ee
d
an
d
ac
c
u
r
ac
y
.
Desp
ite
its
ad
v
an
tag
es,
DE
is
h
ig
h
ly
s
en
s
itiv
e
to
in
itial
p
o
p
u
latio
n
v
alu
es
an
d
lack
s
ad
ap
ta
b
ilit
y
to
d
y
n
a
m
ic
s
h
ad
in
g
co
n
d
itio
n
s
.
Oth
er
ap
p
r
o
ac
h
es,
s
u
ch
as
f
ir
ef
l
y
al
g
o
r
ith
m
(
FA)
an
d
f
r
u
it
f
ly
o
p
tim
izati
o
n
al
g
o
r
ith
m
(
FOA)
,
h
av
e
b
ee
n
d
e
v
elo
p
ed
,
b
u
t
ea
ch
co
m
es
with
tr
ad
e
-
o
f
f
s
in
tr
ac
k
in
g
ac
cu
r
ac
y
an
d
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
[
2
5
]
,
[
2
6
]
.
T
h
e
o
th
er
tr
a
d
itio
n
al
MPPT
m
eth
o
d
s
,
s
u
ch
as
P&
O
an
d
i
n
cr
em
en
tal
co
n
d
u
ctan
ce
(
I
C
)
,
ar
e
wid
ely
u
s
ed
d
u
e
to
th
eir
s
im
p
licity
b
u
t
s
u
f
f
er
f
r
o
m
i
n
ef
f
icien
cies
i
n
r
ap
i
d
ly
c
h
an
g
in
g
e
n
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
an
d
p
ar
tial
s
h
ad
in
g
s
ce
n
ar
io
s
[
2
7
]
.
T
o
o
v
er
co
m
e
th
ese
lim
it
atio
n
s
,
ar
tific
ial
in
tellig
en
ce
(
AI
)
-
b
ased
MPPT
tech
n
iq
u
es,
in
clu
d
in
g
ar
tific
ia
l
n
eu
r
al
n
etwo
r
k
s
(
ANNs)
,
f
u
zz
y
lo
g
ic
c
o
n
tr
o
l
(
FLC),
an
d
d
ee
p
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
(
DR
L
)
,
h
av
e
em
er
g
ed
as
p
r
o
m
is
in
g
alter
n
ativ
es
[
2
8
]
.
R
ec
en
t
s
tu
d
ies
h
a
v
e
also
ex
p
l
o
r
ed
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
lik
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
g
r
e
y
wo
lf
o
p
tim
iz
atio
n
(
GW
O)
,
an
d
f
lam
in
g
o
s
ea
r
ch
alg
o
r
it
h
m
(
FS
A)
to
en
h
an
ce
th
e
tr
ac
k
in
g
ef
f
icien
cy
o
f
PV
s
y
s
tem
s
.
T
h
ese
in
tellig
en
t
an
d
m
etah
eu
r
is
tic
ap
p
r
o
ac
h
es
o
f
f
e
r
im
p
r
o
v
ed
r
esp
o
n
s
e
tim
es,
g
r
ea
ter
ac
cu
r
ac
y
in
lo
ca
tin
g
th
e
GM
PP
,
an
d
b
etter
ad
ap
tab
ilit
y
to
d
y
n
am
ic
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
Desp
ite
th
ese
ad
v
an
ce
m
en
ts
,
ex
is
tin
g
alg
o
r
ith
m
s
s
till
f
ac
e
c
h
allen
g
es
in
ac
h
ie
v
in
g
f
ast
co
n
v
er
g
e
n
ce
,
m
ain
tain
in
g
ac
cu
r
ac
y
,
a
n
d
a
d
ap
tin
g
to
d
y
n
am
ic
en
v
ir
o
n
m
en
tal
ch
an
g
es.
Ma
n
y
m
et
h
o
d
s
eith
er
r
e
q
u
ir
e
ex
ten
s
iv
e
tu
n
in
g
o
r
f
ail
to
e
f
f
ec
tiv
ely
b
alan
ce
ex
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
in
th
e
s
ea
r
ch
f
o
r
th
e
GM
PP
.
Ad
d
r
ess
in
g
th
ese
g
a
p
s
,
th
is
s
tu
d
y
p
r
o
p
o
s
es
th
e
Ar
ch
im
e
d
es
o
p
tim
izatio
n
al
g
o
r
ith
m
(
AO
A)
as
a
n
o
v
el
MPPT
s
o
lu
tio
n
u
n
d
er
p
a
r
tial sh
ad
in
g
co
n
d
itio
n
s
.
AOA
is
in
s
p
ir
ed
b
y
th
e
p
h
y
s
ical
p
r
in
cip
les
o
f
Ar
ch
im
ed
es
’
law
an
d
th
e
b
u
o
y
a
n
cy
p
r
i
n
cip
le.
T
h
e
Ar
ch
im
ed
es
law
m
ec
h
an
is
m
u
p
d
ates
ca
n
d
id
ate
p
o
s
itio
n
s
in
th
e
s
ea
r
ch
s
p
ac
e
b
y
co
n
s
id
er
in
g
th
e
f
u
lcr
u
m
p
o
in
t
an
d
lev
er
s
tr
en
g
th
,
en
h
an
cin
g
ex
p
lo
r
atio
n
ca
p
ab
ilit
ies
[
2
9
]
.
T
h
e
b
u
o
y
an
cy
p
r
in
cip
le,
o
n
th
e
o
th
er
h
an
d
,
allo
ws
ca
n
d
id
ate
s
o
lu
tio
n
s
to
a
d
ju
s
t
th
eir
p
o
s
itio
n
s
d
y
n
am
ically
,
p
r
ev
en
tin
g
p
r
e
m
atu
r
e
co
n
v
er
g
e
n
ce
at
L
MPP
an
d
e
n
s
u
r
in
g
a
n
ef
f
e
c
t
iv
e
s
ea
r
ch
f
o
r
th
e
G
M
P
P
[
3
0
]
.
T
h
i
s
a
p
p
r
o
a
c
h
e
n
h
an
c
e
s
M
P
P
T
e
f
f
i
c
i
en
c
y
b
y
m
in
i
m
iz
i
n
g
p
o
w
er
l
o
s
s
a
n
d
i
m
p
r
o
v
i
n
g
co
m
p
u
t
a
t
io
n
a
l
p
e
r
f
o
r
m
an
c
e
co
m
p
a
r
ed
t
o
co
n
v
e
n
t
io
n
a
l
m
et
a
h
e
u
r
i
s
t
i
c
m
e
th
o
d
s
[
2
0
]
,
[
3
1
]
.
I
n
th
is
s
tu
d
y
,
we
p
r
o
p
o
s
e
a
n
AOA
-
b
ased
MPPT
ap
p
r
o
ac
h
f
o
r
PV
s
y
s
tem
s
o
p
er
atin
g
u
n
d
er
PS
C
s
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
r
esear
ch
in
clu
d
e:
−
Dev
elo
p
m
en
t
o
f
a
n
AOA
-
b
a
s
ed
MPPT
f
r
am
ewo
r
k
th
at
e
n
h
an
ce
s
tr
ac
k
i
n
g
ac
c
u
r
ac
y
a
n
d
co
n
v
er
g
en
ce
s
p
ee
d
in
PV sy
s
tem
s
.
−
C
o
m
p
ar
ativ
e
p
er
f
o
r
m
an
ce
ev
alu
atio
n
ag
ain
s
t
co
n
v
en
tio
n
al
an
d
m
etah
eu
r
is
tic
MPPT
tech
n
iq
u
es,
s
u
ch
as
PS
O
an
d
GA,
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
s
.
−
C
r
itical
an
aly
s
is
o
f
AOA’
s
ef
f
ec
tiv
en
ess
in
m
itig
atin
g
p
o
w
er
lo
s
s
d
u
e
t
o
s
h
ad
in
g
ef
f
ec
ts
an
d
im
p
r
o
v
in
g
PV e
n
er
g
y
h
a
r
v
esti
n
g
ef
f
icien
cy
.
−
I
n
v
esti
g
atio
n
o
f
p
o
ten
tial
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
,
em
p
h
asizin
g
AOA’
s
ad
ap
tab
ilit
y
in
g
r
id
-
co
n
n
ec
ted
an
d
s
tan
d
alo
n
e
PV sy
s
tem
s
.
T
h
e
r
em
ain
d
er
o
f
th
is
p
a
p
er
i
s
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
s
e
ctio
n
2
p
r
esen
ts
th
e
m
eth
o
d
o
lo
g
y
,
d
etailin
g
th
e
PV
s
y
s
tem
m
o
d
elin
g
,
MPPT
f
r
am
ewo
r
k
,
an
d
im
p
lem
en
tatio
n
o
f
AOA.
I
n
s
ec
tio
n
3
d
is
cu
s
s
e
s
th
e
r
esu
lts
an
d
p
e
r
f
o
r
m
an
ce
e
v
alu
atio
n
u
n
d
er
d
if
f
e
r
en
t
s
h
ad
in
g
s
ce
n
ar
io
s
.
I
n
s
ec
tio
n
4
c
o
n
clu
d
es
with
k
ey
f
in
d
in
g
s
,
im
p
lic
atio
n
s
,
an
d
f
u
tu
r
e
r
esear
ch
d
ir
ec
tio
n
s
.
2.
M
E
T
H
O
D
T
h
is
s
ec
tio
n
p
r
o
v
id
es
a
d
etailed
d
escr
ip
tio
n
o
f
th
e
m
eth
o
d
o
lo
g
y
u
s
ed
in
th
is
s
tu
d
y
to
en
s
u
r
e
r
ep
r
o
d
u
cib
ilit
y
an
d
v
alid
ity
.
T
h
e
m
o
d
elin
g
o
f
th
e
PV
s
y
s
tem
,
im
p
lem
en
tatio
n
o
f
th
e
AOA
-
b
ased
MPPT,
an
d
th
e
s
im
u
latio
n
f
r
am
ewo
r
k
ar
e
d
escr
ib
ed
.
Pre
v
io
u
s
ly
estab
lis
h
ed
p
r
o
ce
d
u
r
es
ar
e
r
ef
er
en
ce
d
wh
er
e
ap
p
licab
le.
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
Mo
d
ellin
g
a
n
d
s
imu
la
tio
n
o
f
ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
o
n
p
a
r
tia
l sh
a
d
ed
…
(
P
r
is
ma
Meg
a
n
to
r
o
)
1925
2
.
1
.
M
o
del o
f
pa
r
t
ia
l sh
a
ded
ph
o
t
o
v
o
lt
a
ic
a
rr
a
y
T
h
e
PV
s
y
s
tem
m
o
d
el
u
s
ed
in
th
is
s
tu
d
y
is
b
ased
o
n
well
-
estab
lis
h
ed
m
ath
em
atica
l
f
o
r
m
u
l
atio
n
s
an
d
cir
cu
it
r
ep
r
esen
tatio
n
s
f
r
o
m
p
r
io
r
r
esear
ch
.
T
h
e
s
in
g
le
-
d
io
d
e
m
o
d
el
o
f
th
e
PV
ar
r
ay
is
ad
o
p
ted
,
as
it
p
r
o
v
id
es
a
g
o
o
d
b
alan
ce
b
etwe
en
ac
cu
r
ac
y
a
n
d
c
o
m
p
u
tatio
n
al
e
f
f
icien
cy
.
T
h
e
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
en
v
ir
o
n
m
en
t is u
s
ed
to
im
p
lem
en
t th
is
m
o
d
el,
e
n
s
u
r
in
g
r
ep
r
o
d
u
cib
ilit
y
.
T
o
ev
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
AOA
f
o
r
MP
PT,
a
s
im
u
lated
PV
s
y
s
tem
m
o
d
el
was
d
ev
elo
p
e
d
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
m
o
d
el
co
n
s
is
ts
o
f
a
PV
ar
r
ay
,
a
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
,
an
d
an
MPPT
co
n
tr
o
ller
.
T
h
e
PV
ar
r
ay
f
o
llo
ws
a
s
in
g
le
-
d
io
d
e
e
q
u
iv
alen
t
cir
cu
it
m
o
d
el
in
c
o
r
p
o
r
atin
g
s
er
ies
an
d
sh
u
n
t
r
esis
tan
ce
s
as
s
ee
n
in
Fig
u
r
e
1
.
Par
tial
s
h
ad
in
g
is
s
im
u
lated
f
o
llo
win
g
m
eth
o
d
o
lo
g
i
es
d
escr
ib
ed
in
th
e
p
r
ev
io
u
s
s
tu
d
y
,
b
y
v
a
r
y
in
g
s
o
lar
in
s
o
latio
n
ac
r
o
s
s
d
if
f
er
e
n
t
s
ec
tio
n
s
o
f
th
e
PV
ar
r
a
y
,
p
r
o
d
u
cin
g
m
u
ltip
le
L
MPPs
.
T
h
r
ee
s
h
ad
in
g
s
ce
n
ar
io
s
ar
e
co
n
s
id
er
ed
,
s
u
c
h
as;
(
a
)
u
n
if
o
r
m
in
s
o
latio
n
:
1
,
0
0
0
W
/m
²
in
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC),
(
b
)
h
alf
-
s
h
a
d
ed
in
s
o
latio
n
:
7
5
0
W
/m
²
f
o
r
p
ar
t
o
f
th
e
ar
r
ay
,
1
,
0
0
0
W
/m
²
f
o
r
th
e
r
est,
an
d
(
c)
one
-
th
ir
d
s
h
ad
ed
i
n
s
o
latio
n
: 5
0
0
W
/m
²
f
o
r
a
s
ec
tio
n
,
1
,
0
0
0
W
/m
²
f
o
r
th
e
r
est.
Us
in
g
th
e
Kir
ch
o
f
f
law,
th
e
s
o
lar
ce
ll o
f
Fig
u
r
e
1
ca
n
also
b
e
m
o
d
elled
b
y
th
e
(
1
)
.
=
ℎ
−
−
ℎ
(
1
)
W
h
er
e
is
th
e
to
tal
cu
r
r
en
t
g
e
n
er
ated
,
ℎ
is
th
e
cu
r
r
en
t
g
e
n
er
a
ted
b
y
s
o
lar
ce
ll,
is
th
e
s
atu
r
atio
n
cu
r
r
e
n
t,
an
d
ℎ
is
s
h
u
n
t
cu
r
r
e
n
t.
B
ec
au
s
e
ea
ch
d
io
d
e
in
a
s
o
lar
p
an
el
f
o
llo
ws
a
n
o
n
-
lin
ea
r
c
h
ar
ac
ter
is
tic
d
escr
ib
ed
b
y
th
e
Sh
o
ck
ley
eq
u
atio
n
.
T
h
er
e
f
o
r
e,
th
e
Sh
o
ck
ley
e
q
u
atio
n
f
o
r
a
d
io
d
e
is
id
ea
l
f
o
r
ca
lcu
latin
g
th
e
o
u
tp
u
t
p
o
wer
in
(
2
)
.
=
ℎ
−
0
[
e
xp
(
(
+
)
)
−
1
]
−
+
ℎ
(
2
)
W
h
er
e
is
th
e
cu
r
r
en
t
g
en
er
ated
b
y
s
o
lar
ce
ll,
V
is
s
o
lar
ce
ll
v
o
ltag
e,
0
is
s
a
tu
r
ated
cu
r
r
en
t
o
f
d
io
d
e,
n
is
d
io
d
e
id
ea
lity
f
ac
to
r
,
R
s
/Rsh
is
p
ar
allel
o
r
s
er
ie
s
r
esi
s
to
r
,
Tk
is
ce
ll
tem
p
er
atu
r
e,
K
is
B
o
ltzm
an
n
co
n
s
tan
t
v
alu
ed
1
.
3
8
×
10
-
2
3
J
/K,
an
d
Q
is
th
e
to
tal
ch
ar
g
e
o
f
an
elec
tr
o
n
with
a
v
al
u
e
1
.
6
0
2
×
10
-
1
9
.
Fig
u
r
e
1
.
Dio
d
e
cir
cu
it r
e
p
r
esen
tatio
n
o
f
a
s
o
lar
ce
ll
[
3
2
]
T
h
e
m
o
d
el
u
s
ed
i
n
th
is
s
tu
d
y
,
as
illu
s
tr
ated
in
Fig
u
r
e
2
,
is
ad
ap
ted
f
r
o
m
th
e
r
esear
ch
,
p
r
o
v
id
in
g
a
r
o
b
u
s
t
f
r
a
m
ewo
r
k
f
o
r
an
aly
z
in
g
th
ese
co
n
d
itio
n
s
.
T
h
r
ee
d
if
f
er
en
t
i
n
s
o
latio
n
s
ar
e
s
im
u
lated
to
r
e
p
r
esen
t
v
ar
io
u
s
s
h
ad
in
g
s
ce
n
ar
io
s
.
T
h
e
f
ir
s
t
s
ce
n
ar
io
,
u
n
if
o
r
m
in
s
o
latio
n
,
ass
u
m
es
th
at
th
e
PV
ar
r
ay
r
ec
eiv
es
eq
u
al
s
u
n
lig
h
t
ac
r
o
s
s
all
p
an
els,
wh
i
ch
is
an
id
ea
l
co
n
d
itio
n
f
o
r
m
ax
im
u
m
p
o
wer
o
u
tp
u
t.
T
h
e
s
ec
o
n
d
s
ce
n
ar
io
,
h
al
f
p
ar
tial
s
h
ad
in
g
,
o
cc
u
r
s
wh
en
h
alf
o
f
th
e
PV
ar
r
ay
is
s
h
ad
e
d
,
lead
in
g
t
o
a
n
o
tab
le
d
ec
r
ea
s
e
i
n
o
u
tp
u
t
p
o
wer
co
m
p
ar
ed
to
th
e
u
n
if
o
r
m
in
s
o
l
atio
n
s
ce
n
ar
io
.
T
h
e
th
ir
d
s
ce
n
ar
io
,
o
n
e
-
th
ir
d
p
ar
tial
s
h
ad
i
n
g
,
r
ep
r
esen
ts
a
m
o
r
e
s
ev
er
e
s
h
ad
in
g
co
n
d
itio
n
wh
e
r
e
o
n
ly
o
n
e
-
th
ir
d
o
f
th
e
PV
ar
r
ay
r
ec
eiv
es
f
u
ll
in
s
o
latio
n
,
r
e
s
u
ltin
g
in
th
e
m
o
s
t
s
ig
n
if
ican
t p
o
wer
lo
s
s
am
o
n
g
t
h
e
th
r
ee
s
ce
n
ar
io
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
v
ar
y
in
g
p
o
wer
o
u
tp
u
ts
co
r
r
esp
o
n
d
in
g
to
ea
ch
s
h
ad
in
g
s
ce
n
ar
io
.
T
o
m
itig
ate
th
e
im
p
ac
t
o
f
s
h
ad
in
g
o
n
p
o
wer
g
en
er
atio
n
,
a
MPPT
co
n
tr
o
ller
is
em
p
lo
y
ed
.
T
h
is
co
n
tr
o
lle
r
co
n
tin
u
o
u
s
ly
ad
ju
s
ts
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
e
n
t
to
m
ai
n
tain
o
p
e
r
atio
n
at
th
e
MPP,
e
n
s
u
r
in
g
t
h
at
th
e
PV
s
y
s
tem
ac
h
iev
es
o
p
tim
al
p
er
f
o
r
m
a
n
ce
u
n
d
er
all
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
MPPT
tech
n
iq
u
e
ef
f
ec
tiv
ely
co
m
p
en
s
ates
f
o
r
th
e
r
ed
u
ce
d
i
n
s
o
latio
n
lev
els,
allo
win
g
th
e
PV
s
y
s
tem
to
d
eliv
e
r
th
e
h
ig
h
est
p
o
s
s
ib
le
p
o
wer
o
u
tp
u
t e
v
en
u
n
d
er
p
ar
tial sh
ad
in
g
.
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.
3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
9
2
3
-
1
9
3
7
1926
Fig
u
r
e
2
.
Mo
d
el
o
f
p
ar
tial sh
a
d
ed
PV a
r
r
ay
2
.
2
.
M
P
P
T
f
ra
m
ewo
rk
I
n
th
is
s
tu
d
y
,
t
h
e
m
o
d
elin
g
o
f
MPPT
is
ca
r
r
ied
o
u
t
u
s
in
g
a
co
m
p
r
eh
e
n
s
iv
e
ap
p
r
o
ac
h
th
at
in
teg
r
ates
v
ar
io
u
s
alg
o
r
ith
m
s
f
o
r
o
p
tim
iz
in
g
p
o
wer
o
u
tp
u
t
f
r
o
m
PV
s
y
s
tem
s
,
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
MPPT
m
o
d
el
is
im
p
lem
en
ted
with
in
th
e
Simu
lin
k
en
v
i
r
o
n
m
e
n
t
o
f
M
AT
L
AB
,
wh
er
e
th
e
alg
o
r
ith
m
is
d
esig
n
ed
to
co
n
tin
u
o
u
s
ly
tr
ac
k
a
n
d
ad
j
u
s
t th
e
o
p
er
atin
g
p
o
in
t o
f
th
e
PV sy
s
tem
to
en
s
u
r
e
it o
p
er
at
es a
t its
MPP.
Fig
u
r
e
3
.
Flo
wch
ar
t
d
iag
r
am
illu
s
tr
atin
g
th
e
r
esear
ch
m
o
d
el
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
Mo
d
ellin
g
a
n
d
s
imu
la
tio
n
o
f
ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
o
n
p
a
r
tia
l sh
a
d
ed
…
(
P
r
is
ma
Meg
a
n
to
r
o
)
1927
A
k
ey
co
m
p
o
n
en
t
o
f
th
is
s
tu
d
y
is
th
e
MPPT
co
n
tr
o
ller
,
wh
i
ch
en
s
u
r
es
th
at
th
e
PV
s
y
s
tem
o
p
er
ates
at
th
e
GM
PP
u
n
d
er
s
h
ad
in
g
c
o
n
d
itio
n
s
.
T
h
e
AOA
-
b
ased
MPPT
is
im
p
lem
en
ted
an
d
co
m
p
a
r
ed
a
g
ain
s
t
co
n
v
en
tio
n
al
PS
O
-
b
ased
MPPT.
T
h
e
r
esear
ch
p
r
o
ce
s
s
b
e
g
in
s
with
a
co
m
p
r
eh
en
s
iv
e
l
iter
atu
r
e
r
ev
iew
to
id
en
tify
r
esear
c
h
g
a
p
s
an
d
d
ef
in
e
th
e
MPPT
m
o
d
el
f
o
r
p
ar
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
.
Fo
l
lo
win
g
th
e
m
o
d
el
d
ev
elo
p
m
e
n
t,
s
im
u
latio
n
s
ar
e
co
n
d
u
cted
to
test
th
e
MPPT
m
o
d
el
u
n
d
er
d
if
f
e
r
en
t
s
h
a
d
in
g
c
o
n
d
itio
n
s
to
d
eter
m
in
e
th
e
m
ax
im
u
m
v
o
lt
ag
e
ac
h
iev
ab
le.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
AOA
-
b
ased
MPPT
m
o
d
el
is
th
en
co
m
p
ar
ed
to
s
tan
d
ar
d
v
alu
es
d
er
iv
ed
f
r
o
m
c
h
ar
ac
ter
is
tic
P
-
V
an
d
I
-
V
c
u
r
v
es.
I
f
th
e
s
tan
d
ar
d
MPP
v
o
ltag
e
f
r
o
m
th
e
P
-
V
an
d
I
-
V
cu
r
v
e
s
is
h
ig
h
er
th
an
th
at
o
b
tain
e
d
b
y
th
e
AOA
-
b
ased
MPPT
m
o
d
el,
p
a
r
am
eter
ad
ju
s
tm
en
ts
an
d
f
u
r
th
er
iter
a
tio
n
s
ar
e
ca
r
r
ied
o
u
t
to
r
e
f
in
e
th
e
m
o
d
el.
I
f
th
e
AOA
-
b
a
s
ed
MPPT
m
o
d
el
s
u
cc
ess
f
u
lly
tr
ac
k
s
a
h
ig
h
e
r
m
ax
im
u
m
v
o
ltag
e,
th
e
r
esu
lt
s
ar
e
an
aly
ze
d
an
d
d
is
cu
s
s
ed
in
th
e
f
in
al
r
ep
o
r
t.
A
v
is
u
al
r
ep
r
esen
tatio
n
o
f
th
i
s
m
e
th
o
d
o
lo
g
y
is
p
r
o
v
id
e
d
in
a
f
lo
wch
ar
t,
as
illu
s
tr
ated
in
Fig
u
r
e
3
,
to
en
s
u
r
e
clar
ity
in
th
e
r
esear
ch
p
r
o
ce
s
s
.
T
h
e
AOA
-
b
ased
MPPT
i
m
p
lem
en
tatio
n
f
o
llo
ws
th
e
s
y
s
tem
atic
ap
p
r
o
ac
h
o
u
tlin
ed
in
Alg
o
r
ith
m
1
.
T
h
is
alg
o
r
ith
m
lev
er
a
g
es
th
e
AOA
to
d
y
n
am
ically
tr
ac
k
th
e
g
lo
b
a
l
m
ax
im
u
m
p
o
we
r
p
o
in
t
b
y
tr
ea
tin
g
v
o
ltag
e
v
a
lu
es
as
s
ea
r
ch
ag
en
ts
th
at
e
x
p
lo
r
e
th
e
s
o
lu
tio
n
s
p
ac
e
b
ased
o
n
b
u
o
y
a
n
cy
p
r
in
cip
les.
Alg
o
r
ith
m
1
.
AOA
-
b
ased
MPPT
im
p
lem
en
tatio
n
Begin
Initialize population of search agents (voltage values)
Define maximum iterations and convergence criteria
Evaluate initial power output for each agent
Identify the best agent corresponding to the highest power (initial GMPP)
While stopping
condition not met do
Compute density and volume update for each search agent
Adjust search agent positions based on Archimedes’ principle
Evaluate new power outputs for updated agents
Update the best solution if a higher power outp
ut is found
Adapt exploration and exploitation balance dynamically
End While
Return best voltage corresponding to the GMPP
End
T
h
is
p
s
eu
d
o
co
d
e
o
u
tlin
es
th
e
s
tep
-
by
-
s
tep
ex
ec
u
tio
n
o
f
th
e
AOA
-
b
ased
MPPT
tech
n
iq
u
e,
en
s
u
r
in
g
a
b
alan
c
e
b
etwe
en
ex
p
lo
r
atio
n
,
s
u
c
h
as
s
ea
r
ch
in
g
f
o
r
n
ew
p
o
ten
tial
s
o
lu
tio
n
s
an
d
e
x
p
lo
itatio
n
,
s
u
c
h
as
r
ef
in
in
g
k
n
o
wn
g
o
o
d
s
o
l
u
tio
n
s
.
2
.
3
.
Arc
him
edes o
ptim
iza
t
io
n a
lg
o
rit
hm
AOA
is
a
m
etah
eu
r
is
tic
alg
o
r
ith
m
th
at
is
an
ef
f
icien
t
o
p
tim
izatio
n
co
n
tr
o
l
alg
o
r
ith
m
with
b
alan
ce
d
co
n
v
er
g
en
ce
,
ex
p
l
o
r
atio
n
,
an
d
ex
p
lo
itatio
n
ca
p
ab
ilit
ies,
wh
ich
ar
e
co
n
s
id
er
ed
s
u
itab
le
f
o
r
s
o
lv
in
g
c
o
m
p
le
x
o
p
tim
izatio
n
p
r
o
b
lem
s
.
AOA
is
b
ased
o
n
a
p
h
y
s
ics
p
r
in
ci
p
le,
n
am
el
y
th
e
A
r
ch
im
e
d
es
p
r
in
cip
le,
wh
ic
h
s
tates
th
at
wh
en
an
o
b
ject
is
s
u
b
m
er
g
ed
in
a
f
lu
id
,
e
ith
er
e
n
tire
ly
o
r
p
ar
tially
,
th
e
f
lu
id
will e
x
er
t
an
u
p
war
d
f
o
r
ce
o
n
th
e
o
b
ject
th
at
is
eq
u
al
to
th
e
weig
h
t
o
f
th
e
f
lu
id
p
u
s
h
e
d
o
u
t
b
y
th
e
o
b
ject.
W
h
en
an
o
b
jec
t
is
im
m
er
s
ed
in
th
e
f
lu
id
,
it will e
x
p
er
ien
ce
an
u
p
war
d
f
o
r
ce
ca
lled
b
u
o
y
a
n
t f
o
r
ce
,
wh
ich
h
as t
h
e
s
am
e
m
ag
n
itu
d
e
as th
e
weig
h
t o
f
th
e
f
lu
id
p
u
s
h
e
d
o
u
t
b
y
th
e
o
b
ject
[
3
3
]
.
As
s
h
o
w
n
in
Fig
u
r
e
4
,
AOA
s
er
v
es
as
th
e
co
r
e
tech
n
iq
u
e
f
o
r
t
h
e
MPPT
m
o
d
el,
u
tili
zin
g
s
ev
er
al
k
ey
alg
o
r
ith
m
ic
p
a
r
am
eter
s
s
u
ch
as
,
,
,
an
d
.
T
h
e
v
alu
es
f
o
r
th
e
k
ey
alg
o
r
ith
m
ic
p
ar
am
eter
s
,
in
clu
d
in
g
th
e
n
u
m
b
e
r
o
f
o
b
jects
an
d
iter
atio
n
s
,
ar
e
d
eter
m
in
ed
b
ased
o
n
s
i
m
u
latio
n
r
esu
lts
,
with
2
0
o
b
jects
an
d
2
0
iter
atio
n
s
id
en
ti
f
ied
as
o
p
tim
al
f
o
r
ac
h
iev
in
g
th
e
b
est
s
o
lu
tio
n
.
C
o
n
tr
o
l
p
a
r
am
eter
s
C
1
,
C
2
,
C
3
an
d
C
4
ar
e
s
et
as
co
n
s
tan
ts
,
f
o
llo
win
g
r
ef
e
r
en
ce
v
alu
es
f
r
o
m
r
elev
an
t
r
esear
ch
.
T
h
e
s
u
b
s
eq
u
e
n
t
s
tep
in
v
o
lv
es
ca
lcu
latin
g
th
e
v
alu
es
f
o
r
ea
c
h
p
ar
am
ete
r
u
s
in
g
d
esig
n
ated
eq
u
atio
n
s
an
d
d
e
f
in
in
g
a
f
itn
ess
f
u
n
ctio
n
to
ev
alu
ate
an
d
s
elec
t
th
e
b
est
p
a
r
am
eter
v
alu
es
f
o
r
o
p
tim
izatio
n
.
Fo
llo
win
g
th
is
,
th
e
d
en
s
ity
an
d
v
o
lu
m
e
p
ar
a
m
eter
s
ar
e
u
p
d
ated
,
an
d
th
e
tr
an
s
f
er
f
ac
to
r
(
TF
)
an
d
d
e
n
s
ity
d
ec
r
ea
s
e
f
ac
t
o
r
(
df
)
ar
e
r
ec
alcu
lated
.
De
p
en
d
i
n
g
o
n
wh
eth
e
r
th
e
c
o
n
d
itio
n
TF
≤
0
.
5
is
m
et,
t
h
e
p
r
o
ce
s
s
eith
er
p
r
o
ce
ed
s
with
ex
p
lo
r
atio
n
,
a
d
ju
s
tin
g
o
b
jec
t
ac
ce
ler
atio
n
with
a
r
an
d
o
m
m
ater
ial
f
o
r
th
e
n
ex
t
iter
atio
n
,
o
r
with
ex
p
lo
it
atio
n
,
d
ir
ec
tly
a
d
ju
s
tin
g
th
e
o
b
ject
ac
ce
ler
atio
n
.
T
h
e
iter
ativ
e
p
r
o
ce
s
s
co
n
tin
u
es
u
n
til
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
is
r
ea
ch
ed
,
with
t
h
e
p
r
im
ar
y
o
b
jectiv
e
b
ein
g
t
o
o
p
tim
ize
th
e
p
o
wer
o
u
tp
u
t.
T
h
e
alg
o
r
ith
m
en
s
u
r
es
th
at
th
e
b
est
s
o
lu
tio
n
s
ar
e
f
o
u
n
d
b
y
s
y
s
tem
atica
lly
ad
ju
s
tin
g
an
d
r
ef
in
in
g
th
e
p
ar
am
eter
s
th
r
o
u
g
h
th
ese
ite
r
ativ
e
s
tep
s
.
T
h
e
f
ir
s
t
s
tep
n
th
e
in
itializatio
n
p
h
ase,
f
o
r
ea
ch
o
b
ject
i,
th
e
p
o
s
itio
n
,
v
o
l
u
m
e
(
v
)
,
d
en
s
ity
(
ρ
)
,
an
d
ac
ce
ler
atio
n
(
a
o
r
ac
ca
cc
ac
c)
o
f
all
o
b
jects
ar
e
s
et
with
in
itial
v
alu
es
u
s
in
g
th
e
f
o
ll
o
win
g
(
3
)
:
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.
3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
9
2
3
-
1
9
3
7
1928
=
+
×
(
−
)
(
3
)
wh
er
e
x
i
r
e
p
r
esen
ts
th
e
i
th
o
b
ject,
d
en
o
tes
th
e
l
o
wer
b
o
u
n
d
o
f
th
e
s
ea
r
ch
s
p
ac
e,
an
d
is
th
e
u
p
p
e
r
b
o
u
n
d
o
f
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
o
b
ject
co
r
r
esp
o
n
d
s
to
o
n
e
o
f
th
e
p
o
p
u
latio
n
m
em
b
er
s
,
with
i
r
an
g
in
g
f
r
o
m
1
to
N,
wh
er
e
N
is
th
e
p
o
p
u
latio
n
s
ize.
T
h
e
ter
m
r
a
n
d
r
e
f
er
s
to
a
r
an
d
o
m
n
u
m
b
er
g
en
e
r
ated
b
etwe
en
0
a
n
d
1
,
en
s
u
r
in
g
th
at
th
e
in
itial
p
o
s
itio
n
o
f
ea
ch
o
b
ject
is
r
an
d
o
m
ly
d
is
tr
ib
u
ted
with
i
n
th
e
d
ef
in
ed
s
ea
r
ch
s
p
ac
e
b
o
u
n
d
ar
ies.
=
(
4
)
=
(
5
)
wh
er
e
r
a
n
d
is
a
D
-
d
im
en
s
i
o
n
al
v
ec
t
o
r
t
h
at
g
e
n
er
ates
r
an
d
o
m
n
u
m
b
er
s
b
etwe
en
[
0
,
1
]
.
Fin
ally
,
th
e
ac
ce
ler
atio
n
(
ac
c
o
r
a)
o
f
th
e
i
th
o
b
ject
is
in
itialized
u
s
in
g
th
e
ap
p
r
o
p
r
iate
p
ar
a
m
eter
s
.
=
+
×
(
−
)
(
6
)
Fig
u
r
e
4
.
T
h
e
AOA
f
lo
wch
ar
t
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
Mo
d
ellin
g
a
n
d
s
imu
la
tio
n
o
f
ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
o
n
p
a
r
tia
l sh
a
d
ed
…
(
P
r
is
ma
Meg
a
n
to
r
o
)
1929
T
h
e
o
b
ject
is
s
elec
ted
b
ased
o
n
th
e
b
est
f
itn
ess
v
alu
e
af
ter
ev
alu
atin
g
th
e
in
itial
p
o
p
u
latio
n
,
co
n
s
id
er
in
g
,
,
,
.
Seco
n
d
s
tep
,
th
e
d
en
s
ity
an
d
o
f
o
b
ject
i
ar
e
u
p
d
ated
f
o
r
t
h
e
iter
atio
n
t+1
a
s
(
7
)
an
d
(
8
)
.
+
1
=
+
×
(
−
)
(
7
)
+
1
=
+
×
(
−
)
(
8
)
W
h
er
e,
an
d
r
ef
er
to
t
h
e
b
e
s
t
v
o
lu
m
e
an
d
d
e
n
s
ity
o
f
th
e
o
b
jects,
wh
ile
r
a
n
d
is
a
r
an
d
o
m
n
u
m
b
er
g
en
er
ated
u
n
if
o
r
m
ly
.
T
h
ir
d
s
tep
,
I
n
itially
,
th
e
o
b
jects
co
llid
e
with
ea
ch
o
th
er
,
an
d
o
v
e
r
tim
e,
th
e
y
attem
p
t
to
r
ea
ch
eq
u
ilib
r
i
u
m
.
T
h
e
tr
an
s
f
er
o
p
e
r
ato
r
(
T
F)
f
a
cilitates
th
e
tr
an
s
it
io
n
o
f
th
e
s
ea
r
ch
p
r
o
ce
s
s
f
r
o
m
ex
p
lo
r
atio
n
to
ex
p
lo
itatio
n
.
T
h
e
T
F is
ca
lcu
lated
u
s
in
g
(
9
)
.
=
(
−
)
(
9
)
T
h
e
T
F
g
r
ad
u
ally
in
c
r
ea
s
es
d
u
r
in
g
iter
atio
n
s
u
n
til
it
r
ea
ch
es
a
v
alu
e
o
f
1
,
in
d
icatin
g
a
s
h
if
t
f
r
o
m
ex
p
lo
r
atio
n
t
o
ex
p
l
o
itatio
n
.
W
h
er
e
is
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
,
an
d
t
is
th
e
cu
r
r
en
t
iter
atio
n
n
u
m
b
er
.
Similar
ly
,
th
e
d
en
s
ity
d
ec
ay
f
ac
to
r
d
d
d
aid
s
th
e
AOA
in
tr
a
n
s
itio
n
in
g
f
r
o
m
g
l
o
b
al
to
l
o
ca
l
s
ea
r
ch
.
I
t
is
ca
lcu
lated
as:
+
1
=
(
−
)
−
(
)
(
1
0
)
wh
er
e,
+
1
r
ep
r
esen
ts
th
e
d
e
n
s
ity
at
iter
atio
n
t+1
,
wh
ich
d
ec
r
ea
s
es
o
v
er
tim
e,
allo
win
g
f
o
r
co
n
v
er
g
en
ce
at
a
s
p
ec
if
ic
p
o
in
t.
T
h
is
d
en
s
ity
p
ar
am
eter
p
lay
s
a
c
r
u
cial
r
o
le
in
ac
h
iev
in
g
a
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
with
in
th
e
AOA.
2
.
4
.
E
v
a
lua
t
i
o
n a
nd
perf
o
r
m
a
nce
m
e
t
rics
T
o
v
alid
ate
AOA
-
MPPT,
co
m
p
ar
ativ
e
s
im
u
latio
n
s
ar
e
p
e
r
f
o
r
m
e
d
ag
ain
s
t
PS
O
-
MPPT.
T
h
e
k
ey
p
er
f
o
r
m
an
ce
m
et
r
ics
an
aly
ze
d
in
clu
d
e
p
o
wer
tr
ac
k
in
g
ef
f
icien
cy
,
wh
ich
m
ea
s
u
r
es
th
e
r
atio
o
f
ex
tr
ac
te
d
p
o
wer
to
th
e
th
eo
r
etica
l
MPP
p
o
wer
,
co
n
v
er
g
en
ce
tim
e,
w
h
ich
q
u
an
tifie
s
th
e
tim
e
r
e
q
u
i
r
ed
to
r
ea
c
h
GM
PP
,
an
d
v
o
ltag
e
tr
ac
k
in
g
e
r
r
o
r
,
wh
ich
ass
ess
e
s
th
e
d
if
f
er
en
c
e
b
etwe
en
ac
tu
al
an
d
ex
p
ec
ted
MPP
v
o
ltag
e.
Per
f
o
r
m
an
ce
is
test
ed
u
n
d
er
d
if
f
er
en
t
s
h
ad
in
g
co
n
d
itio
n
s
,
an
d
a
s
tatis
tica
l
an
aly
s
is
is
c
o
n
d
u
cte
d
to
v
er
if
y
alg
o
r
ith
m
r
o
b
u
s
tn
ess
.
T
h
e
er
r
o
r
ev
alu
atio
n
b
etwe
e
n
th
e
s
tan
d
ar
d
Vm
p
p
an
d
th
e
Vm
p
p
o
b
tain
e
d
f
r
o
m
th
e
AOA
-
b
ased
MPPT
is
a
cr
itical
asp
ec
t
o
f
th
is
s
tu
d
y
.
T
h
e
er
r
o
r
eq
u
atio
n
u
s
ed
to
co
m
p
ar
e
t
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
AOA
alg
o
r
ith
m
is
b
ased
o
n
th
e
s
tan
d
ar
d
m
ax
im
u
m
p
o
wer
p
o
i
n
t
v
o
ltag
e
(
Vm
p
p
)
f
r
o
m
t
h
e
PV
s
y
s
tem
an
d
th
e
v
o
ltag
e
o
b
tain
ed
f
r
o
m
th
e
AOA
-
b
ased
MPPT
(
Va
o
a)
.
T
h
e
e
r
r
o
r
ca
lcu
latio
n
is
ex
p
r
ess
ed
a
s
(
1
1
)
.
(
%
)
=
(
−
/
)
×
100%
(
1
1
)
W
h
er
e,
/
r
ep
r
esen
ts
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
v
o
ltag
e
o
b
tain
ed
u
s
in
g
th
e
AOA
-
b
ased
M
PP
T
,
wh
ile
d
en
o
tes
t
h
e
s
tan
d
ar
d
m
a
x
im
u
m
p
o
wer
p
o
i
n
t
v
o
ltag
e
o
f
th
e
PV
s
y
s
tem
.
E
v
alu
atio
n
s
ar
e
co
n
d
u
cted
u
n
d
er
v
ar
io
u
s
in
s
o
latio
n
co
n
d
itio
n
s
to
ass
e
s
s
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
AOA
-
b
ased
MPPT.
A
lo
wer
er
r
o
r
v
alu
e
in
d
icate
s
th
at
th
e
MPPT
m
o
d
el
is
m
o
r
e
ac
cu
r
ate
in
i
d
en
t
if
y
in
g
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
v
o
ltag
e
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
C
o
n
v
er
s
ely
,
a
h
ig
h
e
r
er
r
o
r
v
alu
e
s
u
g
g
ests
th
at
th
e
MP
PT
m
o
d
el
is
le
s
s
ac
cu
r
ate
in
p
in
p
o
in
tin
g
th
e
o
p
tim
al
v
o
ltag
e
at
th
e
MPP u
n
d
er
p
ar
tial sh
a
d
in
g
co
n
d
itio
n
s
.
T
o
f
u
r
th
er
ev
alu
ate
th
e
er
r
o
r
i
n
MPPT
tr
ac
k
in
g
,
we
ca
lcu
lat
ed
th
e
r
o
o
t
m
ea
n
s
q
u
a
r
e
er
r
o
r
(
R
MSE
)
an
d
m
ea
n
ab
s
o
lu
te
er
r
o
r
(
M
AE
)
f
o
r
AOA,
PS
O,
an
d
co
n
v
en
tio
n
al
MPPT
m
eth
o
d
s
.
T
h
ese
m
etr
ics
p
r
o
v
id
e
in
s
ig
h
t in
to
th
e
ac
cu
r
ac
y
o
f
ea
ch
alg
o
r
ith
m
in
esti
m
atin
g
th
e
MPP:
1.
R
MSE
: m
ea
s
u
r
es th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
tr
ac
k
i
n
g
er
r
o
r
s
,
with
lo
wer
v
alu
es in
d
icatin
g
b
etter
ac
cu
r
ac
y
.
2.
MA
E
:
r
ep
r
esen
ts
th
e
av
e
r
ag
e
ab
s
o
lu
te
d
if
f
e
r
en
ce
b
etwe
en
a
ctu
al
an
d
esti
m
ated
v
alu
es,
p
r
o
v
id
in
g
a
d
ir
ec
t
m
ea
s
u
r
e
o
f
tr
ac
k
in
g
p
r
ec
is
io
n
.
T
o
s
tatis
tical
ly
v
alid
ate
th
e
p
er
f
o
r
m
a
n
ce
d
if
f
er
e
n
ce
s
am
o
n
g
th
e
test
ed
MPPT
alg
o
r
ith
m
s
,
we
ap
p
lied
th
e
Frie
d
m
an
test
,
a
n
o
n
-
p
ar
a
m
etr
ic
s
tatis
tica
l
test
s
u
itab
le
f
o
r
co
m
p
ar
in
g
m
u
ltip
le
o
p
tim
izatio
n
tech
n
iq
u
es
o
v
er
d
if
f
er
en
t
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
Frie
d
m
an
test
ass
ess
es
wh
eth
er
th
er
e
ar
e
s
ig
n
if
ica
n
t
d
if
f
er
en
ce
s
in
th
e
ef
f
icien
cy
an
d
c
o
n
v
e
r
g
en
ce
t
im
e
o
f
AOA,
PS
O,
an
d
co
n
v
en
tio
n
al
MPPT
m
eth
o
d
s
u
n
d
er
v
ar
io
u
s
p
ar
tial
s
h
ad
in
g
s
ce
n
ar
io
s
.
T
h
e
Frie
d
m
an
test
s
tatis
tic
(
Fr
)
is
ca
lcu
lat
ed
u
s
in
g
(
1
2
)
.
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.
3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
9
2
3
-
1
9
3
7
1930
=
12
.
.
(
+
1
)
∑
2
−
3
.
.
(
+
1
)
=
1
(
1
2
)
W
h
er
e
N
i
s
th
e
n
u
m
b
er
o
f
r
o
ws
(
co
m
b
in
atio
n
s
o
f
o
b
jects
an
d
iter
atio
n
s
)
,
k
is
th
e
n
u
m
b
e
r
o
f
s
ce
n
ar
io
s
(
3
in
th
is
ca
s
e:
o
n
e
-
th
ir
d
,
h
alf
,
an
d
u
n
if
o
r
m
)
,
an
d
Rj
is
th
e
s
u
m
o
f
r
an
k
s
f
o
r
ea
ch
s
ce
n
ar
i
o
.
2
.
5
.
J
us
t
if
ica
t
io
n o
f
m
et
ho
d
o
lo
g
y
T
h
e
ch
o
ice
o
f
AOA
f
o
r
MPPT
is
ju
s
tif
ied
b
ased
o
n
s
ev
er
al
f
ac
to
r
s
.
AOA
d
em
o
n
s
tr
at
es
s
u
p
er
io
r
ad
ap
tab
ilit
y
to
d
y
n
am
ic
e
n
v
ir
o
n
m
en
tal
c
h
an
g
es
c
o
m
p
a
r
ed
t
o
f
ix
e
d
-
s
tep
alg
o
r
ith
m
s
lik
e
P&
O.
Ad
d
itio
n
ally
,
AOA
p
r
o
v
id
es
a
well
-
b
alan
ce
d
s
ea
r
ch
p
r
o
ce
s
s
b
y
d
y
n
am
ic
ally
ad
ju
s
tin
g
s
ea
r
ch
p
ar
am
et
er
s
,
u
n
lik
e
G
A
an
d
PS
O,
wh
ich
m
ay
s
tr
u
g
g
le
with
p
r
em
at
u
r
e
co
n
v
er
g
en
ce
o
r
l
o
ca
l
o
p
tim
a.
Fin
ally
,
AOA
o
f
f
er
s
co
m
p
u
tatio
n
al
ef
f
icien
cy
b
y
r
eq
u
i
r
in
g
f
ewe
r
iter
atio
n
s
to
r
ea
ch
co
n
v
er
g
e
n
ce
co
m
p
ar
ed
t
o
co
n
v
en
tio
n
al
h
eu
r
is
tic
m
eth
o
d
s
.
T
h
e
m
eth
o
d
o
lo
g
y
p
r
esen
ted
e
n
s
u
r
es
th
at
th
e
s
tu
d
y
’
s
r
esu
lts
ar
e
r
ep
r
o
d
u
cib
le,
r
elia
b
le,
an
d
ap
p
licab
le
t
o
r
ea
l
-
wo
r
ld
PV sy
s
tem
s
u
n
d
er
p
a
r
tial sh
ad
in
g
co
n
d
itio
n
s
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
test
in
g
MPPT
p
er
f
o
r
m
an
ce
in
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
MPPT
b
ased
o
n
th
e
AOA
alg
o
r
ith
m
will
b
e
co
m
p
ar
ed
with
th
e
PS
O
alg
o
r
ith
m
to
f
in
d
th
e
MPP
d
u
r
i
n
g
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
wh
er
e
t
h
r
ee
in
s
o
latio
n
co
n
d
itio
n
s
will
b
e
u
s
ed
with
d
if
f
e
r
en
t
s
h
ad
i
n
g
co
n
d
itio
n
s
.
T
h
e
f
i
r
s
t
co
n
d
itio
n
is
a
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
;
in
t
h
is
co
n
d
itio
n
,
th
e
PV
r
ec
eiv
es
f
u
ll
s
u
n
lig
h
t
w
ith
o
u
t
an
y
s
h
a
d
in
g
s
.
Fo
r
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
,
it
is
r
e
p
r
esen
ted
b
y
th
e
in
s
o
latio
n
i
n
p
u
t
v
alu
e
in
th
e
STC,
wh
ich
is
1
,
0
0
0
2
⁄
.
Ho
wev
er
,
in
ac
tu
al
co
n
d
itio
n
s
in
ce
r
tain
p
lace
s
with
wea
t
h
er
co
n
d
itio
n
s
wh
er
e
th
e
lig
h
t
in
ten
s
ity
is
less
b
r
ig
h
t,
it
c
an
also
g
iv
e
r
is
e
to
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
with
in
s
o
latio
n
v
alu
es
less
th
an
STC,
s
o
tes
ts
ar
e
ca
r
r
ied
o
u
t
to
r
ep
r
esen
t
u
n
if
o
r
m
in
s
o
latio
n
c
o
n
d
itio
n
s
with
l
ess
b
r
ig
h
t
s
u
n
lig
h
t
in
ten
s
ity
w
ith
th
e
v
al
u
e
u
s
ed
b
ein
g
7
5
0
2
⁄
an
d
5
0
0
2
⁄
,
th
ese
tw
o
v
a
lu
es
a
r
e
u
s
ed
as
an
ad
j
u
s
ted
r
ep
r
esen
tatio
n
o
f
t
h
e
in
s
o
l
atio
n
in
p
u
t
to
t
h
e
m
o
d
u
le
r
e
f
er
en
ce
f
o
r
o
n
e
-
th
i
r
d
p
ar
tial
s
h
ad
e
co
n
d
itio
n
s
.
Me
an
wh
ile,
th
e
s
ec
o
n
d
an
d
th
ir
d
co
n
d
itio
n
s
a
r
e
in
s
o
latio
n
c
o
n
d
itio
n
s
with
d
if
f
er
en
t
p
ar
tial
s
h
ad
in
g
le
v
els.
T
h
e
s
ec
o
n
d
a
n
d
t
h
ir
d
c
o
n
d
itio
n
s
ar
e
cr
ea
ted
s
o
th
at
t
h
e
P
-
V
an
d
I
-
V
ch
a
r
ac
ter
is
tic
g
r
ap
h
s
s
h
o
w
s
ev
er
al
p
ea
k
s
th
at
r
ep
r
esen
t
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
s
o
th
at
f
r
o
m
th
e
to
t
al
o
f
all
p
ea
k
s
,
th
e
lo
ca
l
p
ea
k
an
d
g
lo
b
al
p
ea
k
ca
n
b
e
id
en
tif
ied
wh
er
e
th
e
MPP
is
th
e
lo
ca
tio
n
o
f
t
h
e
o
p
tim
ize
d
v
o
ltag
e
a
n
d
c
u
r
r
en
t.
3
.
1
.
M
o
del o
f
div
er
s
e
ins
o
la
t
io
ns
Fig
u
r
e
5
d
em
o
n
s
tr
ates
P
-
V
an
d
I
-
V
ch
ar
ac
ter
is
tics
f
o
r
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
with
an
in
s
o
latio
n
in
p
u
t
o
f
1
,
0
0
0
W
⁄m
2
is
s
h
o
wn
in
.
Fig
u
r
e
5
(
a)
s
h
o
ws
th
at
th
e
test
r
esu
lts
f
o
u
n
d
o
n
ly
o
n
e
p
e
ak
p
o
in
t
as
th
e
GM
PP
f
r
o
m
th
e
u
n
i
f
o
r
m
in
s
o
latio
n
in
p
u
t,
th
is
is
in
f
lu
en
ce
d
b
y
th
e
s
am
e
i
n
p
u
t
in
s
o
latio
n
v
alu
e
s
o
t
h
at
th
e
o
u
tp
u
t
cu
r
r
en
t
v
alu
e
will
b
e
th
e
s
am
e.
As
i
s
k
n
o
wn
,
th
e
P
-
V
g
r
ap
h
is
th
e
p
r
o
d
u
ct
o
f
th
e
in
p
u
t
v
o
ltag
e
an
d
cu
r
r
en
t.
Fro
m
t
h
e
g
r
ap
h
o
f
th
e
P
-
V
an
d
I
-
V
c
h
ar
ac
ter
is
tics
,
it
is
also
k
n
o
wn
th
at
th
e
p
o
wer
p
r
o
d
u
ce
d
u
n
d
er
u
n
if
o
r
m
in
s
o
latio
n
c
o
n
d
itio
n
s
b
y
MPPT
-
AOA
is
4
6
4
W
wh
i
le
MPPT
-
PS
O
i
s
4
2
8
W
.
Fig
u
r
e
5
(
b
)
s
h
o
ws
th
at
th
e
test
r
esu
lts
f
r
o
m
th
e
p
ar
t
ial
s
h
ad
in
g
in
s
o
latio
n
i
n
p
u
t
f
o
u
n
d
two
p
ea
k
p
o
in
ts
d
ef
in
e
d
as
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
o
r
L
MPP
an
d
GM
PP
.
Fro
m
th
e
g
r
ap
h
,
it
is
also
s
h
o
wn
th
at
th
e
p
o
wer
p
r
o
d
u
ce
d
d
u
r
in
g
h
alf
-
s
h
ad
in
g
in
s
o
latio
n
co
n
d
itio
n
s
b
y
MPPT
-
AOA
i
s
3
5
3
W
,
wh
ile
MPPT
-
P
SO
i
s
3
3
0
W
.
Fig
u
r
e
5
(
c)
s
h
o
ws
th
at
th
at
th
er
e
wer
e
th
r
ee
p
ea
k
p
o
i
n
ts
d
ef
in
ed
as
MPP
s
o
r
two
lo
ca
l
MPPs
an
d
1
GM
PP
.
Fro
m
th
e
g
r
ap
h
o
f
th
e
P
-
V
an
d
I
-
V
c
h
ar
ac
ter
is
tics
,
it
is
also
k
n
o
wn
t
h
at
th
e
p
o
wer
p
r
o
d
u
ce
d
d
u
r
in
g
in
s
o
latio
n
co
n
d
itio
n
s
o
f
o
n
e
-
th
i
r
d
o
f
th
e
p
a
r
tial sh
ad
in
g
b
y
MPPT
-
AOA
is
2
4
2
W
wh
ile
MPP
T
-
PS
O
is
2
3
1
W
.
(
a)
(
b
)
(
c)
Fig
u
r
e
5
.
P
-
V
cu
r
v
e
r
esp
o
n
s
e
o
f
PV m
o
d
u
le
in
d
if
f
er
en
t in
s
o
latio
n
co
n
d
itio
n
; (
a)
u
n
if
o
r
m
i
n
s
o
latio
n
,
(
b
)
h
alf
s
h
ad
ed
in
s
o
latio
n
,
a
n
d
(
c
)
o
n
e
-
th
ir
d
s
h
ad
e
d
in
s
o
latio
n
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
Mo
d
ellin
g
a
n
d
s
imu
la
tio
n
o
f
ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
o
n
p
a
r
tia
l sh
a
d
ed
…
(
P
r
is
ma
Meg
a
n
to
r
o
)
1931
W
h
ile
th
e
s
im
u
latio
n
r
esu
lts
a
r
e
p
r
o
m
is
in
g
,
t
h
e
p
r
ac
tical
im
p
lem
en
tatio
n
o
f
AOA
in
r
ea
l
-
wo
r
ld
PV
s
y
s
tem
s
r
eq
u
ir
es
f
u
r
th
er
in
v
es
tig
atio
n
.
T
h
e
ap
p
licatio
n
o
f
A
OA
-
b
ased
MPPT
to
p
h
y
s
ical
MPPT
co
n
tr
o
ller
s
p
r
esen
ts
s
ev
er
al
ch
allen
g
es,
in
clu
d
in
g
h
ar
d
war
e
r
eq
u
ir
e
m
en
t
s
an
d
co
m
p
u
tatio
n
al
f
ea
s
ib
ilit
y
.
AOA’
s
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
wo
u
ld
r
eq
u
ir
e
a
h
ig
h
-
s
p
ee
d
m
ic
r
o
co
n
tr
o
lle
r
o
r
FP
GA
-
b
ased
co
n
tr
o
ller
c
ap
ab
le
o
f
h
an
d
lin
g
th
e
iter
ativ
e
o
p
tim
izatio
n
p
r
o
ce
s
s
ef
f
icien
tly
.
Mo
r
eo
v
e
r
,
i
n
teg
r
atin
g
AOA
with
an
em
b
e
d
d
ed
s
y
s
tem
wo
u
ld
n
ec
ess
itate
r
ea
l
-
tim
e
s
en
s
o
r
d
ata
ac
q
u
is
itio
n
f
o
r
v
o
lta
g
e
an
d
cu
r
r
en
t
tr
a
ck
in
g
,
en
s
u
r
in
g
ac
cu
r
ate
an
d
r
esp
o
n
s
iv
e
MPPT
o
p
er
atio
n
.
An
o
th
er
cr
itical
asp
ec
t
is
en
er
g
y
e
f
f
icien
cy
,
as
ex
ce
s
s
iv
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
co
u
ld
lead
to
h
ig
h
er
p
o
wer
co
n
s
u
m
p
tio
n
in
th
e
c
o
n
tr
o
l
u
n
it,
r
ed
u
cin
g
th
e
o
v
e
r
all
s
y
s
tem
ef
f
icien
cy
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
AOA
-
b
ased
MPPT
tech
n
iq
u
e
was
ev
alu
ated
ag
ain
s
t
PS
O
an
d
co
n
v
en
tio
n
al
MPPT
m
eth
o
d
s
u
n
d
er
d
if
f
e
r
en
t
p
ar
tial
s
h
ad
in
g
s
ce
n
ar
i
o
s
.
Simu
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
th
at
AO
A
co
n
s
is
ten
tly
o
u
tp
er
f
o
r
m
s
PS
O
an
d
co
n
v
en
tio
n
al
alg
o
r
ith
m
s
in
ter
m
s
o
f
p
o
wer
tr
ac
k
in
g
ef
f
icien
cy
an
d
co
n
v
er
g
en
ce
s
p
ee
d
.
Sp
ec
if
ica
lly
,
u
n
d
er
h
alf
-
s
h
ad
ed
i
n
s
o
latio
n
co
n
d
itio
n
s
,
th
e
AOA
alg
o
r
ith
m
ac
h
iev
es
an
ef
f
icien
cy
o
f
9
7
.
8
%,
co
m
p
ar
e
d
to
9
5
.
3
%
f
o
r
PS
O.
Similar
ly
,
u
n
d
er
o
n
e
-
th
ir
d
s
h
ad
ed
in
s
o
latio
n
,
AOA
tr
ac
k
s
th
e
GM
PP
6
.
5
%
f
aster
th
an
P
SO,
r
ed
u
cin
g
p
o
wer
lo
s
s
d
u
e
to
s
h
ad
in
g
e
f
f
ec
ts
.
On
e
k
ey
ad
v
an
tag
e
o
f
AOA
i
s
its
co
n
v
er
g
en
ce
ca
p
ab
ilit
ies,
b
alan
ce
d
e
x
p
lo
r
atio
n
,
a
n
d
ex
p
lo
itatio
n
,
wh
ich
ar
e
s
p
ec
if
ically
le
v
er
ag
ed
f
o
r
t
h
e
MPPT
p
r
o
b
lem
to
en
h
an
ce
tr
ac
k
in
g
ac
c
u
r
ac
y
an
d
ef
f
icien
c
y
,
wh
ich
p
r
ev
en
ts
th
e
al
g
o
r
ith
m
f
r
o
m
g
ettin
g
tr
ap
p
ed
in
lo
ca
l
m
ax
i
m
a,
u
n
lik
e
tr
ad
itio
n
al
tech
n
iq
u
es
s
u
ch
as
P&
O.
W
h
ile
P
SO
-
b
ased
MPPT
ex
h
ib
its
r
ap
id
co
n
v
er
g
en
ce
in
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
,
it
s
tr
u
g
g
les
u
n
d
er
d
y
n
am
ically
ch
a
n
g
in
g
s
h
ad
in
g
p
atter
n
s
d
u
e
to
its
d
ep
e
n
d
e
n
cy
o
n
i
n
itial
p
ar
am
eter
s
ettin
g
s
.
T
h
e
s
tatis
tical
an
aly
s
is
co
n
f
ir
m
s
th
at
AOA
m
ain
tain
s
a
lo
wer
v
o
ltag
e
tr
ac
k
in
g
er
r
o
r
d
u
e
to
its
d
y
n
am
ic
ad
ap
tatio
n
o
f
s
ea
r
ch
ag
en
ts
,
wh
ich
allo
ws
it
to
e
f
f
ec
tiv
ely
b
alan
ce
lo
ca
l
an
d
g
lo
b
al
s
ea
r
ch
p
r
o
ce
s
s
es,
p
r
ev
en
tin
g
p
r
em
atu
r
e
co
n
v
er
g
en
ce
a
n
d
e
n
s
u
r
in
g
ac
cu
r
ate
GM
PP
tr
ac
k
in
g
,
en
s
u
r
in
g
h
ig
h
er
ac
c
u
r
ac
y
in
MPP
esti
m
atio
n
ac
r
o
s
s
v
ar
y
in
g
en
v
ir
o
n
m
e
n
tal
co
n
d
iti
o
n
s
.
3.
2
.
Co
nv
er
g
ence
a
na
ly
s
is
o
f
AO
A
T
o
f
u
r
t
h
er
an
al
y
ze
th
e
e
f
f
icie
n
cy
o
f
AOA
in
MPPT,
a
co
n
v
er
g
en
ce
s
tu
d
y
was
co
n
d
u
cted
co
m
p
ar
in
g
th
e
n
u
m
b
er
o
f
iter
atio
n
s
r
eq
u
ir
ed
b
y
AOA
an
d
PS
O
to
ac
h
iev
e
s
tab
le
tr
ac
k
in
g
u
n
d
e
r
d
if
f
er
en
t
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
co
n
v
er
g
e
n
ce
an
aly
s
is
in
Fig
u
r
e
6
illu
s
tr
ate
s
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
AO
A
-
b
ased
MPPT
in
tr
ac
k
in
g
th
e
GM
PP
u
n
d
er
d
i
f
f
er
en
t
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
r
esu
lts
s
h
o
w
th
at
AOA
r
ap
id
l
y
co
n
v
er
g
es
to
th
e
o
p
tim
al
p
o
wer
p
o
in
t
with
in
th
e
f
ir
s
t
2
0
–
3
0
iter
atio
n
s
,
d
em
o
n
s
tr
atin
g
its
ef
f
icien
c
y
in
p
o
wer
tr
ac
k
in
g
.
T
h
e
tr
ac
k
in
g
p
r
o
ce
s
s
f
o
llo
ws
an
ex
p
o
n
e
n
tial
tr
en
d
,
wh
er
e
p
o
wer
o
u
tp
u
t
i
n
c
r
ea
s
es
s
h
ar
p
l
y
at
th
e
b
eg
in
n
in
g
an
d
s
tab
ilizes
as
it
r
ea
ch
es
th
e
GM
PP
.
T
h
is
r
ap
id
co
n
v
er
g
e
n
ce
is
a
cr
u
cial
ad
v
an
tag
e,
as
it
m
in
im
izes
en
er
g
y
lo
s
s
es a
n
d
im
p
r
o
v
es th
e
r
e
al
-
tim
e
ap
p
licab
ilit
y
o
f
th
e
alg
o
r
ith
m
.
Ad
d
itio
n
ally
,
t
h
e
f
ig
u
r
e
h
ig
h
l
ig
h
ts
th
at
AOA
e
x
h
i
b
its
m
in
i
m
al
o
s
cillatio
n
s
o
n
ce
it
r
ea
c
h
es
s
tead
y
-
s
tate
o
p
er
atio
n
.
Un
lik
e
tr
a
d
itio
n
al
MPPT
m
eth
o
d
s
s
u
c
h
a
s
P&
O
o
r
PS
O,
wh
ich
o
f
ten
s
u
f
f
er
f
r
o
m
s
lo
w
tr
ac
k
in
g
o
r
p
r
em
at
u
r
e
co
n
v
er
g
en
ce
,
AOA
ef
f
icien
tly
b
alan
ce
s
ex
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
,
en
s
u
r
i
n
g
s
tab
le
an
d
r
eliab
le
p
o
wer
o
u
tp
u
t.
T
h
e
r
esu
lts
in
d
icate
th
at
A
OA
-
b
ased
MPPT
co
n
v
er
g
es
3
0
%
f
aster
th
an
co
n
v
en
tio
n
al
tech
n
iq
u
es,
r
ed
u
cin
g
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
an
d
im
p
r
o
v
in
g
p
o
wer
ef
f
icien
cy
.
Fu
r
th
er
m
o
r
e
,
th
e
im
p
ac
t
o
f
p
a
r
tial
s
h
ad
in
g
o
n
p
o
wer
tr
ac
k
in
g
is
ev
id
en
t
in
th
e
r
esu
lts
.
T
h
e
u
n
if
o
r
m
s
h
ad
in
g
s
ce
n
ar
i
o
ac
h
iev
es
th
e
h
ig
h
est
f
in
al
p
o
wer
(
≈
9
9
W
)
,
f
o
llo
wed
b
y
th
e
h
alf
s
h
ad
in
g
s
ce
n
ar
io
(
≈
9
8
W
)
an
d
th
e
o
n
e
-
t
h
ir
d
s
h
ad
in
g
s
ce
n
ar
io
(
≈
9
5
W
)
.
Desp
ite
v
ar
y
in
g
s
h
ad
in
g
lev
els,
AOA
s
u
cc
ess
f
u
lly
ad
ap
ts
to
d
if
f
er
en
t c
o
n
d
itio
n
s
a
n
d
o
p
tim
ally
tr
ac
k
s
th
e
GM
PP
with
m
in
im
al
p
o
wer
f
lu
ctu
atio
n
s
.
Fig
u
r
e
6
.
T
h
e
tr
ac
k
in
g
p
r
o
ce
s
s
o
f
AOA
im
p
lem
en
ted
in
MPPT
wh
ich
m
o
d
eled
in
th
r
ee
in
s
o
latio
n
co
n
d
itio
n
s
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.
3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
9
2
3
-
1
9
3
7
1932
3.
3
.
AO
A
-
M
P
P
T
perf
o
rma
nce
t
est
Fro
m
test
in
g
f
o
r
th
e
t
h
r
ee
in
s
o
latio
n
co
n
d
it
io
n
s
,
th
e
two
al
g
o
r
ith
m
s
wer
e
c
o
m
p
ar
e
d
b
y
t
ak
in
g
in
t
o
ac
co
u
n
t
s
ev
er
al
p
ar
a
m
eter
s
an
d
r
ep
r
esen
tin
g
ea
c
h
co
n
t
r
o
l
al
g
o
r
ith
m
’
s
p
e
r
f
o
r
m
an
ce
.
T
ab
le
1
th
e
p
er
f
o
r
m
an
ce
o
f
PS
O
an
d
AOA
f
o
r
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
with
STC,
m
ed
iu
m
,
an
d
h
alf
u
n
if
o
r
m
in
s
o
latio
n
.
T
h
e
r
esu
lt
o
f
th
is
r
esear
ch
also
co
m
p
ar
ed
to
th
e
r
esu
lt
in
Me
g
a
n
to
r
o
et
a
l.
[
2
3
]
h
av
e
d
o
n
e
f
o
r
t
h
e
MPPT
tech
n
iq
u
e
f
o
r
th
e
s
am
e
m
o
d
el
s
im
u
latio
n
u
s
ed
GA,
FA,
an
d
f
r
u
itfly
o
p
t
im
izatio
n
alg
o
r
ith
m
(
FF
A)
.
Un
d
er
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
,
MPPT
-
PS
O
ca
n
r
ea
c
h
a
m
ax
im
u
m
p
o
we
r
o
f
4
2
8
W
,
clo
s
e
to
th
e
p
ea
k
p
o
in
t
o
f
MPP,
with
a
tr
ac
k
in
g
tim
e
o
f
0
.
0
0
2
3
s
ec
o
n
d
s
.
Me
an
wh
ile,
MPPT
-
AOA
ca
n
r
ea
ch
m
o
r
e
p
o
wer
th
a
n
MPPT
-
PS
O
o
f
4
6
4
W
with
a
tr
ac
k
in
g
tim
e
o
f
0
.
0
7
8
6
s
ec
o
n
d
s
.
T
h
e
r
esu
lts
s
h
o
w
cu
r
r
en
t
7
.
7
%
d
if
f
er
en
ce
o
v
er
th
e
p
o
w
er
p
r
o
d
u
ce
d
b
y
MPPT
-
PS
O
an
d
MPPT
-
AOA.
T
h
en
,
in
h
alf
-
s
h
ad
in
g
in
s
o
latio
n
co
n
d
itio
n
s
,
MPPT
-
PS
O
ca
n
r
ea
ch
a
m
a
x
im
u
m
p
o
wer
o
f
3
3
0
W
with
a
t
r
ac
k
in
g
tim
e
o
f
0
.
0
0
4
5
s
ec
o
n
d
s
.
Me
an
wh
ile,
MPPT
-
AOA
ca
n
s
till
ac
h
iev
e
m
o
r
e
p
o
wer
th
a
n
MPPT
-
PS
O
o
f
3
5
3
W
with
a
tr
ac
k
in
g
t
im
e
o
f
0
.
0
8
4
0
s
ec
o
n
d
s
.
T
h
e
r
esu
lts
s
h
o
w
ar
o
u
n
d
a
6
.
5
4
%
d
if
f
e
r
en
ce
b
etwe
en
th
e
p
o
wer
p
r
o
d
u
c
ed
b
y
MPPT
-
PS
O
an
d
MPPT
-
AOA.
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
r
esu
lts
b
etwe
en
AOA
an
d
o
th
er
E
As f
o
r
MPPT
O
p
t
i
mi
z
a
t
i
o
n
a
l
g
o
r
i
t
h
m
U
n
i
f
o
r
m
i
n
s
o
l
a
t
i
o
n
H
a
l
f
-
sh
a
d
e
d
i
n
so
l
a
t
i
o
n
O
n
e
-
t
h
i
r
d
s
h
a
d
e
d
i
n
so
l
a
t
i
o
n
P
mp
p
(
W
)
Ti
me
(
s)
P
mp
p
(
W
)
Ti
me
(
s)
P
mp
p
(
W
)
Ti
me
(
s)
PSO
4
2
8
0
.
0
0
2
3
3
3
0
0
.
0
0
4
5
2
3
1
0
.
0
0
4
7
A
OA
4
6
4
0
.
0
7
8
6
3
5
3
0
.
0
8
4
0
2
4
2
0
.
0
8
9
4
GA
4
6
3
0
.
1
2
8
0
1
5
7
0
.
1
2
2
4
2
4
1
0
.
1
1
9
9
FA
4
6
3
0
.
0
0
8
6
1
5
9
0
.
0
1
0
0
2
4
1
0
.
0
0
8
6
FFO
4
1
1
0
.
0
0
6
1
1
5
9
0
.
0
0
8
4
2
4
1
0
.
0
0
5
7
Fu
r
th
er
m
o
r
e
,
u
n
d
er
o
n
e
-
th
ir
d
p
ar
tial
s
h
ad
in
g
,
MPPT
-
PS
O
ca
n
r
ea
ch
a
m
ax
im
u
m
p
o
wer
o
f
2
3
1
W
with
a
tr
ac
k
in
g
tim
e
o
f
0
.
0
0
4
7
s
ec
o
n
d
s
.
Me
an
wh
ile,
MPPT
-
AOA
ca
n
s
till
ac
h
iev
e
m
o
r
e
p
o
wer
th
an
MPPT
-
PS
O,
2
4
2
W
,
with
a
tr
ac
k
in
g
tim
e
o
f
0
.
0
8
9
4
s
ec
o
n
d
s
.
T
h
is
is
b
ec
au
s
e
th
e
s
im
u
latio
n
is
ca
r
r
ied
o
u
t
with
s
ev
er
al
in
p
u
t
in
s
o
latio
n
v
alu
es
s
tar
tin
g
f
r
o
m
u
n
if
o
r
m
i
n
s
o
latio
n
lev
el,
h
alf
p
ar
tial
s
h
a
d
in
g
in
s
o
latio
n
,
an
d
o
n
e
-
th
ir
d
p
a
r
tial
s
h
ad
in
g
in
s
o
latio
n
.
T
h
ese
a
f
f
ec
t
th
e
o
u
t
p
u
t
v
o
l
tag
e
an
d
cu
r
r
en
t
p
r
o
d
u
ce
d
a
n
d
AOA’
s
ab
ilit
y
to
f
in
d
th
e
o
p
tim
al
p
o
i
n
t
with
s
e
v
er
al
p
a
r
am
eter
s
th
at
a
r
e
s
p
ec
if
ically
in
th
e
ex
p
l
o
r
atio
n
s
tag
e
an
d
ex
p
lo
itatio
n
.
Nex
t,
th
e
p
o
wer
ef
f
icien
cy
r
esu
ltin
g
f
r
o
m
MPPT
-
PS
O
an
d
MPPT
-
AOA
is
ca
lcu
lated
u
s
in
g
th
e
eq
u
atio
n
.
=
×
100
(1
3
)
is
th
e
p
o
wer
th
e
alg
o
r
ith
m
t
r
ac
k
s
wh
ile
is
th
e
ac
tu
al
o
u
t
p
u
t
p
o
wer
;
f
r
o
m
th
e
ca
lcu
lati
o
n
r
esu
lts
,
th
e
av
er
ag
e
p
o
wer
ef
f
icien
cy
o
f
PS
O
is
9
3
.
4
%
wi
th
an
a
v
er
ag
e
tr
ac
k
in
g
tim
e
o
f
0
.
0
0
3
8
s
ec
o
n
d
s
,
wh
ich
is
s
lig
h
tly
lo
n
g
er
th
an
PS
O.
S
o
,
th
e
MPPT
-
AOA
r
e
s
u
lts
ca
n
p
r
o
d
u
ce
m
ax
im
u
m
p
o
wer
co
n
s
is
ten
tly
in
all
in
s
o
latio
n
co
n
d
itio
n
s
co
m
p
ar
ed
to
PS
O.
Ho
wev
er
,
it
will
also
r
eq
u
ir
e
a
s
lig
h
tly
lo
n
g
er
tr
ac
k
in
g
tim
e
th
a
n
PS
O.
A
co
m
p
ar
is
o
n
b
etwe
en
MPPT
-
PS
O
an
d
MPPT
-
AOA
is
ca
r
r
ied
o
u
t
b
ased
o
n
s
tan
d
ar
d
MPP
o
r
Vm
p
p
v
o
ltag
e
v
alu
es with
Vp
s
o
a
n
d
Vao
a
o
b
tain
ed
f
r
o
m
ea
ch
alg
o
r
ith
m
f
o
r
ea
ch
ty
p
e
o
f
in
s
o
latio
n
co
n
d
itio
n
.
Fro
m
T
ab
le
2
,
th
e
s
tan
d
a
r
d
V
m
p
p
er
r
o
r
with
Vp
s
o
is
k
n
o
w
n
.
Un
d
er
u
n
if
o
r
m
in
s
o
latio
n
c
o
n
d
itio
n
s
,
Vm
p
p
with
Vp
s
o
p
r
o
d
u
ce
s
a
n
er
r
o
r
v
alu
e
o
f
7
.
7
1
%.
T
h
en
,
th
e
h
alf
-
s
h
a
d
in
g
in
s
o
latio
n
c
o
n
d
itio
n
p
r
o
d
u
ce
s
an
er
r
o
r
v
alu
e
o
f
6
.
5
7
%.
Mo
r
eo
v
er
,
u
n
d
er
in
s
o
latio
n
co
n
d
itio
n
s
,
o
n
e
-
th
ir
d
o
f
th
e
p
ar
tial
s
h
ad
in
g
p
r
o
d
u
ce
s
an
er
r
o
r
v
alu
e
o
f
4
.
4
7
%.
W
h
ile
th
e
s
tan
d
ar
d
Vm
p
p
er
r
o
r
with
Vao
a
u
n
d
er
u
n
if
o
r
m
in
s
o
latio
n
co
n
d
itio
n
s
p
r
o
d
u
ce
s
an
er
r
o
r
v
alu
e
o
f
8
.
3
5
%,
th
en
u
n
d
er
h
alf
p
ar
tial
s
h
ad
in
g
in
s
o
latio
n
co
n
d
itio
n
s
,
it
p
r
o
d
u
ce
s
an
e
r
r
o
r
v
alu
e
o
f
7
.
0
4
%,
an
d
th
ir
d
p
ar
tial
s
h
ad
in
g
i
n
s
o
latio
n
p
r
o
d
u
c
es
an
er
r
o
r
v
alu
e
o
f
4
.
6
8
%.
So
,
f
r
o
m
th
e
o
v
er
all
er
r
o
r
v
al
u
e
o
f
Vm
p
p
with
Vp
s
o
,
an
av
er
ag
e
e
r
r
o
r
o
f
6
.
2
5
%
is
o
b
tain
ed
.
W
h
ile
th
e
er
r
o
r
v
alu
e
o
f
Vm
p
p
with
Vao
a
is
6
.
6
9
%.
T
h
is
ca
n
b
e
d
u
e
to
th
e
co
m
p
lex
ity
o
f
th
e
p
a
r
am
eter
s
in
th
e
alg
o
r
ith
m
wh
e
r
e
AOA
h
as
a
m
o
r
e
co
m
p
lex
al
g
o
r
ith
m
s
tr
u
ctu
r
e
th
an
PS
O,
s
o
th
is
ca
n
ca
u
s
e
a
h
ig
h
e
r
lev
el
o
f
s
en
s
itiv
ity
to
v
a
r
iatio
n
s
in
p
ar
am
eter
s
an
d
o
p
er
atin
g
co
n
d
itio
n
s
s
u
ch
as
u
n
if
o
r
m
in
s
o
la
tio
n
co
n
d
itio
n
s
,
h
alf
-
s
h
ad
e
d
a
n
d
o
n
e
-
th
ir
d
p
ar
tial
in
s
o
latio
n
.
T
ab
le
2
.
T
r
ac
k
in
g
e
r
r
o
r
an
aly
s
is
b
etwe
en
MPPT
alg
o
r
ith
m
s
I
n
so
l
a
t
i
o
n
c
o
n
d
i
t
i
o
n
Er
r
o
r
V
p
s
o
(
%)
Er
r
o
r
V
a
o
a
(
%)
U
n
i
f
o
r
m
7
.
7
1
8
.
3
5
H
a
l
f
-
p
a
r
t
i
a
l
s
h
a
d
e
d
6
.
5
7
7
.
0
4
O
n
e
-
t
h
i
r
d
p
a
r
t
i
a
l
s
h
a
d
e
d
4
.
4
7
4
.
6
8
Evaluation Warning : The document was created with Spire.PDF for Python.