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15
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1
,
Feb
r
u
ar
y
20
25
,
p
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1
0
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I
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1
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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8
8
-
8
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0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
1
5
-
1
0
2
6
1016
o
p
er
atin
g
p
o
in
t
o
f
th
e
s
y
s
tem
ca
n
b
e
c
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tr
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lled
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f
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ax
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ith
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it to
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MPP a
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s
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ch
as
in
cr
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(
I
C
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[
3
]
,
p
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tu
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b
a
n
d
o
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v
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(
P&
O)
[
4
]
,
an
d
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ill
clim
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in
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(
HC
)
[
5
]
ca
n
b
e
im
p
lem
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te
d
to
tr
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k
m
ax
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m
p
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lls
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f
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m
th
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p
tim
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lu
tio
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[
6
]
.
I
f
th
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asic
P&
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t
o
b
e
c
h
o
s
en
b
ef
o
r
e
r
u
n
n
in
g
th
e
s
y
s
tem
.
T
h
e
al
g
o
r
ith
m
will
c
o
n
v
er
g
e
s
lo
wly
to
t
h
e
MPP,
i
f
th
e
s
tep
v
al
u
e
is
to
o
l
o
w,
o
th
er
wis
e
if
th
e
s
tep
v
alu
e
is
s
et
to
o
h
ig
h
,
th
e
alg
o
r
ith
m
co
n
v
er
g
es r
ap
id
ly
b
u
t h
i
g
h
f
lu
ctu
atio
n
s
in
o
u
tp
u
t p
o
wer
will a
r
is
e.
T
o
h
elp
o
v
er
co
m
e
th
is
p
r
o
b
lem
,
v
a
r
iab
le
s
tep
P&
O
is
s
u
g
g
ested
b
y
Yad
av
e
t a
l.
[
7
]
.
I
n
o
r
d
er
to
p
r
o
tect
PV
ce
lls
ag
ain
s
t
o
v
er
h
ea
tin
g
d
u
e
t
o
s
h
ad
in
g
,
b
y
p
ass
d
io
d
es
ar
e
co
n
n
e
cted
ac
r
o
s
s
ea
ch
g
r
o
u
p
o
f
ce
lls
.
Ho
wev
er
,
in
ca
s
e
o
f
o
cc
u
r
r
en
ce
o
f
p
ar
tial
s
h
ad
in
g
,
wh
er
e
th
ese
g
r
o
u
p
s
o
f
PV
ce
lls
ar
e
r
ec
eiv
in
g
d
if
f
e
r
en
t
ir
r
ad
ian
ce
am
o
u
n
ts
,
th
e
in
v
o
l
v
em
en
t
o
f
b
y
p
ass
d
io
d
es
will
ca
u
s
e
th
e
P
-
V
cu
r
v
e
to
h
av
e
m
u
ltip
le
p
ea
k
s
[
8
]
an
d
th
er
ef
o
r
e,
m
ak
es
it
ch
allen
g
in
g
to
t
r
ac
k
th
e
MPP.
T
h
er
ef
o
r
e,
th
e
ad
d
itio
n
al
co
s
t
o
f
b
y
p
ass
d
io
d
es
m
u
s
t
n
o
t
wo
r
s
en
th
e
s
y
s
tem
p
er
f
o
r
m
an
ce
a
n
d
th
at
is
ac
h
iev
ab
le
b
y
d
esig
n
in
g
a
s
m
ar
t
co
n
tr
o
l
s
ch
em
e
th
at
tr
ac
k
s
th
e
o
p
tim
al
p
o
in
t w
h
ich
lead
s
to
f
u
ll e
x
p
l
o
itatio
n
o
f
s
y
s
tem
p
o
ten
tials
.
Dete
r
m
in
is
tic
alg
o
r
ith
m
s
s
u
ch
as
P&
O
an
d
I
C
ca
n
n
o
t
alwa
y
s
g
u
ar
an
tee
tr
ac
k
in
g
th
e
MPP
as
th
es
e
alg
o
r
ith
m
s
o
n
ce
c
o
n
v
e
r
g
in
g
t
o
a
s
p
ec
if
ic
s
o
lu
tio
n
it
s
to
p
lo
o
k
in
g
f
o
r
b
etter
s
o
lu
tio
n
s
in
t
h
e
s
ea
r
ch
s
p
ac
e,
i
n
o
th
er
wo
r
d
s
,
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
th
ese
alg
o
r
ith
m
s
ar
e
p
r
o
n
e
to
lo
ca
l
o
p
ti
m
a
en
tr
ap
m
en
t
[
9
]
.
E
n
tr
ap
m
en
t
in
l
o
ca
l
o
p
tim
a
r
e
lates
to
th
e
in
a
b
ilit
y
o
f
th
e
alg
o
r
ith
m
to
d
ec
i
d
e
wh
eth
e
r
th
e
f
o
u
n
d
s
o
lu
tio
n
in
a
lo
ca
l
r
eg
io
n
in
th
e
s
ea
r
ch
s
p
ac
e
is
th
e
o
p
tim
al
s
o
lu
tio
n
in
th
e
en
tire
s
ea
r
ch
s
p
ac
e.
Sin
ce
r
ea
l
en
g
in
ee
r
in
g
p
r
o
b
lem
s
h
a
v
e
a
v
er
y
lar
g
e
n
u
m
b
er
o
f
lo
ca
l
s
o
lu
tio
n
s
,
o
n
e
c
an
n
o
t
r
ely
o
n
d
eter
m
in
is
tic
alg
o
r
ith
m
s
f
o
r
f
in
d
in
g
th
e
g
lo
b
al
o
p
tim
u
m
.
Fo
r
s
o
lv
in
g
o
p
tim
izatio
n
p
r
o
b
lem
s
wh
er
e
th
e
s
ea
r
ch
lan
d
s
ca
p
e
co
n
tain
s
s
ev
er
al
p
ea
k
s
,
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
d
em
o
n
s
tr
ated
ex
c
ellen
t
s
u
b
s
titu
tio
n
to
th
e
d
ete
r
m
in
is
tic
alg
o
r
ith
m
s
.
T
h
an
k
s
to
th
e
r
an
d
o
m
n
ess
in
tr
o
d
u
ce
d
th
e
s
ea
r
ch
f
o
r
th
e
g
lo
b
al
o
p
tim
al
v
alu
e,
m
et
ah
eu
r
is
tic
alg
o
r
ith
m
ca
n
ch
e
ck
f
o
r
e
v
en
b
etter
s
o
lu
tio
n
s
ev
en
af
ter
f
in
d
i
n
g
a
g
o
o
d
s
o
lu
tio
n
i
n
a
s
p
ec
if
ic
r
eg
io
n
in
th
e
s
ea
r
ch
s
p
ac
e.
it
ca
n
s
ea
r
ch
at
th
e
v
icin
ity
o
f
th
e
f
o
u
n
d
b
est
s
o
l
u
tio
n
wh
ich
in
cr
ea
s
e
t
h
e
ch
a
n
ce
o
f
f
in
d
in
g
th
e
g
lo
b
al
o
p
ti
m
al
s
o
lu
tio
n
i
n
th
e
o
v
er
all
s
ea
r
ch
s
p
ac
e
[
1
0
]
.
I
n
th
e
last
two
d
ec
ad
es,
r
esear
ch
er
s
h
a
v
e
p
r
o
p
o
s
ed
m
an
y
t
y
p
es
o
f
alg
o
r
ith
m
s
b
y
im
itatin
g
n
atu
r
al
p
h
en
o
m
en
a.
A
wid
e
n
u
m
b
e
r
o
f
r
esear
ch
er
s
ex
p
lo
ited
m
eta
h
eu
r
is
tic
alg
o
r
ith
m
s
to
tr
ac
k
th
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
[
1
1
]
.
T
h
an
k
s
to
its
f
ast
co
n
v
er
g
en
ce
a
n
d
s
im
p
licity
o
f
im
p
lem
en
tati
o
n
,
s
ev
er
al
s
tu
d
ies
in
[
1
2
]
–
[
1
4
]
s
u
g
g
ested
th
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
to
f
e
tch
f
o
r
th
e
GM
PP
.
Had
ji
et
a
l.
[
1
5
]
p
r
esen
ted
an
MPPT
alg
o
r
ith
m
u
s
in
g
th
e
g
en
etic
alg
o
r
ith
m
.
Dif
f
er
e
n
tial
ev
o
lu
tio
n
alg
o
r
ith
m
[
1
6
]
,
s
n
ak
e
o
p
tim
izer
alg
o
r
ith
m
[
1
7
]
a
n
d
g
r
e
y
-
wo
lf
alg
o
r
ith
m
[
1
8
]
ar
e
ex
p
lo
ited
as
well
in
th
e
d
ev
elo
p
m
en
t
o
f
ef
f
icien
t
MPPT
alg
o
r
ith
m
s
esp
ec
ially
f
o
r
r
ap
id
ly
ch
an
g
i
n
g
atm
o
s
p
h
er
ic
co
n
d
itio
n
s
.
Ma
n
y
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
h
av
e
b
ee
n
s
u
g
g
ested
in
liter
atu
r
e
.
Acc
o
r
d
in
g
t
o
n
o
f
r
ee
lu
n
ch
th
eo
r
em
s
tated
in
[
1
9
]
,
n
o
n
e
o
f
s
u
ch
alg
o
r
ith
m
s
ca
n
s
o
lv
e
all
o
p
tim
izatio
n
p
r
o
b
le
m
s
with
th
e
s
am
e
ef
f
icien
c
y
,
if
o
n
e
o
f
th
ese
alg
o
r
ith
m
s
p
e
r
f
o
r
m
s
well
f
o
r
g
iv
e
n
o
p
tim
i
za
tio
n
p
r
o
b
lem
it
m
ay
lead
t
o
p
o
o
r
s
o
lu
tio
n
s
f
o
r
an
o
th
er
p
r
o
b
lem
.
I
n
th
at
r
eg
a
r
d
,
f
lam
in
g
o
s
ea
r
c
h
alg
o
r
ith
m
[
2
0
]
is
s
u
g
g
ested
to
tr
ac
k
th
e
GM
PP
in
a
PV
s
y
s
tem
.
Nu
m
er
o
u
s
b
en
ch
m
ar
k
test
s
wer
e
co
n
d
u
cted
to
p
r
o
v
e
th
e
s
u
p
er
io
r
ity
in
p
er
f
o
r
m
an
c
e
o
f
th
is
alg
o
r
ith
m
o
v
er
n
u
m
er
o
u
s
p
o
p
u
lar
m
eta
h
eu
r
is
tic
alg
o
r
ith
m
s
.
I
n
ad
d
itio
n
,
th
e
al
g
o
r
ith
m
h
as
b
ee
n
alr
ea
d
y
ex
p
lo
ited
in
d
if
f
er
en
t
f
ield
s
.
T
o
n
am
e
a
f
ew
o
f
its
u
s
es,
I
t
is
u
s
ed
to
f
in
d
o
p
tim
al
r
o
u
tes
in
co
m
p
u
ter
n
etwo
r
k
s
[
2
1
]
,
im
p
lem
en
ted
in
cl
o
u
d
co
m
p
u
t
in
g
f
ield
to
s
ch
ed
u
le
task
s
f
o
r
in
ter
n
et
o
f
th
in
g
s
d
e
v
ice
[
2
2
]
an
d
,
s
u
g
g
ested
to
f
o
r
ec
ast
r
ain
f
alls
[
2
3
]
a
n
d
to
d
etec
t
ca
n
ce
r
v
ia
im
ag
e
p
r
o
ce
s
s
in
g
[
2
4
]
.
T
h
is
p
ap
e
r
is
o
r
g
an
iz
ed
as
f
o
llo
w:
s
o
lar
ce
ll
m
o
d
ellin
g
an
d
p
a
r
tial
s
h
a
d
in
g
c
o
n
d
itio
n
s
ar
e
ex
am
in
e
d
,
im
p
ac
t
o
f
s
elec
tio
n
o
f
DC
-
DC
co
n
v
er
ter
o
n
th
e
s
y
s
tem
is
d
i
s
cu
s
s
ed
af
ter
wo
r
d
,
an
d
n
ex
t,
th
e
f
lam
in
g
o
s
ea
r
c
h
alg
o
r
ith
m
is
ex
p
lain
e
d
b
r
ief
ly
,
th
en
,
th
e
u
s
e
o
f
th
is
alg
o
r
ith
m
to
tr
ac
k
GM
P
P
u
n
d
er
d
if
f
er
e
n
t
s
ce
n
ar
io
s
.
Fin
ally
,
s
im
u
latio
n
is
co
n
d
u
cted
to
ch
ec
k
th
e
tr
ac
k
in
g
p
e
r
f
o
r
m
an
ce
a
n
d
to
o
b
s
er
v
e
th
e
in
f
l
u
en
ce
o
f
p
o
p
u
la
tio
n
s
ize
o
n
th
e
b
eh
av
io
r
o
f
th
e
alg
o
r
ith
m
.
2.
M
E
T
H
O
D
I
n
th
e
f
o
llo
win
g
s
u
b
s
ec
tio
n
s
,
th
e
m
ain
co
m
p
o
n
en
ts
in
v
o
lv
ed
in
o
u
r
m
o
d
el
will
b
e
ex
am
in
ed
.
I
n
ad
d
itio
n
,
th
e
p
ar
tial
s
h
ad
i
n
g
co
n
d
itio
n
an
d
t
h
e
in
s
p
ir
at
io
n
o
f
th
e
alg
o
r
ith
m
will
b
e
d
is
cu
s
s
ed
b
r
ief
ly
.
Ad
ap
tatio
n
o
f
th
e
FS
A
alg
o
r
ith
m
f
o
r
MPPT
is
ex
p
lain
e
d
in
a
f
o
r
m
o
f
a
f
lo
wch
a
r
t.
Fin
ally
,
th
e
elec
tr
ical
ch
ar
ac
ter
is
tics
o
f
th
e
u
s
ed
PV
m
o
d
u
le
alo
n
g
with
s
im
u
latio
n
m
o
d
el
ar
e
p
r
esen
ted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
o
ve
l g
lo
b
a
l m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
b
a
s
ed
o
n
fla
min
g
o
s
ea
r
ch
a
lg
o
r
ith
m
…
(
A
b
d
elg
h
a
n
i D
r
a
o
u
i
)
1017
2
.
1
.
T
he
pa
rt
ia
l sh
a
din
g
ph
e
no
m
ena
Giv
en
th
at
th
e
PV
s
y
s
tem
is
in
s
talled
in
o
u
td
o
o
r
s
p
ac
es,
it
is
o
cc
asio
n
ally
s
u
b
jecte
d
to
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
wh
e
r
e
d
if
f
er
en
t
p
a
r
ts
o
f
th
e
s
y
s
tem
r
ec
eiv
e
d
if
f
er
e
n
t
lev
els
o
f
s
o
lar
ir
r
ad
ian
ce
.
I
n
o
th
e
r
wo
r
d
s
,
if
th
e
PV
p
an
el
is
p
a
r
tially
s
h
ad
ed
,
th
e
lar
g
e
cu
r
r
en
t
g
en
er
ated
b
y
th
e
ce
lls
r
ec
eiv
in
g
th
e
h
i
g
h
est
ir
r
ad
ian
ce
lev
el
will
p
ass
th
r
o
u
g
h
th
e
PV
ce
lls
ex
p
o
s
ed
to
lo
wer
ir
r
ad
ian
ce
lev
els
an
d
th
er
ef
o
r
e
th
e
latter
ce
lls
will
b
e
ac
tin
g
as
a
r
esi
s
tiv
e
lo
ad
,
th
is
latter
will
h
ea
t
u
p
lea
d
in
g
p
r
o
b
ab
ly
to
its
ir
r
ev
er
s
ib
le
d
am
ag
e.
T
o
h
elp
ad
d
r
ess
th
is
is
s
u
e,
an
alter
n
ativ
e
r
o
u
te
f
o
r
th
e
cu
r
r
e
n
t
is
p
r
o
v
id
ed
b
y
co
n
n
ec
tin
g
ea
c
h
g
r
o
u
p
o
f
ce
lls
to
a
b
y
p
ass
d
io
d
e.
Mo
r
eo
v
er
,
th
e
in
teg
r
atio
n
o
f
b
y
p
ass
d
io
d
es
ac
r
o
s
s
ea
ch
g
r
o
u
p
o
f
ce
lls
will
b
e
ca
u
s
in
g
t
h
e
o
v
er
all
P
-
V
cu
r
v
e
to
h
av
e
m
u
ltip
le
p
ea
k
s
[
2
5
]
,
wh
er
e
o
n
ly
o
n
e
p
ea
k
will
lead
to
ex
tr
ac
tio
n
o
f
h
ig
h
est
p
o
wer
f
o
r
th
e
s
y
s
tem
an
d
it
is
r
ef
er
r
ed
as
th
e
GM
PP
wh
ile
th
e
o
th
er
lo
wer
p
ea
k
s
a
r
e
r
ef
er
r
e
d
as
l
o
c
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
L
MPP)
.
T
h
e
m
a
x
im
u
m
p
o
s
s
ib
le
n
u
m
b
er
o
f
p
ea
k
s
in
th
e
P
-
V
cu
r
v
e
is
eq
u
al
to
t
h
e
n
u
m
b
er
o
f
b
y
p
ass
d
io
d
es.
I
n
th
e
t
y
p
ical
PV
p
an
el,
th
r
ee
b
y
p
ass
d
io
d
es
ar
e
u
s
ed
[
2
6
]
.
B
ein
g
u
n
d
er
p
a
r
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
,
F
ig
u
r
e
1
illu
s
tr
ates th
e
d
if
f
er
e
n
t r
esu
ltin
g
P
-
V
cu
r
v
es o
f
th
e
s
y
s
tem
with
an
d
with
o
u
t b
y
p
a
s
s
d
io
d
es
.
Simu
latio
n
will
b
e
ca
r
r
ied
o
u
t
o
n
th
e
co
m
m
e
r
cial
J
in
k
o
s
o
lar
J
KM
1
9
0
M
-
7
2
B
m
o
d
u
le
wh
o
s
e
m
ax
p
o
wer
at
th
e
s
tan
d
ar
d
r
u
n
n
in
g
co
n
d
itio
n
s
is
1
9
0
W
at
a
v
o
lt
ag
e
o
f
3
6
.
6
V.
W
h
en
th
e
m
o
d
u
le
is
s
u
b
jecte
d
to
th
e
s
h
ad
in
g
s
ce
n
ar
io
d
ep
icted
in
Fig
u
r
e
2
(
a)
an
d
wh
o
s
e
co
r
r
esp
o
n
d
in
g
P
-
V
cu
r
v
e
is
s
h
o
wn
in
Fig
u
r
e
2
(
b
)
.
I
t
is
wo
r
th
n
o
tin
g
t
h
at
GM
PP
lo
ca
tio
n
is
s
tr
o
n
g
ly
d
e
p
en
d
e
n
t o
n
th
e
s
h
ad
in
g
p
atter
n
.
Fig
u
r
e
1
.
E
f
f
ec
t o
f
b
y
p
ass
d
io
d
e
o
n
t
h
e
r
esu
ltin
g
P
-
V
c
u
r
v
e
(
a)
(
b
)
Fig
u
r
e
2
.
T
h
e
J
in
k
o
s
o
lar
J
KM
1
9
0
M
-
7
2
B
(
a)
s
im
u
lated
s
h
ad
i
n
g
p
atter
n
on
a
n
d
(
b
)
c
h
ar
ac
te
r
is
tics
cu
r
v
es
wh
en
s
u
b
jecte
d
to
p
ar
tial sh
ad
in
g
co
n
d
itio
n
s
d
ep
icted
i
n
Fig
u
r
e
2
(
a
)
2
.
2
.
DC
-
DC
co
nv
er
t
er
s
elec
t
io
n c
rit
er
ia
I
n
o
r
d
e
r
to
b
e
a
b
le
to
co
n
tr
o
l
th
e
o
p
er
atin
g
p
o
in
t
an
d
ev
en
tu
ally
r
ea
ch
th
e
MPP,
th
e
lo
a
d
m
u
s
t
b
e
co
n
n
ec
ted
to
th
e
PV
s
y
s
tem
v
ia
a
DC
-
DC
co
n
v
er
ter
.
T
h
e
DC
-
DC
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e
is
co
n
tr
o
lled
v
ia
a
s
em
ico
n
d
u
cto
r
s
witch
.
Fo
r
a
g
iv
en
lo
a
d
im
p
ed
an
ce
,
th
e
v
alu
e
o
f
d
u
ty
c
y
cle
at
wh
i
ch
th
is
s
witch
is
o
p
er
ated
will
d
ef
in
e
th
e
v
alu
e
o
f
co
n
v
er
ter
’
s
in
p
u
t
im
p
ed
an
ce
.
T
h
is
in
p
u
t
im
p
e
d
an
ce
s
ee
n
b
y
th
e
PV
s
y
s
tem
as
,
will
lead
to
o
p
er
a
tio
n
at
a
g
iv
en
o
p
e
r
atin
g
p
o
in
t
in
t
h
e
PV
-
cu
r
v
e.
I
n
o
th
e
r
w
o
r
d
s
,
to
en
s
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
1
5
-
1
0
2
6
1018
o
p
er
atio
n
at
th
e
MPP,
th
is
in
p
u
t
im
p
ed
an
ce
s
h
o
u
l
d
m
atch
th
e
wh
ich
is
eq
u
al
to
th
e
r
atio
o
f
o
v
er
.
I
n
ad
d
itio
n
,
th
e
r
an
g
e
o
f
p
o
s
s
ib
le
v
alu
es
o
f
in
p
u
t
im
p
ed
a
n
ce
d
ep
en
d
s
o
n
t
h
e
ty
p
e
o
f
DC
-
DC
co
n
v
er
ter
,
th
e
in
p
u
t
im
p
ed
a
n
ce
v
alu
e
ca
n
b
e
d
ed
u
ce
d
as
th
e
r
atio
o
f
v
o
ltag
e
an
d
cu
r
r
en
t.
T
ab
le
1
s
h
o
ws
th
e
v
alu
es
o
f
cu
r
r
en
t,
v
o
ltag
e
a
n
d
in
p
u
t im
p
ed
an
ce
d
e
p
en
d
in
g
o
n
s
o
m
e
ty
p
es o
f
DC
-
DC
co
n
v
er
ter
s
.
T
ab
le
1
.
I
n
p
u
t a
n
d
o
u
tp
u
t
r
elatio
n
s
h
ip
o
f
s
o
m
e
DC
/DC
co
n
v
er
ter
s
Ty
p
e
o
f
c
o
n
v
e
r
t
e
r
V
o
l
t
a
g
e
e
q
u
a
t
i
o
n
C
u
r
r
e
n
t
e
q
u
a
t
i
o
n
I
mp
e
d
a
n
c
e
e
q
u
a
t
i
o
n
B
u
c
k
=
1
.
=
.
=
1
2
.
B
o
o
st
=
(
1
−
)
.
=
1
1
−
.
=
(
1
−
)
²
.
B
u
c
k
-
B
o
o
st
=
−
1
−
.
=
−
1
−
.
=
(
1
−
)
2
2
.
I
n
o
r
d
er
to
k
n
o
w
th
e
o
p
er
at
io
n
al
r
eg
i
o
n
o
f
ea
c
h
co
n
v
er
ter
,
v
alu
es
o
f
an
d
m
u
s
t
b
e
co
m
p
ar
ed
[
2
7
]
.
Fo
r
in
s
tan
ce
,
f
o
r
a
b
u
c
k
co
n
v
er
ter
,
if
is
les
s
th
an
,
it
is
im
p
o
s
s
ib
le
to
o
p
er
ate
th
e
s
y
s
tem
at
th
e
MP
P.
I
n
ess
en
c
e
th
e
s
elec
tio
n
o
f
co
n
v
er
ter
is
b
ased
o
n
s
ize
o
f
lo
ad
im
p
ed
a
n
ce
s
ee
n
b
y
th
e
PV
p
an
el
an
d
o
n
PV
p
an
el
its
elf
,
m
ax
im
u
m
p
o
we
r
p
o
in
t
im
p
e
d
an
ce
.
Fro
m
Fig
u
r
e
3
(
a
)
it
is
n
o
ticed
th
at
th
e
b
u
ck
co
n
v
er
ter
s
h
o
u
ld
b
e
o
p
e
r
ated
at
a
lo
w
d
u
ty
cy
cle
t
o
en
s
u
r
e
a
h
ig
h
v
o
ltag
e
at
its
in
p
u
t
p
o
r
t.
C
o
n
v
er
s
ely
,
f
r
o
m
F
ig
u
r
e
3
(
b
)
,
it
is
m
an
d
ato
r
y
f
o
r
b
o
o
s
t
co
n
v
er
ter
to
b
e
o
p
er
atin
g
at
h
ig
h
d
u
ty
cy
cle
to
tr
ac
k
th
e
MPP.
Op
er
atin
g
co
n
d
itio
n
s
o
f
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
is
s
im
ilar
to
th
at
o
f
th
e
b
u
ck
c
o
n
v
e
r
ter
a
s
ca
n
b
e
s
ee
n
f
r
o
m
Fig
u
r
e
3
(
c)
.
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
O
p
e
r
atio
n
al
r
e
g
io
n
s
ac
co
r
d
in
g
to
v
alu
es
o
f
an
d
f
o
r
: (
a)
b
u
ck
co
n
v
er
ter
,
(
b
)
b
o
o
s
t
co
n
v
er
ter
,
an
d
(
c)
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
o
ve
l g
lo
b
a
l m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
b
a
s
ed
o
n
fla
min
g
o
s
ea
r
ch
a
lg
o
r
ith
m
…
(
A
b
d
elg
h
a
n
i D
r
a
o
u
i
)
1019
Fo
r
th
e
b
u
c
k
co
n
v
er
ter
th
e
m
in
im
u
m
v
alu
e
wh
ich
e
n
s
u
r
e
o
p
er
ati
n
g
i
n
th
e
co
n
tin
u
o
u
s
m
o
d
e
is
ex
p
r
ess
ed
in
(
1
)
[
2
8
]
.
=
(
1
−
)
2
(
1
)
T
h
e
ca
p
ac
ito
r
o
f
th
e
b
u
c
k
co
n
v
er
ter
s
er
v
es
as
s
m
o
o
th
er
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
,
its
v
alu
e
is
ch
o
s
en
o
n
th
e
b
asis
o
f
th
e
r
ate
o
f
ac
ce
p
tab
le
r
ip
p
les
in
th
e
v
o
ltag
e
wav
e
f
o
r
m
.
is
th
e
l
o
ad
r
esis
tan
ce
v
alu
e
an
d
it
h
as
a
co
n
s
id
er
ab
le
ef
f
ec
t
o
n
th
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
s
y
s
tem
as
d
is
cu
s
s
ed
ea
r
lier
.
I
n
ad
d
itio
n
,
th
e
s
witch
in
g
f
r
eq
u
e
n
cy
o
f
th
e
s
em
ico
n
d
u
ct
o
r
s
witch
o
f
th
e
c
o
n
v
e
r
ter
is
s
elec
ted
as h
ig
h
as th
e
s
witch
ca
n
s
u
p
p
o
r
t
.
2
.
3
.
T
he
f
la
m
ing
o
s
ea
rc
h a
lg
o
rit
hm
F
lam
in
g
o
s
ea
r
ch
alg
o
r
it
h
m
(
F
SA
)
is
a
n
ew
s
war
m
in
tellig
e
n
ce
o
p
tim
izatio
n
alg
o
r
ith
m
.
I
t
is
in
s
p
ir
ed
f
r
o
m
th
e
m
ig
r
ato
r
y
an
d
f
o
r
ag
in
g
b
eh
av
io
r
s
o
f
f
lam
in
g
o
s
.
Flam
in
g
o
b
ir
d
s
ar
e
s
o
cial
m
ig
r
ato
r
y
an
im
als
th
at
f
ee
d
m
o
s
tly
o
n
u
n
d
er
wate
r
p
lan
ts
an
d
in
s
ec
ts
,
F
ig
u
r
e
4
s
h
o
ws
a
g
r
o
u
p
o
f
t
h
ese
an
im
als.
Fig
u
r
e
4
.
A
g
r
o
u
p
o
f
f
lam
in
g
o
b
ir
d
s
T
h
e
Flam
in
g
o
b
ir
d
s
liv
e
in
a
r
ea
s
r
ich
in
f
o
o
d
.
Af
ter
e
x
h
a
u
s
tin
g
th
e
f
o
o
d
in
th
at
ar
ea
,
f
lam
in
g
o
s
p
o
p
u
latio
n
m
o
v
e
elsewh
er
e
w
h
en
th
e
f
o
o
d
in
th
e
r
eg
io
n
is
d
ec
r
ea
s
ed
to
a
q
u
a
n
tity
th
at
is
n
o
t
en
o
u
g
h
f
o
r
t
h
e
g
r
o
u
p
[
2
9
]
.
T
h
e
f
lam
in
g
o
s
ea
r
ch
alg
o
r
ith
m
d
em
o
n
s
tr
ate
a
g
o
o
d
tr
ad
eo
f
f
b
etwe
en
ex
p
lo
itati
o
n
an
d
ex
p
l
o
r
atio
n
o
p
er
atio
n
s
an
d
test
s
o
n
th
is
a
lg
o
r
ith
m
,
p
r
o
v
ed
th
e
s
u
p
er
i
o
r
ity
o
f
th
e
FS
A
o
v
er
m
a
n
y
p
o
p
u
lar
o
p
tim
izatio
n
alg
o
r
ith
m
s
[
2
0
]
.
W
h
en
th
e
s
war
m
o
f
f
lam
in
g
o
b
ir
d
s
ar
e
f
o
r
ag
in
g
f
o
r
f
o
o
d
,
t
h
e
b
ir
d
f
in
d
in
g
a
s
o
u
r
ce
o
f
f
o
o
d
in
th
e
r
eg
io
n
will
s
in
g
to
in
f
o
r
m
f
o
r
th
e
av
ailab
ilit
y
o
f
f
o
o
d
in
its
lo
ca
tio
n
.
W
h
ile
r
em
ain
in
g
im
m
o
b
ile
an
d
th
a
n
k
s
to
its
lo
n
g
n
ec
k
an
d
u
s
in
g
its
b
ea
k
,
th
is
b
ir
d
will
s
tar
t
s
ca
n
n
in
g
th
e
n
eig
h
b
o
r
h
o
o
d
f
o
r
a
lo
ca
tio
n
r
ich
er
in
f
o
o
d
an
d
m
a
y
m
o
v
e
its
b
o
d
y
to
wa
r
d
d
ir
ec
tio
n
with
ab
u
n
d
a
n
t
f
o
o
d
,
th
is
b
eh
a
v
io
r
in
s
p
ir
es
th
e
e
x
p
lo
itatio
n
p
ar
t
o
f
th
e
alg
o
r
ith
m
.
W
h
en
a
f
lam
i
n
g
o
b
ir
d
f
in
d
s
a
s
o
u
r
ce
o
f
f
o
o
d
in
its
cu
r
r
en
t
lo
ca
tio
n
,
its
f
o
r
ag
in
g
b
e
h
av
io
r
co
n
s
is
ts
o
f
s
ca
n
n
in
g
s
lo
wly
t
h
e
n
eig
h
b
o
r
in
g
s
p
ac
e
b
y
m
o
v
in
g
its
f
ee
t,
o
n
e
at
th
e
tim
e
a
n
d
b
y
s
ca
n
n
in
g
th
e
u
n
d
er
wate
r
with
its
b
ea
k
.
In
(
2
)
s
im
u
late
th
e
m
o
v
e
m
en
t o
f
th
e
ℎ
in
d
iv
id
u
al
in
th
e
ℎ
d
im
en
s
io
n
.
+
1
=
(
+
ɛ
1
+
2
|
1
+
ɛ
2
|
)
/
(
2
)
T
o
ac
co
u
n
t
f
o
r
r
an
d
o
m
n
ess
o
f
d
ir
ec
tio
n
o
f
m
o
v
em
en
t
o
f
its
f
ee
t
an
d
to
r
ep
r
esen
t
th
e
r
a
n
d
o
m
b
ea
k
tr
ajec
to
r
y
,
r
an
d
o
m
p
ar
am
eter
s
ɛ
1
,
ɛ
2
,
1
an
d
,
2
ar
e
in
tr
o
d
u
ce
d
.
An
o
t
h
er
r
a
n
d
o
m
K
p
ar
am
eter
is
in
tr
o
d
u
ce
d
to
co
n
s
id
er
th
e
p
h
y
s
ical
d
if
f
er
e
n
ce
s
b
etwe
en
th
e
b
ir
d
s
,
s
u
ch
as
len
g
th
o
f
f
ee
t
an
d
b
ea
k
.
r
ep
r
esen
ts
th
e
cu
r
r
en
t
b
est
lo
ca
tio
n
in
th
e
ℎ
d
im
en
s
io
n
.
W
h
en
f
o
o
d
d
im
i
n
is
h
in
th
e
p
r
esen
t
liv
in
g
ar
ea
,
th
e
f
lam
in
g
o
g
r
o
u
p
tr
a
v
els
to
war
d
s
a
n
ew
ar
ea
r
ich
er
in
f
o
o
d
.
Su
p
p
o
s
in
g
th
at
th
e
p
o
s
itio
n
o
f
th
at
n
ew
ar
ea
in
th
e
ℎ
d
im
en
s
io
n
is
an
d
a
d
o
p
tin
g
th
e
r
an
d
o
m
p
ar
am
eter
w
to
tak
e
in
t
o
co
n
s
id
er
atio
n
th
e
r
a
n
d
o
m
n
ess
in
th
e
d
ec
is
io
n
o
f
ea
ch
b
ir
d
,
th
e
f
o
r
m
u
la
o
f
th
e
m
ig
r
atio
n
o
f
th
e
ℎ
f
lam
in
g
o
b
ir
d
is
s
tated
in
(
3
)
.
p
ar
am
eter
is
a
Gau
s
s
ian
r
an
d
o
m
n
u
m
b
er
u
s
ed
to
ex
p
an
d
th
e
s
ea
r
ch
s
p
ac
e
d
u
r
in
g
th
e
m
i
g
r
atio
n
o
f
f
lam
in
g
o
s
an
d
ac
co
u
n
t
f
o
r
t
h
e
ar
b
itra
r
y
b
e
h
av
io
r
s
o
f
ea
ch
b
ir
d
in
th
e
s
p
ec
if
ic
m
ig
r
atio
n
p
r
o
ce
s
s
.
+
1
=
+
∗
(
−
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
1
5
-
1
0
2
6
1020
I
n
s
u
m
m
ar
y
,
th
e
p
o
p
u
latio
n
o
f
b
ir
d
s
,
in
itially
,
will
b
e
s
u
b
d
iv
id
ed
in
to
a
f
o
r
ag
in
g
g
r
o
u
p
an
d
m
ig
r
atin
g
g
r
o
u
p
.
Fit
n
ess
v
alu
es
o
f
b
i
r
d
s
ar
e
o
b
tain
e
d
,
b
ir
d
s
with
lo
wer
f
itn
ess
v
alu
e
will
jo
in
t
h
e
m
ig
r
atin
g
g
r
o
u
p
an
d
th
e
o
n
es h
av
in
g
h
ig
h
er
f
itn
ess
v
alu
es will jo
in
th
e
f
o
r
ag
in
g
g
r
o
u
p
.
T
h
e
p
o
s
itio
n
o
f
ea
ch
b
ir
d
will b
e
u
p
d
ated
ac
co
r
d
in
g
to
t
h
e
g
r
o
u
p
to
wh
ich
it
b
elo
n
g
s
.
T
h
e
p
o
s
itio
n
o
f
b
est
in
d
iv
id
u
al
w
h
ich
r
ep
r
esen
ts
th
e
o
p
tim
al
s
o
lu
tio
n
is
s
to
r
ed
f
o
r
th
e
n
ex
t
iter
atio
n
.
T
h
e
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
s
to
p
cr
iter
i
a
is
m
et
o
r
u
n
til
all
iter
atio
n
s
ar
e
p
er
f
o
r
m
ed
an
d
elite
is
g
iv
en
as
s
o
lu
tio
n
.
T
h
e
f
lo
w
c
h
ar
t
b
el
o
w
d
e
p
icted
in
F
ig
u
r
e
5
d
em
o
n
s
tr
ates th
ese
s
tep
s
.
Fig
u
r
e
5
.
Flo
wch
ar
t
o
f
th
e
FS
A
2
.
4
.
Ada
pta
t
io
n o
f
F
SA f
o
r
M
P
P
T
a
pp
l
ica
t
io
n
T
h
e
s
u
g
g
ested
MPPT
b
ased
o
n
th
e
FS
A
is
im
p
lem
en
ted
f
o
r
b
atter
y
-
ch
ar
g
in
g
a
p
p
licatio
n
wh
er
e
a
PV
p
an
el
is
ch
ar
g
in
g
a
b
atter
y
v
i
a
a
DC
-
D
C
b
u
ck
co
n
v
er
ter
.
E
ac
h
f
lam
in
g
o
b
i
r
d
r
ep
r
esen
t
s
th
e
v
alu
e
o
f
d
u
ty
cy
cle.
T
h
e
ar
ea
with
p
len
tifu
l
f
o
o
d
c
o
r
r
esp
o
n
d
s
to
th
e
o
p
er
at
in
g
p
o
i
n
ts
at
th
e
v
icin
ity
o
f
th
e
MPP.
T
h
e
b
ir
d
p
o
s
itio
n
r
e
p
r
esen
ts
a
d
u
ty
cy
cle
v
alu
e
r
an
g
in
g
b
etwe
en
0
a
n
d
1
.
T
h
e
c
o
r
r
esp
o
n
d
in
g
f
itn
ess
v
alu
e
is
th
e
m
ea
s
u
r
ed
p
o
wer
o
b
tain
ed
b
y
test
in
g
th
e
s
y
s
tem
with
th
e
g
iv
en
d
u
ty
c
y
cle.
T
h
e
s
am
e
p
r
o
ce
s
s
is
r
ep
ea
ted
f
o
r
p
o
s
itio
n
s
o
f
th
e
o
th
er
r
em
ai
n
in
g
b
ir
d
s
“
d
u
ty
cy
c
les
.
”
T
h
e
d
u
ty
cy
cle
lea
d
in
g
to
th
e
h
ig
h
est o
u
tp
u
t
p
o
wer
will
b
e
ass
ig
n
ed
as
th
e
b
est
p
o
s
itio
n
.
Nex
t,
b
ir
d
p
o
s
itio
n
s
will
b
e
u
p
d
ated
ac
co
r
d
in
g
to
th
eir
f
itn
ess
v
alu
es
an
d
th
e
s
y
s
tem
will
b
e
ev
alu
ated
with
th
e
n
ew
p
o
s
itio
n
s
.
W
h
en
th
e
r
elativ
e
er
r
o
r
o
f
p
o
wer
s
ΔP
o
f
elite
v
alu
es
d
ec
r
ea
s
ed
b
el
o
w
th
e
s
et
v
alu
e,
th
is
in
d
icate
s
th
at
th
e
latest
b
est
d
u
ty
cy
cle
will
l
ea
d
to
o
p
er
atio
n
at
MPP.
R
elat
iv
e
er
r
o
r
ΔP
is
ca
lcu
lated
in
(
4
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
o
ve
l g
lo
b
a
l m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
b
a
s
ed
o
n
fla
min
g
o
s
ea
r
ch
a
lg
o
r
ith
m
…
(
A
b
d
elg
h
a
n
i D
r
a
o
u
i
)
1021
=
|
−
−
1
|
−
1
∗
100%
(
4
)
Sy
s
tem
will
b
e
k
ep
t
o
p
e
r
atin
g
with
th
is
d
u
ty
c
y
cle,
if
s
h
a
d
in
g
co
n
d
itio
n
s
ch
a
n
g
es,
th
e
MPP
will
ch
an
g
e
its
lo
ca
tio
n
in
th
e
PV
cu
r
v
e
ca
u
s
in
g
th
e
r
elativ
e
er
r
o
r
i
n
p
o
wer
to
i
n
cr
ea
s
e
b
e
y
o
n
d
th
e
s
et
v
alu
e,
th
er
ef
o
r
e,
th
e
FS
A
will
r
u
n
ag
ain
.
Simp
licity
o
f
eq
u
atio
n
s
in
v
o
lv
ed
in
th
e
FS
A
alg
o
r
ith
m
,
lead
s
to
f
ast
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
.
T
h
e
f
l
o
w
ch
ar
t b
elo
w
illu
s
tr
ated
in
Fig
u
r
e
6
d
em
o
n
s
tr
ates th
e
MPP
T
-
FS
A
alg
o
r
ith
m
.
Fig
u
r
e
6
.
Flo
w
ch
a
r
t o
f
t
h
e
p
r
o
p
o
s
ed
MPPT
b
ased
o
n
FS
A
2
.
5
.
Sim
ula
t
i
o
n o
f
t
he
s
y
s
t
e
m
T
h
e
PV
p
an
el
ch
ar
ac
te
r
is
tics
ar
e
b
ased
o
n
th
e
co
m
m
e
r
cial
2
5
0
W
7
2
ce
lls
T
h
e
J
i
n
k
o
So
lar
J
KM
1
9
0
M
-
7
2
B
m
o
d
u
le
wh
o
s
e
p
ar
am
eter
s
ar
e
o
b
tain
e
d
f
r
o
m
th
e
Natio
n
al
R
en
ewa
b
le
E
n
er
g
y
L
ab
o
r
ato
r
y
(
NR
E
L
)
s
y
s
tem
ad
v
is
o
r
m
o
d
el
.
T
h
e
m
o
d
el
ac
cu
r
ac
y
is
v
e
r
y
h
i
g
h
as
s
tated
in
[
3
0
]
.
T
a
b
le
2
s
h
o
w
m
o
d
u
le
elec
tr
ical
ch
ar
ac
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u
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ates th
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ed
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o
d
el
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T
L
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u
lin
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I
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N
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2
0
8
8
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8
I
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&
C
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m
p
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n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
1
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1
0
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1022
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RE
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e
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io
s
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en
o
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atin
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n
n
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m
al
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n
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itio
n
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an
d
ii)
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er
atin
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n
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e
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tial
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ad
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n
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itio
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itially
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ize
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f
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u
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et
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ir
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s
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t
o
f
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ize
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d
em
o
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ated
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o
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ith
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ile
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u
r
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a
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,
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6
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ter
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ly
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u
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n
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FS
A
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ased
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ac
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g
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Fig
u
r
e
8
(
d
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s
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o
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u
ty
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y
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en
e
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ated
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ck
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2
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Sy
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t
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r
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ely
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r
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u
r
e
9
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,
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im
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m
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ated
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r
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u
r
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3
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3
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o
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nce
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er
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tem
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e
al
g
o
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ith
m
h
as
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ee
n
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with
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o
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ize
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f
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d
th
en
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o
p
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n
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ize
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.
Fig
u
r
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ased
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ith
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its
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ast an
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r
ate
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n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
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g
I
SS
N:
2088
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u
r
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r
e
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ch
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ass
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r
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s
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o
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a
n
d
ty
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ize
o
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th
e
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y
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tem
f
ast
r
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n
s
e
p
r
o
v
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th
e
h
ig
h
r
eliab
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o
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th
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o
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e
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f
o
r
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V
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tem
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in
s
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eg
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r
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ty
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cle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
1
5
-
1
0
2
6
1024
I
n
ca
s
e
o
f
u
n
if
o
r
m
ir
r
ad
ian
ce
,
th
e
s
im
p
ler
alg
o
r
ith
m
s
s
u
ch
as
P&
O,
HC
an
d
,
I
C
tr
ac
k
s
r
ap
id
ly
a
n
d
with
h
ig
h
ac
c
u
r
ac
y
th
e
MPP,
th
er
ef
o
r
e,
th
e
s
u
g
g
ested
m
et
h
o
d
ca
n
u
s
ed
h
y
b
r
id
ized
with
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n
e
o
f
th
e
s
im
p
le
alg
o
r
ith
m
s
at
th
e
ex
p
e
n
s
e
o
f
ad
d
in
g
s
o
lar
ir
r
a
d
ian
ce
s
en
s
o
r
at
th
e
ce
n
ter
o
f
ea
ch
s
o
lar
g
r
o
u
p
co
m
p
o
s
in
g
th
e
PV
m
o
d
u
le.
T
h
e
s
elec
tio
n
o
f
p
o
p
u
latio
n
s
ize
s
h
o
u
ld
b
e
s
ele
cted
wis
ely
.
A
to
o
h
ig
h
v
alu
e
f
o
r
th
is
p
a
r
am
eter
will
lead
to
u
n
n
ec
ess
ar
y
lar
g
e
n
u
m
b
er
s
o
f
test
s
o
f
th
e
s
y
s
tem
wh
ich
is
c
o
m
p
u
tatio
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ally
e
x
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en
s
iv
e.
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to
o
l
o
w
v
alu
e
s
et
f
o
r
th
is
p
ar
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eter
wi
ll
en
s
u
r
e
f
ast
co
n
v
er
g
en
ce
at
t
h
e
r
is
k
o
f
th
e
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