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n
s
ar
e
p
o
s
s
ib
le,
in
clu
d
in
g
an
d
its
v
ar
iatio
n
,
as
well
as c
o
m
b
in
atio
n
s
s
u
ch
as
with
d
P,
d
P with
d
V,
an
d
d
P with
d
I
.
T
h
e
n
o
v
elty
o
f
th
is
s
tu
d
y
lies
in
th
e
s
elec
tio
n
o
f
s
p
ec
if
ic
i
n
p
u
t
v
ar
iab
les
f
o
r
t
h
e
f
u
zz
y
co
n
tr
o
ller
,
n
am
ely
d
V
an
d
d
P.
W
h
ile
s
u
cc
ess
f
u
l
h
y
b
r
id
p
e
r
tu
r
b
&
o
b
s
er
v
e
(
P&
O
)
-
f
u
zz
y
lo
g
ic
(
FL
)
tech
n
iq
u
es
h
av
e
ac
h
iev
ed
im
p
r
o
v
ed
r
esu
lts
,
th
e
y
h
av
e
n
o
t
u
tili
ze
d
th
ese
p
r
o
p
o
s
ed
in
p
u
t
v
ar
iab
les.
T
h
ese
v
ar
i
ab
les,
r
ep
r
esen
tin
g
ad
ju
s
tm
en
ts
in
p
o
wer
an
d
v
o
lt
ag
e
ac
co
r
d
in
g
o
n
th
e
P
-
V
cu
r
v
e,
p
r
o
v
i
d
e
a
d
ir
ec
t
an
d
r
ap
id
m
eth
o
d
to
o
p
tim
izin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
is
ch
o
ice
was
m
ad
e
to
ad
d
r
ess
k
ey
ch
allen
g
es
ass
o
ciate
d
wi
th
tr
ad
itio
n
al
s
y
s
tem
s
,
s
u
ch
as sl
o
w
r
esp
o
n
s
e
to
ch
an
g
es in
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
a
n
d
lim
ited
ef
f
ec
tiv
en
ess
u
n
d
er
v
a
r
iab
le
o
r
l
o
w
s
o
lar
ir
r
ad
iatio
n
.
T
o
a
d
d
r
ess
th
ese
li
m
itatio
n
s
,
th
e
f
u
zz
y
lo
g
ic
al
g
o
r
ith
m
was
co
m
b
in
ed
with
th
e
co
n
v
en
tio
n
al
P&
O
co
n
tr
o
ller
,
wh
ich
is
s
im
p
le
a
n
d
r
eliab
le,
b
u
t
also
it
m
ay
e
x
h
ib
it
ex
ce
s
s
iv
e
o
s
cillatio
n
s
ar
o
u
n
d
t
h
e
MPP
u
n
d
er
lo
w
ir
r
ad
iatio
n
[
2
0
]
-
[
2
2
]
.
B
y
m
ix
in
g
th
ese
two
alg
o
r
ith
m
s
,
th
e
aim
was
to
lev
er
ag
e
th
e
ad
v
an
tag
es
o
f
b
o
t
h
m
eth
o
d
s
in
d
ev
el
o
p
in
g
a
m
o
r
e
ef
f
ec
tiv
e,
r
ea
ctiv
e,
an
d
s
tab
le
MPPT
tr
ac
k
in
g
s
o
lu
tio
n
,
ca
p
a
b
le
o
f
d
y
n
am
ically
ad
ap
tin
g
to
v
ar
iab
le
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
[
2
3
]
.
T
h
er
e
ar
e
s
ev
er
al
way
s
to
co
m
b
in
e
P&
O
an
d
f
u
zz
y
l
o
g
ic
tech
n
iq
u
es
f
o
r
MPPT
s
y
s
tem
s
,
ea
c
h
o
f
f
er
in
g
u
n
iq
u
e
ad
v
a
n
tag
es
an
d
im
p
r
o
v
em
en
ts
o
v
e
r
c
o
n
v
e
n
tio
n
al
m
eth
o
d
s
.
Acc
o
r
d
in
g
to
ar
ticle
[
2
4
]
,
an
o
p
tim
ized
P&
O
-
f
u
zz
y
m
eth
o
d
f
o
r
a
n
M
PP
T
co
n
tr
o
ller
s
ig
n
if
ican
tly
o
u
tp
er
f
o
r
m
s
tr
ad
itio
n
al
tech
n
iq
u
es,
p
r
o
v
id
in
g
a
f
ast
r
esp
o
n
s
e
tim
e
o
f
0
.
0
1
5
s
ec
o
n
d
s
m
ar
k
ed
l
y
f
aster
t
h
an
th
e
0
.
0
4
s
ec
o
n
d
s
ty
p
ical
o
f
P&
O
a
n
d
0
.
0
2
s
ec
o
n
d
s
f
o
r
f
u
zz
y
lo
g
ic
(
FL
)
.
Ad
d
itio
n
ally
,
th
is
m
eth
o
d
ex
h
ib
its
n
o
o
v
e
r
s
h
o
o
t
an
d
m
ai
n
tain
s
lo
w
o
s
cillatio
n
tim
es
o
f
0
.
0
2
s
ec
o
n
d
s
(
co
m
p
ar
ed
to
0
.
1
2
s
ec
o
n
d
s
f
o
r
P&
O
an
d
0
.
4
5
s
ec
o
n
d
s
f
o
r
FL)
,
en
s
u
r
i
n
g
g
r
ea
ter
s
tab
ilit
y
ev
en
i
n
th
e
p
r
esen
ce
o
f
n
o
is
e
with
in
th
e
P
V
m
o
d
u
le.
T
h
is
co
m
b
in
atio
n
lev
er
ag
es
th
e
s
im
p
licity
a
n
d
wid
esp
r
ea
d
u
s
e
o
f
P&
O
with
th
e
r
esp
o
n
s
iv
e
ca
p
ab
ilit
ies
o
f
f
u
zz
y
lo
g
ic,
r
esu
ltin
g
in
a
r
o
b
u
s
t
an
d
ef
f
icien
t
MPPT
s
y
s
t
em
.
T
h
ese
f
in
d
in
g
s
ar
e
co
r
r
o
b
o
r
ated
b
y
[
3
]
,
wh
ic
h
in
tr
o
d
u
ce
d
a
m
o
d
if
ied
MPPT
p
er
tu
r
b
&
o
b
s
er
v
e
c
o
n
tr
o
ll
er
th
at
in
te
g
r
ates
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
n
ew h
yb
r
id
MPP
T a
lg
o
r
ith
m
co
mb
in
in
g
P
&
O
a
n
d
fu
z
z
y
lo
g
ic
tech
n
iq
u
es
(
Ou
ma
ima
Mr
h
a
r
)
499
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
with
v
ar
iab
le
s
tep
s
izes.
T
h
is
ap
p
r
o
ac
h
ad
d
r
ess
es
th
e
lim
itatio
n
s
o
f
f
i
x
ed
s
tep
s
ize
P&
O
m
eth
o
d
s
,
s
u
ch
as
s
lo
w
co
n
v
er
g
en
ce
an
d
co
n
s
id
er
ab
le
f
lu
ctu
atio
n
s
ar
o
u
n
d
th
e
MPP.
T
h
e
in
co
r
p
o
r
atio
n
o
f
f
u
zz
y
lo
g
ic
allo
ws f
o
r
d
y
n
am
ic
ad
ju
s
tm
en
t o
f
t
h
e
s
tep
s
ize,
lead
in
g
to
f
aster
r
esp
o
n
s
e
tim
es a
n
d
r
ed
u
ce
d
s
tead
y
-
s
tate
o
s
cillatio
n
s
,
th
u
s
b
o
o
s
tin
g
th
e
s
y
s
tem
'
s
o
v
er
all
ef
f
icien
cy
an
d
d
ep
en
d
a
b
ilit
y
.
Mo
r
eo
v
er
[
1
1
]
,
p
r
o
p
o
s
es
a
n
o
v
el
co
n
ce
p
t
th
at
f
in
e
-
tu
n
es
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
’
s
m
em
b
e
r
s
h
ip
f
u
n
cti
o
n
s
b
ased
o
n
a
P&
O
alg
o
r
ith
m
.
T
h
is
m
eth
o
d
ef
f
ec
tiv
el
y
co
m
b
in
es
t
h
e
ad
v
an
tag
es
o
f
b
o
th
tech
n
iq
u
es,
lead
in
g
to
h
ig
h
ly
ef
f
icien
t
r
esu
lts
.
T
h
e
s
y
s
tem
d
em
o
n
s
tr
ated
a
n
im
p
r
ess
iv
e
y
ield
o
f
ap
p
r
o
x
im
ately
9
9
.
6
%
u
n
d
er
v
ar
y
i
n
g
wea
th
er
co
n
d
itio
n
s
,
s
h
o
wca
s
in
g
its
ab
ili
ty
to
ac
cu
r
ately
tr
ac
k
th
e
MPP
with
m
in
im
al
f
lu
ctu
atio
n
s
an
d
n
o
d
iv
er
g
e
n
ce
,
ev
e
n
d
u
r
i
n
g
r
ap
i
d
ch
an
g
es
in
ir
r
ad
ian
ce
.
T
h
e
m
eth
o
d
'
s
ab
ilit
y
to
b
alan
ce
r
esp
o
n
s
e
s
p
ee
d
,
s
t
ab
ilit
y
,
an
d
ef
f
icien
cy
m
a
k
es
it
a
s
tan
d
o
u
t
am
o
n
g
MPPT
tech
n
iq
u
es,
p
ar
ticu
lar
ly
f
o
r
g
r
id
-
co
n
n
ec
ted
PV sy
s
tem
s
[
1
1
]
,
[
2
5
]
-
[
2
8
]
.
T
h
e
in
itial
p
h
o
to
v
o
ltaic
s
y
s
tem
in
co
r
p
o
r
atin
g
MPPT
tech
n
o
lo
g
y
was
u
n
v
eiled
i
n
1
9
6
8
s
p
e
cif
ically
f
o
r
a
s
p
ac
e
ap
p
licatio
n
[
2
9
]
-
[
3
1
]
.
Fo
llo
win
g
th
at,
r
esear
ch
h
as
in
ten
s
if
ied
to
im
p
r
o
v
e
MPPT
tech
n
iq
u
es,
with
s
ig
n
if
ican
t
p
r
o
g
r
ess
in
ter
m
s
o
f
r
eliab
ilit
y
,
ac
c
u
r
ac
y
,
ea
s
e
o
f
u
s
e,
tr
ac
k
in
g
s
p
ee
d
a
n
d
e
f
f
ic
ien
cy
,
u
s
in
g
s
ea
r
ch
alg
o
r
ith
m
s
,
m
o
d
el
-
b
ased
a
p
p
r
o
ac
h
es,
an
d
m
o
r
e
s
o
p
h
is
ticated
elec
tr
o
n
i
c
d
ev
ices.
T
ec
h
n
o
lo
g
ical
ad
v
an
ce
s
h
a
v
e
co
n
tr
ib
u
ted
to
th
e
wid
esp
r
ea
d
ad
o
p
tio
n
o
f
MPPT
in
a
v
ar
iet
y
o
f
a
p
p
licatio
n
s
,
f
r
o
m
s
m
all
s
tan
d
-
alo
n
e
s
y
s
tem
s
to
lar
g
e
g
r
id
-
c
o
n
n
ec
te
d
s
o
lar
in
s
tallatio
n
s
.
T
y
p
ically
,
th
e
id
ea
l
MPPT
alg
o
r
ith
m
d
em
o
n
s
tr
ates
s
wif
t
r
e
s
p
o
n
s
e
an
d
m
in
im
al
f
lu
ctu
atio
n
s
ar
o
u
n
d
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t,
en
ab
lin
g
it
to
ef
f
ec
tiv
el
y
ad
ap
t
to
s
u
d
d
en
v
ar
iatio
n
s
in
o
u
tp
u
t p
o
wer
[
2
9
]
,
[
3
2
]
.
2.
M
E
T
H
O
D
T
h
e
co
r
e
f
o
c
u
s
o
f
th
is
wo
r
k
is
to
s
tu
d
y
t
h
e
im
p
ac
t
o
f
c
o
m
b
i
n
in
g
P&
O
an
d
f
u
zz
y
lo
g
ic
tec
h
n
iq
u
es
o
n
th
e
p
er
f
o
r
m
a
n
ce
o
f
p
h
o
to
v
o
lta
ic
p
an
els
in
o
r
d
er
to
o
p
tim
izin
g
th
e
ef
f
ec
tiv
en
ess
o
f
co
n
v
er
ti
n
g
s
o
lar
en
er
g
y
i
n
to
elec
tr
ical
p
o
wer
,
wh
ich
is
g
en
er
ally
v
er
y
lo
w
ar
o
u
n
d
9
t
o
1
7
%
[
3
3
]
.
T
h
e
PV m
o
d
u
le
was set u
p
b
y
co
n
n
ec
tin
g
th
e
s
u
g
g
ested
p
h
o
to
v
o
ltaic
m
o
d
u
le
to
a
b
o
o
s
t
DC
D
C
co
n
v
er
ter
cr
ea
tin
g
a
u
n
it.
T
o
ass
ess
an
d
co
m
p
ar
e
its
p
er
f
o
r
m
an
ce
th
e
n
ew
m
o
d
el
u
n
d
er
wen
t
s
im
u
latio
n
u
s
in
g
M
AT
L
AB
Simu
lin
k
s
o
f
twar
e,
al
o
n
g
s
id
e
th
e
P&
O
an
d
FL
m
eth
o
d
s
,
as in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
Pro
p
o
s
ed
s
y
s
tem
m
o
d
elin
g
o
n
MA
T
L
AB
/Si
m
u
lin
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
497
-
508
500
T
h
e
f
u
n
d
am
en
tal
o
p
er
atio
n
o
f
th
e
n
ew
m
o
d
el,
as p
r
esen
ted
i
n
Fig
u
r
e
3
,
is
co
m
p
o
s
ed
o
f
f
o
u
r
s
tag
es:
˗
P<
6
10
MPP
:
Du
r
in
g
th
is
in
itial
p
h
ase,
th
e
s
y
s
tem
im
p
lem
en
ts
a
n
alter
n
atio
n
o
f
th
e
d
u
t
y
cy
cle
b
etwe
en
t
h
e
two
MPPT
alg
o
r
ith
m
s
,
P&
O
,
an
d
FL
.
T
h
is
alter
n
atio
n
m
ak
e
s
it
p
o
s
s
ib
le
to
d
eter
m
in
e
th
e
b
est
o
p
tim
izatio
n
m
eth
o
d
d
e
p
en
d
in
g
o
n
th
e
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
MPP
is
ca
lcu
lated
f
o
r
th
e
PV
p
an
el
b
ased
o
n
its
s
p
ec
if
ic
ch
ar
ac
ter
is
tics
,
in
clu
d
in
g
th
e
I
-
V
cu
r
v
e,
as we
ll a
s
th
e
s
im
u
l
atio
n
v
alu
es o
f
tem
p
er
atu
r
e
an
d
ir
r
ad
iatio
n
.
˗
6
10
MPP
P<
9
10
MPP:
in
th
is
tr
an
s
itio
n
s
tag
e,
th
e
m
o
d
el
f
av
o
r
s
th
e
u
s
e
o
f
t
h
e
P&
O
m
eth
o
d
.
T
h
is
d
ec
is
io
n
is
b
ased
o
n
th
e
d
em
o
n
s
tr
ated
ef
f
icien
cy
in
ca
lc
u
latin
g
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
wh
ic
h
is
b
e
tter
th
an
th
e
FL
m
eth
o
d
.
˗
9
10
MPP
P>M
P
P:
W
h
en
th
e
g
en
er
ated
p
o
wer
is
g
r
ea
ter
th
a
n
o
r
eq
u
al
to
9
0
%
o
f
th
e
m
ax
im
u
m
p
o
wer
,
th
e
m
o
d
el
s
witch
es
to
u
s
in
g
th
e
FL
m
eth
o
d
.
T
h
is
m
eth
o
d
is
ch
o
s
en
b
ec
au
s
e
it
h
as
th
e
ad
v
an
tag
e
o
f
n
o
t
ex
h
ib
itin
g
f
l
u
ctu
atin
g
b
eh
av
i
o
r
ar
o
u
n
d
th
e
MPP,
u
n
lik
e
th
e
P&
O
tech
n
iq
u
e.
˗
P=M
PP
: o
n
ce
th
e
MPP is r
ea
c
h
ed
,
th
e
s
am
e
d
u
ty
c
y
cle
is
u
s
ed
.
T
h
u
s
,
th
e
m
o
d
el
ad
a
p
ts
its
o
p
tim
izatio
n
s
tr
ateg
y
b
ased
o
n
p
r
o
x
im
ity
to
th
e
MPP,
u
s
in
g
P
&
O
f
o
r
th
e
tr
an
s
itio
n
an
d
FL
f
o
r
o
p
tim
iza
tio
n
wh
en
th
e
MPP
is
alm
o
s
t
r
ea
ch
ed
,
w
h
ile
k
ee
p
i
n
g
s
tab
ilit
y
wh
en
th
e
MPP
is
m
ain
tain
ed
.
T
a
b
le
1
p
r
o
v
id
es
a
s
et
o
f
p
ar
am
eter
s
u
s
ed
in
b
u
ild
in
g
a
p
h
o
t
o
v
o
ltaic
(
PV
)
m
o
d
u
le
m
o
d
el
in
MA
T
L
AB
-
Simu
lin
k
.
T
h
ese
p
ar
am
eter
s
ar
e
ess
en
tial
to
ch
ar
ac
ter
ize
an
d
v
alid
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
PV
m
o
d
u
le
in
te
r
m
s
o
f
its
cu
r
r
en
t,
v
o
ltag
e
an
d
p
o
wer
ch
ar
ac
ter
is
tics
.
Fig
u
r
e
s
4
(
a
)
a
n
d
4
(
b
)
s
h
o
ws g
r
ap
h
s
o
f
th
e
P
-
V
an
d
I
-
V
ch
a
r
ac
ter
is
tics
o
f
th
e
s
elec
ted
p
h
o
t
o
v
o
ltaic
s
y
s
tem
f
o
r
th
r
ee
d
iv
er
s
e
ir
r
ad
iatio
n
lev
els.
I
t’
s
n
o
ted
th
at
th
e
m
ax
im
u
m
p
o
wer
in
c
r
ea
s
es a
s
th
e
s
o
lar
r
ad
ian
ce
in
c
r
ea
s
es.
Similar
ly
,
th
e
cu
r
r
en
t a
ls
o
i
n
cr
ea
s
es a
s
th
e
lig
h
t
in
ten
s
ity
co
n
tin
u
es
to
in
c
r
ea
s
e
[
2
4
]
,
[
3
4
]
.
Fig
u
r
e
3.
W
o
r
k
f
lo
w
ch
ar
t
o
f
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
T
ab
le
1
.
PV p
an
el
p
ar
am
eter
s
I
t
e
m
V
a
l
u
e
I
t
e
m
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
(
P
m
p
p
)
2
1
3
.
1
5
W
O
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
o
c
)
36
.
3
V
V
o
l
t
a
g
e
a
t
ma
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
V
m
p
2
9
V
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
V
o
c
(
%
/
°
C
)
-
0
.
3
6
0
9
9
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
p
o
i
n
t
I
mp
7
.
3
5
A
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
I
sc
(
%/
°
C
)
0
.
1
0
2
S
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
I
sc)
7
.
8
4
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
n
ew h
yb
r
id
MPP
T a
lg
o
r
ith
m
co
mb
in
in
g
P
&
O
a
n
d
fu
z
z
y
lo
g
ic
tech
n
iq
u
es
(
Ou
ma
ima
Mr
h
a
r
)
501
(
a)
(
b
)
Fig
u
r
e
4
.
PV p
a
n
el
ch
ar
ac
ter
is
tics
:
(
a)
P
-
V
ch
ar
ac
ter
is
tic
an
d
(
b
)
I
-
V
ch
ar
ac
ter
is
tics
2
.
1
.
Alt
er
na
t
io
n
s
t
a
g
e
Sin
ce
th
e
two
m
eth
o
d
s
P&
O
a
n
d
FL
d
o
n
o
t
p
er
f
o
r
m
well
u
n
d
er
lo
w
ir
r
ad
iatio
n
,
th
e
ap
p
r
o
ac
h
in
v
o
lv
es
m
ax
im
izin
g
th
e
r
esp
o
n
s
iv
e
n
e
s
s
o
f
b
o
th
m
eth
o
d
s
b
y
alter
n
atin
g
b
etwe
en
th
em
.
C
o
n
s
e
q
u
en
tly
,
a
s
tr
ateg
ic
ex
ch
an
g
e
o
f
d
u
ty
c
y
cles
b
etwe
en
th
e
two
co
n
v
en
tio
n
al
MPPT
alg
o
r
ith
m
s
P&
O
an
d
FL
is
ap
p
lied
as
m
en
tio
n
e
d
in
Fig
u
r
e
5
.
T
h
e
f
o
llo
win
g
s
ec
tio
n
s
will p
r
o
v
id
e
d
escr
ip
tio
n
s
o
f
MPPT
m
eth
o
d
s
ap
p
lied
: P&
O
an
d
FL.
Fig
u
r
e
5.
Alter
n
atio
n
s
tag
e
in
MA
T
L
AB
/
S
im
u
lin
k
2
.
2
.
P
&O
s
t
a
g
e
T
h
e
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
o
r
P&
O
tech
n
ic
is
c
o
m
m
o
n
ly
u
tili
ze
d
as th
e
p
r
im
a
r
y
MPPT
m
et
h
o
d
b
ec
au
s
e
o
f
its
s
tr
aig
h
tf
o
r
war
d
im
p
lem
e
n
tatio
n
.
Ho
we
v
er
,
it
h
as
ce
r
tai
n
co
n
s
tr
ain
ts
,
s
u
ch
as
v
ar
iatio
n
s
ar
o
u
n
d
th
e
MPP
an
d
s
lu
g
g
is
h
r
esp
o
n
s
e
tim
e
ca
u
s
ed
b
y
v
ar
iatio
n
s
in
s
o
lar
ir
r
ad
ian
ce
[
3
5
]
.
T
h
e
P&
O
tech
n
ic
o
p
er
ates
b
y
co
n
tin
u
o
u
s
ly
m
ea
s
u
r
in
g
th
e
o
u
tp
u
t
p
o
wer
o
f
th
e
p
h
o
to
v
o
ltaic
ar
r
ay
an
d
m
o
n
ito
r
in
g
th
e
c
h
an
g
es
in
b
o
th
PV
cu
r
r
en
t
an
d
v
o
ltag
e
.
Per
io
d
ically
,
th
e
al
g
o
r
ith
m
co
m
p
ar
es
th
e
cu
r
r
en
t
p
o
wer
v
alu
e
with
th
e
p
r
io
r
v
alu
e
t
o
d
eter
m
in
e
w
h
eth
er
to
a
d
ju
s
t
t
h
e
PV
ar
r
ay
v
o
ltag
e
o
r
cu
r
r
e
n
t
(
b
ased
o
n
th
e
co
n
tr
o
l
s
tr
ateg
y
)
in
t
h
e
s
am
e
o
r
o
p
p
o
s
ite
d
ir
ec
tio
n
,
d
ep
en
d
in
g
o
n
wh
eth
e
r
an
au
g
m
en
tatio
n
o
r
r
ed
u
ctio
n
i
n
o
u
tp
u
t
p
o
wer
is
o
b
s
er
v
ed
[
1
2
]
,
[
3
6
]
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
497
-
508
502
[3
9
]
.
T
h
e
alg
o
r
ith
m
was sim
u
l
ated
o
n
MA
T
L
AB
s
o
f
twar
e
,
a
s
d
is
p
lay
ed
in
Fig
u
r
e
6
wh
ile
i
ts
f
lo
w
is
p
r
esen
ted
in
Fig
u
r
e
7
.
Ho
wev
e
r
,
o
n
ce
t
h
e
MPP
is
a
ttain
ed
,
th
e
s
y
s
tem
ten
d
s
to
o
s
cillate
ar
o
u
n
d
it.
T
h
is
p
r
o
b
lem
h
as
b
ee
n
co
r
r
ec
ted
in
th
is
n
ew
m
eth
o
d
,
b
y
o
p
ti
n
g
f
o
r
th
e
d
u
ty
c
y
cle
o
f
th
e
f
u
zz
y
lo
g
ic
m
et
h
o
d
o
n
ly
i
n
o
r
d
e
r
to
m
i
n
im
ize
th
ese
o
s
cillatio
n
s
.
Fig
u
r
e
6.
P&
O
alg
o
r
ith
m
in
MA
T
L
AB
/
Simu
lin
k
Fig
u
r
e
7.
C
h
ar
ac
ter
is
tic
o
f
P&
O
m
eth
o
d
u
s
ed
2
.
3
.
F
uzzy
lo
g
ic
s
t
a
g
e
T
h
e
f
u
n
d
am
en
tal
p
r
in
cip
le
o
f
a
f
u
zz
y
c
o
n
tr
o
ller
is
p
r
esen
ted
in
Fig
u
r
e
8
,
wh
ich
in
v
o
lv
es
c
o
n
v
er
tin
g
cr
is
p
in
p
u
ts
in
to
f
u
zz
y
in
p
u
ts
t
h
r
o
u
g
h
th
e
a
p
p
licatio
n
o
f
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
t
h
eir
r
esp
ec
tiv
e
d
eg
r
ee
s
o
f
m
em
b
er
s
h
ip
(
k
n
o
wn
as
f
u
zz
i
f
icatio
n
)
.
T
h
e
in
f
e
r
en
ce
en
g
in
e
g
en
er
ates
a
f
u
zz
y
o
u
tp
u
t
b
y
t
ak
in
g
in
to
ac
co
u
n
t
th
e
d
eg
r
ee
s
o
f
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
d
escr
ib
e
in
Fig
u
r
es
9
(
a)
-
9
(
c)
,
an
d
th
e
r
u
le
b
ase
i
n
T
ab
le
2
,
em
p
lo
y
in
g
m
eth
o
d
s
s
u
ch
as
im
p
licatio
n
a
n
d
ag
g
r
eg
atio
n
.
T
o
o
b
tain
a
p
r
ec
is
e
o
u
tp
u
t,
th
e
f
u
zz
y
o
u
t
p
u
t is
tr
an
s
f
o
r
m
ed
in
t
o
a
cr
is
p
o
u
tp
u
t
u
s
in
g
v
ar
io
u
s
ap
p
r
o
ac
h
es,
lik
e
th
e
ce
n
ter
o
f
a
r
ea
m
eth
o
d
(
k
n
o
wn
as
d
ef
u
zz
i
f
icatio
n
)
[
1
2
]
.
T
h
e
in
p
u
t v
ar
ia
b
les,
an
d
ar
e
d
e
f
in
ed
b
y
(
1
)
a
n
d
(
2
)
,
r
esp
ec
tiv
ely
:
=
(
)
−
(
−
1
)
(
1
)
=
(
)
−
(
−
1
)
(
2
)
T
h
e
f
u
zz
y
l
o
g
ic
co
n
tr
o
l
f
o
r
s
ea
r
ch
in
g
th
e
MPP
was
d
esig
n
ed
an
d
test
ed
in
Simu
lin
k
s
o
f
twar
e
,
as
r
ev
ea
led
i
n
Fig
u
r
e
1
0
.
T
h
is
s
y
s
tem
u
tili
ze
s
two
in
p
u
ts
,
d
P
an
d
d
V
at
th
e
s
am
p
lin
g
tim
e
k
.
T
h
e
o
u
tp
u
t
o
f
th
e
f
u
zz
y
lo
g
ic
r
eg
u
lato
r
c
o
r
r
esp
o
n
d
s
to
th
e
d
u
ty
cy
cle
D
[
4
0
]
,
[
4
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
n
ew h
yb
r
id
MPP
T a
lg
o
r
ith
m
co
mb
in
in
g
P
&
O
a
n
d
fu
z
z
y
lo
g
ic
tech
n
iq
u
es
(
Ou
ma
ima
Mr
h
a
r
)
503
Fig
u
r
e
8.
B
lo
ck
s
ch
em
atic
o
f
f
u
zz
y
MPPT
alg
o
r
ith
m
(
a)
(
b
)
(
c)
Fig
u
r
e
9.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
(
a
)
i
n
p
u
t
o
f
d
Pp
v
,
(
b
)
i
n
p
u
t
o
f
d
Vp
v
,
an
d
(
c)
o
u
tp
u
t
o
f
d
D
T
ab
le
2
.
Fu
zz
y
r
u
les
I
n
p
u
t
v
a
r
i
a
b
l
e
(
d
V
)
O
u
t
p
u
t
V
a
r
i
a
b
l
e
(
d
P
)
dV
NB
NS
Z
PS
PB
NB
NS
Z
PS
PB
NS
NS
Z
PS
PS
Z
Z
Z
Z
Z
PS
PS
Z
NS
NS
PB
PS
Z
NS
NB
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
497
-
508
504
2
.
4
.
Ret
urn sta
g
e
Af
ter
ac
h
iev
in
g
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t,
it
is
o
f
ten
ad
v
an
tag
eo
u
s
to
co
n
tin
u
e
u
s
in
g
th
e
s
am
e
d
u
ty
cy
cle
th
at
was
em
p
lo
y
ed
ju
s
t
b
ef
o
r
e
r
ea
c
h
in
g
th
e
MPP
,
as
r
ev
ea
led
in
Fig
u
r
e
1
1
.
T
h
is
is
b
ec
au
s
e
at
th
e
MPP,
th
e
PV
s
y
s
tem
o
p
er
ates
at
its
p
ea
k
p
o
wer
o
u
tp
u
t
.
Als
o
,
an
y
s
ig
n
if
ican
t
d
ev
iatio
n
f
r
o
m
th
e
cu
r
r
en
t
o
p
er
atin
g
co
n
d
itio
n
s
co
u
ld
r
esu
lt in
a
d
r
o
p
in
p
o
wer
p
r
o
d
u
ctio
n
.
Fig
u
r
e
1
0
.
FL
a
lg
o
r
ith
m
in
M
AT
L
AB
/Si
m
u
lin
k
Fig
u
r
e
11.
R
etu
r
n
s
tag
e
in
MA
T
L
AB
/Si
m
u
lin
k
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Simu
latio
n
ex
p
er
im
e
n
ts
wer
e
p
er
f
o
r
m
ed
u
s
in
g
t
h
e
s
u
g
g
ested
h
y
b
r
id
P&
O
-
f
u
zz
y
tec
h
n
ic,
f
o
llo
wed
b
y
co
n
v
en
tio
n
al
P&
O
co
n
tr
o
l
a
n
d
f
u
zz
y
l
o
g
ic
tech
n
ics,
with
t
h
e
aim
o
f
e
v
alu
atin
g
a
n
d
co
m
p
ar
in
g
th
e
m
.
W
h
en
ev
alu
atin
g
th
e
ef
f
ec
tiv
en
ess
o
f
ea
ch
MPPT
r
eg
u
lato
r
,
m
o
s
t
im
p
o
r
tan
ce
is
g
iv
en
to
tim
e
r
esp
o
n
s
e,
s
tab
ilit
y
,
o
v
er
s
h
o
t
a
n
d
o
s
cillatio
n
s
.
T
o
ass
ess
th
e
ef
f
icien
cy
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
,
s
ev
er
al
test
s
ce
n
ar
io
s
wer
e
s
im
u
lated
to
co
m
p
a
r
e
th
e
tr
a
d
itio
n
al
P&
O
co
n
tr
o
ller
,
t
h
e
f
u
zz
y
r
eg
u
lato
r
to
th
e
p
r
o
p
o
s
ed
h
y
b
r
i
d
co
n
t
r
o
ller
.
T
h
r
ee
s
ce
n
ar
io
s
wer
e
cr
ea
ted
r
ep
r
esen
tin
g
ab
r
u
p
t
v
ar
iatio
n
s
o
f
s
o
lar
r
ad
iatio
n
lev
els
an
d
th
e
o
p
e
r
atio
n
al
tem
p
er
atu
r
e
o
f
th
e
p
h
o
to
v
o
ltai
c
m
o
d
u
le.
3
.
1
.
Scena
rio
1
:
T
em
pera
t
ure
o
f
2
5
°
C
a
nd
increm
ent
a
l c
ha
ng
e
in
s
o
la
r
irra
dia
t
io
n
I
n
th
is
ca
s
e,
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
r
eg
u
lato
r
s
was
ev
alu
ate
d
at
an
o
p
er
atin
g
tem
p
e
r
atu
r
e
o
f
2
5
°C
u
s
in
g
in
cr
em
e
n
tal
v
ar
iatio
n
s
in
s
o
lar
ir
r
a
d
ian
ce
.
An
ir
r
a
d
ian
ce
s
ig
n
al
was
em
p
lo
y
ed
,
with
in
cr
ea
s
es
o
f
2
0
0
W
/m
²,
s
tar
tin
g
at
4
0
0
W
/m
²
an
d
r
ea
ch
in
g
8
0
0
W
/m
².
I
r
r
ad
ian
ce
v
ar
iatio
n
s
wer
e
a
p
p
lied
e
v
er
y
0
.
0
2
s
ec
o
n
d
s
,
f
o
r
a
to
tal
s
im
u
latio
n
tim
e
o
f
0
.
1
2
s
ec
o
n
d
s
,
as in
Fig
u
r
e
1
2
.
Fig
u
r
e
1
3
illu
s
tr
ates
th
e
o
u
t
p
u
t
p
o
wer
f
o
r
d
if
f
er
en
t
i
n
cr
ea
s
es
in
s
ig
n
al
ir
r
ad
ian
ce
.
I
n
g
en
er
al,
th
e
f
o
llo
win
g
ca
n
b
e
o
b
s
er
v
ed
:
i)
W
h
en
ir
r
ad
iatio
n
=
4
0
0
W
/m
²:
th
e
h
y
b
r
id
co
n
tr
o
ller
g
i
v
es th
e
b
est p
er
f
o
r
m
an
ce
,
f
o
llo
wed
b
y
th
e
P&
O
c
o
n
tr
o
ll
er
an
d
t
h
e
f
u
zz
y
co
n
tr
o
ller
r
eg
ar
d
in
g
r
esp
o
n
s
e
tim
e
a
n
d
s
tab
i
lity
;
th
is
is
r
ef
lecte
d
b
y
th
e
f
ac
t
th
at
t
h
e
c
h
o
s
en
f
u
z
zy
co
n
tr
o
ller
d
o
es n
o
t
g
iv
e
g
o
o
d
p
r
ec
is
io
n
d
u
r
in
g
l
o
w
ir
r
a
d
i
atio
n
[
2
3
]
;
ii)
W
h
en
ir
r
ad
iatio
n
=
6
0
0
W
/m
²:
th
e
h
y
b
r
id
co
n
tr
o
ller
r
em
ain
s
th
e
m
o
s
t
ef
f
icien
t,
wit
h
n
o
ap
p
ar
en
t
o
s
cillatio
n
s
an
d
wit
h
r
em
ar
k
ab
le
s
p
ee
d
; a
n
d
iii)
W
h
en
ir
r
ad
iatio
n
=
8
0
0
W
/m
²:
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
th
r
ee
co
n
t
r
o
ller
s
is
g
en
er
ally
s
atis
f
ac
to
r
y
,
alth
o
u
g
h
th
er
e
a
r
e
s
lig
h
t
f
lu
ctu
atio
n
s
in
th
e
cu
r
v
e
o
f
th
e
P&
O
c
o
n
tr
o
ller
an
d
a
s
lig
h
t
r
esp
o
n
s
e
d
elay
in
th
e
ca
s
e
o
f
th
e
FL
co
n
tr
o
ller
.
Fig
u
r
e
1
2
.
I
n
cr
e
m
en
tal
ch
an
g
e
in
s
o
lar
ir
r
ad
iatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
n
ew h
yb
r
id
MPP
T a
lg
o
r
ith
m
co
mb
in
in
g
P
&
O
a
n
d
fu
z
z
y
lo
g
ic
tech
n
iq
u
es
(
Ou
ma
ima
Mr
h
a
r
)
505
Fig
u
r
e
13.
Ou
tp
u
t
p
o
wer
o
f
th
e
PV m
o
d
u
le
f
o
r
in
cr
e
m
en
tal
v
ar
iatio
n
in
s
o
lar
i
r
r
ad
ian
ce
3
.
2
.
Scena
rio
2
:
T
em
pera
t
ure
=
25
°
C
decr
em
ent
a
l c
ha
ng
e
in
s
o
la
r
irra
dia
t
io
n
T
h
is
s
ce
n
ar
io
d
ea
ls
with
th
e
b
eh
av
io
r
o
f
MPPT
co
n
tr
o
ller
s
with
a
d
ec
r
ea
s
e
in
ir
r
ad
iatio
n
th
at
v
ar
ies
b
etwe
en
8
0
0
,
6
0
0
,
an
d
4
0
0
W
/m
²
,
as
s
ee
n
in
Fig
u
r
e
1
4
,
wh
i
le
m
ain
tain
in
g
a
f
ix
e
d
tem
p
e
r
atu
r
e
o
f
2
5
°C
.
T
h
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
o
b
tain
ed
f
o
r
th
e
ir
r
a
d
ian
ce
le
v
els
o
f
8
0
0
W
/m
²,
6
0
0
W
/m
²
,
an
d
4
0
0
W
/m
²
ar
e
6
8
7
.
2
W
,
5
1
8
W
,
an
d
3
4
5
W
r
esp
ec
tiv
ely
,
in
ac
co
r
d
an
ce
wit
h
th
e
v
alu
es
p
r
esen
ted
in
Fig
u
r
e
1
5
.
H
o
wev
er
,
it'
s
wo
r
th
em
p
h
asizin
g
th
at:
i)
T
h
e
FL
co
n
tr
o
ller
e
x
h
ib
its
s
lo
w
b
e
h
av
io
r
a
n
d
p
o
o
r
tr
ac
k
i
n
g
ac
c
u
r
ac
y
a
t
all
ir
r
a
d
iatio
n
lev
els
co
m
p
ar
ed
to
o
th
e
r
co
n
tr
o
ller
s
test
ed
,
with
th
e
ap
p
ea
r
an
ce
o
f
s
ig
n
if
ican
t
f
lu
ctu
atio
n
s
a
r
o
u
n
d
th
e
m
ax
i
m
u
m
p
o
wer
p
o
in
t
f
o
r
th
e
P&
O
co
n
tr
o
ller
;
ii)
R
eg
ar
d
in
g
th
e
P&
O
co
n
tr
o
ller
,
th
e
r
esp
o
n
s
e
tim
e
in
d
icate
d
in
th
e
cu
r
v
e
is
n
o
tab
ly
h
ig
h
er
th
a
n
th
at
o
f
t
h
e
FL
alg
o
r
ith
m
,
th
e
latter
p
r
e
s
en
ts
a
v
er
y
r
em
a
r
k
ab
le
s
tab
ili
ty
co
m
p
a
r
ed
to
t
h
e
P&
O
; a
n
d
iii)
T
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
P&
O
-
FL
alg
o
r
ith
m
g
en
e
r
ates th
e
b
est r
esu
lts
.
Fig
u
r
e
14.
Dec
r
em
en
tal
ch
a
n
g
e
in
s
o
lar
ir
r
ad
iatio
n
Fig
u
r
e
15.
Ou
tp
u
t
p
o
wer
o
f
th
e
PV m
o
d
u
le
f
o
r
d
ec
r
em
en
tal
v
ar
iatio
n
in
s
o
lar
i
r
r
ad
iatio
n
3
.
3
.
Scena
rio
3
:
So
la
r
irra
dia
t
i
o
n o
f
8
0
0
W/m
²
increm
ent
a
l c
ha
ng
e
in t
em
pera
t
ure
T
h
i
s
l
a
s
t
s
c
e
n
a
r
i
o
e
v
a
l
u
a
t
e
s
t
h
e
e
f
f
e
c
t
i
v
e
n
e
s
s
o
f
t
h
e
M
P
P
T
a
l
g
o
r
i
t
h
m
s
i
n
t
h
e
p
r
e
s
e
n
c
e
o
f
a
g
r
a
d
u
a
l
t
e
m
p
e
r
a
t
u
r
e
v
a
r
i
a
t
i
o
n
,
w
h
i
l
e
m
a
i
n
t
a
i
n
i
n
g
a
f
i
x
e
d
v
a
l
u
e
o
f
i
r
r
a
d
i
a
t
i
o
n
a
t
8
0
0
W
/
m
²
.
T
h
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