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653
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DS
An
A
dv
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MP
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n A
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ficial Bee
Co
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Algo
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for MP
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Ha
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Feb
6
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2
0
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P
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m
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t
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lar
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h
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ra
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teristic
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M
P
P
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n
t
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is
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B
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tlab
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m
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x
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m
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m
p
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©
201
7
In
s
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C
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p
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r
:
Sal
m
i
Ha
s
s
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EEA
&
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m
b
en
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s
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r
ay
s
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m
a
x
i
m
u
m
p
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p
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in
t
tr
ac
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m
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n
co
n
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n
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atin
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in
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P
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1
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[
1
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tech
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3
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4
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5
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s
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.
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Fig
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r
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1
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Gen
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Cha
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ased
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Fig
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r
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1
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Ir
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din
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Co
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Fig
u
r
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3
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r
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ed
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ies
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cted
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.
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er
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(
a)
(
b
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I
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3.
M
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NT
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N
G
Ma
x
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m
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m
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t
tr
ac
k
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n
g
(
MP
PT
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tech
n
iq
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e
is
u
s
ed
to
ex
tr
ac
t
th
e
m
a
x
i
m
u
m
p
o
w
e
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eliv
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ed
b
y
t
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e
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lar
p
an
el.
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n
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o
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ith
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s
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tr
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th
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ax
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m
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m
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h
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m
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s
t
f
a
m
o
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s
is
P
er
tu
r
b
an
d
Ob
s
er
v
e
(
P
&
O)
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I
n
t
h
is
s
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tio
n
,
w
e
o
f
f
er
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n
e
w
co
n
tr
o
ller
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ased
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n
A
B
C
u
n
d
er
s
h
ad
in
g
co
n
d
itio
n
.
3
.
1
.
P
er
t
urb a
nd
o
bs
er
v
e
P
er
tu
r
b
an
d
o
b
s
er
v
e
alg
o
r
ith
m
is
t
h
e
m
o
s
t
u
s
ed
m
et
h
o
d
to
p
u
r
s
u
e
th
e
m
a
x
i
m
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m
p
o
w
e
r
p
o
in
t
o
f
a
p
h
o
to
v
o
ltaic
g
e
n
er
ato
r
.
T
h
e
p
r
in
cip
le
is
to
d
is
r
u
p
t
th
e
v
o
ltag
e
o
r
d
u
t
y
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cle
a
n
d
ca
lcu
lati
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g
t
h
e
p
o
w
er
ter
m
i
n
al
o
f
t
h
e
P
V
m
o
d
u
le.
a.
W
h
en
p
(
k
-
l)
<p
(
k
)
,
th
e
v
o
lta
g
e
is
in
cr
ea
s
ed
.
b.
W
h
en
p
(
k
-
l)
>
p
(
k
)
,
th
e
v
o
lta
g
e
is
d
ec
r
ea
s
ed
.
3
.
2
.
AB
C
Co
ntr
o
ller
O
pti
m
i
za
t
io
n Appli
e
d
t
o
T
ra
ck
t
he
M
P
P
un
der
P
a
rt
ia
l Sha
din
g
Co
nd
it
io
n
:
3
.
2
.
1
.
F
un
da
m
e
nta
l o
f
AB
C
O
pti
m
iza
t
io
n Alg
o
rit
h
m
I
n
th
e
A
B
C
m
o
d
el,
t
h
e
co
lo
n
y
co
n
s
i
s
ts
o
f
t
h
r
ee
g
r
o
u
p
s
o
f
b
ee
s
:
e
m
p
lo
y
ed
b
ee
s
,
o
n
lo
o
k
er
s
an
d
s
co
u
t
s
.
I
t
ass
u
m
es
t
h
at
th
er
e
is
o
n
l
y
o
n
e
ar
ti
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icial
e
m
p
lo
y
ed
b
ee
f
o
r
ea
ch
f
o
o
d
s
o
u
r
ce
.
T
h
e
e
m
p
lo
y
ed
b
ee
s
g
o
to
t
h
eir
f
o
o
d
s
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r
ce
an
d
co
m
e
b
ac
k
t
o
h
iv
e.
T
h
e
y
s
h
ar
e
th
is
d
ata
w
it
h
o
n
lo
o
k
er
b
ee
s
b
y
d
an
ci
n
g
in
t
h
e
d
esig
n
ated
d
an
ce
ar
ea
i
n
s
id
e
t
h
e
h
i
v
e.
T
h
e
n
at
u
r
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o
f
d
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n
ce
i
s
p
r
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p
o
r
t
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h
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tar
co
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te
n
t
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f
f
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o
d
s
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r
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j
u
s
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ex
p
lo
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b
y
t
h
e
d
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g
b
ee
.
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h
e
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n
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ee
s
ar
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w
a
iti
n
g
in
t
h
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h
i
v
e
f
o
r
th
e
d
ata,
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at
ch
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g
t
h
e
d
an
ce
s
o
f
e
m
p
lo
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ed
b
ee
s
a
n
d
ch
o
o
s
in
g
f
o
o
d
s
o
u
r
ce
s
d
ep
en
d
in
g
o
n
d
an
ce
s
.
T
h
er
ef
o
r
e,
g
o
o
d
f
o
o
d
s
o
u
r
ce
s
attr
ac
t
m
o
r
e
o
n
lo
o
k
er
b
ee
s
co
m
p
ar
ed
to
b
ad
o
n
es.
W
h
en
e
v
er
a
f
o
o
d
s
o
u
r
ce
is
ex
p
lo
ited
f
u
ll
y
,
all
t
h
e
e
m
p
lo
y
ed
b
ee
s
ass
o
ciate
d
w
it
h
it
ab
a
n
d
o
n
t
h
e
f
o
o
d
s
o
u
r
ce
,
an
d
b
ec
o
m
e
s
co
u
t.
Sco
u
t
b
ee
s
s
ea
r
c
h
r
an
d
o
m
l
y
f
o
r
n
e
w
f
o
o
d
s
o
u
r
ce
s
[
8
]
.
T
h
e
f
lo
w
ch
ar
t o
f
t
h
e
p
r
o
p
o
s
ed
A
B
C
alg
o
r
ith
m
i
s
g
iv
e
n
i
n
Fi
g
u
r
e
4
[
9
]
:
Fig
u
r
e
4
.
Flo
w
c
h
ar
t o
f
t
h
e
A
B
C
A
lg
o
r
it
h
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
n
a
d
v
a
n
ce
d
MPP
T B
a
s
ed
o
n
A
r
tifi
cia
l B
ee
C
o
lo
n
y
A
lg
o
r
ith
m
fo
r
…
(
S
a
lmi H
a
s
s
a
n
)
651
T
h
e
s
te
p
s
o
f
th
e
A
B
C
alg
o
r
ith
m
ar
e
o
u
tl
in
ed
as
f
o
ll
o
w
s
:
a.
E
m
p
lo
y
ed
b
e
es:
I
n
itial
f
o
o
d
s
o
u
r
ce
s
ar
e
r
an
d
o
m
l
y
g
e
n
er
ate
d
f
o
r
all
e
m
p
lo
y
ed
b
ee
s
w
it
h
in
its
li
m
its
ac
co
r
d
in
g
to
th
e
E
q
u
atio
n
s
.
x
i
= x
m
in
+
r
an
d
[
0
,
1
]
*
(
x
m
ax
-
x
min
)
(
4
)
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h
er
e
x
m
in
a
n
d
x
max
r
ep
r
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t
r
esp
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t
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m
in
i
m
u
m
a
n
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th
e
m
a
x
i
m
u
m
,
i
∈
{1
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2
,
3
…SN}
w
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h
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t
h
e
n
u
m
b
er
o
f
ca
n
d
id
ate.
Af
ter
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itial
izatio
n
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t
h
e
p
o
p
u
latio
n
o
f
th
e
s
o
lu
t
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t
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1
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2
.
.
.
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f
t
h
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s
e
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o
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m
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lo
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ed
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ee
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,
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e
o
n
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o
k
er
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ee
s
a
n
d
th
e
s
co
u
t
b
ee
s
.
Fo
r
ea
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le,
e
v
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y
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m
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ee
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a
f
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d
s
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i
(
E
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atio
n
2
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en
e
s
ti
m
ates i
ts
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tar
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v
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V
i
= x
i
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5
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W
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er
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k
∈
{1
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2
.
.
.
SN}
is
r
an
d
o
m
l
y
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o
s
en
.
Ф
i
∈
[
0
,
1
]
b.
On
lo
o
k
er
b
ee
s
:
E
ac
h
o
n
lo
o
k
e
r
b
ee
s
f
in
d
s
n
e
w
s
o
lu
tio
n
V
i
w
it
h
i
n
th
e
n
e
ig
h
b
o
r
h
o
o
d
o
f
x
i
b
ased
o
n
th
e
p
r
o
b
ab
ilit
y
v
al
u
e
P
i d
ef
in
e
d
as:
P
i
=
∑
(
6
)
W
h
er
e
f
it is
t
h
e
f
it
n
ess
v
al
u
e
o
f
th
e
s
o
lu
tio
n
x
i.
c.
Sco
u
t:
A
b
a
n
d
o
n
ed
f
o
o
d
s
o
u
r
c
es
ar
e
lo
ca
ted
an
d
ar
e
ex
c
h
an
g
ed
w
it
h
t
h
e
n
e
w
f
o
o
d
s
o
u
r
ce
s
f
o
u
n
d
b
y
s
co
u
ts
.
d.
B
est
f
o
o
d
:
A
t
th
e
en
d
o
f
ea
ch
s
ea
r
c
h
c
y
cle,
t
h
e
al
g
o
r
ith
m
m
e
m
o
r
izes
t
h
e
b
est
s
o
l
u
tio
n
ac
h
iev
ed
s
o
f
ar
an
d
r
ep
ea
ts
th
e
p
r
o
ce
d
u
r
e
f
r
o
m
th
e
e
m
p
lo
y
ed
b
ee
s
p
h
ase
u
n
t
il
th
e
m
ax
i
m
u
m
c
y
cle
n
u
m
b
e
r
(
MCN)
.
3
.
2
.
2
Appl
ica
t
io
n o
f
AB
C
a
l
g
o
rit
h
m
t
o
t
he
M
P
P
T
T
o
r
ea
liz
e
th
e
d
ir
ec
t
co
n
t
r
o
l
A
B
C
-
b
as
e
d
M
PP
T
,
ea
ch
s
o
lu
t
io
n
is
d
ef
in
ed
as
th
e
d
u
ty
cy
cle
v
alu
e
d
o
f
th
e
DC
–
DC
c
o
n
v
er
t
e
r
.
E
q
u
at
io
n
s
(
4
)
an
d
(
5
)
b
e
co
m
e:
d
i
=
d
m
in
+
r
an
d
[
0
,
1
]
(
d
m
ax
− d
m
in
)
(
7
)
n
e
w
-
d
i
= d
i
+
фi
(
d
i
− d
k
)
(
8
)
T
h
e
f
itn
e
s
s
o
f
ea
c
h
s
o
l
u
tio
n
(
d
u
t
y
c
y
cle)
i
s
ch
o
s
e
n
a
s
th
e
g
en
er
ated
p
o
w
er
P
pt
o
f
th
e
P
GS.
T
h
en
,
E
q
u
atio
n
(
6
)
b
ec
o
m
e
:
=
∑
(
9
)
W
h
er
e
P
v
i
is
t
h
e
p
o
w
er
o
f
p
h
o
to
v
o
ltaic
ar
r
a
y
f
o
r
th
e
co
r
r
esp
o
n
d
in
g
d
u
t
y
c
y
cle
d
i.
T
o
ev
al
u
ate
th
e
d
u
t
y
c
y
cle
s
,
th
e
d
ig
ita
l
co
n
tr
o
ller
s
u
cc
e
s
s
i
v
el
y
o
u
tp
u
t
s
th
e
P
W
M
s
ig
n
al
ac
co
r
d
in
g
to
th
e
v
al
u
e
o
f
d
i
,
an
d
th
en
t
h
e
P
V
v
o
ltag
e
Vp
v
i
a
n
d
c
u
r
r
en
t
I
p
v
i
ca
n
b
e
m
ea
s
u
r
ed
a
n
d
t
h
e
co
r
r
esp
o
n
d
in
g
p
o
w
er
(
P
p
v
i)
o
f
ea
c
h
d
u
t
y
c
y
cle
d
i
ca
n
b
e
ca
lcu
lated
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
I
n
th
is
s
ec
t
io
n
,
th
e
b
o
th
s
ea
r
ch
alg
o
r
ith
m
s
o
f
m
a
x
i
m
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
p
er
tu
r
b
&
o
b
s
er
v
e
an
d
A
B
C
)
ar
e
s
i
m
u
la
ted
w
it
h
t
h
e
s
o
f
t
w
ar
e
m
atlab
/s
i
m
u
li
n
k
u
n
d
er
s
h
ad
i
n
g
co
n
d
itio
n
.
T
h
e
p
o
w
er
-
v
o
lta
g
e
ch
ar
ac
ter
is
tic
o
f
P
V
ar
r
a
y
s
u
s
ed
in
s
i
m
u
latio
n
w
h
ich
f
o
r
m
e
d
b
y
t
w
o
s
er
ies
co
n
n
ec
ted
P
V
m
o
d
u
les.
O
n
e
o
f
th
e
m
is
s
h
ad
ed
an
d
ac
ts
as
a
lo
ad
in
s
tead
o
f
a
p
o
w
er
s
o
u
r
c
e.
T
h
e
P
-
V
ch
ar
ac
ter
is
tic
ex
h
i
b
its
m
u
lt
ip
le
lo
ca
l
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
s
(
L
MP
P
s
)
(
F
ig
u
r
e
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
0
8
8
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8
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2
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J
u
n
e
2
0
1
7
:
6
4
7
–
6
5
3
652
Fig
u
r
e
5
.
P
-
V
cu
r
v
e
u
n
d
er
s
h
a
d
in
g
co
n
d
itio
n
(
G1
=1
0
0
0
w
/
m
2
an
d
G2
=8
0
0
W
/m
2
)
I
n
a
s
it
u
atio
n
w
h
er
e
t
h
e
P
V
ar
r
ay
is
u
n
d
er
p
ar
tial
s
h
ad
i
n
g
co
n
d
it
io
n
,
P
&
O
al
g
o
r
ith
m
h
as
n
’
t
t
h
e
ca
p
ab
ilit
y
o
f
f
i
n
d
in
g
t
h
e
g
lo
b
al
p
ea
k
(
2
0
0
W
)
an
d
it
u
s
es
p
er
t
u
r
b
atio
n
to
ch
ec
k
i
f
th
e
cu
r
r
e
n
t
o
p
er
atin
g
p
o
in
t
is
th
e
MP
P
.
I
f
t
h
e
c
u
r
r
en
t
o
p
er
atin
g
p
o
in
t
is
n
o
t
t
h
e
MP
P
,
P
&
O
n
ee
d
s
p
er
tu
r
b
atio
n
in
o
r
d
er
to
m
o
v
e
to
th
e
o
p
er
atin
g
p
o
in
t
to
th
e
MP
P
.
T
o
o
s
m
al
l
a
p
er
tu
r
b
atio
n
s
ize
m
ak
e
s
th
e
co
n
v
er
g
e
n
ce
ti
m
e
to
th
e
MP
P
to
o
lo
n
g
an
d
m
a
y
a
ls
o
m
ak
e
it
v
u
ln
er
ab
le
to
s
en
s
o
r
n
o
is
e.
L
ar
g
e
p
er
tu
r
b
atio
n
s
ize
w
ill
ca
u
s
e
o
s
cillatio
n
ar
o
u
n
d
t
h
e
MP
P
.
Ho
w
e
v
er
,
in
th
is
al
g
o
r
ith
m
(
A
B
C
)
,
t
h
e
n
u
m
b
er
o
f
ca
n
d
id
ate
s
o
lu
tio
n
s
SN
(
b
ee
s
)
in
f
l
u
en
ce
s
t
h
e
co
n
v
er
g
e
n
ce
s
p
ee
d
an
d
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
al
g
o
r
ith
m
.
Mo
r
e
o
f
b
ee
s
m
a
k
es
ea
s
ier
to
f
i
n
d
th
e
g
lo
b
al
MP
P
w
it
h
a
g
o
o
d
ac
cu
r
ac
y
a
n
d
v
er
y
q
u
icl
y
.
T
h
e
v
o
ltag
e
s
tar
ts
r
a
n
d
o
m
l
y
b
y
3
2
th
e
n
,
b
y
co
m
p
ar
aiso
n
o
f
t
h
e
ca
n
d
id
ate
s
o
lu
t
io
n
,
i
s
r
ed
u
c
ed
in
to
3
0
w
h
ic
h
co
r
r
esp
o
n
d
o
n
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
(
MP
P
)
at
t
=0
.
0
0
4
s
(
Fig
u
r
e
6
-
7
-
8
)
.
T
h
e
A
B
C
al
g
o
r
ith
m
ca
n
tr
ac
k
th
e
MP
P
v
er
y
q
u
ic
k
l
y
a
n
d
ef
f
ec
tiv
e
l
y
w
it
h
o
u
t
an
y
o
s
cillatio
n
s
in
t
h
e
s
tead
y
s
ta
te.
Du
r
in
g
a
ch
a
n
g
e
i
n
te
m
p
er
atu
r
e
o
r
ir
r
ad
iatio
n
,
t
h
e
A
B
C
a
lg
o
r
it
h
m
r
esets
(
we
co
n
tr
o
l
th
e
f
l
u
ct
u
atio
n
o
f
w
ea
t
h
er
co
n
d
itio
n
s
th
r
o
u
g
h
E
q
u
at
io
n
(
1
0
)
th
en
co
n
v
er
g
es to
th
e
n
e
w
m
ax
i
m
u
m
p
o
w
er
,
w
h
ic
h
m
a
k
es o
u
r
m
o
r
e
r
o
b
u
s
t a
lg
o
r
ith
m
.
(
1
0
)
Fig
u
r
e
6
.
T
r
en
d
o
f
P
PV
f
o
r
A
B
C
m
et
h
o
d
.
Fig
u
r
e
7
.
T
r
en
d
o
f
I
PV
f
o
r
A
B
C
m
et
h
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
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A
n
a
d
v
a
n
ce
d
MPP
T B
a
s
ed
o
n
A
r
tifi
cia
l B
ee
C
o
lo
n
y
A
lg
o
r
ith
m
fo
r
…
(
S
a
lmi H
a
s
s
a
n
)
653
Fig
u
r
e
8
.
T
r
en
d
o
f
V
PV
f
o
r
A
B
C
m
et
h
o
d
.
5.
CO
NCLU
SI
O
N
I
n
th
i
s
w
o
r
k
,
w
e
p
r
ese
n
t
an
o
p
ti
m
izatio
n
o
f
t
h
e
en
er
g
y
p
r
o
d
u
ce
d
b
y
a
P
V
m
o
d
u
le
b
y
a
n
i
m
p
r
o
v
ed
A
B
C
al
g
o
r
ith
m
.
T
h
is
tec
h
n
iq
u
e
is
n
ec
es
s
ar
y
to
m
ar
k
t
h
e
p
o
in
t
o
f
m
ax
i
m
u
m
p
o
w
er
w
h
en
t
h
er
e
ar
e
m
o
r
e
th
a
n
o
n
e
m
a
x
i
m
u
m
p
o
in
t
i
n
t
h
e
I
-
V
ch
ar
ac
ter
is
t
ic
o
f
t
h
e
P
V
m
o
d
u
le.
T
h
e
s
i
m
u
latio
n
s
r
esu
lt
s
s
h
o
w
th
e
ef
f
ec
tiv
e
n
e
s
s
o
f
t
h
i
s
m
et
h
o
d
to
th
e
d
i
f
f
er
en
t
c
li
m
ate
c
h
an
g
e
s
,
w
h
ich
d
e
m
o
n
s
tr
ates
t
h
at
t
h
e
o
p
ti
m
ized
s
e
tti
n
g
s
ar
e
co
r
r
ec
t.
B
esid
e
all
o
f
t
h
at,
it
p
r
o
v
id
e
s
j
u
s
t
o
n
e
o
p
ti
m
al
v
al
u
e
o
f
d
u
t
y
c
y
cle
a
n
d
ca
n
tr
ac
k
t
h
e
MP
P
v
er
y
q
u
ick
l
y
a
n
d
ef
f
ec
ti
v
el
y
w
it
h
o
u
t
an
y
o
s
cil
latio
n
s
in
t
h
e
s
tead
y
s
tate.
I
n
co
n
tr
ast,
w
h
e
n
th
er
e
ar
e
m
o
r
e
t
h
an
o
n
e
m
ax
i
m
u
m
p
o
in
t
i
n
th
e
I
-
V
c
h
ar
ac
ter
is
tic
o
f
t
h
e
P
V
m
o
d
u
le
,
P
&
O
f
in
d
m
an
y
v
al
u
es
o
f
d
u
t
y
c
y
cle,
w
h
ic
h
ca
u
s
e
s
i
n
t
h
e
e
n
d
o
f
t
h
eir
co
n
v
er
g
e
n
ce
a
n
i
n
s
tab
ilit
y
a
n
d
o
s
cillatio
n
s
.
T
h
is
o
s
c
illatio
n
i
s
d
u
e
to
t
h
e
u
n
s
tab
le
v
alu
e
s
o
f
d
u
t
y
c
y
cle
«
d
»
w
h
ich
d
o
es
n
o
t
allo
w
t
h
e
a
lg
o
r
it
h
m
to
lead
t
h
e
P
V
m
o
d
u
le
to
r
ea
ch
th
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t e
f
f
ec
ti
v
el
y
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
is
w
o
r
k
r
etu
r
n
s
th
e
f
r
a
m
e
w
o
r
k
o
f
t
h
e
r
esea
r
ch
p
r
o
j
ec
t
SISA
1
“
M
in
i
i
n
telli
g
e
n
t
P
o
w
er
p
lan
t
”
b
eg
an
b
et
w
ee
n
r
esear
c
h
ce
n
te
r
SISA
a
n
d
o
u
r
Un
i
v
er
s
it
y
.
W
e
ar
e
an
x
io
u
s
to
th
i
n
k
t
h
e
Has
s
an
I
I
Un
i
v
er
s
it
y
o
f
C
asab
lan
ca
f
o
r
th
e
f
i
n
an
ci
n
g
o
f
th
is
p
r
o
j
ec
t.
RE
F
E
R
E
NC
E
S
[1
]
Nith
in
T
.
A
b
ra
h
a
m
,
K.
V
in
o
th
K
u
m
a
r,
V
ick
y
Jo
se
,
Do
n
a
M
a
ria
M
a
th
e
w
,
S
.
S
u
re
sh
Ku
m
a
r,
S
A
R
A
l
g
o
rit
h
m
M
e
th
o
d
in
P
h
o
to
v
o
lt
a
ic
S
y
st
e
m
u
sin
g
M
P
P
T
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
),
Vo
l.
3
,
No
.
4
,
De
c
e
mb
e
r 2
0
1
3
,
p
p
.
4
3
8
~
4
4
3
[2
]
E.
M
.
A
h
m
e
d
a
n
d
M
.
S
h
o
y
a
m
a
,
“
V
a
riab
le
S
tep
S
ize
M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
e
r
Us
in
g
a
S
in
g
le
V
a
riab
le
f
o
r
S
tan
d
-
a
l
o
n
e
Ba
tt
e
ry
S
to
ra
g
e
P
V
S
y
ste
m
s,”
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tr
o
n
ics
,
V
o
l.
1
1
,
No
.
2
,
M
a
rc
h
2
0
1
1
,
p
p
.
2
1
8
-
2
2
7
.
[3
]
N.
F
e
m
ia,
G
.
P
e
tro
n
e
,
G
.
S
p
a
g
n
u
o
lo
a
n
d
M
.
V
it
e
ll
i
,
“
Op
ti
m
iza
ti
o
n
o
f
P
e
rtu
r
b
a
n
d
Ob
se
rv
e
M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
M
e
th
o
d
,
”
I
EE
E
T
RA
NS
ACT
IONS
ON P
OW
ER
E
L
ECT
R
ONICS
,
Vo
l.
2
0
,
No
.
4
,
J
u
ly 2
0
0
5
,
p
p
.
9
6
3
-
9
7
3
.
[4
]
K.S
.
T
e
y
a
n
d
S
.
M
e
k
h
il
e
f
,
“
M
o
d
if
ied
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
M
P
P
T
a
lg
o
rit
h
m
to
m
it
ig
a
te
in
a
c
c
u
ra
te
re
sp
o
n
se
s
u
n
d
e
r
f
a
st
-
c
h
a
n
g
in
g
so
lar i
rra
d
iati
o
n
lev
e
l,
”
S
o
la
r
En
e
rg
y
,
V
o
l
.
1
0
1
,
2
0
1
4
,
p
p
.
3
3
3
-
3
4
2
.
[5
]
F
.
L
iu
,
S
.
Du
a
n
,
F
.
L
iu
,
B.
L
iu
,
a
n
d
Y.
Ka
n
g
,
“
A
V
a
riab
le
S
tep
S
ize
INC
M
P
P
T
M
e
th
o
d
f
o
r
P
V
S
y
ste
m
s,”
IEE
E
T
RA
NS
AC
T
IONS
ON INDU
S
T
RI
AL
EL
EC
T
RONICS
,
Vo
l.
5
5
,
No
.
7
,
Ju
ly
2
0
0
8
,
p
p
.
2
6
2
2
-
2
6
2
8
.
[6
]
S
.
S
il
v
e
ste
r
,
A
.
Bo
ro
n
a
t,
A
.
Ch
o
u
d
e
r,
S
tu
d
y
o
f
by
p
a
ss
d
io
d
e
s co
n
f
ig
u
ra
ti
o
n
o
n
P
V
m
o
d
u
les
,
Ap
p
l
.
En
e
rg
y
8
6
(
2
0
0
9
)
1
6
3
2
–
1
6
4
0
.
[7
]
A
.
Be
n
y
o
u
c
e
f
,
A
.
Ch
o
u
d
e
r,
K
.
Ka
ra
,
S
.
S
il
v
e
stre
,
O
.
A
it
S
a
h
e
d
,”
A
R
T
I
F
I
C
I
AL
B
E
E
C
O
L
ON
Y
B
ASE
D
AL
GO
R
I
T
H
M
F
OR
M
A
X
I
M
UM
P
OW
E
R
P
O
I
N
T
T
R
A
C
K
I
NG
(M
P
P
T
)
F
OR
PV
S
YST
E
M
S
OPE
R
AT
I
NG
UN
D
E
R
P
A
R
T
I
AL
S
HA
D
E
D
C
ON
DI
T
I
ON
S
”
jo
u
rn
a
l
a
p
p
li
e
d
so
ft
c
o
mp
u
ti
n
g
,
v
o
lu
m
e
3
2
issu
e
c
,
ju
ly
2
0
1
5
p
a
g
e
s
3
8
-
48.
[8
]
C.
-
H.
L
in
,
C.
-
H.
Hu
a
n
g
,
Y.
-
C.
Du
,
J.
-
L
.
Ch
e
n
,
M
a
x
im
u
m
p
h
o
to
v
o
lt
a
ic
p
o
w
e
r
trac
k
in
g
f
o
r
th
e
P
V
a
rr
a
y
u
sin
g
th
e
f
ra
c
ti
o
n
a
l
-
o
r
d
e
r
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
m
e
th
o
d
,
Ap
p
l.
En
e
rg
y
8
8
(
2
0
1
1
)
4
8
4
0
-
4
8
4
7
.
[9
]
S
AL
M
I
Ha
ss
a
n
,
BAD
RI
A
b
d
e
lma
ji
d
,
ZE
G
R
A
RI
M
o
u
ra
d
,
M
a
x
i
m
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
(M
P
P
T
)
Us
in
g
A
rti
f
icia
l
Be
e
Co
lo
n
y
Ba
se
d
Alg
o
rit
h
m
f
o
r
P
h
o
to
v
o
l
taic
S
y
ste
m
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
in
t
e
ll
ig
e
n
t
S
y
ste
m,
Vo
lu
m
5
,
Iss
u
e
1
,
Feb
r
u
a
ry
2
0
1
6
,
Pa
g
e
s1
-
4.
[1
0
]
M
.
A
.
El
ta
w
il
a
n
d
Z.
Zh
a
o
,
“
M
P
P
T
tec
h
n
iq
u
e
s
f
o
r
p
h
o
to
v
o
l
taic
a
p
p
li
c
a
ti
o
n
s,”
Ren
e
wa
b
le
a
n
d
S
u
s
ta
in
a
b
le
En
e
rg
y
Rev
iews
,
Vo
l.
2
5
,
2
0
1
3
,
p
p
.
7
9
3
-
8
1
3
.
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