In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
Vo
l
.
1
0
, No
.
2
, Ju
n
e
20
1
9
, p
p
.
1
0
8
1
~
1
089
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
2.pp1081-1089
1081
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Maximum
pow
e
r point tr
acking o
f partiall
y s
h
ading PV system
using cuckoo search algorithm
A. Ibrahim
1
,
Ra
ef
A
bo
elsaud
2
, S. Ob
u
k
h
ov
3
1,
2
Dep
a
rt
m
e
nt
o
f Elect
rical
P
owe
r
a
nd
Mach
in
es E
ng
ineeri
ng, Z
a
g
azi
g Univers
i
t
y
,
Egypt
1
,
2,
3
Dep
a
rt
men
t
of
E
n
ergy
and
Pow
er En
g
i
n
eerin
g,
N
a
t
ion
a
l Res
e
arch T
om
sk P
olyt
echn
i
c U
n
i
v
ersi
ty, Russ
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Dec
8
, 2
0
18
Re
vise
d Mar
3,
201
9
Ac
ce
p
t
ed
M
ar 1
2
,
2
019
Th
is
p
ap
er
p
resent
s
a
cuck
oo
s
earch
(
CS
)
al
go
ri
thm
f
o
r
det
e
rmi
n
in
g
t
h
e
gl
ob
al
m
ax
im
u
m
p
ow
er
point
(
G
M
PP)
t
racki
ng
of
pho
to
volt
a
ic
(
P
V
)
und
er
part
ial
sha
d
ing
conditions
(
PSC
)
.
The
convent
i
onal
m
et
hods
a
re
fai
l
ed
t
o
track
t
h
e
G
M
P
P
u
n
d
e
r
P
S
C,
w
hich
d
ec
reas
e
th
e
reli
ab
i
l
ity
o
f
the
p
o
w
e
r
sy
st
e
m
a
nd
i
ncreas
e
t
h
e
system
l
o
s
s
e
s
.
T
h
e
p
erf
o
rm
ance
of
t
he
C
S
al
gor
ithm
is
c
om
pared
with
p
e
r
t
u
rb
a
n
d
obs
erve
(
P
&
O
)
a
l
g
o
r
ithm
f
o
r
diff
er
ent
cas
es
o
f
op
erati
ons
o
f
P
V
p
an
e
l
s
un
der
P
S
C
.
The
CS
a
lg
ori
t
hm
i
s
u
s
ed
i
n
this
w
ork
t
o
con
t
ro
l
d
i
rectly
t
h
e
d
ut
y
cycl
e
o
f
t
he
D
C-D
C
c
on
verter
w
ith
ou
t
p
r
op
ortion
a
l
in
teg
r
al
d
eriv
a
tive
(P
ID)
c
o
nt
rol
l
er.
Th
e
p
r
op
os
ed
C
S
m
o
d
e
l
can
t
r
a
c
k
t
h
e
GM
PP
v
ery
ac
cu
rate
w
ith
h
igh
ef
fi
ciency
i
n
l
e
ss
tim
e
un
der
d
i
ff
erent
con
d
i
t
i
ons
as
we
ll as
in
P
S
C
.
K
eyw
ord
s
:
Gl
o
b
a
l
max
i
m
u
m
po
w
er
p
oin
t
M
a
xi
mum
power
p
oi
n
t
track
ing
Cuck
oo
search
P
a
rti
a
lly
s
hadi
ng
con
d
i
t
i
o
n
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A.
I
b
r
ah
i
m
Depa
rtem
ent o
f
Elec
t
r
i
c
a
l P
o
wer
and Ma
chi
n
es En
g
i
n
ee
ri
n
g
,
Za
g
azi
g
Uni
v
ersi
ty
, Eg
yp
t.
Em
ail:
i
b
r
a
gim
@
t
p
u.r
u
1.
I
N
TR
OD
U
C
TI
O
N
I
t
i
s
know
n
t
h
a
t
t
h
e
w
orl
d
's
e
le
ctric
i
t
y
c
o
n
su
m
p
tio
n
w
i
l
l
i
n
c
r
e
a
s
e
ann
u
a
ll
y
i
t
i
s
exp
e
ct
ed
t
h
a
t
fu
rth
e
r
grow
t
h
w
i
ll
be
due
t
o
the
i
n
c
r
e
a
se
i
n
t
h
e
nu
m
b
er
o
f
p
o
p
u
l
ati
o
n
a
n
d
t
h
e
i
n
cr
easi
ng
de
ma
nd
s
of
t
he
m
oder
n
w
a
y o
f
li
f
e
s
ty
l
e
[1,
2
]
.
T
he
r
e
f
o
r
e
,
ther
e
i
s
a ne
e
d
to
d
eve
l
o
p
rene
w
a
b
l
e e
n
er
g
y
s
ource
s t
o
e
nsur
e sus
t
a
i
n
a
bi
l
i
t
y
hi
gh
p
o
w
e
r
supp
l
i
e
s
t
o
the
c
o
n
s
um
er
,
as
w
ell
a
s
t
o
r
e
duce
l
o
ca
l
a
nd
g
l
oba
l
r
oom
p
o
llu
t
i
on.
T
h
e
m
ain
pro
b
lem
s
i
n
th
e
pr
actic
a
l
u
se
o
f
P
a
V
pow
er
g
e
n
era
tio
n
sys
t
em
(
P
G
S
)
a
r
e
t
h
e
r
e
l
a
t
i
v
e
l
y
l
o
w
e
f
f
i
c
i
e
n
c
y
o
f
con
v
er
sio
n
o
f
prim
ary
e
n
erg
y
(
fr
om
9
t
o
17%
)
and
the
p
r
on
ou
nce
d
d
e
p
e
nde
nce
o
f
t
he
s
olar
cel
l
'
s
e
n
ergy
c
h
ara
c
t
e
ri
st
i
c
s
o
n
ext
e
rn
al
c
l
i
mat
i
c
c
o
ndi
tion
s
[3
-5
].
S
o
l
a
r
p
a
ne
ls
c
o
n
s
i
st
o
f
se
ve
ral
seri
e
s
-
p
ara
l
le
l
c
onne
ct
e
d
so
l
a
r
modu
les and
are
de
si
g
n
e
d
for
d
i
rec
t
c
o
nve
rs
i
o
n of
s
ol
a
r
e
nergy in
to elec
t
r
i
c
a
l
e
n
er
gy
w
i
t
h
t
he ne
c
e
s
sa
ry
val
u
es
o
f c
onst
a
nt
v
o
lta
ge
an
d
curr
ent.
Th
e
po
we
r
ch
arac
t
e
ri
sti
c
s
o
f
s
o
l
ar
c
e
l
l
s
h
av
e
a
no
n
lin
e
a
r
c
o
n
v
e
x
sh
ap
e
wi
t
h
a
n
ext
r
emu
m
,
s
o
t
o
ob
ta
in
t
he
m
ax
imum
a
va
i
l
ab
l
e
p
ow
er
i
t
is
a
dv
isa
b
le
t
o
ope
ra
te
t
he
m
a
t
t
h
e
m
a
x
i
m
um
p
o
w
e
r
poin
t
(
MP
P
)
.
O
n
the
o
t
her
ha
n
d
,
t
h
e ge
ne
rate
d pow
er o
f s
o
la
r
pa
ne
ls de
p
e
n
ds
o
n
t
h
e
o
p
er
at
ing
co
n
d
i
tio
ns
: the
in
te
n
s
i
t
y
o
f
so
l
a
r
radia
t
i
o
n,
a
mbie
nt
t
em
per
a
t
u
re
[
6].
C
h
a
n
g
i
ng
i
n
o
n
e
or
a
ll
o
f
t
he
se
c
o
n
d
i
t
i
o
ns
w
i
ll
le
ad
t
o
c
h
an
ge
i
n
th
e
pos
it
io
n
of
M
P
P
.
S
o
t
he
s
ea
r
c
h
an
d
trac
k
i
ng
o
f
MP
P
i
n
r
ea
l
oper
at
in
g
con
d
iti
on
s
are
on
e
o
f
t
h
e
w
ay
s
t
o
impro
v
e
th
e
o
p
era
tio
na
l
e
f
fi
c
i
e
n
c
y
o
f
t
h
e
so
lar
pa
n
e
l.
W
i
t
h
n
o
S
h
a
d
ing,
m
any
co
n
v
en
t
i
o
n
a
l
m
etho
ds
o
f
hav
i
ng
be
en
d
evel
o
p
ed
f
or
M
P
P
T,
t
he
m
ost
com
m
on
me
th
ods
a
m
o
n
g
t
he
m
are
a
consta
nt
v
o
l
tage
M
P
P
T,
pert
urb
a
n
d
o
b
se
rve
(P
&O
)
an
d
it
s
num
er
ous
m
o
d
ific
a
t
i
o
ns,
a
nd
i
ncre
me
nt
a
l
i
n
duc
ta
nce
m
e
t
h
o
d
[
7-
1
1
]
.
U
nder
pa
rt
ial
sha
d
in
g,
t
he
P
-V
c
hara
cter
i
s
tic
h
as
m
any
loca
l
pe
a
k
s
a
nd
one
g
lo
ba
l
pe
ak
[
12-
14].
The
con
v
e
n
t
i
ona
l
me
thods
a
re
f
a
i
l
e
d
t
o
t
ra
c
k
t
he
G
MP
P
.
R
ece
ntl
y
,
t
h
e
resea
r
che
r
s
ha
ve
w
o
r
ked
how
t
o
tr
a
c
k
the
G
M
P
P
under
P
S
C usi
ng so
ft c
ompu
t
i
ng
tec
h
ni
q
u
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
1
0
81
–
1
089
1
082
A
m
ong
t
hem
ar
e
th
e
fuzz
y
l
o
gic
co
n
t
r
o
l
(
F
L
C
)
[
1
5]
,
ar
t
i
fic
i
a
l
n
e
u
ral
n
e
two
r
k
s
(
ANN)
[
1
6
]
,
Gen
e
tic
a
l
g
o
r
i
t
h
m
(
GA)
[
17]
,
par
t
ic
l
e
s
w
a
r
m
opt
imi
z
atio
ns
(
P
S
O
)
[
18]
a
n
d
a
n
t
col
o
ny
op
tim
iza
t
i
o
ns
[
19]
.
The
y
t
e
s
t
the per
f
or
m
a
nc
e
of
t
he
ir
a
lg
or
it
hms
u
nder
d
y
n
am
ic
c
ha
ng
e
s
o
f
t
h
e
so
lar
irr
a
dia
n
ce
o
f
t
h
e PV
p
ane
l
.
Alt
h
ou
g
h
th
e
v
e
ry
h
igh
co
st
o
f
i
m
plemen
tation
th
e
ANN
an
d
fu
zzy
log
i
c,
t
he
y
c
a
p
ab
le
o
f
tr
ac
kin
g
t
he
G
MP
P
w
i
th
l
o
wer
o
s
ci
ll
at
i
o
n
i
n
p
o
w
e
r
a
s
co
mp
are
d
t
o
P&O
al
go
rit
h
m.
T
h
e
m
a
jor
di
ffere
n
ce
bet
w
ee
n
the
p
r
o
p
o
se
d
CS
a
n
d
o
t
her
tec
h
ni
q
u
es
i
s
tha
t
t
he
p
r
opose
d
a
l
gor
it
hm
i
s
u
s
e
d
t
o
co
n
t
ro
l the
d
u
t
y
c
yc
le
d
ir
ec
t
l
y w
i
t
h
ou
t u
s
i
ng t
h
e
w
i
t
h
o
u
t
P
r
opor
tio
na
l
I
n
tegr
a
l
D
er
i
v
a
t
ive
(
P
ID
)
con
t
r
o
l
l
er
[
20]
.
I
n
t
his
pa
pe
r
,
t
he
C
S
alg
o
r
i
t
h
m
is
i
ntr
o
d
u
ce
d
t
o
t
r
a
ck
t
he
G
MP
P
o
f
the
P
V
under
fas
t
v
a
r
ia
ti
o
n
o
f
so
lar
i
r
radia
n
c
e
a
s
we
ll
a
s
p
a
rtia
l
sha
d
in
g
con
d
iti
on.
T
he
p
rop
ose
d
a
l
g
or
i
t
hm
i
s
c
o
m
p
ar
ed
w
i
t
h
t
h
e
P
&
O
a
l
g
o
r
i
t
h
m
in
d
i
ffe
ren
t
t
e
s
t
cas
e
s
a
nd
the
ef
fi
cienc
y
o
f
bot
h
of
t
h
e
m
are
mea
s
u
r
ed
i
n
eac
h
t
e
st
c
a
s
e.
S
e
c
t
i
on
tw
o
de
sc
r
i
b
e
s
the
mode
lin
g
o
f
s
i
n
g
l
e
d
i
o
d
e
P
V
c
e
l
l.
T
he
e
f
f
ec
t
o
f
P
S
C
on
P
G
S
i
s
e
xpla
i
ne
d
in
s
ec
tio
n
thr
e
e
.
S
ectio
n
fo
ur
d
e
s
c
r
ibes
t
he
C
S
and
P
&
O
a
nd
its
a
p
p
l
i
ca
t
i
o
n
s
in
P
SC
.
Si
mu
l
a
tion
re
su
lt
s
of
t
h
e
d
e
v
e
l
op
e
d
m
odel a
r
e
exp
l
aine
d
i
n
t
h
e
six
th sec
tio
n.
2.
S
I
NGLE DIO
D
E
PV M
ODEL
A
s
i
n
g
l
e
d
i
o
d
e
e
q
u
i
v
a
l
e
n
t
c
i
r
c
u
i
t
i
s
t
h
e
m
o
s
t
c
o
m
m
o
n
m
a
t
h
e
m
a
t
i
c
a
l
m
ode
l
o
f
P
V
a
r
r
a
ys
t
ha
t
av
a
i
l
a
bl
e
in
t
h
e
l
i
t
erat
u
r
e.
F
i
g
u
r
e
1
illu
st
rat
e
s
th
e
e
qui
v
a
l
e
n
t
c
i
r
c
u
it
of
t
he
P
V
cell
tha
t
u
sed
in
t
he
pr
opose
d
m
ode
l.
F
i
gur
e
1.
T
he
e
qu
i
v
ale
n
t
c
i
r
c
u
it
o
f
a
s
ola
r
c
el
l
The
o
u
tp
ut
c
ur
r
e
nt
o
f
the
P
V
ce
l
l
i
s
c
a
l
c
u
l
a
t
e
d
by
the
f
o
l
l
o
w
i
n
g
equa
tio
ns
[
21
]
:
sc
D
p
II
I
I
(
1
)
0
()
exp
1
SS
sc
p
qV
I
R
V
I
R
II
I
nk
T
R
(
2
)
Wher
e
,
V
,
I
-
is
t
he
v
a
l
ue
o
f
ou
t
p
u
t
v
o
lta
g
e
a
nd
c
u
r
r
ent
of
t
h
e
P
V
c
e
l
l;
I
o
-
rev
e
rse
satu
ration
cu
rren
t
o
f
th
e
di
o
d
e;
R
S
и
R
p
s
e
r
i
e
s
a
n
d
p
a
r
a
l
l
e
l
r
e
s
i
s
t
a
n
c
e
o
f
t
h
e
s
o
l
a
r
c
e
l
l
;
n
i
s
t
h
e
i
d
e
a
l
i
t
y
f
a
c
t
o
r
;
T
-
i
s
t
h
e
a
b
s
o
l
u
t
e
tem
p
er
at
ur
e
of
t
he
P
V
c
e
ll
;
k
=
1.
38
∙1
0
-23
j/k
B
ol
tzm
a
n
n
c
o
n
sta
n
t
.
A
PV
m
odule
c
o
n
s
is
ts
o
f
a
la
r
g
e
num
ber
of
i
de
ntic
a
l
s
o
l
ar
cell
s
c
o
n
n
ec
te
d
i
n
s
e
r
ies
a
n
d
in
p
ar
al
le
l,
w
h
ic
h
a
l
l
o
w
s
i
ncr
e
asi
ng
i
t
s
v
o
lta
ge
a
n
d
o
utpu
t
pow
er
.
Th
e
m
a
in
e
l
ec
tr
i
c
al
p
ar
am
eter
s
of
t
he
P
V
module
t
h
at
use
d
i
n
t
h
i
s
w
or
k
a
r
e
summ
ar
ized
i
n
Ta
ble
1.
Tabl
e 1
.
S
p
e
c
i
fi
ca
ti
o
n
s
o
f
P
V
M
odul
e
Pa
r
a
m
e
t
e
r
V
alue
Ma
xi
m
u
m
powe
r
r
a
ting
P
ma
x
249
w
R
a
t
e
d
volt
a
g
e
V
MP
P
30V
Ope
n
c
ir
c
u
i
t
volt
a
ge
V
OC
8
.
3
A
Short c
i
r
c
uit c
u
r
r
ent
I
SC
8
.
83A
R
a
t
e
d c
u
rre
nt
I
MP
P
36.
8V
T
e
m
p
er
atu
r
e
co
e
f
f
i
ci
en
t
o
f
I
sc
(
0.
06
5±0.
015
) %
/
°C
T
e
m
p
e
r
a
t
u
r
e
c
o
ef
f
i
ci
e
n
t o
f
p
o
w
e
r
-
(
0
.5
±
0
.0
5)
%
/ °
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Max
i
m
u
m
po
w
e
r po
in
t tr
ack
i
ng o
f
p
a
r
t
i
a
l
l
y
sha
d
i
ng
PV sy
stem
usi
ng
Cuc
k
oo
Se
arc
h
…
(
A
.
I
b
rah
i
m
)
1
083
3.
PV
M
ODULE
UN
DER PSC
In
r
e
a
l
op
e
r
at
io
n
s
,
t
h
e
PV
m
o
dul
es
a
re
o
ft
en
s
ub
j
e
ct
w
i
t
h
PSC
,
which
resu
lte
d
from
c
l
o
u
d
s
;
t
r
ees;
bu
i
l
d
i
ng
s;
t
ow
er
s.
A
s
an
e
xa
m
p
le
t
o
s
h
ow
t
he
e
f
f
ec
t
of
t
he
s
ha
d
i
n
g
o
n
t
he
P
V
m
o
d
u
l
e
,
f
o
ur
P
V
pa
n
e
ls
a
r
e
c
o
n
n
ec
ted
i
n
s
er
ies.
T
his
c
o
n
f
ig
ur
a
tio
n
i
s
n
am
ed
“
4s1p”
c
o
n
ne
c
t
i
o
n
,
a
s
show
n
i
n
F
igur
e
2.
T
o
s
i
m
u
la
te
t
h
a
t
m
odel i
n
Ma
t
l
a
b,
P
V
out
p
u
t
cur
r
ent
is
s
u
p
p
l
ie
d
t
o
D
C vol
t
a
ge
c
o
nt
r
o
lle
d
sour
ce
a
s
sh
ow
n
in
F
ig
ur
e
3.
T
he
P
-
V
and
V
-
I
for
t
h
e
s
e
c
a
ses
ar
e
show
n
i
n
F
i
gur
e
4.
Fig
u
r
e
2
.
N
o
r
mal Irrad
i
an
ce
an
d
PSC
o
f P
V
p
an
els
F
i
g
u
r
e 3
.
In
t
e
rfa
c
in
g m
a
them
a
tica
l
P
V modu
l
e
m
odel
t
o
p
hy
si
cal
por
ts
F
i
gur
e
4.
T
he
P
-
V
a
nd
V
-
I
c
h
ar
a
c
ter
i
st
ics
o
f
P
V
p
ane
l
s
un
d
e
r
PS
C
The
cur
r
en
t
ge
ne
r
a
te
d
b
y
P
V
un
de
r
P
S
C
is
not
c
o
n
s
t
an
t.
I
n
c
a
se
of
n
or
m
a
l
ir
r
a
dia
n
ce
o
f
the
P
V
pa
ne
ls,
a
co
ns
t
a
nt
c
ur
r
e
nt
o
f
a
ppr
ox
im
ate
l
y
8
.
3
A
is
g
e
n
er
a
t
ed
at
a
f
un
c
t
i
o
n
a
l
op
e
r
a
t
i
n
g
vo
lt
a
g
e
o
f
0
V
t
o
120
V
a
s
s
how
n
in
F
igur
e
4.
H
ow
eve
r
,
w
h
en
t
he
P
V
is
under
the
P
S
C,
t
h
e
gener
a
ti
ng
curre
nt
can
n
o
t
m
a
in
ta
in
a
c
o
n
s
ta
nt
v
a
l
ue
.
F
o
r
exam
ple,
i
n
P
S
C,
P
V
gener
a
tes
c
o
n
s
ta
nt
c
ur
r
ent
8.
3
A
fr
om
0
V
t
o
25
V
,
t
hen
de
cr
e
a
ses
to
8
A
,
4.
1
A
a
n
d
1.
6
A
a
t
5
5
V
,
100
a
n
d
12
0
V
,
a
s
sh
ow
n
in
F
ig
ur
e
4.
T
h
e
P
S
C
c
a
s
e
de
m
o
ns
tr
a
t
e
f
o
ur
p
ea
ks
be
cau
se
it
r
e
ceive
s
fo
ur
d
i
f
fer
e
nt
l
e
v
e
l
s
of
i
r
r
adia
t
i
o
n
.
4.
CUC
K
OO S
E
ARC
H
(C
S
)
Cuc
k
o
o
S
e
a
rch
(CS)
w
as
f
ir
st
d
e
v
el
o
p
ed
by
[Yan
g
&D
eb]
[2
2].
The
s
e
a
lg
or
i
t
hm
s
u
s
ua
ll
y
w
o
r
k
ba
se
d
on
a
r
a
nd
om
s
ear
ch,
w
h
ic
h
sim
u
la
te
s
the
r
e
pr
o
d
u
c
ti
o
n
s
t
r
a
t
e
gy
o
f
c
u
c
k
o
o
b
i
r
ds.
I
t
i
s
o
b
s
erve
d
th
a
t
se
v
e
r
a
l
spe
c
i
es
o
f
cuc
k
o
o
s
pe
r
f
o
r
m
b
r
ood
p
a
r
a
sit
i
sm
,
i
.
e.
by
la
y
i
ng
the
i
r
eggs
i
n
h
o
s
t
b
ir
ds’
ne
s
t
s.
U
sual
l
y
,
thre
e
t
y
pes
of
b
r
ood
para
s
itis
m
a
r
e
see
n
(
1)
i
n
t
r
a
spec
i
f
i
c
,
(2)
c
ooper
a
tiv
e
and
(
3
)
nest
t
ake
o
ve
r
.
S
ome
host
bir
d
s
en
ga
ge
i
n
dir
ect
c
o
n
f
l
i
c
t
w
i
th
t
he
i
n
t
r
u
d
i
ng
c
u
c
k
o
o
s.
I
f
a
ho
s
t
b
i
r
d
d
i
sc
o
v
er
s
t
h
e
cuck
o
o
e
g
g
s
i
t
w
ill
1
000
W/
m
1
000
W/
m
2
50
0
W/
m
90
0
W/
m
2
N
orm
a
l Irrad
i
ance
Pa
rtial S
h
ad
in
g
1
000
W/
m
1
000
W/
m
1
000
W/
m
10
0
W/
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
1
0
81
–
1
089
1
084
thr
o
w
t
h
ese
al
i
e
n
e
g
gs
a
w
a
y
or
a
ba
n
d
o
n
s
i
t
s
ne
st
a
n
d
bui
l
d
s
a
n
ew
n
es
t
else
wh
e
r
e
.
S
o
m
e
cu
cko
o
s
p
eci
es
h
a
v
e
e
v
o
l
ve
d
i
n
s
uc
h
a
way
tha
t
f
e
m
ale
par
a
sitic
c
uck
o
o
s
m
i
m
i
c
the
s
ha
p
e
a
n
d
c
o
l
o
r
of
t
h
e
e
ggs
o
f
a
few
chos
en
hos
t
spec
ies.
T
o
incr
e
a
ses
its
r
epr
o
d
u
c
t
i
on
pr
oba
bi
lit
y.
4.
1.
Lé
vy
f
l
i
g
h
t
S
e
ar
c
h
i
n
g
for
a
suita
b
l
e
ho
st
b
ir
d’
s
nes
t
i
s
an
i
m
p
or
tan
t
p
ar
t
o
f
c
uc
koo
’
s
r
epr
o
duc
tio
n
str
a
t
e
g
y
.
Nor
m
a
l
ly,
the
sea
r
ch
f
or
t
he
n
es
t
i
s
s
imi
l
ar
t
o
the
sea
r
ch
f
or
f
o
o
d
,
w
h
ic
h
ta
ke
s
pla
c
e
i
n
a
r
a
n
d
o
m
or
i
n
a
qua
si-
r
an
dom
f
or
m.
I
n
ge
ner
a
l
,
w
hi
l
e
s
ea
r
c
hi
ng for
f
o
o
d
,
an
im
al
s
ch
oo
se
d
i
r
ec
ti
on
s
o
r
t
ra
je
c
t
o
r
i
e
s
th
at
c
a
n
b
e
m
odele
d
b
y
c
e
r
ta
in
m
a
t
hem
a
t
i
c
a
l
f
unc
t
i
ons.
O
n
e
o
f
t
he
m
ost
com
m
on
m
ode
l
s
i
s
t
h
e
Lév
y
f
l
i
gh
t.
A
r
e
cent
st
ud
y
b
y
R
e
y
n
o
lds
an
d
F
r
ye
s
h
o
w
s
t
ha
t
a
Lévy
f
l
i
g
h
t
can
b
e
t
h
o
u
ght
o
f
as
a
r
andom
w
a
l
k
w
h
er
e
t
h
e
st
ep
s
i
z
e
ha
s
a
Lé
v
y
p
r
o
b
a
b
i
l
i
t
y
d
istr
i
b
ut
ion.
I
n
CS
,
nest
s
ear
ch
i
ng
is
c
hara
cter
i
z
e
d
by
Lév
y
f
li
gh
t.
M
a
t
he
ma
tica
lly,
a
L
é
v
y
f
l
i
g
h
t
i
s
a
r
a
n
d
o
m
w
a
l
k
w
h
e
r
e
s
t
e
p
s
i
z
e
s
a
r
e
e
x
t
r
a
c
t
e
d
f
r
o
m
Lévy
di
str
i
bu
t
i
o
n
a
cco
r
d
ing
to
a
p
ow
e
r
l
aw
a
s
s
how
n
be
lo
w
[23]
:
y
l
(
3
)
Where
l
is
t
he
f
li
gh
t
le
ng
th
a
nd
λ
i
s
the
va
ri
anc
e
.
S
i
n
c
e
1
<
λ
<
3,
y
h
a
s
an
i
nf
ini
t
e
va
ri
ance
.
Fig
u
re
5
s
how
s
a
n
e
xa
mpl
e
o
f
Lév
y
f
lig
h
t
i
n
a
tw
o-
dim
e
ns
i
ona
l
p
l
ane
.
Fig
u
r
e 5
.
Ex
a
mp
le
o
f
Lévy
fligh
t in
a two
-dimen
s
i
on
a
l
p
lan
e
4.
2.
C
u
ckoo
searc
h
a
l
gor
i
t
h
m
Thr
e
e
i
d
ea
lize
d
r
u
l
es
f
or
C
S
ba
se
d
o
n
c
uc
k
oo’
s
br
o
o
d
pa
r
a
si
tic
be
ha
vi
or
:
(
1
)
Eac
h
c
uc
ko
o
la
ys
o
n
e
e
gg a
t
a
tim
e
and
plac
e
s
it
in
a
r
andom
l
y
ch
o
se
n
nes
t
(
2)
The
b
e
s
t
nes
t
w
i
t
h
the
hig
h
e
s
t
qua
l
i
t
y
o
f e
g
gs
w
ill
b
e
ca
rri
e
d
ov
er
t
o
t
h
e
n
e
xt
g
en
e
r
at
i
o
n
(3
)
T
h
e
nu
mb
e
r
o
f
a
v
a
i
lab
l
e
n
e
s
t
s
i
s
fi
xe
d
a
nd
the
n
u
m
be
r
of
c
uck
o
o
e
g
g
s
di
sco
v
er
ed b
y
t
h
e h
o
st
b
i
r
d
m
a
in
ta
in
s
a
pr
ob
a
b
il
it
y
P
a
,
w
h
e
r
e 0
<
P
a <
1.
W
he
n ge
ne
r
a
t
i
ng
a
ne
w
so
l
u
ti
on f
o
r
a
cuc
k
o
o
,
a
Levy
f
l
ig
h
t
i
s
per
f
or
m
e
d
as
i
n
th
e
fol
l
o
w
i
ng
ex
pr
e
s
si
on
[
24
] [2
5
]
:
(1
)
()
tt
ii
Lé
v
xx
y
(
4
)
Where
t
i
x
a
r
e
s
a
m
p
l
e
s
/
e
g
g
s
,
i
i
s
t
h
e
s
a
m
p
l
e
n
u
m
b
e
r
,
t
i
s
t
h
e
n
u
m
b
e
r
o
f
i
t
e
rati
o
n
a
nd
α
i
s
t
h
e
s
t
ep
s
iz
e,
w
h
i
c
h
is r
ela
t
e
d
to
th
e sc
ales of t
h
e
pro
b
lem
o
f
i
nt
e
r
ests. In m
o
st c
a
s
es, we ca
n use α
=
1.
Th
e
p
rod
u
c
t
⊕
m
ea
n
s
e
ntr
y
w
i
se
m
ult
i
p
lic
a
tio
ns.
The
val
u
e
of
α
i
s
ca
lcul
ated
by
t
h
e
f
o
ll
o
w
i
ng
e
q
ua
tio
n:
()
()
0
()
tt
ji
xx
(
5
)
The
va
lue
o
f
L
évy
(
)
is
f
ou
nd
fr
om
L
é
vy
d
i
str
i
b
u
t
i
on
g
i
ven
in
E
q.
7
()
Lé
y
u
l
v
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Max
i
m
u
m
po
w
e
r po
in
t tr
ack
i
ng o
f
p
a
r
t
i
a
l
l
y
sha
d
i
ng
PV sy
stem
usi
ng
Cuc
k
oo
Se
arc
h
…
(
A
.
I
b
rah
i
m
)
1
085
5.
M
PPT
U
SIN
G
C
S
A
ll
the
vo
l
t
age
s
a
r
e
p
r
o
v
i
de
d
to
t
he
P
V
pa
ne
ls
a
n
d
t
he
o
u
t
p
u
t
p
ower
a
re
calcu
la
te
d
b
y
t
h
e
p
rop
o
se
d
m
odel.
T
he
f
i
t
ne
ss
f
unc
t
i
on
i
n
C
S
i
s
c
o
n
si
d
e
r
e
d
to
b
e
the
ou
tpu
t
d
u
t
y
c
y
cle
t
h
a
t
w
ill
fe
d
to
t
he
D
c
-
DC
b
o
o
st
c
o
n
v
er
ter
a
t
t
he
G
MP
P
of the
P
V
pa
nels,
t
he
d
best
i
s t
h
e
best
one
am
o
n
g
th
e
fi
t
n
ess.
The
d
uty c
y
c
l
e
i
s
c
h
a
n
g
e
d
in
C
S
by
the
f
o
ll
ow
in
g
equa
t
i
o
n
:
(1
)
()
tt
ib
e
s
t
Lé
v
dy
d
(7
)
Where,
d
1
=d
1
,d
2
…n
A si
mp
l
i
f
i
e
d
sch
eme o
f
t
h
e
L
é
v
y
di
st
ri
b
u
ti
on
c
an
b
e e
x
pl
aine
d
b
y:
0
1
()
()
(
()
()
)
bes
t
i
b
es
t
i
u
L
évy
k
v
sd
d
d
d
(8
)
Whe
r
e,
n
=4,
β
=1.
5
a
n
d
k
=
0
.
8
i
s
t
h
e
Lé
v
y
m
ul
t
i
p
l
yi
n
g
c
oe
f
f
ic
ie
nt
(
c
h
o
s
e
n
by
the
des
i
gn
e
r),
w
h
ile
u
a
nd
v
a
r
e
deter
m
ined
f
r
o
m
t
h
e
nor
m
a
l
dis
t
r
i
bu
tio
n
c
u
r
v
es.
The
fl
ow
c
har
t
of
CS
t
hat
i
l
l
ustr
a
t
es
h
ow
t
o
use
the
a
l
g
o
r
i
t
h
m
t
o
ge
t
t
he
M
P
P
of so
la
r
p
a
nel
i
s
s
how
n
in F
ig
ure
6.
F
i
gur
e
6.
T
he
f
low
c
ha
r
t
o
f
t
h
e
CS
a
lgor
i
t
hm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
1
0
81
–
1
089
1
086
6.
S
I
MULAT
I
O
N
S
RESULT
S
The
pr
op
ose
d
m
ode
l
is
c
a
r
r
i
ed
out
i
n
th
e
M
a
tla
b
/
S
i
m
u
lin
k
pr
ogr
a
m
sof
t
w
a
r
e
a
s
show
n
in
F
ig
ur
e
7.
The
D
C
-
D
C
b
oos
t
c
o
n
v
er
ter
is
s
e
l
e
c
te
d
in
t
he
p
r
o
p
o
sed
w
o
r
k
t
o
m
a
t
c
h
t
h
e
M
P
P
c
o
n
t
r
o
l
l
e
r
w
i
t
h
a
r
e
s
i
s
t
i
v
e
l
o
ad
. T
h
e se
l
e
c
t
e
d
p
ara
m
e
t
ers o
f
th
e
con
v
e
rter a
re
;
L=1.
1
m
H
;
c
1
=0
.4
*10
-4
F
,
c
2=
0.
4mF
a
nd
sw
i
t
ch
i
ng fr
eq
uen
c
y
f
=
25 kH
z.
The cr
iter
i
a
f
o
r
sto
p
p
i
ng t
h
e
iter
a
tive
pr
oc
e
ss
o
f
c
a
l
c
u
l
a
ti
ons
a
r
e
t
he
m
axim
um
n
umbe
r
of
i
t
e
r
a
t
i
ons
a
nd
t
he
r
e
l
a
tiv
e
er
r
o
r
in
c
a
l
c
u
l
a
tin
g
the
g
l
oba
l ex
tre
m
um
of the
o
b
j
e
c
t
ive
fu
nct
i
on
:
1
100
0
.
3
ii
bes
t
bes
t
i
be
st
PP
P
(
10)
F
i
gur
e
8
a
n
d
9
show
t
he
p
e
r
f
o
r
m
a
n
ces
o
f
th
e
CS
a
nd
P
&O
f
or
d
e
t
e
rm
ina
t
io
n
t
h
e
G
M
PP
of
t
he
P
V
u
n
d
e
r
no
rma
l
i
rr
a
d
i
a
n
c
e
of
t
he
s
ol
a
r
p
an
el
s
an
d
in
c
a
s
e
of
P
S
C
tha
t
w
a
s
s
how
n
in
F
ig
u
r
e
2.
T
he
f
o
l
l
o
w
i
n
g
e
qua
t
i
o
n
i
s
use
d
f
or
e
val
u
a
t
in
g
the
ef
fic
i
e
n
c
y
o
f
t
h
e
t
w
o
al
gor
it
hms
i
n
a
l
l
c
ases
0
max
100
,
%
P
P
(
11)
Whe
r
e
Р
0
i
s
th
e
va
l
u
e
of
t
he
o
u
t
pu
t
pow
er
o
f
the
P
V
p
a
n
e
l
,
t
h
at
t
r
acke
d
b
y
t
h
e
al
go
rit
h
m;
Р
ma
x
-
t
h
e
va
lue
o
f
t
he
m
axim
um
a
va
i
l
a
b
le
p
ow
er
.
F
i
gur
e
7.
M
A
TLA
B/S
i
m
u
lin
k
of
t
he
p
r
o
p
o
se
d
m
odel
A
s
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
8
t
h
e
C
S
a
l
g
o
r
i
t
h
m
i
s
a
b
l
e
t
o
t
r
a
c
k
t
h
e
G
M
P
P
o
f
t
h
e
so
lar
pa
nel
a
f
ter
o
n
l
y
f
o
u
r
i
ter
a
ti
ons
t
he
o
p
t
i
m
a
l
d
ut
y
c
y
cle
w
a
s
(
d
be
s
t
=0
.47
)
an
d
the
trackin
g
ti
me was 0
.32
s
e
c.
Also
in
c
ase of
P
SC
the
pro
p
o
sed
alg
o
ri
thm
t
r
acke
d
t
he
g
lo
ba
l
pea
k
,
wh
i
l
e
t
h
e
P&O
a
l
gor
ithm
t
r
ap
pe
d
in
l
oca
l
p
eak
w
hic
h
incr
ease
t
h
e
sy
stem
losses
an
d r
e
duce
t
h
e
relia
b
i
l
i
t
y
of t
h
e
PV
p
l
a
n
t
.
(a
)
(
b
)
F
i
gur
e
8.
T
he
p
er
f
o
r
m
ance
o
f
the
tw
o
al
gor
it
hms
in
t
he
nor
m
a
l
c
ase
(a)
CS (b
)
P&O
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Max
i
m
u
m
po
w
e
r po
in
t tr
ack
i
ng o
f
p
a
r
t
i
a
l
l
y
sha
d
i
ng
PV sy
stem
usi
ng
Cuc
k
oo
Se
arc
h
…
(
A
.
I
b
rah
i
m
)
1
087
(a
)
(
b
)
F
i
gur
e
9.
T
he
p
er
f
o
r
m
ance
o
f
the
tw
o
al
gor
ithm
s
i
n
the
P
S
C
(
a
)
CS (b
)
P
&
O
6
.
1
.
F
a
s
t
v
a
r
iatio
n
o
f
t
h
e so
la
r
i
r
ra
d
i
a
n
ce
under
co
nsta
nt temp
er
atu
r
e
C
a
se
3
a
r
e
a
bo
ut
t
he
f
as
t
var
i
a
t
i
o
n
of
t
he
s
o
l
a
r
i
r
r
a
di
a
n
ce
of
t
h
e
PV
p
anel
u
nder
PS
C
.
I
n
c
a
se
3
,
as
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
1
0
.
F
r
o
m
t
i
m
e
t
=
0
t
o
t
=
1
s
e
c
a
l
l
P
V
p
a
n
e
l
s
r
e
cei
ved
t
h
e
sam
e
a
moun
t
o
f
t
he
s
ol
a
r
irr
a
dia
n
ce
G
=10
0
0
w/m
2
,
afte
r
t=
1
se
c
t
h
e
PS
C
oc
curs
w
her
e
,
the
sol
a
r
i
r
radianc
e
o
f
the
P
V
p
ane
l
s
wer
e
G
1
=
1
00
0
w
/
m
2
,
G
2
=
5
00
w
/
m
2
,
G
3
=1
0
00
w
/
m
2
a
n
d
G
4
=
10
0
w
/
m.
O
n
t
h
e
o
t
her
ha
nd,
i
n
c
a
s
e
3
as
s
h
o
w
n
i
n
F
i
g
u
r
e
1
0
af
t
e
r
shif
t
i
ng
fr
om
nor
ma
l
o
p
e
r
at
i
ons
t
o
P
S
C,
t
h
e
C
S
o
n
l
y
c
a
n
h
andl
e
t
h
e
GMPP
i
n
t
hi
s
c
a
s
e
wi
t
h
h
i
gh
ly
t
ra
c
k
i
n
g
ef
fi
ci
en
cy
(
=
99.
7
%
)
,
w
hile
t
he
c
on
ve
nti
o
n
a
l
P
&
O
tr
appe
d
at
t
he
l
oc
a
l
p
ea
k.
Al
s
o
,
c
a
n
b
e
se
en,
the
stea
dy
p
o
w
e
r
p
e
r
f
or
m
a
nce
of
t
he
C
S
ar
e
ve
r
y
w
e
l
l
.
T
a
b
le
2
s
h
o
ws
ill
us
t
r
ates
t
he
d
etai
le
d
c
o
mpa
r
ison
be
t
w
ee
n the
C
S
a
nd P&O
for
all
test c
ases.
(a)
(b
)
F
i
gur
e
1
0
.
(
a
)
The
pe
r
f
o
r
m
a
n
ce
of
C
S
and
P&O
u
nde
r
fas
t
v
a
r
ia
ti
o
n
o
f
t
h
e
PV
under
PS
C.
(
b)
duty
cyc
l
e
of
th
e
CS alg
o
r
ithm
Tab
l
e 2.
Resu
l
t
s
o
f
t
h
e
t
h
ree
c
a
ses
of st
u
d
i
es
C
S
P&
O
ca
s
e
s
tudi
e
s
P
ma
x
,
Watt
Р
0
,
Wa
t
t
,%
P
ma
x
,
Wa
t
t
Р
0
,
Wa
tt
,%
N
o
rm
a
l
Irr
a
d
ia
n
c
e
996
995
99.
8
996
976
97.
9
P
S
C
452
451
99.
7
452
331
73.
9
D
y
n
a
m
i
c
op
e
r
a
t
io
n
wi
th
PSC
484
483
99.
7
484
334
6
9
7.
CONCLUSIONS
I
n
t
h
i
s
s
t
u
dy,
t
he
p
e
r
f
o
r
m
anc
e
o
f
CS
a
lg
or
i
s
m
in
ves
t
i
g
a
t
e
d
t
o
t
ra
ck
t
h
e
G
M
P
P
o
f
t
h
e
s
ol
ar
p
an
el
u
n
d
e
r
PSC
and
co
mp
a
r
e
d
w
it
h
th
e
co
nv
ent
i
o
n
a
l
P&
O
algo
rit
h
m.
T
h
r
e
e
d
i
f
f
e
r
e
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e us
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f t
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p
ro
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CS al
gor
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o
r
a
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tes
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c
as
es, the
tr
a
c
k
i
n
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ff
ic
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nc
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he C
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he deve
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it
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ff
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tly
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f
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ha
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it
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o
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w
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P&O
a
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go
rith
m
in
c
a
p
a
bl
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of
h
andl
in
g
th
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P
S
C
of
t
he
s
o
l
ar
p
ane
l
.
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r
e
su
lts
a
ls
o
in
di
ca
te
t
ha
t
t
h
e
tr
ac
ked
p
o
w
e
r
by
t
h
e
CS
h
as
a
v
er
y
l
o
w
f
l
uc
t
u
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ion
s
of
t
he
s
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ead
y
p
o
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e
r
c
o
mpa
r
ed
t
o
P
&
O
a
l
go
r
i
t
h
m
.
T
he
C
S
has
pr
o
v
e
n
a
c
c
u
r
a
c
y
,
r
obus
tn
e
s
s,
a
nd
eff
e
c
t
i
v
ene
ss
of
e
f
f
ic
ie
nt
e
ne
r
gy
u
t
i
l
i
zat
i
on
for
the
sta
n
da
l
one
P
V
system
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
108
1 –
1
0
89
1
088
REFE
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R.
A
bo
els
a
ud
,
A
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I
b
r
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,
and
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.
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rgan
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e
v
,
“
Rev
i
ew
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f
t
h
r
ee-phas
e
i
nv
ert
e
rs
c
on
trol
f
o
r
u
n
b
al
anced
l
o
a
d
com
p
ens
a
tio
n
,
”
International Journal of
Power
El
e
c
t
r
on
i
c
s and
Dr
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t
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JPED
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)
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Abdel
k
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M
at
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Hlou,
”
A
N
ew
P
h
o
to
vo
ltai
c
Bl
ock
s
M
u
t
u
alizati
on
Sys
t
em
f
o
r
M
icro-Grid
s
U
si
ng
a
n
Ardu
in
o
Bo
ard
an
d
L
abv
i
ew
,
”
In
te
rna
t
io
na
l J
o
urna
l o
f
Powe
r
El
ectr
onics
an
d
D
r
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t
em
(
I
JP
ED
S
)
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B.
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i
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,
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D
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an
d
T
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C
a
i
,
"
P
h
o
t
ovo
lt
aic
DC-Bui
ldin
g-M
odul
e-Bas
e
d
BIP
V
S
y
s
t
e
m
—
Co
nc
ep
t
and
Desig
n
Con
s
i
d
erati
o
n
s
,"
i
n
IEEE Tra
n
s
a
cti
o
n
s
o
n
Power
El
ectr
o
n
i
cs
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429
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REN
2
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, “
Renew
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015
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atu
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r
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14
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A.
G
.
Garganeev,
R.
A
boels
a
ud,
a
nd
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.
Ibrahim
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“
A
N
o
vel
Pre
dictiv
e
Co
nt
ro
l
A
l
g
o
rit
h
m
F
o
r
Auto
no
mo
us
P
o
w
er
S
u
p
p
l
y
S
ystem
s
,”
i
n
Pro
c
eed
in
gs
o
f
t
h
e 4
t
h In
t
e
rn
ati
o
n
a
l
Co
nf
eren
ce
o
n
Fr
on
ti
e
r
s of
Ed
uca
tio
nal T
echn
o
l
o
g
i
es
-
ICFET
’
18,
2
01
8
,
p
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75
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[7]
T.
K
aw
amu
r
a
et al
.
,
“A
nal
y
s
i
s
of
M
PPT
c
harac
t
eristics
i
n
p
hoto
v
o
lta
i
c
p
ower
s
ys
te
m,”
So
l.
Ener
gy M
a
t
e
r.
Sol.
Cell
s
,
19
97
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[8]
C.
T
h
u
l
a
si
ya
mm
al
a
n
d
S
.
S
u
tha,
“
D
e
s
i
gn
a
nd
co
m
p
arati
v
e
an
al
ys
is
o
f
d
c
-d
c
bo
os
t
and
si
ng
le-end
ed
p
rim
a
ry
-
in
du
ctan
ce
con
v
e
rter co
n
v
e
rters
usi
n
g
solar pow
ered m
ax
im
um
pow
er po
i
n
t
t
racki
ng alg
o
rit
h
ms
,”
Am
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J.
Appl.
Sci.
,
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N.
F
e
m
ia,
G
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P
etrone,
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S
pag
n
uolo,
and
M.
V
itelli,
“
A
tech
ni
que
f
or
i
m
p
rovi
ng
P
&
O
M
PPT
p
erf
o
rm
ances
o
f
do
ub
le-s
tage
g
rid
-
con
n
ected
phot
o
voltaic systems,”
IEEE Tr
an
s.
Ind.
El
ectr
o
n
.
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2009
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[1
0]
F
.
Liu
,
Y
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Ka
ng
,
Z.
Y
u
,
a
nd
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Du
a
n
,
“Co
m
p
a
riso
n
o
f
P
&
O
a
n
d
hi
ll
c
lim
b
ing
MP
PT
m
etho
d
s
f
o
r
g
ri
d-co
nnect
ed
PV
c
on
ve
rte
r
,”
i
n
200
8
3rd IEEE
Co
nf
eren
ce on
Ind
u
s
t
ri
a
l
El
ectr
o
n
i
cs
an
d
A
pplica
t
i
ons, ICIEA 2
008
,
200
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[1
1]
A
.
Sa
fa
ri
a
n
d
S
.
Me
k
h
ile
f
,
“Inc
re
m
e
nta
l
c
on
d
u
c
t
a
n
c
e
MPPT
m
e
t
hod
f
or
P
V
sy
st
e
m
s,
”
in
Ca
nadian Con
f
eren
ce
o
n
El
ectrica
l a
n
d
Comp
ut
er
E
ngin
eerin
g
, 2
01
1
.
[1
2]
H
.
Pa
te
l
a
n
d
V.
A
ga
r
w
a
l
,
“M
ATLA
B-based
mo
de
ling
to
s
tudy
t
he
e
ff
ects
o
f
p
arti
al
s
h
a
d
i
ng
o
n
P
V
a
rray
chara
c
t
e
ristics
,
”
IEEE Tr
an
s.
En
e
r
gy
Conver
s.
,
2008
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[13
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K
.
Chen
,
S
.
T
i
a
n,
Y
.
Chen
g,
a
nd
L
.
Bai,
“
An
i
m
p
rov
e
d
M
PPT
co
nt
roll
er
f
o
r
p
h
o
t
o
v
o
lt
aic
sy
ste
m
u
n
d
er
p
arti
al
sh
adi
n
g
con
d
ition,
”
IEE
E
Tr
ans.
S
u
s
t
ain.
En
erg
y
,
20
14
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[1
4]
S
.
Ob
uk
ho
v
,
A
.
Ib
ra
him,
a
n
d
Ra
e
f
A
bo
e
l
so
ua
d
,
“
Ma
x
i
mu
m
Po
we
r
P
o
i
n
t
Track
in
g
O
F
P
arti
all
y
S
hadi
ng
P
V
s
y
stem
Using
Particl
e
S
wa
rm
O
pt
i
m
ization,”
4th
In
t
.
Co
nf.
Fr
on
t.
Educ.
T
ech
nol
. Proc.
,
M
osc
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w,
J
u
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01
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New
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5]
C
.
Be
n
Sa
la
h
a
n
d
M.
O
ua
li,
“
Co
mp
a
r
iso
n
o
f
fu
z
z
y
lo
gic
a
n
d
n
e
u
r
al
n
etw
o
rk
i
n
maxi
mum
pow
er
p
oi
nt
t
racker
f
or
PV sy
s
tems,”
E
l
e
c
t
r.
Po
w
e
r
S
y
s
t
.
Re
s
.
V
o
l
.
8
1
(1),
P
P.
4
3-50
(2
011).
[16
]
S
yaf
a
ru
ddi
n
,
E
.
K
a
ra
t
e
pe,
an
d
T
.
H
i
y
am
a
,
“
Art
i
fi
cial
n
eura
l
netw
ork
-
po
lar
coo
r
di
nated
f
u
zzy
c
o
n
t
r
oller
bas
e
d
ma
x
i
mu
m
po
w
e
r
p
o
int
tr
acking
con
t
ro
l
u
nder
part
ially
s
haded
con
di
tio
ns,
”
IE
T Renew.
P
o
wer
Gener
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Vol.3 (2) (2009)
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[17
]
R
.
Ram
a
prab
ha
a
nd
B
.
M
a
th
ur,
“
G
en
eti
c
A
lg
orith
m
B
a
s
ed
M
ax
i
m
u
m
P
o
wer
P
o
int
Tracki
n
g
f
o
r
P
a
rti
a
ll
y
S
h
ad
ed
Sol
a
r
Photovol
tai
c
Array,”
Int.
J.
Res.
Rev.
In
f
.
Sci.
2
(1),
P
P
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6
1
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2).
[
18
]
S
.
O
b
u
k
hov
a
nd
R
.
A
.
I
brahi
m
,
A,
“
M
a
xim
u
m
P
o
w
e
r
P
o
in
t
Tra
cking
OF
P
arti
a
lly
S
hadi
ng
P
V
sys
t
e
m
Using
P
a
r
t
ic
l
e
S
wa
r
m
O
pt
im
i
z
a
t
io
n,
”
4
t
h
Int
.
Co
n
f
.
F
r
ont.
Ed
uc
.
T
echn
o
l.
Pr
oc.
,
Mosc
o
w
,
Ju
ne
2
5
-
2
7
,
20
18
-
N
e
w
Y
ork
ACM
,
pp
.
16
1–
1
6
5
(2
01
8).
[19
]
K
.
S
u
n
d
aresw
a
ran,
P
.
S
a
nk
ar,
P.
S
.
R.
N
ayak
,
S
.
P
.
S
i
m
o
n
,
an
d
S
.
P
alan
i,
"
E
n
h
a
nced
e
n
e
rgy
o
u
tp
ut
f
rom
a
PV
sy
st
e
m
u
nder
part
ia
ll
y
sh
aded
c
on
di
tio
n
s
t
h
ro
ug
h
art
i
fi
cial
b
ee
c
o
l
on
y,”
IEEE Tran
s.
Su
sta
i
n. En
e
r
gy
.
6
(1),
p
p.
19
8–
20
9
(
2
0
1
5
).
[20
]
J
.
Ahmed
and
Z.
S
al
a
m
,
“
A
M
axi
m
u
m
P
o
w
er
P
oi
nt
T
racki
n
g
(M
P
PT
)
f
o
r
PV
s
ys
tem
usi
n
g
Cucko
o
S
earch
w
ith
part
ial shadi
ng capabi
lity,”
App
l
.
E
n
ergy
,
20
14
.
[21
]
L
aag
ou
bi
,
T.
,
M
.
B
ouzi
,
a
nd
M
.
Bench
a
gr
a,
“
M
P
P
T
a
n
d
P
ow
er
F
actor
C
o
n
t
r
ol
f
or
G
ri
d
Co
nnect
ed
P
V
S
y
st
em
s
with
F
u
zzy
L
ogic
Cont
rollers
,
”
Int
e
rna
t
i
o
n
a
l
Jou
r
n
a
l
of Power
E
l
ectr
o
n
i
cs
a
nd D
r
ive
Sys
t
ems
(
I
J
P
EDS)
,.
9
(
1
):
p
.
10
5-
113
,
2
01
8
[22
]
S
.
J
a
fari,
O.
B
o
z
org
-
Had
d
ad,
an
d
X
.
C
hu,
“
Cuck
oo
o
p
timi
z
at
ion
al
gorith
m
(COA),
”
i
n
S
t
u
d
i
e
s in
Com
put
a
tio
nal
Int
e
ll
ig
ence
,
2
018.
[23
]
A
.
M.
R
ey
no
ld
s
and
M
.
A
.
F
r
y
e
,
“
F
ree-fli
ght
odor
t
rackin
g
in
D
rosophil
a
is
c
onsis
t
ent
w
ith
a
n
opt
i
mal
intermi
t
tent
scal
e-f
r
ee search
,
”
PL
o
S
O
n
e
,
20
07
.
[24
]
X
.
S.
Y
ang
and
S
.
D
eb,
“
Cucko
o S
e
a
r
ch
via
L
évy Fl
ig
h
t
,
”
N
atu
r
e
&
Bi
ol
ogicall
y
I
n
s
p
i
red
Co
mp
utin
g
,
2
009
.
Na
BIC 20
09
. W
o
r
ld
Con
gre
s
s
o
n
. 2
00
9.
[2
5]
H
.
So
ne
j
i
a
nd
R
.
C.
S
a
n
gh
v
i
,
“
Towar
d
s
t
h
e imp
r
ovement
o
f
Cucko
o
s
e
arch
a
l
g
o
r
ith
m
,”
i
n
Proc
e
e
di
ng
s
of
t
h
e
2
0
1
2
Wo
rld
Con
g
ress
o
n
In
f
o
rm
ati
o
n
a
n
d
Comm
unicat
io
n
T
echno
lo
g
i
es,
W
I
CT 20
12
,
20
12
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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1
089
BIOGRAPHI
E
S
OF
AUT
HORS
S.
O
b
u
k
h
o
v
(
Pr
ofe
s
sor)
wa
s
b
o
r
n
i
n
To
msk
,
R
u
ssia
in
1
96
3.
I
n
19
89
h
e
de
fe
nd
e
d
h
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t
he
sis
a
n
d
received
P
h
D
d
e
gree
f
r
o
m
N
at
ional
Research
T
o
m
sk
P
ol
y
t
echn
i
c
U
n
i
v
ersity
,
T
o
m
s
k
,
R
ussia
an
d
continued
his
career
a
t
the
depa
r
t
men
t
i
n
the
position
o
f
s
enio
r
res
earcher.
Th
e
r
e
s
earc
h
i
n
t
erest
cov
e
rs d
iff
e
rent
ty
p
es
o
f
ren
e
wab
l
e en
ergy.
E-mai
l:
sero
b99
@
m
ai
l.
r
u
.
A.
I
brahim
(
Teach
in
g
As
si
stan
t)
w
a
s
b
o
r
n
in
E
L-S
h
arkia,
E
gy
p
t
i
n
19
87
.
He
r
ece
iv
ed
t
h
e
B
.
S
c.
f
r
o
m
t
he
F
acu
lty
of
E
ng
in
eeri
n
g
,
Z
agazi
g
U
n
ivers
ity,
Egy
p
t
in
2
00
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A
n
d
M
.
S
c.
f
rom
th
e
F
acult
y
of
E
ngin
eerin
g,
Z
agazig
Un
iversit
y
,
Egy
p
t
in
2
01
3
.
N
ow
h
e
i
s
teachi
n
g
assistant
in
Nat
i
on
al
R
es
earch
T
o
m
sk
P
o
l
ytechni
c
Un
iv
ersity,
Toms
k
,
R
u
ssia.
Th
e
research
i
nt
erest
covers
diff
e
r
en
t
ty
pes
o
f
r
en
ewabl
e
e
n
e
rgy
,
p
arti
cle
sw
arm
optimizat
io
n,
n
eu
ral
netw
ork
s
,
cuck
oo
op
tim
i
zati
ons
a
nd
its
a
p
p
li
cation
s
i
n
ren
e
wabl
e
en
ergy
.
H
e
i
s
a
s
t
uden
t
m
em
ber
in
I
EEE.
E-mai
l: ibragi
m@t
p
u.ru
.
Ra
e
f
A
b
o
e
l
sa
ud
(
Te
a
c
hing
A
ss
ista
n
t
)
wa
s
bo
rn
i
n
Za
ga
z
i
g,
E
g
y
p
t,
i
n
19
87.
H
e
rec
e
iv
ed
t
h
e
B.S
c
.
d
e
gree
(with
h
o
n
o
r
s)
a
n
d
t
he
M
.S
c.
d
eg
re
e
in
e
lectri
cal
e
n
g
i
n
eerin
g
f
r
om
Zag
a
zi
g
Un
iv
ersit
y
,
Z
a
gazig
,
E
g
y
pt
,
in
2
0
0
9
and
20
13
,
res
p
ectiv
el
y.
H
e
is
c
u
r
rent
ly
w
o
r
k
i
ng
to
ward
t
he
P
h.D.
D
egree
in
e
lect
rical
e
n
g
i
n
eerin
g
a
t
T
o
m
s
k
P
o
l
y
t
echn
i
c
Univ
ersi
ty,
Toms
k
,
Rus
s
ia
.
His
current
r
es
earch
i
nt
eres
ts
i
nclu
de
power
e
l
ectron
i
c
c
onv
erters
a
nd
c
on
tro
l
s
yste
m
s
app
lied
to
r
en
ewabl
e
e
nerg
y
co
nv
ersio
n
a
n
d
e
n
e
rgy
st
orag
e,
H
e
i
s
a
st
ud
ent
m
e
mb
er
i
n
IEEE.
Ema
il:
r
s
ahmed@eng.zu.
e
du.
eg.
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