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n
t
l
y
n
o
n
l
i
n
e
a
r
a
n
d
h
i
g
h
l
y
r
e
l
i
a
n
t
o
n
t
e
m
p
e
r
a
t
u
r
e
a
n
d
s
o
l
a
r
i
r
r
a
d
i
a
n
c
e
,
c
r
e
at
i
n
g
a
c
o
m
p
le
x
r
e
l
a
t
i
o
n
s
h
i
p
b
e
t
w
e
e
n
v
o
lta
g
e
a
n
d
p
o
w
e
r
g
e
n
e
r
a
t
i
o
n
[
4
]
.
T
o
a
d
d
r
e
s
s
t
h
is
c
o
m
p
l
e
x
i
t
y
a
n
d
e
n
s
u
r
e
t
h
a
t
PV
s
y
s
t
e
m
s
o
p
e
r
a
t
e
at
t
h
e
i
r
m
a
x
i
m
u
m
p
o
t
e
n
t
i
a
l
,
t
h
e
i
m
p
l
e
m
e
n
t
a
t
i
o
n
o
f
e
f
f
i
c
ie
n
t
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
in
g
(
M
P
P
T
)
a
l
g
o
r
i
t
h
m
s
is
n
e
ce
s
s
a
r
y
[
5
]
.
M
PP
T
al
g
o
r
i
t
h
m
s
p
l
a
y
a
k
e
y
r
o
le
in
a
c
c
u
r
a
t
e
l
y
i
d
e
n
t
i
f
y
i
n
g
a
n
d
m
ai
n
t
a
i
n
i
n
g
t
h
e
MP
P
,
t
h
e
r
e
b
y
b
o
o
s
t
i
n
g
t
h
e
o
v
e
r
a
l
l
e
f
f
i
c
ie
n
c
y
,
e
f
f
e
c
t
i
v
e
n
ess
,
a
n
d
s
t
a
b
il
i
t
y
o
f
P
V
s
y
s
t
e
m
s
.
B
y
e
n
s
u
r
i
n
g
o
p
t
i
m
al
p
o
w
e
r
e
x
t
r
a
c
ti
o
n
,
t
h
e
s
e
a
l
g
o
r
i
t
h
m
s
h
el
p
h
a
r
n
es
s
t
h
e
f
u
ll
p
o
t
e
n
ti
al
o
f
s
o
l
a
r
e
n
e
r
g
y
,
m
a
k
i
n
g
P
V
s
y
s
t
e
m
s
m
o
r
e
r
e
li
a
b
l
e
s
o
u
r
c
e
o
f
c
le
a
n
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
[
6
]
.
MPPT
m
eth
o
d
s
ar
e
ess
en
tial
f
o
r
m
ax
im
izin
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
PV
s
y
s
tem
s
,
p
ar
ticu
lar
ly
in
lar
g
e
-
s
ca
le
s
o
lar
en
er
g
y
p
r
o
jects
wh
er
e
s
y
s
tem
ef
f
icien
cy
d
ir
ec
tly
im
p
ac
ts
en
er
g
y
p
r
o
d
u
c
tio
n
an
d
ec
o
n
o
m
ic
f
ea
s
ib
ilit
y
[
7
]
.
B
y
p
r
ec
is
ely
tr
ac
k
in
g
th
e
MPP,
MPPT
alg
o
r
ith
m
s
n
o
t
o
n
ly
o
p
tim
ize
p
o
wer
o
u
tp
u
t
b
u
t
also
co
n
tr
ib
u
te
t
o
r
ed
u
cin
g
s
y
s
tem
co
s
ts
,
an
im
p
o
r
ta
n
t
co
n
s
id
er
a
tio
n
in
th
e
d
ep
lo
y
m
en
t
o
f
lar
g
e
PV
ar
r
ay
s
[
1
]
.
A
wid
e
ar
r
ay
o
f
MPPT
tech
n
iq
u
es,
r
an
g
in
g
f
r
o
m
d
i
r
ec
t
to
in
d
ir
ec
t
m
eth
o
d
s
,
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
th
e
liter
atu
r
e,
ea
ch
with
its
in
h
er
en
t
ad
v
an
tag
es
an
d
lim
i
tatio
n
s
.
T
h
is
p
ap
er
in
v
esti
g
ates
th
e
p
r
ac
tical
co
n
s
id
er
atio
n
s
o
f
th
ese
tech
n
i
q
u
es,
ad
d
r
ess
in
g
f
ac
to
r
s
s
u
ch
as
s
y
s
tem
co
m
p
lex
ity
,
co
m
p
u
tatio
n
al
d
em
a
n
d
s
,
an
d
s
en
s
itiv
ity
to
e
n
v
ir
o
n
m
en
tal
ch
an
g
es.
I
t
aim
s
to
i
d
en
tif
y
th
e
m
o
s
t
s
u
itab
le
MPPT
ap
p
r
o
ac
h
f
o
r
s
p
ec
if
ic
ap
p
licatio
n
s
an
d
o
p
er
atio
n
al
s
ce
n
ar
io
s
[
6
]
.
W
h
ile
co
n
v
en
tio
n
al
MPPT
tech
n
iq
u
es,
s
u
ch
as
Per
tu
r
b
an
d
Ob
s
er
v
e,
h
ill
clim
b
in
g
,
an
d
I
n
cr
em
en
tal
C
o
n
d
u
ctan
ce
,
ar
e
r
elativ
ely
ea
s
y
to
im
p
lem
en
t
an
d
r
eq
u
ir
e
m
i
n
im
al
h
ar
d
war
e,
th
ey
f
ac
e
s
ig
n
if
ican
t lim
itatio
n
s
in
lo
ca
tin
g
a
g
lo
b
al
MPP
u
n
d
er
p
ar
tial sh
ad
in
g
(
PS
)
co
n
d
itio
n
s
[
8
]
.
T
h
ese
tech
n
iq
u
es
o
f
ten
s
tr
u
g
g
le
to
n
av
ig
ate
m
u
ltip
le
lo
ca
l
m
ax
im
a
in
th
e
PV
cu
r
v
e,
a
c
o
m
m
o
n
o
cc
u
r
r
en
ce
in
r
ea
l
-
wo
r
ld
PV
s
y
s
tem
s
s
u
b
jecte
d
to
s
h
ad
in
g
f
r
o
m
o
b
jects
lik
e
tr
ee
s
,
b
u
ild
in
g
s
,
o
r
clo
u
d
s
.
S
u
ch
p
ar
tial
s
h
ad
i
n
g
ca
n
lead
to
s
u
b
s
tan
tial
f
lu
ctu
atio
n
s
in
p
o
wer
o
u
tp
u
t,
th
er
eb
y
r
ed
u
cin
g
th
e
s
y
s
tem
’
s
o
v
er
a
ll
p
er
f
o
r
m
an
ce
[
9
]
.
T
o
o
v
er
c
o
m
e
th
ese
ch
allen
g
e
s
,
ad
v
an
ce
d
tech
n
iq
u
es
lev
er
ag
in
g
ar
tific
ial
in
tellig
en
ce
(
AI
)
,
s
u
ch
as
n
eu
r
al
n
etwo
r
k
s
(
NNs),
g
e
n
etic
alg
o
r
ith
m
s
(
GAs),
an
d
f
u
zz
y
lo
g
i
c
(
FL)
,
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
.
Ho
wev
er
,
th
ese
AI
-
b
ased
m
eth
o
d
s
o
f
ten
d
em
an
d
h
ig
h
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
,
co
m
p
lex
im
p
lem
en
tatio
n
,
an
d
ex
ten
s
iv
e
tu
n
in
g
,
wh
ich
m
ay
n
o
t b
e
f
ea
s
ib
le
f
o
r
all
ap
p
licatio
n
s
[
1
0
]
.
I
n
r
esp
o
n
s
e
to
th
ese
ch
allen
g
e
s
,
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
lik
e
PS
O,
g
r
ey
wo
lf
o
p
tim
izatio
n
(
GW
O)
,
an
d
s
im
u
lated
an
n
ea
lin
g
(
SA)
h
av
e
g
ain
ed
p
o
p
u
lar
ity
as
v
ia
b
le
alter
n
ativ
es.
T
h
ese
tech
n
i
q
u
es
ar
e
k
n
o
w
n
f
o
r
th
eir
s
im
p
licity
,
ef
f
icien
cy
,
an
d
ab
ilit
y
to
s
o
lv
e
co
m
p
lex
o
p
tim
izatio
n
p
r
o
b
lem
s
with
o
u
t
ex
ten
s
iv
e
co
m
p
u
tatio
n
al
p
o
wer
[
1
1
]
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
th
e
ap
p
licatio
n
o
f
PS
O
to
MP
PT,
p
ar
ticu
lar
ly
in
en
v
ir
o
n
m
en
ts
with
v
ar
y
i
n
g
ir
r
ad
ian
ce
co
n
d
itio
n
s
,
an
d
ex
p
l
o
r
es
th
e
ef
f
ec
tiv
en
ess
o
f
r
ein
itializatio
n
s
tr
ateg
ies
to
en
h
an
ce
th
e
alg
o
r
ith
m
'
s
p
er
f
o
r
m
an
ce
an
d
r
o
b
u
s
tn
ess
u
n
d
er
ch
allen
g
in
g
o
p
er
atin
g
co
n
d
it
io
n
s
[
1
2
]
.
PS
O
is
a
p
o
wer
f
u
l
s
to
ch
asti
c
o
p
tim
iza
tio
n
ap
p
r
o
ac
h
in
s
p
ir
e
d
b
y
t
h
e
b
e
h
av
io
r
o
f
s
war
m
s
,
wh
er
e
m
u
ltip
le
ag
en
ts
(
p
ar
ticles)
wo
r
k
co
llab
o
r
ativ
el
y
to
ex
p
lo
r
e
a
s
o
lu
tio
n
s
p
ac
e
[
1
3
]
.
E
ac
h
p
ar
ticle
ad
ju
s
ts
its
p
o
s
itio
n
ac
co
r
d
i
n
g
to
its
o
wn
b
est
-
f
o
u
n
d
s
o
lu
tio
n
(
Pb
est)
an
d
th
e
b
est
g
lo
b
al
s
o
lu
tio
n
(
Gb
est)
d
eter
m
in
e
d
b
y
th
e
s
war
m
.
T
h
is
co
o
p
er
ativ
e
m
ec
h
a
n
is
m
h
elp
s
g
u
id
e
th
e
s
ea
r
ch
p
r
o
ce
s
s
,
b
alan
cin
g
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
to
a
v
o
id
p
r
em
atu
r
e
c
o
n
v
er
g
en
ce
to
l
o
c
al
o
p
tim
a
[
3
]
.
T
h
e
s
tu
d
y
le
v
e
r
ag
es
PS
O
to
o
p
tim
ize
PV
s
y
s
tem
p
er
f
o
r
m
a
n
ce
u
n
d
er
v
a
r
io
u
s
ir
r
ad
ian
ce
co
n
d
itio
n
s
,
in
clu
d
in
g
s
tan
d
ar
d
,
s
tep
-
ch
an
g
e,
an
d
p
ar
tial
s
h
ad
in
g
s
ce
n
ar
io
s
,
en
s
u
r
in
g
ad
ap
tab
ilit
y
to
r
ea
l
-
wo
r
ld
c
o
n
d
itio
n
s
.
C
o
m
p
ar
e
d
to
tr
ad
itio
n
al
MPPT
m
eth
o
d
s
,
P
SO
s
h
o
ws
b
etter
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
co
n
v
er
g
en
ce
r
ate,
s
tab
ilit
y
,
an
d
o
p
tim
al
p
o
wer
ex
tr
ac
tio
n
,
m
a
k
in
g
it
a
m
o
r
e
ef
f
ec
tiv
e
ap
p
r
o
ac
h
f
o
r
m
ax
im
izin
g
en
er
g
y
o
u
t
p
u
t in
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
[
1
4
]
.
Desp
ite
th
e
ad
v
an
tag
es,
th
e
s
tan
d
ar
d
PS
O
alg
o
r
ith
m
h
as
s
ev
er
al
lim
itatio
n
s
wh
en
a
p
p
lied
to
MPPT.
First,
it
o
f
ten
s
u
f
f
er
s
f
r
o
m
p
r
e
m
atu
r
e
co
n
v
er
g
e
n
ce
,
wh
er
e
p
ar
ticles
g
et
tr
ap
p
ed
in
lo
ca
l
o
p
tim
a
u
n
d
e
r
p
ar
tial
s
h
ad
in
g
o
r
r
ap
id
l
y
ch
an
g
in
g
ir
r
ad
ian
ce
.
Seco
n
d
,
its
co
n
v
e
r
g
e
n
ce
s
p
ee
d
is
n
o
t
alwa
y
s
s
u
f
f
ic
ien
t
d
u
r
in
g
s
u
d
d
e
n
s
tep
ch
an
g
es
in
s
u
n
lig
h
t,
d
ela
y
in
g
th
e
s
y
s
tem
’
s
ab
ilit
y
to
r
ea
ch
th
e
t
r
u
e
m
ax
im
u
m
p
o
w
er
p
o
i
n
t.
T
h
i
r
d
,
t
h
e
s
tan
d
ar
d
v
el
o
city
an
d
p
o
s
itio
n
u
p
d
ate
eq
u
atio
n
s
lack
a
d
ap
ta
b
ilit
y
,
r
ed
u
cin
g
r
o
b
u
s
tn
ess
u
n
d
er
h
i
g
h
ly
d
y
n
am
ic
co
n
d
itio
n
s
.
T
h
ese
s
h
o
r
tc
o
m
i
n
g
s
lim
it
th
e
p
r
ac
tical
ef
f
e
ctiv
en
ess
o
f
s
tan
d
ar
d
PS
O
in
r
e
al
-
wo
r
ld
PV
en
v
ir
o
n
m
en
ts
[
1
5
]
.
T
o
ad
d
r
ess
th
ese
g
ap
s
,
th
is
s
tu
d
y
in
tr
o
d
u
ce
s
an
AI
PS
O
th
at
in
teg
r
ates
a
r
ein
itializatio
n
s
tr
ateg
y
an
d
m
o
d
if
ie
d
v
elo
cit
y
,
p
o
s
itio
n
u
p
d
ates,
th
er
eb
y
en
h
an
cin
g
g
lo
b
al
s
ea
r
ch
ca
p
a
b
ilit
y
,
co
n
v
er
g
en
ce
s
p
ee
d
,
an
d
t
r
ac
k
in
g
r
eliab
ilit
y
.
R
ec
o
g
n
izin
g
th
e
im
p
o
r
tan
ce
o
f
en
h
a
n
cin
g
PS
O
-
b
ased
MPPT
alg
o
r
ith
m
s
,
th
is
p
ap
er
p
r
o
p
o
s
es
an
ad
ap
tiv
e
in
tellig
en
ce
-
b
ased
PS
O
(
AI
PS
O)
alg
o
r
ith
m
to
f
u
r
t
h
er
im
p
r
o
v
e
co
n
v
er
g
en
ce
r
ate
s
,
tr
ac
k
in
g
ac
cu
r
ac
y
,
an
d
o
v
er
all
s
y
s
tem
ef
f
icien
c
y
.
T
h
e
p
r
o
p
o
s
ed
AI
PS
O
in
tr
o
d
u
ce
s
two
k
ey
m
o
d
if
icatio
n
s
:
a
r
ein
itializatio
n
s
tr
ateg
y
to
ef
f
ec
tiv
el
y
h
an
d
le
s
tep
-
ch
an
g
e
i
r
r
ad
ian
ce
co
n
d
itio
n
s
an
d
im
p
r
o
v
e
d
v
elo
city
an
d
p
o
s
itio
n
u
p
d
ate
eq
u
atio
n
s
[
1
5
]
.
T
h
ese
m
o
d
if
ic
atio
n
s
en
h
an
ce
th
e
alg
o
r
ith
m
’
s
co
n
v
er
g
e
n
ce
b
eh
a
v
io
r
an
d
a
cc
u
r
ac
y
in
tr
ac
k
in
g
th
e
MPP
[
1
6
]
.
Ad
d
itio
n
ally
,
th
e
in
clu
s
io
n
o
f
an
im
p
r
o
v
is
atio
n
f
ac
to
r
in
th
e
v
elo
city
eq
u
atio
n
im
p
r
o
v
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
a
p
tive
in
tellig
en
t P
S
O
-
B
a
s
ed
MPP
T tec
h
n
iq
u
e
fo
r
P
V
s
ystems
u
n
d
er
…
(
Mu
h
a
mma
d
G
u
l E
.
I
s
la
m
)
2843
tr
ac
k
in
g
s
p
ee
d
an
d
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
a
n
ce
[
1
7
]
.
T
h
e
r
ein
itializatio
n
s
tr
ateg
y
,
in
p
ar
ticu
lar
,
p
r
o
v
es
v
alu
ab
le
in
ad
d
r
ess
in
g
s
u
d
d
e
n
ch
an
g
es
in
ir
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a
d
ian
ce
,
en
s
u
r
in
g
m
o
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r
eliab
le
an
d
ef
f
icie
n
t
o
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er
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u
n
d
er
d
y
n
am
ic
e
n
v
ir
o
n
m
en
tal
co
n
d
it
io
n
s
[
1
8
]
,
[
1
9
]
.
T
h
i
s
s
t
u
d
y
f
o
c
u
s
es
o
n
t
h
e
k
e
y
c
o
n
t
r
i
b
u
t
i
o
n
s
:
i
)
A
n
a
d
a
p
t
i
v
e
PS
O
u
p
d
a
t
e
w
i
t
h
C
3
a
n
d
a
r
e
i
n
it
i
a
l
iz
a
t
i
o
n
t
r
i
g
g
e
r
;
i
i
)
A
b
u
c
k
–
b
o
o
s
t
d
e
s
i
g
n
a
n
d
p
a
r
a
m
e
t
e
r
bounds
l
i
n
k
e
d
t
o
d
u
t
y
r
a
t
i
o
c
o
n
t
r
o
l
;
i
i
i
)
E
v
a
l
u
a
t
i
o
n
u
n
d
e
r
u
n
i
f
o
r
m
,
s
t
e
p
c
h
a
n
g
e
,
a
n
d
PS
C
w
it
h
c
o
n
v
e
r
g
e
n
c
e
t
i
m
e
,
e
f
f
ic
i
e
n
c
y
,
a
n
d
o
s
c
il
l
a
ti
o
n
m
e
t
r
i
cs
;
a
n
d
i
v
)
p
r
a
c
ti
c
a
l
l
i
m
i
ts
a
n
d
d
e
p
l
o
y
m
e
n
t
g
u
i
d
an
c
e
.
T
h
e
r
e
m
a
i
n
i
n
g
s
e
ct
i
o
n
s
a
r
e
s
t
r
u
c
t
u
r
e
d
as
f
o
l
l
o
ws
:
S
ec
t
i
o
n
2
p
r
e
s
e
n
ts
t
h
e
m
e
t
h
o
d
o
l
o
g
y
e
m
p
l
o
y
e
d
i
n
t
h
e
s
t
u
d
y
,
i
n
c
l
u
d
i
n
g
a
c
o
m
p
r
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e
n
s
i
v
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o
v
e
r
v
i
e
w
o
f
t
h
e
s
t
a
n
d
a
r
d
P
S
O
al
g
o
r
i
t
h
m
.
S
e
c
t
i
o
n
3
p
r
es
e
n
ts
t
h
e
r
e
s
u
l
t
s
an
d
p
e
r
f
o
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m
a
n
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e
e
v
a
l
u
a
t
i
o
n
o
f
A
I
P
SO
,
c
o
m
p
a
r
i
n
g
it
wi
t
h
o
t
h
er
M
P
PT
t
e
c
h
n
i
q
u
es
.
F
i
n
a
l
l
y
,
S
e
c
ti
o
n
4
p
r
o
v
i
d
e
s
c
o
n
c
l
u
s
i
o
n
s
a
n
d
f
u
t
u
r
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c
o
m
m
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n
d
a
t
i
o
n
s
i
n
t
h
i
s
d
o
m
a
i
n
.
2.
M
E
T
H
O
D
O
L
O
G
Y
T
h
e
o
v
e
r
a
l
l
m
e
t
h
o
d
o
l
o
g
y
u
s
e
d
i
n
t
h
is
r
es
e
a
r
c
h
i
s
i
ll
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
1
.
T
h
e
w
o
r
k
f
l
o
w
i
n
c
l
u
d
e
s
a
s
e
r
i
es
o
f
s
y
s
te
m
a
t
i
c
s
t
e
p
s
d
e
s
i
g
n
e
d
to
d
e
v
e
l
o
p
a
n
d
v
a
l
i
d
a
te
a
n
e
n
h
a
n
c
e
d
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(
MP
PT
)
s
c
h
e
m
e
u
t
il
i
z
i
n
g
t
h
e
A
I
PS
O
alg
o
r
i
t
h
m
f
o
r
P
V
s
y
s
t
e
m
s
.
E
a
c
h
p
h
a
s
e
o
f
t
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r
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s
ea
r
c
h
i
s
d
es
c
r
i
b
e
d
a
s
f
o
l
l
o
ws
.
Fig
u
r
e
1
.
G
en
e
r
al
wo
r
k
f
lo
w
2
.
1
.
M
o
delin
g
o
f
P
V
m
o
du
le
Mo
d
elin
g
PV
s
y
s
tem
s
is
e
s
s
en
tial
in
f
o
r
ec
asti
n
g
th
eir
elec
tr
ical
p
er
f
o
r
m
an
ce
u
n
d
er
v
ar
io
u
s
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
s
u
ch
as
ch
an
g
es
in
tem
p
er
at
u
r
e
an
d
ir
r
ad
ia
n
ce
.
PV
s
y
s
t
em
s
ar
e
g
en
er
ally
r
ep
r
esen
ted
u
s
in
g
eq
u
iv
ale
n
t
c
ir
cu
it
m
o
d
els
th
at
ca
p
tu
r
e
th
e
elec
tr
ical
p
r
o
p
er
ties
o
f
s
o
lar
c
ells
,
in
clu
d
in
g
th
ei
r
cu
r
r
en
t
-
v
o
ltag
e
(
I
-
V
)
c
h
ar
ac
t
er
is
tics
[
2
0
]
.
T
h
e
s
e
m
o
d
e
l
s
c
a
n
b
e
e
m
p
i
r
i
c
a
l
,
b
a
s
e
d
o
n
e
x
p
e
r
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m
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n
t
a
l
d
a
t
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,
o
r
a
n
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l
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al
,
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n
g
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n
m
a
t
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m
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b
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e
b
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a
v
i
o
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e
P
V
ce
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ls
.
M
o
r
e
a
d
v
a
n
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d
m
o
d
e
l
s
t
a
k
e
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a
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n
t
f
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s
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ch
a
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p
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at
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r
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r
i
a
ti
o
n
s
,
s
h
a
d
i
n
g
,
a
n
d
s
y
s
t
e
m
i
n
e
f
f
i
c
i
en
c
i
e
s
[
2
1
]
.
P
r
ec
i
s
e
m
o
d
e
l
i
n
g
is
c
r
u
c
ia
l
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p
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m
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d
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n
,
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t
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m
a
t
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,
a
n
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-
t
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m
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e
m
p
e
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f
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r
m
a
n
c
e
i
n
p
r
a
c
t
i
c
a
l
s
et
t
i
n
g
s
[
2
2
]
.
A
f
t
e
r
r
e
v
i
e
w
i
n
g
t
h
e
l
ite
r
a
t
u
r
e
,
a
P
V
s
y
s
t
e
m
is
d
e
s
i
g
n
e
d
a
p
a
r
t
f
r
o
m
M
P
P
T
a
n
d
p
o
w
e
r
c
o
n
v
e
r
t
e
r
.
C
o
m
p
r
e
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s
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v
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i
n
f
o
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m
a
ti
o
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b
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o
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r
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V
m
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d
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l
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is
s
u
m
m
a
r
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e
d
i
n
T
a
b
l
e
1
[
1
9
]
T
ab
le
1
.
Par
am
eter
s
o
f
PV
m
o
d
u
le
P
a
r
a
me
t
e
r
s
V
a
l
u
e
P
m
ax
(W)
2
4
0
N
c
e
l
l
60
V
ope
n
c
i
r
c
u
i
t
(V)
3
7
.
1
I
s
hor
t
c
i
r
c
u
i
t
(A)
8
.
5
8
V
mp
(V)
2
9
.
7
I
mp
(A)
8
.
0
7
2
.
2
.
Desig
nin
g
a
nd
s
im
ula
t
io
n o
f
DC
-
DC
bu
ck
-
bo
o
s
t
co
n
v
er
t
er
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
d
esi
g
n
o
f
a
DC
-
DC
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
tailo
r
e
d
f
o
r
p
h
o
t
o
v
o
l
taic
(
PV)
ap
p
licatio
n
s
.
T
h
e
b
u
ck
-
b
o
o
s
t
to
p
o
lo
g
y
is
s
elec
ted
f
o
r
its
ab
ilit
y
to
o
p
er
ate
in
b
o
th
s
tep
-
u
p
an
d
s
tep
-
d
o
w
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2841
-
2
8
5
9
2844
m
o
d
es,
m
ak
i
n
g
it
h
i
g
h
ly
s
u
it
ab
le
f
o
r
PV
s
y
s
tem
s
[
2
3
]
.
T
h
is
d
u
al
-
m
o
d
e
f
u
n
ctio
n
ality
en
s
u
r
es
s
tab
le
p
o
wer
d
eliv
er
y
u
n
d
er
f
lu
ctu
atin
g
s
o
lar
ir
r
ad
ian
ce
co
n
d
itio
n
s
,
p
ar
ti
cu
lar
ly
in
s
y
s
tem
s
em
p
lo
y
in
g
MPPT
[
2
4
]
.
T
h
e
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
also
o
f
f
er
s
h
ig
h
er
ef
f
icien
cy
co
m
p
ar
e
d
to
b
u
ck
a
n
d
b
o
o
s
t
c
o
n
v
er
te
r
s
,
r
ed
u
cin
g
en
er
g
y
lo
s
s
es
an
d
en
h
an
cin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
[
2
5
]
.
T
h
e
c
o
n
v
er
ter
is
d
esig
n
ed
to
o
p
e
r
ate
in
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
ac
r
o
s
s
th
e
en
tire
in
p
u
t
r
an
g
e
t
o
m
a
in
tain
lo
w
cu
r
r
en
t
r
ip
p
le
an
d
e
n
h
an
ce
r
eliab
ilit
y
.
Fig
u
r
e
2
r
ep
r
esen
ts
th
e
s
ch
em
atic
d
iag
r
am
o
f
th
e
DC
-
DC
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
ass
o
ciate
d
with
th
e
PV
ar
r
a
y
m
o
d
u
le.
Ke
y
d
esig
n
c
o
n
s
id
er
a
tio
n
s
in
clu
d
e
th
e
s
elec
tio
n
o
f
ap
p
r
o
p
r
iate
s
witch
in
g
f
r
e
q
u
en
cy
,
in
d
u
cto
r
s
izin
g
,
an
d
co
n
tr
o
l
s
tr
ateg
y
to
o
p
tim
i
ze
ef
f
icien
cy
an
d
m
ain
tain
ac
c
ep
tab
le
v
o
ltag
e
an
d
cu
r
r
en
t
r
ip
p
le
lev
els
u
n
d
e
r
all
o
p
er
atin
g
co
n
d
itio
n
s
[
2
6
]
.
De
s
ig
n
p
ar
am
eter
s
,
as
s
u
m
m
ar
iz
ed
in
T
a
b
le
2
,
ar
e
d
eter
m
in
e
d
th
r
o
u
g
h
d
etailed
an
aly
tical
ca
lcu
latio
n
s
p
r
o
v
id
e
d
in
th
e
s
u
b
s
eq
u
en
t sectio
n
s
.
Fig
u
r
e
2
.
Sch
em
atic
o
f
DC
-
DC
b
u
ck
b
o
o
s
t c
o
n
v
e
r
ter
I
n
p
h
o
to
v
o
ltaic
(
PV)
ap
p
licatio
n
s
,
b
o
th
th
e
in
p
u
t
v
o
lt
ag
e,
V
i
an
d
o
u
t
p
u
t
v
o
ltag
e,
V
o
v
ar
y
co
n
tin
u
o
u
s
ly
,
an
d
th
e
d
u
ty
cy
cle,
D
f
lu
ctu
ates
ac
co
r
d
in
g
ly
.
As
a
r
esu
lt,
co
n
v
en
tio
n
al
s
te
ad
y
-
s
tate
eq
u
atio
n
s
ar
e
n
o
t
d
ir
ec
tly
ap
p
licab
le
f
o
r
d
esig
n
in
g
a
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
in
s
u
ch
d
y
n
am
ic
co
n
d
i
tio
n
s
[
2
7
]
.
Fo
r
th
e
d
esig
n
in
g
o
f
DC
-
DC
b
u
ck
b
o
o
s
t
co
n
v
e
r
ter
s
o
m
e
o
f
g
e
n
er
al
ass
u
m
p
tio
n
s
ar
e
d
escr
ib
ed
in
T
ab
le.
2
.
T
h
ese
ass
u
m
p
tio
n
s
ar
e
m
ad
e
wh
ile
co
n
s
id
er
in
g
r
ea
l
tim
e
b
eh
av
io
r
of
PV
m
o
d
u
les
an
d
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
.
As
th
e
ir
r
ad
ian
ce
is
not
u
n
if
o
r
m
t
h
r
o
u
g
h
o
u
t
th
e
d
ay
an
d
h
e
n
ce
th
e
p
o
wer
ex
tr
ac
tio
n
also
v
ar
i
es
ac
co
r
d
in
g
ly
.
T
h
e
s
witch
in
g
f
r
eq
u
e
n
cy
,
c
u
r
r
e
n
t
r
ip
p
le,
an
d
v
o
ltag
e
r
ip
p
le
f
ac
to
r
s
ar
e
ch
o
s
en
as
p
er
s
tan
d
ar
d
h
ar
d
war
e
s
etu
p
f
o
r
im
p
r
o
v
e
d
p
er
f
o
r
m
a
n
ce
.
T
ab
le
2
.
Gen
e
r
al
a
s
s
u
m
p
tio
n
s
f
o
r
d
esig
n
i
n
g
o
f
b
u
c
k
b
o
o
s
t c
o
n
v
er
ter
I
n
p
u
t
p
o
w
e
r
(
P
in
)
1
0
0
W
t
o
1
0
0
0
W
I
n
p
u
t
v
o
l
t
a
g
e
(
V
in
)
1
0
V
t
o
1
0
0
V
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
,
f
sw
2
5
k
H
z
M
a
x
i
m
u
m
i
n
d
u
c
t
o
r
c
u
r
r
e
n
t
r
i
p
p
l
e
,
Δi
L
4
0
%
O
u
t
p
u
t
v
o
l
t
a
g
e
r
i
p
p
l
e
,
ΔV
o
/V
o
1
5
%
i)
Step
1
: L
o
ad
r
esis
tan
ce
r
an
g
e
d
eter
m
in
atio
n
Sin
ce
th
e
o
u
tp
u
t v
o
ltag
e
is
n
o
t r
eg
u
lated
,
it v
ar
ies with
d
u
ty
cy
cle
an
d
in
p
u
t v
o
ltag
e.
T
o
estab
lis
h
th
e
b
o
u
n
d
ar
y
c
o
n
d
itio
n
s
f
o
r
p
o
we
r
d
eliv
er
y
,
we
s
tar
t w
ith
:
o
ut
=
2
⇒
=
2
out
(
1
)
Usi
n
g
th
e
b
u
ck
-
b
o
o
s
t o
u
tp
u
t
r
elatio
n
s
h
ip
:
=
−
1
−
⋅
(
2
)
Ass
u
m
in
g
p
r
ac
tical
d
u
ty
c
y
cle
lim
its
o
f
0
.
1
0
.
9
D
th
e
wo
r
s
t
-
ca
s
e
o
u
tp
u
t v
o
ltag
e:
−
90
V
≤
≤
−
11
.
1
V
(
3
)
T
h
is
r
esu
lts
in
a
r
an
g
e
o
f
lo
ad
r
esis
tan
ce
:
0
.
123
≤
≤
81
(
4
)
Fo
r
th
is
d
esig
n
,
a
f
ix
e
d
lo
a
d
o
f
1
0
Ω
is
s
elec
ted
,
wh
ich
c
o
m
f
o
r
tab
ly
lies
with
in
th
e
v
alid
o
p
er
atin
g
r
eg
i
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
a
p
tive
in
tellig
en
t P
S
O
-
B
a
s
ed
MPP
T tec
h
n
iq
u
e
fo
r
P
V
s
ystems
u
n
d
er
…
(
Mu
h
a
mma
d
G
u
l E
.
I
s
la
m
)
2845
ii)
Step
2
:
d
u
ty
c
y
cle
r
an
g
e
Usi
n
g
th
e
f
o
r
m
u
la:
=
|
|
|
|
+
(
5
)
T
h
e
r
an
g
e
o
f
d
u
ty
c
y
cle:
0
.
240
≤
≤
0
.
909
(
6
)
iii)
Step
3
:
in
d
u
cto
r
s
izin
g
T
o
en
s
u
r
e
th
e
co
n
v
er
ter
o
p
er
ates
in
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
u
n
d
er
all
co
n
d
itio
n
s
,
th
e
in
d
u
cto
r
is
s
ized
to
lim
it
th
e
r
ip
p
le
cu
r
r
e
n
t
to
4
0
%
o
f
t
h
e
av
er
a
g
e
in
p
u
t
c
u
r
r
e
n
t.
T
h
e
r
ip
p
le
cu
r
r
e
n
t
is
ca
lcu
lated
as
(
7
)
.
=
0
.
4
(
7
)
Usi
n
g
th
is
r
ip
p
le,
th
e
r
e
q
u
ir
ed
in
d
u
ctan
ce
is
g
iv
e
n
b
y
(
8
)
:
=
⋅
⋅
(
8
)
wh
er
e
D
is
th
e
d
u
t
y
c
y
cle,
V
in
is
th
e
in
p
u
t
v
o
ltag
e,
an
d
f
sw
is
th
e
s
witch
in
g
f
r
eq
u
en
cy
,
s
et
at
2
5
k
Hz.
T
h
e
in
d
u
cto
r
was
s
ized
b
ased
o
n
t
h
e
r
an
g
e
o
f
in
p
u
t
v
o
ltag
e
an
d
p
o
wer
.
Am
o
n
g
all
ca
s
es,
th
e
lo
w
p
o
wer
at
h
ig
h
v
o
ltag
e
s
ce
n
a
r
io
d
em
an
d
s
th
e
lar
g
est
in
d
u
ctan
ce
to
m
ain
tai
n
co
n
tin
u
o
u
s
cu
r
r
en
t
f
lo
w.
T
h
er
ef
o
r
e
,
to
en
s
u
r
e
r
eliab
le
C
C
M
o
p
er
atio
n
ac
r
o
s
s
all
v
o
ltag
es
a
n
d
p
o
we
r
lev
e
ls
,
an
in
d
u
cto
r
v
al
u
e
o
f
1
m
H
is
s
elec
ted
.
T
h
is
g
u
ar
an
tees
th
at
th
e
in
d
u
cto
r
cu
r
r
en
t
n
e
v
er
f
alls
to
ze
r
o
,
t
h
er
eb
y
m
ai
n
tain
in
g
s
tab
le
co
n
v
er
ter
p
e
r
f
o
r
m
an
ce
o
v
er
th
e
e
n
tire
d
u
ty
cy
cle
r
an
g
e.
iv
)
Step
4
: O
u
tp
u
t c
ap
ac
ito
r
s
izin
g
T
h
e
o
u
tp
u
t
ca
p
ac
ito
r
is
s
elec
ted
to
lim
it
th
e
v
o
ltag
e
r
ip
p
l
e
to
with
in
1
.
5
%
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
,
en
s
u
r
in
g
s
tab
le
o
p
er
atio
n
an
d
m
in
im
izin
g
s
tr
ess
o
n
th
e
lo
ad
.
T
h
e
r
e
q
u
ir
ed
ca
p
ac
itan
ce
is
ca
lcu
lated
u
s
in
g
th
e
s
tan
d
ar
d
r
ip
p
le
v
o
ltag
e
e
q
u
ati
o
n
:
=
⋅
⋅
(
9
)
wh
er
e
ΔV
o
is
th
e
a
llo
wab
le
r
ip
p
le
v
o
ltag
e
(
1
.
5
%
o
f
V
o
)
.
T
o
en
s
u
r
e
th
e
d
esig
n
is
r
o
b
u
s
t,
th
e
ca
lcu
latio
n
is
b
ased
o
n
th
e
w
o
r
s
t
-
ca
s
e
o
p
er
a
tin
g
co
n
d
itio
n
.
T
o
ac
c
o
u
n
t
f
o
r
r
ea
l
-
wo
r
ld
f
ac
t
o
r
s
s
u
ch
as
tem
p
er
atu
r
e
v
ar
iatio
n
,
ag
in
g
,
an
d
to
ler
a
n
ce
d
r
if
t,
a
s
lig
h
tly
lar
g
er
ca
p
ac
ito
r
o
f
4
7
0
μ
F
is
s
elec
ted
.
T
h
is
e
n
s
u
r
es
th
at
th
e
r
ip
p
le
v
o
ltag
e
r
em
ain
s
with
in
ac
ce
p
tab
le
lim
its
u
n
d
er
all
co
n
d
itio
n
s
.
v)
Step
5
: I
n
p
u
t c
ap
ac
ito
r
s
izin
g
T
h
e
in
p
u
t
ca
p
ac
ito
r
,
C
in
is
cr
itical
f
o
r
r
ed
u
cin
g
h
ig
h
-
f
r
eq
u
en
cy
v
o
ltag
e
r
i
p
p
le
at
th
e
i
n
p
u
t
an
d
f
o
r
s
tab
ilizin
g
th
e
in
p
u
t
cu
r
r
en
t
d
r
awn
f
r
o
m
th
e
PV
s
o
u
r
ce
,
esp
ec
ially
d
u
r
in
g
f
ast
s
witch
in
g
ev
en
ts
.
T
h
e
in
p
u
t
ca
p
ac
ito
r
is
ca
lcu
lated
u
s
in
g
t
h
e
f
o
llo
win
g
ex
p
r
ess
io
n
:
=
⋅
⋅
(
1
0
)
U
s
i
n
g
t
h
e
w
o
r
s
t
-
c
as
e
c
o
n
d
i
tio
n
,
t
h
e
c
a
l
c
u
l
a
t
e
d
ca
p
a
c
i
t
a
n
ce
i
s
a
p
p
r
o
x
i
m
a
t
el
y
3
6
4
μ
F
.
T
o
e
n
s
u
r
e
p
r
a
c
t
i
c
al
i
m
p
l
e
m
e
n
t
a
ti
o
n
a
n
d
a
c
c
o
u
n
t
f
o
r
t
e
m
p
e
r
a
t
u
r
e
v
a
r
i
a
ti
o
n
s
,
v
o
l
ta
g
e
d
e
r
a
t
i
n
g
,
a
n
d
s
ta
n
d
a
r
d
c
o
m
p
o
n
e
n
t
a
v
a
i
l
a
b
il
i
t
y
,
a
c
o
m
m
e
r
c
i
a
l
l
y
a
v
a
i
l
a
b
l
e
c
a
p
a
ci
to
r
v
a
l
u
e
o
f
4
7
0
μ
F
is
s
e
l
ec
t
e
d
.
T
h
i
s
c
h
o
i
c
e
p
r
o
v
i
d
e
s
a
d
e
q
u
a
te
m
a
r
g
i
n
a
b
o
v
e
t
h
e
c
a
l
c
u
l
a
te
d
v
a
l
u
e
,
e
n
s
u
r
i
n
g
s
t
a
b
le
o
p
e
r
a
t
i
o
n
a
n
d
r
e
d
u
c
e
d
i
n
p
u
t
v
o
l
t
a
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p
p
l
e
a
c
r
o
s
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al
l
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d
i
tio
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s
.
T
ab
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3
p
r
esen
ts
th
e
f
in
al
d
esig
n
v
alu
es
o
f
th
e
cr
itical
c
o
m
p
o
n
en
ts
;
in
p
u
t
ca
p
ac
itan
ce
,
in
d
u
ctan
ce
,
o
u
tp
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p
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an
d
lo
ad
r
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tan
ce
u
s
ed
in
th
e
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
.
T
h
ese
p
ar
a
m
etr
ic
v
alu
es
wer
e
d
er
iv
ed
f
r
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m
(
4
)
,
(
8
)
,
(
9
)
,
an
d
(
1
0
)
,
b
ased
o
n
th
e
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co
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ain
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Fu
r
th
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ar
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s
.
T
ab
le
3
.
Par
am
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s
o
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b
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k
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I
SS
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:
2
0
8
8
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8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2841
-
2
8
5
9
2846
2
.
3
.
Desig
nin
g
o
f
a
n AIPSO
-
ba
s
ed
M
P
P
T
a
lg
o
rit
hm
f
o
r
v
a
ria
ble ir
ra
dia
nce
co
nd
it
io
ns
T
h
is
s
ec
tio
n
ex
p
lain
s
th
e
d
e
s
ig
n
o
f
th
e
p
r
o
p
o
s
ed
AI
PS
O
MPPT
alg
o
r
ith
m
,
b
e
g
in
n
in
g
with
th
e
s
tan
d
ar
d
PS
O
an
d
f
o
llo
wed
b
y
en
h
a
n
ce
m
en
ts
to
im
p
r
o
v
e
its
p
er
f
o
r
m
an
ce
.
T
h
e
co
n
v
en
tio
n
a
l
PS
O
alg
o
r
ith
m
is
k
n
o
wn
f
o
r
its
s
im
p
licity
an
d
f
ast
co
n
v
er
g
e
n
ce
,
b
u
t
it
o
f
ten
s
u
f
f
er
s
f
r
o
m
p
r
em
atu
r
e
c
o
n
v
e
r
g
en
ce
an
d
r
ed
u
ce
d
ac
cu
r
ac
y
u
n
d
e
r
r
ap
i
d
ly
ch
a
n
g
i
n
g
ir
r
a
d
ian
ce
c
o
n
d
itio
n
s
.
T
o
o
v
er
co
m
e
t
h
ese
lim
itatio
n
s
,
th
e
ad
ap
tiv
e
im
p
r
o
v
ed
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
AI
PS
O
)
in
tr
o
d
u
ce
s
d
y
n
am
ic
ad
ju
s
tm
en
t
m
ec
h
a
n
is
m
s
f
o
r
in
er
tia
weig
h
t
an
d
ac
ce
ler
atio
n
co
e
f
f
icien
ts
,
allo
win
g
b
etter
e
x
p
lo
r
atio
n
a
n
d
e
x
p
lo
itatio
n
o
f
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
al
g
o
r
ith
m
is
f
u
r
th
er
r
e
f
in
ed
b
y
in
teg
r
atin
g
ad
ap
tiv
e
p
er
tu
r
b
atio
n
s
tr
ateg
ie
s
to
m
ain
tain
d
iv
er
s
ity
am
o
n
g
p
ar
ticles
an
d
av
o
id
lo
ca
l
o
p
tim
a.
Simu
latio
n
r
esu
lts
u
n
d
er
v
ar
iab
le
ir
r
ad
ia
n
ce
p
r
o
f
iles
d
em
o
n
s
tr
ate
th
at
AI
P
SO
ac
h
iev
es
f
aste
r
tr
ac
k
in
g
an
d
h
ig
h
er
ef
f
icien
cy
co
m
p
ar
ed
to
s
tan
d
ar
d
MPPT
tech
n
iq
u
es.
2
.
3
.
1
.
Sta
nd
a
rd
P
SO
PS
O
is
an
o
p
tim
izatio
n
ap
p
r
o
ac
h
p
r
esen
ted
b
y
R
eg
ay
a
et
a
l
.
[
2
8
]
.
T
h
e
p
o
s
itio
n
,
v
elo
city
,
an
d
f
itn
ess
v
alu
e
o
f
a
p
ar
ticle
d
ef
in
e
its
p
r
o
p
er
ties
.
A
p
ar
ticle'
s
p
o
s
it
io
n
an
d
s
p
ee
d
ar
e
d
y
n
am
ically
m
o
d
if
ied
b
y
its
o
wn
ex
p
er
ien
ce
as
well
as
b
y
th
e
m
o
tio
n
o
f
o
t
h
er
p
ar
ticles
[
2
9
]
.
PS
O
ca
n
attain
o
p
tim
izatio
n
th
r
o
u
g
h
r
ep
ea
ted
iter
atio
n
s
.
T
h
e
v
e
l
o
c
i
t
y
a
n
d
p
o
s
i
ti
o
n
o
f
p
a
r
t
i
c
l
es
a
r
e
r
e
v
is
e
d
b
a
s
e
d
o
n
(
1
1
)
a
n
d
(
1
2
)
[
3
0
]
.
(
+
1
)
=
×
(
)
+
1
×
1
×
(
−
(
)
)
+
2
×
2
×
(
−
(
)
)
(
1
1
)
(
+
1
)
=
(
)
+
(
+
1
)
(
1
2
)
V
i
(
t
+1
)
is
th
e
u
p
d
ate
d
v
elo
cit
y
o
f
p
ar
ticle
i
at
iter
atio
n
t
+1
,
V
i
(
t)
is
th
e
cu
r
r
en
t
v
elo
city
o
f
p
ar
ticle
i
at
iter
atio
n
t
,
ω
is
th
e
i
n
er
tia
weig
h
t,
b
alan
cin
g
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
.
C
1
is
co
g
n
itiv
e
co
ef
f
icien
t
an
d
C
2
is
ca
lled
as
a
s
o
cial
co
ef
f
i
cien
t
[
3
1
]
.
T
h
e
r
1
an
d
r
2
ar
e
r
an
d
o
m
n
u
m
b
er
s
b
etwe
en
[
0
,
1
]
.
P
i
is
th
e
p
er
s
o
n
al
b
est
an
d
G
is
th
e
g
lo
b
al
b
est p
o
s
itio
n
o
f
a
p
a
r
ticle
,
a
n
d
X
i
(
t)
is
th
e
p
ar
ticle
’
s
cu
r
r
en
t p
o
s
itio
n
at
iter
atio
n
t
.
T
h
e
s
lo
w
co
n
v
er
g
en
ce
s
p
ee
d
a
n
d
d
if
f
icu
lties
lo
ca
tin
g
th
e
GM
PP
ar
e
th
e
is
s
u
es
with
th
e
tr
ad
itio
n
al
PS
O
tech
n
iq
u
e
.
Du
r
in
g
t
h
e
iter
atio
n
s
,
W
,
r
1
,
a
n
d
r
2
s
tay
c
o
n
s
tan
t
s
in
ce
th
e
y
ar
e
ass
ig
n
ed
to
f
ix
e
d
v
al
u
es
b
ased
o
n
ex
p
er
ie
n
ce
.
Alth
o
u
g
h
a
lar
g
e
v
al
u
e
o
f
W
r
esu
lts
in
a
m
o
r
e
r
esil
ien
t
g
lo
b
al
s
ea
r
ch
,
th
e
h
ig
h
p
a
r
ticle
s
p
ee
d
ca
n
ca
u
s
e
f
lu
ctu
atio
n
s
in
th
e
g
lo
b
al
r
eg
i
o
n
a
n
d
r
ed
u
ce
th
e
l
o
ca
l
s
ea
r
c
h
p
o
te
n
tial
[
3
2
]
.
A
lo
wer
v
alu
e
o
f
W
ca
n
ca
u
s
e
a
m
o
r
e
r
esil
ien
t
lo
ca
l
s
ea
r
ch
,
h
o
wev
er
its
g
lo
b
al
s
ea
r
ch
c
ap
ab
ilit
y
d
ec
r
ea
s
es,
wh
ich
c
an
ca
u
s
e
a
n
ea
r
ly
co
n
v
er
g
en
ce
to
war
d
s
lo
ca
l
o
p
tim
u
m
.
Ho
wev
er
,
th
e
im
p
ac
t
o
f
in
itial
p
ar
ticle
p
o
s
itio
n
r
an
d
o
m
izatio
n
o
n
th
e
p
ar
ticle
s
war
m
's
ab
ilit
y
to
lo
ca
te
th
e
g
lo
b
al
m
ax
im
u
m
ca
n
’
t
b
e
d
is
r
eg
ar
d
e
d
.
T
h
e
r
a
n
d
o
m
in
itial
p
ar
ticle
p
lace
m
en
ts
m
ay
co
n
v
er
g
e
to
l
o
ca
l m
ax
im
u
m
v
alu
es a
b
r
u
p
tl
y
[
3
3
]
.
2
.
3
.
2
.
I
m
pro
v
is
ed
v
elo
cit
y
a
nd
po
s
it
io
n up
da
t
es
T
h
e
s
tan
d
ar
d
eq
u
atio
n
s
f
o
r
u
p
d
atin
g
th
e
v
elo
city
an
d
p
o
s
itio
n
in
PS
O
ar
e
p
r
esen
te
d
in
(
1
1
)
an
d
(
1
2
)
,
wh
ich
f
o
r
m
th
e
f
o
u
n
d
atio
n
o
f
th
e
alg
o
r
ith
m
'
s
iter
ativ
e
im
p
r
o
v
e
m
en
t
p
r
o
ce
s
s
.
Ho
wev
er
,
in
th
e
p
r
o
p
o
s
ed
AI
PS
O,
s
ig
n
if
ican
t
m
o
d
if
ica
tio
n
s
h
av
e
b
ee
n
in
tr
o
d
u
ce
d
to
en
h
an
ce
th
e
alg
o
r
ith
m
'
s
p
er
f
o
r
m
a
n
ce
b
y
in
co
r
p
o
r
atin
g
ad
d
itio
n
al
f
ac
t
o
r
s
in
to
th
e
u
p
d
ate
e
q
u
atio
n
s
.
Sp
ec
if
ically
,
th
e
v
el
o
city
u
p
d
ate
eq
u
atio
n
in
AI
PS
O
is
ad
ju
s
ted
to
in
clu
d
e
a
n
ew
ter
m
C3
⋅
(
G
−
Pi
)
,
w
h
ich
ac
co
u
n
ts
f
o
r
th
e
d
y
n
am
i
c
in
f
lu
en
ce
o
f
t
h
e
d
if
f
er
en
ce
b
etwe
en
th
e
Pb
est
an
d
th
e
G
b
est
p
o
s
itio
n
,
th
er
eb
y
b
alan
ci
n
g
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
[
3
4
]
.
T
h
is
m
o
d
if
icatio
n
is
p
r
esen
te
d
in
(
1
3
)
:
(
+
1
)
=
×
(
)
+
1
×
1
×
(
−
(
)
)
+
2
×
2
×
(
−
(
)
)
+
3
×
(
−
(
)
)
(
1
3
)
Similar
ly
,
th
e
p
o
s
itio
n
u
p
d
ate
eq
u
atio
n
h
as
b
ee
n
r
ef
in
e
d
in
AI
PS
O
to
in
co
r
p
o
r
ate
a
s
ca
lin
g
f
ac
to
r
o
f
0
.
6
,
wh
ich
co
n
tr
o
ls
th
e
m
ag
n
itu
d
e
o
f
th
e
v
elo
city
'
s
co
n
tr
ib
u
tio
n
to
p
o
s
itio
n
u
p
d
ates
[
3
5
]
.
T
h
is
ch
an
g
e
en
s
u
r
es
a
m
o
r
e
g
r
ad
u
al
a
d
ju
s
tm
en
t
in
p
ar
ticle
p
o
s
itio
n
s
,
p
r
ev
en
tin
g
ab
r
u
p
t
ch
an
g
es
th
at
co
u
ld
d
estab
ilize
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
T
h
e
u
p
d
ated
p
o
s
itio
n
eq
u
atio
n
is
g
iv
e
n
in
(
1
4
)
:
(
+
1
)
=
(
)
+
0
.
6
×
(
+
1
)
(
1
4
)
T
h
e
t
e
r
m
a
d
a
p
t
i
v
e
i
s
u
s
e
d
b
e
c
a
u
s
e
i
t
a
u
g
m
e
n
t
s
P
S
O
w
i
t
h
a
n
a
d
a
p
t
i
v
e
c
o
e
f
f
i
c
i
e
n
t
C
3
i
n
t
h
e
v
e
l
o
c
i
t
y
u
p
d
a
t
e
(
1
3
)
a
n
d
a
r
e
-
i
n
i
t
i
a
l
i
z
a
t
i
o
n
t
r
i
g
g
e
r
w
h
e
n
t
h
e
P
V
p
o
w
e
r
d
e
v
i
a
t
e
s
f
r
o
m
i
t
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ates
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m
t
h
e
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o
r
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o
f
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e
p
r
o
p
o
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ed
AI
PS
O
alg
o
r
ith
m
.
T
h
e
MPPT
o
p
er
ates
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n
t
h
e
d
u
ty
r
atio
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;
c
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v
e
r
ter
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ip
p
le
r
elatio
n
s
ab
o
v
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b
o
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n
d
th
e
s
ea
r
ch
an
d
i
n
f
o
r
m
th
e
a
d
ap
tiv
e
g
ain
C3
n
ea
r
s
teep
p
o
wer
g
r
ad
ien
ts
.
As
d
em
o
n
s
tr
ated
in
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
a
p
tive
in
tellig
en
t P
S
O
-
B
a
s
ed
MPP
T tec
h
n
iq
u
e
fo
r
P
V
s
ystems
u
n
d
er
…
(
Mu
h
a
mma
d
G
u
l E
.
I
s
la
m
)
2847
r
esu
lts
s
ec
tio
n
,
th
ese
m
o
d
if
icatio
n
s
lead
to
a
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
in
o
p
tim
izatio
n
p
e
r
f
o
r
m
an
ce
,
o
f
f
er
in
g
f
aster
co
n
v
er
g
en
ce
a
n
d
b
etter
s
o
lu
tio
n
s
in
co
m
p
a
r
is
o
n
to
th
e
s
tan
d
ar
d
PS
O
alg
o
r
ith
m
.
2
.
3
.
3
.
Co
nv
er
t
er
lev
el
m
o
deli
ng
a
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rippl
e
co
ns
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dera
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io
n
T
h
e
f
ix
e
d
-
f
r
eq
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e
n
cy
PW
M
F
SW
=
25
k
Hz
h
as
b
ee
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s
ed
with
D
∈
[
0
.
0
5
–
0
.
9
5
]
.
I
n
co
n
tin
u
o
u
s
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n
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u
ctio
n
m
o
d
e,
th
e
i
n
d
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ct
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t
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o
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n
d
s
as
s
tated
in
(
1
5
)
,
a
n
d
(
1
6
)
r
esp
ec
tiv
ely
.
∆
IL
=
V
i
n
.
D
L
.
f
s
w
(
1
5
)
∆
Vo
=
Io
.
D
C
.
f
s
w
(
1
6
)
T
h
ese
r
elatio
n
s
in
ter
p
r
et
th
e
co
m
p
o
n
en
t
v
alu
es
alr
ea
d
y
lis
ted
in
th
e
p
ap
er
an
d
ex
p
lain
t
h
e
o
b
s
er
v
ed
p
o
wer
r
ip
p
le
d
u
r
i
n
g
s
tep
ir
r
ad
ia
n
ce
/PS
C
.
M
PP
T
d
u
ty
u
p
d
ates
ar
e
s
lew
-
lim
ited
to
av
o
id
ex
ce
s
s
iv
e
lo
w
-
f
r
eq
u
en
cy
p
o
wer
r
ip
p
le.
2
.
3
.
4
.
Reinit
ia
liza
t
io
n
s
t
ra
t
eg
y
PS
O
is
wid
ely
r
eg
ar
d
ed
as
o
n
e
o
f
th
e
m
o
s
t
ef
f
e
ctiv
e
alg
o
r
it
h
m
s
f
o
r
MPPT
in
p
h
o
to
v
o
ltai
c
s
y
s
tem
s
[
3
6
]
.
H
o
wev
er
,
a
s
ig
n
i
f
ican
t
lim
itatio
n
o
f
PS
O
is
its
in
ab
ilit
y
to
ef
f
ec
tiv
ely
r
esp
o
n
d
t
o
b
o
th
s
u
d
d
en
a
n
d
g
r
ad
u
al
c
h
an
g
es
in
ir
r
ad
ian
ce
co
n
d
itio
n
s
,
wh
ich
ca
n
s
ev
er
el
y
im
p
ac
t
th
e
o
v
er
all
e
f
f
icien
c
y
o
f
t
h
e
s
y
s
tem
.
T
o
tack
le
th
is
i
s
s
u
e,
a
r
ein
itializ
atio
n
tech
n
iq
u
e
h
as
b
ee
n
p
r
o
p
o
s
ed
to
en
h
an
ce
PS
O’
s
tr
ac
k
in
g
ca
p
ab
ilit
ies
in
f
lu
ctu
atin
g
ir
r
ad
ia
n
ce
en
v
ir
o
n
m
en
ts
[
3
7
]
.
T
h
is
tech
n
iq
u
e
i
n
v
o
lv
es
r
ein
itializin
g
th
e
alg
o
r
ith
m
wh
en
ev
e
r
a
ch
an
g
e
in
ir
r
ad
ian
ce
is
d
etec
ted
,
allo
win
g
it
to
m
o
r
e
ac
c
u
r
ately
tr
ac
k
th
e
MPP
an
d
im
p
r
o
v
e
o
v
e
r
all
s
y
s
tem
ef
f
icien
cy
[
3
8
]
.
T
h
e
r
ei
n
itializatio
n
p
r
o
ce
s
s
is
tr
ig
g
er
e
d
wh
e
n
th
e
ch
a
n
g
e
in
p
o
wer
e
x
ce
ed
s
o
r
eq
u
als
5
%
o
f
th
e
to
tal
p
o
wer
,
as
d
escr
ib
ed
i
n
(
17
)
.
|
(
)
−
(
−
1
)
(
−
1
)
|
>
(
1
7
)
T
h
is
co
n
d
itio
n
e
n
s
u
r
es
th
at
th
e
s
y
s
tem
ad
a
p
ts
q
u
ic
k
ly
t
o
s
ig
n
if
ican
t
ch
an
g
es
in
ir
r
a
d
ian
ce
,
im
p
r
o
v
in
g
p
er
f
o
r
m
an
ce
an
d
s
tab
ilit
y
.
T
h
e
p
r
o
p
o
s
ed
r
ein
itializatio
n
s
tr
ateg
y
co
n
tr
ib
u
tes
t
o
e
n
h
an
ce
d
tr
ac
k
in
g
ef
f
icien
cy
an
d
o
v
er
all
o
p
tim
izatio
n
o
f
th
e
s
y
s
tem
.
2
.
3
.
5
.
P
ro
po
s
ed
AIPSO
Fig
u
r
e
3
illu
s
tr
ates
th
e
f
lo
w
ch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
AI
PS
O
b
ased
MPPT
ap
p
r
o
ac
h
,
s
p
ec
if
ically
d
esig
n
ed
f
o
r
PV
s
y
s
tem
s
o
p
er
atin
g
u
n
d
er
v
ar
ia
b
le
ir
r
ad
ian
ce
co
n
d
itio
n
s
.
T
h
e
a
d
ap
tiv
e
n
atu
r
e
o
f
th
e
AI
PS
O
alg
o
r
ith
m
allo
ws
it
to
d
y
n
am
i
ca
lly
b
alan
ce
th
e
tr
ad
e
-
o
f
f
b
e
twee
n
ex
p
lo
r
in
g
th
e
s
ea
r
ch
s
p
ac
e
an
d
ex
p
lo
itin
g
p
r
o
m
is
in
g
r
e
g
io
n
s
,
m
a
k
in
g
it
p
ar
ticu
lar
ly
ef
f
ec
tiv
e
f
o
r
co
m
p
lex
,
n
o
n
lin
ea
r
o
p
tim
izatio
n
p
r
o
b
lem
s
[
2
9
]
.
T
h
e
alg
o
r
ith
m
'
s
p
er
f
o
r
m
a
n
ce
is
o
p
tim
ized
b
y
tu
n
in
g
s
ev
er
a
l
cr
itical
p
ar
am
eter
s
,
in
clu
d
in
g
th
e
co
g
n
itiv
e
co
ef
f
icien
t
(
C
1
)
,
s
o
cial
co
ef
f
i
cien
t
(
C
2
)
,
im
p
r
o
v
is
atio
n
co
e
f
f
icien
t
(
C
3
)
,
in
er
tia
weig
h
t
(
W
)
,
an
d
p
o
p
u
latio
n
s
ize
[
3
9
]
.
T
h
ese
p
ar
am
eter
s
,
s
u
m
m
ar
ized
in
T
ab
le
4
,
ar
e
es
s
en
tial
f
o
r
ac
h
iev
in
g
an
o
p
tim
al
b
alan
ce
b
etwe
en
co
n
v
er
g
en
ce
s
p
ee
d
a
n
d
tr
ac
k
i
n
g
ac
c
u
r
ac
y
,
th
er
e
b
y
e
n
h
an
ci
n
g
th
e
ef
f
icien
c
y
o
f
MPPT
o
p
er
atio
n
[
2
8
]
.
T
h
e
in
tr
o
d
u
ctio
n
o
f
an
im
p
r
o
v
is
a
tio
n
co
ef
f
icien
t
in
th
e
v
elo
ci
ty
an
d
p
o
s
itio
n
u
p
d
ate
eq
u
at
io
n
s
im
p
r
o
v
es
th
e
alg
o
r
ith
m
’
s
co
n
v
er
g
e
n
ce
r
at
e
co
m
p
ar
ed
to
c
o
n
v
e
n
tio
n
al
PS
O.
T
h
is
m
o
d
if
icatio
n
n
o
t
o
n
ly
ac
ce
ler
ates
co
n
v
er
g
en
ce
b
u
t
also
e
n
h
an
c
es
th
e
s
y
s
tem
’
s
ab
ilit
y
to
a
d
a
p
t
to
d
y
n
am
ic
ch
an
g
es
in
ir
r
ad
ian
ce
co
n
d
itio
n
s
,
th
er
eb
y
im
p
r
o
v
in
g
o
v
er
all
MP
PT
ef
f
icien
cy
[
4
0
]
.
T
ab
le
4
.
Par
am
eter
s
o
f
PS
O
a
lg
o
r
ith
m
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
C
o
g
n
i
t
i
v
e
c
o
e
f
f
i
c
i
e
n
t
,
C
1
1
.
4
I
n
e
r
t
i
a
w
e
i
g
h
t
,
W
0
.
5
S
o
c
i
a
l
c
o
e
f
f
i
c
i
e
n
t
,
C
2
1
.
7
N
u
mb
e
r
o
f
p
a
r
t
i
c
l
e
s
3
I
mp
r
o
v
i
s
i
n
g
c
o
e
f
f
i
c
i
e
n
t
,
C
3
0
.
6
T
h
e
AI
PS
O
alg
o
r
ith
m
b
eg
in
s
b
y
in
itializin
g
k
ey
p
ar
a
m
eter
s
,
in
clu
d
in
g
th
e
in
er
tia
weig
h
t,
W,
C
1
,
C
2
,
an
d
th
e
im
p
r
o
v
is
atio
n
f
ac
to
r
,
C
3
.
A
p
o
p
u
latio
n
o
f
p
a
r
ticles,
ea
ch
r
e
p
r
esen
tin
g
a
p
o
ten
ti
al
s
o
lu
tio
n
,
is
t
h
en
g
en
er
ated
.
Du
r
in
g
ea
ch
iter
a
tio
n
,
th
e
f
itn
ess
o
f
ea
ch
p
ar
ticle
is
ev
alu
ated
u
s
in
g
a
p
r
ed
ef
in
ed
o
b
jectiv
e
f
u
n
ctio
n
[
4
1
]
.
I
f
a
p
a
r
ticle
d
is
co
v
er
s
a
n
ew
p
e
r
s
o
n
al
b
est
s
o
lu
tio
n
,
its
p
er
s
o
n
al
b
est
p
o
s
itio
n
(
Pb
est)
is
u
p
d
ated
ac
co
r
d
in
g
l
y
[
4
2
]
.
Similar
ly
,
t
h
e
g
lo
b
al
b
est
p
o
s
itio
n
(
G
best
)
is
u
p
d
ated
b
ased
o
n
th
e
b
est
s
o
lu
tio
n
id
e
n
tifie
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2841
-
2
8
5
9
2848
ac
r
o
s
s
th
e
en
tire
s
war
m
.
Su
b
s
eq
u
en
tly
,
ea
c
h
p
ar
ticle’
s
v
elo
c
ity
an
d
p
o
s
itio
n
a
r
e
u
p
d
ated
b
ased
o
n
its
P
best
,
th
e
cu
r
r
en
t
G
best
,
an
d
th
e
im
p
r
o
v
is
atio
n
f
ac
to
r
.
T
h
is
iter
ativ
e
p
r
o
ce
s
s
co
n
tin
u
es
u
n
til
a
p
r
e
d
ef
in
ed
ter
m
in
atio
n
cr
iter
io
n
is
m
et
—
eith
er
a
m
a
x
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
o
r
a
s
atis
f
ac
to
r
y
f
itn
ess
v
alu
e.
T
h
e
f
in
al
Gb
est
p
o
s
itio
n
r
ep
r
esen
ts
th
e
o
p
tim
a
l so
lu
tio
n
to
th
e
MPPT
o
p
tim
i
za
tio
n
p
r
o
b
lem
[
2
9
]
.
Fig
u
r
e
3
.
Flo
w
c
h
a
r
t o
f
a
d
ap
ti
v
e
PS
O
b
ased
MPPT
a
lg
o
r
ith
m
2
.
4
.
I
m
ple
m
ent
a
t
io
n a
nd
v
a
l
ida
t
io
n in MA
T
L
A
B
Sim
uli
nk
MA
T
L
AB
/S
im
u
lin
k
was
u
tili
ze
d
to
s
im
u
late
an
d
v
alid
ate
t
h
e
ef
f
ec
tiv
en
ess
o
f
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
.
I
n
itially
,
a
b
u
ck
-
b
o
o
s
t
co
n
v
e
r
ter
was
s
im
u
lated
to
estab
li
s
h
a
b
aselin
e
f
o
r
co
m
p
ar
is
o
n
.
Su
b
s
eq
u
en
tly
,
a
s
tan
d
ar
d
PV
s
y
s
tem
co
n
f
ig
u
r
a
tio
n
,
in
co
r
p
o
r
atin
g
a
DC
-
DC
co
n
v
er
ter
,
was
s
im
u
lated
an
d
v
alid
ated
.
T
o
ass
ess
th
e
r
esil
ien
ce
o
f
t
h
e
PS
O
alg
o
r
ith
m
,
it
was
s
u
b
jecte
d
to
b
o
t
h
s
tep
ch
an
g
es
a
n
d
g
r
ad
u
al
v
ar
i
atio
n
s
in
ir
r
ad
ia
n
ce
co
n
d
itio
n
s
.
T
h
e
r
esu
lts
in
d
ica
ted
th
at
th
e
s
tan
d
ar
d
PS
O
alg
o
r
ith
m
s
tr
u
g
g
led
to
ac
c
u
r
ate
ly
lo
ca
te
th
e
MPP
u
n
d
er
d
y
n
am
ic
c
o
n
d
itio
n
s
.
T
o
ad
d
r
ess
th
is
lim
itatio
n
,
a
n
ew
ad
ap
tiv
e
in
tellig
en
t
s
tr
ateg
y
was
im
p
lem
en
ted
,
s
ig
n
if
ican
tly
en
h
an
ci
n
g
th
e
al
g
o
r
ith
m
'
s
ab
ilit
y
to
ad
ap
t
to
ch
an
g
in
g
co
n
d
itio
n
s
an
d
im
p
r
o
v
in
g
th
e
ef
f
icie
n
cy
an
d
co
n
v
er
g
en
ce
o
f
th
e
PV
s
y
s
tem
u
n
d
er
v
ar
y
in
g
ir
r
a
d
ian
ce
co
n
d
itio
n
s
[
4
3
]
.
Fin
ally
,
th
e
e
f
f
ec
tiv
en
ess
o
f
th
e
AI
PS
O
-
b
ased
MPPT
s
y
s
tem
was
ev
alu
ated
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
d
em
o
n
s
tr
atin
g
its
ca
p
ab
ilit
y
in
tr
ac
k
in
g
th
e
GM
PP
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
co
m
p
lete
Simu
lin
k
m
o
d
el
o
f
th
e
PV
s
y
s
tem
,
i
n
clu
d
in
g
t
h
e
b
u
c
k
-
b
o
o
s
t
co
n
v
er
ter
an
d
th
e
PS
O
-
b
ased
MPPT
alg
o
r
ith
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Dr
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N:
2088
-
8
6
9
4
A
d
a
p
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S
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Mu
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I
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la
m
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2849
Fig
u
r
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4.
Simu
lin
k
m
o
d
el
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f
P
V
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with
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RE
SU
L
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D
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h
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a
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it
h
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P
P
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,
s
t
e
p
c
h
a
n
g
e
i
r
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a
d
i
a
n
ce
c
o
n
d
i
t
i
o
n
,
a
n
d
P
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c
o
n
d
i
t
i
o
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t
e
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y
s
t
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p
.
T
h
e
a
n
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l
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is
f
o
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s
e
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n
t
h
e
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e
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s
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c
y
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n
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m
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u
m
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d
t
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r
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d
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r
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t
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n
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h
e
t
r
a
c
k
i
n
g
d
u
r
a
t
i
o
n
r
e
f
e
r
s
t
o
t
h
e
ti
m
e
ta
k
e
n
f
o
r
t
h
e
s
y
s
te
m
t
o
f
i
n
d
t
h
e
o
p
t
i
m
a
l
s
o
l
u
t
i
o
n
.
A
I
P
SO
’
s
f
as
t
e
r
c
o
n
v
e
r
g
e
n
c
e
w
i
t
h
z
e
r
o
s
t
ea
d
y
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s
t
at
e
o
s
c
ill
a
t
i
o
n
s
r
e
d
u
c
es
l
o
w
-
f
r
e
q
u
e
n
cy
P
V
p
o
w
e
r
r
i
p
p
l
e
t
r
a
n
s
f
e
r
r
e
d
t
o
t
h
e
DC
li
n
k
.
T
h
is
l
o
w
e
r
s
c
u
r
r
e
n
t
-
l
o
o
p
e
f
f
o
r
t
i
n
a
g
r
i
d
-
t
i
e
d
i
n
v
e
r
te
r
a
n
d
a
v
o
i
d
s
P
L
L
p
e
r
t
u
r
b
a
t
i
o
n
s
.
B
e
c
a
u
s
e
M
PP
T
r
u
n
s
w
e
ll
b
el
o
w
s
wi
t
c
h
i
n
g
a
n
d
c
u
r
r
e
n
t
-
l
o
o
p
b
a
n
d
w
i
d
t
h
s
,
i
n
t
e
r
a
c
ti
o
n
i
s
u
n
l
i
k
e
l
y
.
T
a
b
l
e
5
,
p
r
e
s
e
n
t
s
t
h
e
d
e
f
i
n
i
t
i
o
n
s
o
f
m
e
t
r
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c
s
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s
e
d
i
n
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u
l
ts
a
n
d
d
i
s
c
u
s
s
i
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n
s
e
c
t
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o
n
t
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v
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l
i
d
at
e
t
h
e
e
f
f
ec
t
i
v
e
n
e
s
s
a
n
d
s
h
o
w
c
o
m
p
a
r
i
s
o
n
o
f
p
r
o
p
o
s
e
d
A
I
P
SO
w
i
t
h
o
t
h
e
r
s
t
a
n
d
a
r
d
a
l
g
o
r
i
t
h
m
s
.
S
i
m
i
l
a
r
l
y
,
T
a
b
le
6
d
e
s
c
r
i
b
e
s
t
h
e
i
r
r
a
d
i
a
n
ce
t
es
t
p
r
o
f
i
l
e
s
u
s
e
d
i
n
t
h
is
s
t
u
d
y
t
o
v
al
i
d
a
t
e
t
h
e
e
f
f
e
c
t
i
v
e
n
ess
o
f
t
h
e
p
r
o
p
o
s
e
d
A
I
P
SO
a
l
g
o
r
i
t
h
m
.
T
ab
le
5
.
Me
tr
ic
d
e
f
in
itio
n
s
M
e
t
r
i
c
s
D
e
f
i
n
i
t
i
o
n
C
o
n
v
e
r
g
e
n
c
e
t
i
me
Th
e
f
i
r
st
t
i
me
t
o
a
t
t
a
i
n
t
h
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
.
P
o
w
e
r
Th
e
ma
x
i
mu
m
e
x
t
r
a
c
t
e
d
p
o
w
e
r
Ef
f
i
c
i
e
n
c
y
%
Th
e
p
e
r
c
e
n
t
a
g
e
o
f
e
x
t
r
a
c
t
e
d
p
o
w
e
r
f
r
o
m i
d
e
a
l
p
o
w
e
r
.
Ef
f
i
c
i
e
n
c
y
%
=
(
P
ou
t
/P
i
de
a
l
)
*
1
0
0
S
t
e
a
d
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st
a
t
e
o
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i
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t
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Th
e
sma
l
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f
l
u
c
t
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a
t
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o
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s
a
f
t
e
r
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t
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h
e
s
t
h
e
ma
x
i
mu
m
p
o
w
e
r
p
o
i
n
t
.
T
ab
le
6
.
T
est
p
r
o
f
iles
u
s
ed
in
t
h
is
s
tu
d
y
Te
st
s
c
e
n
a
r
i
o
s
I
r
r
a
d
i
a
n
c
e
(
W
/
m
2
)
Te
mp
e
r
a
t
u
r
e
(
o
C)
R
e
mar
k
s
U
n
i
f
o
r
m
i
r
r
a
d
i
a
n
c
e
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o
n
d
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t
i
o
n
1
0
0
0
W
/
m
2
2
5
o
C
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t
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n
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r
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s
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o
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t
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e
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u
p
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c
h
a
n
g
e
c
o
n
d
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t
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n
(
3
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-
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)
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/
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5
o
C
su
d
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h
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w
sec
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d
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t
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p
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o
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r
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(
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sec
o
n
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a
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(
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/
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2
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5
o
C
Th
r
e
e
P
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d
u
l
e
s
w
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d
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f
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n
t
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p
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a
d
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d
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5
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C
Th
r
e
e
P
V
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d
u
l
e
s
w
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t
h
d
i
f
f
e
r
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n
t
i
r
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a
d
i
a
n
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e
l
e
v
e
l
s
a
r
e
u
s
e
d
t
o
i
n
i
t
i
a
t
e
p
a
r
t
i
a
l
sh
a
d
i
n
g
3
.
1
.
Unifo
r
m
irra
dia
nce
co
n
ditio
n
wit
ho
ut
M
P
P
T
I
n
th
is
s
ec
tio
n
,
a
PV
s
y
s
tem
in
teg
r
ated
with
a
DC
-
D
C
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
is
s
im
u
lated
u
n
d
er
u
n
if
o
r
m
ir
r
ad
ia
n
ce
co
n
d
itio
n
s
with
o
u
t
u
s
in
g
a
n
y
MPPT
alg
o
r
ith
m
.
T
h
e
g
o
al
is
to
d
eter
m
in
e
th
e
r
an
g
e
o
f
d
u
t
y
cy
cle
v
alu
es
th
at
y
ield
m
a
x
i
m
u
m
o
u
t
p
u
t
p
o
wer
f
o
r
ea
ch
ir
r
ad
ian
ce
lev
el.
T
h
e
s
im
u
l
atio
n
was
in
itially
co
n
d
u
cte
d
at
an
ir
r
ad
ian
ce
le
v
el
o
f
1
0
0
W
/m
²
an
d
a
n
am
b
ien
t
tem
p
er
atu
r
e
o
f
2
5
°C
.
T
h
e
d
u
ty
cy
cle
was
m
an
u
ally
v
a
r
ied
f
r
o
m
0
t
o
1
in
f
in
e
in
cr
e
m
en
ts
,
an
d
t
h
e
co
r
r
esp
o
n
d
in
g
o
u
tp
u
t
p
o
wer
was
r
ec
o
r
d
ed
.
T
h
is
p
r
o
ce
d
u
r
e
was
s
y
s
tem
atica
lly
r
ep
ea
ted
f
o
r
all
f
ix
ed
ir
r
ad
ian
c
e
lev
els
r
an
g
in
g
f
r
o
m
1
0
0
W
/m
²
to
1
0
0
0
W
/m
²
in
1
0
0
W
/m
2
s
tep
s
.
An
aly
s
is
o
f
t
h
e
r
esu
lts
r
ev
ea
led
th
at
t
h
e
o
p
t
im
al
d
u
ty
cy
cle
—
co
r
r
esp
o
n
d
i
n
g
to
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
—
co
n
s
is
ten
tly
f
alls
with
in
th
e
r
an
g
e
o
f
0
.
3
5
to
0
.
6
5
ac
r
o
s
s
all
test
ed
ir
r
ad
ian
ce
s
.
T
ab
le
7
s
u
m
m
ar
izes
th
e
m
o
s
t
s
u
itab
le
d
u
ty
cy
cle
v
alu
es
f
o
r
ea
ch
u
n
if
o
r
m
i
r
r
ad
ian
ce
c
o
n
d
itio
n
,
h
ig
h
lig
h
tin
g
th
e
co
n
v
er
ter
’
s
b
eh
av
i
o
r
in
th
e
ab
s
en
ce
o
f
an
MPPT
co
n
t
r
o
ller
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2841
-
2
8
5
9
2850
T
ab
le
7
.
Mo
s
t
s
u
itab
le
d
u
ty
cy
cle
v
alu
es c
o
r
r
esp
o
n
d
in
g
to
M
PP
with
o
u
t M
PP
T
a
lg
o
r
ith
m
No
I
r
r
a
d
i
a
n
c
e
(
W
/
m
2
)
D
u
t
y
c
y
c
l
e
a
t
M
P
P
1
1
0
0
0
.
3
6
2
2
0
0
0
.
4
4
3
3
0
0
0
.
4
8
4
4
0
0
0
.
5
3
5
5
0
0
0
.
5
5
6
6
0
0
0
.
5
7
7
7
0
0
0
.
5
9
8
8
0
0
0
.
6
0
9
9
0
0
0
.
6
2
10
1
0
0
0
0
.
6
4
3
.
2
.
Unifo
r
m
irra
dia
nce
co
n
ditio
n wit
h
M
P
P
T
I
n
th
is
s
ec
tio
n
,
th
e
PV
s
y
s
tem
is
s
im
u
lated
u
n
d
er
u
n
if
o
r
m
ir
r
ad
ian
ce
co
n
d
itio
n
s
u
s
in
g
v
ar
io
u
s
MPPT
alg
o
r
ith
m
s
.
T
h
e
alg
o
r
ith
m
s
co
n
s
id
er
ed
in
clu
d
e
th
e
co
n
v
en
ti
o
n
al
HC
m
eth
o
d
,
s
tan
d
ar
d
PS
O,
th
e
FA,
an
d
th
e
p
r
o
p
o
s
ed
AI
PS
O
m
eth
o
d
.
T
h
e
s
im
u
latio
n
was
in
itially
co
n
d
u
cted
at
an
ir
r
ad
ia
n
ce
lev
el
o
f
1
0
0
W
/m
²
an
d
a
tem
p
er
atu
r
e
o
f
2
5
°C
.
E
ac
h
MPPT
alg
o
r
ith
m
was
ap
p
lie
d
in
d
ep
e
n
d
en
tly
,
an
d
th
e
r
esu
ltin
g
p
er
f
o
r
m
a
n
ce
m
etr
ics
—
s
u
ch
as
co
n
v
er
g
en
c
e
s
p
ee
d
,
tr
ac
k
in
g
ac
cu
r
ac
y
,
an
d
s
tead
y
-
s
tate
o
s
cillatio
n
—
wer
e
r
ec
o
r
d
ed
.
T
h
is
p
r
o
ce
s
s
was
r
ep
ea
ted
f
o
r
ea
c
h
f
ix
ed
ir
r
ad
ian
ce
le
v
el
u
p
to
1
0
0
0
W
/m
²
in
i
n
cr
em
en
ts
o
f
1
0
0
W
/m
².
Fig
u
r
e
5
p
r
esen
ts
a
p
er
f
o
r
m
a
n
ce
co
m
p
ar
is
o
n
o
f
all
f
o
u
r
alg
o
r
ith
m
s
u
n
d
er
a
h
ig
h
ir
r
ad
ian
ce
c
o
n
d
i
tio
n
o
f
1
0
0
0
W
/m
².
T
h
e
f
ig
u
r
e
h
i
g
h
lig
h
ts
th
e
s
u
p
er
io
r
tr
ac
k
i
n
g
ca
p
ab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
AI
PS
O
m
eth
o
d
,
d
em
o
n
s
tr
atin
g
f
aster
co
n
v
er
g
en
ce
an
d
m
in
im
al
o
s
c
illatio
n
ar
o
u
n
d
t
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
A
co
m
p
r
e
h
en
s
iv
e
s
u
m
m
ar
y
o
f
th
e
s
im
u
latio
n
r
esu
lts
ac
r
o
s
s
all
ir
r
ad
ian
ce
lev
els
is
p
r
o
v
id
e
d
in
T
ab
le
8
.
T
h
e
d
ata
clea
r
l
y
in
d
icate
s
th
at
th
e
p
r
o
p
o
s
ed
AI
PS
O
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
s
t
h
e
o
t
h
er
m
eth
o
d
s
i
n
ter
m
s
o
f
ef
f
icien
cy
,
r
o
b
u
s
tn
e
s
s
,
an
d
ac
cu
r
ac
y
in
tr
ac
k
in
g
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
Ov
er
all,
th
e
AI
PS
O
-
b
ased
MPPT
ap
p
r
o
ac
h
ex
h
ib
its
s
ig
n
if
ican
tly
im
p
r
o
v
e
d
d
y
n
am
ic
an
d
s
tead
y
-
s
tate
p
er
f
o
r
m
an
ce
,
v
alid
atin
g
its
ef
f
ec
tiv
en
ess
f
o
r
PV
s
y
s
tem
s
o
p
er
atin
g
u
n
d
er
co
n
s
tan
t
ir
r
ad
ian
ce
co
n
d
itio
n
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
h
ig
h
l
ig
h
t
th
at
AI
PS
O
r
ea
ch
es
th
e
MPP
q
u
ick
ly
with
n
eg
lig
ib
le
s
tead
y
-
s
tate
r
ip
p
le,
m
atch
in
g
th
e
h
ig
h
est p
o
we
r
an
d
ef
f
icien
cy
am
o
n
g
co
m
p
ar
ed
m
eth
o
d
s
.
Fig
u
r
e
5.
Per
f
o
r
m
an
c
e
co
m
p
ar
is
o
n
u
n
d
er
u
n
if
o
r
m
ir
r
ad
ian
ce
co
n
d
itio
n
s
(
1
0
0
0
W
/m
2
)
T
ab
le
8.
C
o
m
p
a
r
is
o
n
o
f
d
if
f
e
r
en
t M
PP
T
alg
o
r
ith
m
s
u
n
d
e
r
u
n
if
o
r
m
ir
r
ad
ian
ce
c
o
n
d
itio
n
s
A
l
g
o
r
i
t
h
m
C
o
n
v
e
r
g
e
n
c
e
t
i
me
(
s)
P
o
w
e
r
(
W
)
Ef
f
i
c
i
e
n
c
y
(
%)
S
t
e
a
d
y
st
a
t
e
o
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i
l
l
a
t
i
o
n
s
S
t
a
n
d
a
r
d
P
S
O
0
.
3
3
2
3
9
.
1
9
9
.
5
Ze
r
o
F
i
r
e
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l
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l
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o
r
i
t
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m
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.
6
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.
8
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1
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P
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.
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8
Ze
r
o
Evaluation Warning : The document was created with Spire.PDF for Python.