I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
15
,
No
.
4
,
A
u
g
u
s
t
20
25
,
p
p
.
3
6
2
1
~
3
6
3
1
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
15
i
4
.
pp
3
6
2
1
-
3
6
3
1
3621
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
Ra
pid an
d e
ff
icie
nt
ma
x
im
um po
w
er point
tracking
in
pho
tov
o
ltaic sy
stems with
mo
dified
fuzzy lo
g
ic appro
a
ch
El
-
bo
t
Sa
id
1
,
Ya
s
s
i
ne
E
l
M
o
uja
hid
2
,
Cha
f
ik
E
l Id
ri
s
s
i
M
o
ha
m
ed
1
,
Abdes
s
a
m
a
d B
enl
a
f
k
ih
1
1
A
d
v
a
n
c
e
d
S
y
st
e
ms
En
g
i
n
e
e
r
i
n
g
La
b
o
r
a
t
o
r
y
,
N
a
t
i
o
n
a
l
S
c
h
o
o
l
o
f
A
p
p
l
i
e
d
S
c
i
e
n
c
e
s,
I
b
n
-
To
f
a
i
l
U
n
i
v
e
r
si
t
y
,
K
e
n
i
t
r
a
,
M
o
r
o
c
c
o
2
La
b
o
r
a
t
o
r
y
o
f
M
a
t
e
r
i
a
l
P
h
y
si
c
s
a
n
d
S
u
b
a
t
o
mi
c
,
F
a
c
u
l
t
y
o
f
S
c
i
e
n
c
e
s
,
I
b
n
-
T
o
f
a
i
l
U
n
i
v
e
r
si
t
y
,
K
e
n
i
t
r
a
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Sep
2
3
,
2
0
2
4
R
ev
is
ed
Ap
r
1
2
,
2
0
2
5
Acc
ep
ted
Ma
y
2
4
,
2
0
2
5
P
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
s
(P
Vs
)
o
f
ten
fa
c
e
d
iffi
c
u
l
ti
e
s
i
n
m
a
x
imiz
in
g
th
e
ir
o
u
tp
u
t
p
o
we
r
a
n
d
m
a
in
tain
in
g
a
sta
b
le
DC
-
DC
c
o
n
n
e
c
ti
o
n
v
o
lt
a
g
e
,
e
sp
e
c
ially
u
n
d
e
r
v
a
riab
le
we
a
th
e
r
c
o
n
d
i
ti
o
n
s
(VWC).
Th
e
p
o
we
r
p
ro
d
u
c
e
d
b
y
p
h
o
t
o
v
o
lt
a
ic
p
a
n
e
ls
is
v
e
ry
se
n
siti
v
e
to
c
h
a
n
g
e
s
in
su
n
li
g
h
t
a
n
d
tem
p
e
ra
tu
re
,
wh
ich
v
a
r
y
th
ro
u
g
h
o
u
t
t
h
e
d
a
y
.
T
h
is p
a
p
e
r
p
r
e
se
n
ts t
h
e
d
e
sig
n
o
f
a
n
i
n
telli
g
e
n
t
c
o
n
tro
ll
e
r
a
p
p
ro
a
c
h
b
a
se
d
o
n
m
o
d
ifi
e
d
fu
z
z
y
lo
g
ic (M
F
LC),
a
d
a
p
ted
to
e
n
a
b
l
e
th
e
m
o
st
e
ffe
c
ti
v
e
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
(M
P
P
T)
o
f
a
p
h
o
t
o
v
o
l
taic
so
lar
m
o
d
u
le.
T
h
e
tec
h
n
iq
u
e
re
d
u
c
e
s
d
e
lay
s
in
M
P
P
T
a
n
d
su
sta
in
s
e
fficie
n
c
y
d
e
sp
it
e
c
h
a
n
g
i
n
g
e
n
v
ir
o
n
m
e
n
tal
c
o
n
d
it
io
n
s.
A
DC
-
DC
b
o
o
st
c
o
n
v
e
rter
is
c
o
n
n
e
c
ted
t
o
t
h
e
p
h
o
t
o
v
o
lt
a
ic
s
o
l
a
r
m
o
d
u
le,
w
h
ich
i
n
tu
rn
is
l
in
k
e
d
to
a
lo
a
d
,
a
n
d
c
o
m
p
u
ter
sim
u
latio
n
s
u
sin
g
M
ATLAB/S
imu
li
n
k
we
re
u
se
d
t
o
v
a
li
d
a
te
th
e
m
e
th
o
d
'
s
e
ffe
c
ti
v
e
n
e
ss
.
Re
su
lt
s
re
v
e
a
l
th
a
t
th
e
M
F
LC
c
o
n
tro
ll
e
r
sig
n
ifi
c
a
n
t
ly
e
n
h
a
n
c
e
s
t
h
e
e
fficie
n
c
y
o
f
t
h
e
P
Vs
,
a
c
h
iev
in
g
imp
ro
v
e
m
e
n
t
s
o
f
u
p
t
o
9
7
.
0
5
%
,
with
a
ra
p
i
d
se
tt
li
n
g
ti
m
e
o
f
les
s
th
a
n
1
0
m
il
l
ise
c
o
n
d
s
a
c
ro
ss
a
ll
tes
t
sc
e
n
a
rio
s.
K
ey
w
o
r
d
s
:
B
o
o
s
t c
o
n
v
er
ter
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
Fu
zz
y
lo
g
ic
Ma
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
Ph
o
to
v
o
ltaic
s
y
s
tem
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
El
-
b
o
t Said
Ad
v
an
ce
d
Sy
s
tem
s
E
n
g
i
n
ee
r
in
g
L
ab
o
r
ato
r
y
,
Natio
n
al
Sch
o
o
l
o
f
Ap
p
lied
Scien
ce
s
,
I
b
n
-
T
o
f
ail
Un
iv
er
s
ity
,
B
P 1
3
3
,
1
4
0
0
0
Ke
n
itra
,
Mo
r
o
cc
o
E
m
ail:
s
aid
.
elb
o
t@
u
it.a
c.
m
a
1.
I
NT
RO
D
UCT
I
O
N
Giv
en
th
e
r
is
in
g
g
lo
b
al
e
n
er
g
y
d
em
an
d
an
d
en
v
i
r
o
n
m
e
n
tal
co
n
ce
r
n
s
as
well
as
th
e
d
ep
letio
n
o
f
f
o
s
s
il
f
u
el
r
eser
v
es,
th
e
n
ec
ess
ity
o
f
s
u
s
tain
ab
le
en
er
g
y
s
o
lu
tio
n
s
h
as
b
ec
o
m
e
in
cr
ea
s
in
g
ly
ap
p
ar
en
t.
Ph
o
to
v
o
ltaic
(
PV
)
s
y
s
tem
s
ar
e
an
im
p
o
r
ta
n
t
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
as
th
ey
g
en
er
ate
clea
n
elec
tr
icity
.
Ho
wev
er
,
th
e
v
ar
iab
ilit
y
o
f
s
o
lar
en
e
r
g
y
a
f
f
ec
ted
b
y
f
lu
ctu
atio
n
s
in
ir
r
ad
i
an
ce
,
tem
p
er
atu
r
e,
an
d
wea
th
er
p
r
esen
ts
cr
itical
ch
allen
g
es
in
en
s
u
r
in
g
o
p
tim
a
l
en
er
g
y
co
n
v
er
s
io
n
e
f
f
icien
cy
[
1
]
,
[
2
]
th
is
v
ar
iab
ilit
y
u
n
d
e
r
s
co
r
es
th
e
n
ee
d
f
o
r
ad
v
an
ce
d
co
n
tr
o
l
s
tr
ateg
ies
to
en
ab
le
p
h
o
to
v
o
l
taic
s
y
s
tem
s
(
PVs
)
to
r
eliab
ly
tr
ac
k
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
(
MPP)
.
T
h
e
k
ey
r
esear
ch
p
r
o
b
lem
a
d
d
r
ess
ed
in
th
is
p
ap
er
is
th
e
i
n
h
er
en
t
lim
itatio
n
s
o
f
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
i
n
g
(
MPPT)
tech
n
iq
u
es
u
n
d
er
d
y
n
am
ic
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
W
h
ile
tr
ad
itio
n
al
MP
PT
alg
o
r
ith
m
s
,
s
u
ch
as
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
[
3
]
,
an
d
in
cr
em
en
tal
co
n
d
u
ctan
ce
(
I
n
C
)
[
4
]
,
wh
ile
ef
f
ec
tiv
e
u
n
d
er
s
tab
le
co
n
d
itio
n
s
,
o
f
te
n
s
tr
u
g
g
le
to
p
er
f
o
r
m
o
p
tim
ally
u
n
d
er
d
y
n
am
ic
an
d
u
n
p
r
ed
ictab
le
clim
atic
s
itu
atio
n
s
.
L
ea
d
in
g
to
is
s
u
es su
ch
as sl
o
w
r
esp
o
n
s
e,
tr
ac
k
i
n
g
er
r
o
r
s
,
an
d
Failu
r
e
to
ac
h
iev
e
th
e
o
p
tim
al
MPPT,
I
n
o
r
d
er
to
h
an
d
le
th
ese
is
s
u
es,
s
ev
er
al
MPPT
alg
o
r
ith
m
s
h
a
v
e
b
ee
n
d
e
v
elo
p
e
d
r
ec
e
n
tly
;
t
h
o
s
e
ca
n
b
e
d
iv
id
e
d
in
to
s
o
m
e
ca
teg
o
r
ies
s
u
ch
as
co
n
v
en
tio
n
al
alg
o
r
ith
m
s
,
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
,
h
y
b
r
id
al
g
o
r
ith
m
s
,
m
ath
em
atics
-
b
ased
alg
o
r
ith
m
s
,
ar
tific
ial
in
tellig
en
ce
(
AI
)
alg
o
r
ith
m
,
al
g
o
r
ith
m
b
ased
o
n
a
ch
a
r
ac
ter
is
tic
cu
r
v
e,
a
n
d
o
t
h
er
m
is
ce
llan
eo
u
s
alg
o
r
ith
m
s
[
5
]
–
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
2
1
-
3631
3622
T
h
is
p
ap
er
p
r
esen
ts
th
e
m
o
d
if
ied
f
u
zz
y
lo
g
ic
c
o
n
tr
o
ller
(
MF
L
C
)
,
wh
ich
is
d
esig
n
ed
to
o
v
e
r
co
m
e
t
h
e
lim
itatio
n
s
o
f
th
e
co
n
v
en
tio
n
a
l
MPPT
tech
n
iq
u
es.
T
h
e
MF
L
C
ex
p
lo
its
th
e
i
n
h
er
en
t
s
tr
en
g
th
s
o
f
f
u
zz
y
lo
g
ic,
its
ab
ilit
y
to
h
an
d
le
u
n
ce
r
tain
ties
an
d
n
o
n
-
lin
ea
r
ities
,
wh
ile
in
co
r
p
o
r
atin
g
s
p
ec
if
ic
m
o
d
if
icatio
n
s
to
im
p
r
o
v
e
its
p
er
f
o
r
m
a
n
ce
u
n
d
er
d
y
n
am
ic
wea
th
er
co
n
d
itio
n
s
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
ad
d
r
ess
es
cr
itical
is
s
u
es
s
u
ch
as
MPPT
s
ettl
in
g
tim
e
d
elay
s
an
d
ef
f
icien
cy
d
eg
r
ad
atio
n
u
n
d
e
r
r
ap
id
ly
ch
an
g
in
g
wea
th
e
r
c
o
n
d
itio
n
s
.
A
b
o
o
s
t
DC
-
DC
co
n
v
er
ter
is
in
t
eg
r
ated
in
to
p
h
o
to
v
o
ltaics
to
m
ax
im
ize
en
er
g
y
tr
an
s
f
er
an
d
s
tab
ilize
th
e
co
n
n
ec
tio
n
v
o
ltag
e,
e
n
s
u
r
in
g
r
eliab
le
o
p
e
r
atio
n
in
a
v
ar
iety
o
f
s
ce
n
ar
io
s
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
MFL
C
-
b
ased
MPPT
ap
p
r
o
ac
h
is
v
alid
ated
b
y
co
m
p
r
eh
en
s
iv
e
s
im
u
latio
n
s
p
er
f
o
r
m
ed
in
MA
T
L
AB
/Si
m
u
lin
k
v
er
s
io
n
2
0
2
4
a.
T
h
e
r
esu
lts
co
n
f
ir
m
th
e
o
u
ts
tan
d
in
g
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
e
d
m
eth
o
d
,
with
en
er
g
y
co
n
v
er
s
io
n
ef
f
icien
cies
o
f
u
p
to
9
7
.
0
5
%
an
d
a
f
ast
-
s
ettlin
g
tim
e
o
f
less
th
an
1
0
m
s
u
n
d
er
all
test
co
n
d
itio
n
s
.
T
h
ese
r
esu
lts
h
ig
h
lig
h
t
t
h
e
p
o
ten
tial
o
f
th
e
MFL
C
tech
n
i
q
u
e
to
s
ig
n
i
f
ican
tly
im
p
r
o
v
e
th
e
ef
f
icien
c
y
,
s
tab
ilit
y
,
an
d
s
ettlin
g
tim
e
o
f
PVs
,
m
ak
in
g
it a
p
r
o
m
is
in
g
s
o
lu
tio
n
f
o
r
r
e
n
ewa
b
le
en
e
r
g
y
a
p
p
licat
io
n
s
.
T
h
er
e
ar
e
f
iv
e
p
o
r
tio
n
s
in
t
h
is
wo
r
k
.
T
h
e
elec
tr
ical
m
o
d
elin
g
an
d
p
r
o
p
er
ties
o
f
s
o
lar
s
y
s
t
em
s
u
n
d
er
ch
an
g
in
g
co
n
d
itio
n
s
ar
e
ex
a
m
in
ed
in
s
ec
tio
n
2
.
T
h
e
s
u
g
g
ested
s
tr
ateg
y
is
d
escr
ib
ed
in
s
ec
tio
n
3
.
T
h
e
s
im
u
latio
n
r
esu
lts
an
d
th
eir
an
aly
s
is
ar
e
s
h
o
wn
in
s
ec
tio
n
4
.
L
astl
y
,
th
e
k
ey
f
in
d
in
g
s
ar
e
h
ig
h
lig
h
ted
in
th
e
co
n
clu
s
io
n
s
ec
tio
n
.
2.
E
L
E
C
T
RIC
AL
M
O
DE
L
I
N
G
O
F
A
P
Vs
Fig
u
r
e
1
illu
s
tr
ates
th
e
b
lo
c
k
d
iag
r
am
o
f
th
e
PV
s
y
s
tem
,
c
o
m
p
r
is
in
g
k
ey
c
o
m
p
o
n
en
ts
s
u
c
h
as
th
e
PV
p
an
el,
DC
-
DC
b
o
o
s
t
co
n
v
er
te
r
,
MPPT
co
n
tr
o
l,
an
d
l
o
ad
.
T
h
e
PV
p
an
el
ca
p
tu
r
es
s
u
n
lig
h
t
an
d
co
n
v
er
ts
it
in
to
elec
tr
ical
en
er
g
y
.
T
h
e
g
en
er
at
e
d
p
o
wer
,
o
n
th
e
o
th
er
h
an
d
,
i
s
r
eg
u
lated
an
d
s
u
p
p
lied
f
o
r
c
o
n
s
u
m
p
tio
n
d
ir
ec
tly
to
th
e
lo
ad
,
th
e
n
th
e
b
o
o
s
t
co
n
v
er
ter
in
cr
ea
s
es
th
e
v
o
ltag
e
t
o
as
p
er
t
h
e
l
o
ad
r
eq
u
i
r
em
en
t.
T
h
e
lo
ad
is
tak
e
n
o
u
t
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
o
u
t
p
u
t
as
s
h
o
wn
b
elo
w.
T
h
is
PVs
o
p
e
r
ates
in
two
d
is
tin
ct
m
o
d
e
s
:
C
o
n
s
tan
t
Vo
ltag
e
C
o
n
tr
o
l
m
o
d
e
in
w
h
ich
th
e
in
v
er
ter
wo
r
k
s
to
c
o
n
tr
o
l
th
e
o
u
tp
u
t
v
o
ltag
e
,
wh
ile
MP
PT
m
o
d
e
wo
r
k
s
to
m
ax
im
ize
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
th
e
s
o
lar
p
an
el
[
8
]
.
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
c
ell
m
o
del
T
h
e
co
r
e
co
m
p
o
n
e
n
ts
o
f
PVs
ar
e
PV
ce
ll
s
an
d
m
o
d
u
les,
wh
ich
ab
s
o
r
b
p
h
o
to
n
s
f
r
o
m
s
u
n
lig
h
t
an
d
r
elea
s
e
elec
tr
o
n
ch
ar
g
es,
th
er
e
b
y
co
n
v
er
tin
g
s
o
lar
en
er
g
y
d
i
r
ec
tly
in
to
elec
tr
ical
p
o
wer
[
9
]
.
Am
o
n
g
th
e
m
o
s
t
co
m
m
o
n
l
y
u
tili
ze
d
m
o
d
els
f
o
r
d
escr
ib
in
g
PV
b
eh
av
io
r
a
r
e
t
h
e
s
in
g
le
-
d
i
o
d
e
an
d
d
o
u
b
le
-
d
i
o
d
e
m
o
d
els
[
1
0
]
.
I
n
th
is
s
tu
d
y
,
we
em
p
lo
y
th
e
s
in
g
le
d
io
d
e
m
o
d
el,
wh
e
r
e
th
e
d
io
d
e
(
D)
s
y
m
b
o
lizes th
e
P
-
N
ju
n
ctio
n
,
to
ac
cu
r
ately
ch
ar
a
cter
ize
th
e
elec
tr
ical
p
r
o
p
er
ties
o
f
PV c
ells
[
1
1
]
.
As
s
h
o
wn
in
Fig
u
r
e
2
,
th
e
s
in
g
le
-
d
io
d
e
m
o
d
el
c
o
n
s
is
ts
o
f
a
p
ar
allel
d
io
d
e
(
D)
,
a
s
h
u
n
t
r
esis
tan
ce
(
R
s
h
)
,
an
d
a
s
er
i
es
r
esis
tan
ce
(
R
s
)
.
T
h
e
g
o
v
er
n
in
g
e
q
u
atio
n
s
f
o
r
its
elec
tr
ical
p
er
f
o
r
m
a
n
c
e
ar
e
s
o
u
r
ce
d
f
r
o
m
p
r
io
r
s
tu
d
ies
[
1
2
]
,
[
1
3
]
.
Usi
n
g
Kir
ch
h
o
f
f
'
s
L
aw,
(
1
)
d
ef
in
es
th
e
cu
r
r
en
t
-
v
o
ltag
e
(
I
-
V
)
r
elatio
n
s
h
ip
g
o
v
e
r
n
in
g
th
e
cir
cu
it.
T
h
is
f
u
n
d
am
e
n
tal
eq
u
atio
n
f
o
r
m
s
th
e
b
asis
f
o
r
an
aly
zin
g
an
d
o
p
tim
izin
g
PV c
ell
p
er
f
o
r
m
an
ce
.
I
pv
=
I
ph
−
I
d
−
I
R
sh
(
1
)
−
So
lar
-
g
en
er
ated
cu
r
r
e
n
t in
th
e
b
asic
p
h
o
to
v
o
ltaic
ce
ll:
I
ph
=
(
I
cc
+
K
i
Δ
T
)
(
3
)
−
C
u
r
r
en
t p
ass
in
g
th
r
o
u
g
h
th
e
p
ar
allel
-
co
n
f
ig
u
r
ed
d
io
d
e:
I
d
=
I
0
[
e
xp
(
q
(
V
pv
+
R
s
I
pv
)
A
K
T
)
−
1
]
(
4
)
−
T
h
e
s
h
u
n
t c
u
r
r
en
t t
h
r
o
u
g
h
th
e
r
esis
tan
ce
:
I
Rs
h
=
V
pv
+
R
s
I
pv
R
sh
(
5
)
I
0
Den
o
tes
th
e
d
io
d
e’
s
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t,
wh
ile
V
pv
an
d
I
pv
r
ep
r
esen
t
th
e
o
u
tp
u
t
v
o
ltag
e
a
n
d
cu
r
r
e
n
t.
C
o
n
s
tan
ts
in
clu
d
e
q
(
elec
tr
o
n
ch
ar
g
e,
1
.
6
0
2
×1
0
⁻¹⁹
C
)
,
A
(
id
ea
lity
f
ac
to
r
)
,
a
n
d
k
(
B
o
ltzm
an
n
co
n
s
tan
t,
1
.
3
8
×1
0
⁻²³
J
/K)
.
T
h
e
p
o
wer
-
v
o
ltag
e
(
P
-
V)
,
an
d
cu
r
r
en
t
-
v
o
ltag
e
(
I
-
V)
cu
r
v
es
p
r
esen
ted
in
Fig
u
r
e
3
ar
e
b
ased
o
n
r
esu
lts
o
b
tain
ed
u
s
in
g
th
e
a
d
v
an
ce
d
s
o
lar
h
y
d
r
o
win
d
p
o
w
er
API
1
5
6
P
-
2
0
0
p
h
o
to
v
o
ltaic
m
o
d
u
le.
T
h
e
a
r
r
ay
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
a
p
id
a
n
d
efficien
t m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
in
p
h
o
t
o
vo
lta
ic
s
ystems
…
(
El
-
b
o
t S
a
id
)
3623
co
n
f
ig
u
r
atio
n
in
clu
d
es
a
s
in
g
le
s
er
ies
m
o
d
u
le
with
o
n
e
p
a
r
all
el
s
tr
in
g
.
Fig
u
r
es
3
(
a)
a
n
d
3
(
b
)
illu
s
tr
ate
th
e
p
r
o
p
er
ties
o
f
PV
ce
lls
u
n
d
er
d
if
f
er
en
t
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
s
u
ch
as
tem
p
er
atu
r
e
an
d
ir
r
ad
ian
ce
.
So
lar
r
ad
iatio
n
an
d
tem
p
er
at
u
r
e
a
lter
atio
n
s
cr
itically
im
p
ac
t
PV
b
eh
av
io
r
o
win
g
to
t
h
e
s
y
s
tem
’
s
n
o
n
lin
ea
r
o
p
er
atio
n
al
d
y
n
am
ics.
As
a
r
e
s
u
lt,
v
ar
iatio
n
s
in
th
ese
p
ar
am
eter
s
ca
n
s
ig
n
if
ican
tly
in
f
lu
en
ce
th
e
p
er
f
o
r
m
a
n
ce
an
d
ef
f
icien
c
y
o
f
PV c
ells
[
1
4
]
.
Fig
u
r
e
1
.
Ph
o
to
v
o
ltaic
s
y
s
tem
with
MPPT
co
n
tr
o
l
Fig
u
r
e
2
.
PV c
ell
eq
u
i
v
alen
t c
i
r
cu
it
(
a)
(
b
)
Fig
u
r
e
3
.
Pro
p
er
ties
o
f
PV c
ell
s
u
n
d
er
d
i
f
f
er
en
t
v
ar
iab
le
wea
t
h
er
co
n
d
itio
n
s
(
VW
C
)
:
(
a)
d
if
f
e
r
en
t te
m
p
e
r
atu
r
es
an
d
(
b
)
d
if
f
er
en
t ir
r
ad
iatio
n
s
2
.
2
.
T
he
DC
-
DC
bo
o
s
t
co
nv
er
t
er
T
h
e
B
o
o
s
t
co
n
v
er
ter
s
tep
s
u
p
th
e
in
p
u
t
DC
v
o
ltag
e
to
a
h
ig
h
er
o
u
t
p
u
t
lev
el
.
I
ts
d
esig
n
in
Fig
u
r
e
4
in
clu
d
es
a
DC
s
o
u
r
ce
V
,
in
d
u
ct
o
r
(
L
)
,
MO
SF
E
T
,
d
io
d
e
(
D)
,
an
d
ca
p
ac
ito
r
s
(
C
i
n
t
,
C
o
ut
)
,
as
p
ar
am
et
er
ized
in
T
ab
le
1
.
B
y
lev
er
a
g
in
g
(
6
)
an
d
(
7
)
,
it
d
y
n
am
ically
a
d
ju
s
ts
th
e
PV
p
an
el’
s
o
p
er
atin
g
p
o
i
n
t
to
ac
h
iev
e
MPPT,
en
s
u
r
in
g
o
p
tim
al
lo
ad
m
atch
in
g
[
1
5
]
,
[
1
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
2
1
-
3631
3624
d
I
L
dt
=
V
A
L
(
6
)
d
V
0
dt
=
−
V
0
C
o
u
t
R
L
(
7
)
A
PW
M
p
u
ls
e
g
en
er
ato
r
p
r
o
v
id
es
d
u
ty
p
u
ls
es.
W
h
en
is
wi
th
in
th
e
in
ter
v
al
[
α
T
,
T
]
,
th
e
t
r
an
s
is
to
r
is
in
ac
tiv
e.
Her
e,
r
ep
r
esen
ts
th
e
p
er
io
d
o
f
th
e
s
tatic
co
n
v
er
ter
,
wh
ile
α
in
d
icate
s
th
e
d
u
ty
cy
cle.
T
h
e
co
n
v
er
ter
'
s
b
eh
av
io
r
is
d
escr
ib
ed
b
y
(
8
)
an
d
(
9
)
.
T
h
e
co
n
v
er
ter
'
s
f
u
n
ctio
n
in
g
is
co
n
tr
o
lled
b
y
a
s
witch
,
co
m
m
o
n
l
y
a
MO
SF
E
T
,
wh
i
ch
s
witch
es
b
etwe
en
o
p
en
an
d
clo
s
ed
s
tates
d
ep
en
d
en
t
o
n
th
e
d
u
ty
cy
cle
g
en
er
ated
b
y
th
e
MPPT
p
r
o
ce
s
s
[
1
7
]
,
[
1
8
]
.
d
V
0
dt
=
i
L
C
o
u
t
−
V
0
C
o
u
t
R
L
(
8
)
d
I
L
dt
=
V
A
−
V
0
L
(
9
)
Fig
u
r
e
4
.
DC
-
DC
b
o
o
s
t c
o
n
v
e
r
ter
T
ab
le
1
.
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
s
p
ec
if
icatio
n
s
P
a
r
a
me
t
e
r
V
a
l
u
e
I
n
d
u
c
t
a
n
c
e
(
L)
1
0
mH
C
a
p
a
c
i
t
y
(
C
i
n
t
)
4
μF
C
a
p
a
c
i
t
y
(
C
o
u
t
)
2
0
μF
F
r
e
q
u
e
n
c
y
(
f
s)
2
0
k
H
z
Lo
a
d
6
0
Ω
3.
P
RO
P
O
SE
D
M
E
T
H
O
D
3
.
1
.
T
he
M
P
P
T
-
ba
s
ed
f
uzzy
lo
g
ic
co
ntr
o
ller
T
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
is
i
n
cr
ea
s
in
g
ly
a
p
p
lied
i
n
v
a
r
io
u
s
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
d
u
e
to
th
eir
s
im
p
licity
an
d
ef
f
ec
tiv
en
ess
.
Ov
er
th
e
p
ast
d
ec
ad
e,
t
h
e
d
e
m
an
d
f
o
r
FLC
h
as
g
r
o
wn
s
i
g
n
if
ican
tly
,
lar
g
ely
b
ec
au
s
e
it
ca
n
m
a
n
ag
e
im
p
r
ec
is
e
in
p
u
ts
with
o
u
t
n
ee
d
i
n
g
an
ac
cu
r
ate
m
ath
em
atica
l
m
o
d
el
[
1
9
]
–
[
2
1
]
.
FLC
is
p
ar
ticu
lar
ly
ad
e
p
t
at
h
an
d
lin
g
n
o
n
lin
ea
r
co
n
d
itio
n
s
,
m
a
k
in
g
it
an
ex
ce
lle
n
t
ch
o
ice
f
o
r
m
ax
im
izin
g
p
o
wer
o
u
tp
u
t
f
r
o
m
PV
m
o
d
u
les.
I
t
c
an
o
p
er
ate
ef
f
ec
tiv
ely
u
n
d
er
d
iv
er
s
e
wea
th
er
co
n
d
itio
n
s
an
d
ad
ap
t
to
ch
an
g
es
in
tem
p
er
atu
r
e
a
n
d
lig
h
t
in
ten
s
i
ty
.
T
h
r
ee
cr
ite
r
ia
ca
n
b
e
u
s
ed
to
class
if
y
FLC
p
r
o
ce
s
s
es:
a)
f
u
zz
if
icatio
n
,
b
)
ev
alu
atio
n
o
f
r
u
les
,
an
d
c)
d
ef
u
zz
if
icatio
n
a
s
d
ep
icte
d
in
F
ig
u
r
e
5
.
Fig
u
r
e
5
.
T
h
e
f
r
a
m
ewo
r
k
o
f
a
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
a
p
id
a
n
d
efficien
t m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
in
p
h
o
t
o
vo
lta
ic
s
ystems
…
(
El
-
b
o
t S
a
id
)
3625
3
.
2
.
T
he
M
P
P
T
-
ba
s
ed
f
uzzy
lo
g
ic
co
ntr
o
ller
T
h
e
f
u
zz
if
icatio
n
p
r
o
ce
s
s
is
t
h
e
f
ir
s
t
s
tag
e
o
f
an
MFL
C
,
an
d
it
i
s
a
b
ig
d
ea
l.
T
h
e
r
ea
s
o
n
f
o
r
th
is
is
th
at
it
is
th
e
f
ir
s
t
s
tag
e
o
f
an
MFL
C
,
b
ec
au
s
e
th
is
i
s
th
e
p
ar
t
wh
er
e
clea
r
,
p
r
ec
is
e
in
p
u
ts
a
r
e
tr
an
s
f
o
r
m
e
d
in
to
f
u
zz
y
v
alu
es.
I
t
in
v
o
lv
es
tak
i
n
g
d
ata
s
u
ch
as
v
o
ltag
e
lev
el
ch
an
g
es
an
d
r
u
n
n
in
g
th
em
t
h
r
o
u
g
h
p
r
ed
e
f
in
ed
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
to
t
r
an
s
f
o
r
m
th
em
in
to
er
r
o
r
s
ets.
T
h
i
s
s
tep
is
cr
u
cial
as
it
estab
li
s
h
es
a
f
r
am
ewo
r
k
f
o
r
th
e
co
n
tr
o
ller
to
d
ea
l w
ith
u
n
c
er
tain
ty
an
d
m
ak
e
b
etter
d
ec
is
io
n
s
.
3
.
2
.
1
.
F
uzzif
ica
t
i
on
T
h
e
f
u
zz
if
icatio
n
u
n
it
is
r
esp
o
n
s
ib
le
f
o
r
co
n
v
er
tin
g
r
ea
l
v
a
r
iab
les
in
to
f
u
zz
y
v
a
r
iab
les
[
2
2
]
.
I
n
th
is
ca
s
e,
th
e
in
p
u
ts
to
th
e
MFL
C
r
ep
r
esen
ted
as
(
)
a
n
d
(
)
,
ar
e
ca
lcu
lated
u
s
in
g
(
1
0
)
a
n
d
(
1
1
)
r
esp
ec
tiv
ely
.
T
h
e
er
r
o
r
s
ig
n
al
(
)
a
n
d
its
d
er
iv
ativ
e
(
at
tim
e
s
tep
)
s
er
v
e
as
th
e
d
u
al
in
p
u
ts
to
th
e
MFL
C
,
wh
ic
h
co
m
p
u
tes th
e
d
u
ty
cy
cle
m
o
d
i
f
icatio
n
(
d
D)
as its
o
u
tp
u
t.
E
(
k
)
=
P
(
k
)
−
P
(
k
−
1
)
V
(
k
)
−
V
(
k
−
1
)
(
1
0
)
CE
(
k
)
=
E
(
k
)
−
E
(
k
−
1
)
(
1
1
)
Fig
u
r
es
6
(
a)
-
(
b
)
,
an
d
7
s
h
o
w
th
e
f
u
zz
y
v
ar
iab
les
E
,
C
E
,
an
d
d
D
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
.
A
m
o
n
g
th
e
s
ev
er
al
ty
p
es
o
f
m
em
b
er
s
h
i
p
f
u
n
ctio
n
s
ac
ce
s
s
ib
le,
th
e
s
y
m
m
etr
ic
tr
ian
g
u
lar
f
u
n
ctio
n
was
ch
o
s
en
f
o
r
its
s
im
p
licity
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
.
T
o
c
o
r
r
ec
tly
r
ef
lect
r
ea
l
s
ig
n
als,
th
e
f
u
zz
y
v
ar
ia
b
les'
r
an
g
e
lim
itatio
n
s
ar
e
o
f
t
en
ad
ju
s
ted
b
etwe
en
-
1
an
d
+1
u
s
in
g
a
g
ain
f
ac
to
r
.
Fo
r
th
is
in
v
esti
g
atio
n
,
th
e
s
y
m
m
etr
ic
tr
ian
g
u
la
r
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
wer
e
u
t
ilized
,
with
r
an
g
e
lim
itatio
n
s
o
f
(
[
-
3
0
,
1
0
]
,
[
-
3
0
,
3
0
]
,
an
d
[
0
,
1
]
)
f
o
r
E
,
C
E
,
an
d
d
D,
r
esp
ec
tiv
ely
.
(
a)
(
b
)
Fig
u
r
e
6
.
T
h
e
f
u
zz
y
v
a
r
iab
les:
(
a)
I
n
p
u
t v
a
r
iab
le
er
r
o
r
an
d
(
b
)
Var
iab
le
c
h
an
g
e
i
n
er
r
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
2
1
-
3631
3626
Fig
u
r
e
7
.
T
h
e
f
u
zz
y
v
a
r
iab
les:
Ou
tp
u
t v
ar
iab
le
d
D
3
.
2
.
2
.
E
v
a
lua
t
io
n o
f
r
ules
T
h
e
m
o
s
t
im
p
o
r
ta
n
t
p
ar
t
o
f
th
e
f
u
zz
y
in
f
e
r
en
ce
,
n
o
r
m
ally
r
ef
er
r
ed
to
as
t
h
e
‘
h
ea
r
t,’
co
n
s
is
ts
o
f
th
e
b
asic
s
et
o
f
“I
F
-
T
HE
N”
r
u
le
s
th
at
co
n
tr
ib
u
te
to
a
f
u
zz
y
in
f
er
en
ce
.
Su
ch
r
u
les
ca
n
b
e
d
ef
in
ed
u
s
in
g
th
e
ex
p
er
ien
ce
an
d
k
n
o
wled
g
e
o
f
s
p
ec
ialis
ts
in
th
e
n
atu
r
al
lan
g
u
ag
e
p
r
o
ce
s
s
in
g
d
o
m
ain
[
2
3
]
.
T
h
e
f
in
al
f
u
zz
y
co
n
clu
s
io
n
is
d
er
iv
ed
b
y
co
n
s
id
er
in
g
th
e
m
em
b
er
s
h
ip
d
eg
r
e
es
o
f
th
e
in
p
u
t
v
ar
iab
les
in
th
e
f
u
zz
y
s
ets
alo
n
g
with
th
e
ap
p
lied
f
u
zz
y
r
u
les.
Sev
er
al
ap
p
r
o
ac
h
es
ca
n
b
e
u
s
ed
to
p
er
f
o
r
m
f
u
zz
y
in
f
e
r
en
ce
an
d
s
u
ch
a
n
u
m
b
er
o
f
ap
p
r
o
ac
h
es
ca
n
y
ield
d
if
f
e
r
en
t
r
esu
lts
.
E
m
p
lo
y
in
g
th
e
Ma
x
-
Min
co
m
p
o
s
itio
n
al
ap
p
r
o
ac
h
,
th
e
Ma
m
d
an
i
in
f
er
en
ce
s
y
s
tem
is
a
co
r
n
er
s
to
n
e
o
f
FLC
an
d
d
ec
is
io
n
an
aly
s
is
.
T
h
e
in
f
er
en
ce
r
u
le
tab
le
is
p
r
esen
ted
in
T
ab
l
e
2
.
T
ab
le
2
.
T
a
b
le
o
f
in
f
er
en
ce
r
u
l
es
CE
E
GP
PM
PP
Z
NP
GP
P
P
P
P
P
PM
Z
Z
Z
Z
Z
PP
N
N
N
Z
Z
Z
Z
Z
Z
P
N
NP
Z
Z
Z
P
P
3
.
2
.
3
.
Def
uzzif
ica
t
io
n
T
h
e
d
e
f
u
zz
if
icatio
n
s
tep
tr
an
s
f
o
r
m
s
th
e
f
u
zz
y
o
u
tp
u
t
in
to
a
p
r
ec
is
e,
n
o
n
-
f
u
z
zy
v
alu
e,
w
h
ich
is
cr
u
cial
f
o
r
co
n
tr
o
llin
g
t
h
e
p
r
o
ce
s
s
.
T
h
is
p
r
o
ce
s
s
tak
es
a
f
u
zz
y
s
et
as
in
p
u
t
an
d
p
r
o
d
u
ce
s
a
s
in
g
l
e
n
u
m
er
ic
v
alu
e
th
at
ca
n
b
e
u
s
ed
as
th
e
f
in
al
co
n
tr
o
l
o
u
t
p
u
t.
Sin
ce
t
h
e
s
y
s
tem
r
eq
u
ir
es
a
n
o
n
-
f
u
zz
y
co
n
tr
o
l
o
u
tp
u
t
f
o
r
e
f
f
ec
tiv
e
o
p
er
atio
n
,
d
ef
u
zz
if
icatio
n
is
a
cr
itical
co
m
p
o
n
en
t o
f
p
r
o
ce
s
s
co
n
tr
o
l.
Fo
r
th
e
g
iv
e
n
s
am
p
le
d
ata,
th
e
ar
ith
m
etic
m
ea
n
is
o
b
tain
ed
v
ia
(
1
2
)
.
T
h
e
d
ef
u
zz
if
icatio
n
r
esu
lts
ar
e
m
u
ltip
lied
b
y
a
g
ai
n
f
ac
to
r
,
y
ield
in
g
th
e
co
n
tr
o
l
s
ig
n
al
in
Fig
u
r
e
6
th
at
r
ef
in
es t
h
e
f
u
zz
y
lo
g
ic
MPPT
m
ec
h
an
i
s
m
.
=
∑
=
1
(
)
−
∑
=
1
(
)
(1
2
)
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
I
n
th
is
Simu
latio
n
,
a
n
API
1
5
6
P2
0
0
p
h
o
to
v
o
ltaic
p
a
n
el
was
u
s
ed
,
an
d
a
s
im
u
latio
n
m
o
d
el
th
at
in
co
r
p
o
r
ates
an
en
h
an
ce
d
MPPT
co
n
tr
o
l
m
et
h
o
d
b
ased
o
n
MFL
C
.
A
b
o
o
s
t
co
n
v
er
te
r
,
s
h
o
wn
in
Fig
u
r
e
8
,
was
em
p
lo
y
ed
t
o
m
an
ag
e
t
h
e
lo
ad
.
T
h
e
p
ar
ticu
lar
s
p
ec
if
icatio
n
s
o
f
th
e
p
h
o
to
v
o
ltaic
m
o
d
u
les
wer
e
d
escr
ib
ed
in
T
ab
le
3
,
an
d
s
im
u
latio
n
s
wer
e
ca
r
r
ied
o
u
t
at
a
co
n
s
tan
t
t
em
p
er
atu
r
e
o
f
2
5
°C
.
T
h
is
r
esear
ch
f
o
cu
s
es
o
n
v
alid
atin
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
s
o
lar
PVs
,
with
p
ar
ticu
lar
atten
tio
n
to
th
eir
im
p
ac
t
o
n
o
u
tp
u
t
p
o
wer
an
d
s
tab
ilizatio
n
tim
e.
T
ab
le
4
p
r
o
v
id
es
a
s
u
m
m
a
r
y
o
f
th
e
s
im
u
latio
n
r
esu
lts
.
Ad
d
itio
n
ally
,
T
ab
le
5
p
r
esen
ts
a
co
m
p
ar
ativ
e
a
n
aly
s
is
o
f
th
e
s
y
s
tem
'
s
s
tab
il
izatio
n
tim
e
an
d
ef
f
icien
c
y
r
elativ
e
to
th
r
e
e
o
th
er
tech
n
i
q
u
es,
d
em
o
n
s
tr
atin
g
th
e
s
u
p
er
i
o
r
it
y
o
f
th
e
p
r
o
p
o
s
ed
MFL
C
m
eth
o
d
i
n
ac
h
iev
i
n
g
h
ig
h
e
f
f
icien
cy
a
n
d
r
a
p
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
a
p
id
a
n
d
efficien
t m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
in
p
h
o
t
o
vo
lta
ic
s
ystems
…
(
El
-
b
o
t S
a
id
)
3627
s
tab
ilizatio
n
.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
aim
s
to
en
s
u
r
e
f
ast
a
n
d
s
tab
le
tr
ac
k
in
g
o
f
th
e
MPPT.
T
h
e
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
f
r
o
m
th
e
PV
p
a
n
el
ar
e
u
s
ed
as
in
p
u
ts
to
co
m
p
u
te
th
e
E
an
d
E
C
,
wh
ich
ar
e
t
h
e
n
p
r
o
ce
s
s
ed
b
y
t
h
e
MFL
C
,
as d
ep
icted
in
Fig
u
r
e
9
.
Fig
u
r
e
8
.
T
h
e
co
m
p
r
eh
e
n
s
iv
e
s
y
s
tem
m
o
d
el
in
MA
T
L
AB
/Si
m
u
lin
k
T
ab
le
3
.
T
ec
h
n
ical
s
p
ec
if
icatio
n
s
o
f
th
e
API
1
5
6
P2
0
0
PV
m
o
d
u
le
an
d
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
P
a
r
a
me
t
e
r
V
a
l
u
e
A
P
I
1
5
6
P
2
0
0
s
o
l
a
r
P
V
mo
d
u
l
e
N
um
b
e
r
of
c
e
ll
s
p
e
r
m
o
dul
e
60
(
)
3
6
V
(
)
7
.
7
5
A
(
)
2
8
.
7
V
(
)
6
.
9
7
A
(
)
2
0
0
.
0
3
9
W
T
ab
le
4
.
Ou
tco
m
es o
f
th
e
th
r
e
e
ca
s
e
s
tu
d
ies
I
r
r
a
d
i
a
n
c
e
(
w
m
2
⁄
)
(
)
(
)
(
)
(
)
S
e
t
t
l
i
n
g
t
i
me
(
ms)
Ef
f
i
c
i
e
n
c
y
(
%)
6
0
0
1
2
1
.
2
2
5
1
.
3
9
6
8
3
.
7
7
1
1
1
6
.
9
8
9
12
9
7
.
0
2
8
0
0
1
6
1
.
4
1
6
1
.
6
1
3
9
6
.
8
8
1
5
6
.
3
7
8
9
7
.
0
0
1
0
0
0
2
0
0
.
0
1
0
1
.
7
9
9
1
0
7
.
8
6
2
1
9
4
.
0
0
10
9
7
.
0
5
Fig
u
r
e
9
.
T
h
e
MFL
C
ca
lcu
lato
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
2
1
-
3631
3628
4
.
1
.
Resul
t
s
a
nd
d
is
cu
s
s
io
n
T
h
e
MFL
C
’
s
ca
p
ab
ilit
y
to
o
p
tim
ize
PV
s
y
s
tem
s
i
s
co
n
f
ir
m
ed
b
y
s
im
u
latio
n
s
,
ex
ce
llin
g
in
r
ap
id
,
h
ig
h
-
ac
cu
r
ac
y
MPPT.
At
v
ar
y
in
g
ir
r
ad
ian
ce
lev
els
o
f
6
0
0
,
8
0
0
,
a
n
d
1
0
0
0
W
/m
²,
t
h
e
M
FLC
s
h
o
wca
s
ed
its
ab
ilit
y
to
q
u
ick
ly
s
tab
ilize
th
e
s
y
s
tem
an
d
m
ain
tain
ef
f
icie
n
cy
.
Fo
r
in
s
tan
ce
,
Fig
u
r
e
1
0
(
a)
in
d
icate
s
a
r
ap
id
r
esp
o
n
s
e
tim
e
o
f
4
.
6
m
illi
s
ec
o
n
d
s
f
o
r
in
p
u
t
p
o
we
r
,
with
m
in
im
al
o
v
e
r
s
h
o
o
t
an
d
wea
k
r
i
p
p
le
in
s
tead
y
-
s
tate
co
n
d
it
io
n
s
.
T
h
is
p
er
f
o
r
m
a
n
ce
h
ig
h
lig
h
ts
th
e
co
n
tr
o
ller
'
s
ca
p
ab
ilit
y
to
s
wif
tly
an
d
p
r
ec
is
ely
r
ea
ch
th
e
MPP,
en
s
u
r
in
g
o
p
tim
al
en
er
g
y
h
a
r
v
e
s
tin
g
.
T
h
e
p
o
wer
o
u
tp
u
t
a
n
aly
s
is
,
p
r
esen
ted
in
Fig
u
r
e
1
0
(
b
)
,
s
h
o
ws
th
at
s
tab
ilizatio
n
o
cc
u
r
r
ed
with
in
8
m
illi
s
ec
o
n
d
s
u
n
d
er
n
o
r
m
al
co
n
d
itio
n
s
,
with
a
s
lig
h
t
in
cr
ea
s
e
to
1
2
m
illi
s
ec
o
n
d
s
at
r
ed
u
ce
d
ir
r
ad
ian
ce
lev
els
(
G
=
6
0
0
W
/m
²)
.
Fig
u
r
es
1
1
(
a)
an
d
1
1
(
b
)
f
u
r
th
er
v
alid
ate
t
h
e
s
tab
ilit
y
o
f
o
u
tp
u
t
v
o
ltag
e
an
d
c
u
r
r
en
t,
wh
er
e
th
e
MFL
C
ef
f
ec
tiv
ely
m
in
im
i
ze
d
o
s
cillatio
n
s
.
Ov
e
r
all,
th
e
MF
L
C
ac
h
iev
ed
a
n
MPPT
ef
f
icien
cy
o
f
9
7
.
0
5
%
with
a
f
ast
s
tab
ilizatio
n
tim
e
o
f
1
0
m
illi
s
ec
o
n
d
s
,
d
em
o
n
s
tr
atin
g
its
r
o
b
u
s
tn
ess
an
d
s
u
it
ab
ilit
y
f
o
r
d
y
n
am
ic
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
M
FLC
ca
n
s
ig
n
if
ican
tly
im
p
r
o
v
e
th
e
o
p
er
atio
n
o
f
p
h
o
to
v
o
ltaic
s
y
s
tem
s
in
n
o
n
-
lin
ea
r
o
p
er
atin
g
s
itu
atio
n
s
b
y
p
r
o
v
id
i
n
g
f
ast
an
d
ac
cu
r
ate
tr
ac
k
in
g
o
f
th
e
MPP,
u
n
lik
e
co
n
v
en
tio
n
al
m
eth
o
d
s
,
with
m
in
im
al
en
er
g
y
lo
s
s
es,
m
ak
in
g
it
o
n
e
o
f
th
e
m
o
s
t
s
u
itab
le
o
p
tio
n
s
f
o
r
r
ea
l
-
wo
r
ld
r
en
ewa
b
le
en
e
r
g
y
ap
p
licatio
n
s
.
(
a)
(
b
)
Fig
u
r
e
1
0
.
T
h
e
s
im
u
latio
n
r
esu
lt f
o
r
: (
a
)
th
e
in
p
u
t
p
o
wer
an
d
(
b
)
t
h
e
o
u
t
p
u
t p
o
wer
(
a)
(
b
)
Fig
u
r
e
1
1
.
T
h
e
s
im
u
latio
n
r
esu
lts
f
o
r
: (
a)
th
e
o
u
tp
u
t c
u
r
r
en
t
an
d
(
b
)
th
e
o
u
tp
u
t
v
o
ltag
e
4
.
2
.
Co
m
pa
riso
n o
f
t
est
re
s
ults
Simu
latio
n
r
esu
lts
ev
alu
ated
th
e
MFL
C
’
s
p
er
f
o
r
m
an
ce
r
el
ativ
e
to
P&
O
an
d
I
NC
,
h
ig
h
lig
h
tin
g
its
p
r
ec
is
io
n
an
d
ad
ap
ta
b
ilit
y
in
d
y
n
am
ic
co
n
d
itio
n
s
.
T
h
is
co
m
p
ar
ativ
e
s
tu
d
y
was c
o
n
d
u
cted
u
s
in
g
a
p
h
o
to
v
o
ltaic
p
an
el
u
n
d
er
v
ar
io
u
s
ir
r
ad
iatio
n
lev
els.
T
h
e
co
m
p
ar
is
o
n
e
x
a
m
in
ed
s
ev
er
al
k
ey
asp
ec
ts
,
in
clu
d
in
g
e
f
f
icien
cy
,
ac
cu
r
ac
y
,
s
ettlin
g
tim
e,
an
d
r
o
b
u
s
tn
ess
,
as
s
u
m
m
ar
ized
in
T
ab
le
5
.
T
h
e
o
u
ts
tan
d
in
g
r
es
u
lts
o
b
tain
ed
b
y
th
e
MFL
C
ap
p
r
o
ac
h
,
p
a
r
ticu
lar
ly
in
ter
m
s
o
f
ef
f
icien
c
y
,
p
r
ec
is
io
n
,
an
d
s
tab
ilizatio
n
tim
e,
h
ig
h
lig
h
t
its
clea
r
s
u
p
er
io
r
ity
o
v
er
th
e
o
th
e
r
o
p
ti
m
izatio
n
m
eth
o
d
s
.
T
h
ese
f
in
d
i
n
g
s
u
n
d
er
s
co
r
e
th
e
MFL
C
m
eth
o
d
'
s
ef
f
ec
tiv
en
ess
f
o
r
MPPT
in
p
h
o
to
v
o
ltaic
p
o
w
er
s
y
s
tem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
a
p
id
a
n
d
efficien
t m
a
ximu
m
p
o
w
er p
o
in
t tra
ck
in
g
in
p
h
o
t
o
vo
lta
ic
s
ystems
…
(
El
-
b
o
t S
a
id
)
3629
T
ab
le
5
.
R
esu
lts
o
f
th
e
co
m
p
ar
is
o
n
b
etwe
en
FLC an
d
th
r
ee
o
th
er
tech
n
iq
u
es
Te
c
h
n
i
q
u
e
s
P
&O
[
2
4
]
I
n
C
[
2
4
]
I
N
C
[
2
5
]
F
LC
Ef
f
i
c
i
e
n
c
y
(
%)
9
6
.
0
7
9
6
.
9
5
9
6
,
8
5
9
7
,
0
2
S
e
t
t
l
i
n
g
t
i
me
(
ms)
2
9
3
3
0
0
7
7
.
6
10
Tr
a
c
k
i
n
g
sp
e
e
d
V
e
r
y
s
l
o
w
V
e
r
y
s
l
o
w
S
l
o
w
V
e
r
y
f
a
s
t
Tr
a
c
k
i
n
g
a
c
c
u
r
a
c
y
M
o
d
e
r
a
t
e
M
o
d
e
r
a
t
e
M
o
d
e
r
a
t
e
G
o
o
d
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
s
h
o
ws
th
at
an
M
FLC
is
ef
f
ec
tiv
e
in
o
p
tim
izin
g
th
e
p
er
f
o
r
m
an
c
e
o
f
PVs
.
T
h
e
MFL
C
co
n
s
is
ten
tly
d
em
o
n
s
tr
ated
q
u
i
ck
r
esp
o
n
s
e
tim
es,
m
in
im
al
o
v
er
s
h
o
o
t,
an
d
s
tab
le
o
p
er
atio
n
ev
en
u
n
d
e
r
v
ar
y
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
as
s
h
o
wn
in
s
im
u
latio
n
s
co
n
d
u
cted
at
d
if
f
er
en
t
ir
r
ad
iatio
n
lev
e
ls
o
f
6
0
0
,
8
0
0
,
a
n
d
1
0
0
0
W
/m
².
T
h
e
MFL
C
ac
h
iev
ed
a
h
ig
h
MPPT
ef
f
icien
cy
o
f
9
7
.
0
5
%
an
d
d
em
o
n
s
tr
ated
f
ast
s
tab
ilizatio
n
,
with
a
p
er
f
o
r
m
an
ce
o
f
ju
s
t
1
0
m
illi
s
ec
o
n
d
s
in
r
e
ac
h
in
g
th
e
MPP.
T
h
e
s
im
u
latio
n
r
esu
l
ts
co
n
f
ir
m
th
at
th
e
p
r
o
p
o
s
ed
MFL
C
p
r
o
v
id
es
a
r
o
b
u
s
t
an
d
p
r
ec
is
e
co
n
tr
o
l
s
tr
ateg
y
f
o
r
PVs
,
with
p
ar
ticu
lar
s
tr
en
g
th
in
m
ain
tain
in
g
s
y
s
tem
s
tab
ilit
y
a
n
d
o
p
tim
izin
g
e
n
er
g
y
h
ar
v
est
ac
r
o
s
s
a
wid
e
r
an
g
e
o
f
o
p
er
at
in
g
co
n
d
itio
n
s
.
I
ts
ab
ilit
y
to
r
ed
u
ce
o
s
cillatio
n
s
an
d
en
s
u
r
e
s
m
o
o
th
tr
a
n
s
itio
n
s
b
etwe
en
s
tates
m
ak
es
it
h
ig
h
ly
s
u
itab
le
f
o
r
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
.
Ov
er
all,
th
e
MFL
C
o
f
f
er
s
a
p
o
wer
f
u
l
s
o
lu
tio
n
f
o
r
in
c
r
ea
s
in
g
th
e
ef
f
icie
n
cy
an
d
r
eliab
ilit
y
o
f
PVs
,
co
n
tr
ib
u
tin
g
to
th
e
d
e
v
elo
p
m
en
t
o
f
r
e
n
ewa
b
le
en
er
g
y
tech
n
o
l
o
g
ies.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
ar
e
g
r
atef
u
l
to
t
h
e
Facu
lty
o
f
Scien
ce
s
,
I
b
n
-
T
o
f
ail
Un
iv
er
s
ity
f
o
r
p
r
o
v
id
i
n
g
ex
ce
llen
t
r
esear
ch
f
ac
ilit
ies an
d
a
s
u
p
p
o
r
tiv
e
en
v
ir
o
n
m
en
t.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
e
au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
is
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
El
-
b
o
t Said
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Yass
in
e
E
l M
o
u
jah
id
✓
✓
✓
✓
✓
✓
✓
C
h
af
ik
E
l I
d
r
is
s
i M
o
h
am
ed
✓
✓
✓
✓
✓
✓
✓
✓
Ab
d
ess
am
ad
B
en
laf
k
ih
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
I
NF
O
RM
E
D
CO
NS
E
N
T
W
e
h
av
e
o
b
tain
ed
in
f
o
r
m
ed
c
o
n
s
en
t f
r
o
m
all
in
d
iv
id
u
als in
c
lu
d
ed
in
t
h
is
s
tu
d
y
.
E
T
H
I
CAL AP
P
RO
V
AL
T
h
is
r
esear
ch
d
o
es
n
o
t
r
e
q
u
ir
e
eth
ical
ap
p
r
o
v
al
as
it
d
o
es
n
o
t
in
v
o
lv
e
h
u
m
an
p
ar
ticip
an
ts
,
an
im
al
s
u
b
jects,
o
r
s
en
s
itiv
e
d
ata.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
2
1
-
3631
3630
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
d
ata
s
u
p
p
o
r
tin
g
th
is
s
tu
d
y
'
s
f
in
d
in
g
s
ar
e
av
ailab
le
f
r
o
m
th
e
co
r
r
esp
o
n
d
in
g
a
u
th
o
r
,
B
S,
u
p
o
n
r
ea
s
o
n
ab
le
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
Q
.
H
a
ssa
n
e
t
a
l
.
,
“
Th
e
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
r
o
l
e
i
n
t
h
e
g
l
o
b
a
l
e
n
e
r
g
y
t
r
a
n
sf
o
r
m
a
t
i
o
n
s,”
Re
n
e
w
a
b
l
e
En
e
rg
y
F
o
c
u
s
,
v
o
l
.
4
8
,
p
.
1
0
0
5
4
5
,
M
a
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
e
f
.
2
0
2
4
.
1
0
0
5
4
5
.
[
2
]
A
.
I
.
O
sma
n
e
t
a
l
.
,
“
C
o
st
,
e
n
v
i
r
o
n
men
t
a
l
i
mp
a
c
t
,
a
n
d
r
e
s
i
l
i
e
n
c
e
o
f
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
u
n
d
e
r
a
c
h
a
n
g
i
n
g
c
l
i
m
a
t
e
:
a
r
e
v
i
e
w
,
”
En
v
i
r
o
n
m
e
n
t
a
l
C
h
e
m
i
s
t
ry
L
e
t
t
e
rs
,
v
o
l
.
2
1
,
n
o
.
2
,
p
p
.
7
4
1
–
7
6
4
,
A
p
r
.
2
0
2
3
,
d
o
i
:
1
0
.
1
0
0
7
/
s1
0
3
1
1
-
0
2
2
-
0
1
5
3
2
-
8.
[
3
]
M
.
Z
.
N
a
z
e
r
i
,
N
.
H
a
n
i
s
,
a
n
d
A
.
R
a
h
man
,
“
M
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
u
s
i
n
g
p
e
r
t
u
r
b
a
n
d
o
b
ser
v
e
t
e
c
h
n
i
q
u
e
,
”
J
o
u
r
n
a
l
o
f
En
g
i
n
e
e
ri
n
g
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
1
0
,
n
o
.
1
,
p
p
.
2
0
4
–
2
1
0
,
2
0
2
2
.
[
4
]
L.
S
h
a
n
g
,
H
.
G
u
o
,
a
n
d
W
.
Zh
u
,
“
A
n
i
mp
r
o
v
e
d
M
P
P
T
c
o
n
t
r
o
l
s
t
r
a
t
e
g
y
b
a
s
e
d
o
n
i
n
c
r
e
me
n
t
a
l
c
o
n
d
u
c
t
a
n
c
e
a
l
g
o
r
i
t
h
m
,
”
P
ro
t
e
c
t
i
on
a
n
d
C
o
n
t
ro
l
o
f
M
o
d
e
r
n
P
o
w
e
r
S
y
s
t
e
m
s
,
v
o
l
.
5
,
n
o
.
1
,
p
.
1
4
,
D
e
c
.
2
0
2
0
,
d
o
i
:
1
0
.
1
1
8
6
/
s
4
1
6
0
1
-
0
2
0
-
0
0
1
6
1
-
z.
[
5
]
K
.
W
a
n
g
,
J.
M
a
,
K
.
L
.
M
a
n
,
K
.
H
u
a
n
g
,
a
n
d
X
.
H
u
a
n
g
,
“
C
o
m
p
a
r
a
t
i
v
e
s
t
u
d
y
o
f
mo
d
e
r
n
h
e
u
r
i
s
t
i
c
a
l
g
o
r
i
t
h
ms
f
o
r
g
l
o
b
a
l
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
i
n
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
ms u
n
d
e
r
p
a
r
t
i
a
l
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s,”
Fr
o
n
t
i
e
rs i
n
E
n
e
r
g
y
Re
s
e
a
rc
h
,
v
o
l
.
1
0
,
S
e
p
.
2
0
2
2
,
d
o
i
:
1
0
.
3
3
8
9
/
f
e
n
r
g
.
2
0
2
2
.
9
4
6
8
6
4
.
[
6
]
M
.
A
.
M
.
R
a
ml
i
,
S
.
Tw
a
h
a
,
K
.
I
sh
a
q
u
e
,
a
n
d
Y
.
A
.
A
l
-
T
u
r
k
i
,
“
A
r
e
v
i
e
w
o
n
ma
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
sy
st
e
ms
w
i
t
h
a
n
d
w
i
t
h
o
u
t
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s,
”
Re
n
e
w
a
b
l
e
a
n
d
S
u
s
t
a
i
n
a
b
l
e
En
e
r
g
y
Re
v
i
e
w
s
,
v
o
l
.
6
7
,
p
p
.
1
4
4
–
1
5
9
,
Ja
n
.
2
0
1
7
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
ser.
2
0
1
6
.
0
9
.
0
1
3
.
[
7
]
Y
.
E
l
M
o
u
j
a
h
i
d
,
N
.
El
H
a
r
f
a
o
u
i
,
A
.
H
a
d
j
o
u
d
j
a
,
a
n
d
A
.
B
e
n
l
a
f
k
i
h
,
“
A
d
v
a
n
c
e
d
p
a
r
t
i
c
l
e
sw
a
r
m
o
p
t
i
m
i
z
a
t
i
o
n
f
o
r
e
f
f
i
c
i
e
n
t
a
n
d
f
a
s
t
g
l
o
b
a
l
ma
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
u
n
d
e
r
p
a
r
t
i
a
l
s
h
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
E
l
e
c
t
r
i
c
a
l
a
n
d
C
o
m
p
u
t
e
r
En
g
i
n
e
e
ri
n
g
,
v
o
l
.
1
4
,
n
o
.
4
,
p
p
.
3
5
7
0
–
3
5
7
9
,
A
u
g
.
2
0
2
4
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
e
c
e
.
v
1
4
i
4
.
p
p
3
5
7
0
-
3
5
7
9
.
[
8
]
M
.
L.
K
a
t
c
h
e
,
A
.
B
.
M
a
k
o
k
h
a
,
S
.
O
.
Za
c
h
a
r
y
,
a
n
d
M
.
S
.
A
d
a
r
a
mo
l
a
,
“
A
c
o
mp
r
e
h
e
n
si
v
e
r
e
v
i
e
w
o
f
m
a
x
i
m
u
m p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(
M
P
P
T)
t
e
c
h
n
i
q
u
e
s
u
se
d
i
n
so
l
a
r
P
V
s
y
st
e
ms,
”
E
n
e
r
g
i
e
s
,
v
o
l
.
1
6
,
n
o
.
5
,
p
.
2
2
0
6
,
F
e
b
.
2
0
2
3
,
d
o
i
:
1
0
.
3
3
9
0
/
e
n
1
6
0
5
2
2
0
6
.
[
9
]
D
.
R
e
k
i
o
u
a
a
n
d
E.
M
a
t
a
g
n
e
,
O
p
t
i
m
i
z
a
t
i
o
n
o
f
p
h
o
t
o
v
o
l
t
a
i
c
p
o
w
e
r
sys
t
e
m
s
.
L
o
n
d
o
n
:
S
p
r
i
n
g
e
r
L
o
n
d
o
n
,
2
0
1
2
.
[
1
0
]
K
.
D
i
n
g
,
X
.
B
i
a
n
,
H
.
L
i
u
,
a
n
d
T.
P
e
n
g
,
“
A
M
A
TLA
B
-
s
i
mu
l
i
n
k
-
b
a
se
d
P
V
mo
d
u
l
e
m
o
d
e
l
a
n
d
i
t
s
a
p
p
l
i
c
a
t
i
o
n
u
n
d
e
r
c
o
n
d
i
t
i
o
n
s
o
f
n
o
n
u
n
i
f
o
r
m
i
r
r
a
d
i
a
n
c
e
,
”
I
E
EE
T
ra
n
sa
c
t
i
o
n
s
o
n
En
e
rg
y
C
o
n
v
e
rs
i
o
n
,
v
o
l
.
2
7
,
n
o
.
4
,
p
p
.
8
6
4
–
8
7
2
,
D
e
c
.
2
0
1
2
,
d
o
i
:
1
0
.
1
1
0
9
/
TE
C
.
2
0
1
2
.
2
2
1
6
5
2
9
.
[
1
1
]
A
.
K
a
b
b
a
n
i
a
n
d
H
.
M
o
h
a
me
d
S
h
a
i
k
,
“
P
V
c
e
l
l
p
a
r
a
m
e
t
e
r
s
mo
d
e
l
i
n
g
a
n
d
t
e
mp
e
r
a
t
u
r
e
e
f
f
e
c
t
a
n
a
l
y
s
i
s,”
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
Re
n
e
w
a
b
l
e
E
n
e
r
g
y
D
e
v
e
l
o
p
m
e
n
t
,
v
o
l
.
1
0
,
n
o
.
3
,
p
p
.
5
6
3
–
5
7
1
,
A
u
g
.
2
0
2
1
,
d
o
i
:
1
0
.
1
4
7
1
0
/
i
j
r
e
d
.
2
0
2
1
.
3
3
8
4
5
.
[
1
2
]
S
.
S
.
D
h
e
e
b
a
n
,
N
.
B
.
M
u
t
h
u
S
e
l
v
a
n
,
a
n
d
L.
K
r
i
s
h
n
a
v
e
n
i
,
“
P
e
r
f
o
r
m
a
n
c
e
i
mp
r
o
v
e
m
e
n
t
o
f
p
h
o
t
o
-
v
o
l
t
a
i
c
p
a
n
e
l
s
b
y
s
u
p
e
r
-
si
f
t
Lu
o
c
o
n
v
e
r
t
e
r
i
n
st
a
n
d
a
l
o
n
e
a
p
p
l
i
c
a
t
i
o
n
,
”
M
a
t
e
ri
a
l
s
T
o
d
a
y
:
Pr
o
c
e
e
d
i
n
g
s
,
v
o
l
.
3
7
,
p
p
.
1
1
6
3
–
1
1
7
1
,
2
0
2
1
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
ma
t
p
r
.
2
0
2
0
.
0
6
.
3
5
2
.
[
1
3
]
M
.
G
.
V
i
l
l
a
l
v
a
,
J.
R
.
G
a
z
o
l
i
,
a
n
d
E.
R
.
F
.
,
“
M
o
d
e
l
i
n
g
a
n
d
c
i
r
c
u
i
t
-
b
a
s
e
d
s
i
m
u
l
a
t
i
o
n
o
f
p
h
o
t
o
v
o
l
t
a
i
c
a
r
r
a
y
s,”
El
e
t
r
ô
n
i
c
a
d
e
P
o
t
ê
n
c
i
a
,
v
o
l
.
1
4
,
n
o
.
1
,
p
p
.
3
5
–
4
5
,
2
0
0
9
,
d
o
i
:
1
0
.
1
8
6
1
8
/
r
e
p
.
2
0
0
9
.
1
.
0
3
5
0
4
5.
[
1
4
]
Y
.
El
M
o
u
j
a
h
i
d
,
A
.
B
e
n
l
a
f
k
i
h
,
A
.
H
a
d
j
o
u
d
j
a
,
a
n
d
N
.
El
H
a
r
f
a
o
u
i
,
I
m
p
r
o
v
e
a
n
d
a
n
a
l
y
ze
t
h
e
p
e
rf
o
rm
a
n
c
e
o
f
p
h
o
t
o
v
o
l
t
a
i
c
sys
t
e
m
s
c
o
n
t
r
o
l
l
e
d
b
y
a
n
a
d
v
a
n
c
e
d
f
u
zz
y
l
o
g
i
c
m
e
t
h
o
d
f
o
r f
a
s
t
a
n
d
s
t
a
b
l
e
MP
PT
,
v
o
l
.
1
7
,
n
o
.
2
4
.
2
0
2
2
.
[
1
5
]
H
.
M
.
H
.
F
a
r
h
,
A
.
M
.
E
l
t
a
ma
l
y
,
a
n
d
M
.
S
.
A
l
‐
S
a
u
d
,
“
I
n
t
e
r
l
e
a
v
e
d
b
o
o
st
c
o
n
v
e
r
t
e
r
f
o
r
g
l
o
b
a
l
m
a
x
i
mu
m
p
o
w
e
r
e
x
t
r
a
c
t
i
o
n
f
r
o
m
t
h
e
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
m
u
n
d
e
r
p
a
r
t
i
a
l
s
h
a
d
i
n
g
,
”
I
ET
R
e
n
e
w
a
b
l
e
P
o
w
e
r
G
e
n
e
ra
t
i
o
n
,
v
o
l
.
1
3
,
n
o
.
8
,
p
p
.
1
2
3
2
–
1
2
3
8
,
J
u
n
.
2
0
1
9
,
d
o
i
:
1
0
.
1
0
4
9
/
i
e
t
-
r
p
g
.
2
0
1
8
.
5
2
5
6
.
[
1
6
]
A.
H
a
y
a
t
,
D
.
S
i
b
t
a
i
n
,
A
.
F
.
M
u
r
t
a
z
a
,
S
.
S
h
a
h
z
a
d
,
M
.
S
.
J
a
j
j
a
,
a
n
d
H
.
K
i
l
i
c
,
“
D
e
s
i
g
n
a
n
d
a
n
a
l
y
si
s
o
f
i
n
p
u
t
c
a
p
a
c
i
t
o
r
i
n
DC
–
D
C
b
o
o
s
t
c
o
n
v
e
r
t
e
r
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
-
b
a
s
e
d
s
y
st
e
ms,
”
S
u
s
t
a
i
n
a
b
i
l
i
t
y
,
v
o
l
.
1
5
,
n
o
.
7
,
p
.
6
3
2
1
,
A
p
r
.
2
0
2
3
,
d
o
i
:
1
0
.
3
3
9
0
/
s
u
1
5
0
7
6
3
2
1
.
[
1
7
]
E.
M
.
A
l
i
,
A
.
K
.
A
b
d
e
l
s
a
l
a
m,
K
.
H
.
Y
o
u
ssef,
a
n
d
A
.
A
.
H
o
ssam
-
E
l
d
i
n
,
“
A
n
e
n
h
a
n
c
e
d
c
u
c
k
o
o
se
a
r
c
h
a
l
g
o
r
i
t
h
m
f
i
t
t
i
n
g
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
ms’
g
l
o
b
a
l
ma
x
i
mu
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
u
n
d
e
r
p
a
r
t
i
a
l
sh
a
d
i
n
g
c
o
n
d
i
t
i
o
n
s
,
”
En
e
rg
i
e
s
,
v
o
l
.
1
4
,
n
o
.
2
1
,
p
.
7
2
1
0
,
N
o
v
.
2
0
2
1
,
d
o
i
:
1
0
.
3
3
9
0
/
e
n
1
4
2
1
7
2
1
0
.
[
1
8
]
N
.
P
r
a
b
a
h
a
r
a
n
a
n
d
K
.
P
a
l
a
n
i
sam
y
,
“
A
n
a
l
y
si
s
a
n
d
i
n
t
e
g
r
a
t
i
o
n
o
f
mu
l
t
i
l
e
v
e
l
i
n
v
e
r
t
e
r
c
o
n
f
i
g
u
r
a
t
i
o
n
w
i
t
h
b
o
o
s
t
c
o
n
v
e
r
t
e
r
s
i
n
a
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
m,”
E
n
e
r
g
y
C
o
n
v
e
rsi
o
n
a
n
d
M
a
n
a
g
e
m
e
n
t
,
v
o
l
.
1
2
8
,
p
p
.
3
2
7
–
3
4
2
,
N
o
v
.
2
0
1
6
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
e
n
c
o
n
ma
n
.
2
0
1
6
.
0
9
.
0
8
8
.
[
1
9
]
H
.
O
u
i
f
a
k
a
n
d
A
.
I
d
r
i
,
“
A
c
o
mp
r
e
h
e
n
si
v
e
r
e
v
i
e
w
o
f
f
u
z
z
y
l
o
g
i
c
b
a
se
d
i
n
t
e
r
p
r
e
t
a
b
i
l
i
t
y
a
n
d
e
x
p
l
a
i
n
a
b
i
l
i
t
y
o
f
m
a
c
h
i
n
e
l
e
a
r
n
i
n
g
t
e
c
h
n
i
q
u
e
s
a
c
r
o
ss
d
o
m
a
i
n
s,
”
N
e
u
ro
c
o
m
p
u
t
i
n
g
,
v
o
l
.
6
4
7
,
p
.
1
3
0
6
0
2
,
S
e
p
.
2
0
2
5
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
n
e
u
c
o
m.
2
0
2
5
.
1
3
0
6
0
2
.
[
2
0
]
A
.
Y
o
u
s
sf
i
,
A
.
A
l
i
o
u
i
,
a
n
d
Y
.
A
.
E
l
K
a
d
i
,
“
S
t
u
d
y
,
s
i
m
u
l
a
t
i
o
n
a
n
d
r
e
a
l
i
z
a
t
i
o
n
o
f
a
f
u
z
z
y
l
o
g
i
c
-
b
a
s
e
d
M
P
P
T
c
o
n
t
r
o
l
l
e
r
i
n
a
n
i
s
o
l
a
t
e
d
D
C
mi
c
r
o
g
r
i
d
,
”
I
n
d
o
n
e
s
i
a
n
J
o
u
r
n
a
l
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
a
n
d
C
o
m
p
u
t
e
r
S
c
i
e
n
c
e
,
v
o
l
.
3
4
,
n
o
.
3
,
p
.
1
4
2
0
,
Ju
n
.
2
0
2
4
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
e
e
c
s.
v
3
4
.
i
3
.
p
p
1
4
2
0
-
1
4
3
3
.
[
2
1
]
J.
C
a
o
e
t
a
l
.
,
“
F
u
z
z
y
i
n
f
e
r
e
n
c
e
s
y
st
e
m
w
i
t
h
i
n
t
e
r
p
r
e
t
a
b
l
e
f
u
z
z
y
r
u
l
e
s:
A
d
v
a
n
c
i
n
g
e
x
p
l
a
i
n
a
b
l
e
a
r
t
i
f
i
c
i
a
l
i
n
t
e
l
l
i
g
e
n
c
e
f
o
r
d
i
s
e
a
se
d
i
a
g
n
o
s
i
s
—
A
c
o
m
p
r
e
h
e
n
si
v
e
r
e
v
i
e
w
,
”
I
n
f
o
rm
a
t
i
o
n
S
c
i
e
n
c
e
s
,
v
o
l
.
6
6
2
,
p
.
1
2
0
2
1
2
,
M
a
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
i
n
s.
2
0
2
4
.
1
2
0
2
1
2
.
[
2
2
]
A
.
Y
o
u
ssf
i
a
n
d
Y
.
Y
o
u
s
sef
E
l
K
a
d
i
,
“
N
e
w
a
d
v
a
n
c
e
d
st
r
a
t
e
g
y
f
o
r
c
o
n
t
r
o
l
l
i
n
g
t
h
e
c
h
a
r
g
i
n
g
a
n
d
d
i
s
c
h
a
r
g
i
n
g
o
f
a
st
o
r
a
g
e
u
n
i
t
i
n
a
mi
c
r
o
g
r
i
d
u
s
i
n
g
a
f
i
n
i
t
e
c
o
n
t
r
o
l
s
e
t
p
r
e
d
i
c
t
i
v
e
m
o
d
e
l
,
”
S
o
l
a
r
E
n
e
r
g
y
a
n
d
S
u
st
a
i
n
a
b
l
e
D
e
v
e
l
o
p
m
e
n
t
J
o
u
r
n
a
l
,
p
p
.
3
8
–
5
2
,
D
e
c
.
2
0
2
4
,
d
o
i
:
1
0
.
5
1
6
4
6
/
j
ses
d
.
v
1
4
i
S
I
_
M
S
M
S
2
E
.
4
0
4
.
[
2
3
]
K
.
U
l
l
a
h
,
M
.
I
sh
a
q
,
F
.
Tc
h
i
e
r
,
H
.
A
h
mad
,
a
n
d
Z.
A
h
ma
d
,
“
F
u
z
z
y
-
b
a
s
e
d
m
a
x
i
mu
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(
M
P
P
T
)
c
o
n
t
r
o
l
s
y
st
e
m
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
p
o
w
e
r
g
e
n
e
r
a
t
i
o
n
s
y
st
e
m,”
Re
su
l
t
s
i
n
En
g
i
n
e
e
ri
n
g
,
v
o
l
.
2
0
,
p
.
1
0
1
4
6
6
,
D
e
c
.
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
i
n
e
n
g
.
2
0
2
3
.
1
0
1
4
6
6
.
[
2
4
]
B
.
B
e
n
d
i
b
,
H
.
B
e
l
m
i
l
i
,
a
n
d
F
.
K
r
i
m
,
“
A
su
r
v
e
y
o
f
t
h
e
m
o
st
u
s
e
d
M
P
P
T
m
e
t
h
o
d
s:
C
o
n
v
e
n
t
i
o
n
a
l
a
n
d
a
d
v
a
n
c
e
d
a
l
g
o
r
i
t
h
ms
a
p
p
l
i
e
d
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
s
y
st
e
ms,
”
R
e
n
e
w
a
b
l
e
a
n
d
S
u
st
a
i
n
a
b
l
e
E
n
e
r
g
y
Re
v
i
e
w
s
,
v
o
l
.
4
5
,
p
p
.
6
3
7
–
6
4
8
,
M
a
y
2
0
1
5
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
ser.
2
0
1
5
.
0
2
.
0
0
9
.
[
2
5
]
M
.
H
.
I
b
r
a
h
i
m
,
S
.
P
.
A
n
g
,
M
.
N
.
D
a
n
i
,
M
.
I
.
R
a
h
ma
n
,
R
.
P
e
t
r
a
,
a
n
d
S
.
M
.
S
u
l
t
h
a
n
,
“
O
p
t
i
mi
z
i
n
g
st
e
p
-
s
i
z
e
o
f
p
e
r
t
u
r
b
&
o
b
s
e
r
v
e
a
n
d
i
n
c
r
e
me
n
t
a
l
c
o
n
d
u
c
t
a
n
c
e
M
P
P
T
t
e
c
h
n
i
q
u
e
s
u
s
i
n
g
P
S
O
f
o
r
g
r
i
d
-
t
i
e
d
P
V
s
y
st
e
m,
”
I
EEE
Ac
c
e
ss
,
v
o
l
.
1
1
,
p
p
.
1
3
0
7
9
–
1
3
0
9
0
,
2
0
2
3
,
d
o
i
:
1
0
.
1
1
0
9
/
A
C
C
ESS
.
2
0
2
3
.
3
2
4
2
9
7
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.