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R
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J
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21
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ev
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ed
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ted
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1
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21
P
a
rti
a
l
sh
a
d
i
n
g
c
o
n
d
it
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o
n
(P
S
C)
is
c
o
m
m
o
n
a
n
d
c
o
m
p
li
c
a
ted
in
a
ll
t
y
p
e
s
o
f
P
V
p
o
we
r
p
lan
t
s
.
Th
e
re
fo
re
,
t
h
e
p
o
we
r
p
ro
d
u
c
t
io
n
o
f
a
so
lar
sy
ste
m
wo
u
ld
b
e
a
ffe
c
ted
b
y
th
e
m
ism
a
tch
p
h
e
n
o
m
e
n
a
p
ro
d
u
c
e
d
b
y
P
S
C
.
F
u
rth
e
r
m
o
re
,
wh
e
n
th
e
a
rra
y
is
p
a
rti
a
ll
y
sh
a
d
e
d
,
t
h
e
P
–
V
c
h
a
ra
c
teristics
b
e
c
o
m
e
m
o
re
c
o
m
p
lex
,
wh
ich
c
a
u
se
s
m
u
lt
ip
le
p
e
a
k
s
o
f
t
h
e
P
-
V
c
u
rv
e
.
S
o
,
t
h
e
sim
p
le
m
a
x
i
m
u
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
(M
P
P
T)
m
e
th
o
d
s
s
u
c
h
a
s
p
e
rt
u
rb
a
n
d
o
b
se
rv
e
(P
&
O)
will
fa
il
.
To
a
d
d
re
ss
th
e
a
b
o
v
e
issu
e
,
th
is
p
a
p
e
r
p
ro
p
o
se
s
a
c
o
m
b
i
n
a
ti
o
n
o
f
t
wo
d
iffere
n
t
a
p
p
ro
a
c
h
e
s,
im
p
lem
e
n
ti
n
g
d
istr
ib
u
te
d
M
P
P
T
(DM
P
P
T)
a
n
d
o
p
ti
m
ize
d
fu
z
z
y
/b
e
e
a
lg
o
rit
h
m
(OFBA).
D
M
P
P
T
c
a
n
b
e
u
ti
li
z
e
d
to
m
a
x
i
m
ize
so
lar
e
n
e
rg
y
b
y
a
ll
o
wi
n
g
e
a
c
h
m
o
d
u
le,
o
r
g
ro
u
p
o
f
m
o
d
u
les
,
to
b
e
m
a
n
a
g
e
d
in
d
e
p
e
n
d
e
n
t
ly
.
Also
,
d
u
e
t
o
t
h
e
o
u
tp
u
t
p
o
we
r
o
sc
il
lati
o
n
s
a
ro
u
n
d
th
e
o
p
e
ra
ti
n
g
p
o
i
n
t
i
n
t
h
e
P
&
O
m
e
th
o
d
,
a
n
O
F
BA
is
e
m
p
lo
y
e
d
,
w
h
ich
a
ll
o
wi
n
g
f
o
r
t
h
e
d
e
c
re
a
se
o
f
o
u
tp
u
t
p
o
we
r
o
sc
il
la
ti
o
n
s
wit
h
o
u
t
t
h
e
u
sa
g
e
o
f
tem
p
e
ra
tu
re
a
n
d
li
g
h
t
se
n
so
rs.
T
h
e
re
su
lt
sh
o
ws
t
h
a
t
u
ti
l
izin
g
o
f
DM
P
P
T
c
o
n
tro
l
a
p
p
r
o
a
c
h
in
c
o
n
ju
n
c
ti
o
n
wit
h
t
h
e
OFBA
b
o
o
st
s th
e
o
u
tp
u
t
g
e
n
e
ra
ted
p
o
we
r.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
ted
m
ax
im
u
m
p
o
wer
Fu
zz
y
/B
ee
h
y
b
r
id
m
eth
o
d
Par
tial
s
h
ad
in
g
co
n
d
itio
n
Po
wer
p
r
o
d
u
ctio
n
PV sy
s
tem
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Af
s
h
in
B
alal
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
C
o
m
p
u
ter
E
n
g
in
ee
r
in
g
T
ex
as T
ec
h
Un
iv
er
s
ity
9
1
0
B
o
s
to
n
Av
e,
L
u
b
b
o
ck
,
T
X,
USA
E
m
ail: A
f
s
h
in
.
b
alal@
ttu
.
ed
u
1.
I
NT
RO
D
UCT
I
O
N
B
ec
au
s
e
o
f
th
e
s
ca
r
city
o
f
f
o
s
s
il
f
u
els
a
n
d
th
e
e
f
f
ec
ts
o
f
clim
at
e
ch
an
g
e,
r
en
ewa
b
le
en
er
g
y
is
b
ec
o
m
in
g
in
cr
ea
s
in
g
ly
attr
ac
tiv
e.
So
la
r
en
er
g
y
is
a
p
o
llu
tio
n
-
f
r
ee
s
y
s
tem
wi
th
lo
wer
m
ain
te
n
an
ce
c
o
s
ts
d
is
tr
ib
u
ted
all
o
v
er
th
e
ea
r
th
[
1
]
.
T
h
e
PV
s
o
u
r
ce
'
s
m
ain
d
is
ad
v
an
tag
e
is
n
o
t
wo
r
k
in
g
d
u
r
in
g
clo
u
d
y
d
a
y
s
o
r
n
ig
h
t
tim
e
[
2
]
.
Al
s
o
,
th
e
PV sy
s
tem
d
o
es
n
o
t w
o
r
k
p
r
o
p
er
ly
with
h
av
in
g
p
ar
tially
s
h
ad
ed
m
o
d
u
les
,
an
d
PS
C
g
en
er
ate
s
s
ev
er
al
MPP
s
in
th
e
P
-
V
cu
r
v
e
[
3
]
,
[
4
]
.
T
o
ac
h
iev
e
h
ig
h
o
p
er
atio
n
al
p
o
in
ts
,
th
e
o
u
tp
u
t v
o
ltag
e
o
f
t
h
e
PV
s
y
s
tem
m
u
s
t
b
e
co
n
tin
u
o
u
s
ly
ad
j
u
s
ted
to
m
atch
ch
an
g
in
g
atm
o
s
p
h
er
i
c
co
n
d
itio
n
s
,
e
n
s
u
r
in
g
t
h
at
p
o
wer
g
e
n
er
ated
is
co
n
s
tan
tly
at
its
m
ax
im
u
m
v
alu
e
[
5
]
,
[
6
]
.
Ma
x
im
u
m
p
o
wer
p
r
o
d
u
ctio
n
ca
n
b
e
r
ea
ch
e
d
in
a
p
h
o
to
v
o
ltaic
s
y
s
tem
b
y
m
o
d
i
f
y
in
g
th
e
o
p
e
r
atin
g
p
o
in
t
o
f
th
e
ar
r
ay
s
f
o
r
s
p
ec
if
ic
co
n
d
itio
n
s
.
T
h
e
m
ain
d
is
ad
v
an
tag
es
o
f
s
o
lar
PV
s
y
s
tem
s
ar
e
th
at
th
eir
p
o
wer
o
u
tp
u
t
is
m
ain
ly
d
ep
en
d
en
t
o
n
clim
atic
f
ac
to
r
s
s
u
ch
as
s
u
n
s
h
in
e
an
d
clim
ate
tem
p
er
atu
r
e,
b
o
th
o
f
wh
ich
h
a
v
e
n
o
n
lin
ea
r
P
-
I
an
d
V
-
I
ch
ar
ac
ter
is
tics
[
7
]
.
As
a
r
esu
lt,
P
V
s
y
s
tem
s
h
av
e
lo
w
ef
f
icien
cy
,
an
d
it
is
n
o
t
p
o
s
s
ib
l
e
to
ef
f
ec
tiv
ely
u
s
e
s
o
lar
e
n
er
g
y
in
v
ar
ied
co
n
d
itio
n
s
[
8
]
,
[
9
]
.
Fig
u
r
e
1
s
h
o
ws
th
e
d
if
f
er
en
t
p
o
s
s
ib
le
MPP
s
o
f
th
e
s
y
s
tem
b
y
ch
an
g
in
g
t
h
e
s
u
n
r
ad
iatio
n
,
am
b
ie
n
t te
m
p
er
atu
r
e
,
an
d
PS
C
s.
Sev
er
al
ty
p
es
o
f
r
esear
ch
e
h
a
v
e
b
ee
n
d
o
n
e
to
in
cr
ea
s
e
t
h
e
o
u
tp
u
t
s
o
lar
p
o
wer
b
y
u
s
in
g
i
n
tellig
en
t
alg
o
r
ith
m
s
.
T
h
e
au
t
h
o
r
s
o
f
[
1
0
]
ex
am
in
e
th
e
F
u
to
s
h
ik
i
p
u
zz
le
m
o
d
el
u
n
d
er
PS
C
s
,
wh
ich
in
cr
ea
s
es
o
u
tp
u
t
p
o
wer
b
y
ch
an
g
i
n
g
th
e
p
lace
o
f
p
an
e
ls
w
ith
o
u
t
alter
in
g
th
e
m
o
d
u
les'
elec
tr
ical
co
n
n
ec
tio
n
s
.
I
n
[
1
1
]
,
a
g
lo
b
al
MPPT
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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&
Dr
i Sy
s
t
I
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N:
2
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8
8
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8
694
Op
timiz
ed
g
en
era
ted
p
o
w
er o
f a
s
o
la
r
P
V
s
ystem
u
s
in
g
a
n
in
tellig
en
t tra
ck
in
g
tech
n
iq
u
e
(
A
fs
h
in
B
a
la
l
)
2581
(
GM
PP
T
)
alg
o
r
ith
m
is
in
v
esti
g
ated
b
y
u
tili
zin
g
a
n
ar
tific
ial
b
ee
co
lo
n
y
(
AB
C
)
to
g
e
n
er
ate
th
e
b
est
d
u
ty
cy
cles
f
r
o
m
ea
c
h
s
u
b
s
tr
in
g
.
T
h
e
s
u
g
g
ested
m
eth
o
d
allo
ws
f
o
r
a
c
o
n
s
id
er
ab
le
d
ec
r
ea
s
e
in
th
e
n
u
m
b
er
o
f
v
o
ltag
e
an
d
cu
r
r
en
t
s
en
s
o
r
s
.
T
h
e
a
u
th
o
r
s
o
f
[
1
2
]
p
r
o
p
o
s
ed
an
MPPT
b
ased
o
n
ar
tific
ial
b
ee
co
lo
n
ies.
T
h
e
d
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n
ed
alg
o
r
i
th
m
p
r
o
d
u
ce
s
a
s
im
p
le
an
d
r
esil
ie
n
t
MPPT
s
ch
em
e
th
at
d
em
o
n
s
tr
ates
ex
ce
llen
t
p
er
f
o
r
m
an
ce
.
I
n
[
1
3
]
,
th
e
au
th
o
r
ex
am
in
es a
b
u
c
k
/b
o
o
s
t c
o
n
v
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ter
f
o
r
a
DM
PP
T
s
y
s
tem
th
at
c
an
g
et
s
u
itab
le
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u
t
p
u
t u
n
d
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d
i
f
f
er
en
t c
o
n
d
itio
n
s
.
T
h
e
aim
o
f
th
is
p
ap
er
is
to
in
cr
ea
s
e
p
o
wer
p
r
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d
u
ctio
n
b
y
u
s
in
g
th
e
DM
PP
T
a
lo
n
g
s
id
e
with
i
n
tellig
en
t
tr
ac
k
in
g
tech
n
iq
u
e.
DM
PP
T
to
p
o
lo
g
y
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in
wh
ich
ea
ch
PV
m
o
d
u
le
is
co
n
n
ec
t
ed
to
th
e
en
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y
s
y
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v
ia
in
d
ep
en
d
en
t
MPPT
co
n
v
er
te
r
s
,
m
ax
im
izes
th
e
ca
p
ac
ity
o
f
th
e
p
h
o
to
v
o
lta
ic
m
o
d
u
le
an
d
also
in
cr
ea
s
es
ef
f
icien
cy
.
Fu
r
t
h
er
m
o
r
e,
th
er
e
ar
e
d
if
f
e
r
en
t
b
asic
an
d
o
p
ti
m
ized
MPPT
alg
o
r
ith
m
s
in
P
V
s
y
s
tem
s
to
attain
m
ax
im
u
m
p
o
we
r
,
s
u
ch
as
P&
O,
in
cr
em
en
tal
co
n
d
u
ctan
ce
(
I
C
)
,
an
d
s
o
o
n
[
1
4
]
-
[
1
8
]
.
I
n
t
h
is
p
ap
er
,
P&
O
an
d
f
u
zz
y
lo
g
ic
co
n
tr
o
l
(
FLC)
m
et
h
o
d
s
ar
e
b
ein
g
s
tu
d
ie
d
.
Ho
wev
er
,
b
ec
au
s
e
o
f
th
e
o
u
tp
u
t
p
o
wer
o
s
cillatio
n
s
ar
o
u
n
d
th
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
P&
O
m
eth
o
d
an
d
th
e
lo
west
s
p
ee
d
o
f
th
e
FLC
m
eth
o
d
,
a
n
o
p
tim
ized
f
u
zz
y
/b
ee
alg
o
r
ith
m
is
u
s
ed
,
wh
ic
h
d
ec
r
e
ases
th
e
o
u
tp
u
t p
o
wer
o
s
cillat
io
n
an
d
also
in
cr
ea
s
es th
e
s
p
ee
d
o
f
f
i
n
d
in
g
MPP
s
.
Fig
u
r
e
1
.
Dif
f
e
r
en
t m
a
x
im
u
m
p
o
wer
p
o
in
ts
2.
SO
L
AR
P
V
D
E
SI
G
N
B
ec
au
s
e
PV p
o
wer
p
r
o
d
u
ctio
n
is
in
f
lu
en
ce
d
b
y
d
if
f
er
e
n
t su
n
r
ad
iatio
n
an
d
wea
th
er
s
,
th
er
ef
o
r
e
o
u
tp
u
t
p
o
wer
f
lu
ctu
ates
[
1
9
]
.
I
n
o
r
d
er
to
co
n
s
tr
u
ct
an
a
p
p
r
o
p
r
iate
s
o
lar
s
y
s
tem
,
ce
ll tem
p
er
atu
r
e
an
d
s
o
lar
ir
r
ad
iatio
n
,
as
well
as
in
f
o
r
m
atio
n
o
n
th
e
s
y
s
tem
'
s
co
m
p
o
s
itio
n
,
s
u
ch
a
s
r
ated
p
o
wer
,
n
u
m
b
er
o
f
p
an
els,
an
d
s
o
o
n
,
ar
e
n
ec
ess
ar
y
[
2
0
]
.
2
.
1
.
So
la
r
ce
ll c
ircuit
Fig
u
r
e
2
d
ep
icts
a
s
o
lar
ce
ll'
s
o
n
e
-
d
io
d
e
e
q
u
iv
alen
t
ci
r
cu
it.
So
lar
p
an
els,
o
f
co
u
r
s
e,
ar
e
m
ad
e
u
p
o
f
a
s
u
cc
ess
io
n
o
f
s
o
lar
ce
lls
ar
r
an
g
ed
in
a
p
ar
allel
p
atter
n
.
Fig
u
r
e
2
.
An
eq
u
iv
ale
n
t m
o
d
el
o
f
a
o
n
e
d
io
d
e
ce
ll
I
n
Fig
u
r
e
2
,
th
e
I
-
V
ch
ar
ac
ter
is
tic
o
f
th
e
ce
ll
is
s
tated
u
s
in
g
(
1
)
.
B
y
u
s
in
g
(
1
)
,
th
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
PV
s
y
s
tem
will b
e
d
ef
in
ed
.
=
−
[
(
(
+
)
)
−
1
]
−
(
+
)
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
5
8
0
–
2
5
92
2582
W
h
er
e
an
d
ar
e
th
e
s
er
ies
an
d
p
ar
allel
r
esis
tan
ce
o
f
th
e
s
o
lar
ce
ll,
V
a
n
d
I
a
r
e
th
e
v
o
ltag
e
a
n
d
th
e
o
u
tp
u
t
cu
r
r
en
t,
is
th
e
d
io
d
e’
s
s
atu
r
atio
n
cu
r
r
en
t,
a
n
d
ar
e
th
e
n
u
m
b
er
s
o
f
p
ar
allel
an
d
s
er
ie
s
ce
lls
,
T
is
th
e
ce
ll
tem
p
er
atu
r
e
in
ter
m
s
o
f
Kelv
in
,
an
d
A
is
th
e
id
ea
l
co
ef
f
icien
t
f
o
r
d
i
o
d
e,
K
is
B
o
ltzm
an
n
'
s
co
n
s
tan
t
wh
ich
is
eq
u
al
to
=
1
.
23
×
10
23
an
d
=
1
.
6
×
10
−
19
is
th
e
c
h
ar
g
e
o
f
an
elec
tr
o
n
in
u
n
its
o
f
co
u
lo
m
b
(
C
)
,
an
d
is
th
e
p
h
o
to
v
o
ltaic
cu
r
r
e
n
t
[
2
1
]
.
2
.
2
.
Cha
ra
c
t
er
is
t
ic
o
f
t
he
s
o
l
a
r
m
o
du
le
T
h
e
ch
ar
ac
ter
is
tics
o
f
a
PV
p
an
el
th
at
is
u
s
ed
ar
e
in
d
icate
d
in
T
ab
le
1
.
E
ac
h
p
an
el
in
th
e
PV
s
y
s
tem
h
as 9
6
ce
lls
co
n
n
ec
te
d
in
s
er
ie
s
.
T
ab
le
1
.
Featu
r
es o
f
th
e
PV m
o
d
u
le
u
n
d
er
STC co
n
d
itio
n
C
e
l
l
s
p
e
r
mo
d
u
l
e
96
Ti
l
t
a
n
g
l
e
25
0
C
O
p
e
r
a
t
i
o
n
t
e
mp
e
r
a
t
u
r
e
-
40
0
C
t
o
+
8
5
0
C
La
t
i
t
u
d
e
3
3
.
6
0
0
C
mo
d
u
l
e
s
1
4
4
Lo
n
g
i
t
u
d
e
1
0
1
.
8
9
0
C
Ef
f
i
c
i
e
n
c
y
1
8
.
7
1
%
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z
i
m
u
t
h
1
8
0
0
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s
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a
t
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p
o
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e
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3
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2
2
w
F
r
a
me
C
l
a
s
s
1
b
l
a
c
k
a
n
o
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z
e
d
a
l
u
m
i
n
u
m
V
o
l
t
a
g
e
V
(
O
C
)
6
4
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2
0
V
W
e
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g
h
t
2
0
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6
k
g
C
u
r
r
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(
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9
6
A
S
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z
e
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1
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2
i
n
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6
1
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3
i
n
M
a
x
i
m
u
m
M
P
P
c
u
r
r
e
n
t
5
.
5
8
A
Ty
p
e
o
f
m
o
d
u
l
e
M
o
n
o
c
r
y
st
a
l
l
i
n
e
M
a
x
i
m
u
m
M
P
P
v
o
l
t
a
g
e
5
4
.
6
8
V
M
o
u
n
t
i
n
g
s
y
s
t
e
m
F
i
x
e
d
r
a
c
k
T
h
e
s
y
s
tem
r
e
p
o
r
ted
in
th
is
s
tu
d
y
h
as
a
r
ated
DC
p
o
we
r
p
er
m
o
d
u
le
o
f
3
0
5
.
2
2
watts,
a
V
OC
o
f
6
4
.
2
v
o
lts
,
an
d
a
n
I
SC
o
f
5
.
9
6
am
p
e
r
es
.
T
h
en
,
in
T
ab
le
1
,
all
o
f
th
e
r
eq
u
ir
e
d
p
ar
am
ete
r
s
ar
e
lis
ted
,
in
clu
d
i
n
g
R
ated
p
o
wer
,
I
SC
,
V
OC
,
V
MPP
,
an
d
I
MPP
.
I
n
T
ab
le
2
,
th
e
PV
ce
ll’s
p
ar
am
eter
s
wh
ich
a
r
e
s
ig
n
if
i
ca
n
tly
tem
p
e
r
atu
r
e
-
d
ep
en
d
e
n
t
,
ar
e
lis
ted
b
elo
w
f
o
r
0
°
C
,
2
5
°
C
,
an
d
5
0
°
C
.
T
h
en
,
th
e
o
p
er
atin
g
p
o
in
ts
o
f
t
h
e
I
-
V
ch
ar
ac
ter
is
tic
cu
r
v
es c
o
u
l
d
b
e
ca
lcu
lated
.
T
ab
le
2
.
C
ell’
s
p
ar
am
eter
s
in
d
if
f
er
en
t te
m
p
er
atu
r
e
0
°
C
2
5
°
C
5
0
°
C
D
C
p
o
w
e
r
P
DC
3
3
1
.
3
0
W
3
0
5
.
2
2
W
2
7
9
.
0
1
W
Li
g
h
t
-
g
e
n
e
r
a
t
e
d
c
u
r
r
e
n
t
I
L
5
.
9
5
A
5
.
9
6
A
5
.
9
8
A
S
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
I
SC
5
.
9
4
V
5
.
9
6
A
5
.
9
7
A
O
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
V
OC
6
8
.
4
9
V
6
4
.
2
0
V
5
9
.
8
5
V
V
o
l
t
a
g
e
a
t
ma
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
V
MP
5
9
.
2
4
V
5
4
.
6
8
V
5
0
.
1
5
V
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
p
o
i
n
t
I
MP
5
.
5
9
A
5
.
5
8
A
5
.
5
6
A
Ef
f
i
c
i
e
n
c
y
2
0
.
3
1
%
1
8
.
7
1
%
1
7
.
1
1
%
Als
o
,
ac
co
r
d
in
g
to
t
h
e
Fig
u
r
e
3
,
th
e
P
-
V
an
d
I
-
V
cu
r
v
es
f
o
r
t
h
e
d
if
f
er
e
n
t
tem
p
er
atu
r
e
h
as
b
ee
n
p
lo
tted
in
MA
T
L
AB
.
B
ased
o
n
Fig
u
r
e
3
,
b
y
in
cr
ea
s
in
g
t
h
e
tem
p
er
at
u
r
e
,
th
e
g
en
er
ated
p
o
wer
d
ec
r
ea
s
es.
T
h
er
ef
o
r
e,
0
°
C
h
as th
e
h
ig
h
est p
o
wer
,
p
r
o
d
u
ctio
n
an
d
th
e
tem
p
e
r
atu
r
e
o
f
5
0
°
C
h
as th
e
lo
wer
p
o
wer
p
r
o
d
u
ctio
n
.
Fig
u
r
e
3
.
I
-
V
an
d
P
-
V
cu
r
v
e
o
f
0
°C
,
2
5
°C
,
an
d
5
0
°C
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:
2
0
8
8
-
8
694
Op
timiz
ed
g
en
era
ted
p
o
w
er o
f a
s
o
la
r
P
V
s
ystem
u
s
in
g
a
n
in
tellig
en
t tra
ck
in
g
tech
n
iq
u
e
(
A
fs
h
in
B
a
la
l
)
2583
3.
CO
NT
RO
L
L
E
R
DE
SI
G
N
T
h
e
o
p
tim
u
m
c
o
n
v
e
r
ter
m
u
s
t
b
e
ch
o
s
en
to
tr
an
s
f
er
th
e
h
ig
h
e
s
t a
m
o
u
n
t
o
f
p
o
wer
f
r
o
m
th
e
s
o
lar
ce
ll to
th
e
o
u
tp
u
t
lo
ad
.
T
h
en
,
a
b
u
ck
-
b
o
o
s
t
d
c
-
d
c
(
B
B
DC
)
co
n
v
er
ter
m
ay
m
atch
t
h
e
r
e
q
u
ir
e
d
v
o
ltag
e
in
th
e
s
u
b
s
y
s
tem
lo
ad
to
c
h
an
g
e
t
h
e
o
u
tp
u
t
v
o
lt
ag
e
o
f
t
h
e
s
o
lar
ce
lls
[
2
2
]
,
[
2
3
]
.
As
a
r
esu
lt,
it
ap
p
ea
r
s
th
at
a
B
B
D
C
co
n
v
er
ter
is
a
g
o
o
d
o
p
tio
n
.
T
h
e
co
n
tr
o
ller
p
ar
t
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
co
n
s
is
ts
o
f
a
B
B
DC
co
n
v
er
ter
t
h
at
u
s
es
th
e
MPP
T
s
y
s
tem
b
y
im
p
lem
en
tin
g
P&
O,
FLC,
an
d
FB
A
m
eth
o
d
s
to
ac
h
iev
e
m
ax
im
u
m
p
o
wer
.
3
.
1
.
B
uck
-
bo
o
s
t
dc
t
o
dc
co
n
v
er
t
er
I
n
o
r
d
e
r
to
u
tili
ze
a
B
B
DC
co
n
v
er
ter
,
th
e
ca
p
ac
ito
r
an
d
in
d
u
cto
r
v
alu
es
ar
e
d
eter
m
in
ed
in
(
2
)
an
d
(
3
)
[
2
4
]
,
[
2
5
]
.
E
q
u
atio
n
2
d
ef
i
n
es
th
e
in
d
u
ct
o
r
v
alu
e
o
f
th
e
B
B
D
C
,
an
d
(
3
)
also
d
ef
in
es
th
e
ca
p
ac
ito
r
v
alu
e
o
f
th
e
co
n
v
er
ter
.
=
(
1
−
)
2
2
(
2
)
=
∆
(
3
)
In
(
2
)
,
I
OB
is
th
e
o
u
tp
u
t b
o
u
n
d
ar
y
cu
r
r
en
t,
a
n
d
in
E
q
u
atio
n
(
3
)
,
∆
V
is
th
e
o
u
tp
u
t
v
o
ltag
e
r
i
p
p
le.
Fig
u
r
e
4
s
h
o
ws
a
s
ch
em
atic
o
f
a
B
B
D
C
co
n
v
er
ter
.
Acc
o
r
d
in
g
to
Fig
u
r
e
4
,
a
B
B
DC
co
n
v
er
ter
co
n
s
is
ts
o
f
a
MO
SF
E
T
co
n
n
ec
ted
to
th
e
D
C
s
o
u
r
ce
s
,
an
in
d
u
cto
r
,
a
d
io
d
e,
an
d
a
ca
p
ac
ito
r
to
r
ed
u
ce
th
e
r
ip
p
le
o
f
th
e
o
u
tp
u
t.
Fig
u
r
e
4
.
Simu
latio
n
o
f
a
B
B
DC
co
n
v
er
ter
3
.
2
.
M
a
x
i
m
um
po
wer
po
int
t
ra
ck
ing
(
M
P
P
T
)
T
h
e
I
-
V
c
h
ar
ac
ter
is
tic
o
f
n
o
n
l
in
ea
r
s
o
lar
ar
r
a
y
s
is
af
f
ec
ted
b
y
r
ad
iatio
n
an
d
tem
p
er
atu
r
e
c
h
an
g
es,
as
m
en
tio
n
ed
ea
r
lier
.
A
n
MPPT
s
y
s
tem
m
u
s
t b
e
cr
ea
ted
to
tack
l
e
th
is
p
r
o
b
lem
.
As s
h
o
wn
in
F
ig
u
r
e
5
,
th
e
B
B
D
C
co
n
v
er
ter
is
u
s
ed
as
a
p
o
wer
p
r
o
ce
s
s
o
r
to
m
atch
t
h
e
lo
ad
t
o
th
e
s
o
lar
ar
r
a
y
an
d
ab
s
o
r
b
as
m
u
ch
en
er
g
y
as
p
o
s
s
ib
le
[
2
6
]
,
[
2
7
]
.
Acc
o
r
d
in
g
to
Fig
u
r
e
5
,
a
n
MPPT
co
n
tr
o
l
ler
co
n
s
is
ts
o
f
PV
ar
r
ay
s
,
a
B
B
DC
co
n
v
er
ter
,
an
d
v
o
ltag
e
an
d
cu
r
r
en
t m
ea
s
u
r
em
en
t sen
s
o
r
s
.
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
am
o
f
th
e
MPPT
s
y
s
tem
3
.
3
.
P
er
t
urb a
nd
o
bs
er
v
e
met
ho
d (
P
&O
)
As
s
tated
in
th
e
i
n
tr
o
d
u
ctio
n
,
a
r
an
g
e
o
f
s
tr
ateg
ies
an
d
ap
p
r
o
ac
h
es
ca
n
b
e
em
p
lo
y
ed
t
o
ca
r
r
y
o
u
t
t
h
e
co
n
ce
p
t
o
f
tr
ac
k
in
g
th
e
MPP.
T
h
e
P&
O
ap
p
r
o
ac
h
is
th
e
m
o
s
t
well
-
k
n
o
wn
o
f
th
em
[
2
8
]
,
[
2
9
]
.
P&
O
alg
o
r
ith
m
ca
n
b
e
s
ee
n
in
Fig
u
r
e
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
5
8
0
–
2
5
92
2584
(
a)
(
b
)
Fig
u
r
e
6
.
P &
O
m
eth
o
d
,
(
a)
P
&
O
alg
o
r
ith
m
,
a
n
d
(
b
)
P
-
V
cu
r
v
e
Acc
o
r
d
in
g
to
Fig
u
r
e
6
(
a)
,
a
s
lig
h
t
p
e
r
tu
r
b
atio
n
∆
is
u
s
ed
to
c
au
s
e
th
e
PV
m
o
d
u
le'
s
p
o
wer
t
o
v
a
r
y
.
On
a
r
eg
u
lar
b
asis
,
th
e
PV
o
u
t
p
u
t
p
o
wer
is
m
ea
s
u
r
ed
an
d
co
m
p
ar
ed
to
th
e
p
r
e
v
io
u
s
p
o
wer
.
I
f
th
e
o
u
tp
u
t
p
o
wer
in
cr
ea
s
es,
th
e
p
r
o
ce
d
u
r
e
is
r
ep
ea
ted
;
o
th
er
wis
e,
th
e
p
er
tu
r
b
atio
n
is
r
ev
er
s
ed
.
As
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
,
wh
e
n
u
tili
zin
g
th
e
P&
O
m
eth
o
d
,
th
e
r
atio
o
f
eq
u
als ze
r
o
at
th
e
h
ig
h
est p
o
wer
p
o
in
t,
is
p
o
s
itiv
e
p
r
io
r
to
th
is
p
o
in
t,
an
d
th
en
b
ec
o
m
es
n
eg
ativ
e
af
t
er
th
at.
If
is
p
o
s
itiv
e,
it
s
h
o
u
ld
k
ee
p
g
o
in
g
in
th
e
s
am
e
d
ir
ec
tio
n
u
n
til
it
h
its
ze
r
o
;
I
f
it'
s
n
eg
ativ
e,
it
s
h
o
u
ld
k
ee
p
g
o
in
g
in
th
e
o
th
er
d
ir
ec
ti
o
n
u
n
til
it
g
ets
th
e
i
n
ten
d
ed
r
esu
lt.
W
h
en
ch
o
o
s
in
g
MPPT
s
y
s
tem
s
,
th
er
e
ar
e
two
m
ain
th
in
g
s
to
co
n
s
id
er
:
s
im
p
licity
an
d
ac
c
u
r
ac
y
w
h
ich
ar
e
th
e
m
ain
f
ea
tu
r
es
o
f
P&
O
m
eth
o
d
[
3
0
]
,
[
3
1
]
.
Ho
w
ev
er
,
th
is
m
eth
o
d
is
s
lo
w,
an
d
it
g
en
er
ates
o
u
tp
u
t
p
o
wer
o
s
c
illa
tio
n
ar
o
u
n
d
th
e
o
p
er
atio
n
al
p
o
in
ts
u
n
d
er
a
v
ar
i
ety
o
f
co
n
d
itio
n
s
,
s
u
ch
as c
lo
u
d
y
d
ay
s
.
3
.
4
.
F
uzzy
lo
g
ic
co
ntr
o
l
(
F
L
C)
Fo
r
u
n
if
o
r
m
ir
r
ad
iatio
n
cir
c
u
m
s
tan
ce
s
,
co
n
tr
o
ller
m
o
d
elin
g
is
ea
s
ier
.
Ho
wev
e
r
,
wh
e
n
i
t
co
m
es
to
d
esig
n
in
g
f
o
r
th
e
PS
C
,
th
e
p
r
o
b
lem
b
ec
o
m
es
im
p
o
r
tan
t
s
in
ce
th
e
s
y
s
tem
will
b
e
u
n
n
ec
ess
ar
ily
co
m
p
licated
.
T
h
e
en
tire
t
r
ac
k
in
g
p
r
o
ce
s
s
m
u
s
t
b
e
en
h
an
ce
d
in
o
r
d
er
to
i
n
cr
ea
s
e
ef
f
icien
cy
,
p
a
r
ticu
lar
l
y
wh
en
tr
ac
k
in
g
in
r
ap
id
ly
ch
an
g
in
g
wea
th
er
co
n
d
itio
n
s
.
T
h
e
PV
s
y
s
tem
m
u
s
t
b
e
m
ath
em
atica
lly
m
o
d
e
led
b
ef
o
r
e
th
e
co
n
tr
o
ller
ca
n
b
e
d
esig
n
ed
.
As
a
r
esu
lt,
an
in
tellig
en
t
tech
n
iq
u
e
was
d
ev
elo
p
e
d
th
at
d
o
es
n
o
t
r
e
q
u
i
r
e
th
e
s
y
s
tem
to
b
e
m
ath
em
atica
lly
m
o
d
e
led
.
T
r
ac
k
er
s
th
at
r
ely
o
n
FLC
ar
e
co
n
s
i
d
er
ed
to
b
e
s
m
ar
t
b
ec
a
u
s
e
th
e
co
n
tr
o
ller
ac
h
iev
es
h
ig
h
ef
f
icien
cy
r
e
g
ar
d
less
o
f
wh
eth
er
th
e
in
f
o
r
m
atio
n
is
ac
cu
r
ate
o
r
n
o
t
[
3
2
]
-
[
34]
.
T
h
is
FLC
h
as
two
k
ey
ad
v
an
tag
es
o
v
er
o
th
er
tec
h
n
iq
u
es:
1
)
FLC
is
ab
le
to
wo
r
k
with
o
u
t
h
av
in
g
a
p
er
f
ec
t
m
o
d
el,
an
d
2
)
th
e
FLC
d
esig
n
is
s
o
lely
in
th
e
h
an
d
s
o
f
h
u
m
an
s
[
3
5
]
.
T
h
e
f
u
zz
y
r
u
les,
wh
ich
ar
e
o
n
e
o
f
th
r
ee
m
ain
co
m
p
o
n
en
ts
,
ar
e
d
esig
n
ed
u
s
in
g
h
u
m
a
n
e
x
p
er
ti
s
e.
Fu
zz
if
icatio
n
,
f
u
zz
y
r
u
les,
an
d
d
ef
u
zz
if
icatio
n
ar
e
th
e
th
r
ee
s
tag
es
o
f
th
e
FLC
ap
p
r
o
ac
h
in
g
e
n
er
al
[
3
6
]
-
[
3
8
]
.
T
h
e
in
p
u
ts
f
o
r
t
h
e
PV
s
y
s
tem
ar
e
tu
r
n
ed
in
t
o
lin
g
u
is
tic
p
ar
am
eter
s
d
u
r
in
g
f
u
zz
if
icatio
n
.
T
h
e
m
ain
p
u
r
p
o
s
e
o
f
if
-
th
en
r
u
les
is
to
p
r
o
v
id
e
lin
g
u
is
tic
v
ar
ia
b
les
p
a
r
am
eter
s
b
y
a
p
p
ly
in
g
h
u
m
an
u
n
d
er
s
tan
d
i
n
g
[
3
9
]
.
Def
u
zz
if
icatio
n
is
a
f
u
zz
if
ica
tio
n
o
p
p
o
s
ite
p
r
o
ce
d
u
r
e
th
at
u
s
es
m
ath
em
atica
l
r
elatio
n
s
t
o
ex
tr
ac
t
lin
g
u
is
tic
p
ar
am
eter
s
.
T
h
e
FLC
o
u
tp
u
t
is
co
n
v
er
t
ed
f
r
o
m
a
lin
g
u
is
tic
v
ar
iab
le
to
a
n
u
m
er
ical
v
ar
iab
le
d
u
r
in
g
th
e
d
ef
u
zz
if
icatio
n
p
h
ase,
an
d
th
i
s
is
f
ed
in
to
th
e
co
n
v
er
ter
as
an
an
alo
g
s
ig
n
al
[
4
0
]
.
T
h
e
tr
i
an
g
le
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
f
o
r
b
o
th
th
e
s
y
s
tem
'
s
in
p
u
t
a
n
d
o
u
tp
u
t
in
th
is
s
y
s
tem
,
th
e
s
in
g
leto
n
f
u
zz
if
ie
r
,
t
h
e
Ma
m
d
an
i
in
f
er
en
c
e
en
g
in
e,
an
d
th
e
av
er
a
g
e
ce
n
ter
d
ef
u
zz
if
ier
wer
e
em
p
lo
y
ed
.
T
h
e
d
if
f
er
e
n
t in
p
u
t le
v
els ar
e
d
e
f
in
ed
in
T
ab
le
3
s
o
th
at
th
ey
s
h
o
u
l
d
f
u
lly
co
v
er
th
e
v
a
r
iatio
n
r
a
n
g
e.
As T
ab
le
3
i
n
d
icate
s
,
th
er
e
ar
e
2
5
f
u
zz
y
r
u
les
-
b
ased
.
T
h
er
ef
o
r
e,
it
f
u
lly
co
v
e
r
s
f
iv
e
v
ar
iab
les
,
in
clu
d
in
g
n
eg
ativ
e
b
ig
(
NB
)
,
n
eg
ativ
e
s
m
all
(
NS)
,
Z
E
(
ze
r
o
)
,
PS
(
p
o
s
itiv
e
s
m
all)
,
P
S
(
p
o
s
it
iv
e
s
m
all)
,
PB
(
p
o
s
itiv
e
b
ig
)
.
A
th
o
r
o
u
g
h
u
n
d
er
s
tan
d
i
n
g
o
f
th
e
b
eh
av
io
r
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
is
r
eq
u
ir
ed
to
d
ev
elo
p
a
f
u
zz
y
co
n
tr
o
ller
an
d
s
elec
t
f
u
zz
y
r
u
les.
T
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t
,
ac
co
r
d
in
g
to
Fig
u
r
e
6
,
h
as
an
i
m
p
o
r
tan
t a
ttrib
u
te
o
f
=
0
.
T
h
e
p
o
i
n
ts
h
av
in
g
th
e
p
r
o
p
er
ty
o
f
>
0
h
av
e
th
e
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:
2
0
8
8
-
8
694
Op
timiz
ed
g
en
era
ted
p
o
w
er o
f a
s
o
la
r
P
V
s
ystem
u
s
in
g
a
n
in
tellig
en
t tra
ck
in
g
tech
n
iq
u
e
(
A
fs
h
in
B
a
la
l
)
2585
v
o
ltag
e
less
th
an
th
e
v
o
ltag
e
o
f
th
e
o
p
tim
al
p
o
in
t
(
MPP)
,
an
d
th
e
p
o
i
n
ts
with
th
e
p
r
o
p
er
ty
o
f
<
0
h
av
e
m
o
r
e
th
an
th
e
v
o
ltag
e
o
f
th
e
o
p
tim
a
l
p
o
in
t.
T
h
e
ab
o
v
e
-
m
en
tio
n
ed
b
eh
av
io
r
al
t
r
ait
will
b
e
ex
p
lo
it
ed
in
th
is
p
ap
er
to
d
eter
m
in
e
th
e
m
ax
i
m
u
m
p
o
we
r
p
o
i
n
t
b
y
FLC
[
4
1
]
.
Fig
u
r
e
7
i
n
d
icate
s
th
e
u
s
e
o
f
th
is
tech
n
iq
u
e
f
o
r
PV.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
f
o
llo
win
g
v
ar
ia
b
l
es a
r
e
g
en
er
ated
:
(
)
=
(
)
−
(
−
1
)
(
)
−
(
−
1
)
(
4
)
(
)
=
(
)
−
(
−
1
)
(
5
)
I
n
(
4
)
an
d
(
5
)
,
P
(
t)
an
d
V
(
t)
ar
e
th
e
in
s
tan
tan
e
o
u
s
p
o
wer
an
d
v
o
ltag
e
v
alu
es,
r
esp
ec
tiv
e
ly
.
I
n
t
h
is
p
ap
er
,
th
e
f
u
zz
y
c
o
n
tr
o
ller
in
p
u
t
(
)
an
d
(
)
,
an
d
t
h
e
o
u
tp
u
t
is
th
e
p
u
ls
e
s
ig
n
al.
Var
iab
le
(
)
r
e
p
r
esen
ts
th
e
v
ar
iatio
n
o
f
p
o
wer
to
v
o
ltag
e
v
ar
iatio
n
s
,
an
d
(
)
r
ep
r
esen
ts
th
e
v
ar
iatio
n
r
ate
o
f
(
)
;
th
ese
v
ar
iab
les
will
b
e
av
ailab
le
to
th
e
f
u
zz
y
in
f
er
en
ce
m
ac
h
in
e
af
ter
f
u
z
z
if
icatio
n
s
o
th
at
th
e
f
u
zz
y
v
ar
iab
le
CD
(
t
)
ca
n
b
e
d
eter
m
in
ed
,
w
h
ich
is
eq
u
al
to
:
CD
(
t
)
=
D
(
t
)
−
D
(
T
−
1
)
(
6
)
Fig
u
r
e
7
.
B
lo
ck
d
iag
r
am
o
f
FL
C
tech
n
iq
u
e
T
ab
le
3
.
Fu
zz
y
r
u
le
b
ase
NB
NS
Z
PS
PB
NB
NB
NB
NB
Z
Z
NS
NS
NS
NS
Z
Z
Z
NS
Z
Z
Z
PS
PS
Z
Z
PS
PS
PS
PB
Z
Z
PB
PB
PB
3
.
5
.
Art
if
ici
a
l
bee
co
lo
ny
(
A
B
C)
AB
C
is
a
d
if
f
er
en
t w
ay
,
u
s
ed
in
MPPT
ap
p
licatio
n
an
d
in
s
p
i
r
ed
b
y
h
o
n
ey
b
ee
s
'
attem
p
ts
f
o
r
f
o
o
d
a
n
d
th
eir
p
r
o
p
er
co
o
p
er
atio
n
.
T
h
e
an
alo
g
y
o
f
h
o
n
ey
b
ee
s
is
im
p
l
em
en
ted
in
th
e
ap
p
licatio
n
o
f
t
h
is
ap
p
r
o
ac
h
.
T
h
ese
h
o
n
ey
b
ee
s
r
esid
e
in
co
lo
n
ies
an
d
d
iv
id
e
th
em
s
elv
es
in
to
g
r
o
u
p
s
to
f
in
d
f
o
o
d
.
Similar
ly
,
th
e
o
p
tim
al
MPP
i
s
f
o
u
n
d
b
y
ass
ig
n
in
g
ea
ch
tr
ac
k
in
g
o
p
er
atio
n
to
its
o
wn
p
r
o
ce
s
s
.
Ho
n
ey
b
ee
s
ca
n
b
e
d
iv
id
ed
in
to
th
r
ee
g
r
o
u
p
s
:
em
p
lo
y
ed
,
o
n
lo
o
k
er
s
,
an
d
s
co
u
ts
.
I
n
f
o
r
m
atio
n
ab
o
u
t
t
h
e
f
o
o
d
wh
ich
is
g
ath
e
r
ed
b
y
th
e
e
m
p
lo
y
ed
h
o
n
ey
b
e
e
k
ick
s
o
f
f
th
e
p
r
o
ce
d
u
r
e.
I
n
a
s
y
s
tem
atic
m
ath
em
atica
l
ap
p
r
o
ac
h
,
th
e
in
f
o
r
m
atio
n
is
p
ass
ed
o
n
to
th
e
o
b
s
er
v
e
r
h
o
n
ey
b
ee
s
[
4
2
]
,
[
4
3
]
.
At
t
h
e
s
am
e
tim
e,
th
e
s
co
u
ts
ar
e
lo
o
k
in
g
f
o
r
s
u
b
s
titu
te
m
ea
ls
.
No
n
ee
d
to
m
en
tio
n
th
at
ea
ch
n
ec
tar
s
o
u
r
ce
'
s
lo
ca
tio
n
o
f
f
er
s
a
s
o
lu
tio
n
to
th
e
p
r
o
b
le
m
.
T
h
e
f
itn
ess
o
f
th
e
r
elate
d
s
o
lu
tio
n
is
p
r
o
p
o
r
tio
n
al
to
th
e
n
ec
tar
am
o
u
n
t
o
f
t
h
e
n
ec
tar
s
o
u
r
ce
.
As
s
h
o
wn
in
(
7
)
,
in
d
icate
s
th
e
b
ee
s
th
at
m
atch
to
th
e
i’
th
h
o
n
ey
s
o
u
r
ce
lo
o
k
f
o
r
a
n
ew
h
o
n
ey
s
o
u
r
ce
.
I
n
ad
d
itio
n
,
th
e
co
r
r
esp
o
n
d
in
g
h
ir
ed
b
ee
s
b
ec
o
m
e
s
co
u
t b
ee
s
,
an
d
th
e
s
co
u
t
b
ee
s
u
s
e
th
e
(
8
)
t
o
f
in
d
ad
d
itio
n
al
p
r
o
b
ab
le
s
o
lu
tio
n
s
.
=
+
(
−
)
(
7
)
=
+
(
0
,
1
)
(
−
)
(
8
)
W
h
er
e
an
d
ar
e
th
e
lo
wer
an
d
u
p
p
er
b
o
u
n
d
s
,
r
esp
ec
tiv
ely
,
i =
1
,
2
,
3
,
4
,
5
,
…,
N,
d
=
1
,
2
,
3
,
4
,
5
,
…,
D,
is
a
r
an
d
o
m
n
u
m
b
er
b
etwe
en
(
-
1
,
1
)
.
Fin
ally
,
ea
ch
o
n
lo
o
k
er
b
ee
ch
o
o
s
es
a
h
o
n
ey
s
o
u
r
ce
b
ased
o
n
p
r
o
b
a
b
ilit
y
,
wh
ich
is
co
m
p
u
ted
ac
co
r
d
i
n
g
to
(
9
)
.
=
∑
=
1
(
9
)
W
h
er
e
is
th
e
a
d
ap
tiv
e
v
alu
e
o
f
as
a
p
o
ten
tial
s
o
lu
tio
n
.
T
h
e
u
ltima
te
g
o
al
is
to
co
llect
in
f
o
r
m
atio
n
o
n
th
e
m
o
s
t
p
le
n
tifu
l
f
o
o
d
s
u
p
p
ly
.
T
h
e
alg
o
r
ith
m
p
er
f
o
r
m
s
b
etter
wh
en
t
h
e
n
u
m
b
er
o
f
h
ir
e
d
b
ee
s
in
th
e
g
r
o
u
p
is
m
o
r
e
ab
u
n
d
a
n
t.
T
h
is
f
o
o
d
-
f
in
d
in
g
m
eth
o
d
is
well
-
s
u
ited
to
PV
s
y
s
tem
s
,
wh
ich
u
s
e
t
h
e
r
ig
h
t
ac
tiv
atio
n
ap
p
r
o
ac
h
to
f
in
d
th
e
o
p
tim
u
m
p
o
in
t
[
4
4
]
.
A
lo
ca
tio
n
o
f
MPP
is
tr
ac
k
ed
m
u
ch
b
etter
u
s
in
g
t
h
is
tech
n
iq
u
e.
T
h
e
ef
f
icien
cy
o
f
th
e
AB
C
tech
n
iq
u
e
is
alm
o
s
t 9
8
p
er
ce
n
t
[
4
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
5
8
0
–
2
5
92
2586
4.
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
e
n
o
v
elty
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
th
at
th
is
ar
ticle
p
r
o
p
o
s
es
a
c
o
m
b
in
atio
n
o
f
tw
o
s
ep
ar
ate
ap
p
r
o
ac
h
es
,
in
clu
d
in
g
DM
PP
T
an
d
th
e
i
n
tellig
en
t Fu
zz
y
/B
ee
tr
ac
k
in
g
m
et
h
o
d
.
4
.
1
.
Dis
t
ribute
d m
a
x
i
m
um
p
o
wer
po
int
t
ra
ck
ing
(
DM
P
P
T
)
T
h
e
DM
PP
T
ap
p
r
o
ac
h
is
u
s
ed
to
r
ed
u
ce
th
e
o
u
tp
u
t
p
o
wer
d
r
o
p
p
r
o
d
u
ce
d
b
y
PV
m
o
d
u
le
o
p
er
atio
n
co
n
d
itio
n
s
th
at
ar
en
'
t
co
m
p
atib
le
[
4
6
]
.
I
n
th
is
s
ce
n
ar
io
,
as
s
h
o
wn
in
Fig
u
r
e
8
,
a
p
ar
allel
r
ath
er
th
an
a
s
er
ies
co
n
n
ec
tio
n
o
f
m
o
d
u
les
is
in
v
es
tig
ated
.
Gr
id
-
c
o
n
n
ec
ted
in
v
e
r
t
er
s
h
av
e
a
d
if
f
e
r
en
t
in
p
u
t
v
o
lta
g
e.
T
o
g
en
e
r
ate
th
e
d
esire
d
o
u
tp
u
t
p
o
wer
,
a
s
er
ies
o
f
PV
m
o
d
u
les
ar
e
co
m
m
o
n
l
y
co
n
n
ec
ted
in
s
er
ies
to
p
r
o
v
i
d
e
an
in
p
u
t
v
o
ltag
e
with
in
th
e
i
n
v
er
ter
'
s
o
p
er
atin
g
r
an
g
e,
an
d
id
en
tical
s
tr
in
g
s
ar
e
th
en
co
n
n
ec
ted
i
n
p
ar
allel.
A
s
y
s
tem
m
ad
e
u
p
o
f
a
s
eq
u
en
ce
o
f
p
ar
allel
s
tr
in
g
s
will
b
e
ev
alu
ated
f
o
r
th
ese
r
e
aso
n
s
.
Mic
r
o
in
v
er
ter
s
ca
n
b
e
u
s
ed
to
co
n
v
er
t
DC
v
o
ltag
e
f
r
o
m
ea
c
h
m
o
d
u
le
to
AC
p
o
wer
in
a
PV
s
y
s
tem
wi
th
a
s
m
aller
n
u
m
b
er
o
f
m
o
d
u
l
es.
T
h
e
PV
s
y
s
tem
d
escr
ib
ed
in
th
is
s
tu
d
y
is
m
ad
e
u
p
o
f
eig
h
t
s
tr
in
g
s
,
ea
ch
wit
h
1
8
m
o
d
u
les.
I
n
th
is
in
s
tan
ce
,
s
tr
in
g
in
v
er
ter
s
ar
e
th
e
o
p
tim
u
m
ty
p
e
o
f
i
n
v
e
r
ter
.
T
h
e
g
r
id
-
co
n
n
ec
ted
s
o
lar
p
o
w
er
s
y
s
tem
with
d
is
tr
ib
u
ted
m
a
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
u
tili
zin
g
s
tr
in
g
in
v
er
t
er
s
is
s
h
o
wn
in
Fig
u
r
e
9
.
Acc
o
r
d
in
g
to
Fig
u
r
e
9
,
in
th
e
p
r
o
p
o
s
ed
DM
PP
T
,
th
r
ee
ar
r
ay
s
ar
e
in
s
er
ies
to
g
eth
er
,
wh
ich
ar
e
p
ar
alleled
with
o
th
er
g
r
o
u
p
s
o
f
th
r
ee
ar
r
a
y
s
to
b
e
co
n
tr
o
lle
d
in
d
ep
en
d
en
tly
.
(
a)
(
b
)
Fig
u
r
e
8
.
Dis
tr
ib
u
ted
PV sy
s
tem
,
(
a)
d
is
tr
ib
u
ted
s
er
ies m
o
d
u
l
es (
b
)
d
is
tr
ib
u
ted
p
ar
allel
m
o
d
u
les
Fig
u
r
e
9
.
Gr
id
-
co
n
n
ec
ted
s
o
lar
p
o
wer
s
y
s
tem
with
d
is
tr
ib
u
te
d
m
ax
im
u
m
p
o
wer
p
o
in
t t
r
ac
k
in
g
4
.
2
.
I
nte
llig
ent
F
uzzy
/B
ee
co
ntr
o
ller
des
ig
n
B
y
ap
p
ly
in
g
th
is
o
p
tim
ized
f
u
n
ctio
n
to
a
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
,
a
n
o
v
el
ap
p
r
o
ac
h
is
cr
ea
ted
,
wh
ich
,
wh
en
co
m
p
ar
ed
to
P&
O
an
d
f
u
zz
y
m
et
h
o
d
s
,
r
esu
lts
in
a
s
ig
n
if
ican
t in
cr
ea
s
e
in
o
u
tp
u
t
p
o
w
er
.
Fig
u
r
e
1
0
s
h
o
ws
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:
2
0
8
8
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8
694
Op
timiz
ed
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en
era
ted
p
o
w
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s
o
la
r
P
V
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ystem
u
s
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g
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n
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tellig
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t tra
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g
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e
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la
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2587
th
e
d
iag
r
am
o
f
th
e
p
r
o
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o
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ed
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eth
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d
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I
n
f
u
zz
y
ap
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licatio
n
s
,
f
u
zz
y
o
p
tim
izatio
n
is
a
cr
itic
al
to
p
ic.
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
f
u
zz
y
/b
ee
co
n
tr
o
l
m
eth
o
d
,
as
ca
n
b
e
s
ee
n
in
Fig
u
r
e
1
0
,
in
o
r
d
er
to
o
v
er
co
m
e
th
i
s
tr
o
u
b
lin
g
is
s
u
e.
I
n
th
e
p
r
o
p
o
s
ed
in
tellig
e
n
t
f
u
zz
y
/b
ee
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o
r
ith
m
,
th
e
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
s
o
f
t
h
e
f
u
zz
y
m
eth
o
d
h
av
e
b
ee
n
o
p
tim
ized
with
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e
h
o
n
ey
b
ee
alg
o
r
ith
m
,
w
h
ich
ca
u
s
es
a
f
ast
ap
p
r
o
ac
h
[
4
7
]
.
B
ased
o
n
Fig
u
r
e
1
0
an
d
(
7
)
,
(
8
)
,
an
d
(
9
)
,
in
o
r
d
er
to
ass
ess
th
e
AB
C
p
o
p
u
latio
n
,
th
e
f
itn
ess
f
u
n
ctio
n
(
o
b
jectiv
e
f
u
n
ctio
n
)
is
d
ef
in
ed
b
y
m
ea
n
s
q
u
ar
e
er
r
o
r
(
MSE
)
,
r
ep
r
esen
t
ed
b
y
(
10
)
.
/
=
1
∑
(
(
)
−
(
)
)
2
=
1
(
1
0
)
W
h
er
e
(
)
is
th
e
o
u
tp
u
t
i
n
th
e
i’
th
s
am
p
le
with
a
25
-
r
u
le
b
ase
wh
ich
co
v
e
r
s
f
iv
e
v
a
r
iab
les
in
clu
d
in
g
n
eg
ativ
e
b
ig
(
NB
)
,
n
eg
ativ
e
s
m
all
(
NS)
,
Z
E
(
ze
r
o
)
,
PS
(
p
o
s
itiv
e
s
m
all)
,
an
d
PB
(
p
o
s
itiv
e
b
ig
)
.
I
n
Fig
u
r
e
1
1
,
o
p
tim
ized
m
em
b
er
s
h
ip
f
u
n
cti
o
n
s
h
av
e
b
ee
n
s
h
o
wn
.
I
n
th
is
p
ap
er
,
we
co
n
s
id
er
a
4
4
k
W
s
o
lar
P
V
s
y
s
tem
with
th
e
b
ee
alg
o
r
ith
m
in
wh
ic
h
th
e
n
u
m
b
e
r
o
f
b
ee
s
is
2
0
0
,
a
n
d
th
e
m
in
im
u
m
o
f
iter
atio
n
is
3
0
0
.
Fig
u
r
e
1
0
.
Diag
r
am
o
f
Fu
zz
y
/
B
ee
Alg
o
r
ith
m
Fig
u
r
e
1
1
.
Fu
zz
y
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
o
p
tim
ized
with
th
e
B
ee
alg
o
r
ith
m
with
f
iv
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
5.
SI
M
UL
A
T
I
O
N
A
ND
RE
SU
L
T
S
On
th
e
b
asis
o
f
v
ar
ied
s
o
lar
r
ad
iatio
n
s
an
d
tem
p
er
atu
r
e
lev
els,
s
ev
er
al
asp
ec
ts
o
f
So
lar
P
V
p
o
wer
m
o
d
u
les
ar
e
in
v
esti
g
ated
.
T
h
e
PV
s
y
s
tem
d
escr
ib
ed
in
th
i
s
s
tu
d
y
is
m
ad
e
u
p
o
f
eig
h
t
s
tr
in
g
s
,
ea
ch
with
1
8
m
o
d
u
les.
Fu
r
th
e
r
m
o
r
e
,
th
e
i
n
c
r
em
en
t
-
d
ec
r
e
m
en
t
s
tep
s
ize
in
th
e
P&
O
alg
o
r
ith
m
is
0
.
0
3
5
.
Als
o
,
th
e
g
en
er
ate
d
p
o
wer
is
d
is
cu
s
s
ed
u
s
in
g
MA
T
L
AB
Simu
lin
k
.
Fig
u
r
e
1
2
s
h
o
ws
th
e
o
u
tp
u
t
p
o
wer
o
f
o
n
e
m
o
d
u
le
b
y
s
im
p
le
MPPT
u
s
in
g
th
e
P&
O
m
eth
o
d
.
As
it
i
s
o
b
v
io
u
s
b
ased
o
n
Fig
u
r
e
1
3
,
th
e
o
s
cillatio
n
ar
o
u
n
d
th
e
o
p
er
atin
g
p
o
in
t
in
th
e
P&
O
m
eth
o
d
is
h
ig
h
,
wh
ich
ca
u
s
es
s
o
m
e
l
o
s
s
es
an
d
lo
wer
s
th
e
e
f
f
icien
cy
b
y
u
s
in
g
th
is
tech
n
i
q
u
e.
In
ad
d
itio
n
,
Fig
u
r
e
1
4
d
is
p
lay
s
th
e
o
u
tp
u
t
p
o
wer
o
f
a
s
in
g
le
m
o
d
u
le
u
s
in
g
th
e
f
u
zz
y
tech
n
iq
u
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2
5
8
0
–
2
5
92
2588
Fig
u
r
e
1
2
.
Po
wer
E
x
tr
ac
tio
n
o
f
o
n
e
m
o
d
u
le
b
y
I
n
d
iv
i
d
u
al
M
PP
T
with
P&
O
m
eth
o
d
Fig
u
r
e
1
3
.
Oscill
atio
n
ar
o
u
n
d
th
e
o
p
er
atin
g
p
o
i
n
t w
ith
th
e
P
&
O
m
eth
o
d
Fig
u
r
e
1
4
.
Po
w
er
E
x
tr
ac
tio
n
o
f
o
n
e
m
o
d
u
le
b
y
i
n
d
iv
id
u
al
M
PP
T
with
Fu
zz
y
m
eth
o
d
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:
2
0
8
8
-
8
694
Op
timiz
ed
g
en
era
ted
p
o
w
er o
f a
s
o
la
r
P
V
s
ystem
u
s
in
g
a
n
in
tellig
en
t tra
ck
in
g
tech
n
iq
u
e
(
A
fs
h
in
B
a
la
l
)
2589
No
n
ee
d
to
m
en
tio
n
t
h
at
th
e
f
lu
ctu
atio
n
o
f
p
o
wer
a
r
o
u
n
d
th
e
o
p
er
atin
g
p
o
in
t
i
n
th
e
f
u
zz
y
m
eth
o
d
is
m
u
ch
less
th
an
th
e
P&
O
m
et
h
o
d
,
wh
ich
ca
n
b
e
s
ee
n
in
Fig
u
r
e
1
5
.
Fin
ally
,
u
tili
zin
g
th
e
f
u
zz
y
/b
ee
ap
p
r
o
ac
h
,
Fig
u
r
e
1
6
s
h
o
ws
th
e
o
u
tp
u
t
p
o
wer
o
f
a
s
in
g
le
m
o
d
u
le
.
Acc
o
r
d
in
g
to
Fig
u
r
e
1
6
,
th
e
g
en
e
r
at
ed
p
o
wer
is
a
litt
le
h
ig
h
er
th
a
n
th
e
p
r
ev
io
u
s
tech
n
iq
u
es.
Fig
u
r
e
1
5
.
L
o
wer
o
s
cillatio
n
ar
o
u
n
d
th
e
o
p
er
atin
g
p
o
in
t w
ith
Fu
zz
y
m
eth
o
d
Fig
u
r
e
1
6
.
Po
wer
E
x
tr
ac
tio
n
o
f
o
n
e
m
o
d
u
le
b
y
I
n
d
iv
i
d
u
al
M
PP
T
with
Fu
zz
y
/B
ee
m
eth
o
d
T
h
er
ef
o
r
e,
i
n
th
e
f
u
zz
y
/b
ee
m
e
th
o
d
,
f
u
zz
y
m
em
b
e
r
s
h
ip
f
u
n
cti
o
n
s
ar
e
o
p
tim
ized
b
y
th
e
b
ee
c
o
lo
n
y
o
p
tim
izatio
n
alg
o
r
ith
m
s
o
th
at
th
e
o
u
t
p
u
t
p
o
wer
in
th
e
f
u
zz
y
/
b
ee
alg
o
r
ith
m
is
m
o
r
e
th
an
th
e
f
u
zz
y
m
et
h
o
d
.
T
a
b
le
4
s
h
o
ws
th
e
ex
tr
ac
ted
p
o
wer
o
f
th
e
p
r
e
s
en
ted
s
o
lar
s
y
s
tem
b
y
th
r
ee
p
r
o
p
o
s
ed
m
et
h
o
d
s
.
T
ab
le
4
.
T
h
e
g
en
e
r
ated
p
o
wer
o
f
o
n
e
m
o
d
u
le
with
th
r
ee
d
if
f
e
r
en
t m
eth
o
d
s
P
&O
F
LC
F
B
A
G
e
n
e
r
a
t
e
d
p
o
w
e
r
o
f
e
a
c
h
mo
d
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l
e
a
t
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o
l
a
r
n
o
o
n
2
8
4
.
9
7
W
2
9
2
.
1
1
W
2
9
6
.
8
4
W
G
e
n
e
r
a
t
e
d
p
o
w
e
r
o
f
t
h
e
w
h
o
l
e
P
V
sy
s
t
e
m
a
t
s
o
l
a
r
n
o
o
n
4
1
0
3
5
.
6
4
W
4
2
0
6
3
.
8
4
W
4
2
7
4
4
.
9
6
W
T
h
e
o
u
tp
u
t
p
o
wer
in
th
e
ab
o
v
e
th
r
ee
v
ar
io
u
s
m
eth
o
d
s
v
ar
ies
,
as
s
h
o
wn
in
T
ab
le
4
.
At
a
s
te
ad
y
-
s
tate,
th
e
h
ig
h
est
o
u
tp
u
t
p
o
wer
f
o
r
th
e
en
tire
s
y
s
tem
u
s
in
g
th
e
F
B
A
i
s
2
9
6
W
.
Du
e
to
ch
an
g
es
in
ir
r
ad
ian
ce
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.