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[
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,
[
3
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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K
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2781
So
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4
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[
7
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d
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tech
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[
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e
wid
ely
u
s
ed
d
u
e
to
th
eir
s
im
p
licity
,
lo
w
co
s
t
,
an
d
r
eliab
ilit
y
u
n
d
e
r
s
tab
le
co
n
d
itio
n
s
.
Ho
wev
e
r
,
t
h
ey
s
u
f
f
e
r
f
r
o
m
in
e
f
f
ec
tiv
en
es
s
in
r
ap
id
ly
ch
an
g
in
g
clim
atic
co
n
d
itio
n
s
,
s
lo
wer
co
n
v
er
g
en
ce
to
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
,
an
d
p
o
ten
tial
o
s
cillatio
n
s
ar
o
u
n
d
th
e
p
ea
k
,
wh
ich
ca
n
r
ed
u
ce
th
e
o
v
er
all
s
y
s
tem
ef
f
icien
c
y
.
T
o
ad
d
r
ess
th
ese
p
r
o
b
lem
s
,
in
te
llig
en
t
an
d
n
o
n
lin
ea
r
MPPT
m
eth
o
d
s
h
a
v
e
b
ee
n
in
tr
o
d
u
ce
d
,
s
u
ch
as
f
u
zz
y
l
o
g
i
c
(
FL)
,
wh
ich
is
p
r
esen
ted
in
[
9
]
.
T
h
e
wo
r
k
in
[
1
0
]
p
r
o
p
o
s
ed
an
ar
tific
ial
n
eu
r
al
n
etwo
r
k
(
ANN)
.
I
n
teg
r
atin
g
ANN
in
to
p
h
o
to
v
o
ltaic
s
y
s
tem
s
o
f
f
er
s
a
p
r
o
m
is
in
g
s
o
lu
tio
n
,
p
o
ten
tially
in
cr
ea
s
in
g
ef
f
icien
cy
b
y
2
–
3
%.
Par
tial
s
war
m
o
p
tim
izatio
n
(
PS
O)
is
s
tu
d
ied
in
[
1
1
]
.
I
n
n
o
n
lin
ea
r
co
n
t
r
o
ller
s
[
1
2
]
p
r
o
p
o
s
ed
a
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
(
SMC
)
an
d
[
1
3
]
p
r
o
p
o
s
ed
a
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
.
Hy
b
r
i
d
tech
n
iq
u
es
aim
to
im
p
r
o
v
e
tr
a
ck
in
g
ac
cu
r
ac
y
,
s
p
ee
d
,
an
d
ad
ap
tab
ilit
y
b
y
tak
i
n
g
ad
v
an
tag
e
o
f
b
o
t
h
tr
ad
itio
n
al
an
d
ad
v
an
ce
d
tech
n
i
q
u
es.
T
h
e
wo
r
k
[
1
4
]
p
r
esen
ts
an
o
p
tim
al
f
u
zz
y
lo
g
ic
co
n
t
r
o
ller
-
b
ased
PS
O
f
o
r
a
p
h
o
to
v
o
ltaic
s
y
s
tem
.
[
1
5
]
p
r
o
p
o
s
ed
an
MPPT
tech
n
i
q
u
e
b
a
s
ed
o
n
ar
tific
ial
n
e
u
r
al
n
etwo
r
k
s
co
m
b
in
ed
with
b
ac
k
s
tep
p
in
g
.
I
n
[
1
6
]
,
th
e
a
u
th
o
r
s
p
r
o
p
o
s
e
a
co
m
b
in
atio
n
o
f
i
n
cr
em
en
tal
co
n
d
u
ctio
n
an
d
f
u
zz
y
lo
g
ic.
T
h
is
p
ap
er
c
o
m
p
ar
es
a
n
MPPT
tech
n
iq
u
e
b
ased
o
n
ar
tifi
cial
n
eu
r
al
n
etwo
r
k
s
with
s
ev
er
al
o
th
er
tech
n
iq
u
es,
b
o
th
n
o
n
lin
ea
r
an
d
c
o
n
v
e
n
tio
n
al,
i
n
clu
d
in
g
f
u
zz
y
lo
g
ic
,
b
ac
k
s
tep
p
in
g
,
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
atio
n
,
an
d
in
cr
em
en
tal
co
n
d
u
ctan
ce
.
T
h
is
co
m
p
ar
is
o
n
aim
s
to
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
o
f
ea
ch
tech
n
iq
u
e
in
ter
m
s
o
f
s
p
ee
d
,
ef
f
icien
cy
,
an
d
s
tab
ilit
y
u
n
d
er
co
n
s
tan
t
o
r
v
ar
iab
le
clim
a
tic
co
n
d
itio
n
s
.
T
h
is
d
etailed
an
aly
s
is
p
r
o
v
id
es
a
d
ee
p
er
u
n
d
e
r
s
tan
d
in
g
o
f
th
e
s
tr
en
g
th
s
an
d
lim
itatio
n
s
o
f
ea
ch
tech
n
iq
u
e,
g
iv
i
n
g
r
esear
ch
er
s
th
e
in
f
o
r
m
atio
n
n
ec
ess
ar
y
to
s
elec
t
th
e
m
o
s
t
s
u
itab
le
tech
n
iq
u
e
f
o
r
th
eir
p
h
o
to
v
o
ltaic
s
y
s
tem
ap
p
licatio
n
.
T
h
is
ch
o
ice
s
h
o
u
ld
b
e
b
ased
o
n
im
p
o
r
ta
n
t
m
et
r
ics
s
u
ch
as
p
e
r
f
o
r
m
an
ce
,
co
s
t,
an
d
co
m
p
lex
ity
.
T
h
e
p
ap
er
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
i)
Sectio
n
2
d
etails
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
;
ii)
Sectio
n
3
p
r
esen
ts
th
e
tech
n
iq
u
e
f
o
r
tr
ac
k
in
g
m
ax
im
u
m
p
o
wer
p
o
i
n
ts
;
iii)
Sectio
n
4
p
r
esen
ts
th
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
;
an
d
iv
)
T
h
e
p
ap
er
co
n
clu
d
es with
a
c
o
n
clu
s
io
n
.
2.
P
H
O
T
O
VO
L
T
A
I
C
SY
ST
E
M
T
h
e
p
u
r
p
o
s
e
o
f
th
e
PV
s
y
s
tem
s
h
o
wn
in
Fig
u
r
e
1
is
to
m
a
x
im
ize
th
e
p
o
wer
ex
tr
ac
ted
f
r
o
m
th
e
PV
ar
r
ay
.
T
h
e
c
o
n
tr
o
l
m
ec
h
a
n
is
m
o
f
t
h
e
s
y
s
tem
in
clu
d
es
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
,
wh
ich
tak
es
th
e
d
u
t
y
cy
cle
(
D)
g
en
e
r
ated
b
y
th
e
MPPT
tech
n
iq
u
e
as
in
p
u
t
to
p
r
o
d
u
ce
a
co
n
tr
o
l
s
ig
n
al
th
at
r
e
g
u
lates
th
e
DC
-
DC
co
n
v
er
ter
s
witch
S
(
ty
p
ically
a
MO
SF
E
T
o
r
I
GB
T
)
[
1
7
]
.
T
h
e
MPPT
tech
n
iq
u
e
d
y
n
am
i
ca
lly
ad
ju
s
ts
D
to
m
ain
tain
th
e
PV a
r
r
ay
at
its
MPP,
ad
ap
tin
g
to
v
ar
iatio
n
s
in
s
o
lar
ir
r
ad
ian
ce
a
n
d
tem
p
e
r
atu
r
e
[
1
5
]
.
T
h
e
DC
-
DC
co
n
v
er
ter
m
o
d
u
lates
v
o
ltag
e
V
pv
an
d
c
u
r
r
e
n
t
I
pv
o
f
th
e
ar
r
a
y
to
m
atch
th
e
l
o
ad
r
eq
u
i
r
em
e
n
ts
,
en
s
u
r
in
g
th
at
th
e
PV a
r
r
ay
r
em
ain
s
at
its
MPP.
Fig
u
r
e
1
.
Ph
o
to
v
o
ltaic
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2780
-
2
7
9
1
2782
T
h
e
m
ath
em
atica
l m
o
d
el
o
f
t
h
e
s
y
s
tem
is
d
escr
ib
ed
b
y
(
1
)
-
(
3
)
.
{
ⅆ
ⅆ
=
−
ⅆ
ⅆ
=
−
(
1
−
)
ⅆ
ⅆ
=
(
1
−
)
−
(
1
)
(
2
)
(
3
)
T
h
e
o
u
t
p
u
t
v
o
lt
a
g
e
o
f
t
h
e
DC
-
DC
c
o
n
v
er
te
r
ca
n
b
e
ex
p
r
ess
e
d
as
(
4
)
:
=
1
1
−
(
4
)
w
h
e
r
e
D
is
b
o
u
n
d
e
d
w
it
h
i
n
th
e
i
n
te
r
v
al
[
0
,
1
]
.
3.
M
AXI
M
U
M
P
O
WE
R
P
O
I
N
T
T
RA
CK
I
NG
T
E
CH
NIQU
E
3
.
1
.
ANN
-
ba
s
ed
M
P
P
T
t
ec
h
niq
ue
An
ar
tific
ial
n
eu
r
al
n
etwo
r
k
is
a
ty
p
e
o
f
co
m
p
u
tatio
n
al
m
o
d
el
in
s
p
ir
ed
b
y
th
e
s
tr
u
ctu
r
e
an
d
f
u
n
ctio
n
o
f
b
io
lo
g
ical
n
eu
r
o
n
s
.
I
t
co
n
s
i
s
ts
o
f
in
ter
co
n
n
ec
ted
n
o
d
es,
c
alled
ar
tific
ial
n
eu
r
o
n
s
,
wh
ich
ar
e
r
esp
o
n
s
ib
le
f
o
r
p
r
o
ce
s
s
in
g
an
d
tr
an
s
m
itti
n
g
i
n
f
o
r
m
atio
n
.
I
n
teg
r
atin
g
ANN
in
to
p
h
o
to
v
o
ltaic
s
y
s
tem
s
h
as
th
e
p
o
ten
tial
to
im
p
r
o
v
e
en
er
g
y
e
f
f
icien
cy
an
d
o
p
tim
ize
p
o
wer
o
u
t
p
u
t.
B
y
a
n
aly
zin
g
d
ata
f
r
o
m
v
ar
io
u
s
clim
atic
f
ac
to
r
s
,
th
ese
n
etwo
r
k
s
ca
n
p
r
e
d
ict
en
er
g
y
p
r
o
d
u
cti
o
n
an
d
im
p
r
o
v
e
th
e
o
v
er
all
m
an
ag
em
e
n
t
o
f
PV
s
y
s
tem
s
[
1
8
]
,
[
1
9
]
.
T
h
er
e
ar
e
d
if
f
e
r
en
t
ty
p
es
o
f
a
r
tific
ial
n
eu
r
al
n
etwo
r
k
ar
c
h
itectu
r
es.
Fig
u
r
e
2
illu
s
tr
ates
th
e
f
ee
d
f
o
r
war
d
n
eu
r
al
n
etwo
r
k
ar
c
h
itectu
r
e,
wh
ich
i
s
ch
ar
ac
ter
ized
b
y
its
s
im
p
licity
.
I
n
th
is
ty
p
e
o
f
n
etwo
r
k
,
d
ata
f
lo
ws
d
ir
ec
tly
f
r
o
m
th
e
in
p
u
t
lay
er
to
t
h
e
o
u
t
p
u
t
lay
e
r
with
o
u
t
cy
cles o
r
l
o
o
p
s
[
2
0
]
.
T
h
e
i
n
ter
co
n
n
ec
ted
n
e
u
r
o
n
s
a
r
e
ar
r
an
g
e
d
in
to
lay
er
s
,
with
ea
ch
la
y
er
f
u
l
ly
co
n
n
ec
ted
to
th
e
s
u
b
s
eq
u
en
t
o
n
e.
I
t
tak
es
s
o
lar
ir
r
ad
ia
n
ce
an
d
tem
p
e
r
atu
r
e
as
in
p
u
ts
an
d
v
o
ltag
e
at
MPP
(
V
mpp
)
as
o
u
tp
u
t.
T
h
e
er
r
o
r
b
etw
ee
n
th
e
V
mpp
an
d
th
e
ac
tu
al
p
h
o
to
v
o
ltaic
v
o
ltag
e
(V
pv
)
is
th
en
ca
lcu
lated
.
T
h
e
r
esu
ltin
g
er
r
o
r
s
ig
n
al
is
f
ed
in
to
a
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI)
co
n
tr
o
ller
.
T
h
e
PI
co
n
tr
o
ller
p
r
o
ce
s
s
es
th
e
er
r
o
r
an
d
g
e
n
er
ates
D
u
s
ed
t
o
co
n
tr
o
l
th
e
b
o
o
s
t
co
n
v
er
ter
.
B
y
co
n
tin
u
o
u
s
ly
ad
j
u
s
tin
g
th
e
d
u
ty
cy
cle,
t
h
e
co
n
tr
o
ller
en
s
u
r
es
th
at
th
e
p
h
o
to
v
o
ltai
c
s
y
s
tem
o
p
er
ates
at
its
m
ax
i
m
u
m
p
o
wer
p
o
in
t,
th
er
eb
y
o
p
tim
izin
g
th
e
ef
f
icie
n
cy
o
f
th
e
en
e
r
g
y
c
o
n
v
e
r
s
io
n
.
Fig
u
r
e
2
.
Ar
c
h
itectu
r
e
o
f
th
e
ANN
-
b
ased
MPPT
tech
n
iq
u
e
f
o
r
p
h
o
to
v
o
ltaic
s
y
s
tem
s
3
.
2
.
F
uzzy
lo
g
ic
co
ntr
o
ller
Fu
z
zy
lo
g
i
c
is
a
m
at
h
em
ati
ca
l
f
r
am
ew
o
r
k
d
es
ig
n
e
d
t
o
m
o
d
el
th
e
u
n
c
er
tai
n
t
y
a
n
d
i
m
p
r
ec
is
i
o
n
i
n
h
e
r
e
n
t
in
h
u
m
an
r
ea
s
o
n
i
n
g
,
a
ll
o
wi
n
g
f
o
r
v
a
r
i
a
b
le
d
eg
r
e
es o
f
tr
u
t
h
b
etwe
e
n
0
a
n
d
1
,
r
at
h
er
th
a
n
b
i
n
a
r
y
v
al
u
es o
f
0
o
r
1
(
t
r
u
e
o
r
f
als
e)
[
2
1
]
,
[
2
2
]
.
T
h
is
c
o
n
tr
o
l
le
r
is
c
o
m
m
o
n
l
y
e
m
p
l
o
y
e
d
i
n
s
y
s
te
m
s
wi
th
c
o
m
p
le
x
o
r
p
o
o
r
l
y
m
o
d
el
e
d
d
y
n
am
ics
,
s
u
c
h
as
P
V
s
y
s
te
m
s
,
w
h
e
r
e
it
o
p
ti
m
iz
es
p
o
we
r
o
u
t
p
u
t
b
y
a
d
j
u
s
ti
n
g
p
a
r
a
m
et
e
r
s
t
o
ch
an
g
in
g
cli
m
at
ic
co
n
d
iti
o
n
s
[
1
4
]
,
[
2
3
]
.
Fi
g
u
r
e
3
s
h
o
ws
th
e
g
e
n
er
al
s
tr
u
ct
u
r
e
o
f
th
e
FL
co
n
t
r
o
ll
er
.
-
Fu
zz
if
icatio
n
:
T
h
is
b
lo
ck
r
ec
ei
v
es
th
e
er
r
o
r
=
−
−
1
−
−
1
an
d
t
h
e
er
r
o
r
r
at
e
as
in
p
u
ts
an
d
co
n
v
er
ts
th
e
cr
is
p
in
p
u
t
v
alu
es
i
n
to
f
u
zz
y
s
ets.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
u
s
ed
to
ass
ig
n
d
eg
r
ee
s
o
f
m
e
m
b
er
s
h
ip
t
o
th
e
in
p
u
ts
in
p
r
ed
e
f
in
ed
f
u
zz
y
s
e
ts
,
s
u
ch
as
p
o
s
itiv
e
b
ig
(
PB
)
,
p
o
s
itiv
e
s
m
all
(
PS
)
,
ze
r
o
(
Z
)
,
n
eg
ativ
e
b
ig
(
NB
)
,
an
d
n
e
g
ativ
e
s
m
all
(
NS)
.
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
N
-
b
a
s
ed
MPP
T fo
r
p
h
o
to
v
o
lta
ic
s
ystems
:
p
erfo
r
ma
n
ce
a
n
a
lysi
s
a
n
d
…
(
K
h
a
d
ija
A
b
d
o
u
n
i
)
2783
-
I
n
f
er
en
ce
m
ec
h
a
n
is
m
:
T
h
is
is
th
e
b
r
ain
o
f
th
e
FL
co
n
tr
o
ller
.
I
t
ap
p
lies
r
u
les
f
r
o
m
th
e
r
u
le
b
ase,
as
s
h
o
wn
in
T
ab
le
1
,
to
th
e
f
u
zz
y
in
p
u
ts
.
T
h
e
r
u
les
ar
e
i
n
th
e
f
o
r
m
o
f
"if
-
th
en
"
s
tatem
en
ts
;
f
o
r
ex
am
p
le,
if
th
e
er
r
o
r
is
P
S
an
d
th
e
e
r
r
o
r
r
ate
is
PB
,
th
en
th
e
o
u
tp
u
t is
NB
.
-
Def
u
zz
if
icatio
n
:
On
ce
th
e
in
f
er
en
ce
m
ec
h
an
is
m
h
as
d
eter
m
in
ed
th
e
o
u
tp
u
t
f
u
zz
y
s
et
b
ased
o
n
th
e
r
u
les,
th
is
b
lo
ck
co
n
v
er
ts
th
e
f
u
zz
y
o
u
tp
u
t b
ac
k
in
to
a
c
r
is
p
v
alu
e,
wh
ich
is
th
e
d
u
ty
c
y
cle
r
ate
.
Fig
u
r
e
3
.
Stru
ctu
r
e
o
f
th
e
FL
c
o
n
tr
o
ller
T
ab
le
1
.
Fu
zz
y
lo
g
ic
r
u
les
R
u
l
e
s
E(
K
)
PS
PB
Z
NB
NS
PS
NS
NB
Z
PB
Z
PB
NB
Z
NS
PB
Z
Z
NS
NB
Z
PS
PS
NB
Z
NB
PS
Z
PB
NS
Z
NB
Z
PB
PS
3
.
3
.
B
a
c
k
s
t
eppin
g
c
o
ntr
o
ller
T
h
e
b
a
c
k
s
t
e
p
p
i
n
g
c
o
n
t
r
o
l
l
e
r
,
a
L
y
a
p
u
n
o
v
-
b
a
s
e
d
n
o
n
l
i
n
e
a
r
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
,
i
s
a
d
o
p
t
e
d
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
s
y
s
t
e
m
s
d
u
e
t
o
its
r
e
c
u
r
s
i
v
e
d
es
i
g
n
m
e
t
h
o
d
o
l
o
g
y
t
h
a
t
e
n
s
u
r
e
s
g
l
o
b
a
l
s
t
a
b
il
i
t
y
[
2
4
]
.
I
n
t
h
e
M
P
P
T
t
e
c
h
n
i
q
u
e
,
i
t
a
d
j
u
s
ts
t
h
e
c
o
n
t
r
o
l
i
n
p
u
t
t
o
e
n
s
u
r
e
t
h
a
t
t
h
e
s
y
s
t
em
o
p
e
r
a
t
e
s
a
t
i
t
s
MP
P
w
h
il
e
m
a
i
n
t
a
i
n
i
n
g
s
ta
b
i
l
it
y
u
n
d
e
r
v
a
r
y
i
n
g
c
l
i
m
a
t
i
c
c
o
n
d
i
ti
o
n
s
[
2
5
]
,
[
2
6
]
.
T
h
e
d
e
s
i
g
n
p
r
o
c
e
s
s
o
f
t
h
e
t
e
c
h
n
i
q
u
e
is
d
i
v
i
d
e
d
in
t
o
t
w
o
m
a
i
n
s
t
e
p
s
:
a)
Step
1
T
h
e
f
i
r
s
t
e
r
r
o
r
1
is
d
e
f
i
n
e
d
b
y
:
1
=
−
,
wh
e
r
e
=
a
n
d
=
0
(
=
0
a
t
M
P
P
)
.
1
̇
=
(
)
=
(
)
=
(
+
)
(
5
)
Usi
n
g
(
1
)
,
(
5
)
b
ec
o
m
es
(
6
)
.
1
̇
=
1
(
−
)
(
2
+
2
2
)
(
6
)
T
h
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
1
=
1
2
1
2
is
a
m
ath
em
atica
l
t
o
o
l
f
o
r
an
aly
zin
g
th
e
s
tab
ilit
y
o
f
d
y
n
a
m
ic
s
y
s
tem
s
,
en
s
u
r
in
g
asy
m
p
to
tic
s
tab
ilit
y
b
y
m
ain
tain
i
n
g
p
o
s
itiv
e
en
er
g
y
an
d
a
n
eg
ativ
e
tim
e
d
er
iv
ativ
e.
T
h
e
(
7
)
ex
p
r
ess
es its
d
er
iv
ativ
e.
̇
1
=
1
̇
1
=
1
1
(
−
)
(
2
+
2
2
)
(
7
)
T
h
e
s
ec
o
n
d
e
r
r
o
r
is
2
=
−
1
,
w
h
er
e
1
is
a
v
i
r
t
u
al
c
o
n
t
r
o
l
in
p
u
t
t
h
at
is
e
x
p
r
ess
e
d
in
(
8
)
.
1
=
1
1
2
+
2
2
+
(
8
)
T
h
e
(
7
)
b
e
co
m
es
(
9
)
u
s
in
g
(
8
)
.
̇
1
=
−
1
1
2
−
1
(
2
+
2
2
)
1
2
(
9
)
W
h
e
r
e
1
i
s
a
p
o
s
i
t
i
v
e
c
o
n
s
t
a
n
t
.
T
o
e
l
i
m
i
n
a
t
e
t
h
e
t
e
r
m
1
(
2
+
2
2
)
1
2
i
n
(
9
)
,
w
e
p
r
o
c
e
e
d
t
o
s
te
p
2
.
b)
Step
2
B
ased
o
n
(
2
)
,
th
e
s
ec
o
n
d
e
r
r
o
r
is
e
x
p
r
ess
e
d
i
n
(
1
0
)
.
̇
2
=
1
[
−
(
1
−
)
]
−
̇
1
(
1
0
)
C
o
n
s
id
er
t
h
e
s
e
c
o
n
d
L
y
a
p
u
n
o
v
f
u
n
ct
io
n
2
=
1
+
1
2
2
2
,
its
d
er
iv
ativ
e
is
g
i
v
en
in
(
1
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2780
-
2
7
9
1
2784
̇
2
=
̇
1
+
2
̇
2
(
1
1
)
T
h
e
(
1
1
)
b
ec
o
m
es
(
1
2
)
u
s
i
n
g
(
1
0
)
a
n
d
(
9
)
.
̇
2
=
−
1
1
2
+
[
−
1
(
2
+
2
2
)
1
+
1
(
−
)
+
1
−
̇
1
]
2
(
1
2
)
T
h
e
d
u
t
y
c
y
cl
e
f
o
r
c
o
n
t
r
o
lli
n
g
th
e
b
o
o
s
t
co
n
v
e
r
t
er
is
g
iv
e
n
i
n
(
1
3
)
.
=
(
1
(
2
+
2
2
)
1
−
1
(
−
)
+
̇
1
−
2
2
)
(
1
3
)
T
h
er
ef
o
r
e
̇
2
=
−
1
1
2
−
2
2
2
<
0
,
w
h
er
e
K
2
is
a
p
o
s
iti
v
e
co
n
s
t
a
n
t
;
c
o
n
s
e
q
u
en
tl
y
,
o
u
r
s
y
s
t
em
is
g
l
o
b
a
ll
y
asy
m
p
t
o
tic
all
y
s
ta
b
l
e.
3
.
4
.
P
er
t
urba
t
io
n a
nd
o
bs
er
v
a
t
io
n
T
h
e
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
a
tio
n
tech
n
iq
u
e
is
b
ased
o
n
co
n
tin
u
o
u
s
ly
ad
ju
s
tin
g
th
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
PV
ar
r
ay
a
n
d
o
b
s
er
v
in
g
th
e
r
esu
ltin
g
ch
an
g
es
in
o
u
t
p
u
t
p
o
wer
.
T
h
e
tech
n
iq
u
e
a
d
ju
s
ts
D
b
ased
o
n
t
h
e
s
ig
n
o
f
d
P
an
d
d
V
[
2
7
]
.
I
f
dP
dV
=
0
it
m
ea
n
s
th
at
th
e
s
y
s
tem
is
at
th
e
MPP.
I
f
d
P
an
d
d
V
h
av
e
th
e
s
am
e
s
ig
n
,
th
e
d
u
ty
c
y
cle
is
r
ed
u
ce
d
b
y
s
u
b
tr
ac
tin
g
th
e
f
ix
ed
s
tep
s
ize
Δ
D
o
th
er
wis
e
,
th
e
d
u
ty
c
y
cle
is
in
cr
ea
s
ed
to
m
o
v
e
to
war
d
s
th
e
MPP
[
4
]
,
[
2
8
]
.
Fig
u
r
e
4
s
h
o
ws th
e
f
lo
wch
a
r
t o
f
th
e
P&
O
tech
n
iq
u
e.
3
.
5
.
I
ncre
m
ent
a
l c
o
nd
uct
a
nce
T
h
e
in
cr
em
en
tal
co
n
d
u
ctan
ce
tech
n
iq
u
e
is
co
n
s
id
er
ed
o
n
e
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
MPPT
t
ec
h
n
iq
u
es
d
u
e
to
its
b
alan
ce
o
f
co
s
t
-
ef
f
e
ctiv
en
ess
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
.
I
t
is
b
ased
o
n
an
aly
z
in
g
th
e
s
lo
p
e
o
f
th
e
cu
r
r
en
t
-
v
o
ltag
e
c
u
r
v
e
dI
d
V
.
I
f
dI
d
V
=
0
,
t
h
e
s
y
s
tem
is
at
th
e
MPP
,
an
d
th
e
d
u
ty
cy
cle
r
em
ain
s
c
o
n
s
tan
t
u
n
til
clim
atic
co
n
d
itio
n
s
c
h
an
g
e
.
I
f
dI
d
V
<
0
th
e
o
p
er
atin
g
p
o
in
t
is
to
th
e
r
i
g
h
t
o
f
th
e
MPP
;
th
u
s
,
th
e
d
u
ty
cy
cle
m
u
s
t
b
e
in
cr
ea
s
ed
[
2
9
]
.
C
o
n
v
er
s
ely
,
if
dI
d
V
>
0
,
th
e
d
u
ty
p
o
in
t
is
to
th
e
lef
t
o
f
th
e
MPP
,
an
d
th
e
d
u
ty
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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lec
&
Dr
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s
t
I
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N:
2088
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8
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n
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f
f
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h
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t
i
o
n
9
9
.
2
9
0
.
7
1
0
.
0
3
M
e
d
i
u
m
9
9
.
2
2
0
.
7
7
0
.
0
5
Lo
w
9
9
.
2
8
0
.
7
1
0
.
0
1
M
e
d
i
u
m
9
9
.
2
3
0
.
7
6
0
.
0
0
5
M
e
d
i
u
m
5.
CO
NCLU
SI
O
N
MPPT
tech
n
iq
u
es
ar
e
ess
en
tial
f
o
r
o
p
tim
izin
g
t
h
e
e
n
er
g
y
p
r
o
d
u
ctio
n
o
f
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
to
en
s
u
r
e
th
at
th
e
y
o
p
er
ate
at
m
ax
im
u
m
p
o
wer
ev
en
u
n
d
er
v
ar
iab
le
clim
atic
c
o
n
d
itio
n
s
.
I
n
t
h
is
s
tu
d
y
,
th
e
p
er
f
o
r
m
an
ce
o
f
an
ANN
-
b
a
s
ed
MPPT
co
n
tr
o
ller
u
n
d
e
r
d
if
f
er
en
t
s
ce
n
ar
i
o
s
o
f
clim
atic
co
n
d
itio
n
s
was
ev
alu
ated
u
s
in
g
MA
T
L
AB
/
S
im
u
lin
k
an
d
co
m
p
ar
ed
with
co
n
v
e
n
tio
n
al
tech
n
iq
u
es
s
u
ch
as
p
er
tu
r
b
an
d
o
b
s
er
v
e,
in
c
r
em
en
tal
co
n
d
u
cta
n
ce
,
f
u
zz
y
lo
g
ic
c
o
n
tr
o
ller
,
an
d
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
.
T
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
wed
th
at
ANN
-
b
ased
MP
PT
o
u
tp
er
f
o
r
m
ed
th
e
o
t
h
er
te
ch
n
iq
u
es,
ac
h
ie
v
in
g
t
h
e
h
ig
h
e
s
t
ef
f
icien
cy
(
u
p
to
9
9
.
9
4
%)
with
f
ast
tr
ac
k
in
g
a
n
d
lo
w
o
s
cillatio
n
.
I
ts
r
o
b
u
s
tn
ess
u
n
d
er
r
a
p
id
ly
ch
a
n
g
in
g
clim
atic
co
n
d
itio
n
s
allo
wed
it to
m
ain
tain
s
tab
le
o
u
tp
u
t p
o
wer
wh
ile
ac
cu
r
ately
tr
ac
k
in
g
th
e
MPP.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
e
au
th
o
r
s
d
ec
lar
e
th
at
n
o
f
u
n
d
in
g
was r
ec
eiv
e
d
to
s
u
p
p
o
r
t
th
is
r
esear
ch
.
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
Kh
ad
ija
Ab
d
o
u
n
i
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Mo
s
taf
a
B
en
b
o
u
k
o
u
s
✓
✓
✓
✓
✓
✓
✓
Dr
ig
h
il Asm
aa
✓
✓
✓
✓
✓
✓
✓
✓
Hich
am
B
ah
r
i
✓
✓
✓
Mo
h
am
ed
B
o
u
r
✓
✓
✓
✓
✓
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.
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