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I
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2088
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3567
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o
r
ith
m
'
s
ab
ilit
y
to
d
is
tin
g
u
is
h
an
d
r
ea
c
h
th
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
GM
PP
)
wh
ile
av
o
id
in
g
lo
ca
l
m
ax
im
u
m
p
o
wer
p
o
in
ts
(
L
MPP)
,
wh
ich
ca
n
lead
to
s
ig
n
if
ican
t
en
e
r
g
y
l
o
s
s
es
if
s
elec
ted
b
y
m
is
tak
e.
T
h
is
is
s
u
e
b
ec
o
m
es
cr
itical
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
wh
e
r
e
class
ical
s
o
lu
tio
n
s
,
s
u
ch
as
th
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
,
h
ill
clim
b
in
g
(
HC
)
,
an
d
in
cr
em
en
tal
co
n
d
u
ctan
ce
(
I
NC
)
m
eth
o
d
s
,
alth
o
u
g
h
s
im
p
le
an
d
wid
ely
u
s
ed
,
m
ay
s
h
o
w
lim
itatio
n
s
in
id
en
tif
y
in
g
an
d
tr
ac
k
in
g
th
e
g
lo
b
al
p
o
w
er
[
2
]
.
T
h
e
ce
n
tr
al
p
r
o
b
lem
is
as
f
o
llo
ws:
to
d
esig
n
an
MPPT
alg
o
r
ith
m
th
at
ef
f
icien
tly
id
en
tifie
s
th
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
wh
ile
m
in
im
izin
g
en
er
g
y
lo
s
s
es,
ev
en
u
n
d
er
c
o
m
p
lex
co
n
d
itio
n
s
s
u
c
h
as
p
a
r
tial
s
h
ad
in
g
.
I
n
th
is
c
o
n
tex
t,
th
e
P&
O
m
eth
o
d
is
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
ap
p
r
o
ac
h
es
f
o
r
MPPT
d
u
e
to
its
s
i
m
p
licity
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
.
Ho
wev
er
,
it
h
as
s
o
m
e
s
ig
n
if
ican
t
lim
itat
io
n
s
,
s
u
ch
as
s
lo
w
tr
ac
k
in
g
s
p
ee
d
d
u
r
in
g
s
u
d
d
en
wea
th
er
ch
an
g
es
an
d
p
h
o
to
v
o
ltaic
p
o
wer
f
lu
ctu
atio
n
s
ar
o
u
n
d
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
(
MPP)
,
lead
in
g
to
co
n
s
id
er
ab
le
en
e
r
g
y
l
o
s
s
es
[
3
]
,
[
4
]
.
Fu
r
th
er
m
o
r
e,
th
e
r
is
k
o
f
lo
s
in
g
th
e
tr
ac
k
i
n
g
p
o
in
t
in
cr
ea
s
es
u
n
d
er
p
ar
tia
l
s
h
ad
in
g
co
n
d
itio
n
s
o
r
a
b
r
u
p
t
v
ar
iatio
n
s
in
s
o
lar
ir
r
ad
ia
n
c
e.
T
o
o
v
e
r
co
m
e
th
ese
lim
ita
tio
n
s
,
r
esear
ch
er
s
in
[
4
]
–
[
6
]
h
a
v
e
p
r
o
p
o
s
ed
u
s
in
g
a
v
ar
iab
le
s
tep
s
ize
in
s
tead
o
f
a
f
ix
ed
s
tep
s
ize
to
im
p
r
o
v
e
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
class
ical
P&
O
m
eth
o
d
[
7
]
,
[
8
]
.
Ho
wev
er
,
m
o
s
t
o
f
th
ese
s
tu
d
i
es
h
av
e
f
o
cu
s
ed
o
n
v
ar
iatio
n
s
in
tem
p
er
atu
r
e
a
n
d
ir
r
ad
ian
ce
wh
ile
n
e
g
lectin
g
th
e
s
p
ec
if
ic
ch
allen
g
es a
s
s
o
ciate
d
with
p
ar
tial sh
ad
in
g
co
n
d
itio
n
s
.
Sti
ll
aim
in
g
to
s
o
lv
e
th
e
p
r
o
b
l
em
o
f
g
lo
b
al
p
o
wer
tr
ac
k
in
g
a
n
d
m
i
n
im
ize
p
o
wer
lo
s
s
es
u
n
d
er
p
a
r
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
,
n
u
m
er
o
u
s
m
etah
eu
r
is
tic
tech
n
iq
u
es
h
av
e
b
ee
n
p
r
o
p
o
s
ed
,
c
o
llectiv
ely
k
n
o
wn
as
m
etah
eu
r
is
tic
tech
n
iq
u
es.
T
h
ese
alg
o
r
ith
m
s
,
b
ased
o
n
s
war
m
in
tellig
en
ce
,
ar
e
u
tili
ze
d
in
m
o
d
e
r
n
MPPT
co
n
tr
o
ller
s
[
9
]
.
T
h
ey
o
f
ten
d
r
aw
in
s
p
ir
atio
n
f
r
o
m
a
n
im
al
b
eh
av
io
r
,
p
h
y
s
ical
p
h
en
o
m
en
a,
an
d
ev
o
lu
tio
n
ar
y
co
n
ce
p
ts
[
1
0
]
,
p
r
o
v
id
in
g
s
tr
ateg
ies
o
r
r
u
les
to
ex
p
lo
r
e
an
d
ex
p
lo
it
th
e
s
ea
r
ch
s
p
ac
e
e
f
f
ec
tiv
ely
.
T
h
is
en
a
b
les
th
em
to
s
o
lv
e
tr
ac
k
in
g
p
r
o
b
le
m
s
ac
r
o
s
s
d
if
f
er
en
t
s
o
lar
ir
r
ad
iatio
n
co
n
d
itio
n
s
with
h
ig
h
ef
f
icien
cy
.
No
tab
ly
,
th
e
B
AT
s
ea
r
ch
alg
o
r
ith
m
is
an
o
p
tim
izatio
n
tech
n
iq
u
e
in
s
p
i
r
ed
b
y
th
e
ec
h
o
lo
ca
tio
n
b
eh
a
v
io
r
o
f
n
atu
r
al
b
ats
to
d
etec
t sp
ec
if
ic
p
r
ey
,
as r
ec
o
m
m
en
d
ed
b
y
Osh
ab
a
in
[
1
1
]
.
An
o
th
er
r
ec
en
t stu
d
y
p
u
b
lis
h
e
d
in
[
1
2
]
in
tr
o
d
u
ce
s
an
alg
o
r
ith
m
th
at
em
u
lates
th
e
s
o
cial
b
eh
av
io
r
o
f
h
o
r
s
e
h
er
d
s
th
r
o
u
g
h
o
u
t
th
eir
liv
es.
Ad
d
itio
n
ally
,
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
s
o
m
e
m
eth
o
d
o
l
o
g
ies
d
r
aw
in
s
p
ir
atio
n
f
r
o
m
wh
ale
b
e
h
av
io
r
,
as
m
en
tio
n
ed
in
[
1
3
]
,
wh
ile
o
th
er
s
,
s
u
c
h
as
a
r
tific
ial
b
ee
c
o
lo
n
y
alg
o
r
ith
m
s
f
o
r
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
[
1
4
]
,
h
a
v
e
b
ee
n
d
ev
elo
p
e
d
to
o
p
tim
ize
p
o
wer
ex
tr
ac
tio
n
in
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
.
Oth
er
n
o
tab
le
alg
o
r
ith
m
s
in
clu
d
e
th
e
cu
ck
o
o
s
ea
r
ch
m
eth
o
d
,
p
r
o
p
o
s
ed
b
y
Hu
s
s
aian
in
[
1
5
]
,
an
t
co
l
o
n
y
o
p
tim
izatio
n
[
1
6
]
,
th
e
p
o
wer
f
u
l
b
io
-
in
s
p
ir
ed
f
i
r
e
f
ly
alg
o
r
ith
m
,
p
u
b
li
s
h
ed
b
y
T
itr
i
in
[
1
7
]
,
th
e
s
alp
s
war
m
alg
o
r
ith
m
[
1
8
]
,
m
o
th
-
f
lam
e
o
p
tim
izatio
n
[
1
9
]
,
g
r
ass
h
o
p
p
er
o
p
tim
izatio
n
,
as
p
r
esen
ted
in
r
esear
c
h
p
u
b
lis
h
ed
in
[
2
0
]
–
[
2
2
]
,
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
,
p
r
o
p
o
s
ed
in
[
2
3
]
,
[
2
4
]
.
Ho
wev
er
,
m
o
s
t
o
f
th
ese
m
etah
e
u
r
is
tic
tech
n
iq
u
es
f
ac
e
co
m
m
o
n
ch
allen
g
es
in
ter
m
s
o
f
p
r
ec
is
io
n
,
g
l
o
b
al
p
o
wer
tr
ac
k
in
g
,
a
n
d
lo
n
g
r
esp
o
n
s
e
tim
es
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
is
is
wh
y
th
ei
r
p
r
ac
tical
ad
o
p
tio
n
r
em
ain
s
l
im
ited
.
Fu
r
th
er
m
o
r
e,
th
e
cu
r
r
en
t
r
esear
ch
tr
en
d
h
a
s
s
h
if
ted
to
war
d
h
y
b
r
id
alg
o
r
ith
m
s
.
Gr
ey
wo
lf
o
p
tim
izatio
n
(
G
W
O)
is
an
ap
p
r
o
ac
h
d
e
v
elo
p
ed
b
y
Mir
jalili
[
2
5
]
,
in
s
p
ir
ed
b
y
th
e
o
r
g
an
izatio
n
o
f
wo
lv
es
an
d
th
eir
h
u
n
tin
g
tech
n
iq
u
es,
p
ar
ticu
lar
ly
in
te
r
m
s
o
f
tr
ac
k
in
g
an
d
en
cir
clin
g
p
r
e
y
.
I
t
is
n
o
tewo
r
th
y
th
at
th
is
tech
n
iq
u
e
h
as
b
en
ef
ited
f
r
o
m
h
y
b
r
id
izatio
n
with
o
th
er
alg
o
r
ith
m
s
to
im
p
r
o
v
e
its
p
er
f
o
r
m
an
ce
,
esp
ec
ially
co
n
ce
r
n
in
g
th
e
r
e
d
u
ctio
n
o
f
o
s
cillatio
n
s
an
d
tr
ac
k
in
g
tim
e.
I
n
teg
r
a
tio
n
with
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
(
FLC)
h
as
s
ig
n
if
ican
tly
r
e
d
u
ce
d
o
u
tp
u
t
p
o
wer
o
s
cillatio
n
s
[
2
5
]
,
Ho
wev
er
,
th
is
n
ec
ess
itates
th
e
in
clu
s
io
n
o
f
ce
r
tain
ap
p
r
o
x
im
atio
n
s
ac
h
iev
ed
th
r
o
u
g
h
t
r
ial
an
d
er
r
o
r
[
2
6
]
.
An
o
th
er
s
tu
d
y
p
u
b
lis
h
ed
b
y
L
ax
m
an
in
[
2
7
]
p
r
o
p
o
s
es
an
o
p
tim
ized
GW
O
with
f
u
zz
y
lo
g
ic
f
o
r
s
m
o
o
th
an
d
ef
f
ici
en
t
tr
ac
k
in
g
.
So
m
e
r
esear
ch
er
s
h
av
e
o
p
te
d
f
o
r
co
m
b
in
atio
n
s
with
o
th
er
m
e
tah
eu
r
is
tic
tech
n
iq
u
es,
s
u
ch
as
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
as
s
ee
n
in
th
e
wo
r
k
s
p
r
esen
te
d
in
[
2
8
]
,
[
2
9
]
,
wh
e
r
ea
s
Yad
av
in
[
3
0
]
r
ec
o
m
m
en
d
e
d
h
y
b
r
id
izatio
n
with
g
en
etic
al
g
o
r
ith
m
s
.
Ad
d
itio
n
ally
,
th
e
wo
r
k
p
u
b
lis
h
ed
b
y
Salim
in
[
3
1
]
is
n
o
tab
le
f
o
r
p
r
o
p
o
s
in
g
p
o
wer
m
a
x
im
izatio
n
th
r
o
u
g
h
h
y
b
r
id
izatio
n
o
f
cu
ck
o
o
s
ea
r
ch
an
d
g
r
ey
w
o
lf
o
p
tim
izer
in
p
ar
tial
s
h
ad
in
g
c
o
n
d
itio
n
s
.
Fu
r
th
e
r
m
o
r
e,
in
te
r
m
s
o
f
tim
e
ef
f
icien
cy
an
d
s
tab
ilizatio
n
,
an
o
th
er
h
y
b
r
id
izatio
n
tech
n
iq
u
e
k
n
o
wn
as
g
r
ey
wo
lf
o
p
tim
izer
with
d
if
f
er
en
tial
e
v
o
lu
tio
n
(
GW
ODE
)
h
as
b
ee
n
p
r
o
p
o
s
ed
[
3
2
]
,
[
3
3
]
.
I
n
ad
d
itio
n
t
o
th
e
co
m
p
lex
ity
ass
o
ciate
d
with
th
e
im
p
lem
en
tatio
n
o
f
th
ese
h
y
b
r
id
alg
o
r
ith
m
s
,
th
eir
ex
ec
u
tio
n
r
eq
u
ir
es
co
n
s
id
er
ab
l
e
co
m
p
u
t
atio
n
tim
e
[
2
6
]
.
T
h
is
is
wh
y
we
en
co
u
r
a
g
e
r
esear
c
h
er
s
to
e
x
p
lo
r
e
o
th
er
ty
p
es
o
f
h
y
b
r
id
izatio
n
,
as
p
r
esen
ted
i
n
th
is
s
tu
d
y
,
wh
e
r
e
we
s
el
e
cted
th
e
h
y
b
r
id
izatio
n
b
etwe
en
a
m
etah
e
u
r
is
tic
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
.
4
,
Au
g
u
s
t
20
25
:
3
5
6
6
-
3582
3568
alg
o
r
ith
m
,
GW
O,
an
d
a
class
ical
alg
o
r
ith
m
wid
ely
u
s
ed
i
n
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
,
P
&
O.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
is
b
o
t
h
ef
f
icien
t a
n
d
e
asy
to
im
p
lem
en
t.
T
h
e
n
o
v
elty
a
n
d
o
b
jectiv
e
o
f
th
is
s
tu
d
y
lie
in
th
e
s
im
u
lat
io
n
o
f
a
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
u
b
jecte
d
to
v
ar
io
u
s
co
m
p
le
x
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
ch
ar
ac
ter
ized
b
y
m
u
ltip
le
lo
ca
l
m
ax
im
u
m
p
o
wer
p
o
in
ts
.
T
h
e
GW
O
-
P&
O
h
y
b
r
id
izatio
n
ac
h
iev
es
ex
ce
llen
t
r
esu
lts
in
tr
ac
k
in
g
g
l
o
b
al
p
o
wer
,
av
o
id
in
g
en
tr
ap
m
en
t
i
n
lo
ca
l
m
ax
im
a,
wh
ile
o
f
f
e
r
in
g
r
ed
u
ce
d
r
esp
o
n
s
e
tim
e
a
n
d
r
e
m
ar
k
ab
le
e
f
f
icien
cy
u
n
d
er
v
ar
io
u
s
atm
o
s
p
h
e
r
ic
co
n
d
itio
n
s
.
A
c
o
m
p
ar
ativ
e
s
tu
d
y
was
co
n
d
u
cted
i
n
ter
m
s
o
f
co
n
v
e
r
g
en
ce
,
tr
ac
k
in
g
,
o
s
cill
atio
n
,
an
d
r
esp
o
n
s
e
tim
e
to
war
d
th
e
GM
PP
,
to
ev
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
co
m
p
ar
e
d
to
th
e
GW
O
an
d
P&
O
alg
o
r
ith
m
s
u
n
d
er
p
ar
tial
o
r
u
n
if
o
r
m
s
h
ad
i
n
g
co
n
d
itio
n
s
.
T
h
is
wo
r
k
ex
p
lo
r
ed
all
p
o
s
s
ib
le
co
m
b
in
atio
n
s
,
tr
an
s
itio
n
in
g
f
r
o
m
o
n
e
ir
r
a
d
iatio
n
co
n
d
itio
n
to
a
n
o
th
er
f
o
u
r
t
im
es in
a
s
in
g
le
s
im
u
latio
n
.
T
h
e
s
tu
d
y
is
o
r
g
a
n
iz
ed
i
n
to
s
e
v
er
al
s
ec
tio
n
s
as
f
o
llo
ws:
th
e
s
ec
o
n
d
s
ec
tio
n
p
r
esen
ts
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
an
d
ex
p
lain
s
th
e
p
ar
tia
l
s
h
ad
in
g
p
h
e
n
o
m
en
o
n
.
T
h
e
th
ir
d
s
ec
tio
n
d
escr
ib
es
th
e
p
r
o
p
o
s
ed
h
y
b
r
i
d
GW
O
-
P&
O
m
eth
o
d
in
d
etail.
T
h
e
f
o
u
r
th
s
ec
tio
n
co
v
er
s
th
e
s
im
u
latio
n
o
f
th
e
p
h
o
t
o
v
o
ltaic
s
y
s
tem
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
an
d
d
is
cu
s
s
es
th
e
r
esu
lt
s
,
wh
ile
th
e
f
if
th
s
ec
tio
n
p
r
o
v
id
es
th
e
co
n
cl
u
s
io
n
o
f
th
e
s
tu
d
y
'
s
f
in
d
in
g
s
.
2.
P
H
O
T
O
VO
L
T
A
I
C
SY
ST
E
M
2
.
1
.
M
a
t
hem
a
t
ica
l
m
o
del o
f
a
ph
o
t
o
v
o
lt
a
ic
ce
ll
Ph
o
to
v
o
ltaic
g
en
e
r
ato
r
s
ar
e
r
eg
ar
d
ed
as
v
o
ltag
e
-
co
n
tr
o
lled
cu
r
r
en
t
g
en
er
ato
r
s
[
3
4
]
.
Sev
er
al
eq
u
iv
alen
t
cir
c
u
its
ar
e
u
tili
ze
d
f
o
r
m
o
d
elin
g
a
p
h
o
to
v
o
ltai
c
ce
ll,
with
th
e
m
o
s
t
c
o
m
m
o
n
b
ein
g
s
in
g
le
an
d
d
o
u
b
le
-
d
io
d
e
m
o
d
els
[
3
5
]
.
T
h
e
cir
cu
it
d
ep
icted
in
Fig
u
r
e
1
is
em
p
lo
y
ed
th
r
o
u
g
h
o
u
t
th
e
r
em
ain
d
er
o
f
th
e
s
tu
d
y
f
o
r
m
o
d
elin
g
p
u
r
p
o
s
es.
I
=
I
ph
−
I
d
−
I
sh
(
1
)
ℎ
r
ep
r
esen
ts
th
e
p
h
o
to
v
o
ltaic
cu
r
r
en
t
g
en
er
ated
b
y
th
e
illu
m
in
atio
n
,
a
n
d
r
ep
r
esen
ts
th
e
d
io
d
e
cu
r
r
en
t
,
wh
ich
is
g
iv
en
b
y
(
2
)
:
=
0
[
(
.
(
+
)
.
.
.
)
−
1
]
(
2
)
Usi
n
g
Kir
ch
h
o
f
f
'
s
v
o
ltag
e
law
(
KVL
)
,
we
h
av
e:
ℎ
ℎ
−
−
=
0
(
3
)
ℎ
=
+
ℎ
(
4
)
Fin
ally
,
th
e
ex
p
r
ess
io
n
f
o
r
th
e
cu
r
r
en
t
g
en
er
ated
b
y
th
e
p
h
o
to
v
o
ltaic
ce
ll is
wr
itten
as
(
5
)
:
=
ℎ
−
0
[
(
.
(
+
)
.
.
.
)
−
1
]
−
+
ℎ
(
5
)
Fig
u
r
e
1
.
E
q
u
iv
alen
t
r
ep
r
esen
t
ativ
e
cir
cu
it o
f
a
p
h
o
t
o
v
o
ltaic
ce
ll
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
Ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
tech
n
i
q
u
e
b
a
s
ed
o
n
th
e
g
r
e
y
w
o
lf o
p
timiz
a
tio
n
…
(
Leg
h
r
ib
B
ila
l
)
3569
A
s
in
g
le
p
h
o
to
v
o
ltaic
ce
ll
ty
p
ically
p
r
o
d
u
ce
s
a
v
er
y
lo
w
p
o
wer
,
ap
p
r
o
x
im
ately
2
W
,
f
o
r
a
v
o
ltag
e
o
f
0
.
5
V
[
3
6
]
.
Du
e
to
th
is
r
ea
s
o
n
,
ce
lls
ar
e
ar
r
an
g
ed
in
s
er
ies
an
d
p
ar
allel
co
n
f
ig
u
r
atio
n
s
t
o
g
en
er
ate
s
u
f
f
icien
t
cu
r
r
en
t
an
d
v
o
ltag
e
f
o
r
a
g
iv
e
n
o
p
er
atio
n
.
Her
e,
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
ce
lls
in
p
ar
allel
an
d
d
en
o
tes
th
e
n
u
m
b
er
o
f
ce
lls
in
s
er
ies,
ass
u
m
in
g
all
ce
lls
ar
e
id
en
ti
ca
l
u
n
d
er
th
e
s
am
e
ir
r
a
d
iatio
n
an
d
tem
p
er
atu
r
e
co
n
d
itio
n
s
.
E
q
u
atio
n
(
5
)
ca
n
t
h
en
b
e
wr
itten
as
(
6
)
:
=
ℎ
−
0
[
(
.
(
+
)
.
.
.
)
−
1
]
−
+
ℎ
(
6
)
2
.
2
.
P
a
rt
ia
l sh
a
din
g
T
h
e
is
s
u
e
o
f
p
ar
tial sh
ad
in
g
is
a
n
ea
r
ly
co
n
s
tan
t p
r
o
b
lem
th
at
m
u
s
t b
e
tak
en
in
to
co
n
s
id
er
atio
n
d
u
e
to
its
s
ig
n
if
ican
t
in
f
lu
en
ce
o
n
th
e
ef
f
icien
cy
o
f
s
o
lar
p
an
el
in
s
ta
llatio
n
s
.
I
t
o
cc
u
r
s
wh
e
n
a
p
o
r
ti
o
n
o
f
a
s
o
lar
p
a
n
el
is
s
h
ad
ed
b
y
p
h
en
o
m
en
a
s
u
ch
as
clo
u
d
s
,
tr
ee
s
,
o
r
e
v
en
d
u
s
t.
T
h
is
s
h
ad
in
g
h
as
a
d
ir
ec
t
im
p
ac
t
o
n
th
e
p
o
wer
cu
r
v
e,
ca
u
s
in
g
l
o
ca
l
p
o
wer
p
ea
k
s
th
at
ar
e
less
s
ig
n
if
ican
t
th
an
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t.
T
h
is
o
f
ten
tr
a
p
s
co
n
v
en
tio
n
al
m
ax
im
izatio
n
te
ch
n
iq
u
es
lik
e
P&
O
o
r
in
cr
e
m
en
tal
m
eth
o
d
s
,
wh
ic
h
co
n
v
er
g
e
to
war
d
s
t
h
ese
less
s
ig
n
if
ican
t p
o
wer
p
o
in
ts
in
s
tead
o
f
th
e
g
lo
b
al
m
ax
im
u
m
p
o
w
er
p
o
in
t.
Mo
d
elin
g
o
f
p
ar
tial
s
h
ad
in
g
is
co
n
d
u
cted
u
s
in
g
MA
T
L
AB
s
o
f
twar
e
with
th
e
Simu
lin
k
d
iag
r
am
s
h
o
wn
in
Fig
u
r
e
2
.
Fo
u
r
id
en
tical
p
h
o
to
v
o
ltaic
p
a
n
els
ar
e
p
lace
d
i
n
s
er
ies,
with
t
h
eir
ch
ar
ac
ter
is
tics
d
eter
m
in
ed
b
y
T
ab
le
1
.
E
ac
h
p
an
el
is
s
u
b
jecte
d
to
s
o
lar
ir
r
ad
iatio
n
s
ep
ar
ately
,
in
clu
d
in
g
u
n
if
o
r
m
ir
r
a
d
iatio
n
wh
er
e
ea
ch
p
a
n
el
r
ec
eiv
es
id
e
n
tical
ir
r
ad
iatio
n
o
f
1
0
0
0
W
/m
².
T
h
e
v
ar
io
u
s
p
o
wer
-
v
o
ltag
e
cu
r
v
es
o
b
tain
e
d
ar
e
r
ep
r
esen
ted
i
n
Fig
u
r
e
3
.
T
h
ese
L
MPP
o
n
t
h
e
p
o
wer
-
v
o
ltag
e
(
P
-
V)
cu
r
v
e
m
a
k
e
it
m
o
r
e
d
if
f
icu
lt
to
id
e
n
tify
th
e
GM
PP
.
T
h
e
p
r
im
ar
y
f
u
n
ctio
n
o
f
MPPT
alg
o
r
ith
m
s
is
to
m
o
n
ito
r
th
e
m
ax
im
u
m
p
o
wer
o
u
t
p
u
t
o
f
p
h
o
to
v
o
ltaic
p
an
els an
d
en
s
u
r
e
th
ey
ca
n
d
el
iv
er
a
h
ig
h
-
p
o
wer
lev
el,
ev
e
n
u
n
d
er
p
ar
ti
al
s
h
ad
in
g
co
n
d
itio
n
s
.
C
o
n
v
en
tio
n
al
alg
o
r
ith
m
s
ar
e
less
ef
f
ec
tiv
e
u
n
d
er
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
lead
in
g
to
s
ig
n
if
ican
t
en
er
g
y
lo
s
s
es.
Ho
wev
er
,
u
n
d
er
u
n
if
o
r
m
o
p
er
atin
g
co
n
d
i
tio
n
s
,
th
e
P&
O
al
g
o
r
ith
m
d
em
o
n
s
tr
ates
g
o
o
d
ef
f
icien
cy
in
p
o
wer
ex
tr
ac
ti
o
n
,
as
s
h
o
wn
b
y
p
r
ev
io
u
s
r
esear
ch
[
3
7
]
.
I
n
c
o
n
tr
ast
GW
O
u
s
ed
as
a
m
etah
eu
r
is
tic
tech
n
iq
u
e,
ca
n
tr
ac
k
th
e
g
l
o
b
al
m
ax
im
u
m
p
o
wer
p
o
i
n
t
u
n
d
er
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
wh
er
e
P&
O
f
ails
,
th
o
u
g
h
it
p
r
esen
ts
n
o
ticea
b
le
o
s
cillatio
n
s
ar
o
u
n
d
th
e
o
p
tim
al
p
o
wer
p
o
in
t
[
3
8
]
.
T
o
ad
d
r
e
s
s
th
ese
ch
allen
g
es,
th
is
s
tu
d
y
p
r
o
p
o
s
es
h
y
b
r
id
izin
g
th
e
GW
O
with
th
e
P&
O
alg
o
r
ith
m
to
en
ab
le
r
a
p
id
an
d
ac
cu
r
ate
co
n
v
e
r
g
en
ce
to
th
e
GM
PP
,
r
eg
ar
d
less
o
f
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
wh
eth
er
u
n
d
er
p
ar
tial
o
r
u
n
if
o
r
m
s
h
ad
in
g
.
W
e
s
im
u
lated
f
o
u
r
ty
p
es
o
f
s
o
lar
i
r
r
ad
iatio
n
c
o
n
d
itio
n
s
(
SIC),
ea
ch
ass
o
ciate
d
with
a
s
p
ec
if
ic
GM
PP
.
T
h
e
d
etails
o
f
th
ese
co
n
d
itio
n
s
ar
e
s
u
m
m
a
r
ized
in
T
ab
le
2
.
Fig
u
r
e
2
.
T
h
e
p
ar
tial sh
ad
i
n
g
u
n
d
er
MA
T
L
AB
/
Simu
lin
k
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
.
4
,
Au
g
u
s
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20
25
:
3
5
6
6
-
3582
3570
Fig
u
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PV Po
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t
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t
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f
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t
o
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30
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0
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T
ab
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2
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Dif
f
e
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en
t sh
ad
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at
ter
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s
S
o
l
a
r
i
r
r
a
d
i
a
n
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e
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o
n
d
i
t
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n
s
P
a
r
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i
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l
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s
G
M
P
P
(
W
)
S
I
C
1
[
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
]
9
9
6
S
I
C
2
S
I
C
3
S
I
C
4
[
5
0
0
8
0
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1
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1
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0
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[
1
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0
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[
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7
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0
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6
3
7
.
8
4
8
3
.
8
5
6
7
.
9
3
.
P
RO
P
O
SE
D
G
WO
-
P
&O
A
L
G
O
RIT
H
M
3
.
1
.
Desig
nin
g
t
he
G
WO
a
lg
o
rit
hm
T
h
e
g
r
a
y
wo
lf
o
p
tim
izer
(
GW
O)
is
an
o
p
tim
izatio
n
alg
o
r
ith
m
in
s
p
ir
ed
b
y
th
e
s
o
cial
b
eh
a
v
io
r
o
f
g
r
a
y
wo
lv
es.
I
t
r
elies
o
n
s
o
cial
h
ie
r
ar
ch
y
an
d
wo
lf
-
h
u
n
tin
g
in
te
r
ac
tio
n
s
to
s
o
lv
e
co
m
p
lex
o
p
ti
m
izatio
n
p
r
o
b
lem
s
.
GW
O
i
s
a
m
eta
-
h
eu
r
is
tic
s
w
ar
m
in
tel
lig
en
ce
o
p
tim
izatio
n
tech
n
iq
u
e,
w
h
er
e
in
tellig
en
c
e
em
er
g
es
f
r
o
m
th
e
co
llectiv
e
ac
tio
n
s
o
f
s
im
p
le
ag
en
ts
[
2
5
]
.
T
h
e
alg
o
r
ith
m
m
im
ics
p
r
ey
-
s
ee
k
in
g
,
g
r
o
u
p
i
n
g
,
an
d
h
ier
ar
c
h
y
-
u
p
d
atin
g
b
e
h
av
io
r
s
o
b
s
er
v
ed
in
wo
lv
es.
T
h
er
e
ar
e
f
o
u
r
lev
e
ls
o
f
lead
er
s
h
ip
in
th
is
o
r
g
an
i
za
tio
n
.
L
ea
d
er
s
ar
e
d
ef
in
ed
as
alp
h
a
(
α
)
,
wh
ile
s
u
b
-
lead
er
s
ar
e
ca
te
g
o
r
ized
as
b
eta
(
β),
d
elta
(
∆)
,
an
d
o
m
e
g
a
(
ω
)
,
d
e
p
en
d
i
n
g
o
n
th
eir
p
o
s
itio
n
s
with
in
th
e
h
ier
ar
ch
y
[
3
9
]
.
T
h
e
h
u
n
tin
g
p
r
o
ce
s
s
in
v
o
lv
es
p
u
r
s
u
in
g
th
e
ta
r
g
et,
f
o
llo
wed
b
y
p
r
o
g
r
ess
iv
ely
ap
p
r
o
ac
h
in
g
it u
n
til
it
is
s
u
r
r
o
u
n
d
e
d
.
T
h
en
,
th
e
tar
g
et
is
attac
k
e
d
an
d
im
m
o
b
i
lized
,
as
illu
s
tr
ated
in
Fig
u
r
e
4
.
All
wo
lv
es
iter
ativ
ely
u
p
d
ate
t
h
eir
p
o
s
itio
n
s
r
elativ
e
to
th
o
s
e
h
ig
h
e
r
in
th
e
p
ec
k
in
g
o
r
d
er
,
r
esu
lti
n
g
in
th
e
b
est
s
o
lu
tio
n
[
4
0
]
,
[
4
1
]
,
cl
ass
if
ied
as
Alp
h
a,
B
eta,
an
d
Delta
wo
lv
es,
r
esp
ec
tiv
ely
.
G
W
O
is
r
en
o
wn
ed
f
o
r
its
ab
ilit
y
to
f
in
d
e
f
f
ec
tiv
e
s
o
lu
tio
n
s
to
d
if
f
ic
u
lt
p
r
o
b
lem
s
.
T
h
e
g
r
ea
ter
th
e
n
u
m
b
e
r
o
f
iter
atio
n
s
,
th
e
m
o
r
e
o
p
tim
al
th
e
s
o
lu
tio
n
b
ec
o
m
es.
Ho
wev
er
,
t
h
is
in
cr
ea
s
es
th
e
alg
o
r
ith
m
'
s
ex
ec
u
tio
n
tim
e.
Fo
r
th
is
r
ea
s
o
n
,
t
h
e
n
u
m
b
er
o
f
iter
atio
n
s
in
GW
O
m
u
s
t
b
e
ca
r
ef
u
lly
d
eter
m
in
ed
b
ased
o
n
th
e
ty
p
e
an
d
d
if
f
icu
lt
y
o
f
th
e
p
r
o
b
lem
to
b
e
s
o
lv
ed
[
4
0
]
.
T
h
e
b
eh
a
v
io
r
o
f
wo
lv
es wh
ile
h
u
n
tin
g
b
y
cir
clin
g
th
eir
p
r
ey
ca
n
b
e
m
o
d
eled
b
y
(
7
)
an
d
(
8
)
:
=
|
.
(
)
−
(
)
|
(
7
)
(
+
1
)
=
(
)
−
.
(
8
)
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
Ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
tech
n
i
q
u
e
b
a
s
ed
o
n
th
e
g
r
e
y
w
o
lf o
p
timiz
a
tio
n
…
(
Leg
h
r
ib
B
ila
l
)
3571
I
n
th
e
e
q
u
atio
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s
p
r
o
v
id
ed
,
r
ep
r
esen
ts
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e
cu
r
r
en
t
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n
.
T
h
e
v
ec
to
r
s
(
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an
d
(
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r
esp
ec
tiv
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in
d
icate
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e
p
o
s
itio
n
o
f
th
e
g
r
ay
wo
lf
an
d
th
e
p
o
s
itio
n
o
f
th
e
p
r
e
y
.
Vec
to
r
s
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d
ar
e
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et
s
o
f
co
ef
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icien
ts
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alu
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ete
r
m
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(
9
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1
1
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=
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.
1
−
(
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(
9
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=
2
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2
(
1
0
)
(
)
=
2
−
(
2
.
)
/
(
1
1
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T
h
e
r
an
d
o
m
n
u
m
b
er
s
1
an
d
2
ar
e
s
elec
ted
f
r
o
m
th
e
in
ter
v
al
b
etwe
en
ze
r
o
an
d
o
n
e,
an
d
th
e
y
ar
e
u
tili
ze
d
t
o
u
p
d
ate
th
e
p
o
s
itio
n
s
o
f
wo
lv
e
s
with
in
th
e
s
ea
r
ch
ar
ea
.
T
h
e
p
ar
am
eter
d
ec
r
ea
s
es
lin
ea
r
ly
f
r
o
m
2
t
o
0
d
u
r
in
g
iter
atio
n
s
,
wh
ile
r
ep
r
esen
ts
t
h
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
iter
a
tio
n
s
u
s
ed
in
th
e
s
ea
r
ch
alg
o
r
ith
m
[
2
5
]
,
[
4
2
]
.
I
n
th
is
s
ce
n
ar
io
,
th
e
p
r
ey
is
s
u
r
r
o
u
n
d
ed
b
y
g
r
ay
wo
l
v
es.
T
h
e
m
em
b
er
s
o
f
th
e
p
ac
k
f
ir
s
t
f
o
llo
w
th
e
in
s
tr
u
ctio
n
s
o
f
th
e
lead
er
(
alp
h
a
wo
lf
)
,
th
en
t
h
o
s
e
o
f
th
e
b
e
ta
wo
lv
es,
an
d
f
in
ally
th
o
s
e
o
f
th
e
d
elta
w
o
lv
es.
E
ac
h
wo
lf
a
d
ju
s
ts
its
p
o
s
itio
n
to
g
et
as
clo
s
e
as
p
o
s
s
ib
le
to
th
e
p
r
e
y
[
3
0
]
,
[
4
3
]
.
T
h
e
d
ec
is
io
n
s
tep
s
o
f
th
e
GW
O
alg
o
r
ith
m
ar
e
p
r
esen
ted
in
Fig
u
r
e
5
.
T
h
is
b
eh
a
v
io
r
is
d
escr
ib
ed
b
y
(
1
2
)
-
(
1
4
)
:
{
=
|
1
.
(
)
−
(
)
|
=
|
2
.
(
)
−
(
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|
=
|
3
.
∆
(
)
−
(
)
|
(
1
2
)
{
1
=
(
)
−
1
.
(
)
2
=
(
)
−
2
.
(
)
3
=
∆
(
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−
3
.
(
)
(
1
3
)
(
+
1
)
=
1
+
2
+
3
3
(
1
4
)
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
4
.
T
h
e
h
u
n
tin
g
b
eh
av
i
o
r
o
f
g
r
ay
wo
l
v
es:
(
a)
tar
g
et
p
u
r
s
u
it,
(
b
)
ap
p
r
o
ac
h
in
g
th
e
tar
g
e
t
,
(
c)
en
cir
clem
en
t
,
an
d
(
d
)
t
he
t
ar
g
et
is
attac
k
ed
,
it n
o
lo
n
g
e
r
m
o
v
es
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
.
4
,
Au
g
u
s
t
20
25
:
3
5
6
6
-
3582
3572
Fig
u
r
e
5
.
Dec
is
io
n
s
tep
s
o
f
t
h
e
GW
O
alg
o
r
ith
m
3
.
2
.
P
&O
a
lg
o
rit
hm
T
h
is
m
eth
o
d
is
b
ased
o
n
ca
lcu
latin
g
th
e
p
h
o
to
v
o
ltaic
p
o
we
r
(
)
b
y
m
ea
s
u
r
in
g
th
e
c
u
r
r
e
n
t
(
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an
d
th
e
v
o
ltag
e
(
)
,
an
d
co
m
p
ar
in
g
it
with
th
e
p
r
ev
io
u
s
p
o
wer
v
alu
e
(
−
1
)
.
T
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t
is
ac
h
iev
ed
wh
en
ΔP
.
W
h
en
th
e
d
if
f
er
e
n
ce
b
etwe
en
t
h
e
two
p
o
wer
v
alu
es
is
n
o
t
ze
r
o
,
th
e
alg
o
r
ith
m
will
attem
p
t to
f
in
d
th
e
o
p
tim
al
p
o
i
n
t to
th
e
lef
t o
r
r
ig
h
t o
f
th
e
r
ec
en
t p
o
wer
v
alu
e
[
4
4
]
.
T
h
er
e
f
o
r
e,
th
e
p
er
tu
r
b
atio
n
o
f
th
e
d
u
ty
cy
cle
r
atio
Δ
D
d
ep
en
d
s
o
n
th
e
s
ig
n
o
f
th
e
l
ast
p
er
tu
r
b
atio
n
an
d
th
e
s
ig
n
o
f
t
h
e
last
p
o
wer
in
cr
em
en
t
[
6
]
,
wh
ic
h
ar
e
u
s
ed
to
d
ec
id
e
t
h
e
d
ir
ec
tio
n
o
f
th
e
n
ex
t
p
e
r
tu
r
b
atio
n
[
4
5
]
ac
c
o
r
d
in
g
to
th
e
d
ec
is
io
n
f
lo
wch
ar
t
(
P&
O
p
ar
t)
.
T
h
e
p
e
r
tu
r
b
atio
n
m
u
s
t
b
e
m
ai
n
tain
ed
in
th
e
s
am
e
d
i
r
ec
tio
n
i
f
th
e
p
o
wer
in
cr
ea
s
es,
a
n
d
if
th
e
p
o
wer
d
ec
r
ea
s
es,
th
e
n
e
x
t p
er
tu
r
b
atio
n
s
h
o
u
ld
b
e
in
th
e
o
p
p
o
s
ite
d
ir
ec
tio
n
.
3
.
3
.
M
P
P
T
wit
h
G
WO
-
P
&O
co
m
bin
a
t
io
n
T
h
e
ap
p
r
o
ac
h
is
s
tr
aig
h
tf
o
r
wa
r
d
:
f
ir
s
t,
th
e
GW
O
m
eth
o
d
is
u
s
ed
to
d
eter
m
in
e
th
e
o
p
tim
al
d
u
ty
cy
cle
to
ac
h
iev
e
m
ax
im
u
m
p
o
wer
.
T
h
is
r
esu
lt
is
th
en
u
s
ed
as
a
s
tar
tin
g
p
o
in
t
an
d
f
u
r
th
e
r
r
ef
in
ed
b
y
th
e
P&
O
m
eth
o
d
f
o
r
g
r
ea
ter
p
r
ec
is
io
n
.
B
y
co
m
b
in
in
g
b
o
th
m
eth
o
d
s
,
lo
ca
l
m
ax
im
u
m
p
o
wer
p
o
in
ts
ar
e
av
o
id
e
d
wh
ile
b
en
ef
itin
g
f
r
o
m
th
e
e
f
f
icien
cy
an
d
s
im
p
licity
o
f
th
e
P&
O
a
lg
o
r
ith
m
.
Fig
u
r
e
6
illu
s
tr
ates
th
e
GM
PP
th
at
th
e
h
y
b
r
id
alg
o
r
ith
m
aim
s
to
a
ch
iev
e
with
o
u
t
b
ein
g
tr
a
p
p
e
d
in
L
MPP.
I
t
also
h
ig
h
lig
h
ts
th
e
ch
allen
g
e
s
en
co
u
n
ter
e
d
u
n
d
e
r
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
.
T
h
e
co
m
b
in
a
tio
n
p
r
o
ce
s
s
is
il
lu
s
tr
ated
in
t
h
e
f
lo
wch
ar
t
o
f
th
e
T
h
e
alg
o
r
ith
m
is
wr
itten
in
t
h
e
f
o
r
m
o
f
a
n
eq
u
atio
n
wh
ic
h
will
h
av
e
th
e
v
alu
e
o
f
en
ter
in
g
th
e
p
h
o
t
o
v
o
ltaic
v
o
ltag
e
V
pv
an
d
th
e
p
h
o
to
v
o
ltaic
cu
r
r
e
n
t
I
pv
T
h
e
f
ir
s
t
s
tep
is
th
e
in
itializ
atio
n
o
f
th
e
m
a
g
n
if
ier
v
al
u
e
s
in
th
e
f
o
r
m
o
f
a
ze
r
o
m
atr
ix
,
as
well
as
th
e
in
itializatio
n
o
f
d
if
f
er
e
n
t
v
alu
es
o
f
th
e
d
u
ty
c
y
cle
(
)
with
v
alu
es b
etwe
en
0
.
1
an
d
1
,
wh
e
r
e
(
)
r
ep
r
esen
ts
th
e
to
tal
n
u
m
b
e
r
o
f
wo
lv
es.
C
al
c
u
la
tio
n
o
f
th
e
o
b
je
c
tiv
e
f
u
n
c
tio
n
th
a
t
w
ill
b
e
n
a
m
e
d
=
∗
an
d
attrib
u
ti
o
n
o
f
th
e
p
o
s
it
io
n
o
f
t
h
e
wo
lv
es
in
r
elati
o
n
to
th
e
f
it
n
es
s
v
alu
e
as
f
o
ll
o
ws
:
<
ℎ
ℎ
=
&
ℎ
_
=
(
)
<
ℎ
&
>
=
&
_
=
(
)
<
ℎ
&
<
&
>
=
&
_
=
∆
(
)
I
n
th
is
s
ec
tio
n
,
we
ca
lcu
late
t
h
e
v
alu
es
1
,
2
,
3
ac
co
r
d
i
n
g
to
(
1
3
)
an
d
d
eter
m
in
e
th
e
v
alu
e
o
f
(
+
1
)
ac
co
r
d
in
g
to
(
1
4
)
f
o
r
all
d
u
t
y
cy
cle
v
alu
es.
T
h
is
u
p
d
ate
is
d
o
n
e
at
ea
ch
iter
atio
n
to
o
b
tai
n
th
e
b
est
v
alu
e
o
f
d
u
ty
c
y
cle
(
)
th
at
y
ield
s
th
e
o
p
ti
m
al p
o
wer
v
alu
e
.
At
th
is
s
tag
e,
th
e
P&
O
alg
o
r
ith
m
is
in
itiated
ac
co
r
d
in
g
to
th
e
f
lo
wch
ar
t
(
P&
O
p
a
r
t
)
to
r
ef
in
e
a
n
d
d
eter
m
in
e
th
e
n
e
w
d
u
ty
cy
cle
v
alu
e
as f
o
llo
ws:
=
+
∆
=
−
∆
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
Ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
tech
n
i
q
u
e
b
a
s
ed
o
n
th
e
g
r
e
y
w
o
lf o
p
timiz
a
tio
n
…
(
Leg
h
r
ib
B
ila
l
)
3573
GW
O
-
P&
O
h
y
b
r
id
izatio
n
p
r
e
s
en
ted
in
Fig
u
r
e
7
a
n
d
ex
p
lai
n
ed
in
d
etail
i
n
th
e
f
lo
wc
h
ar
t
o
f
th
e
GW
O
-
P&
O
alg
o
r
ith
m
in
Fig
u
r
e
8
.
Fig
u
r
e
6
.
P
-
V
g
r
ap
h
o
f
th
e
p
r
o
p
o
s
ed
MPPT
tech
n
iq
u
e
Fig
u
r
e
7
.
Flo
wch
ar
t
o
f
th
e
GW
O
-
P&
O
h
y
b
r
id
izatio
n
Run G
WO
Sta
rt
O
bta
ini
ng
=
ena
bles
a
chiev
ing
t
he
m
a
x
i
m
um
po
wer
a
nd
it
s
co
rr
esp
o
nd
i
ng
Ca
lcula
t
e
m
ea
s
ured
a
rr
a
y
P
o
wer
=
∗
Run P
&O
=
±
∆
E
nd
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
.
4
,
Au
g
u
s
t
20
25
:
3
5
6
6
-
3582
3574
Fig
u
r
e
8
.
Flo
wch
ar
t
o
f
th
e
GW
O
-
P&
O
alg
o
r
ith
m
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
s
im
u
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
p
o
wer
m
a
x
im
izatio
n
m
eth
o
d
is
illu
s
tr
ated
in
Fig
u
r
e
9
.
Fo
u
r
id
en
tical
p
h
o
to
v
o
ltaic
(
PV)
p
an
els
ar
e
co
n
n
ec
ted
in
s
er
ies
to
f
o
r
m
a
s
in
g
le
ar
r
ay
,
with
th
eir
s
p
ec
if
ic
ch
ar
ac
ter
is
tics
d
etailed
in
T
ab
le
1
.
T
h
e
s
im
u
latio
n
was
co
n
d
u
cted
u
n
d
er
v
a
r
io
u
s
c
o
n
d
itio
n
s
,
in
clu
d
in
g
u
n
if
o
r
m
ir
r
ad
iatio
n
a
n
d
p
ar
tial
s
h
ad
in
g
,
all
s
u
m
m
ar
ized
i
n
T
ab
le
2
.
I
n
itially
,
th
e
p
h
o
t
o
v
o
ltaic
(
PV)
p
an
els
wer
e
s
u
b
jecte
d
t
o
p
a
r
tial
s
h
ad
in
g
r
e
p
r
esen
ted
b
y
SIC4
.
Su
b
s
eq
u
en
tly
,
at
=
0
.
4
s
,
s
o
lar
ir
r
ad
iatio
n
b
ec
am
e
u
n
if
o
r
m
ac
r
o
s
s
th
e
f
o
u
r
g
r
o
u
p
s
o
f
p
an
els,
with
an
in
ten
s
ity
o
f
1
0
0
0
W
/m
²
f
o
r
ea
ch
g
r
o
u
p
.
At
=
0
.
8
s
,
a
d
is
tu
r
b
an
ce
in
t
r
o
d
u
ce
d
p
ar
tial
s
h
ad
in
g
r
ep
r
esen
ted
b
y
SIC3
.
Fin
ally
,
at
=
1
.
2
s
,
t
h
e
s
y
s
tem
tr
an
s
itio
n
ed
to
ir
r
ad
iatio
n
r
e
p
r
esen
ted
b
y
SIC2
.
T
h
u
s
,
th
e
s
o
lar
s
y
s
tem
u
n
d
er
in
v
esti
g
atio
n
was
ex
p
o
s
ed
to
s
ev
er
al
ty
p
es
o
f
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
tr
a
n
s
itio
n
in
g
s
eq
u
en
tially
f
r
o
m
p
ar
tial
s
h
ad
in
g
to
u
n
if
o
r
m
ir
r
ad
iatio
n
,
t
h
en
t
o
an
o
th
e
r
s
h
ad
in
g
co
n
d
itio
n
,
an
d
f
in
ally
to
a
s
h
ad
in
g
co
n
d
itio
n
d
is
tin
ct
f
r
o
m
th
e
p
r
ev
io
u
s
o
n
e
s
.
All
th
ese
s
ce
n
ar
io
s
wer
e
s
im
u
lated
u
s
in
g
th
e
th
r
ee
m
eth
o
d
s
:
P&
O,
GW
O,
an
d
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
GW
O
-
P&
O,
wh
ich
wer
e
p
r
ev
io
u
s
ly
s
tu
d
ied
an
d
ex
p
lai
n
ed
.
Fig
u
r
e
1
0
s
h
o
ws
th
e
m
ax
im
u
m
g
lo
b
al
p
o
wer
f
o
r
ea
ch
s
o
lar
ir
r
ad
iatio
n
co
n
d
itio
n
th
at
th
e
p
h
o
to
v
o
ltaic
s
y
s
te
m
m
u
s
t
ac
h
iev
e
as
ac
cu
r
ately
an
d
q
u
ic
k
ly
as
p
o
s
s
ib
le
at
ea
ch
s
tag
e
o
f
th
e
s
im
u
latio
n
.
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
Ma
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
tech
n
i
q
u
e
b
a
s
ed
o
n
th
e
g
r
e
y
w
o
lf o
p
timiz
a
tio
n
…
(
Leg
h
r
ib
B
ila
l
)
3575
Fig
u
r
e
9
.
B
lo
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
in
Simu
lin
k
/
MA
T
L
AB
Fig
u
r
e
1
0
.
GM
PP
u
n
d
er
d
i
f
f
er
en
t so
lar
ir
r
ad
iatio
n
co
n
d
itio
n
s
At
th
e
b
eg
in
n
in
g
o
f
th
e
s
im
u
latio
n
,
ea
ch
o
f
th
e
f
o
u
r
p
an
el
s
is
s
u
b
jecte
d
to
a
d
if
f
er
en
t
i
r
r
ad
iatio
n
,
r
ep
r
esen
ted
b
y
SIC4
,
as
f
o
llo
ws:
2
0
0
,
7
0
0
,
1
0
0
0
,
an
d
1
0
0
0
W
/m
².
Fig
u
r
e
1
1
s
h
o
ws
th
at
th
e
GW
O
alg
o
r
ith
m
ex
h
ib
its
s
tead
y
-
s
tate
o
s
cillatio
n
s
,
wh
ile
th
e
P&
O
alg
o
r
ith
m
s
tr
u
g
g
les
to
tr
a
c
k
th
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
,
as
clea
r
ly
illu
s
tr
ated
in
SIC4
o
f
Fig
u
r
e
1
2
.
I
n
c
o
n
tr
ast,
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
,
s
h
o
wn
in
Fig
u
r
e
1
3
,
ac
h
iev
es
a
r
esp
o
n
s
e
tim
e
o
f
0
.
0
7
s
an
d
s
u
cc
ess
f
u
lly
tr
ac
k
s
th
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
a
t
5
6
7
.
6
W
,
with
a
ca
lcu
lated
ef
f
i
cien
cy
o
f
9
9
.
9
5
%,
d
em
o
n
s
tr
atin
g
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
.
At
t
=
0
.
4
s
,
wh
e
n
th
e
ir
r
a
d
iatio
n
b
ec
o
m
es
u
n
if
o
r
m
ac
r
o
s
s
th
e
f
o
u
r
p
an
els
at
1
0
0
0
W
/m
²,
r
ep
r
esen
ted
b
y
SIC1
,
th
e
GW
O
-
P&
O
alg
o
r
ith
m
s
h
o
ws
th
e
b
est
r
esp
o
n
s
e
tim
e,
0
.
0
4
s
,
with
an
ef
f
ici
en
cy
o
f
9
9
.
9
5
%.
I
n
co
n
tr
ast,
Fig
u
r
e
1
1
s
h
o
ws
th
at
th
e
GW
O
alg
o
r
ith
m
h
as
a
h
ig
h
r
esp
o
n
s
e
tim
e
o
f
0
.
2
4
s
.
Fig
u
r
e
1
2
in
d
icate
s
th
at
th
e
P&
O
alg
o
r
ith
m
,
alth
o
u
g
h
s
u
p
p
o
s
ed
to
p
e
r
f
o
r
m
well
u
n
d
er
u
n
if
o
r
m
ir
r
a
d
iatio
n
co
n
d
itio
n
s
,
s
h
o
ws
a
r
esp
o
n
s
e
tim
e
o
f
0
.
1
5
s
an
d
a
n
ef
f
icien
cy
o
f
9
9
.
4
%.
At
t
=
0
.
8
s
,
ea
ch
o
f
t
h
e
f
o
u
r
p
a
n
els
ag
ain
r
ec
eiv
es
d
i
f
f
er
en
t
ir
r
a
d
iatio
n
s
:
1
0
0
,
6
0
0
,
8
0
0
,
a
n
d
8
0
0
W
/m
².
U
n
d
er
th
ese
co
n
d
i
tio
n
s
(
SIC3
s
eq
u
en
ce
)
,
b
o
th
t
h
e
P&
O
an
d
ev
e
n
GW
O
alg
o
r
ith
m
s
,
wh
ich
is
a
m
etah
eu
r
is
tic
alg
o
r
ith
m
,
f
ail
to
tr
ac
k
th
e
g
lo
b
al
m
ax
i
m
u
m
p
o
wer
,
as
s
h
o
wn
in
Fig
u
r
es
1
2
an
d
1
1
,
r
esp
ec
tiv
ely
.
I
n
c
o
n
tr
ast,
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
tr
a
ck
s
th
is
g
lo
b
al
p
o
wer
,
s
h
o
win
g
4
8
3
.
6
W
with
an
ef
f
icien
cy
o
f
9
9
.
9
5
% m
ain
tain
ed
an
d
a
r
esp
o
n
s
e
tim
e
o
f
0
.
0
7
s
,
as illu
s
tr
ated
in
Fig
u
r
e
1
3
i
n
th
e
SIC3
s
ec
t
io
n
.
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