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
)
V
o
l.
10, N
o.
1, Mar
ch 20
19,
p
p.
548~
5
6
1
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
5
48-
56
1
548
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
C
r
itical evaluation of soft co
m
puting m
e
thods f
o
r maxim
u
m
power point trac
king algorit
hms of phot
ovoltaic systems
N
o
raz
l
an
Hash
i
m
1
, Zain
a
l
S
a
lam
2
1
F
acult
y of Electri
cal E
ng
in
e
e
ri
n
g
, Un
i
vers
i
t
i
Tek
n
o
lo
gi
M
ARA,
M
alays
i
a
2
S
c
hoo
l of Electri
cal E
ng
in
e
e
ri
n
g
, F
aculty
o
f
En
g
i
n
eering
,
U
ni
ve
rsiti Teknologi
Malaysia, Malay
sia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Jun
12
,
2
0
18
Re
vise
d N
ov
29,
201
8
A
c
c
e
pte
d
D
ec 16,
2
0
1
8
With
t
he
p
ro
l
i
f
e
rati
on
o
f
n
u
m
e
rou
s
s
o
f
t
co
m
puti
ng
(S
C)–
b
ased
m
a
ximum
po
wer
po
int
tra
c
ki
ng
(
M
P
P
T
)
alg
o
rith
ms
f
or
p
h
o
to
vo
lt
aic
(P
V
)
s
y
stems
,
det
e
rm
in
i
n
g
wh
i
c
h
al
gori
t
hm
p
erf
o
rm
s
b
e
tt
er
t
han
oth
e
rs
i
s
beco
min
g
in
creasin
gl
y
d
i
fficu
lt.
T
h
is
i
s
p
r
im
aril
y
du
e
t
o
t
h
e
a
b
s
en
ce
o
f
s
tand
ardi
zed
me
tho
d
s
t
o
be
n
c
hm
a
r
k
th
e
i
r
pe
rfo
r
ma
nc
e
s
u
sin
g
c
o
n
s
iste
nt
a
n
d
sy
stem
ati
c
p
r
oc
e
d
ure
s
.
More
ov
e
r
,
th
e
m
o
d
u
le
t
e
c
h
no
log
y
,
po
we
r
r
a
ting
s,
a
n
d
environment
a
l
c
o
nditions
r
eport
e
d
by
n
umer
ous
publ
ications
a
l
l
diff
er.
Based
on
t
h
e
se
c
o
n
cern
s
,
t
h
i
s
p
aper
p
resen
t
s
a
crit
ical
e
val
u
ati
o
n
o
f
t
h
e
f
i
v
e
m
o
s
t
im
p
o
rt
a
n
t
and
recent
S
C
-bas
ed
M
P
P
Ts,
n
a
m
e
ly,
gen
e
ti
c
alg
o
ri
thm
(G
A
)
,
cuck
oo
s
ear
ch
(
CS
),
p
arti
cle
s
w
ar
m
opt
i
mizati
o
n
(PSO)
,
d
i
f
f
e
ren
ti
a
l
evo
l
u
t
i
on
(DE),
and
evol
utio
nary
p
rogr
am
mi
ng
(E
P)
.
To
p
erform
a
f
a
i
r
com
p
ariso
n
,
th
e
i
n
iti
a
li
za
t
i
o
n
,
selecti
o
n
,
a
n
d
s
t
o
p
p
in
g
crit
e
r
i
a
f
o
r
al
l
m
e
tho
d
s
are
f
i
x
e
d
in
s
imil
ar
c
on
diti
on
s
.
T
h
u
s,
t
h
e
p
erf
o
rm
ance
is
d
et
er
m
i
n
e
d
by
i
t
s
resp
ectiv
e
repro
d
u
c
tio
n
p
r
oces
s.
S
imul
a
tion
tes
t
s
are
perf
ormed
u
s
i
n
g
t
h
e
M
A
TLAB/
S
I
MULINK
en
vi
ronm
e
n
t.
T
h
e
p
erf
o
rman
ce
of
each
a
l
gorith
m
is
com
p
are
d
a
n
d
e
v
a
lu
ated
b
as
ed
o
n
its
s
peed
o
f
conv
ergen
c
e,
a
c
c
ur
ac
y,
com
p
lexity
,
and
su
ccess
rate.
The
res
u
lt
s
i
n
d
i
ca
t
e
t
hat
EP
a
p
p
e
ars
to
b
e
th
e
m
o
st
p
romisi
ng
an
d
encou
r
agi
n
g
S
C
a
l
g
o
r
it
hm
t
o
be
u
s
e
d
in
M
PPT
f
o
r
a
PV
sy
st
e
m
u
n
d
er t
he
m
ultim
od
al
p
arti
al s
had
i
ng
con
d
i
t
i
on.
K
eyw
ord
s
:
CS
DE
EP
GA
MPP
T
Pa
rti
a
l sha
d
in
g
PSO
S
o
ft
c
om
p
u
t
i
n
g (
S
C)
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:
Nora
zlan
H
ash
i
m,
F
a
cult
y o
f
E
l
e
c
t
rica
l
En
gine
erin
g,
U
n
i
v
ersi
ti
T
e
k
no
l
o
g
i
M
A
R
A
,
404
5
0
S
hah
A
l
a
m
,
Mala
ysia
.
Em
ail:
azla
n
4
4
7
7
@
sa
la
m.
uit
m
.edu.
my
/
az
l
an4
4
7
7
@
yah
o
o
.c
om
1.
I
N
TR
OD
U
C
TI
O
N
Ma
xim
u
m
p
o
w
er
poi
nt
t
r
acki
n
g
(
M
P
P
T)
i
s
a
co
n
t
rol
a
l
g
o
r
ithm
em
be
d
d
e
d
i
nside
a
D
C
–D
C
p
o
w
e
r
con
v
er
t
e
r
t
o
e
x
t
ra
ct
t
he
m
ax
i
m
um
power
f
r
o
m
a
ph
o
t
o
v
o
ltaic
(
PV)
a
rr
ay.
The
ob
jec
t
ive
is
t
o
e
n
s
u
re
t
h
a
t
t
h
e
pow
er
t
o
be
e
x
t
ra
cte
d
a
l
w
a
y
s
ma
tches
t
h
e
pe
ak
v
a
l
ue
o
f
t
h
e
pow
e
r-vo
lta
ge
(
P-V)
c
ha
rac
t
e
r
istic
c
urve
u
nder
varying
solar
irradiati
on
(G
)
an
d
tem
p
era
t
ure
(T)
.
T
he
i
de
a
o
f
th
e
t
r
ac
ki
ng
i
s
to
l
o
c
k
t
h
e
c
o
nv
e
r
t
e
r
o
p
e
rat
i
n
g
vo
lta
ge
a
nd
c
u
rre
nt
t
o
the
m
a
ximum
po
w
e
r
poi
n
t
(
M
P
P
)
o
f
t
h
e
P
V
ar
ray.
T
he
M
P
P
,
w
h
en
i
n
a
norm
a
l
un
iform
i
r
rad
i
a
n
c
e
c
o
n
d
i
ti
on,
e
xh
i
b
i
t
s
a
un
iq
ue
p
e
a
k
of
t
he
P
-V
c
u
r
v
e
.
The
t
r
ac
kin
g
h
as
t
o
b
e
a
cco
mp
l
i
sh
ed
rapi
dl
y t
o
e
nsur
e t
h
a
t
t
he pow
e
r
is
n
o
t
los
t
d
uri
n
g
the
c
h
a
n
ges
i
n G
an
d
T. In a
d
d
iti
o
n
, the
M
PP
T
m
u
st
b
e able
to
c
orr
ectl
y
l
o
cate
the
MPP
dur
in
g
the
occ
u
rrenc
e
of
p
ar
t
i
al
s
h
ad
i
n
g—a
con
d
i
t
i
o
n
i
n
w
hic
h
a
port
i
o
n
o
f
the
PV
a
r
r
ay
i
s
sh
ad
ed
w
h
i
l
e
o
t
h
e
r
p
a
r
t
s
r
emai
n
uni
fo
rml
y
i
rrad
i
a
t
e
d.
D
ur
i
n
g
pa
rt
ia
l
sh
a
d
i
ng,
t
he
P
-V
c
urve
exh
i
bi
t
s
m
ult
i
p
l
e
p
ea
ks,
th
u
s
t
r
a
ns
form
in
g
t
h
e
pro
b
lem
from
s
i
n
gle
m
oda
l
t
o
m
u
lti
m
odal,
t
ha
t
i
s
,
w
i
th
m
u
l
t
i
p
l
e
m
a
x
i
m
a
p
o
i
n
t
s
.
T
h
u
s
,
t
h
e
p
r
o
b
l
e
m
b
e
c
o
m
e
s
m
u
c
h
m
o
r
e
c
o
m
plica
t
e
d
a
s
the
MP
PT
a
l
gor
it
hm
n
eed
s
to co
n
t
i
n
uo
u
s
l
y
tra
ck
t
he
con
ti
n
u
o
u
s
varia
t
i
ons o
f
sever
a
l
pe
ak
s that changes
wi
th
G
an
d
T
.
D
e
spite
a
l
a
r
g
e
num
ber
of
c
on
v
e
nti
ona
l
MP
P
T
a
lgor
ithm
s
p
u
b
lis
he
d
in
l
i
t
era
t
u
r
e
[1]
-
[5],
only
sever
a
l
m
e
t
h
o
d
s
a
r
e
w
i
de
l
y
i
m
p
lem
e
n
t
ed,
n
a
me
ly,
the
pe
rtur
b
an
d
o
bserv
e
(
P
&
O),
incr
em
ental
c
o
nd
uc
ta
n
c
e
(IC),
a
nd
hill
c
l
i
m
b
ing
(HC)
m
ethods
.
These
algorit
h
m
s
a
re
b
as
e
d
on
c
he
ck
in
g
t
h
e
slo
p
e
of
t
he
c
urve
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Cri
t
i
c
a
l
eva
lu
at
ion
o
f
so
ft
c
o
mp
ut
ing
met
hod
s fo
r m
a
xi
mum p
o
w
e
r
poi
nt
t
r
a
c
k
i
ng
…
(No
r
azlan
Ha
shim)
54
9
peri
od
ica
l
l
y
t
o
ensure
t
hat
the
pea
k
i
s
d
e
tec
t
ed
(
w
h
e
n
t
he
s
l
o
p
e
is
z
ero).
Ge
nera
l
l
y,
i
t
o
p
er
ates
s
a
tis
fa
c
t
or
i
l
y
un
der
the
u
n
i
form
i
rra
di
a
n
ce
c
o
n
d
iti
o
n
,
t
h
a
t
i
s,
w
he
n
the
P
-
V
c
urve
h
a
s
a
u
n
i
que
p
e
a
k
.
H
o
w
e
ve
r,
dur
in
g
part
ial
sha
d
in
g
,
t
he
a
l
g
orith
m
c
a
nno
t
loca
te
t
he
c
orre
ct
M
P
P
b
e
ca
use
the
pro
b
l
em
h
as
t
r
a
ns
form
ed
t
o
a
mult
imo
d
a
l
,
and
i
t
c
a
n
not
d
iffe
ren
tia
te
b
e
t
w
e
en
t
he
l
oc
al
a
nd
g
l
oba
l
pe
a
k
s.
T
his
is
i
n
e
vi
ta
bl
e
bec
a
u
se
t
he
nat
u
re
o
f
t
h
e
s
e
al
gor
it
hms
is
b
a
s
e
d
o
n
th
e
pea
k
d
e
t
ec
ti
on
p
r
i
nc
i
p
l
e
,
th
a
t
i
s,
w
h
e
n
it
l
o
cat
e
s
a
p
e
r
ce
i
v
ed
ma
ximum
po
i
n
t,
it
loc
k
s
i
t
se
lf
w
it
hi
n
the
vic
i
nit
y
o
f
t
h
a
t
poi
n
t.
I
f
t
h
e
p
eak
i
s
l
o
cal,
s
ubs
t
a
n
t
ia
l
loss
o
f
PV
pow
er
r
e
s
ul
ts.
To
a
d
d
r
e
ss
t
h
is
p
ro
blem
,
a
soft
c
om
pu
t
i
n
g
(
S
C
)
M
PP
T
is
p
r
o
p
o
se
d.
S
in
ce
the
S
C
a
l
g
o
r
it
hm
s
e
a
r
c
h
e
s
f
o
r
a
l
l
t
h
e
p
e
a
k
s
o
v
e
r
t
h
e
e
n
t
i
r
e
P
-
V
c
u
r
v
e
,
f
i
n
d
i
n
g
t
he
g
l
oba
l
M
P
P
is
v
ery
l
i
ke
ly.
T
h
e
a
u
th
ors
in
[
1
]-[
3
],
[
5
]
-[
16]
h
av
e
don
e
e
x
t
e
ns
iv
e
rev
i
e
w
s
o
n
t
h
e
ap
pli
c
a
t
io
n
of
S
C
fo
r
MPP
T
;
the
s
e
i
n
cl
u
d
e
fuzz
y
lo
g
i
c
con
t
ro
l
l
er
(
FLC),
ar
t
i
fic
i
a
l
n
eura
l
netw
ork
(A
NN),
p
arti
cle
swa
rm
o
p
t
imiz
a
tio
n
(PSO
),
g
ene
t
ic
a
l
gor
it
h
m
(G
A)
,
differe
n
t
ia
l
e
v
o
l
uti
on
(
D
E),
ant
c
o
l
o
ny
o
p
tim
i
z
a
t
i
o
n
(A
CO
),
B
ayesia
n
fusio
n
(
BF
),
c
uc
ko
o
s
e
a
r
ch
(C
S)
, an
d
c
h
aot
i
c se
arc
h
(C
h
S).
With
t
he
p
r
o
lif
e
ration
o
f
S
C
-bas
ed
M
P
P
T
tech
n
i
q
u
es
(
a
nd
t
h
e
i
r
v
a
r
iat
i
o
n
s)
,
determ
i
n
i
ng
w
h
ich
alg
o
ri
t
h
m
is
m
or
e
effec
tive
tha
n
o
the
r
s
is
d
iffi
c
u
l
t
a
s
no
p
r
o
p
e
r
e
va
l
u
a
t
i
o
n
t
o
c
r
i
t
i
ca
l
l
—
p
rim
a
ril
y
b
eca
use
o
f
t
h
e
fa
ct
t
h
a
t
no
t
w
o
me
t
h
od
s
are
co
mp
are
d
f
ai
rly
,
n
o
r
a
re
t
he
y
verifie
d
in
d
e
pen
d
e
n
t
l
y
. Th
is is bec
a
u
se in m
o
st
pu
b
l
i
s
he
d
w
o
rks,
t
he
m
o
d
u
l
e
t
e
c
h
no
log
y
,
expe
r
i
me
nt
a
l
s
e
t
up,
p
ow
e
r
r
at
ing
s
,
a
n
d
envi
ron
m
e
n
t
c
ondi
ti
o
n
s
(par
t
i
c
u
la
rly
t
h
e
va
ria
t
ions
i
n
G
and
T)
i
n
w
h
ic
h
the
P
V
s
ys
tem
s
e
t
u
p
w
as
s
u
b
j
ect
ed
t
o
are
a
l
l
d
i
f
f
e
re
n
t
.
In
add
i
tio
n,
the
p
artia
l sha
d
in
g e
xper
i
m
e
nts th
a
t
ha
v
e bee
n
car
rie
d o
u
t are
ne
ver un
ique
.
Th
is raises q
u
e
s
ti
ons on
the
le
gi
t
i
ma
cy
o
f
the
c
l
a
i
ms
a
s
di
ffere
n
t
s
h
ad
i
ng
pa
tter
n
s
resu
lt
y
a
ss
e
s
s
th
e
i
r
p
e
rfo
rma
n
ce
s
exi
s
ts.
Th
e
aut
h
ors’
c
laim
s
on the
s
u
pe
ri
o
r
ity
o
f
the
i
r
ow
n
t
e
ch
n
i
q
u
es a
re
unjus
t
i
fia
b
le
i
n
di
ffere
n
t M
P
P
T
effic
ienc
ie
s.
Wit
h
r
egar
d
to
t
he
se
c
onc
er
ns,
th
is
p
ape
r
a
i
m
s
t
o
p
ro
vi
d
e
a
s
ta
nd
a
r
di
zed
p
ro
c
e
d
u
re
t
o
crit
i
c
al
ly
eva
l
ua
t
e
t
he
p
e
r
form
ance
s
of
v
ar
ious
S
C
M
P
P
T
t
ec
hn
ique
s.
T
hre
e
we
ll-e
s
t
a
blis
hed
m
e
t
h
o
d
s
ar
e
co
ns
i
d
ere
d
,
nam
e
ly,
P
S
O,
G
A,
a
nd
D
E
,
a
l
on
g
w
i
th
t
w
o
r
e
c
e
n
tl
y
prop
ose
d
a
l
g
or
i
t
hm
s,
c
uck
oo
se
arc
h
(
CS
)
and
evo
l
ut
iona
r
y
p
r
ogram
ming
(EP
)
.
A
ltho
u
gh
ther
e
ex
is
t
sev
e
ral
com
para
ti
ve
s
t
u
di
e
s
a
mo
ng
G
A
,
D
E,
a
nd
P
S
O,
the
y
o
n
l
y
offe
r
ge
nera
l
rev
i
e
w
s
w
i
th
ou
t
a
n
y
e
v
a
l
ua
t
i
on
o
n
t
heir
r
espec
t
i
v
e
perfor
m
a
n
ces.
Eac
h
a
lg
ori
t
hm
i
s
assessed
i
n
t
e
r
m
s
o
f
a
ccur
acy,
spee
d,
c
om
pl
e
x
i
t
y,
a
n
d
s
ucce
ss
r
at
e
of
c
o
nverg
e
n
ce.
T
wo
s
t
a
tist
i
c
a
l
proce
dures—
n
am
ely,
t
he
m
ean
a
bs
o
l
u
t
e
error
(
M
A
E
)
and
stan
da
rd
d
e
v
i
a
t
i
o
n
(
S
T
D
)
—
a
r
e
u
s
e
d
f
o
r
benc
hm
ar
kin
g
.
In
a
dd
i
t
i
o
n
,
t
h
e
rela
tive
c
o
mple
x
i
t
y
o
f
t
h
e
alg
o
r
i
t
h
m
is
d
e
t
e
r
mine
d
b
y
m
ea
suri
ng
t
he
a
vera
ge
CP
U
t
i
m
e
t
a
k
e
n
f
or
eac
h
i
t
era
tio
n.
T
he
p
ro
pos
ed
e
va
lua
t
i
on
w
i
l
l
a
ssist
t
he
r
e
s
e
a
rc
hers
a
nd
prac
t
i
t
i
o
n
e
r
s
i
n
selec
t
i
n
g the
b
e
st a
lgor
it
hm
to de
sig
n
t
heir
MP
P
T appl
ica
tio
ns.
2.
OVE
RVIEW
O
F S
C
-BASED
M
PPT
S
o
f
t
c
o
m
p
u
t
i
n
g
(
S
C
)
i
s
a
c
o
l
l
e
c
t
i
o
n
o
f
f
l
e
x
i
b
l
e
,
a
d
a
p
t
a
b
l
e
,
a
n
d
i
n
t
el
l
i
ge
n
t
p
r
o
bl
e
m
-
s
olv
i
ng
me
tho
d
s
to
e
x
p
lo
it
t
h
e
t
o
ler
a
nce
for
i
m
pre
c
isi
on
t
o
a
c
h
i
e
ve
t
rac
t
a
b
il
it
y,
r
ob
us
tne
ss,
a
nd
l
o
w
-
cos
t
s
o
l
u
t
i
ons
[
17
]
.
I
n
gene
ra
l,
S
C
ca
n
be
c
l
a
ssifie
d
i
nt
o
tw
o
broa
d
ca
t
e
gorie
s,
s
in
gle
-po
i
nt
a
nd
p
opu
l
a
t
i
o
n
-
bas
e
d
sea
r
c
h
.
Fo
r
th
e
form
er
,
the
alg
o
ri
thm
scans
t
h
e
so
lut
i
ons
i
n
the
w
hole
sea
r
ch
s
pa
ce
o
f
t
h
e
p
rob
l
em
(
in
t
he
c
a
s
e
for
t
h
e
P
V
syste
m
,
the
se
a
r
ch
s
pa
ce
i
s
t
he
e
n
tire
P
-
V
c
u
rve)
u
s
i
n
g
one
a
ge
nt
a
t
a
time
.
O
n
the
ot
her
h
a
nd,
f
or
t
he
po
p
u
l
a
tio
n-ba
se
d
sea
r
ch
t
y
p
e,
t
he
a
l
gor
it
hm
o
pe
ra
te
s
on
se
vera
l
a
gen
t
s
(i
n
par
a
lle
l)
w
it
hin
the
se
arc
h
s
pace
.
Th
e
l
a
t
t
er
i
s
un
iqu
e
b
ec
au
se
t
h
e
se
s
i
m
pl
e
a
g
ent
s
c
oop
e
r
at
e
a
n
d
in
t
e
ra
c
t
w
i
t
h
o
n
e
a
n
o
t
he
r
t
o
a
cco
m
p
lis
h
com
p
le
x
task
s.
T
o
da
te
,
the
re
por
ted
S
C
-ba
s
e
d
M
P
P
T
alg
o
ri
t
h
m
s
u
se
d
t
o
s
ol
ve
p
art
i
a
l
s
ha
di
ng
pr
o
b
le
ms
a
re
show
n
i
n
F
i
g
u
r
e
1.
S
ome
of
t
he
i
m
p
ortan
t
f
e
a
t
u
re
s
of
t
h
e
se
m
eth
o
d
s
h
a
ve
b
ee
n
desc
ribe
d
brie
fly
i
n
t
he
in
t
r
od
uc
ti
on.
I
n
t
h
is
p
aper
,
on
l
y
p
o
p
u
l
a
t
ion-
base
d
a
l
g
o
r
ithm
s
w
i
ll
be
d
i
s
cuss
ed
g
ive
n
t
he
ir
s
u
p
e
r
i
o
rity
i
n
so
l
v
i
ng m
u
l
tim
oda
l o
p
t
i
miza
t
i
on
pr
ob
l
e
ms.
-
F
L
C
-
A
N
N
-
B
F
-
C
h
S
- P
S
O
- A
C
O
-
BCO
- C
S
- G
A
- D
E
- E
P
S
o
f
t
C
o
m
pu
t
i
ng
(
SC
)
P
o
p
u
la
ti
o
n
-
B
a
s
e
d
S
ear
ch
A
l
g
o
r
i
t
h
m
S
i
ng
l
e
P
o
i
nt
S
e
ar
ch
A
l
g
o
r
i
t
h
m
F
i
gure
1.
R
e
p
o
r
ted S
C
-based
M
P
P
T
a
lgori
t
h
ms use
d to so
l
ve pa
r
t
i
al sh
a
d
i
ng pr
o
b
le
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
54
8 –
56
1
55
0
2
.
1
.
G
e
nera
lized pro
c
es
ses
The
w
a
y
i
n
w
hic
h
t
he
p
o
p
u
l
ati
on-
base
d
S
C
o
p
timize
s
t
he
s
ol
ut
i
o
n
c
a
n
b
e
ge
ner
a
l
i
z
e
d
i
n
t
o
t
hre
e
ma
jor
pr
ocesse
s,
n
a
m
e
l
y,
i
ni
ti
a
l
iza
t
ion,
r
e
p
ro
duc
t
i
o
n
,
a
n
d
se
l
e
ct
i
on.
I
n
the
i
n
it
ial
i
za
t
i
o
n
s
t
e
p,
t
he i
nit
i
a
l
pa
r
ent
f
o
r
th
e
pop
ul
a
t
ion
si
ze
w
i
t
h
n
c
an
di
d
a
t
e
s
is
g
en
e
r
a
t
ed
.
In
r
ep
r
od
uct
i
on,
t
he
o
f
f
s
p
ri
ng
a
r
e
cr
eated
f
r
o
m
the
selec
t
e
d
p
are
n
ts
t
hrou
g
h
a
u
ni
q
u
el
y
form
u
l
ated
e
q
u
a
t
i
o
n,
a
cc
ord
i
n
g
t
o
t
he
S
C
ty
pe.
F
i
nal
l
y
,
t
h
e
se
lec
t
ion
st
a
g
e
i
s
t
he
d
i
s
c
r
imi
n
a
t
ory
p
r
ocess
t
o
c
h
oose
t
h
e
i
n
d
i
vid
u
a
l
s
t
o
sur
v
ive
for
t
h
e
nex
t
g
e
n
era
tio
n.
T
he
repr
od
uct
i
on
a
nd se
l
e
ct
i
on pr
oce
sses a
r
e
repe
ated
iter
a
t
i
ve
ly
u
n
til a
pr
espe
cifie
d
stop
p
i
n
g
c
r
iterio
n
is m
e
t.
2.2.
I
n
itializ
a
t
i
o
n
I
n
t
he
c
o
n
te
x
t
o
f
MP
P
T
,
the te
rm
pop
u
l
at
i
on
is
r
efe
rre
d
t
o
t
he
pow
er
c
on
v
e
rter’
s
(
norm
a
lly
D
C–D
C
)
du
ty
c
yc
le
(
D
)
,
w
h
i
l
e
t
h
e
o
p
t
i
ma
l
s
o
lu
t
i
o
n
i
s
t
h
e
ma
x
i
m
u
m
PV
a
r
ra
y
’
s
ou
tpu
t
powe
r
(
P
PV
).
A
s
mal
l
po
p
u
l
a
tio
n
s
i
z
e
leads
to
p
o
o
r
so
lu
tio
ns
;
o
n
t
he
o
the
r
h
a
n
d,
a
l
arge
p
op
u
l
at
io
n
i
n
c
r
ea
se
s
t
h
e
com
p
uta
t
i
on
t
i
me
.
H
e
nc
e,
a
t
rade
-off
i
s
ne
e
d
e
d
t
o
a
c
h
ieve
c
r
e
di
b
l
e
so
l
u
t
i
on
s
w
i
th
a
r
ea
so
na
ble
num
ber
o
f
i
tera
tio
ns.
V
a
r
i
o
u
s
me
tho
d
s
t
o
c
h
oos
e
p
o
p
u
l
a
t
i
o
n
s
i
z
e
a
r
e
r
ec
o
m
m
e
nde
d
in
[
1
8
,
19]
;
in
t
h
i
s
st
udy
,
th
e
pop
ula
t
ion
si
z
e
w
a
s
s
et
t
o
5
bec
a
use
i
t
w
a
s
f
ou
n
d
(
b
y
t
rial
a
nd
error
)
t
o
prod
uce
t
h
e
bes
t
r
e
s
ul
ts.
In
m
o
s
t
case
s
,
th
e
v
a
l
u
e
s
a
tt
ache
d
t
o
the
in
it
ia
l
pop
ula
t
io
n
(D
initi
al
)
a
r
e
ge
ne
rated
ra
nd
oml
y
.
H
o
w
e
ver,
r
andom
ness
pro
duc
es
d
i
ffe
re
n
t
results
on
succe
ssi
ve
r
un
s,
e
ven
if
t
h
o
s
e
r
uns
w
e
r
e
in
it
ia
l
i
z
e
d
i
d
e
n
t
i
c
a
l
l
y.
T
o
e
l
im
ina
t
e
t
h
i
s
u
ncer
t
a
in
ty,
th
e
c
o
n
t
ro
lle
d
in
itia
l
i
za
ti
o
n
m
e
t
hod
i
s
pre
f
er
red.
F
or
n
p
op
ula
t
i
on,
t
he
i
n
i
ti
a
l
i
z
a
t
i
o
n
w
ith
u
ni
form
l
y
d
istr
ib
u
t
ed
e
le
me
nts
w
ithi
n
t
he
i
nter
val
0
D
1
i
s
give
n b
y
t
he
fo
l
low
i
ng
:
1
1
n
n
.....
1
n
2
1
n
1
D
initial
(1
)
S
o
a
t
t
h
e
be
g
i
n
n
in
g
o
f
t
he
s
e
a
r
c
h
,
five
d
iffere
nt
v
a
l
ue
s
o
f
D
w
i
t
h
ac
co
rd
an
c
e
t
o
(1
)
a
r
e
u
s
ed
t
o
fi
nd
the be
st
v
a
l
ue
o
f P
PV
.
2.3.
Rep
roduct
i
o
n
Re
pr
o
d
uc
t
i
o
n
i
s
the
m
o
s
t
c
rucia
l
s
te
p
as
i
t
d
i
ffere
n
tia
t
e
s
the
ab
il
ity
o
f
th
e
alg
o
ri
thm
t
o
p
ro
duc
e
th
e
n
e
xt
p
opu
l
a
ti
on
g
e
n
e
r
at
i
o
n
.
T
h
e
f
i
r
s
t
s
e
l
e
c
t
e
d
po
pul
a
tion
i
s
c
a
l
l
e
d
t
h
e
p
a
r
e
n
t
(
D
init
ial
)
;
t
h
e
s
e
c
o
n
d
a
n
d
sub
s
e
q
ue
nt
p
opu
la
ti
o
n
(
af
t
e
r
go
ing
t
h
ro
ug
h
t
h
e
repr
o
d
u
c
tio
n)
i
s
c
a
lled
the
o
f
fs
pri
n
g
(
D
Ne
w
).
S
wa
r
m
-based
alg
o
ri
t
h
ms
(
P
S
O
,
A
CO,
a
nd
CS
)
ar
e
ba
se
d
on
the
soc
i
a
l
b
eha
v
i
o
r
o
f
i
nse
c
ts
o
r
a
n
im
al.
The
y
u
til
ize
s
p
e
c
ific
repr
od
uct
i
on
o
p
era
t
or
s
suc
h
a
s
pa
rtic
l
e
v
e
l
oc
it
y
(for
P
S
O
)
and
L
é
v
y
f
lig
ht
(
fo
r
C
S
)
t
o
c
r
e
at
e
D
Ne
w
.
On
t
he
ot
her
ha
n
d
,
evo
l
uti
onar
y
-ba
s
ed
a
lg
ori
t
hm
s
(EP,
D
E,
a
nd
G
A
)
g
en
e
rate
D
Ne
w
t
h
r
o
u
g
h
n
a
t
u
r
a
l
g
e
n
e
t
i
c
s
evo
l
ut
ion.
T
h
e
y
use
ge
ne
tic
oper
a
t
o
rs
s
uc
h
a
s
c
ross
o
v
e
r
(
also
c
al
le
d
rec
o
mbi
n
a
t
io
n)
a
nd
mu
tat
i
o
n
.
T
he
crosso
ver
e
x
c
h
ange
s
som
e
p
a
r
t
s
o
f
tw
o
ind
i
vi
d
u
al
s,
w
hile
t
he
m
u
tat
i
on
op
e
r
a
t
or
c
ha
n
g
e
s
the
va
lue
o
f
t
he
rand
om
ly c
hos
e
n
in
d
i
v
i
du
al.
2.4.
S
ele
c
tion
S
e
lec
t
i
o
n
is
t
h
e
p
roce
ss
t
o
d
i
sc
rimina
t
e
(
is
ola
t
e
)
t
he
b
est
i
n
d
ivi
d
ual
s
f
or
t
he
n
e
x
t
ge
ner
a
t
i
o
n
(
D
Ne
w
).
I
t
i
s
b
a
s
e
d
o
n
t
h
e
f
u
l
f
i
l
l
m
e
n
t
o
f
c
r
i
t
e
r
i
a
s
e
t
b
y
t
h
e
f
i
t
n
e
s
s
f
u
n
c
t
i
on.
T
he
s
e
l
ec
tio
n
sh
oul
d be
c
h
o
se
n
suc
h
t
ha
t
it
con
v
er
ges
t
o
t
he
g
l
oba
l
o
p
t
i
m
um
s
olu
t
ion
(i.e
.,
P
PV
_
B
e
s
t
)
w
i
t
h
o
u
t
h
a
v
in
g
t
o
s
acr
if
i
c
e
to
o
m
u
ch
c
on
ve
rgenc
e
spee
d.
The
re exi
st
se
l
ec
t
i
o
n
s
c
h
em
es pr
opos
e
d
i
n li
t
e
rat
u
re
; th
e mos
t
c
o
m
m
on a
r
e rou
l
et
te
whe
el, t
o
u
r
n
am
ent,
rank
in
g,
a
n
d
s
tead
y
sta
t
e
sel
ecti
o
n.
A
c
om
prehe
n
si
ve
a
n
a
ly
sis
o
f
a
l
l
t
h
ese
sc
hem
e
s
ha
s
bee
n
r
ep
o
r
ted
in
[2
0],
[21]
.
In
t
hi
s
w
o
rk,
t
h
e
ra
n
k
i
ng
se
l
e
c
t
io
n
sc
he
me
i
s
c
h
os
e
n
g
i
ve
n
it
s
simp
lic
i
t
y
a
nd,
a
t
the
sa
me
time
,
yie
l
ds
g
oo
d re
sults.
The
b
a
s
i
c
e
qua
t
i
o
n
f
or
t
h
i
s sc
hem
e
is gi
ve
n
b
y
t
he
f
o
l
low
i
ng
:
D
Ne
w
=
D
Ne
w
D
Ne
w
D
Ol
d
D
Ol
d
(2
)
2.5.
Stop
p
in
g cr
i
t
eri
on
The
st
o
p
p
i
ng
c
riteri
on
i
s
t
h
e
term
ina
t
i
ng
c
o
n
d
i
t
i
on
t
ha
t
h
a
lt
s
the
a
l
gor
it
hm
.
It
o
c
c
u
rs
w
he
n
o
n
e
or
mo
re
p
re
sc
ri
b
e
d
c
o
ndi
tio
ns a
r
e
me
t
.
Th
e
mo
st
co
m
mo
nl
y
use
d
s
to
p
p
i
n
g
cr
i
te
r
i
a a
r
e
the fo
l
l
owi
n
g:
a.
G
e
ne
rati
o
n
N
u
m
be
r
—
A
thr
e
shol
d
val
u
e
i
s
s
e
t
.
T
h
e
al
g
o
ri
thm
s
t
o
ps
t
he
itera
ti
o
n
a
ft
e
r
car
rying
o
u
t
a
ce
rtai
n num
ber
of iter
a
t
i
o
n
s.
b.
Bes
t
F
i
t
ne
ss
T
hr
esh
o
l
d
—
Th
is
s
t
ops
t
h
e
ite
rat
i
o
n
w
he
n
the
m
a
x
i
mu
m
val
u
e
of
o
bjec
tiv
e
f
u
nct
i
o
n
(P
PV
_
B
e
s
t
)
is less tha
n
the set value
(
P
P
V
_S
pe
c
i
fi
e
d
).
c.
P
opu
la
ti
o
n
C
o
nver
g
e
n
ce
—
Th
is
s
t
o
ps
t
he
i
t
e
rat
i
on
w
h
e
n
t
he
d
iff
er
en
ce
b
e
t
w
e
e
n
t
h
e
m
axim
um
a
nd
m
i
nim
u
m
va
lu
es of all i
n
d
i
v
i
dua
l
s
(
D
Ne
w
)
in
the
pop
ula
t
i
o
n
is less
t
h
a
n
t
he
pr
e
scribe
d t
o
le
ranc
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Cri
t
i
c
a
l
eva
lu
at
ion
o
f
so
ft
c
o
mp
ut
ing
met
hod
s fo
r m
a
xi
mum p
o
w
e
r
poi
nt
t
r
a
c
k
i
ng
…
(No
r
azlan
Ha
shim)
55
1
d.
F
itne
ss
C
o
nver
g
e
n
ce
—
T
h
i
s st
ops the itera
ti
on
w
h
e
n
t
he d
i
ffe
re
nc
e be
tw
e
e
n t
h
e
m
a
x
i
m
u
m and minim
u
m
val
u
es
o
f ob
jec
t
i
v
e
func
t
i
o
n
(P
PV
)
for
all i
n
d
i
vi
dua
ls (
D
New
)
i
s
l
e
ss tha
n
t
he
p
resc
ribed t
o
l
e
ra
nce
.
I
n
t
hi
s
s
t
u
dy,
t
he
f
i
t
n
ess
c
o
n
v
e
rge
n
c
e
,
t
h
a
t
i
s
,
t
he
P
V
p
o
w
e
r
(
P
PV
)
,
is
c
h
o
s
e
n
a
s
t
h
e
s
t
o
p
p
i
n
g
c
r
i
t
e
r
i
o
n
bec
a
u
s
e
i
t
g
i
v
es
b
et
ter
r
e
sul
t
s
tha
n
t
he
o
t
h
ers.
T
his
te
ll
s
the
a
lgor
it
hm
t
o
s
t
op
se
arc
h
ing
for
the
op
ti
m
u
m
sol
u
tion
(
P
PV
_B
est
) w
h
en the
fi
t
ness of
a
l
l
ind
i
v
i
dua
l
s
ar
e
q
u
i
te cl
o
se t
o o
n
e an
o
t
her,
t
ha
t i
s
,
w
ith
i
n
t
he
r
an
ge o
f
1 W. Sm
a
ller
t
o
ler
a
nce
s
re
s
ult in
g
rea
t
e
r
sim
ul
a
tio
n
acc
urac
y b
u
t
,
i
n
g
e
n
er
al,
l
o
w
e
r c
onve
rge
n
ce
spee
d.
3.
SELECT
E
D
SC ALGORITHM
S
Ea
ch
s
e
l
e
c
t
e
d
S
C
alg
o
ri
thm
has
i
t
s
ow
n
r
e
pro
duc
t
i
o
n
o
pe
r
a
tor
pa
r
a
m
e
t
e
r
:
c
r
o
s
s
o
v
e
r
c
o
n
s
t
a
n
t
(
C
R
)
and
muta
tio
n
r
a
te
(
F
)
f
or
G
A
and
D
E
,
sea
r
ch
s
te
p
(
o
r
β
)
f
o
r
C
S
a
n
d
E
P
,
a
n
d
a
c
c
e
l
e
r
a
t
i
o
n
c
o
n
s
t
a
n
t
s
(
C
1
a
nd
C
2
)
for
P
S
O.
T
he
m
a
i
n
co
ns
eque
nce
o
f
t
he
o
pe
rat
o
r
i
s
t
h
e
s
te
p
siz
e;
i
f
t
h
e
st
e
p
s
i
z
e
is
l
arg
e
,
th
e
sea
r
c
h
i
s
rapi
d,
b
ut
t
he
t
a
r
gete
d
gl
o
b
al
p
eak
m
ay
b
e
m
i
sse
d.
O
n
the
o
t
he
r
h
an
d
,
i
f
t
h
e
st
ep
s
i
z
e
i
s
t
o
o
s
ma
ll
,
th
e
se
arc
h
w
o
u
l
d
be
v
er
y
lo
n
g
;
m
o
s
t
p
r
o
b
a
b
l
y,
t
h
e
i
rradia
n
c
e
h
as
c
ha
nge
d
t
o
a
ne
w
val
u
e
be
for
e
t
he
g
l
o
bal
p
e
a
k
i
s
succe
ssfu
lly
t
ra
cked.
In
p
r
a
c
t
ice,
t
rial-and-err
or
t
uning
deter
m
i
nes
the
pa
r
a
m
e
ters’
valu
es
t
ha
t
yie
l
d
t
h
e
be
st
op
tim
ize
d
r
esu
l
t
s
(
P
PV
_
B
e
s
t
)
.
T
he
o
p
t
i
m
iza
t
i
o
n
is
p
e
rform
ed
b
e
f
ore
t
h
e
e
x
ec
uti
o
n
of
t
he
a
l
g
o
r
i
t
h
m
,
a
n
d
t
h
e
s
e
val
u
es
a
r
e
f
ixe
d
t
hro
u
g
h
o
u
t
t
he
r
u
n
.
H
o
w
e
ve
r,
c
hoosi
n
g
the
ri
g
h
t
pa
ram
e
te
r
i
s
o
fte
n
tim
e-c
onsum
i
n
g
;
t
h
e
norm
a
l
pr
oce
d
ure
is
t
o
se
t
t
h
e
p
a
ram
e
t
e
r
va
lue
a
nd
the
n
o
b
s
e
r
ve
t
h
e
r
esul
t
s
.
F
u
r
t
h
e
rm
ore,
b
e
cause
r
a
n
d
o
m
f
u
n
c
t
i
o
n
s
e
x
i
s
t
i
n
t
h
e
r
e
p
r
o
d
u
c
t
i
o
n
f
o
r
m
u
l
a
,
t
h
e
s
e
a
r
c
h
r
e
s
u
l
t
of
e
a
c
h
met
hod
v
a
r
i
e
s
at
e
ach
i
t
e
ra
tion
.
To
addre
s
s
th
is,
t
h
e
simu
la
t
i
o
n
w
as
r
un
w
i
t
h
100
tria
ls,
and
th
e
r
esu
l
ts
a
re
a
vera
ged.
T
he
b
es
t
val
u
es
o
f
t
h
e
repr
od
uct
i
on
p
a
ram
e
ter
s
f
or
each
a
l
gor
ithm
ar
e
tabu
la
ted
i
n
T
ab
le
s
1-
5.
F
or
c
onsis
t
e
nc
y,
e
ac
h
S
C
a
lg
ori
t
hm
is
i
mp
lem
e
nte
d
b
ased
o
n the
p
r
op
ose
d
be
n
c
h
ma
rk m
etho
d
o
l
o
g
y
as
d
i
s
c
u
ss
e
d
in t
h
e
prev
i
ous sec
t
i
o
n
.
3.1.
Gen
e
t
i
c alg
o
r
i
th
m (
G
A
)
G
A
i
s
an
o
p
t
i
m
iza
t
i
o
n
a
l
gor
i
t
hm
i
n
s
p
i
r
e
d
by
na
tur
a
l
ge
n
e
t
i
c
e
v
o
l
u
ti
on
a
nd
se
lec
t
i
o
n.
T
o
pro
d
u
ce
a
new
o
f
fspri
n
g,
G
A
use
s
t
w
o
m
ain
ge
ne
tic
o
pe
rat
o
rs,
na
m
e
ly,
cr
os
s
o
v
e
r
a
n
d
m
u
ta
ti
on.
T
he
r
e
p
r
o
du
c
t
i
o
n
opera
to
r
of
t
he G
A
algori
t
hm
u
se
d in
t
h
i
s pa
per
can
b
e
d
e
scribe
d
as follows
[
22]-[24]:
a.
S
e
le
ct
t
w
o
c
a
n
d
i
date
s
from
the
pa
ren
t
p
op
u
l
at
ion
(
P
ar
ent
1
a
nd
P
a
r
en
t
2
)
a
t
r
a
ndom;
t
h
e
y
m
u
s
t
b
e
mutua
l
ly d
i
ffe
r
e
nt
f
rom
e
ach
o
the
r
.
b.
A
p
p
l
y
a
s
i
n
g
l
e
-
po
in
t
cross
o
v
e
r
and
m
u
ta
tio
n
o
p
e
r
at
or
t
o
yie
l
d
a
n
offspr
ing
pop
ula
t
io
n
ac
cord
in
g
t
o
t
he
f
o
ll
o
w
i
ng:
Of
fs
p
r
i
n
g
1
=α
∙P
a
r
ent
1
+
1-α
∙P
a
r
ent
2
Of
fs
p
r
i
n
g
2
=
1-α
∙P
ar
e
n
t
1
+α
∙P
a
r
ent
2
Of
fs
p
r
i
n
g
3-
5
=±
β+
P
a
ren
t
3-
5
(
3
)
wher
e
i
s
the
c
r
ossove
r
ra
t
e
a
nd
i
s
t
h
e
m
u
ta
t
i
on
r
a
te.
The
va
lues
o
f
th
e
G
A
r
epr
o
duc
tio
n
par
a
m
e
ters
u
sed
in t
h
i
s
stud
y
are
tabu
la
te
d
i
n
T
ab
le
1
.
Ta
ble
1.
G
A
para
me
t
e
rs
Pa
r
a
m
e
t
e
rs
V
a
l
ue
s
P
opula
t
i
o
n
s
i
ze
,
N
P
5
C
r
ossove
r
ra
t
e
,
[
±
0
.8
]
M
u
t
a
ti
o
n
r
a
te
,
[
±
0.
05]
M
a
x
i
m
u
m
ge
ne
r
a
t
i
o
n
s
,
G
m
a
x
2
5
3.2.
Particle
s
war
m
o
p
t
i
m
i
z
ati
o
n
(
P
S
O
)
P
S
O
a
t
te
mp
ts
t
o
m
i
m
i
c
t
h
e
so
cial
b
eha
v
ior
o
f
f
l
o
ck
i
n
g
bi
r
d
s
whe
n
se
arc
h
ing
for
f
o
od
.
In
P
S
O
,
ea
ch
in
div
i
dua
l
of
t
he
p
o
t
en
t
i
a
l
s
o
l
u
t
i
on,
c
a
lle
d
a
par
tic
l
e
,
flie
s
a
r
ou
nd
in
a
m
u
l
tid
im
ens
i
o
n
a
l
s
ea
rch
spac
e,
l
o
o
k
i
ng
f
o
r
t
h
e
op
ti
ma
l
so
l
u
t
i
on
b
as
e
d
o
n
it
s
o
w
n
an
d
it
s
n
e
i
ghb
ors’
e
x
pe
rie
n
ce
s.
T
he
r
epro
duc
ti
o
n
oper
a
tor
o
f
t
he
P
S
O
a
l
gor
ithm
used
i
n
th
i
s
p
a
p
er
c
a
n
be
descr
i
be
d a
s
f
ol
l
o
w
s
[
2
5]-
[
2
9
]:
a.
D
e
term
ine
t
h
e
pa
rtic
l
e
’s be
s
t
kn
ow
n p
o
s
iti
o
n
,
P
best
, a
nd the
popu
la
ti
on’s b
e
st
k
now
n pos
i
t
i
o
n,
G
bes
t
.
b.
Ca
l
c
u
l
a
t
e
the
p
a
re
nt ve
l
oc
i
t
y t
o
yie
l
d
a
n of
fs
pri
n
g
p
o
p
u
l
a
tio
n
acc
ord
i
ng
t
o
the
f
o
llow
i
n
g
:
Vel
i+1
=K∙
Vel
i
+C
1
∙ra
n
d
P
be
st
i
-Pa
r
e
n
t
i
+C
2
∙r
a
n
d
G
be
sti
-Pa
r
ent
i
O
ffspr
ing
i+
1
=P
ar
ent
i
+Ve
l
i+
1
(4
)
w
h
e
r
e
K
i
s
t
h
e
i
n
e
r
t
i
a
w
e
i
g
h
t
a
n
d
C
1
a
nd
C
2
i
s
t
h
e
acc
e
l
er
a
tio
n
c
ons
t
a
nt
.
The
P
S
O
p
a
ra
me
t
e
rs
u
sed
in
t
his
stud
y
are
tabu
l
a
ted
i
n
Tab
le
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
54
8 –
56
1
55
2
Tabl
e 2
.
P
SO
p
ara
m
e
t
ers
P
a
ra
m
e
te
rs
Va
lu
e
s
Popula
tion
Siz
e
,
NP
5
Ac
ce
l
e
r
a
tion
C
ons
ta
nts,
C
1
=C
2
1
.
5
I
n
e
r
t
i
a
we
i
ght,
W
0.
5
Ma
xi
m
u
m
G
e
n
e
r
a
tions,
G
ma
x
2
5
3.3.
D
i
f
fer
e
n
t
ia
l
ev
olu
t
ion
(D
E)
D
E
i
s
a
simp
le
e
v
o
lu
t
i
o
n
a
r
y
al
g
o
ri
thm
u
s
i
n
g
s
i
m
ilar
ope
rat
o
r-
l
i
ke
G
A
s
s
uch
a
s
c
r
o
ss
o
v
e
r
a
n
d
m
u
t
a
t
i
o
n
.
T
h
e
m
a
i
n
d
i
f
f
e
r
e
n
c
e
i
s
t
h
a
t
G
A
r
e
l
i
e
s
p
r
i
m
a
r
i
l
y
o
n
c
r
oss
over,
w
hile
D
E
relies
o
n
m
uta
t
io
n
opera
tio
n.
D
E
cre
a
tes
an
o
f
f
s
p
ri
ng
b
y
c
omb
i
n
i
ng
t
h
e
pare
nt
i
nd
i
vi
d
u
al
a
nd
s
e
v
er
al
o
th
er
i
n
d
iv
id
ua
ls
o
f
t
h
e
sam
e
p
o
p
u
la
t
i
o
n.
I
n
t
h
is
p
a
p
er
,
the
“
D
E/ra
nd-
t
o
-
b
e
s
t
/
1/
b
i
n” sc
h
e
m
e
h
a
s
b
een
sel
ect
ed
b
ec
au
se
o
f
it
s
go
od
perform
ance
f
or
t
he
c
a
s
e
un
der
st
udy.
D
E’s
reprod
uc
ti
on
o
p
e
r
at
o
r
c
a
n
be
d
escr
i
b
e
d
a
s
foll
ow
s
10],
[30],
[31]
:
a.
S
e
le
ct th
e
p
o
pula
tio
n’s be
s
t
k
now
n in
d
i
v
i
du
al,
G
best
.
b.
S
e
le
ct
t
w
o
c
a
n
d
i
date
s
from
the
pa
ren
t
p
op
u
l
at
ion
(
P
ar
ent
1
a
nd
P
a
r
en
t
2
)
a
t
r
a
ndom;
t
h
e
y
m
u
s
t
b
e
mutua
l
ly d
i
ffe
r
e
nt
f
rom
e
ach
o
the
r
.
c.
A
p
p
l
y
m
u
ta
ti
o
n
a
n
d
c
ross
ov
er
opera
to
r
s
t
o
pr
od
uce
t
h
e
tr
i
a
l
i
n
d
iv
id
ua
l
and
offs
prin
g
a
c
c
o
r
d
i
n
g
t
o
t
h
e
f
o
ll
o
w
i
ng:
Tr
i
a
l
i
=P
ar
ent
i
+
F·
G
be
s
t
‐Pa
r
e
n
t
i
+
F·
Pa
r
e
n
t
1
‐P
ar
ent
2
Offspring
i
=
Tr
i
a
l
i
,
if rand
<
CR
Pa
ren
t
i
,
otherwise
(5
)
w
h
er
e
F
is
t
he
m
utat
ion
ra
t
e
a
nd
CR
i
s
t
he
m
uta
t
io
n
rate.
T
h
e
D
E
para
me
te
rs
u
se
d
i
n
t
his
stu
dy
a
r
e
ta
bu
late
d
in Ta
b
le
3.
Table
3. D
E
par
a
m
e
ters
P
a
ra
m
e
te
rs
Va
lue
s
Popula
tion
Si
ze
,
N
P
5
C
r
ossove
r
Ra
t
e
,
C
R
0
.
9
Muta
tion Ra
te, F
0
.7
Ma
xim
u
m
G
e
n
e
r
a
tions,
G
m
a
x
25
3.4.
C
u
c
k
oo s
e
arch
(C
S
)
CS
i
s
in
sp
ire
d
by
t
h
e
o
b
l
i
ga
te
b
roo
d
p
ara
s
i
t
i
s
m
of
s
om
e
spe
c
ie
s
o
f
a
b
i
rd
f
am
ily
c
a
lle
d
cuc
k
o
o
i
n
com
b
i
n
a
t
i
o
n
w
i
t
h
t
he
L
é
v
y
fl
i
ght
b
eha
v
i
o
r
o
f
s
om
e
b
i
rds
a
nd
fru
i
t
flie
s
.
The
c
o
nce
p
t
o
f
C
S
is
s
im
ilar
to
P
S
O
(usi
ng
par
tic
l
e
s),
but
t
he
s
te
p
sizes
i
n
CS
a
re
c
hara
cteriz
ed
b
y
t
h
e
rand
om
w
a
l
k
ba
se
d
o
n
L
év
y
f
l
i
g
ht.
Ma
them
at
ica
l
l
y
,
Lé
vy
fl
i
g
h
t
h
a
s
m
ovem
e
n
t
l
en
gt
hs
c
h
o
se
n
from
a
proba
bi
l
ity
d
is
tri
but
i
on
w
i
th
a
pow
er
-law
tai
l
,
~
1
3
,
w
h
e
r
e
x
is
t
he
s
te
p
le
ngt
h
a
nd
i
s
th
e
var
i
a
n
ce.
T
he
r
eproduc
ti
on
oper
a
tor
o
f
the
CS
a
lgori
t
h
m
can
b
e
d
e
scribe
d
as
f
o
llow
s
[
12],
[32]-
[
3
4
]
:
a.
S
e
le
ct th
e
p
o
pula
tio
n’s be
s
t
k
now
n in
d
i
v
i
du
al,
G
best
.
b.
A
p
p
l
y
a
Lév
y
fl
i
g
h
t
s
oper
a
tor to y
ie
ld
a
n
of
fs
pri
ng p
o
p
u
l
a
tio
n
a
c
c
o
r
di
ng
to
t
h
e
fol
l
o
wing
:
i
=
β·
α·r
a
n
dn/abs
r
a
ndn
1
1.5
·(P
a
r
e
nt
i
‐G
be
s
t
)
O
ffspr
ing
i
=P
ar
ent
i
+
i
·
i
0,1
(6
)
wher
e
is the
Lév
y
coef
f
icie
nt a
nd
is t
h
e
sc
al
in
g
fa
c
t
or. The C
S
p
a
r
am
eter
s use
d
in t
h
is st
u
dy a
r
e ta
b
u
la
te
d
in Ta
b
le
4.
Ta
b
l
e
4.
CS
param
e
te
rs
P
a
ra
m
e
te
rs
Valu
es
P
opula
t
i
on
Siz
e
,
NP
5
L
e
v
y
c
o
e
f
f
i
ci
en
t
,
0.
7
S
c
a
ling
fac
t
or
,
0.
0
1
Ma
xi
m
u
m
Ge
n
e
r
a
t
i
ons,
G
m
a
x
25
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Cri
t
i
c
a
l
eva
lu
at
ion
o
f
so
ft
c
o
mp
ut
ing
met
hod
s fo
r m
a
xi
mum p
o
w
e
r
poi
nt
t
r
a
c
k
i
ng
…
(No
r
azlan
Ha
shim)
55
3
3.5.
Evo
lu
tio
n
ary p
r
ogr
am
min
g
(
EP)
EP
i
s
a
sea
r
ch
a
l
g
ori
t
h
m
d
e
s
igne
d
to
s
i
m
ulate
d
e
vo
l
u
tio
n
tha
t
i
t
e
rat
i
ve
l
y
g
e
n
era
t
e
s
i
ncre
as
i
ngl
y
appr
opr
i
a
t
e
s
ol
ut
i
ons.
It
w
as
f
irst
p
rop
o
se
d
a
s
a
n
al
ter
n
a
t
i
v
e
a
p
p
r
o
a
c
h
t
o
cl
assi
c
art
i
fi
c
i
al
i
nt
el
li
g
e
n
c
e
(AI)
in
com
p
u
t
e
r
s.
E
P
has
the
a
dva
n
t
a
g
e
of
u
s
i
n
g
a
m
ut
a
t
i
on-
on
l
y
r
epr
o
d
uc
t
i
on
o
p
er
at
or
a
nd
c
a
n
e
a
s
i
l
y
be
d
es
ig
ne
d
for
a
d
a
p
t
i
ng
th
e
par
a
m
e
ter
s
o
f
the
m
u
tat
i
on
ope
ra
tor
d
u
rin
g
t
he
r
epr
o
d
u
c
tio
n
proc
ess.
I
n
t
h
is
p
a
p
er,
classica
l
E
P
,
w
h
i
c
h
u
s
e
s
a
G
a
u
s
s
i
a
n
d
i
s
t
r
i
b
u
t
i
o
n
f
u
n
c
t
i
o
n
f
o
r
u
p
d
a
t
i
n
g
t
h
e
of
fspr
i
ng,
h
as
b
e
e
n
s
e
le
ct
ed
b
ec
aus
e
o
f
i
t
s
ea
se
o
f
use
a
n
d
pro
v
i
d
es
c
o
m
pa
rati
vel
y
g
o
o
d
resu
lt
s.
T
he
r
eprod
uc
tio
n
oper
a
tor
of
t
he
E
P
a
l
gor
ithm
ca
n
be
descr
i
be
d a
s
f
o
l
l
o
w
s
[
3
5
-3
9]:
A
p
p
l
y
muta
t
i
o
n oper
a
tor to y
i
e
ld
a
n o
ffspri
n
g po
p
u
la
t
i
o
n
a
cc
ord
in
g t
o
the
f
ol
low
i
ng
:
i
=β
∙
(
P
PV
i
/P
PV
ma
x
)
O
ffspr
ing
i
=P
a
r
e
n
t
i
+
i
∙
i
0,1
(
7
)
wher
e
is the
scal
in
g fac
t
or.
A
ll EP
p
a
r
am
e
t
er
s
used i
n
thi
s
stu
dy a
r
e
t
a
b
u
l
a
te
d in Ta
b
le
5.
Tab
l
e 5.
EP
pa
ram
e
ter
s
P
a
ra
m
e
te
rs
Valu
es
P
opula
t
i
on S
i
z
e
,
NP
5
S
c
a
ling
fac
t
or
,
β
0
.
0
1
M
u
ta
t
i
on
Te
c
hnique
G
a
ussia
n
[±
]
M
a
x
i
m
u
m
G
e
ne
r
a
ti
o
n
s
,
G
m
a
x
25
4.
BENCHMARKING M
E
THODOLOGY FOR
S
C-BAS
E
D
MPPT
To
e
va
l
u
ate
t
h
e
per
f
orm
a
nce
s
o
f
differ
en
t
S
C
M
P
P
T
alg
o
ri
thms
f
a
irl
y
,
a
stan
dar
d
i
z
e
d
e
va
lua
t
i
on
proce
s
s
is
r
eq
u
i
re
d.
U
nfor
t
u
n
a
t
e
ly,
this
p
roc
e
s
s
is
a
bsen
t
in
p
re
v
i
ou
s
lit
e
r
at
u
r
e;
t
h
u
s,
t
h
e
p
erf
o
rman
c
e
s
o
f
t
h
e
MP
P
T
a
lgori
t
h
ms
a
re
not
v
e
r
ifie
d
in
de
pe
nde
n
t
l
y
.
M
o
r
e
over
,
t
he
m
od
ul
e
tec
h
n
o
l
o
gy
,
pow
er
r
a
ting
s
,
an
d
env
i
ro
nm
en
t
c
o
n
d
it
i
o
n
s
in
w
h
ic
h t
h
e
e
x
peri
m
e
nts
w
e
re set
up ar
e
a
ll
d
iffe
rent. In add
iti
on,
t
he part
i
al sha
din
g
expe
r
i
me
n
t
s
c
a
r
r
i
e
d
o
ut
a
r
e
n
e
v
er
u
ni
q
u
e.
T
hi
s
ra
i
s
e
s
q
u
e
s
tio
ns
on
t
h
e
le
gi
tim
acy
o
f
th
e
cla
i
m
s
a
s
d
i
ffe
r
en
t
sha
d
i
n
g
pa
t
t
e
r
ns
r
esul
t
i
n
d
iffe
rent
M
P
P
T
e
f
f
i
c
i
e
n
c
i
es.
With
t
h
ese
c
oncer
ns,
t
h
is
p
a
p
e
r
a
ttem
p
t
s
t
o
pr
o
pose
a
me
tho
dol
o
gy
to
b
e
n
c
h
m
a
r
k
t
he
S
C
M
P
P
T
a
lg
ori
t
h
ms
b
as
ed
o
n
a
s
i
mp
l
e
f
l
o
w
d
i
agra
m
show
n
in
F
i
gure
2
.
Be
ca
use
of
t
he
ir
r
e
cent
p
o
p
u
l
arit
y,
f
i
v
e
d
i
ffe
re
nt
a
lgor
it
hm
s
a
re
c
ho
sen,
n
a
m
e
l
y,
d
iffe
ren
t
ial
ev
o
l
u
tio
n
(
D
E)
,
evo
l
ut
iona
r
y
p
rogra
m
m
i
ng
(
EP
),
c
uc
k
oo
s
ear
ch
(
CS
),
p
artic
le
s
w
a
rm
o
pt
imiz
a
t
i
o
n
(P
S
O
),
a
nd
gene
t
i
c
a
l
go
rith
m (
G
A
)
.
St
a
r
t
In
i
t
i
a
l
i
z
a
t
i
o
n
(
C
o
n
t
ro
l
l
e
d
/
F
i
x
)
R
e
pr
oduct
i
on
(
M
u
t
a
t
i
on
, C
r
o
s
s
o
v
e
r
,
L
e
vy
F
l
i
g
ht,
P
ar
t
i
cl
e
V
e
l
o
ci
t
y
)
Se
l
e
c
t
i
o
n
(
R
a
nki
n
g
)
S
t
op
pi
n
g
C
r
i
t
e
r
i
on
(I
f
P
PV
m
a
x
-P
PV
mi
n
<
1
W
)
St
o
p
Ye
s
No
F
i
gure
2.
T
he be
n
c
h
m
a
rk
m
etho
do
l
o
g
y
f
or po
p
u
la
t
i
o
n
-
b
as
ed
S
C a
l
g
orit
h
m
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
54
8 –
56
1
55
4
4.1.
Prob
le
m for
m
u
l
ati
o
n
F
o
r
consi
s
te
nc
y,
t
h
e
i
n
i
ti
a
liz
a
tio
n,
s
e
l
e
c
t
i
on,
a
nd
s
t
op
p
i
n
g
c
r
iter
i
a
a
r
e
fixe
d
at t
he
s
a
m
e
c
ond
it
i
ons
a
s
di
sc
usse
d
i
n
t
h
e
p
revi
ou
s
se
ct
io
n.
T
hu
s,
t
he
p
erforma
n
ce
o
f
e
a
c
h
a
l
gor
it
h
m
i
s
t
e
st
e
d
b
a
s
ed
o
n
i
t
s
ow
n
un
i
q
u
e
me
taph
or
i
n
th
e
reprodu
c
t
i
o
n
st
a
g
e.
F
urther
more
,
benc
hma
r
ki
ng
t
he
p
e
rfor
m
a
n
ce
of
M
P
P
T
usi
ng
t
h
e
norm
a
l
i
rrad
i
a
n
c
e
(u
nif
o
rm)
co
n
d
i
t
i
on
i
s
not
a
d
e
quat
e
a
s
t
h
e
re
su
lt
i
n
g
P
-
V
c
u
r
v
e
i
s
s
i
n
g
l
e
m
o
d
a
l
(
i
.
e
.
,
w
i
t
h
o
n
l
y
o
n
e
un
ique
p
e
a
k),
a
n
d
w
ith
s
uc
h
a
sim
p
l
e
c
o
n
d
iti
o
n
,
al
l
MP
P
T
s
are
a
b
l
e
to
c
o
nve
r
g
e
to
t
he
p
ea
k
ve
ry
q
uic
k
ly.
A
s
a
result,
c
lear
l
y
d
iffer
e
n
tia
t
i
n
g
t
h
e
pe
rform
a
n
c
es of the
al
g
o
r
ithm
is di
f
f
i
c
u
lt.
A
m
o
re
c
ha
ll
eng
i
ng
s
it
ua
tion
is
t
o
s
u
b
j
ect
t
he
P
V
sys
t
em
t
o
p
a
r
t
i
a
l
s
h
a
d
i
ng
c
on
di
t
i
on
.
Th
e
phe
n
o
m
e
na
a
re
d
ue
t
o
the
s
h
a
dow
s
from
c
l
o
u
d
s,
n
e
i
gh
b
o
rin
g
b
u
i
l
d
ings,
trees,
c
himneys,
t
o
w
ers,
e
tc.
,
w
here
ce
rtai
n
part
s
o
f
t
he
P
V
arr
a
y
ar
e
shade
d
w
h
ile
o
t
h
er
s
rec
e
i
v
e
u
n
i
form
i
rradia
nce.
D
uri
n
g
par
tia
l
s
h
ad
i
ng,
t
he
sha
d
ed
m
o
d
u
le
s
e
x
perien
c
e
a
l
arge
a
m
o
un
t
of
r
u
s
h
c
u
rr
ent
s
,
re
su
l
t
i
ng
i
n
e
xc
ess
i
ve
h
ea
t
(ho
t
s
p
o
t
)
t
h
a
t
m
ay
ca
use
perm
ane
n
t
dam
a
ge.
T
o
r
e
l
ie
ve
t
h
e
s
tress
o
n
t
he
s
ha
de
d
mod
u
l
es,
by
pass
d
iode
s
are
fi
tt
e
d
acr
oss
t
h
em
[1
5].
H
o
w
e
ve
r,
m
ulti
ple
pea
k
s
in
t
he
P
-V
c
urve
a
re
t
he
n
c
r
e
a
ted
.
Conse
q
ue
n
tly,
the
pr
o
b
lem
is
t
ra
ns
fo
rm
ed
from
s
in
g
l
e
moda
l
to
m
u
ltim
oda
l.
T
h
i
s
co
n
d
i
t
i
o
n
pose
s
a
s
erio
us
c
ha
l
l
en
ge
t
o
a
n
y
M
P
PT
t
e
c
h
n
i
q
u
e
be
c
a
use
of
t
he
d
iffic
u
lt
y to d
is
t
i
n
g
u
is
h the
g
l
oba
l
fro
m
the
l
oca
l
p
e
a
k
s.
5.
PV S
YS
T
E
M M
O
D
E
L
I
NG
The
t
w
o-
di
ode
PV
c
el
l
m
odel
[
4
0
]-[42],
depict
e
d
i
n
F
i
gure
3
,
is
u
t
i
l
i
z
e
d
f
or
s
im
u
l
a
t
i
on.
I
t
is
c
hose
n
bec
a
u
s
e
of
i
t
s
s
up
erior
a
ccur
a
cy,
pa
rtic
u
l
arl
y
a
t
a
low
irr
a
dia
nce
l
e
ve
l.
T
he
o
ut
p
u
t
c
u
rrent
o
f
t
h
e
ce
ll
is
g
i
v
en
by t
h
e
fol
l
ow
i
n
g:
I
=
I
PV
-I
o1
ex
p
V+
I
R
s
a
1
V
T1
-1
-I
o2
exp
V+
IR
s
a
2
V
T2
-1
-
V+
I
R
s
IR
p
(8
)
Whe
r
e
I
o1
a
nd
I
o2
a
r
e
t
he
r
ev
e
r
se
s
a
t
u
r
at
i
on
curr
ents
o
f
d
i
ode
s
1
(D
1
)
and
2
(D
2
),
r
e
s
p
e
ct
iv
el
y
,
V
T1
and
V
T2
a
re
t
he
t
herm
al vol
tag
e
s
of t
he
r
espe
c
t
i
v
e
d
i
o
d
es,
and
a
1
a
n
d
a
2
r
e
p
r
e
s
e
n
t
t
h
e
d
i
o
d
e
i
d
e
a
l
i
t
y c
o
n
s
t
a
n
t
s
.
The
I
o2
t
e
r
m
in (
9) c
ompe
nsa
t
es the
r
ec
ombi
nat
i
on l
o
ss i
n
t
he
d
ep
le
t
i
o
n
regi
o
n
,
as
d
escribe
d
i
n [41].
F
i
gure
3.
A
Tw
o
-
d
io
de
m
od
el of
P
V
c
e
l
l
F
o
r a string with
N
n
u
m
b
er
o
f
modu
les
in
s
e
r
i
e
s (
N
ce
ll
)
, (
9)
can be ext
e
nded
to the
fo
ll
ow
in
g:
I
I
I
e
x
p
1
I
exp
1
(9
)
The
simu
la
t
i
o
n
s
m
ode
l
of
t
he
P
V
syst
e
m
w
as
b
ase
d
o
n
a
MA
TLA
B
/
S
i
m
u
li
nk
s
i
mu
la
to
r
devel
o
pe
d
in
[
4
3
].
T
he
a
rra
y is
s
imu
l
a
t
e
d
us
i
n
g
the
BP
MS
X
-
60
m
o
du
l
e
. Its
spec
i
f
i
c
a
t
i
ons a
t
t
h
e
sta
ndar
d
tes
t
c
o
n
d
i
t
i
o
n
s
(S
TC)
a
r
e show
n
i
n
T
ab
le
6
.
Ta
b
l
e 6.
Elec
t
rical pa
r
am
ete
r
s
of
M
SX-60
mod
u
l
e
at S
TC
Par
a
met
e
r
s
Va
lue
s
Pa
r
a
met
e
rs
Value
s
Ma
xim
u
m
Powe
r
(P
ma
x
)
6
0
W
T
e
m
p
e
r
at
u
r
e
c
o
ef
f
i
ci
e
n
t
o
f
V
oc
-(80±
10)
m
V
/
0
C
Volta
g
e
at
Pmax (V
mpp
)
17.
1
V
Tem
p
e
r
a
t
ure
c
o
e
f
f
i
c
i
e
n
t
of I
sc
-(0.
065±0.
0
1
5
)
%
/
0
C
Cu
r
r
e
n
t
at P
max
(
I
mp
p
)
3.
5
A
Tem
p
e
r
a
t
ure
c
o
e
f
f
i
c
i
e
n
t
of powe
r
-
(
0
.
5
±0.
0
5
)
%
/
0
C
O
p
e
n
c
i
r
c
u
it
volt
a
ge
(
V
oc
)
21.
1
V
N
O
C
T
47±2
0
C
Short
c
i
r
c
uit c
u
rrent
(
I
sc
)
3.
8
A
O
p
e
r
a
t
i
ng
T
e
m
p
e
r
a
t
ur
e
25
0
C
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Cri
t
i
c
a
l
eva
lu
at
ion
o
f
so
ft
c
o
mp
ut
ing
met
hod
s fo
r m
a
xi
mum p
o
w
e
r
poi
nt
t
r
a
c
k
i
ng
…
(No
r
azlan
Ha
shim)
55
5
Fo
r
si
mp
li
ci
ty
,
o
n
ly
a
s
t
a
nd
-al
o
n
e
s
y
s
t
e
m
w
i
th
a
D
C
–
D
C
b
oo
st
c
o
nv
ert
e
r
l
o
ad
i
s
c
o
n
s
i
d
e
r
ed
.
Th
e
c
i
r
c
u
i
t
i
s
s
h
o
w
n
i
n
F
i
g
u
r
e
4
.
I
t
c
o
n
s
i
s
t
s
o
f
f
i
v
e
m
o
d
u
l
e
s
in
a
se
ri
es
,
c
o
nn
ec
t
e
d
t
o
t
h
e
c
onv
e
r
t
e
r
wi
th
t
h
e
M
P
P
T
con
t
ro
l
l
er.
The
syste
m
n
ee
d
not
b
e
e
x
t
e
n
d
e
d
t
o
a
g
rid-t
i
ed
one
be
ca
us
e
the
o
b
j
ec
ti
v
e
i
s
to
e
va
lua
t
e
the
perform
ance
o
f
the
MPPT
,
whic
h
i
s
o
n
the
D
C
s
ide.
T
he
o
p
t
imum
v
a
l
u
e
o
f
t
h
e
ci
rc
u
i
t
co
mp
on
en
ts
u
se
d
i
n
th
i
s
s
tu
d
y
a
re
d
isc
u
ss
e
d
i
n
d
e
ta
il
in
[
4
4
].
T
he
c
o
nve
r
t
er-
s
w
itc
hi
n
g
f
r
e
q
u
e
ncy
(
s)
i
s
20
k
H
z.
M
e
a
n
w
hi
l
e
,
th
e
in
duc
t
o
r
(
L
)
is
s
et
t
o
1
mH
,
t
h
e
f
i
l
t
er
c
a
p
ac
it
or
(
C
1
a
n
d
C
2
)
v
a
l
u
e
i
s
4
7
μF,
a
n
d
the
l
o
a
d
r
esis
tor
(
R
)
is
2
0
0
.
A
ll t
h
e MP
P
T
alg
ori
t
hm
s a
r
e
code
d
us
ing
th
e
M-file.
The
inp
u
t
v
aria
bl
e
s
a
r
e
G
a
nd
T.
F
i
gure
4. The
sim
u
l
a
t
i
on m
o
d
e
l of sta
n
d
-a
lo
ne
P
V system
The
g
o
a
l
o
f
the
op
t
i
m
i
za
ti
o
n
is
to
t
r
a
c
k
t
he
M
P
P
as
fas
t as
pos
sibl
e
and
wi
th
t
h
e
h
ighest
c
ons
i
stenc
y
.
In te
r
m
s
o
f
o
b
j
e
ctive
func
tio
n
form
ul
a
t
i
o
n,
that g
o
a
l
can
b
e
de
scribe
d
as
t
he
fo
l
low
i
ng
:
N
n
PVn
PVn
I
V
f
1
max
(
1
0
)
The
ob
jec
tive (
f
i
t
n
ess) func
t
i
on (
) i
s
t
he o
ut
pu
t p
o
w
e
r
of t
h
e
P
V
,
w
hile
N
i
s t
h
e nu
mb
er o
f
modu
l
e
s.
Var
i
ab
l
e
s
V
PV
a
n
d
I
PV
a
re
t
he
P
V
arr
a
y’s
ou
tp
u
t
v
o
lta
g
e
a
n
d
c
urre
nt
,
re
sp
e
c
ti
ve
l
y
.
D
ur
i
n
g
in
i
t
i
a
liz
a
tio
n,
f
i
v
e
di
ffe
re
nt
v
al
ue
s
of
d
uty
c
y
c
l
e
(
D
1
t
o
D
5
)
are
gener
a
te
d
w
i
th
a
c
c
orda
nce
t
o
(
2).
Ea
ch
o
f
the
s
e
d
u
t
y
c
yc
l
es
w
ill
be
s
e
n
t
to
t
he
P
WM
b
loc
k
t
o
ge
ner
a
te
a
P
W
M
s
w
i
tc
hi
n
g
w
a
vefor
m
t
o
t
h
e
MOSF
ET
at
a
s
a
m
pl
i
n
g
r
a
te
o
f
0.1
s
[4
4].
Then
t
h
e
M
P
P
T
block
w
ill
ca
lc
ula
t
e
the
PV
pow
er
b
a
s
e
d
o
n
the
s
e
ns
in
g
P
V
a
rray
v
o
lta
ge
(
V
PV
)
a
nd
curr
ent (
I
PV
).
The
sam
e
proce
s
s
w
i
l
l
b
e
r
e
pea
t
ed fo
r
each
iteration.
6.
RESULT
S
A
N
D
ANALY
S
IS
I
n
t
h
i
s
s
t
ud
y,
t
he
a
rra
y
in
F
ig
ure
5
is
p
artia
l
l
y
s
h
ade
d
w
it
h
f
i
v
e
di
ffe
r
en
t
v
a
l
u
es
o
f
i
r
ra
d
i
an
ce
pat
t
erns,
a
s
d
e
s
cribe
d
i
n
Ta
bl
e
7.
B
eca
use
o
f
t
h
e
o
pera
tio
n
of
t
h
e
b
ypa
ss
d
i
o
de,
t
h
e
s
t
e
p
w
ave
f
orm
I-V
c
urv
e
show
n
in
F
ig
u
r
e
6
is
c
r
e
a
t
ed.
F
i
gu
r
e
7
s
ho
w
s
t
he
r
es
ul
t
i
n
g
P
-V
cur
v
e.
B
es
i
d
e
s
t
he
g
loba
l
pea
k
(
MP
P
)
,
the
curve
e
x
h
i
b
i
ts
f
our
o
t
h
er
l
oca
l
p
ea
ks.
The
MP
P
volta
ge
a
nd
c
u
rr
e
n
t
ar
e
loc
a
t
e
d
a
t
5
1
.
4
7
9
V
a
nd
2.1
81
A
,
respe
c
t
i
ve
l
y
, w
hile
t
he m
axim
um
pow
er
(
i.e., the
f
i
n
a
l
fit
nes
s
va
lue
)
t
o
be a
chie
ve
d is 1
12.
27
8
W.
The
perfor
m
a
n
ce
of
eac
h
SC-base
d
M
P
P
T
a
l
g
o
ri
t
h
m
is
e
va
lua
t
e
d
b
a
se
d
o
n
s
e
v
era
l
c
ri
teria,
n
am
ely
,
spee
d,
a
cc
urac
y,
c
om
ple
x
it
y,
a
n
d
s
ucce
ss
ra
te
o
f
c
o
nver
g
e
n
ce.
T
he
overall
r
e
s
u
lt
s
of
eac
h
perform
ance
c
r
i
t
e
r
i
o
n
a
r
e
t
a
b
u
l
a
t
e
d
i
n
T
a
b
l
e
8
.
A
l
s
o
,
t
h
e
r
a
n
k
i
n
g
o
f
e
a
c
h
c
ri
ter
i
a
i
s
i
nd
i
c
a
t
ed
b
y
su
bsc
r
i
p
t
(
i
n
bra
c
k
et)
numbe
r i
n
T
ab
le 8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
54
8 –
56
1
55
6
F
i
gure
5.
F
ive
P
V
m
odul
e
s
co
nne
c
t
e
d
in
se
ri
es un
d
e
r
pa
r
ti
a
l
sha
de
d
co
n
d
i
t
i
o
n
g
i
ve
n i
n
Ta
b
le
7
Tab
l
e
7.
I
rr
adiance
for sha
d
i
n
g pa
t
e
r
n
M
o
dul
e
A
(G
A
)
B
(G
B
)
C
(G
C
)
D
(G
D
)
E
(G
E
)
Irra
dia
n
ce
(
G =
1.
0 =
1000
W/
m
2
)
0.
2
0.
4
0.
6
0.
8
1.
0
St
ar
t
I
n
it
ia
l
i
z
a
t
io
n
(
C
o
n
t
ro
l
l
ed
/
F
i
x
)
R
epr
oduc
t
i
on
(
M
u
t
a
t
i
o
n
,
C
r
o
s
s
ove
r
,
L
ev
y
Fl
i
ght
,
Pa
r
t
i
c
l
e
V
e
l
oci
t
y
)
Se
l
e
c
t
i
o
n
(
R
a
n
k
in
g
)
S
t
o
p
pi
n
g
C
r
i
t
e
r
i
on
(I
f
P
PV
m
a
x
-P
PV
m
i
n
<
1
W
)
St
o
p
Ye
s
No
0
20
40
60
80
100
0
20
40
60
80
100
120
[
P
=
6
4
.
20
2,
V
=
93.
074
]
[
P
=
1
04.
191,
V
=
7
2
.
46
5
]
[
P=
112.
278
,
V
=
51.
479
]
[
P=
9
0.
7
26,
V
=
3
1
.
38
5
]
[
P
=
4
3.
4
84,
V
=
12.
538
]
Vo
l
t
a
g
e
(
V
)
P
o
w
er
(W
)
P
V
C
u
r
v
e
(
P
a
r
t
ia
l
S
h
a
d
in
g
)
0
20
40
60
80
100
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
[
I
=
0
.
6
9
,
V
=
9
3.
07
4
]
[
I
=
1
.4
3
8
,V
=
7
2
.
4
6
5
]
[
I
=
2
.1
8
1
,
V
=
5
1
.4
7
9
]
[
I
=
2
.8
9
1
,V
=
3
1
.3
8
5
]
[
I
=
3
.
4
6
8
,
V
=
12.
53
8
]
Vo
l
t
a
g
e
(
V
)
Cur
r
e
n
t
(
A)
I
V
C
u
r
v
e
(
P
a
r
t
ia
l
S
h
a
d
in
g
)
F
i
gure
6.
P
-V & I-V
cha
rac
t
erist
i
c
s
u
nder
pa
r
t
ia
l
sha
d
e
d
c
o
n
d
i
t
i
o
n gi
ve
n
in
T
ab
le
7
6.1.
Sp
eed of con
v
erge
n
c
e
The
spe
e
d
o
f
con
v
er
ge
nce
i
s
t
he
numbe
r
o
f
i
tera
tio
ns
r
eq
uire
d
b
y
t
h
e
al
gor
ithm
to
r
ea
ch
t
he
f
in
al
fi
t
n
ess
va
l
u
e
.
Be
c
a
u
se o
f the
i
r
sto
c
ha
st
ic na
t
ure,
t
he
a
l
gori
t
h
m
s
pr
o
d
u
ce
di
ffe
r
e
nt r
es
u
l
ts
at eac
h
r
u
n.
T
h
i
s
c
a
n
be
obser
ve
d
by
t
he
v
a
r
iat
i
on
i
n
t
h
e
t
r
ajec
tor
i
e
s
p
r
o
duc
ed
b
y
ev
er
y
ru
n,
a
s
show
n
i
n
F
igu
r
es
7
–
11.
T
here
fore
,
tak
i
ng
a
c
o
n
c
l
us
io
n
from
a
s
in
g
l
e
ru
n
w
o
u
l
d
no
t
be
a
f
air
re
pre
se
nt
a
tio
n
of
t
he
a
l
gor
i
t
h
m
’s
p
er
form
ance
.
T
o
overc
ome
th
is
a
mbig
u
ity,
e
a
c
h
M
PP
T
m
e
th
od
is
e
xec
u
t
e
d
for
1
0
0
r
uns,
and
the
r
e
su
lts
a
re
a
vera
ged
as
i
n
F
i
g
u
r
e
1
2
.
T
h
e
i
t
e
r
a
t
i
o
n
l
i
m
i
t
a
t
e
a
c
h
r
u
n
i
s
s
e
t
a
t
1
5
s
i
n
c
e
m
ost
o
f
t
he
m
etho
ds
c
o
nve
rge
t
o
t
he
s
ol
u
tio
n
i
n
less t
h
an
t
h
i
s p
r
e
s
cribed
v
a
l
ue
.
As
can
b
e
see
n
,
EP
i
s
t
h
e
fastes
t
a
l
g
o
ri
th
m
to
r
e
ach
M
PP
(P
PV
m
a
x
)
conver
g
e
n
ce
.
I
n
a
ve
rage
,
it
requ
ire
s
6
iter
a
tio
ns.
Mor
e
o
v
er,
it
s
c
onve
r
g
enc
e
t
raje
c
t
ories
a
re
l
es
s
sc
attere
d
a
s
c
om
pare
d
to
o
ther
s;
G
A
requ
ire
s
8
,
w
h
ile
C
S
,
P
S
O
,
and
D
E
c
on
ve
rge
to
M
P
P
a
fte
r
10
iter
a
tio
ns.
The
rapi
d
c
o
n
v
e
rge
n
ce
o
f
E
P
is
d
ue
to
t
he
s
imple
G
a
ussia
n
d
i
s
trib
u
t
ed
r
a
n
d
o
m
num
bers
i
n
g
e
nera
tin
g
a
n
offs
pri
ng,
a
s
de
scribe
d
b
y
(
8).
The
rand
om
numbe
r
s
a
re
g
ener
ated
b
y
t
h
e
co
ntr
o
lle
d
sc
a
l
i
n
g
fa
c
t
or
(
i
).
A
s
t
h
e
itera
t
i
on incre
a
s
es
a
nd
the
trac
ked
pow
er
a
ppr
oac
h
es
M
P
P
,
i
w
il
l
decr
ease
as
s
how
n
i
n
F
ig
u
r
e
13.
A
s
a
r
e
sul
t
,
the
s
t
e
p
s
i
z
e
w
i
ll
dec
r
ea
se
a
nd
th
us
p
reve
n
t
u
nnece
ssa
r
y se
arc
h
ing
w
i
t
h
i
n
t
he
a
re
a
w
h
ere the
gl
ob
al
M
PP d
o
e
s no
t
e
x
i
s
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Cri
t
i
c
a
l
eva
lu
at
ion
o
f
so
ft
c
o
mp
ut
ing
met
hod
s fo
r m
a
xi
mum p
o
w
e
r
poi
nt
t
r
a
c
k
i
ng
…
(No
r
azlan
Ha
shim)
55
7
Av
e
r
a
g
e
d
Bes
t
F
it
ne
s
s
Co
n
v
erg
en
ce
Av
er
a
g
e
Co
n
v
erg
ed
a
t
8
i
t
era
t
i
o
n
Div
e
r
g
ed
A
v
er
a
g
e
d
B
es
t
F
i
t
n
es
s
C
o
nv
er
g
e
n
c
e
A
v
er
a
g
e
Co
n
v
er
g
e
d
at
10
i
t
e
r
at
i
o
n
Div
e
rg
ed
F
i
g
u
r
e
7
. Co
n
v
e
rge
n
ce
trajec
t
o
r
y
of
trac
ked
be
st
f
itn
e
s
s
(M
PP
)
f
o
r
G
A
F
i
g
u
r
e
8
. Co
n
v
e
rge
n
ce
trajec
t
o
ry of
trac
ked
be
st
fitn
ess (
M
PP) f
o
r
CS
A
v
er
a
g
e
d
B
es
t
Fi
tn
e
s
s
Co
nv
e
r
g
e
nc
e
A
v
er
a
g
e
C
o
n
v
er
g
e
d
at
1
0
i
t
e
r
at
i
o
n
Di
v
e
r
g
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