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Co
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to
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stems:
c
la
ss
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l,
f
uzzy
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ic,
and s
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ATLAB/S
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a
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d
it
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T
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se
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su
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p
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n
ti
a
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S
M
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b
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d
M
P
P
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sy
ste
m
s
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fficie
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sili
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f
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wa
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rg
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ti
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s,
m
a
k
in
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th
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m
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f
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d
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p
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t
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n
v
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m
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n
tal
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d
it
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s
.
K
ey
w
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r
d
s
:
C
o
n
tr
o
l
Fu
zz
y
lo
g
ic
MPPT
Ph
o
to
v
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ltaic
Sli
d
in
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m
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s
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CC B
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C
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A
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Scien
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g
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Ma
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L
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)
Natio
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al
Sch
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o
l o
f
Ap
p
lied
Sc
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s
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I
b
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ity
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ail:
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u
.
u
iz.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
in
cr
ea
s
in
g
wo
r
ld
wid
e
n
ee
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f
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clea
n
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s
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s
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ab
le
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g
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as
in
ten
s
if
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th
e
f
o
cu
s
o
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en
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b
le
en
er
g
y
s
o
u
r
ce
s
,
p
a
r
ticu
lar
ly
s
o
lar
p
o
wer
.
Ph
o
t
o
v
o
ltaic
(
PV)
s
y
s
tem
s
ar
e
at
t
h
e
f
o
r
ef
r
o
n
t
o
f
t
h
is
tr
an
s
itio
n
,
o
f
f
er
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g
a
p
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m
is
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g
s
o
lu
tio
n
to
m
ee
t e
n
er
g
y
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ee
d
s
wh
ile
r
ed
u
cin
g
ca
r
b
o
n
em
is
s
io
n
s
[
1
]
.
Ho
wev
er
,
th
e
ef
f
icien
cy
o
f
PV
s
y
s
tem
s
is
in
h
er
en
tly
lim
ited
b
y
th
eir
ab
ilit
y
to
co
n
tin
u
o
u
s
ly
o
p
er
at
e
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
,
wh
ich
v
ar
ies
d
u
e
to
ch
an
g
in
g
e
n
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
,
s
u
c
h
as
ir
r
ad
ian
ce
a
n
d
tem
p
er
atu
r
e
.
T
h
is
ch
allen
g
e
u
n
d
er
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
ef
f
ec
tiv
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
in
g
(
MPPT
)
tech
n
iq
u
es
[
2
]
.
Sig
n
if
ican
t
r
esear
ch
h
as
b
ee
n
co
n
d
u
cte
d
to
en
h
an
ce
th
e
en
er
g
y
ef
f
i
cien
cy
o
f
PVSs
b
y
im
p
lem
en
tin
g
p
r
e
d
ictiv
e
an
d
t
r
ac
k
in
g
tech
n
iq
u
es
f
o
r
m
ax
im
u
m
p
o
wer
p
o
in
t
ex
tr
ac
tio
n
[
3
]
.
A
r
eliab
le
co
n
tr
o
l
s
y
s
tem
co
n
s
is
ten
tly
tr
ac
k
s
th
e
MPP
u
n
d
er
all
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
,
en
s
u
r
in
g
th
e
s
y
s
tem
o
p
er
ates
at
o
p
tim
al
p
er
f
o
r
m
an
ce
.
Va
r
io
u
s
MPPT
m
eth
o
d
s
h
av
e
b
ee
n
d
ev
elo
p
ed
to
o
p
tim
ize
th
e
en
er
g
y
ex
tr
ac
tio
n
f
r
o
m
PV
s
y
s
tem
s
.
Am
o
n
g
th
ese,
th
e
co
n
v
e
n
tio
n
al
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O
)
[
4
]
,
in
cr
e
m
en
tal
co
n
d
u
cta
n
ce
(
I
NC
)
[
5
]
,
b
ac
k
s
tep
p
in
g
[
6
]
,
f
u
zz
y
lo
g
ic
(
FL)
[
7
]
,
an
d
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
(
SMC
)
[
8
]
.
T
h
ese
m
eth
o
d
s
ca
n
b
e
ch
o
s
en
b
ased
o
n
p
e
r
f
o
r
m
an
c
e
p
ar
am
eter
s
s
u
ch
as
co
m
p
le
x
ity
,
co
n
v
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r
g
en
ce
r
ate
,
s
p
ee
d
,
s
o
f
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co
s
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en
s
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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E
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g
I
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N:
2252
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8
7
9
2
C
o
mp
a
r
a
tive
a
n
a
lysi
s
o
f MP
P
T tec
h
n
iq
u
es fo
r
p
h
o
t
o
vo
lta
ic
s
ystem
s
:
… (
Mo
h
a
med
E
l H
a
f
yd
y
)
689
r
eq
u
ir
em
e
n
t
,
an
d
r
eliab
ilit
y
[
9
]
.
T
y
p
ically
,
MPPT
m
eth
o
d
s
ad
ju
s
t
a
r
ef
er
e
n
ce
s
ig
n
al
—
p
o
s
itiv
e
o
r
n
e
g
ativ
e
—
b
ased
o
n
th
e
o
p
er
atin
g
s
tate
o
f
PVSs
.
W
h
ile
m
o
s
t
tech
n
iq
u
es
p
er
f
o
r
m
well
in
s
tab
le
co
n
d
itio
n
s
,
th
ey
o
f
ten
s
tr
u
g
g
le
wh
e
n
f
ac
e
d
with
r
a
p
id
ch
a
n
g
es
in
wea
th
er
o
r
l
o
ad
.
Ma
n
y
o
f
th
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m
eth
o
d
s
ar
e
b
ased
o
n
th
e
in
cr
em
en
tal
co
n
d
u
ctan
ce
(
I
n
C
o
n
)
an
d
P&
O
alg
o
r
ith
m
s
[
1
0
]
,
wh
ich
r
el
y
o
n
PV
elec
tr
ical
p
ar
am
eter
s
to
d
eter
m
in
e
th
e
MPP.
Ho
wev
er
,
th
ese
ap
p
r
o
ac
h
es
ca
n
lead
to
p
r
ec
is
io
n
er
r
o
r
s
d
u
e
to
th
e
tim
e
lo
s
t
d
u
r
in
g
th
e
s
ea
r
ch
f
o
r
th
e
m
a
x
im
u
m
p
o
w
er
p
o
in
t
[
1
1
]
.
T
o
ad
d
r
ess
th
ese
ch
allen
g
es,
an
im
p
r
o
v
ed
M
PP
T
alg
o
r
ith
m
h
as
b
ee
n
d
ev
elo
p
ed
,
as
h
ig
h
lig
h
te
d
in
[
1
2
]
.
T
h
is
e
n
h
an
ce
d
a
p
p
r
o
ac
h
c
o
m
b
in
es
P&
O
with
FL
co
n
tr
o
l,
aim
i
n
g
to
o
v
er
co
m
e
th
e
lim
itatio
n
s
o
f
tr
ad
itio
n
al
P&
O
m
eth
o
d
s
.
B
y
d
y
n
am
ically
ad
j
u
s
tin
g
th
e
p
er
t
u
r
b
atio
n
am
p
litu
d
e
with
in
th
e
P&
O
alg
o
r
ith
m
,
t
h
is
tech
n
iq
u
e
en
h
a
n
ce
s
tr
an
s
ien
t
r
esp
o
n
s
e
an
d
m
i
n
im
izes
s
tead
y
-
s
tate
v
o
ltag
e
o
s
cillatio
n
s
,
lead
in
g
to
m
o
r
e
e
f
f
icien
t a
n
d
r
eliab
le
p
o
wer
tr
a
ck
in
g
.
Als
o
,
Nad
k
ar
n
i
et
a
l
.
[
1
3
]
en
h
an
ce
s
tr
ad
itio
n
al
MPPT
m
eth
o
d
s
b
y
m
o
d
i
f
y
in
g
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
(
FLC)
an
d
P&
O
te
ch
n
iq
u
es.
T
h
ese
im
p
r
o
v
em
e
n
ts
aim
to
r
e
d
u
ce
s
tead
y
-
s
tate
v
o
ltag
e
o
s
cillatio
n
s
an
d
im
p
r
o
v
e
tr
an
s
ien
t
r
esp
o
n
s
e
in
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
T
wo
MPPT
m
eth
o
d
s
a
r
e
co
m
p
ar
ed
:
P&
O
an
d
SMC
[
1
4
]
.
P&
O
is
g
en
er
ally
ap
p
lie
d
in
s
im
p
le
o
r
s
tan
d
-
alo
n
e
i
n
s
tallatio
n
s
,
wh
ile
SMC
is
b
ette
r
s
u
ited
f
o
r
lar
g
e
r
s
y
s
tem
s
,
s
o
th
e
SMC
h
as
g
ain
ed
a
l
o
t
o
f
attr
ac
tio
n
i
n
th
e
d
esig
n
in
g
o
f
n
o
n
lin
ea
r
co
n
tr
o
l
s
y
s
tem
s
d
u
e
to
its
s
im
p
licity
,
r
o
b
u
s
t
-
n
ess
,
an
d
g
o
o
d
d
y
n
am
ic
b
eh
av
i
o
r
[
1
5
]
.
On
th
e
o
th
er
h
an
d
,
th
e
SMC
tech
n
iq
u
e,
ch
o
s
en
f
o
r
its
r
o
b
u
s
tn
ess
an
d
lo
w
co
m
p
u
tatio
n
al
co
m
p
lex
it
y
,
is
co
m
p
ar
ed
with
tr
ad
itio
n
al
m
eth
o
d
s
lik
e
p
r
o
p
o
r
tio
n
al
in
teg
r
al
d
er
iv
ativ
e
PID
an
d
P&
O,
s
h
o
win
g
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
in
h
an
d
lin
g
s
u
d
d
e
n
ir
r
ad
ian
ce
ch
an
g
es.
E
x
p
er
im
en
tal
v
alid
atio
n
o
n
a
PV
r
o
o
f
to
p
in
s
tallatio
n
c
o
n
f
ir
m
ed
th
e
ap
p
r
o
ac
h
'
s
ef
f
ec
tiv
en
ess
in
m
ax
im
izin
g
en
er
g
y
o
u
t
p
u
t
[
1
6
]
.
MPPT
alg
o
r
ith
m
s
p
la
y
a
cr
u
cial
r
o
le
in
m
a
x
im
izin
g
p
o
wer
o
u
t
p
u
t
u
n
d
er
v
ar
y
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
r
ad
itio
n
al
MPPT
tech
n
iq
u
es,
s
u
ch
as
th
e
P&
O
m
eth
o
d
,
o
f
ten
s
tr
u
g
g
le
to
ad
ap
t
ef
f
ec
tiv
el
y
to
r
ap
id
an
d
u
n
p
r
ed
ictab
le
ch
an
g
es
in
s
o
lar
ir
r
ad
ian
ce
[
1
7
]
,
l
ea
d
in
g
t
o
s
u
b
o
p
tim
al
en
er
g
y
h
ar
v
esti
n
g
.
T
o
ad
d
r
ess
th
ese
lim
itatio
n
s
,
th
is
p
ap
er
p
r
o
p
o
s
es
ad
v
an
ce
d
MPPT
tech
n
iq
u
e
s
b
ased
o
n
SMC
an
d
FLC.
S
MC
i
s
r
en
o
wn
ed
f
o
r
its
r
o
b
u
s
tn
ess
ag
ain
s
t
d
i
s
tu
r
b
an
ce
s
an
d
u
n
ce
r
tain
ties
[
1
8
]
,
wh
ile
FLC
o
f
f
er
s
f
lex
ib
ilit
y
in
h
an
d
lin
g
n
o
n
lin
ea
r
s
y
s
tem
s
an
d
co
m
p
lex
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
es
[
1
9
]
.
B
y
lev
er
ag
in
g
t
h
e
s
tr
en
g
th
s
o
f
b
o
th
ap
p
r
o
ac
h
es,
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
aim
to
en
h
an
ce
th
e
p
r
ec
is
io
n
,
r
esp
o
n
s
e
s
p
ee
d
,
an
d
o
v
er
all
p
er
f
o
r
m
a
n
ce
o
f
MPPT
in
PV
s
y
s
tem
s
.
T
h
is
p
ap
er
aim
s
to
ev
alu
ate
an
d
c
o
m
p
ar
e
t
h
e
e
f
f
ec
tiv
en
ess
o
f
th
ese
th
r
ee
MPPT
tech
n
iq
u
es
in
m
ax
im
izin
g
th
e
ef
f
icien
cy
o
f
PV
s
y
s
tem
s
.
B
y
an
aly
zin
g
th
eir
p
er
f
o
r
m
a
n
ce
u
n
d
er
v
ar
y
i
n
g
ir
r
ad
ian
ce
lev
els,
th
e
s
tu
d
y
s
ee
k
s
to
id
en
tif
y
th
e
m
o
s
t
r
eliab
le
a
n
d
e
f
f
icien
t
m
eth
o
d
f
o
r
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
in
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
.
T
h
e
r
est o
f
th
is
ar
ticle
is
o
r
g
an
ized
as f
o
llo
ws.
Sectio
n
2
p
r
esen
ts
th
e
m
o
d
elin
g
o
f
th
e
PV sy
s
tem
an
d
th
e
ass
o
ciate
d
b
o
o
s
t
co
n
v
er
te
r
,
estab
lis
h
in
g
th
e
f
o
u
n
d
atio
n
al
elem
en
ts
n
ec
ess
ar
y
f
o
r
im
p
lem
en
tin
g
MPPT
alg
o
r
ith
m
s
.
I
n
s
ec
tio
n
3
,
th
e
t
h
r
ee
MPPT
tech
n
i
q
u
es
P&
O,
FLC,
an
d
SMC
ar
e
e
x
p
lain
ed
in
d
etail,
alo
n
g
with
th
eir
r
esp
ec
tiv
e
d
esig
n
p
r
o
ce
s
s
es.
Sectio
n
4
o
f
f
er
s
a
s
im
u
latio
n
s
tu
d
y
co
n
d
u
cte
d
in
MA
T
L
AB
/S
im
u
lin
k
,
co
m
p
ar
in
g
th
e
p
e
r
f
o
r
m
an
ce
o
f
th
ese
th
r
ee
MPPT
m
eth
o
d
s
u
n
d
er
v
a
r
io
u
s
co
n
d
itio
n
s
.
2.
M
E
T
H
O
D
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
m
o
del
R
esear
ch
er
s
h
av
e
d
ev
el
o
p
ed
v
ar
io
u
s
m
o
d
els
to
s
im
u
late
t
h
e
b
eh
a
v
io
r
o
f
p
h
o
to
v
o
ltaic
ce
lls
u
n
d
er
d
if
f
er
en
t
co
n
d
itio
n
s
.
E
ac
h
m
o
d
el
b
u
ild
s
u
p
o
n
th
e
id
ea
l
r
ep
r
esen
tatio
n
,
wh
ich
co
n
s
is
ts
o
f
a
cu
r
r
e
n
t
s
o
u
r
ce
t
o
ca
p
tu
r
e
s
o
lar
en
er
g
y
an
d
a
d
i
o
d
e
to
r
ef
lect
th
e
ch
a
r
ac
ter
is
tics
o
f
th
e
P
-
N
ju
n
ctio
n
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
eq
u
iv
alen
t
elec
tr
ical
cir
cu
it
o
f
th
e
o
n
e
-
d
io
d
e
PV
m
o
d
el
[
2
0
]
.
A
p
h
o
to
v
o
ltaic
c
ell
ca
n
b
e
r
ep
r
esen
ted
as
a
cu
r
r
en
t
s
o
u
r
ce
in
p
a
r
allel
with
a
s
im
p
le
P
-
N
d
io
d
e
an
d
a
s
h
u
n
t
r
esis
to
r
(
R
s
h
)
,
all
co
n
n
ec
ted
in
s
er
ies
with
a
r
esis
tan
ce
(
R
s
)
.
Usi
n
g
Kir
ch
h
o
f
f
'
s
cu
r
r
en
t la
w,
th
e
o
u
tp
u
t c
u
r
r
en
t o
f
th
e
s
o
lar
ce
ll
ca
n
b
e
g
i
v
en
b
y
(
1
)
.
I
PV
=
I
ph
−
I
d
−
I
sh
(
1
)
B
ased
o
n
Sh
o
ck
ley
'
s
d
io
d
e
eq
u
atio
n
,
I
d
is
ex
p
r
ess
ed
as:
I
d
=
I
0
[
e
xp
(
V
pv
+
R
s
I
pv
n
V
T
)
−
1
]
(
2
)
I
0
=
I
rs
.
(
T
T
n
)
3
e
xp
[
q
.
E
g0
n
.
K
×
(
1
T
n
−
1
T
)
]
(
3
)
I
=
I
ph
−
I
0
[
e
xp
(
V
pv
+
R
s
I
pv
n
V
T
)
−
1
]
−
V
pv
+
R
s
I
pv
R
sh
(
4
)
V
T
=
K
T
q
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
8
8
-
700
690
w
h
er
e
I
PV
is
th
e
o
u
tp
u
t
te
r
m
in
al
cu
r
r
en
t,
I
ph
is
th
e
p
h
o
to
c
u
r
r
e
n
t
g
en
er
ated
b
y
th
e
ce
ll
u
n
d
er
s
tan
d
ar
d
t
est
c
o
n
d
itio
n
s
(
STC)
with
G=
1
0
0
0
W
/m
²
an
d
T
=
2
5
°C
,
I
d
is
th
e
c
u
r
r
en
t
p
ass
in
g
th
r
o
u
g
h
th
e
d
io
d
e,
an
d
I
sh
is
th
e
s
h
u
n
t
r
esis
to
r
c
u
r
r
en
t.
I
0
is
th
e
s
atu
r
atio
n
cu
r
r
en
t,
q
is
th
e
ele
ctr
o
n
c
h
ar
g
e,
K
is
t
h
e
B
o
ltzm
an
n
c
o
n
s
tan
t,
n
is
th
e
id
ea
lity
f
ac
t
o
r
r
elativ
e
to
th
e
m
o
d
u
le,
a
n
d
T
is
th
e
d
io
d
e
ju
n
ctio
n
tem
p
er
at
u
r
e
[
2
1
]
.
T
ab
le
1
p
r
esen
ts
th
e
p
ar
am
eter
s
o
f
th
e
PV
m
o
d
el
u
s
ed
in
th
is
s
tu
d
y
,
s
p
ec
if
ically
th
e
p
o
ly
cr
y
s
tallin
e
ty
p
e,
wi
th
a
p
ea
k
p
o
wer
o
f
2
4
0
W
c
u
n
d
er
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC).
I
ph
=
[
I
sc
+
k
i
(
T
−
T
n
)
]
×
G
1000
(
6
)
I
d
=
I
rs
.
(
T
T
n
)
3
e
xp
[
q
.
E
g0
n
.
K
×
(
1
T
n
−
1
T
)
]
(
7
)
Fig
u
r
e
1
.
PV c
ell
m
o
d
el
T
ab
le
1
.
PV p
ar
a
m
etr
es
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
M
a
x
i
m
u
m
p
o
w
e
r
P
m
a
x
2
4
0
W
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
I
p
m
7
.
9
A
V
o
l
t
a
g
e
a
t
m
a
x
i
m
u
m
p
o
w
e
r
V
p
m
3
0
.
2
V
S
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
I
c
c
8
.
3
3
A
O
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
V
o
c
3
7
.
2
V
S
h
u
n
t
r
e
si
st
a
n
c
e
R
sh
1
0
0
0
Ω
S
e
r
i
e
s r
e
si
s
t
a
n
c
e
R
s
0
.
0
0
8
Ω
I
d
e
a
l
i
t
y
f
a
c
t
o
r
n
1
.
2
2
.
2
.
B
o
o
s
t
c
o
nv
er
t
er
T
h
e
b
o
o
s
t
co
n
v
er
ter
is
co
m
m
o
n
ly
u
s
ed
in
r
en
ewa
b
le
en
er
g
y
ap
p
licatio
n
s
,
in
clu
d
i
n
g
s
o
lar
an
d
win
d
p
o
wer
.
Du
e
t
o
th
e
in
ter
m
itten
t
n
atu
r
e
o
f
s
o
lar
en
e
r
g
y
p
r
o
d
u
c
tio
n
,
it
is
im
p
o
r
tan
t
t
o
ad
d
r
ess
th
is
v
ar
iab
ilit
y
to
en
h
an
ce
o
v
er
all
s
y
s
tem
ef
f
icien
cy
[
2
2
]
.
On
e
s
ig
n
if
ica
n
t
ap
p
licatio
n
o
f
th
e
b
o
o
s
t
co
n
v
er
t
er
is
in
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
s
y
s
tem
s
.
Fig
u
r
e
2
illu
s
tr
ates
th
e
s
tr
u
ctu
r
e
o
f
a
b
o
o
s
t
co
n
v
er
ter
,
wh
ic
h
co
n
s
is
ts
o
f
a
PV
Vp
v
,
a
c
o
n
tr
o
lled
s
witch
(
T
)
,
a
n
in
d
u
cto
r
(
L
)
,
a
d
io
d
e
(
D)
,
a
f
ilter
ca
p
ac
ito
r
(
C
)
,
an
d
a
lo
ad
r
esis
tan
ce
o
f
R
=1
0
0
o
h
m
s
.
T
h
e
co
n
v
er
ter
o
p
er
ates
in
c
o
n
tin
u
o
u
s
co
n
d
u
cti
o
n
m
o
d
e
(
C
C
M)
,
with
its
b
eh
av
io
r
d
ep
en
d
in
g
o
n
wh
eth
er
th
e
s
witch
T
is
co
n
d
u
ctin
g
o
r
n
o
t
.
As
a
DC
/DC
c
o
n
v
er
ter
,
th
e
b
o
o
s
t
co
n
v
er
ter
in
cr
ea
s
es
th
e
in
p
u
t
v
o
ltag
e
to
a
h
ig
h
er
lev
el
at
th
e
o
u
tp
u
t.
I
t
r
eg
u
lates
th
e
v
o
lta
g
e
at
th
e
PV
p
an
el
ter
m
in
als
b
ased
o
n
th
e
ch
o
s
en
co
n
tr
o
l stra
teg
y
,
w
h
i
c
h
i
s
i
m
p
le
m
e
n
t
e
d
b
y
a
d
j
u
s
ti
n
g
t
h
e
d
u
t
y
c
y
c
l
e
o
f
t
h
e
v
o
l
t
a
g
e
a
p
p
li
e
d
t
o
th
e
s
w
it
c
h
g
a
t
e
(
T
)
.
Fig
u
r
e
2
.
B
o
o
s
t c
o
n
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
C
o
mp
a
r
a
tive
a
n
a
lysi
s
o
f MP
P
T tec
h
n
iq
u
es fo
r
p
h
o
t
o
vo
lta
ic
s
ystem
s
:
… (
Mo
h
a
med
E
l H
a
f
yd
y
)
691
T
h
e
p
o
wer
f
l
o
w
is
r
eg
u
lated
b
y
ad
ju
s
tin
g
th
e
d
u
ty
cy
cle
α
o
f
th
e
s
witch
in
g
p
er
io
d
T
s
.
Dep
en
d
in
g
o
n
wh
eth
er
th
e
s
witch
(
S)
is
o
n
o
r
o
f
f
,
th
e
c
o
n
v
e
r
ter
o
p
er
ates
in
two
d
is
tin
ct
s
tates:
S
=
0
;
t
ϵ
]
0
;
α
T
s
]
:
W
h
en
th
e
s
witch
is
o
n
,
th
e
d
io
d
e
is
r
e
v
e
r
s
e
-
b
iased
,
p
r
ev
en
tin
g
c
u
r
r
en
t
f
lo
w
th
r
o
u
g
h
it.
D
u
r
in
g
th
is
p
h
ase,
th
e
in
d
u
cto
r
s
to
r
es
en
er
g
y
b
y
d
r
awin
g
cu
r
r
en
t
f
r
o
m
th
e
in
p
u
t
v
o
ltag
e
s
o
u
r
ce
,
wh
ile
th
e
ca
p
ac
ito
r
s
u
p
p
lies
p
o
wer
to
th
e
lo
ad
b
y
d
is
ch
ar
g
in
g
th
r
o
u
g
h
th
e
r
esis
to
r
.
T
h
e
co
r
r
esp
o
n
d
i
n
g
eq
u
atio
n
s
f
o
r
th
is
s
tate
ar
e:
V
−
L
d
i
L
dt
=
0
(
8
)
V
o
u
t
R
−
L
d
V
o
u
t
dt
=
0
(
9
)
t
h
e
two
eq
u
atio
n
s
ab
o
v
e
ca
n
b
e
p
r
esen
ted
in
m
atr
ix
f
o
r
m
as
(1
0
).
[
d
i
L
dt
d
V
o
u
t
dt
]
=
[
0
0
0
−
1
RC
]
[
i
L
V
o
ut
]
+
[
1
L
0
]
V
pv
(1
0
)
S
=
0
;
t
ϵ
[
α
T
s
.
;
T
s
.
]
w
h
en
th
e
s
witch
is
o
f
f
,
th
e
d
io
d
e
D
b
ec
o
m
es
f
o
r
war
d
-
b
ias
ed
,
allo
win
g
cu
r
r
en
t
t
o
f
l
o
w
th
r
o
u
g
h
it.
Du
r
in
g
th
is
p
h
ase,
t
h
e
en
er
g
y
s
to
r
ed
i
n
th
e
in
d
u
ct
o
r
L
is
tr
an
s
f
er
r
e
d
to
th
e
ca
p
ac
ito
r
C
,
wh
ich
h
elp
s
m
ain
tain
th
e
o
u
tp
u
t v
o
ltag
e.
T
h
e
eq
u
atio
n
s
f
o
r
th
is
s
tag
e
ar
e:
V
pv
−
V
o
ut
−
L
d
i
L
dt
=
0
(1
1
)
i
L
−
Vc
R
−
C
d
V
o
u
t
dt
=
0
(1
2
)
t
h
e
two
in
(1
1
)
a
n
d
(
1
2
)
ca
n
al
s
o
b
e
p
r
esen
ted
i
n
m
atr
ix
f
o
r
m
as
(1
3
).
[
d
i
L
dt
d
V
o
u
t
dt
]
=
[
0
−
1
L
1
C
−
1
RC
]
[
i
L
V
o
ut
]
+
[
1
L
0
]
V
pv
(1
3
)
T
h
e
s
tate
-
s
p
ac
e
av
er
ag
in
g
tec
h
n
iq
u
e
h
elp
s
d
er
i
v
e
a
s
im
p
lifie
d
m
o
d
el
o
f
th
e
co
n
v
er
ter
o
v
er
a
f
u
ll
s
witch
in
g
p
er
io
d
.
E
s
s
en
tially
,
th
is
ap
p
r
o
ac
h
r
ep
lace
s
th
e
in
s
tan
tan
eo
u
s
s
tate
-
s
p
ac
e
r
ep
r
esen
tatio
n
with
an
av
er
ag
ed
m
o
d
el
th
at
ca
p
tu
r
e
s
th
e
cir
cu
it
'
s
o
v
er
all
b
eh
av
io
r
th
r
o
u
g
h
o
u
t
T
s
.
Ap
p
ly
in
g
th
is
m
eth
o
d
,
th
e
m
o
d
if
ied
a
v
er
ag
e
d
m
o
d
el
is
ex
p
r
ess
ed
as:
A
=
A
1
α
+
A
2
(
1
−
α
)
(1
4
)
B
=
B
1
α
+
B
2
(
1
−
α
)
(1
5
)
w
h
er
e
th
e
m
atr
ices
A
1
,
A
1
,
B
1
,
an
d
B
2
ar
e
g
iv
en
by
(1
6
).
A
1
=
[
0
0
0
−
1
RC
]
A
2
=
[
0
−
1
L
1
C
−
1
RC
]
B
1
=
[
1
L
0
]
B
2
=
[
1
L
0
]
(1
6
)
Usi
n
g
t
h
e
e
q
u
ati
o
n
s
a
b
o
v
e
t
o
o
b
ta
in
t
h
e
a
v
er
ag
e
d
s
t
at
e
-
s
p
a
ce
m
o
d
el
o
f
th
e
c
o
n
v
e
r
t
er
o
v
e
r
t
h
e
e
n
t
ir
e
p
er
i
o
d
T
s
.
[
d
i
L
dt
d
V
o
u
t
dt
]
=
[
0
−
(
1
−
α
)
L
(
1
−
α
)
C
−
1
RC
]
[
i
L
V
o
ut
]
+
[
1
L
0
]
V
pv
(1
7
)
Def
in
in
g
th
e
s
tate
v
ec
to
r
as
(
18
).
x
=
[
il
V
o
ut
]
T
(
18
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
8
8
-
700
692
T
h
e
(
1
7
)
ca
n
b
e
ex
p
r
ess
ed
as
(
19
)
an
d
(
2
0
).
x
̇
=
Ax
+
B
V
in
(
19
)
y
=
Cx
(2
0
)
W
h
er
e
y
is
th
e
o
u
tp
u
t v
ec
to
r
a
n
d
th
e
s
y
s
tem
m
atr
ices a
r
e
d
e
f
in
ed
as
in
(
2
1
).
A
=
[
0
−
(
1
−
α
)
L
1
−
α
C
−
1
RC
]
B
=
[
1
L
0
]
C
=
[
01
]
(2
1
)
2
.
3
.
M
P
P
T
c
o
ntr
o
llers
2
.
3
.
1
.
P
er
t
urb a
nd
o
bs
er
v
e
m
et
ho
d (
P
&O
)
I
n
a
p
h
o
to
v
o
ltaic
s
y
s
tem
,
th
e
P&
O
m
eth
o
d
is
u
s
ed
to
c
o
n
tr
o
l
a
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
,
wh
ich
tr
an
s
f
o
r
m
s
th
e
f
lu
ctu
atin
g
D
C
v
o
ltag
e
f
r
o
m
s
o
lar
p
a
n
els
in
to
a
s
tab
le
DC
o
u
tp
u
t
s
u
itab
le
f
o
r
th
e
l
o
ad
.
As
illu
s
tr
ated
in
Fig
u
r
e
3
,
th
e
P&
O
alg
o
r
ith
m
r
eg
u
lates
th
is
co
n
v
er
te
r
b
y
co
n
tin
u
o
u
s
ly
ad
ju
s
tin
g
th
e
d
u
t
y
cy
cle
α
o
f
th
e
s
witch
(
S)
.
T
h
is
en
s
u
r
es
th
at
th
e
o
u
tp
u
t
v
o
ltag
e
r
em
ain
s
at
th
e
lev
el
co
r
r
esp
o
n
d
in
g
to
th
e
MPP
o
f
th
e
s
o
lar
p
an
els.
T
h
e
P&
O
m
eth
o
d
is
wid
ely
u
s
ed
f
o
r
MPPT
in
p
h
o
to
v
o
ltaic
s
y
s
tem
s
d
u
e
to
its
s
im
p
licity
an
d
lo
w
d
ep
en
d
e
n
cy
o
n
s
y
s
tem
p
a
r
am
eter
s
.
I
t
wo
r
k
s
b
y
p
e
r
io
d
ically
ad
ju
s
tin
g
th
e
ar
r
ay
v
o
ltag
e
(
e
ith
er
in
cr
ea
s
in
g
o
r
d
ec
r
ea
s
in
g
it
)
a
n
d
co
m
p
ar
in
g
th
e
r
esu
ltin
g
p
o
wer
with
t
h
e
p
r
e
v
io
u
s
cy
cle.
I
f
th
e
p
o
wer
in
cr
ea
s
es,
th
e
p
er
tu
r
b
atio
n
co
n
tin
u
es
in
th
e
s
am
e
d
ir
ec
tio
n
;
o
th
er
wis
e,
it
r
ev
er
s
es.
As
a
r
esu
lt,
ea
c
h
M
PP
T
cy
cle
ca
u
s
es
a
s
lig
h
t
f
lu
ctu
atio
n
in
th
e
a
r
r
ay
’
s
ter
m
in
al
v
o
ltag
e.
W
h
ile
th
e
P&
O
alg
o
r
ith
m
ef
f
ec
tiv
ely
t
r
a
ck
s
th
e
MPP
u
n
d
er
s
tab
le
co
n
d
itio
n
s
,
it
m
ay
s
tr
u
g
g
le
wh
en
atm
o
s
p
h
er
ic
co
n
d
itio
n
s
ch
an
g
e
g
r
a
d
u
ally
o
r
co
n
ti
n
u
o
u
s
ly
,
p
o
ten
tially
lead
in
g
to
p
o
wer
lo
s
s
[
2
3
]
.
2
.
3
.
2
.
F
uzzy
l
o
g
ic
c
o
ntr
o
l
(
F
L
C
)
R
ec
en
tly
,
a
n
u
m
b
er
o
f
ar
t
if
icial
in
tellig
en
ce
-
in
s
p
ir
ed
s
tr
ateg
ies
h
av
e
b
ee
n
d
ev
el
o
p
ed
an
d
im
p
lem
en
ted
as
MPPT
alg
o
r
ith
m
s
,
o
f
ten
r
ef
er
r
ed
to
as
‘
in
tellig
en
t’
d
u
e
to
th
eir
r
o
b
u
s
tn
ess
an
d
ab
ilit
y
to
to
ler
ate
m
o
d
elin
g
in
ac
c
u
r
ac
ie
s
[
2
4
]
.
Am
o
n
g
th
ese
s
tr
ateg
ie
s
is
FL
.
T
h
e
FL
th
eo
r
y
allo
w
s
f
o
r
th
e
m
o
d
elin
g
an
d
r
ig
o
r
o
u
s
p
r
o
ce
s
s
in
g
o
f
i
m
p
r
ec
is
e,
u
n
ce
r
tain
,
an
d
s
u
b
j
ec
tiv
e
in
f
o
r
m
atio
n
,
m
ak
in
g
it
p
ar
ticu
lar
ly
s
u
itab
le
f
o
r
ap
p
r
o
x
im
atin
g
n
o
n
lin
ea
r
f
u
n
ctio
n
s
.
Ho
wev
er
,
im
p
lem
e
n
tin
g
a
f
u
zz
y
lo
g
ic
s
y
s
tem
r
e
q
u
ir
es
a
th
o
r
o
u
g
h
a
n
d
co
m
p
lete
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
s
y
s
tem
to
ac
cu
r
ately
estab
lis
h
th
e
in
f
er
en
ce
r
u
les.
Desig
n
in
g
a
f
u
zz
y
co
n
tr
o
ller
,
s
u
ch
as
th
e
MA
MD
ANI
ty
p
e
u
s
ed
as
a
n
MPPT
alg
o
r
ith
m
,
in
v
o
lv
es
f
o
u
r
k
ey
s
tep
s
:
f
u
zz
if
icatio
n
,
r
u
le
d
ef
in
itio
n
,
f
u
zz
y
in
f
e
r
en
c
e,
an
d
d
ef
u
zz
if
icatio
n
.
T
h
ese
s
tep
s
ar
e
illu
s
tr
ated
in
Fig
u
r
e
4
.
Fig
u
r
e
3
.
P&
O
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
C
o
mp
a
r
a
tive
a
n
a
lysi
s
o
f MP
P
T tec
h
n
iq
u
es fo
r
p
h
o
t
o
vo
lta
ic
s
ystem
s
:
… (
Mo
h
a
med
E
l H
a
f
yd
y
)
693
Fig
u
r
e
4
.
C
o
n
tr
o
l
s
tr
u
ctu
r
e
o
f
MPPT
FL
T
h
e
p
r
o
p
o
s
ed
f
u
zz
y
MPPT
co
n
tr
o
ller
h
as
two
in
p
u
ts
an
d
o
n
e
o
u
tp
u
t.
T
h
e
two
in
p
u
t
v
a
r
ia
b
les
o
f
th
e
FLC
ar
e
th
e
er
r
o
r
(
e)
an
d
th
e
ch
an
g
e
in
er
r
o
r
(
∆e
)
m
ea
s
u
r
ed
at
ea
ch
s
am
p
lin
g
s
tep
,
wh
ile
th
e
o
u
tp
u
t
v
ar
iab
le
(∆
⍺
)
r
ep
r
esen
ts
th
e
in
cr
em
en
t
o
f
th
e
d
u
ty
cy
cle.
T
h
e
two
i
n
p
u
ts
e
an
d
∆e
ar
e
d
ef
in
e
d
as f
o
l
lo
ws:
e
=
∆
Vpv
∆
Ip
v
Ipv
+
Vpv
(2
2
)
∆
e
=
e
(
n
)
−
e
(
n
−
1
)
(2
3
)
w
h
er
e
∆V
p
v
a
n
d
∆
I
p
v
ar
e
r
es
p
ec
tiv
ely
th
e
v
ar
iatio
n
s
in
v
o
l
tag
e
an
d
c
u
r
r
e
n
t
o
f
th
e
s
o
u
r
ce
s
m
ea
s
u
r
ed
at
two
s
am
p
lin
g
p
er
io
d
s
n
an
d
n
-
1
.
T
h
e
v
alu
e
o
f
th
e
er
r
o
r
e(
n
)
ac
tu
ally
r
ef
lects
th
e
s
y
s
tem
's
r
esp
o
n
s
e
in
th
e
'
p
er
tu
r
b
an
d
o
b
s
er
v
e'
m
eth
o
d
,
in
d
icati
n
g
h
o
w
f
ar
it
is
to
th
e
r
ig
h
t
o
r
lef
t
o
f
th
e
o
p
tim
al
v
alu
e.
T
h
e
v
alu
e
o
f
Δ
e(
n
)
d
eter
m
in
es th
e
co
n
tr
o
l e
f
f
o
r
t n
ee
d
ed
to
r
ea
c
h
th
e
o
p
tim
u
m
in
f
in
ite
tim
e.
2
.
3
.
3
.
S
lid
ing
m
o
de
co
ntr
o
l
(
SM
C)
Sli
d
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
is
a
n
o
n
lin
ea
r
co
n
t
r
o
l
ap
p
r
o
ac
h
in
itially
d
esig
n
ed
f
o
r
s
y
s
tem
s
with
ch
an
g
in
g
s
tr
u
ctu
r
es.
On
e
o
f
it
s
k
ey
s
tr
en
g
th
s
is
its
ab
ilit
y
to
en
s
u
r
e
s
tab
ilit
y
wh
ile
r
em
ai
n
in
g
h
i
g
h
ly
r
o
b
u
s
t
ag
ain
s
t
s
ig
n
if
ican
t
v
ar
iatio
n
s
in
s
y
s
tem
p
ar
am
eter
s
o
r
e
x
ter
n
al
d
is
tu
r
b
an
ce
s
.
Un
lik
e
th
e
cla
s
s
ical
m
eth
o
d
u
s
ed
in
s
o
m
e
wo
r
k
s
to
d
ete
r
m
in
e
t
h
e
s
lid
in
g
s
u
r
f
ac
e
b
y
ca
lcu
lati
n
g
s
lid
in
g
c
o
ef
f
icien
ts
,
th
e
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
co
n
ce
p
t
m
o
d
ele
d
in
th
is
s
tu
d
y
is
d
esig
n
e
d
t
o
d
r
iv
e
th
e
s
y
s
tem
to
o
p
er
ate
at
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t
,
m
ea
n
in
g
th
at
t
h
e
s
lid
in
g
s
u
r
f
a
ce
is
eq
u
iv
alen
t to
th
e
MPP
co
n
d
itio
n
[2
5
].
T
h
e
f
ir
s
t
s
tep
in
d
esig
n
in
g
th
e
co
n
tr
o
l
in
v
o
lv
es
s
elec
tin
g
t
h
e
s
lid
in
g
s
u
r
f
ac
e
.
T
h
is
s
u
r
f
a
ce
ca
n
b
e
ch
o
s
en
as
(2
4
).
d
P
pv
d
I
pv
=
d
I²
pv
R
pv
d
I
pv
=
I
pv
(
2R
pv
+
I
pv
d
R
pv
d
I
pv
)
=
0
(2
4
)
Kn
o
win
g
th
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
co
n
d
itio
n
is
g
iv
en
b
y
(2
5
).
d
P
pv
d
I
pv
=
0
(2
5
)
W
h
er
e
R
pv
=
V
pv
I
pv
i
s
th
e
eq
u
iv
alen
t
lo
ad
co
n
n
ec
ted
to
th
e
PV
an
d
I
p
v
i
s
th
e
PV
cu
r
r
en
t.
T
h
e
s
o
lu
tio
n
o
f
(
2
5
)
is
:
2R
pv
+
I
pv
d
R
pv
d
I
pv
.
C
o
n
s
eq
u
en
tly
,
th
e
s
lid
in
g
s
u
r
f
ac
e
is
d
ef
in
ed
as
(2
6
).
S
=
2R
pv
+
I
pv
d
R
pv
d
I
pv
(
2
6
)
Fig
u
r
e
5
illu
s
tr
ates
th
e
P
-
V
c
h
ar
ac
ter
is
tics
an
d
h
o
w
th
e
MPP
s
h
if
ts
alo
n
g
th
e
s
lid
in
g
s
u
r
f
ac
e.
W
h
en
ex
am
in
in
g
th
e
P
-
V
ch
ar
ac
ter
is
tics
o
f
th
e
PV
p
an
el
u
n
d
er
s
p
ec
if
ic
wea
th
er
co
n
d
itio
n
s
,
Fig
u
r
e
6
ca
n
b
e
d
iv
id
e
d
in
to
two
d
is
tin
ct
zo
n
es,
s
ep
ar
ated
b
y
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
,
wh
er
e
th
e
s
lo
p
e
o
f
th
e
cu
r
v
e
is
ze
r
o
(
S=0
)
.
Z
o
n
e
1
co
r
r
esp
o
n
d
s
to
a
p
o
s
itiv
e
s
lo
p
e
(
S
<
0
)
,
wh
ile
zo
n
e
2
c
o
r
r
esp
o
n
d
s
to
a
n
e
g
a
tiv
e
s
lo
p
e
(
S
>
0
)
.
Fo
r
in
s
tan
ce
,
if
th
e
o
p
er
atin
g
p
o
in
t
is
to
th
e
lef
t
o
f
th
e
M
PP
,
th
e
co
n
t
r
o
l
s
h
o
u
ld
m
o
v
e
to
war
d
th
e
s
lid
in
g
s
u
r
f
ac
e
b
y
in
cr
ea
s
in
g
th
e
PV
v
o
ltag
e
Vp
v
.
C
o
n
v
e
r
s
ely
,
if
th
e
o
p
er
atin
g
p
o
in
t
is
to
th
e
r
ig
h
t
o
f
th
e
MPP,
th
e
co
n
tr
o
l
s
h
o
u
ld
ad
ju
s
t
to
war
d
th
e
s
lid
in
g
s
u
r
f
ac
e
b
y
d
ec
r
ea
s
in
g
Vp
v
.
T
o
ac
h
iev
e
th
is
,
th
e
s
witch
in
g
co
n
tr
o
l
law
is
d
ef
in
ed
b
y
(2
7
)
.
α
=
{
α
+
∆
α
if
S
>
0
α
−
∆
α
if
S
<
0
(2
7
)
C
o
n
s
id
er
a
tim
e
-
d
ep
e
n
d
en
t
n
o
n
lin
ea
r
s
witch
in
g
s
y
s
tem
d
ef
in
ed
b
y
(
28
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
8
8
-
700
694
x
̇
(
t
)
=
g
(
x
(
t
)
)
+
φ
(
x
(
t
)
)
.
α
eq
(
28
)
T
h
e
eq
u
iv
ale
n
t c
o
n
tr
o
l is d
eter
m
in
ed
f
r
o
m
(
29
)
.
S
̇
=
[
dS
dx
]
T
X
̇
=
[
dS
dx
]
T
(
f
(
X
)
+
g
(
X
)
)
α
eq
(
29
)
T
h
e
eq
u
iv
ale
n
t c
o
n
tr
o
l c
an
b
e
o
b
tain
ed
f
r
o
m
(3
0
)
.
α
eq
=
[
dS
dx
]
T
f
(
X
)
[
dS
dx
]
T
g
(
X
)
=
1
−
V
e
V
s
(3
0
)
T
h
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
d
ef
i
n
ed
b
y
(3
1
)
.
V
=
1
2
S²
(3
1
)
Fo
r
th
e
s
u
r
f
ac
e
S=0
t
o
b
e
attr
a
ctiv
e,
it is
s
u
f
f
icien
t f
o
r
th
e
d
e
r
iv
ativ
e
with
r
esp
ec
t to
V
to
b
e
n
eg
ativ
e.
V
̇
=
S
̇
S
;
∀
S
≠
0
(3
2
)
T
o
f
in
d
th
is
s
lid
in
g
m
o
d
e
ex
is
ten
ce
th
eo
r
em
,
we
ca
lcu
late
th
e
d
er
iv
ativ
e
o
f
th
e
s
u
r
f
ac
e
S.
S
̇
=
[
dS
dx
]
T
X
̇
=
(
3
d
R
pv
d
I
pv
+
I
pv
∂
²
R
pv
∂
²
I
pv
)
X
̇
(3
3
)
T
h
e
eq
u
iv
ale
n
t d
u
ty
cy
cle
m
u
s
t lie
in
0
<
α
eq
<
1
.
T
h
e
r
ea
l c
o
n
tr
o
l s
i
g
n
a
l
α
is
p
r
o
p
o
s
ed
as
(3
4
).
α
=
1
if
α
eq
+
k
∗
S
≥
1
α
=
α
eq
+
k
∗
S
if
0
<
eq
+
k
∗
S
≤
1
α
=
0
if
α
eq
+
k
∗
S
≤
0
(3
4
)
Fig
u
r
e
5
.
P
-
V
ch
a
r
ac
ter
is
tics
Fig
u
r
e
6
.
I
-
V
an
d
P
-
V
ch
ar
ac
t
er
is
tic
cu
r
v
e
o
f
t
h
e
s
o
lar
ce
ll u
n
d
er
f
i
x
ed
ir
r
a
d
ian
ce
an
d
at
d
if
f
er
en
t te
m
p
er
atu
r
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
C
o
mp
a
r
a
tive
a
n
a
lysi
s
o
f MP
P
T tec
h
n
iq
u
es fo
r
p
h
o
t
o
vo
lta
ic
s
ystem
s
:
… (
Mo
h
a
med
E
l H
a
f
yd
y
)
695
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
MPPT
m
eth
o
d
b
ased
o
n
FLC
an
d
SMC
.
T
o
ev
alu
ate
th
e
r
o
b
u
s
tn
ess
an
d
r
esp
o
n
s
e
s
p
ee
d
o
f
th
e
c
o
n
tr
o
ller
s
,
th
e
s
im
u
latio
n
i
n
v
o
lv
es
v
ar
y
in
g
th
e
ir
r
ad
ian
ce
o
f
th
e
PV
p
an
el
o
v
er
a
1
-
s
ec
o
n
d
p
er
io
d
.
T
h
e
s
im
u
latio
n
s
wer
e
co
n
d
u
cted
u
s
in
g
MA
T
L
AB
Simu
lin
k
.
W
e
b
eg
i
n
b
y
p
r
esen
tin
g
th
e
V
-
I
a
n
d
P
-
I
ch
a
r
ac
ter
is
tics
o
f
th
e
PV
m
o
d
el
u
s
ed
in
th
is
s
tu
d
y
.
T
h
e
ch
ar
ac
ter
is
tic
cu
r
v
es
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
s
h
o
w
th
e
co
r
r
elatio
n
b
etwe
en
cu
r
r
en
t
an
d
v
o
ltag
e,
an
d
b
etwe
en
p
o
wer
an
d
v
o
ltag
e.
T
h
ese
n
o
n
lin
ea
r
cu
r
v
es
d
e
p
en
d
o
n
t
h
e
lev
el
o
f
s
o
lar
ir
r
ad
ian
ce
a
n
d
t
h
e
tem
p
er
atu
r
e
o
f
th
e
ce
ll.
Fig
u
r
e
7
s
h
o
ws
th
e
I
-
V
c
h
ar
ac
ter
is
tic
cu
r
v
e
o
f
th
e
s
o
lar
ce
ll
u
n
d
er
f
ix
ed
i
r
r
ad
ian
ce
an
d
at
d
if
f
er
e
n
t
tem
p
e
r
atu
r
es
,
an
d
Fig
u
r
e
8
u
n
d
er
f
ix
e
d
te
m
p
er
atu
r
e
an
d
at
d
if
f
er
en
t
ir
r
ad
ian
ce
.
T
o
ev
al
u
ate
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
tec
h
n
iq
u
es
f
o
r
MPPT,
Fig
u
r
e
8
s
h
o
ws
th
e
ir
r
ad
ian
ce
p
r
o
f
ile
s
u
b
jecte
d
to
s
u
d
d
en
v
ar
iatio
n
s
.
T
h
e
ir
r
ad
ian
ce
r
ap
id
l
y
ch
an
g
es
b
etwe
en
1
0
0
0
W
/m
²
an
d
7
0
0
W
/m
²,
wh
ile
th
e
tem
p
er
atu
r
e
is
k
ep
t c
o
n
s
tan
t a
t
2
5
°C
.
Fig
u
r
e
7
.
I
-
V
an
d
P
-
V
ch
ar
ac
t
er
is
tic
cu
r
v
e
o
f
t
h
e
s
o
lar
ce
ll
u
n
d
er
f
i
x
ed
tem
p
e
r
atu
r
e
a
n
d
at
d
if
f
er
en
t ir
r
ad
ian
ce
Fig
u
r
e
8
.
I
r
r
ad
ia
n
ce
p
r
o
f
ile
Fig
u
r
es
9
th
r
o
u
g
h
13
p
r
o
v
id
e
a
co
m
p
r
eh
e
n
s
iv
e
ev
alu
atio
n
o
f
th
e
MPPT
p
er
f
o
r
m
a
n
ce
ac
r
o
s
s
th
r
ee
m
eth
o
d
s
:
P&
O,
FLC,
an
d
S
MC.
Fig
u
r
e
9
illu
s
tr
ates
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
'
s
r
esp
o
n
s
e
with
o
u
t
an
y
MPPT
r
eg
u
latio
n
,
r
ev
ea
lin
g
a
s
ig
n
if
i
ca
n
t
d
is
cr
ep
an
c
y
b
etwe
en
t
h
e
ac
tu
al
p
o
wer
o
u
tp
u
t
an
d
th
e
p
o
ten
tial
p
o
wer
t
h
at
co
u
ld
b
e
ac
h
iev
e
d
u
s
in
g
an
M
PP
T
co
n
tr
o
ller
.
T
h
is
h
ig
h
lig
h
ts
th
e
s
u
b
s
tan
tial
en
er
g
y
lo
s
s
es
d
u
e
t
o
th
e
lac
k
o
f
o
p
tim
al
MPP
tr
ac
k
in
g
.
Fig
u
r
e
s
10
to
12
s
h
o
wca
s
e
th
e
s
y
s
te
m
’
s
p
er
f
o
r
m
a
n
ce
with
th
e
P&
O,
FLC,
an
d
SM
C
m
eth
o
d
s
,
r
esp
ec
tiv
ely
.
T
h
e
P
&
O
m
eth
o
d
,
as
d
e
p
icted
in
Fig
u
r
e
10
,
is
ch
ar
ac
ter
ized
b
y
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP.
Du
r
in
g
s
u
d
d
en
ch
an
g
e
s
in
ir
r
ad
ian
ce
,
th
e
P&
O
alg
o
r
ith
m
r
e
q
u
ir
es
tim
e
to
r
ee
s
tab
lis
h
th
e
MP
P,
r
esu
ltin
g
in
tem
p
o
r
ar
y
p
o
we
r
lo
s
s
es.
T
h
ese
o
s
cillatio
n
s
a
n
d
d
elay
s
illu
s
tr
ate
th
e
m
eth
o
d
'
s
lim
i
tatio
n
s
i
n
r
esp
o
n
s
iv
en
ess
an
d
ac
cu
r
ac
y
u
n
d
er
d
y
n
am
ic
e
n
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
.
I
n
co
n
tr
ast,
Fig
u
r
e
11
s
h
o
ws
th
at
th
e
FLC
m
eth
o
d
p
r
o
v
i
d
es
ef
f
ec
tiv
e
an
d
s
tab
le
tr
ac
k
in
g
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t,
d
em
o
n
s
tr
atin
g
its
r
o
b
u
s
tn
ess
an
d
a
d
ap
tab
ilit
y
to
v
a
r
y
in
g
co
n
d
iti
o
n
s
.
Fin
ally
,
Fig
u
r
e
12
h
ig
h
lig
h
ts
th
e
SMC
-
b
ased
MPPT
m
eth
o
d
,
wh
ich
ac
h
iev
e
s
p
r
ec
is
e
an
d
ef
f
icien
t
tr
ac
k
in
g
o
f
t
h
e
MPP.
T
h
is
f
ig
u
r
e
u
n
d
er
s
co
r
es
th
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
an
d
r
eliab
ilit
y
o
f
SMC
,
p
ar
ticu
lar
ly
in
f
lu
ctu
atin
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
o
f
f
er
in
g
a
s
ig
n
if
ica
n
t a
d
v
an
ta
g
e
in
m
ain
tain
i
n
g
o
p
tim
al
p
o
wer
o
u
tp
u
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
8
8
-
700
696
Fig
u
r
e
9
.
PV r
esp
o
n
s
e
with
o
u
t
MPPT
Fig
u
r
e
1
0
.
MPPT
with
P&
O
Fig
u
r
e
1
1
.
MPPT
with
FLC
Fig
u
r
e
1
2
.
MPPT
with
SMC
Fig
u
r
e
13
p
r
esen
ts
a
co
m
p
ar
i
s
o
n
o
f
th
e
th
r
ee
MPPT
co
n
tr
o
l
m
eth
o
d
s
ap
p
lied
to
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
.
T
h
ese
m
eth
o
d
s
wer
e
ev
alu
ated
u
n
d
er
a
ch
a
n
g
e
in
i
r
r
ad
ian
ce
f
r
o
m
1
0
0
0
W
/m
²
to
8
0
0
W
/m
².
I
n
th
e
tr
an
s
ien
t
r
eg
im
e,
all
th
r
ee
m
eth
o
d
s
ex
h
ib
it
s
im
ilar
r
esp
o
n
s
e
tim
es,
with
th
e
SMC
m
eth
o
d
s
h
o
win
g
a
s
lig
h
t
ad
v
an
tag
e
i
n
s
p
ee
d
co
m
p
ar
e
d
to
th
e
P&
O
an
d
FLC
m
eth
o
d
s
.
I
n
th
e
s
tead
y
-
s
tate
r
eg
im
e
,
all
th
r
ee
m
eth
o
d
s
ef
f
ec
tiv
ely
tr
ac
k
th
e
d
esire
d
p
o
wer
r
ef
er
en
ce
.
Ho
wev
er
,
a
n
o
tab
le
d
if
f
er
e
n
ce
is
o
b
s
er
v
ed
i
n
th
e
P&
O
m
eth
o
d
,
wh
ich
ex
h
i
b
its
o
s
cillatio
n
s
ar
o
u
n
d
th
e
r
ef
er
e
n
ce
p
o
wer
,
wh
ile
th
e
FLC
an
d
SMC
m
eth
o
d
s
m
ain
tain
a
s
m
o
o
th
er
tr
ac
k
i
n
g
p
e
r
f
o
r
m
an
c
e.
T
o
m
o
r
e
p
r
ec
is
ely
ev
alu
ate
th
e
q
u
ality
o
f
ea
c
h
m
et
h
o
d
,
a
s
ta
tis
tical
an
aly
s
is
was
co
n
d
u
cted
u
s
in
g
th
e
m
ea
n
ab
s
o
lu
te
p
er
ce
n
ta
g
e
er
r
o
r
(
MA
PE)
.
T
h
is
in
d
icato
r
q
u
a
n
tifie
s
th
e
m
ag
n
itu
d
e
o
f
th
e
e
r
r
o
r
as
a
p
er
ce
n
ta
g
e,
p
r
o
v
id
i
n
g
a
n
o
b
jectiv
e
an
d
c
o
m
p
ar
ativ
e
ass
ess
m
en
t
o
f
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
d
i
f
f
er
en
t
m
eth
o
d
s
[
2
5
].
T
h
e
ca
lcu
latio
n
o
f
th
is
in
d
ex
is
b
as
ed
o
n
t
h
e
r
elativ
e
er
r
o
r
e
q
u
ati
o
n
in
(
35
).
M
A
PE
=
1
N
∑
|
P
o
u
t
−
P
r
ef
P
o
u
t
|
N
t
0
∗
100
(
35
)
Fu
r
th
er
m
o
r
e
,
to
d
eter
m
in
e
th
e
ef
f
icien
cy
o
f
ea
ch
MPPT
co
n
tr
o
ller
in
ter
m
s
o
f
p
o
wer
,
th
e
ef
f
icien
cy
is
ca
lcu
lated
r
elativ
e
t
o
th
e
m
a
x
im
u
m
p
o
wer
th
at
a
PV
s
y
s
tem
co
u
l
d
th
e
o
r
etica
lly
p
r
o
d
u
ce
.
T
h
is
ef
f
icien
cy
,
d
en
o
ted
as η
_
MPPT,
is
d
ef
in
e
d
as
(
36
).
η
MPP
T
=
∫
P
o
u
t
(
t
)
dt
t
0
∫
P
m
ax
(
t
)
dt
t
0
(
36
)
T
h
e
r
esu
lts
o
f
th
e
s
tatis
t
ical
an
aly
s
is
co
n
f
ir
m
ed
th
at
th
e
MPPT
co
n
tr
o
ller
b
ased
o
n
s
lid
in
g
m
o
d
e
co
n
tr
o
l
is
m
o
r
e
ac
cu
r
ate
(
MA
PE
=
2
.
6
4
%)
co
m
p
ar
e
d
to
th
e
co
n
tr
o
ller
b
ased
o
n
th
e
P&
O
alg
o
r
ith
m
(
MA
PE
=
1
1
.
2
5
%)
an
d
FLC
(
MA
PE
=
3
.
1
%).
T
ab
le
2
p
r
esen
ts
th
e
ef
f
icien
cy
an
d
MA
PE
o
f
ea
c
h
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
tech
n
i
q
u
e
f
o
r
th
e
p
r
o
p
o
s
ed
p
h
o
t
o
v
o
l
taic
s
y
s
tem
:
th
e
MPPT
b
ased
o
n
th
e
P&
O
m
eth
o
d
an
d
th
e
MPPT
b
ased
o
n
FL
C
an
d
SM
C
.
T
h
e
r
esu
lts
clea
r
ly
in
d
icate
th
at
th
e
SMC
-
b
a
s
ed
MPPT
ac
h
iev
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
C
o
mp
a
r
a
tive
a
n
a
lysi
s
o
f MP
P
T tec
h
n
iq
u
es fo
r
p
h
o
t
o
vo
lta
ic
s
ystem
s
:
… (
Mo
h
a
med
E
l H
a
f
yd
y
)
697
a
h
ig
h
er
ef
f
icien
cy
(
η
_
MPPT
=
9
8
.
1
1
%)
co
m
p
ar
ed
to
th
e
P&
O
-
b
ased
MPPT
(
η
_
MP
PT
=
9
2
.
8
3
%)
an
d
FLC
(
η
_
MPPT
=
9
5
.
3
2
%).
T
h
is
m
ea
n
s
th
at
SMC
is
m
o
r
e
ef
f
ec
tiv
e
at
ex
tr
ac
tin
g
t
h
e
m
ax
im
u
m
p
o
wer
f
r
o
m
t
h
e
s
o
lar
s
y
s
tem
,
allo
win
g
f
o
r
b
etter
u
tili
za
tio
n
o
f
r
en
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
an
d
m
o
r
e
o
p
tim
al
en
er
g
y
p
r
o
d
u
ctio
n
.
T
h
e
s
u
p
er
i
o
r
p
e
r
f
o
r
m
an
ce
o
f
SMC
in
ter
m
s
o
f
ef
f
icien
cy
i
n
d
icate
s
th
at
it
c
an
m
o
r
e
ac
cu
r
ately
tr
ac
k
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t o
f
th
e
p
h
o
t
o
v
o
ltaic
s
y
s
tem
.
Fig
u
r
e
1
3
.
C
o
m
p
ar
is
o
n
o
f
th
e
th
r
ee
MPPT
co
n
tr
o
l m
et
h
o
d
s
T
ab
le
2
.
MA
PE
an
d
th
e
ef
f
icie
n
cy
o
f
ea
ch
MPPT
C
o
n
t
r
o
l
m
e
t
h
o
d
M
A
P
E
Ef
f
i
c
i
e
n
c
y
P
&O
1
1
.
2
5
%
9
2
.
8
3
%
F
LC
3
.
1
%
9
5
.
3
2
%
S
M
C
2
.
6
4
%
9
8
.
1
1
%
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
p
r
o
v
i
d
es
a
th
o
r
o
u
g
h
ev
alu
atio
n
o
f
th
r
ee
MPPT
tech
n
iq
u
es
:
p
er
tu
r
b
an
d
o
b
s
e
r
v
e
(
P&
O)
,
f
u
zz
y
lo
g
ic
co
n
tr
o
l
(
FLC),
an
d
s
lid
in
g
m
o
d
e
co
n
t
r
o
l
(
SMC
)
f
o
r
o
p
tim
izin
g
p
h
o
to
v
o
ltaic
s
y
s
tem
p
er
f
o
r
m
an
ce
.
W
h
ile
all
th
r
ee
m
eth
o
d
s
d
em
o
n
s
tr
ated
th
e
ab
ilit
y
to
ef
f
ec
ti
v
ely
tr
ac
k
th
e
m
ax
im
u
m
p
o
w
er
p
o
i
n
t,
th
e
SMC
-
b
ased
MPPT
m
eth
o
d
clea
r
ly
d
is
tin
g
u
is
h
ed
its
elf
with
s
u
p
er
io
r
ac
c
u
r
ac
y
an
d
ef
f
icien
cy
.
T
h
is
en
h
an
ce
d
p
er
f
o
r
m
an
ce
s
u
g
g
ests
th
at
SMC
o
f
f
er
s
a
m
o
r
e
r
eliab
le
an
d
r
o
b
u
s
t
s
o
lu
tio
n
u
n
d
e
r
v
ar
y
in
g
en
v
i
r
o
n
m
e
n
tal
co
n
d
itio
n
s
,
m
ak
in
g
it
a
h
ig
h
ly
ef
f
ec
tiv
e
ap
p
r
o
a
ch
f
o
r
im
p
r
o
v
in
g
th
e
ef
f
icien
c
y
an
d
s
tab
ilit
y
o
f
p
h
o
to
v
o
ltaic
en
er
g
y
s
y
s
tem
s
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
h
ig
h
lig
h
t th
e
p
o
ten
t
ial
o
f
SMC
a
s
a
lead
in
g
ch
o
ic
e
f
o
r
ad
v
an
ci
n
g
th
e
p
er
f
o
r
m
an
ce
o
f
r
e
n
ewa
b
le
e
n
er
g
y
tech
n
o
lo
g
ies,
p
ar
ticu
lar
l
y
in
a
p
p
licatio
n
s
wh
er
e
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
ar
e
u
n
p
r
ed
ictab
le
an
d
r
ap
i
d
ly
ch
an
g
in
g
.
ACK
NO
WL
E
DG
M
E
N
T
S
Au
th
o
r
s
m
ay
ac
k
n
o
wled
g
e
a
n
y
p
er
s
o
n
,
in
s
titu
tio
n
,
o
r
d
e
p
ar
tm
en
t
th
at
s
u
p
p
o
r
ted
t
o
a
n
y
p
ar
t
o
f
th
e
s
tu
d
y
.
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
in
v
o
lv
e
d
.
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