I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
(
I
J
P
E
DS
)
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
,
p
p
.
1
7
4
4
~
1
7
5
5
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v8
i
4
.
pp
1
7
4
4
-
1755
1744
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JP
E
DS
Practical
Perf
o
r
m
a
nce
Ev
a
lua
tion o
f
M
a
x
i
m
u
m
P
o
w
e
r P
o
int
Tra
ck
ing
Alg
o
rit
h
m
s
in A
Photo
v
o
ltaic Sy
ste
m
H
a
s
s
a
n Abo
uo
ba
ida
1
,
E
L
B
eid Sa
id
2
1,
2
L
a
b
o
ra
to
ry
o
f
En
g
in
e
e
rin
g
S
c
ien
c
e
s f
o
r
En
e
rg
y
.
Na
ti
o
n
a
l
S
c
h
o
o
l
o
f
A
p
p
li
e
d
S
c
ien
c
e
s
El
Ja
d
id
a
.
C
h
o
u
a
ib
-
D
o
u
k
k
a
li
Un
i
v
e
rsit
y
,
M
o
ro
c
c
o
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Sep
t 2
,
2
0
1
7
R
ev
i
s
ed
Oct
30
,
2
0
1
7
A
cc
ep
ted
No
v
2
2
,
2
0
1
7
T
h
is
p
a
p
e
r
a
d
d
re
ss
e
s
a
p
e
rf
o
r
m
a
n
c
e
e
v
a
lu
a
ti
o
n
o
f
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
tec
h
n
iq
u
e
s
(M
P
P
T
)
in
a
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
.
T
h
is
re
s
e
a
rc
h
w
o
rk
f
in
d
s
it
s
a
p
p
li
c
a
ti
o
n
s
i
n
p
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
s
p
ro
d
u
c
i
n
g
e
lec
tri
c
p
o
w
e
r
w
it
h
a
b
e
tt
e
r
e
n
e
rg
y
e
ff
icie
n
c
y
,
w
h
ich
will
lea
d
to
a
n
im
p
ro
v
e
d
re
latio
n
sh
i
p
b
e
tw
e
e
n
th
e
c
o
s
t
a
n
d
th
e
a
m
o
u
n
t
o
f
th
e
p
ro
d
u
c
e
d
p
o
w
e
r.
T
h
e
i
m
p
o
rtan
c
e
o
f
th
is
w
o
rk
re
sid
e
s
o
n
th
e
o
n
e
h
a
n
d
in
t
h
e
e
v
a
lu
a
ti
o
n
o
f
th
e
p
e
rf
o
r
m
a
n
c
e
s
o
f
th
e
d
iff
e
re
n
t
M
P
P
T
s
a
c
c
o
rd
in
g
to
t
h
re
e
c
rit
e
ria
in
ste
a
d
o
f
o
n
e
o
r
tw
o
c
rit
e
ria
in
o
t
h
e
r
w
o
rk
s
o
f
th
e
li
tera
tu
re
a
n
d
o
n
th
e
o
th
e
r
h
a
n
d
in
th
e
stu
d
y
o
f
F
o
u
r
a
lg
o
rit
h
m
s
in
o
n
e
p
a
p
e
r
a
n
d
th
e
ir
c
o
m
p
a
ris
o
n
s.
T
h
is
p
a
p
e
r
d
isc
u
ss
e
s
th
e
p
e
rf
o
r
m
a
n
c
e
e
v
a
lu
a
ti
o
n
o
f
th
e
M
P
P
T
a
lg
o
rit
h
m
s
c
a
ll
e
d
P
&
O,
In
c
-
C
o
n
d
,
Hil
l
-
Cli
m
b
in
g
a
n
d
F
u
z
z
y
a
lg
o
rit
h
m
s
b
a
se
d
si
m
u
latio
n
re
su
lt
s
a
n
d
p
ra
c
ti
c
a
l
v
a
li
d
a
ti
o
n
.
T
h
e
p
e
rf
o
r
m
a
n
c
e
s
o
f
th
e
se
a
lg
o
rit
h
m
s
a
re
e
v
a
lu
a
ted
a
c
c
o
rd
in
g
to
th
e
f
o
ll
o
w
in
g
c
rit
e
ria:
T
h
e
re
sp
o
n
se
ti
m
e
,
th
e
a
m
p
li
tu
d
e
o
f
th
e
o
sc
il
lati
o
n
s
a
ro
u
n
d
t
h
e
o
p
ti
m
al
p
o
i
n
t
a
n
d
th
e
a
c
c
u
ra
c
y
.
Th
e
o
b
jec
ti
v
e
s
in
t
h
is
a
rti
c
le
a
re
su
m
m
a
rize
d
in
t
h
e
f
o
ll
o
w
in
g
p
o
in
ts:
(a
)
m
o
d
e
li
n
g
th
e
p
h
o
to
v
o
lt
a
ic
sy
ste
m
s,
(b
)
p
re
se
n
ti
n
g
a
n
d
d
e
taili
n
g
e
a
c
h
M
P
P
T
a
lg
o
rit
h
m
(c
)
p
re
s
s
e
n
ti
n
g
a
n
d
d
isc
u
ss
in
g
th
e
sim
u
latio
n
re
su
lt
s
in
M
a
tl
a
b
/S
im
u
li
n
k
a
n
d
p
ra
c
ti
c
a
l
v
a
li
d
a
ti
o
n
(d
)
e
v
a
lu
a
ti
n
g
th
e
p
e
rf
o
rm
a
n
c
e
o
f
e
a
c
h
a
lg
o
r
it
h
m
.
T
h
is
p
a
p
e
r
is
c
o
m
p
lete
d
b
y
a
s
u
m
m
a
r
y
o
n
th
e
a
re
a
s o
f
u
se
f
o
r
e
a
c
h
a
lg
o
rit
h
m
a
n
d
c
o
n
c
lu
sio
n
s.
K
ey
w
o
r
d
:
Fu
zz
y
Hill
-
c
li
m
b
i
n
g
I
n
c
-
co
n
d
MP
PT
P
&
O
Co
p
y
rig
h
t
©
201
7
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Hass
a
n
A
b
o
u
o
b
aid
a,
L
ab
o
r
ato
r
y
o
f
E
n
g
in
ee
r
i
n
g
Sci
en
ce
s
f
o
r
E
n
er
g
y
.
E
l J
ad
id
a
C
h
o
u
aib
-
Do
u
k
k
ali
U
n
i
v
er
s
it
y
Natio
n
al
Sc
h
o
o
l o
f
A
p
p
lied
Scien
ce
s
R
o
u
te
d
'
az
ze
m
o
u
r
,
Natio
n
ale
N°1
.
E
lh
ao
u
zia
B
P
: 1
1
6
6
E
l J
a
d
id
a
2
4
0
0
2
Mo
r
o
cc
o
E
m
ail:
h
as
s
an
ab
o
u
o
b
aid
a@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
A
ct
u
all
y
,
th
e
p
r
o
d
u
ctio
n
o
f
elec
tr
ic
p
o
w
er
f
r
o
m
r
en
e
w
ab
le
en
er
g
y
i
s
a
m
o
n
g
t
h
e
m
o
s
t
r
ec
o
m
m
e
n
d
ed
s
o
lu
tio
n
s
n
o
n
-
p
o
llu
ti
n
g
en
er
g
y
s
o
u
r
ce
.
T
h
ese
s
o
lu
tio
n
s
h
a
v
e
m
a
n
y
ad
v
an
tag
e
s
.
On
t
h
e
o
n
e
h
an
d
,
th
e
s
e
s
o
u
r
ce
s
a
llo
w
t
h
e
p
r
eser
v
a
tio
n
o
f
t
h
e
e
n
v
ir
o
n
m
en
t,
as
th
e
y
ar
e
ec
o
-
f
r
ien
d
l
y
.
O
n
t
h
e
o
th
er
h
an
d
,
th
e
u
s
e
o
f
th
ese
s
o
u
r
ce
s
is
r
elate
d
to
th
e
p
r
o
d
u
ctio
n
co
m
p
eti
n
g
w
i
th
f
o
s
s
il
s
o
u
r
ce
s
.
Fo
r
th
e
p
r
o
d
u
ctio
n
o
f
elec
tr
ic
p
o
w
er
f
r
o
m
r
en
e
w
ab
le
r
eso
u
r
ce
s
,
r
ec
o
u
r
s
e
to
s
o
u
r
ce
s
f
o
r
b
asic
p
h
o
to
v
o
ltaic
en
er
g
y
is
e
s
s
e
n
tial,
h
o
w
e
v
er
,
th
e
p
o
w
er
s
u
p
p
lied
b
y
a
s
o
lar
p
an
el
is
r
elate
d
to
th
r
ee
p
ar
am
eter
s
:
i
r
r
ad
iatio
n
,
te
m
p
er
atu
r
e
an
d
t
h
e
lo
ad
.
h
en
ce
,
P
V
s
y
s
te
m
s
s
u
f
f
er
f
r
o
m
r
elat
i
v
el
y
lo
w
co
n
v
er
s
io
n
ef
ficie
n
c
y
.
T
o
m
a
x
i
m
ize
th
e
o
u
tp
u
t
p
o
w
er
o
f
P
V
ar
r
ay
an
d
to
co
n
tin
u
o
u
s
l
y
tr
ac
k
t
h
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t (
MP
P
)
,
s
ev
er
al
MP
PT
alg
o
r
ith
m
s
ar
e
p
r
o
p
o
s
ed
in
t
h
e
liter
at
u
r
e;
C
o
m
p
ar
in
g
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
s
e
tech
n
iq
u
e
s
s
ee
m
s
a
v
er
y
in
ter
e
s
ti
n
g
s
p
o
t
to
d
eter
m
in
e
w
h
ich
o
n
e
i
s
m
o
s
t
s
u
itab
le
a
n
d
e
f
f
ic
ien
t
f
o
r
a
g
iv
en
P
V
s
y
s
te
m
.
N
u
m
er
o
u
s
w
o
r
k
s
h
av
e
ad
d
r
ess
ed
t
h
e
co
m
p
ar
i
s
o
n
o
f
MP
PT
alg
o
r
ith
m
s
.
I
n
s
o
m
e
p
ap
er
s
,
t
h
is
co
m
p
ar
is
o
n
is
g
e
n
er
all
y
li
m
ited
to
a
th
eo
r
etica
l
s
tu
d
y
an
d
lack
s
o
f
p
r
ac
tical
i
m
p
le
m
en
ta
tio
n
[
1
]
-
[
2
]
.
Oth
er
ar
ticles
h
av
e
co
m
p
ar
ed
d
if
f
e
r
en
t
MP
PT
b
y
ch
o
o
s
i
n
g
a
f
e
w
cr
iter
ia
r
elate
d
to
th
e
alg
o
r
it
h
m
s
p
e
r
f
o
r
m
a
n
ce
r
e
g
ar
d
less
t
h
e
r
esp
o
n
s
e
ti
m
e
o
r
th
e
co
n
v
er
g
e
n
ce
r
ate
o
f
MP
PT
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
a
ctica
l P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f Ma
ximu
m
P
o
w
e
r
P
o
in
t
Tr
a
ck
in
g
A
lg
o
r
ith
ms….
(
Ha
s
s
a
n
A
b
o
u
o
b
a
id
a
)
1745
In
th
i
s
p
ap
er
,
w
e
s
t
u
d
y
t
h
e
p
er
f
o
r
m
an
ce
e
v
al
u
atio
n
o
f
s
o
m
e
MP
PT
alg
o
r
ith
m
s
.
T
h
e
ev
alu
a
tio
n
i
s
b
ased
o
n
cr
iter
ia
r
elate
d
to
r
esp
o
n
s
e
ti
m
e,
ac
cu
r
ac
y
,
o
s
cillatio
n
ar
o
u
n
d
MP
P
an
d
Si
m
p
lici
t
y
o
f
i
m
p
le
m
en
ta
tio
n
.
T
h
r
o
u
g
h
o
u
t
t
h
is
w
o
r
k
,
ea
ch
al
g
o
r
ith
m
i
s
p
r
esen
ted
a
n
d
ex
p
lai
n
ed
an
d
a
t
h
eo
r
etica
l v
alid
atio
n
is
estab
lis
h
ed
in
Ma
tlab
/
Si
m
u
lin
k
.
T
h
e
ex
p
er
i
m
e
n
tal
v
alid
atio
n
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
w
i
th
a
p
er
f
o
r
m
a
n
ce
s
co
m
p
ar
i
s
o
n
ar
e
g
iv
e
n
at
t
h
e
en
d
o
f
t
h
is
p
ap
er
.
T
h
is
ass
es
s
m
e
n
t
w
i
ll
b
e
b
en
e
ficial
to
r
esear
ch
er
s
an
d
p
r
ac
titi
o
n
er
s
i
n
P
V
s
y
s
te
m
s
g
i
v
en
th
at
it
ca
n
s
er
v
e
a
s
a
s
u
itab
le
r
e
f
er
en
ce
f
o
r
s
elec
tio
n
,
u
n
d
er
s
tan
d
i
n
g
d
if
f
er
e
n
t
w
a
y
s
an
d
m
ea
n
s
o
f
MP
PT
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
a
n
ized
as
f
o
llo
w
s
.
W
h
ile
s
ec
tio
n
2
d
ea
ls
m
ai
n
l
y
w
i
th
t
h
e
m
o
d
elin
g
o
f
t
h
e
s
t
u
d
ied
p
h
o
to
v
o
ltaic
s
y
s
te
m
,
a
p
r
esen
tatio
n
o
f
ea
c
h
alg
o
r
ith
m
is
d
etailed
in
Sectio
n
3
.
Si
m
u
latio
n
r
es
u
lts
ar
e
p
r
esen
ted
w
it
h
co
m
m
e
n
t
s
in
Sectio
n
4
.
Sectio
n
5
i
s
d
ev
o
ted
to
p
r
ac
tical
v
alid
atio
n
a
n
d
r
esu
lt
s
w
i
th
a
p
p
licatio
n
ar
ea
s
o
f
ea
ch
MPPT
alg
o
r
ith
m
.
Sectio
n
6
p
r
esen
ts
t
h
e
co
n
clu
s
io
n
s
d
r
a
w
n
f
r
o
m
t
h
is
s
tu
d
y
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
p
o
w
er
cir
cu
i
t
co
n
s
is
ts
o
f
a
P
V
ar
r
a
y
m
o
d
u
le,
d
c
-
to
-
d
c
b
o
o
s
t
co
n
v
er
ter
a
n
d
a
lo
ad
as
s
h
o
w
n
i
n
Fig
u
r
e
1
.
T
h
e
b
o
o
s
t
ch
o
p
p
er
is
th
e
c
ir
cu
it
th
at
ad
j
u
s
t
s
t
h
e
p
o
w
er
ex
tr
ac
ted
i
n
th
e
p
o
w
er
d
e
m
an
d
ed
b
y
t
h
e
lo
ad
.
I
t a
llo
w
s
o
p
er
atio
n
at
m
a
x
i
m
u
m
p
o
w
er
o
f
p
h
o
to
v
o
ltaic
p
an
el
[
3
]
-
[
4
]
.
Fig
u
r
e
1
.
P
h
o
to
v
o
ltaic
p
o
w
er
cir
cu
it
2
.
1
.
P
V
m
o
del
T
h
e
eq
u
iv
ale
n
t
m
o
d
el
o
f
a
s
o
lar
p
an
el
co
n
s
is
t
s
o
f
a
cu
r
r
en
t
s
o
u
r
ce
t
h
at
d
ep
en
d
s
o
n
th
e
s
o
lar
ir
r
ad
iatio
n
in
p
ar
allel
w
it
h
a
d
io
d
e
an
d
t
w
o
r
esis
to
r
s
,
th
e
f
ir
s
t
in
t
h
e
s
er
ies
an
d
t
h
e
s
ec
o
n
d
is
a
p
ar
allel
w
h
ic
h
r
ep
r
esen
t th
e
i
n
ter
n
al
j
o
u
le
lo
s
s
es
[
5
]
-
[
7
]
.
T
h
e
eq
u
iv
ale
n
t
-
cir
cu
it
m
o
d
el
o
f
P
V
is
ill
u
s
tr
ated
in
Fi
g
u
r
e
2
.
Fig
u
r
e
2
.
E
q
u
iv
ale
n
t
m
o
d
el
o
f
th
e
P
V
p
an
el
Usi
n
g
t
h
e
eq
u
i
v
ale
n
t
m
o
d
el
o
f
th
e
P
V
p
an
el
(
F
i
g
u
r
e
2
,
th
e
p
h
o
to
v
o
ltaic
cu
r
r
en
t
i
s
ex
p
r
e
s
s
ed
as
a
f
u
n
ctio
n
o
f
t
h
e
v
o
lta
g
e
b
y
t
h
e
f
o
llo
w
in
g
r
elatio
n
:
=
ℎ
−
(
+
.
.
−
1
)
−
+
(
1
)
W
h
er
e
I
p
h
i
s
t
h
e
P
V
o
u
tp
u
t
cu
r
r
en
t
(
A
)
,
Up
v
i
s
t
h
e
P
V
o
u
tp
u
t
v
o
lta
g
e
(
V)
,
q
is
th
e
ch
ar
g
e
o
f
a
n
elec
tr
o
n
,
k
is
B
o
ltz
m
a
n
n
’
s
co
n
s
tan
t
i
n
J
/K,
A
is
t
h
e
p
–
n
j
u
n
c
tio
n
id
ea
lit
y
f
ac
to
r
,
T
is
th
e
ce
ll
te
m
p
er
at
u
r
e
(
K)
,
an
d
I
s
at
is
t
h
e
r
ev
er
s
e
s
at
u
r
ati
o
n
cu
r
r
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
4
4
–
1
7
5
5
1746
3
.
1
.
B
O
O
ST
m
o
del
T
h
e
d
y
n
a
m
ics
m
o
d
el
o
f
th
e
a
d
a
p
tatio
n
cir
cu
it
i
llu
s
tr
ated
i
n
F
ig
u
r
e
3
is
ex
p
r
ess
ed
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
:
−
=
(
1
−
)
.
−
(
2
)
.
̇
+
.
=
−
(
1
−
)
.
(
3
)
W
h
er
e
L
a
n
d
I
L
r
ep
r
esen
ts
th
e
s
to
r
ag
e
i
n
d
u
cta
n
ce
a
n
d
t
h
e
c
u
r
r
en
t
ac
r
o
s
s
it,
U
s
i
s
t
h
e
o
u
t
p
u
t
v
o
lta
g
e
an
d
u
is
th
e
co
n
tr
o
l si
g
n
al.
Fig
u
r
e
3
.
P
h
o
to
v
o
ltaic
s
y
s
te
m
T
h
e
m
in
i
m
u
m
i
n
d
u
cta
n
ce
is
c
alcu
lated
f
r
o
m
t
h
e
m
a
x
i
m
u
m
p
er
m
i
s
s
ib
le
r
ip
p
le
o
f
t
h
e
c
u
r
r
en
t
I
L
.
I
t
is
ex
p
r
ess
ed
b
y
th
e
f
o
llo
w
i
n
g
r
el
atio
n
:
=
.
.
∆
_
(
4
)
W
h
er
e
Up
v
i
s
i
n
p
u
t
v
o
lta
g
e,
D
is
a
d
u
t
y
c
y
cle,
f
s
i
s
a
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
o
f
th
e
co
n
v
er
ter
an
d
L
is
a
s
elec
ted
i
n
d
u
cto
r
v
a
lu
e.
T
h
e
m
i
n
i
m
u
m
ca
p
ac
ito
r
i
s
ca
lc
u
la
ted
f
r
o
m
th
e
m
a
x
i
m
u
m
p
er
m
i
s
s
ib
le
r
ip
p
le
o
f
th
e
o
u
tp
u
t v
o
lta
g
e.
I
t is e
x
p
r
ess
ed
b
y
t
h
e
f
o
llo
w
in
g
r
elatio
n
:
=
.
.
∆
_
(
5
)
3.
P
RO
B
L
E
M
O
VE
RVIE
W
A
s
ill
u
s
tr
ated
in
F
ig
u
r
e
4
,
th
e
p
o
w
er
ch
ar
ac
ter
is
tic
o
f
a
p
h
o
t
o
v
o
ltaic
m
o
d
u
le
s
h
o
w
s
t
h
at
t
h
e
p
o
w
er
i
s
m
ax
i
m
u
m
ac
co
r
d
in
g
to
v
alu
e
o
f
ir
r
ad
iatio
n
o
r
tem
p
er
at
u
r
e
at
a
d
eter
m
i
n
ed
p
o
in
t
o
f
t
h
e
cu
r
v
e.
C
al
led
MP
P
(
m
ax
i
m
u
m
p
o
w
er
p
o
in
t)
,
th
i
s
p
o
in
t
is
ch
ar
ac
ter
ized
b
y
a
n
ex
tr
ac
tio
n
o
f
th
e
m
a
x
i
m
u
m
p
o
w
er
o
f
th
e
P
V
m
o
d
u
le
is
a
s
i
n
g
le
p
o
in
t
o
f
th
e
p
o
w
er
c
u
r
v
e.
T
o
o
p
er
ate
th
e
p
h
o
to
v
o
ltaic
g
en
er
ato
r
at
th
is
p
o
i
n
t,
it
is
n
ec
es
s
ar
y
to
u
s
e
an
al
g
o
r
ith
m
ca
lled
MPPT
(
m
ax
i
m
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
)
w
h
o
s
e
f
u
n
ct
io
n
is
to
co
llect
th
e
v
ar
iatio
n
s
in
cu
r
r
en
t
an
d
v
o
lt
ag
e
to
d
eter
m
i
n
e
th
e
MP
P
.
T
h
en
,
t
h
e
co
n
tr
o
l
u
n
it
p
r
o
d
u
ce
s
th
e
ad
eq
u
ate
d
u
t
y
c
y
cle
to
th
e
p
o
w
er
co
n
v
er
ter
t
o
o
p
er
ate
th
e
P
V
m
o
d
u
le
at
th
e
MP
P.
T
h
is
p
r
o
ce
s
s
co
n
tin
u
e
s
to
s
ea
r
ch
th
e
MP
P
s
in
ce
th
e
w
ea
t
h
er
ca
n
c
h
a
n
g
e
.
W
h
ich
i
m
p
lie
s
t
h
at
t
h
e
o
p
ti
m
al
p
o
in
t
m
o
v
es
w
h
e
n
e
v
er
t
h
er
e
is
a
ch
a
n
g
e
i
n
te
m
p
er
atu
r
e
o
r
ir
r
ad
iatio
n
.
Fig
u
r
e
. 4
. P
o
w
er
cu
r
v
e
o
f
P
V
p
an
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
a
ctica
l P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f Ma
ximu
m
P
o
w
e
r
P
o
in
t
Tr
a
ck
in
g
A
lg
o
r
ith
ms….
(
Ha
s
s
a
n
A
b
o
u
o
b
a
id
a
)
1747
4.
M
AXI
M
U
M
P
O
WE
R
P
O
I
NT
T
RA
CK
I
N
G
(
M
P
P
T
)
AL
G
O
RI
T
H
M
S
T
o
d
ete
r
m
i
n
e
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t,
s
e
v
er
al
al
g
o
r
it
h
m
s
ar
e
d
is
c
u
s
s
ed
i
n
th
e
liter
atu
r
e.
T
h
is
p
ap
er
s
tu
d
y
is
li
m
ited
to
P
&
O
,
I
n
c
-
C
o
n
d
,
f
u
zz
y
a
n
d
Hill
-
cli
m
b
in
g
MP
P
T
alg
o
r
ith
m
s
.
4
.
1
.
H
ill cli
m
bin
g
T
h
e
p
r
in
cip
le
o
f
th
e
alg
o
r
ith
m
ca
lled
Hill
c
li
m
b
i
n
g
i
s
ill
u
s
tr
ated
in
Fig
u
r
e
5
.
T
h
is
alg
o
r
ith
m
is
b
ased
o
n
th
e
co
n
ti
n
u
o
u
s
-
m
ea
s
u
r
in
g
v
ar
iatio
n
s
in
th
e
p
o
w
er
o
f
th
e
P
V
m
o
d
u
le
an
d
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e
th
e
d
u
t
y
r
atio
ac
co
r
d
in
g
to
t
h
is
c
h
a
n
g
e.
I
f
t
h
e
p
o
w
er
c
h
a
n
g
e
is
p
o
s
it
i
v
e,
w
h
ich
i
m
p
l
ies
t
h
at
t
h
e
o
p
t
i
m
u
m
p
o
in
t
i
s
r
i
g
h
t
w
o
r
k
i
n
g
p
o
in
t.
I
n
t
h
is
ca
s
e,
t
h
e
co
n
tr
o
l
u
n
i
t
ad
j
u
s
t
s
t
h
e
d
u
t
y
c
y
cle
to
i
n
cr
ea
s
e
th
e
v
o
lta
g
e
o
f
t
h
e
p
h
o
to
v
o
ltaic
m
o
d
u
le.
I
f
th
e
ch
a
n
g
e
in
p
o
w
er
is
n
e
g
ati
v
e,
w
h
ic
h
i
m
p
li
es
th
at
th
e
o
p
ti
m
u
m
p
o
i
n
t
is
to
th
e
lef
t
o
f
th
e
o
p
er
atin
g
p
o
in
t.
I
n
th
is
ca
s
e,
th
e
co
n
tr
o
l
ad
j
u
s
ts
th
e
d
u
t
y
c
y
cle
to
d
ec
r
ea
s
e
th
e
v
o
ltag
e
o
f
th
e
p
h
o
to
v
o
ltaic
m
o
d
u
le.
W
h
e
n
t
h
e
s
y
s
te
m
f
in
d
s
t
h
e
o
p
ti
m
al
p
o
i
n
t,
it
o
s
cillates
ar
o
u
n
d
t
h
at
p
o
in
t.
T
o
m
in
i
m
ize
t
h
e
s
e
o
s
cillatio
n
s
,
th
e
co
n
tr
o
l
u
n
it
m
u
s
t
u
s
e
a
v
ar
iab
le
s
tep
to
ad
j
u
s
t th
e
d
u
t
y
c
y
cle
[
8
]
-
[
9
]
.
Fig
u
r
e
5
.
T
h
e
f
lo
w
c
h
ar
t o
f
h
i
ll
cli
m
b
in
g
al
g
o
r
ith
m
4
.
2
.
P
&O
(
pert
urb a
nd
o
bs
e
rv
)
T
h
e
p
r
in
cip
le
o
f
th
e
P
&
O
alg
o
r
ith
m
is
ill
u
s
tr
ated
in
Fi
g
u
r
e
6
.
T
h
is
MP
PT
alg
o
r
ith
m
i
s
b
a
s
ed
o
n
t
h
e
co
n
tin
u
o
u
s
-
m
ea
s
u
r
i
n
g
v
ar
iatio
n
s
i
n
t
h
e
p
o
w
er
an
d
v
o
ltag
e
o
f
th
e
P
V
m
o
d
u
le.
I
f
t
h
e
p
o
w
er
ch
an
g
e
is
p
o
s
it
iv
e
an
d
t
h
e
v
o
ltag
e
ch
a
n
g
e
i
s
p
o
s
itiv
e
w
h
ich
i
m
p
l
ies
t
h
at
t
h
e
o
p
ti
m
al
p
o
in
t
i
s
r
i
g
h
t
o
f
th
e
o
p
er
atin
g
p
o
in
t.
T
h
e
n
th
e
r
e
f
er
en
ce
v
o
lta
g
e
i
s
ad
j
u
s
t
ed
to
co
in
cid
e
w
it
h
t
h
e
o
p
ti
m
u
m
p
o
in
t.
I
f
t
h
e
p
o
w
er
c
h
an
g
e
is
n
e
g
ati
v
e
a
n
d
th
e
v
o
ltag
e
c
h
a
n
g
e
is
p
o
s
it
iv
e
w
h
i
ch
i
m
p
lies
t
h
at
th
e
o
p
ti
m
al
p
o
in
t
i
s
le
f
t
o
f
th
e
o
p
er
atin
g
p
o
i
n
t.
I
n
th
i
s
ca
s
e,
t
h
e
r
ef
er
en
ce
v
o
ltag
e
is
ad
j
u
s
ted
t
o
th
e
o
p
ti
m
u
m
p
o
in
t.
O
n
c
e
th
e
r
e
f
er
en
ce
v
o
ltag
e
th
at
co
r
r
esp
o
n
d
s
to
th
e
o
p
tim
a
l
p
o
in
t
is
f
o
u
n
d
,
t
h
e
co
n
tr
o
l
u
n
it
r
e
g
u
lates
th
e
P
V
v
o
ltag
e
b
y
ad
j
u
s
ti
n
g
th
e
d
u
t
y
c
y
cle.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
co
n
tin
u
o
u
s
l
y
ac
co
r
d
in
g
to
te
m
p
er
at
u
r
e
o
r
r
ad
iatio
n
ch
an
g
e
w
h
ic
h
h
a
s
r
ep
er
cu
s
s
i
o
n
s
o
n
th
e
p
o
s
itio
n
o
f
th
e
MP
P
.
W
h
en
th
e
MP
P
T
alg
o
r
ith
m
f
i
n
d
s
t
h
e
o
p
ti
m
al
p
o
in
t,
it
o
s
cillate
s
ar
o
u
n
d
it.
T
o
m
in
i
m
ize
th
e
s
e
o
s
cillatio
n
s
,
It
is
n
ec
e
s
s
ar
y
to
u
s
e
a
v
ar
iab
le
s
tep
s
ize
to
ad
j
u
s
t th
e
v
o
ltag
e
r
e
f
er
en
ce
[
10
]
-
[
11
].
4
.
3
.
I
ncre
m
ent
a
l c
o
nd
uct
a
n
ce
T
h
e
MP
PT
alg
o
r
ith
m
ca
lled
I
n
c
-
C
o
n
d
i
s
b
ased
o
n
th
e
ca
lcu
latio
n
o
f
th
e
co
n
d
u
cta
n
ce
t
h
at
is
d
ef
i
n
ed
b
y
t
h
e
cu
r
r
en
t
c
h
an
g
e
d
iv
id
ed
b
y
th
e
v
o
ltag
e
ch
a
n
g
e.
I
f
th
e
co
n
d
u
ctan
ce
i
s
g
r
ea
ter
th
a
n
th
e
r
atio
(
-
I
p
v
/
Up
v
)
i
m
p
lies
th
at
th
e
o
p
ti
m
al
p
o
in
t
is
to
th
e
lef
t
o
f
t
h
e
o
p
er
atin
g
p
o
in
t
o
th
er
w
is
e
th
e
o
p
ti
m
al
p
o
in
t
is
to
t
h
e
r
ig
h
t.
W
h
en
t
h
e
co
n
d
u
cta
n
ce
a
n
d
th
e
ter
m
(
-
I
p
v
/
Up
v
)
ar
e
eq
u
al,
th
e
s
y
s
te
m
o
p
er
ates
at
th
e
o
p
tim
a
l
p
o
in
t.
T
h
e
co
n
tr
o
l
m
u
s
t
m
ai
n
tai
n
th
is
o
p
er
atio
n
u
n
til
th
e
d
etec
tio
n
o
f
a
ch
a
n
g
e
i
n
cli
m
atic
c
o
n
d
itio
n
s
.
F
ig
u
r
e
7
s
u
m
m
ar
izes t
h
e
p
r
in
cip
le
o
f
t
h
e
I
n
c
-
C
o
n
d
MP
PT
alg
o
r
ith
m
[
1
2
]
-
[1
3
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
4
4
–
1
7
5
5
1748
Fig
u
r
e
6
.
T
h
e
f
lo
w
c
h
ar
t o
f
P
&
O
alg
o
r
ith
m
Fi
g
u
r
e.
7
.
T
h
e
f
lo
w
ch
ar
t
o
f
I
n
c
-
c
o
n
d
alg
o
r
it
h
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
a
ctica
l P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f Ma
ximu
m
P
o
w
e
r
P
o
in
t
Tr
a
ck
in
g
A
lg
o
r
ith
ms….
(
Ha
s
s
a
n
A
b
o
u
o
b
a
id
a
)
1749
4
.
4
.
F
uzzy
lo
g
ic
M
P
P
T
T
h
is
MP
PT
alg
o
r
ith
m
i
s
b
as
ed
o
n
th
e
F
u
zz
y
lo
g
ical
t
h
eo
r
y
.
T
h
e
F
u
zz
y
MP
PT
co
n
s
is
t
s
o
f
t
h
r
ee
in
ter
n
a
l
s
tep
s
:
f
u
zz
if
ica
tio
n
,
i
n
f
er
e
n
ce
an
d
d
if
u
zz
i
f
icatio
n
.
T
h
e
in
p
u
t
v
ar
iab
les
ar
e
t
h
e
er
r
o
r
an
d
th
e
er
r
o
r
ch
an
g
e.
T
h
ese
v
ar
iab
les
ar
e
d
ef
in
ed
ac
co
r
d
in
g
to
th
e
eq
u
atio
n
3
an
d
eq
u
at
io
n
4
r
esp
e
ctiv
el
y
.
T
h
e
in
p
u
t
v
ar
iab
les ar
e
co
n
v
er
ted
i
n
th
e
f
u
zz
if
ica
tio
n
s
tag
e
o
f
a
d
ig
ital
f
o
r
m
to
a
lan
g
u
ag
e
f
o
r
m
.
A
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
is
s
et
u
p
to
p
er
f
o
r
m
th
e
f
u
zz
if
icatio
n
o
f
th
e
i
n
p
u
ts
.
T
h
e
Fu
zz
y
co
n
tr
o
ller
d
eter
m
i
n
es
f
r
o
m
r
u
le
t
ab
le
w
h
at
ad
j
u
s
t
m
e
n
t
s
h
o
u
ld
b
e
d
o
n
e
o
n
th
e
d
u
t
y
c
y
cle.
T
h
e
o
u
tp
u
t
o
f
Fu
zz
y
-
MP
PT
is
th
e
d
u
t
y
c
h
a
n
g
e
d
α
v
ar
iab
le
t
h
at
r
ep
r
esen
ts
th
e
c
h
an
g
e
n
ee
d
t
o
p
er
f
o
r
m
o
n
th
e
d
u
t
y
c
y
c
le
[
1
4
]
-
[1
5]
.
E
q
u
atio
n
s
3
an
d
4
d
escr
ib
e
th
e
in
p
u
t
v
ar
iab
les
o
f
th
e
f
u
zz
y
MP
P
T
.
Fig
u
r
e
8
s
h
o
w
s
h
o
w
to
ch
o
o
s
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
in
a
f
u
zz
y
MP
PT
alg
o
r
ith
m
.
(
)
(
1
)
()
(
)
(
1
)
p
v
p
v
p
v
p
v
p
n
p
n
en
u
n
u
n
(
3
)
(
)
(
)
(
1
)
d
e
n
e
n
e
n
(
4
)
Fig
u
r
e
8
.
T
h
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
T
h
e
m
o
d
el
o
f
p
h
o
to
v
o
ltaic
m
o
d
u
le,
p
o
w
er
b
o
o
s
t
co
n
v
er
t
er
m
o
d
el
an
d
th
e
MP
P
T
alg
o
r
ith
m
ar
e
i
m
p
le
m
en
ted
in
Ma
tlab
/
Si
m
u
l
in
k
.
I
n
t
h
is
s
t
u
d
y
,
t
h
e
P
V
p
an
el
p
r
o
v
id
e
a
m
a
x
i
m
u
m
p
o
w
er
o
f
1
KW
.
T
h
e
P
V
m
o
d
u
le
i
s
b
ased
o
n
R
SM
-
6
0
th
at
d
eli
v
er
a
m
a
x
i
m
u
m
p
o
wer
o
f
6
0
W
atts
.
T
h
e
s
p
ec
if
ica
tio
n
o
f
t
h
e
co
n
tr
o
l
p
ar
am
eter
s
an
d
th
e
m
a
in
c
h
ar
ac
ter
is
tics
o
f
th
e
P
V
m
o
d
u
le
ar
e
s
u
m
m
ar
ized
in
T
ab
l
e
1
an
d
T
a
b
le
2
r
esp
ec
tiv
el
y
.
Ou
r
g
o
al
i
s
to
ev
alu
ate
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
MP
PT
alg
o
r
ith
m
s
.
I
n
t
h
is
co
n
tex
t,
th
e
P
V
p
o
w
er
s
y
s
te
m
i
s
s
u
b
j
ec
t
to
an
ec
h
elo
n
o
f
s
o
lar
ir
r
ad
iatio
n
.
T
h
e
ev
alu
atio
n
i
s
b
ased
o
n
th
e
r
esp
o
n
s
e
ti
m
e,
ac
cu
r
ac
y
an
d
th
e
o
s
cilla
tio
n
s
ar
o
u
n
d
th
e
o
p
tim
a
l
p
o
in
t.
I
n
th
e
s
i
m
u
la
tio
n
test
,
t
h
e
te
m
p
er
at
u
r
e
is
k
ep
t
eq
u
al
to
2
5
°C
.
Fig
u
r
e
9
s
h
o
w
s
s
i
m
u
lat
io
n
r
e
s
u
lts
i
n
r
esp
o
n
s
e
to
a
s
tep
c
h
an
g
e
o
f
ir
r
ad
iatio
n
o
f
5
0
0
to
1
0
0
0
W
/m
2
as
s
h
o
w
n
i
n
F
ig
u
r
e
9
.
a
Fig
u
r
e
9
.
b
illu
s
tr
ates
th
e
r
esp
o
n
s
e
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
te
m
in
ca
s
e
o
f
th
e
P
&
O
al
g
o
r
ith
m
.
I
t
s
ee
n
th
at
t
h
e
P
V
v
o
ltag
e
r
ea
c
h
es
th
e
o
p
ti
m
u
m
p
o
in
t
a
f
ter
0
.
2
s
ec
o
n
d
.
On
ce
t
h
e
o
p
ti
m
u
m
p
o
in
t
is
f
o
u
n
d
,
th
e
alg
o
r
ith
m
p
er
f
o
r
m
s
o
s
cil
latio
n
s
ar
o
u
n
d
th
e
MP
P
w
h
o
s
e
a
m
p
litu
d
e
d
o
es
n
o
t
ex
ce
ed
1
v
o
lt.
W
h
en
ap
p
l
y
i
n
g
o
f
th
e
ir
r
ad
iati
o
n
s
tep
ch
a
n
g
e,
th
e
MP
PT
alg
o
r
ith
m
f
i
n
d
s
t
h
e
n
e
w
o
p
ti
m
al
p
o
in
t a
f
ter
0
.
0
0
1
s
ec
o
n
d
an
d
co
n
tin
u
e
s
to
o
s
cillate
ar
o
u
n
d
t
h
i
s
p
o
in
t.
Oth
er
alg
o
r
it
h
m
s
ar
e
v
a
lid
at
ed
u
n
d
er
t
h
e
s
a
m
e
co
n
d
itio
n
s
m
e
n
tio
n
ed
ab
o
v
e.
Fig
u
r
e
9
.
c,
Fig
u
r
e
9
.
d
an
d
Fig
u
r
e
9
.
e
s
h
o
w
th
e
r
esp
o
n
s
e
o
f
th
e
P
V
s
y
s
te
m
in
ca
s
e
o
f
Hill
-
c
li
m
b
i
n
g
,
F
u
zz
y
a
n
d
I
n
c
-
C
o
n
d
MP
PT
.
T
ab
le
1
.
C
o
n
tr
o
l
P
a
r
am
eter
s
U
s
ed
in
th
e
Si
m
u
la
tio
n
T
ab
le
2
.
Ma
in
C
h
ar
ac
ter
is
tic
s
o
f
th
e
P
V
P
an
el
P
a
r
a
me
t
e
r
s
V
a
l
u
e
U
n
i
t
M
a
x
i
m
u
m
p
o
w
e
r
P
max
60W
R
L
10
Ω
M
a
x
i
m
u
m
p
o
w
e
r
V
max
16V
c
1
2
μF
O
u
t
p
u
t
v
o
l
t
a
g
e
a
t
P
m
a
x
V
oc
2
1
.
5
V
c
2
4
7
0
0
μF
O
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
I
cc
3
.
8
A
L
0
.
0
0
2
H
S
h
o
r
t
c
i
r
c
u
i
t
P
max
60W
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
4
4
–
1
7
5
5
1750
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
9
.
(
a)
Step
ir
r
a
d
ian
ce
,
(
b
)
Fu
zz
y
,
(
c)
Hill C
li
m
b
i
n
g
,
(
d
)
P
&
O,
(
e)
I
n
cCo
n
d
T
h
e
ev
alu
atio
n
o
f
t
h
e
p
er
f
o
r
m
an
ce
s
o
f
th
e
s
tu
d
ied
MP
PT
al
g
o
r
ith
m
s
is
p
er
f
o
r
m
ed
in
ca
s
e
o
f
a
h
ig
h
an
d
lo
w
ir
r
ad
iatio
n
.
T
h
e
cr
iter
ia
ar
e
th
e
r
esp
o
n
s
e
ti
m
e,
ac
cu
r
ac
y
an
d
t
h
e
a
m
p
litu
d
e
o
f
t
h
e
o
s
cillatio
n
ar
o
u
n
d
th
e
o
p
ti
m
u
m
p
o
i
n
t.
I
n
t
h
e
ca
s
e
o
f
h
ig
h
ir
r
ad
iatio
n
(
Fi
g
u
r
e
1
0
,
Fig
u
r
e
1
1
a
n
d
Fi
g
u
r
e
1
2
)
,
th
e
o
s
cil
latio
n
s
ar
o
u
n
d
t
h
e
MP
P
in
t
h
e
F
u
zz
y
a
n
d
I
n
c
-
C
o
n
d
MP
PT
ar
e
s
m
all
co
m
p
ar
ed
to
P
&
O
a
n
d
Hill
-
c
li
m
b
i
n
g
MP
P
T
w
h
ile
t
h
e
r
esp
o
n
s
e
ti
m
e
o
f
P
&
O,
I
n
c
-
C
o
n
d
an
d
Hill
-
C
li
m
b
in
g
MP
PT
is
a
b
etter
t
h
an
F
u
zz
y
MP
P
T
.
A
cc
o
r
d
in
g
to
Fi
g
u
r
e
1
2
,
th
e
e
r
r
o
r
f
r
o
m
t
h
e
th
eo
r
etica
l
v
al
u
e
in
I
n
c
-
C
o
n
d
al
g
o
r
ith
m
is
i
m
p
o
r
tan
t
co
m
p
ar
ed
to
th
e
o
th
er
s
al
g
o
r
ith
m
s
.
I
n
t
h
e
c
ase
o
f
lo
w
ir
r
ad
iatio
n
(
Fig
u
r
e1
3
,
Fig
u
r
e
1
4
an
d
Fig
u
r
e
1
5
)
th
e
s
a
m
e
r
e
m
ar
k
s
ar
e
r
ec
o
r
d
e
d
.
Fig
u
r
e
1
0
.
C
o
m
p
ar
ati
v
e
g
r
ap
h
o
f
t
i
m
e
r
esp
o
n
s
e
(
m
S)
Fig
u
r
e
11
.
C
o
m
p
ar
ati
v
e
g
r
ap
h
o
f
ac
cu
r
ac
y
(
m
V)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
a
ctica
l P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f Ma
ximu
m
P
o
w
e
r
P
o
in
t
Tr
a
ck
in
g
A
lg
o
r
ith
ms….
(
Ha
s
s
a
n
A
b
o
u
o
b
a
id
a
)
1751
Fig
u
r
e
12
.
C
o
m
p
ar
ati
v
e
g
r
ap
h
o
f
r
ip
p
le
(
m
V)
Fig
u
r
e
1
3
.
C
o
m
p
ar
ati
v
e
g
r
ap
h
o
f
t
i
m
e
r
esp
o
n
s
e
(
m
S)
Fig
u
r
e
14
.
C
o
m
p
ar
ati
v
e
g
r
ap
h
o
f
ac
cu
r
ac
y
(
m
V)
Fig
u
r
e
15
.
C
o
m
p
ar
ati
v
e
g
r
ap
h
o
f
r
ip
p
le
(
m
V)
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
6
.
P
r
ac
tical
im
p
le
m
e
n
tatio
n
,
(
a)
B
o
o
s
t c
o
n
tr
o
l a
cr
o
s
s
L
ab
j
ac
k
U1
2
C
ar
d
,
(
b
)
B
o
o
s
t c
o
n
v
er
ter
ca
r
d
,
(
c)
PW
M
C
ar
d
,
(
d
)
R
SM
-
6
0
PV P
an
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
7
4
4
–
1
7
5
5
1752
6.
P
RACTI
CAL
V
AL
I
DA
T
I
O
N
T
h
e
ev
al
u
atio
n
in
t
h
e
s
i
m
u
l
atio
n
p
h
a
s
e
r
e
m
ai
n
s
in
s
u
f
f
ic
ien
t
b
ec
a
u
s
e
t
h
e
s
i
m
u
lat
io
n
s
tu
d
y
ar
e
p
er
f
o
r
m
ed
b
ased
o
n
m
a
n
y
s
i
m
p
li
f
icatio
n
s
i
n
th
e
m
o
d
el
an
d
s
ev
er
al
p
ar
a
m
eter
s
ar
e
o
v
er
lo
o
k
ed
.
I
n
clu
d
e
f
o
r
ex
a
m
p
le,
t
h
e
ti
m
e
o
f
ac
q
u
i
s
iti
o
n
o
f
c
u
r
r
en
t
a
n
d
v
o
lta
g
e
s
e
n
s
o
r
s
,
th
e
in
ter
n
a
l
r
es
is
to
r
o
f
t
h
e
co
il,
th
e
s
w
i
tch
in
g
ti
m
e
o
f
t
h
e
MO
SF
E
T
an
d
t
h
e
ac
q
u
is
it
io
n
t
i
m
e
o
f
t
h
e
co
m
m
an
d
ca
r
d
.
T
o
d
ev
elo
p
a
p
er
f
o
r
m
a
n
ce
e
v
al
u
atio
n
w
it
h
a
b
etter
p
r
ec
is
io
n
,
th
e
b
o
o
s
t
ch
o
p
p
er
an
d
th
e
cu
r
r
en
t
an
d
v
o
ltag
e
s
en
s
o
r
s
o
f
a
P
V
p
an
el
ar
e
ex
p
er
i
m
e
n
tall
y
r
ea
li
ze
d
.
T
h
e
MP
PT
alg
o
r
ith
m
s
ar
e
i
m
p
le
m
en
ted
in
Ma
tlab
/
Si
m
u
li
n
k
.
T
h
e
F
i
g
u
r
e
1
6
s
h
o
w
s
th
e
d
iag
r
a
m
o
f
t
h
e
p
r
ac
tical
v
a
lid
atio
n
.
A
L
ab
j
ac
k
-
U1
2
ca
r
d
is
u
s
ed
as a
n
i
n
ter
f
ac
e
f
o
r
t
h
e
ac
q
u
is
itio
n
t
h
r
o
u
g
h
th
e
an
alo
g
to
d
ig
ital
co
n
v
er
s
i
o
n
o
f
P
V
cu
r
r
en
t
an
d
v
o
ltag
e.
T
h
is
ca
r
d
is
ch
ar
ac
ter
ized
b
y
a
1
2
-
b
it
r
eso
lu
tio
n
an
d
a
p
o
s
s
ib
ilit
y
o
f
co
n
v
er
s
io
n
o
f
8
an
alo
g
ch
a
n
n
e
ls
.
T
o
m
ea
s
u
r
e
th
e
P
V
cu
r
r
en
t
an
d
v
o
ltag
e,
th
e
AC
S7
1
2
an
d
I
SO
-
1
2
4
ar
e
u
s
ed
.
T
o
m
o
d
u
late
t
h
e
d
u
t
y
c
y
cle
a
P
W
M
ca
r
d
is
r
ea
l
ized
.
T
h
e
f
r
eq
u
en
c
y
o
f
t
h
e
P
W
M
co
n
tr
o
l
is
s
et
to
2
0
KH
Z
an
d
th
e
s
tep
s
ize
is
eq
u
al
to
0
.
0
1
.
T
o
en
s
u
r
e
d
ec
o
u
p
ag
e
f
u
n
c
tio
n
in
th
e
s
w
itc
h
i
n
g
p
o
w
er
co
n
v
er
ter
,
t
h
e
I
R
F2
5
0
MO
SF
E
T
is
u
s
ed
.
T
h
e
p
o
w
er
s
w
itc
h
is
c
h
ar
ac
ter
ized
b
y
a
m
ax
i
m
u
m
c
u
r
r
en
t
o
f
3
0
Am
p
s
an
d
s
u
p
p
o
r
ts
a
v
o
ltag
e
eq
u
al
to
2
0
0
Vo
lts
.
T
h
e
MP
PT
alg
o
r
ith
m
s
ar
e
i
m
p
le
m
e
n
ted
i
n
Ma
tlab
/Si
m
u
l
in
k
.
Go
o
d
k
n
o
wled
g
e
o
f
o
p
ti
m
u
m
p
o
i
n
t
r
eq
u
ir
es
k
n
o
w
led
g
e
o
f
t
h
e
p
an
el
p
o
w
er
cu
r
v
e.
T
h
e
f
ir
s
t
s
tep
is
to
id
en
ti
f
y
t
h
e
p
o
w
er
c
u
r
v
e
o
f
t
h
e
p
h
o
to
v
o
ltaic
p
a
n
el
.
Fig
u
r
e
17
-
1
9
s
h
o
w
t
h
e
p
o
w
e
r
cu
r
v
e
s
p
lo
tted
f
o
r
v
ar
io
u
s
ir
r
ad
iatio
n
s
.
I
n
ter
m
s
o
f
p
r
ac
tical
test
s
,
t
h
e
m
ea
s
u
r
e
d
tem
p
er
at
u
r
e
is
al
m
o
s
t c
o
n
s
ta
n
t e
q
u
al
to
3
0
°C
.
Fig
u
r
e
1
7
.
P
r
ac
tical
id
en
tif
icat
io
n
o
f
th
e
p
o
w
er
cu
r
v
e
a
n
d
th
e
cu
r
r
en
t
-
v
o
lta
g
e
ch
ar
ac
ter
i
s
tic
o
f
th
e
P
V
m
o
d
u
le
i
n
cli
m
atic
c
o
n
d
itio
n
s
(
G
=
7
0
0
W
/
m
2
a
n
d
T
=
3
0
°C
)
Fig
u
r
e
1
8
P
r
ac
tical
id
en
tif
icati
o
n
o
f
th
e
p
o
w
er
cu
r
v
e
a
n
d
th
e
cu
r
r
en
t
-
v
o
lta
g
e
ch
ar
ac
ter
i
s
tic
o
f
th
e
P
V
m
o
d
u
le
i
n
cli
m
atic
c
o
n
d
itio
n
s
(
G
=
6
5
0
W
/m
2
a
n
d
T
=
3
1
°
C
)
Fig
u
r
e
1
9
.
P
r
ac
tical
id
en
tif
icat
io
n
o
f
th
e
p
o
w
er
cu
r
v
e
a
n
d
th
e
cu
r
r
en
t
-
v
o
lta
g
e
ch
ar
ac
ter
i
s
tic
o
f
th
e
P
V
m
o
d
u
le
i
n
cli
m
atic
c
o
n
d
itio
n
s
(
G
=
4
6
0
W
/m
2
a
n
d
T
=
3
0
°C
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
a
ctica
l P
erfo
r
ma
n
ce
E
va
lu
a
tio
n
o
f Ma
ximu
m
P
o
w
e
r
P
o
in
t
Tr
a
ck
in
g
A
lg
o
r
ith
ms….
(
Ha
s
s
a
n
A
b
o
u
o
b
a
id
a
)
1753
P
r
ac
tical
v
alid
atio
n
i
s
co
n
d
u
c
ted
at
th
r
ee
le
v
els
o
f
s
o
lar
ir
r
ad
iatio
n
.
A
cc
o
r
d
in
g
to
t
h
e
p
o
w
er
c
u
r
v
e
illu
s
tr
ated
in
Fi
g
u
r
e
17
-
1
9
,
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
(
MP
P
)
is
s
tr
o
n
g
l
y
d
ep
en
d
en
t
o
n
t
h
e
ir
r
ad
iatio
n
le
v
el
an
d
m
o
v
es
w
it
h
ea
c
h
c
h
a
n
g
e
o
f
t
h
e
l
ig
h
t
in
te
n
s
it
y
.
A
t
th
e
ti
m
e
o
f
p
r
ac
tical
v
alid
atio
n
o
f
P
&
O
alg
o
r
it
h
m
,
s
o
lar
ir
r
ad
iatio
n
w
a
s
ab
o
u
t
7
0
0
W
/
m
2
an
d
a
te
m
p
er
at
u
r
e
is
3
0
°C
.
Fig
u
r
e
2
0
-
2
3
s
h
o
w
s
t
h
e
p
o
w
er
o
f
P
V
m
o
d
u
le,
t
h
e
P
V
v
o
ltag
e
a
n
d
th
e
lo
ad
v
o
ltag
e
ac
co
r
d
in
g
to
th
e
t
i
m
e
ch
an
g
e.
I
n
t
h
e
p
r
ev
io
u
s
l
y
m
en
tio
n
ed
w
ea
t
h
er
co
n
d
itio
n
s
,
it
f
i
n
d
s
th
at
t
h
e
a
v
er
ag
e
P
V
p
o
w
er
is
4
4
w
a
tts
a
n
d
th
e
P
V
v
o
ltag
e
p
er
f
o
r
m
s
o
s
cillatio
n
ar
o
u
n
d
1
3
Vo
lts
.
T
h
e
a
m
p
li
tu
d
e
o
f
t
h
e
o
s
cillatio
n
s
is
2
v
o
lt
s
.
I
t c
a
n
b
e
n
o
ticed
th
at
t
h
e
P
V
v
o
lta
g
e
r
ea
ch
es
th
e
MP
P
af
ter
2
s
ec
o
n
d
s
ac
co
r
d
in
g
to
F
ig
u
r
e
2
0
.
b
.
B
ased
o
n
th
e
p
o
w
er
cu
r
v
e
g
iv
e
n
in
Fi
g
u
r
e
1
7
,
th
e
o
p
tim
al
p
o
in
t
is
ch
ar
ac
ter
ized
b
y
a
v
o
lta
g
e
o
f
1
3
v
o
lts
a
n
d
a
p
o
w
er
o
f
4
4
W
atts
,
w
h
ic
h
co
in
cid
es
w
it
h
t
h
e
id
en
ti
f
icatio
n
p
o
w
e
r
cu
r
v
e
u
n
d
er
t
h
e
s
a
m
e
test
co
n
d
itio
n
s
.
He
n
ce
,
it
ca
n
b
e
co
n
cl
u
d
ed
th
at
t
h
e
o
p
ti
m
al
p
o
in
t
is
f
o
u
n
d
an
d
t
h
e
P
&
O
alg
o
r
ith
m
is
v
alid
ated
.
T
h
e
n
ex
t
s
tep
is
to
v
alid
ate
th
e
Hil
l
-
C
li
m
b
i
n
g
a
lg
o
r
it
h
m
.
A
cc
o
r
d
in
g
to
F
ig
u
r
e
2
1
,
th
e
m
ea
s
u
r
ed
ir
r
ad
iatio
n
is
eq
u
al
to
6
0
0
W
at
ts
/
m
2
.
T
h
e
m
ea
s
u
r
ed
v
o
ltag
e
i
s
1
5
Vo
lts
an
d
th
e
av
er
ag
e
p
o
w
er
is
eq
u
al
to
3
7
.
5
W
atts
.
I
t
is
f
o
u
n
d
t
h
at
t
h
e
P
V
v
o
ltag
e
r
ea
c
h
es
t
h
e
o
p
ti
m
al
v
alu
e
in
le
s
s
t
h
a
n
1
s
e
co
n
d
a
n
d
o
s
cillates
ar
o
u
n
d
th
e
MP
P
w
i
th
a
n
a
v
er
ag
e
a
m
p
litu
d
e
o
f
0
.
5
Vo
lt.
T
h
ese
r
es
u
lts
s
h
o
w
t
h
at
t
h
e
Hi
ll
-
c
li
m
b
i
n
g
alg
o
r
it
h
m
tr
ac
k
s
th
e
MP
P
.
I
n
t
h
e
f
o
llo
w
in
g
test
,
t
h
e
F
u
zz
y
MP
P
T
alg
o
r
ith
m
i
s
v
alid
ated
.
T
h
e
cli
m
atic
co
n
d
itio
n
s
ar
e
ch
ar
ac
ter
ized
b
y
a
s
u
d
d
e
n
tr
an
s
it
io
n
o
f
t
h
e
ir
r
ad
iatio
n
f
r
o
m
6
0
0
W
atts
/m
2
to
6
8
0
W
att/
m
2
.
T
h
e
s
tep
ch
an
g
e
i
s
a
ch
allen
g
e
w
h
ic
h
s
h
o
w
s
th
e
ab
ilit
y
o
f
th
e
MP
P
T
alg
o
r
ith
m
to
tr
ac
k
th
e
MP
P
.
A
cc
o
r
d
i
n
g
to
F
ig
u
r
e
2
2
,
it
is
f
o
u
n
d
th
a
t
t
h
e
m
ea
s
u
r
ed
v
al
u
e
o
f
t
h
e
v
o
lta
g
e
i
s
eq
u
al
to
1
5
.
2
Vo
lts
an
d
t
h
e
p
o
w
er
v
al
u
e
i
s
eq
u
al
to
3
6
W
atts
an
d
p
ass
es to
4
2
W
atts
at
ti
m
e
t=1
1
5
Seco
n
d
s
.
B
ased
o
n
Fig
u
r
e
2
2
,
th
e
P
V
v
o
ltag
e
r
ea
ch
es t
h
e
d
esire
d
v
al
u
e
af
ter
1
0
Seco
n
d
s
.
I
t c
an
b
e
n
o
ticed
th
at
th
e
F
u
zz
y
MP
P
T
alg
o
r
ith
m
is
ab
le
to
f
in
d
q
u
ick
l
y
t
h
e
n
e
w
o
p
ti
m
al
p
o
in
t
i
n
5
s
ec
o
n
d
s
.
W
h
en
th
e
s
y
s
te
m
f
i
n
d
s
th
e
MP
P
it
r
e
m
ai
n
s
t
h
er
e
an
d
o
s
cillates
ar
o
u
n
d
t
h
e
MP
P
w
ith
an
a
m
p
lit
u
d
e
o
f
0
.
5
Vo
lt.
T
h
e
p
r
ac
tical
v
alid
atio
n
r
es
u
lts
o
f
t
h
e
I
n
c
-
C
o
n
d
MPP
T
alg
o
r
ith
m
ar
e
illu
s
tr
ated
in
F
ig
u
r
e
2
3
.
T
h
e
P
V
s
y
s
te
m
is
ex
p
o
s
ed
to
ir
r
ad
i
atio
n
ch
a
n
g
e
f
r
o
m
6
0
0
W
atts
/
m
2
to
9
0
0
W
atts
/
m
2
.
A
t
th
e
MP
P
,
th
e
P
V
v
o
ltag
e
r
ea
ch
es
th
e
co
r
r
esp
o
n
d
in
g
v
a
lu
e
o
f
1
4
Vo
lts
in
a
1
Seco
n
d
.
T
h
e
r
esu
lts
g
iv
en
b
y
F
i
g
u
r
e
2
3
d
em
o
n
s
tr
ate
th
at
t
h
e
I
n
c
-
C
o
n
d
MP
PT
is
ab
le
t
o
f
in
d
th
e
o
p
ti
m
u
m
p
o
in
t.
L
o
g
ica
ll
y
,
t
h
e
p
r
ac
tical
r
esu
lt
s
d
o
n
o
t
allo
w
to
j
u
d
g
e
w
h
ic
h
o
f
th
e
s
e
ap
p
r
o
ac
h
es
is
th
e
b
est.
E
ac
h
MP
PT
alg
o
r
ith
m
h
a
s
d
if
f
er
en
t
p
er
f
o
r
m
a
n
ce
t
h
a
n
th
e
o
t
h
er
o
n
e.
I
t
w
as
f
o
u
n
d
th
a
t
th
e
c
o
n
v
e
n
tio
n
al
MP
P
T
(
P
&
O
an
d
H
ill
-
cli
m
b
in
g
)
ar
e
ef
f
icie
n
t
to
s
ea
r
ch
t
h
e
MP
P
ev
en
in
t
h
e
p
r
esen
ce
o
f
t
h
e
m
o
s
t
i
m
p
o
r
tan
t
o
s
cillatio
n
s
th
a
n
t
h
e
o
th
er
s
M
P
PT
alg
o
r
ith
m
s
.
I
f
t
h
e
o
s
cilla
tio
n
s
ar
e
d
is
ad
v
a
n
tag
e
s
,
th
e
P
&
O
an
d
I
n
c
-
C
o
n
d
alg
o
r
ith
m
s
ar
e
ea
s
y
an
d
s
i
m
p
l
e
to
im
p
le
m
e
n
t
p
r
ac
ticall
y
.
I
t
i
s
i
m
p
o
r
tan
t
to
n
o
te
t
h
at
th
e
r
es
p
o
n
s
e
ti
m
e
a
n
d
th
e
o
s
cillatio
n
s
o
f
th
e
P
&
O
a
n
d
I
n
c
-
C
o
n
d
al
g
o
r
ith
m
s
ar
e
g
r
ea
t
er
th
an
t
h
e
o
th
er
s
MP
PT
alg
o
r
ith
m
s
.
T
h
er
e
is
a
co
m
p
r
o
m
is
e
b
et
w
ee
n
r
esp
o
n
s
e
ti
m
e
a
n
d
th
e
o
s
cillatio
n
s
ar
o
u
n
d
t
h
e
MP
P
.
T
h
e
MP
PT
alg
o
r
ith
m
b
ased
o
n
Fu
zz
y
lo
g
ic
tak
e
s
a
lo
n
g
er
t
i
m
e
to
f
i
n
d
th
e
o
p
ti
m
al
p
o
in
t
b
u
t
h
as
s
m
a
ller
o
s
cillatio
n
s
.
I
n
ad
d
itio
n
,
th
i
s
ap
p
r
o
ac
h
p
r
esen
ts
a
m
o
r
e
co
m
p
licated
alg
o
r
ith
m
an
d
v
er
y
d
i
f
f
icu
lt
in
its
i
m
p
le
m
en
ta
t
io
n
.
T
h
e
I
n
c
-
C
o
n
d
MP
PT
alg
o
r
ith
m
is
s
i
m
p
le
i
n
its
i
m
p
le
m
en
ta
tio
n
a
n
d
h
as
s
m
aller
o
s
ci
llatio
n
s
ar
o
u
n
d
MP
P
b
u
t
f
i
n
d
s
d
i
f
f
ic
u
lt
to
ca
r
r
y
o
u
t r
eq
u
es
ted
eq
u
al.
A
cc
o
r
d
in
g
to
th
is
co
m
p
ar
ati
v
e
s
tu
d
y
,
t
h
e
ap
p
licatio
n
ar
ea
s
o
f
th
e
p
r
o
p
o
s
ed
MPPT
alg
o
r
ith
m
s
ar
e
as
f
o
llo
w
s
:
a.
I
n
th
e
f
ie
ld
s
o
f
s
atelli
tes
s
p
ac
e,
lo
o
k
in
g
f
o
r
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
m
u
s
t
b
e
as
s
h
o
r
tes
t
ti
m
e
as
p
o
s
s
ib
le.
It
is
in
ter
est
in
g
i
n
th
i
s
co
n
te
x
t
to
u
s
e
th
e
P
&
O
tech
n
iq
u
e
s
,
R
C
C
al
g
o
r
ith
m
o
r
Hill
-
cli
m
b
i
n
g
ap
p
r
o
ac
h
.
b.
I
n
t
h
e
s
o
lar
v
e
h
icles
ap
p
licati
o
n
s
,
lo
o
k
i
n
g
f
o
r
m
a
x
i
m
u
m
p
o
in
t
m
u
s
t
b
e
e
f
f
icien
t.
I
t
i
s
r
ec
o
m
m
e
n
d
ed
to
u
s
e
t
h
e
MP
PT
b
ased
o
n
f
u
zz
y
lo
g
ic.
c.
T
h
e
f
ield
o
f
p
u
b
lic
lig
h
ti
n
g
with
s
o
lar
p
o
w
er
,
t
h
e
b
atter
y
m
u
s
t
b
e
ch
ar
g
ed
d
u
r
i
n
g
t
h
e
d
a
y
to
w
o
r
k
t
h
e
n
ig
h
t.
A
le
s
s
co
m
p
lex
MP
P
T
eg
Hi
ll
C
li
m
b
in
g
o
r
P
&
O
o
r
o
th
er
s
tec
h
n
iq
u
es
d
is
c
u
s
s
ed
in
th
e
liter
at
u
r
e
w
il
l b
e
m
o
r
e
s
u
itab
le.
Fig
u
r
e
2
0
P
r
ac
tical
v
alid
atio
n
r
esu
lt
s
o
f
t
h
e
P
&
O
MP
PT
,
(
a
)
P
V
p
o
w
er
(
b
)
P
V
v
o
ltag
e
an
d
o
u
tp
u
t v
o
lta
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.