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I
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2252
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8
7
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2
C
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3
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wer
p
o
in
t
(
L
MPP)
as
th
e
f
ir
s
t
p
ea
k
f
o
u
n
d
is
ass
u
m
ed
to
b
e
th
e
h
ig
h
est
an
d
tak
e
tim
e
to
r
ea
ch
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
[
6
]
.
As
a
co
n
s
eq
u
en
ce
,
th
is
lim
itatio
n
r
esu
lts
in
h
u
g
e
p
o
w
er
lo
s
s
es si
n
ce
th
e
GM
PP
i
s
u
s
u
ally
f
ar
f
r
o
m
t
h
e
s
ea
r
ch
in
itia
l p
o
in
t
[
5
]
,
[
7
]
,
[
8
]
.
T
o
o
v
er
c
o
m
e
th
is
is
s
u
e,
m
etah
eu
r
is
tic
b
ased
o
p
tim
izatio
n
m
eth
o
d
s
h
av
e
b
ee
n
in
cr
ea
s
in
g
ly
u
tili
ze
d
.
B
o
th
o
f
th
ese
alg
o
r
ith
m
s
ar
e
b
ased
o
n
in
er
tial
b
ased
g
r
o
u
p
m
o
v
em
en
t
an
d
also
s
o
cial
co
g
n
itio
n
,
s
u
ch
as
th
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
o
r
u
tili
ze
m
ec
h
an
is
m
s
lik
e
co
m
b
in
at
o
r
ial
L
év
y
f
li
g
h
t
b
ase
d
p
r
o
ce
s
s
es
co
u
p
led
with
lo
ca
l
p
o
llin
atio
n
f
o
r
s
o
lv
i
n
g
c
o
m
p
le
x
lan
d
s
ca
p
e
p
r
o
b
lem
s
[
9
]
-
[
1
1
]
.
T
h
ese
ar
e
f
o
cu
s
ed
m
eth
o
d
s
wh
ich
h
av
e
p
r
ev
io
u
s
ly
b
ee
n
s
h
o
wn
as
ca
p
ab
le
o
f
a
cc
u
r
ately
id
en
tify
in
g
GM
PP
s
u
n
d
er
p
a
r
tial
s
h
ad
e
co
n
d
itio
n
s
[
1
2
]
,
[
1
3
]
.
T
h
eir
d
ir
ec
t
ap
p
licab
ilit
y
is
lim
ited
b
y
a
s
tr
o
n
g
d
ep
en
d
en
ce
o
n
p
ar
am
eter
tu
n
in
g
,
t
h
e
s
am
p
lin
g
r
ate
an
d
also
b
y
p
o
w
er
co
n
v
e
r
ter
d
y
n
am
ics.
Oth
er
l
im
itatio
n
s
ar
e
th
er
e
wer
e
lo
n
g
s
ettlin
g
tim
e
n
ee
d
,
tr
an
s
ien
t
o
s
cillatio
n
s
,
as
well
as
an
in
cr
ea
s
ed
p
r
o
b
ab
ilit
y
o
f
p
r
em
at
u
r
e
co
n
v
er
g
e
n
ce
if
d
iv
er
s
ity
am
o
n
g
th
e
s
ea
r
ch
p
o
p
u
latio
n
b
ec
o
m
es to
o
s
m
all
[
2
]
,
[
1
4
]
,
[
1
5
]
.
W
h
ile
th
er
e
h
a
v
e
b
ee
n
m
an
y
p
u
b
licatio
n
s
r
esear
ch
o
n
MP
PT
ar
ea
,
two
m
ajo
r
r
esear
ch
g
ap
s
h
a
v
e
b
ee
n
h
ig
h
lig
h
ted
in
s
ev
er
al
r
ec
en
t
liter
atu
r
e
r
ev
iews.
T
o
illu
s
tr
ate,
m
o
s
t
co
m
p
ar
ativ
e
s
tu
d
ies
h
av
e
o
n
ly
in
v
esti
g
ated
a
s
m
all
r
an
g
e
o
f
s
h
ad
in
g
co
n
d
itio
n
s
o
r
less
r
ep
r
esen
tativ
e
s
ce
n
ar
io
s
th
at
d
o
n
o
t
clo
s
ely
r
esem
b
le
r
ea
l
-
wo
r
ld
co
n
d
itio
n
s
.
Seco
n
d
,
th
er
e
is
s
till
n
o
g
o
o
d
s
tan
d
ar
d
f
o
r
r
ep
o
r
tin
g
o
n
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
c
e
in
d
icato
r
s
ac
r
o
s
s
a
m
u
lti
-
p
ea
k
cu
r
v
e
test
in
g
s
u
c
h
as
co
n
v
er
g
e
n
ce
tim
e,
tr
an
s
ien
t r
ip
p
le,
an
d
r
esis
tan
ce
o
f
lo
ca
l
v
alu
e
tr
ap
s
.
Mo
r
eo
v
e
r
,
ex
p
e
r
im
en
tal
v
alid
atio
n
in
h
ar
d
wa
r
e
-
in
-
th
e
-
l
o
o
p
(
HI
L
)
o
r
o
u
td
o
o
r
test
in
g
is
s
til
l
lim
ited
wh
en
c
o
m
p
ar
e
d
to
p
r
o
o
f
s
b
ased
s
o
lely
o
n
s
o
f
twar
e
s
im
u
latio
n
s
.
Ad
d
itio
n
ally
,
o
th
er
o
p
er
atio
n
al
asp
ec
ts
s
u
ch
as
p
ar
tial
s
h
ad
o
w
d
etec
tio
n
an
d
m
ec
h
an
is
m
s
to
r
estar
t
an
attac
k
ed
alg
o
r
it
h
m
h
a
v
e
n
o
t
b
ee
n
co
m
p
r
eh
e
n
s
iv
ely
s
tu
d
ied
[
2
]
,
[
1
6
]
-
[
1
8
]
.
Alth
o
u
g
h
o
th
er
o
p
tio
n
s
o
f
m
e
ta
-
h
eu
r
is
tics
ar
e
also
p
o
s
s
ib
le
f
o
r
m
u
ltimo
d
al
PV
lan
d
s
ca
p
es,
s
u
ch
as
g
en
etic
alg
o
r
ith
m
s
(
GA)
o
r
g
r
ey
wo
lf
o
p
tim
izatio
n
(
GW
O)
,
th
is
wo
r
k
ap
p
r
o
ac
h
es
a
c
o
m
p
ar
ativ
e
an
al
y
s
is
b
etwe
en
PS
O
an
d
f
lo
wer
p
o
lli
n
atio
n
alg
o
r
ith
m
(
FP
A)
(
co
n
v
en
tio
n
al
m
eth
o
d
s
)
.
T
h
e
r
ea
s
o
n
to
ch
o
o
s
e
PS
O
an
d
FP
A
i
s
b
ec
au
s
e
th
ey
h
av
e
r
esp
ec
tiv
e
b
en
ef
its
in
p
r
eser
v
in
g
th
e
p
ath
way
s
o
f
g
lo
b
al
ex
p
lo
r
atio
n
an
d
lo
ca
l
ex
p
lo
itatio
n
ef
f
ec
tiv
ely
.
FP
A
ap
p
lies
d
y
n
am
ic
tr
an
s
itio
n
p
r
o
b
ab
ilit
ies
to
alter
n
ate
b
etwe
e
n
g
lo
b
al
s
ea
r
ch
an
d
lo
ca
l
ex
p
lo
itatio
n
,
r
esu
ltin
g
in
FP
A
b
ein
g
v
er
y
ad
ap
ta
b
le
f
o
r
n
o
n
lin
ea
r
o
p
tim
izatio
n
p
r
o
b
lem
[
1
9
]
,
[
2
0
]
.
Me
an
wh
ile,
PS
O
is
f
am
o
u
s
f
o
r
its
tr
ajec
to
r
y
f
lex
ib
ilit
y
o
f
p
ar
ticles
in
d
is
tin
g
u
is
h
in
g
lo
ca
l
to
g
lo
b
al
p
ea
k
s
[
2
1
]
.
T
h
e
two
m
eth
o
d
s
h
av
e
p
r
o
v
en
to
b
e
co
n
s
is
ten
tly
m
o
r
e
s
tab
le
an
d
co
m
p
etitiv
e
in
s
ea
r
ch
in
g
th
e
s
o
lu
tio
n
s
p
ac
e
g
iv
en
th
e
c
h
ar
ac
ter
is
tics
o
f
s
h
ad
o
we
d
PV sy
s
tem
s
[
2
2
]
.
Hen
ce
,
th
e
o
b
jectiv
e
o
f
th
is
m
an
u
s
cr
ip
t
is
to
s
h
o
w
an
ex
ten
s
iv
e
co
m
p
ar
ativ
e
s
tu
d
y
b
et
wee
n
P&
O,
I
n
C
,
PS
O
an
d
FP
A
f
o
r
a
to
tal
o
f
s
ix
ir
r
ad
iatio
n
lev
els
co
n
s
t
r
ain
ed
to
o
b
tai
n
u
p
to
f
i
v
e
d
if
f
er
en
t
cr
ests
in
th
e
P
–
V
cu
r
v
e.
T
h
is
r
ep
ea
ts
f
o
r
e
ac
h
s
ce
n
ar
io
,
s
u
ch
th
at
th
e
G
MPP
p
o
s
itio
n
v
ar
ies
wild
ly
b
e
twee
n
s
tar
tin
g
at
th
e
f
ir
s
t
p
ea
k
an
d
f
in
is
h
in
g
o
n
th
e
“e
d
g
e”
(
th
e
f
if
th
p
ea
k
)
.
T
h
i
s
m
eth
o
d
p
u
ts
th
e
L
MPP
-
av
er
s
e
p
r
o
p
er
t
y
o
f
th
e
alg
o
r
ith
m
u
n
d
er
s
tr
in
g
en
t
s
cr
u
tin
y
.
T
ests
co
n
d
u
cted
o
n
a
PV
s
tr
in
g
m
o
d
el
attac
h
ed
to
b
o
th
a
b
y
p
ass
d
io
d
e
an
d
b
o
o
s
t
co
n
v
e
r
ter
ar
e
th
e
n
in
s
p
e
cted
v
ia
p
ar
am
eter
s
,
in
clu
d
in
g
tr
ac
k
in
g
p
r
ec
is
io
n
,
co
n
v
er
g
e
n
ce
tim
e
len
g
th
,
an
d
s
tead
y
-
s
tate
s
tab
ilit
y
.
T
h
is
f
r
am
ewo
r
k
is
in
ten
d
ed
to
v
er
if
y
a
test
in
g
m
ea
s
u
r
e
o
f
s
y
s
tem
ac
cu
r
ac
y
,
p
er
f
o
r
m
an
ce
an
d
d
e
p
en
d
a
b
ilit
y
f
o
r
o
u
td
o
o
r
u
s
es
[
1
]
-
[
3
]
,
[
2
3
]
,
[
2
4
]
.
T
h
is
s
tu
d
y
m
ak
es
t
h
r
ee
m
ain
co
n
tr
ib
u
tio
n
s
.
T
h
e
n
u
m
b
er
o
n
e
is
th
e
c
r
ea
tio
n
o
f
a
u
n
if
ied
m
u
lti
-
s
ce
n
ar
io
test
b
ed
,
u
n
d
er
p
in
n
in
g
o
n
th
e
f
if
th
p
ea
k
s
ce
n
ar
io
wh
i
ch
was
id
en
tifie
d
as
th
e
h
a
r
d
e
s
t
p
ar
t
to
s
ea
r
ch
b
y
an
y
way
.
Seco
n
d
,
it
o
f
f
er
s
a
d
ee
p
s
y
n
th
esis
o
f
p
er
f
o
r
m
an
c
e
tr
ad
e
-
o
f
f
s
:
class
ical
alg
o
r
ith
m
s
ar
e
f
ast
b
u
t
f
ail,
wh
ile
m
etah
eu
r
is
tics
en
s
u
r
e
(
i
n
th
eo
r
y
)
g
lo
b
al
s
ea
r
ch
i
n
ex
c
h
an
g
e
f
o
r
ex
tr
a
tim
e.
T
h
ir
d
,
b
ased
o
n
th
e
test
in
g
d
ata
we
p
r
o
v
id
e
a
p
r
ac
tical
g
u
id
e
f
o
r
s
y
s
tem
d
esig
n
e
r
s
to
ch
o
o
s
e
am
o
n
g
a
m
u
lti
o
f
test
ed
alg
o
r
ith
m
s
th
eir
s
in
g
le
MPPT
alg
o
r
ith
m
th
at
is
clo
s
er
to
th
e
co
n
d
itio
n
s
th
ey
will
b
e
wo
r
k
in
g
with
in
t
h
e
f
ield
,
th
e
r
ef
o
r
e
h
elp
in
g
th
e
m
av
o
i
d
co
m
p
lex
h
y
b
r
id
a
p
p
r
o
ac
h
es.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
ar
ticle
i
s
as
f
o
llo
ws:
Sectio
n
2
p
r
o
v
id
es
s
p
ec
if
icatio
n
s
ab
o
u
t
th
e
PV
s
y
s
tem
,
co
n
v
er
ter
an
d
i
r
r
ad
iatio
n
m
o
d
elin
g
d
esig
n
.
Sectio
n
3
p
r
e
s
en
ts
th
e
co
m
p
ar
ativ
e
p
er
f
o
r
m
an
ce
o
f
th
e
f
o
u
r
alg
o
r
ith
m
s
,
f
o
c
u
s
in
g
o
n
a
r
e
v
iew
o
f
ac
cu
r
ac
y
an
d
r
esp
o
n
s
e
tim
e
d
y
n
am
ics
as
well
as
an
an
aly
s
is
o
f
s
ea
r
ch
f
ailu
r
e
wh
en
t
h
e
p
ea
k
p
o
in
t
ass
u
m
es
th
e
last
p
o
s
itio
n
.
Sectio
n
4
d
is
cu
s
s
es
a
cr
o
s
s
-
s
ce
n
ar
io
s
y
n
th
esis
an
d
p
r
ac
tical
im
p
licatio
n
s
f
o
r
d
es
ig
n
o
f
c
o
n
tr
o
ller
s
.
L
astl
y
,
Se
ctio
n
5
p
r
esen
ts
r
esear
ch
f
in
d
in
g
s
an
d
s
u
g
g
ests
f
u
tu
r
e
s
tu
d
y
,
f
o
cu
s
in
g
o
n
h
ar
d
war
e
-
in
-
th
e
-
lo
o
p
v
alid
atio
n
[
2
]
,
s
en
s
itiv
ity
s
tu
d
ies
[
1
5
]
,
an
d
o
p
tim
izatio
n
o
f
co
m
p
u
tatio
n
al
l
o
ad
im
p
o
s
ed
i
n
em
b
ed
d
ed
d
ev
ices
[
2
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.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
4
2
2
-
1
4
3
8
1424
2.
M
E
T
H
O
D
2
.
1
.
M
o
delin
g
o
f
c
a
s
e
s
ce
na
rio
s
T
h
e
PV
s
y
s
tem
o
n
th
is
r
esea
r
ch
co
n
s
is
ts
o
f
a
f
iv
e
-
m
o
d
u
le
p
h
o
to
v
o
ltaic
(
PV)
s
tr
in
g
co
n
n
ec
ted
in
s
er
ies,
with
ea
ch
m
o
d
u
le
eq
u
i
p
p
ed
with
b
y
p
ass
d
io
d
es
to
p
r
ev
en
t
r
ev
e
r
s
e
-
b
ias
s
tr
ess
an
d
h
o
t
-
s
p
o
t
f
o
r
m
atio
n
u
n
d
er
n
o
n
-
u
n
i
f
o
r
m
ir
r
ad
ian
ce
[
1
]
,
[
3
]
.
T
h
is
co
n
f
ig
u
r
atio
n
s
ce
n
ar
io
was
s
elec
ted
to
g
en
er
ate
a
m
u
lti
-
p
ea
k
p
o
wer
–
v
o
ltag
e
(
P
–
V)
cu
r
v
e
an
d
f
o
r
e
n
ab
lin
g
s
y
s
tem
atic
ev
alu
atio
n
o
f
MPPT
alg
o
r
i
th
m
s
u
n
d
er
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
(
Fig
u
r
e
1
)
.
T
h
e
d
etail
o
f
tech
n
ical
s
p
ec
if
icatio
n
s
f
o
r
ea
c
h
m
o
d
u
le
is
lis
ted
in
T
ab
le
1
.
B
y
p
ass
d
io
d
es
im
p
lem
en
ted
f
o
r
p
r
o
v
id
in
g
an
alter
n
ativ
e
cu
r
r
en
t
p
at
h
wh
en
ce
lls
ar
e
s
h
ad
ed
,
r
e
d
u
cin
g
o
f
p
o
wer
lo
s
s
an
d
f
o
r
p
r
e
v
en
tin
g
th
e
d
am
ag
e
im
p
ac
t.
Un
d
e
r
n
o
r
m
al
c
o
n
d
itio
n
s
,
th
ese
d
io
d
es
r
em
ain
r
ev
er
s
e
-
b
iased
;
h
o
wev
er
,
wh
e
n
s
h
ad
i
n
g
o
cc
u
r
s
,
th
ey
will
b
ec
o
m
e
as
f
o
r
war
d
-
b
iased
,
ac
t
an
d
allo
win
g
cu
r
r
e
n
t
to
b
y
p
ass
s
h
ad
ed
ce
lls
.
T
h
is
d
esig
n
to
e
n
s
u
r
es r
ea
lis
tic
m
o
d
elin
g
o
f
PV b
e
h
av
io
r
u
n
d
e
r
d
y
n
a
m
ic
ir
r
ad
ian
ce
.
On
th
is
r
esear
ch
,
th
e
r
e
wer
e
s
ix
ir
r
ad
ian
ce
test
b
ed
s
ce
n
a
r
i
o
s
to
em
u
late
u
n
if
o
r
m
an
d
al
s
o
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
(
T
ab
le
2
)
.
Scen
ar
io
1
r
ep
r
esen
ts
u
n
if
o
r
m
ir
r
ad
ian
ce
an
d
p
r
o
d
u
cin
g
a
s
in
g
le
p
ea
k
,
wh
ile
o
n
Scen
ar
io
s
2
–
6
in
tr
o
d
u
ce
th
e
p
r
o
ce
s
s
o
f
m
u
ltip
le
p
ea
k
s
,
with
th
e
GM
PP
m
ig
r
atin
g
f
r
o
m
th
e
f
ir
s
t
to
th
e
f
if
th
p
ea
k
.
T
h
is
s
y
s
tem
atic
v
ar
iatio
n
will
ch
allen
g
e
all
o
f
alg
o
r
it
h
m
s
th
at
ch
o
o
s
e
,
f
o
r
f
in
d
in
g
th
e
ab
ilit
y
to
av
o
id
lo
ca
l
m
ax
im
a
an
d
tr
ac
k
th
e
tr
u
e
GM
PP
,
r
e
f
lectin
g
r
ea
l
-
wo
r
ld
s
h
a
d
in
g
p
atter
n
s
ca
u
s
ed
b
y
clo
u
d
s
o
r
o
b
s
tr
u
ctio
n
s
[
3
]
,
[
1
6
]
.
Fig
u
r
e
1
.
Mo
d
eled
P
–
V
ch
a
r
a
cter
is
tic
cu
r
v
es f
o
r
s
h
ad
in
g
s
c
en
ar
io
s
T
ab
le
1
.
Ph
o
t
o
v
o
ltaic
s
p
ec
if
ic
atio
n
s
P
a
r
a
me
t
e
r
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
(
p
m
p
p
)
6
0
0
W
p
M
a
x
i
m
u
m
v
o
l
t
a
g
e
(
v
m
pp
)
4
1
.
2
4
V
M
a
x
i
m
u
m
c
u
r
r
e
n
t
(
i
m
pp
)
1
4
.
5
5
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
v
oc
)
4
8
.
9
8
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
i
sc
)
1
5
,
4
1
A
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
V
oc
-
0
.
2
5
%/
ºC
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
I
sc
0
.
0
4
5
%
/
º
C
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
s
tu
d
y
o
f MP
P
T a
lg
o
r
ith
m
o
n
p
h
o
to
vo
lta
ic
s
tr
in
g
u
n
d
er
p
a
r
tia
l sh
a
d
in
g
(
Dikp
r
id
e
Desp
a
)
1425
T
ab
le
2.
I
r
r
ad
ian
ce
lev
els f
o
r
p
ar
tial sh
ad
in
g
s
ce
n
ar
i
o
s
S
c
e
n
a
r
i
o
I
r
r
a
d
i
a
n
c
e
(
W
/
m
2
)
M
1
M
2
M
3
M
4
M
5
1
1
,
0
0
0
1
,
0
0
0
1
,
0
0
0
1
,
0
0
0
1
,
0
0
0
2
1
,
0
0
0
9
0
0
8
0
0
7
0
0
6
0
0
3
1
,
0
0
0
8
5
0
7
0
0
5
5
0
4
0
0
4
1
,
0
0
0
8
0
0
6
0
0
4
0
0
2
0
0
5
9
5
0
6
0
0
3
5
0
2
5
0
1
5
0
6
9
5
0
3
5
0
2
0
0
1
0
0
50
2
.
2
.
M
o
delin
g
s
y
s
t
em
s
Af
ter
th
e
P
-
V
cu
r
v
e
v
ar
iatio
n
s
test
b
ed
s
wer
e
alr
ea
d
y
s
im
u
lated
,
MPPT
was
p
e
r
f
o
r
m
ed
with
f
o
u
r
alg
o
r
ith
m
s
:
i)
P&
O,
ii)
I
n
C
,
iii)
PS
O,
an
d
iv
)
FP
A.
T
h
e
tr
ac
k
in
g
p
r
o
ce
s
s
was
d
ev
elo
p
ed
o
n
MA
T
L
AB
-
Simu
lin
k
R
2
0
2
1
a
s
o
f
twar
e,
a
n
d
u
s
in
g
a
d
is
cr
ete
f
ix
ed
-
s
tep
s
o
lv
er
.
T
h
e
s
tep
s
ize
was set to
1
×
10
−
5
s
,
at
least
ten
tim
es
f
aster
th
an
th
e
PW
M
p
er
io
d
,
to
ac
cu
r
ately
ca
p
tu
r
e
s
witch
in
g
d
y
n
am
ics.
T
h
e
t
o
tal
s
im
u
latio
n
tim
e
was
s
et
to
1
.
5
s
p
er
s
ce
n
ar
io
,
s
u
f
f
icien
t
to
o
b
s
er
v
e
f
u
ll
co
n
v
er
g
en
ce
.
C
ell
tem
p
er
atu
r
e
was
f
ix
ed
s
et
v
alu
e
at
2
5
°C
,
an
d
s
en
s
o
r
n
o
is
e
was d
is
ab
led
to
is
o
late
alg
o
r
ith
m
ic
p
er
f
o
r
m
a
n
ce
.
T
h
ese
ass
u
m
p
tio
n
s
alig
n
with
p
r
io
r
MPPT
b
en
ch
m
a
r
k
in
g
s
tu
d
ies
at
s
ev
er
al
wo
r
k
s
[
2
]
,
[
3
]
,
[
2
6
]
.
T
h
e
MPPT
co
n
tr
o
ller
will
co
m
p
u
t
e
th
e
o
p
tim
al
d
u
ty
c
y
cle
an
d
ap
p
lies
it
to
th
e
b
o
o
s
t
co
n
v
er
ter
to
r
e
g
u
late
PV
o
u
tp
u
t
v
o
ltag
e.
C
o
n
v
e
r
ter
p
ar
am
eter
s
f
o
llo
w
at
T
ab
le
3
;
in
p
u
t/o
u
tp
u
t
ca
p
ac
ito
r
s
in
=
out
=
110
F
,
in
d
u
cto
r
=
930
H
,
s
witch
in
g
f
r
e
q
u
en
c
y
=
5
k
Hz
,
an
d
l
o
ad
=
120
Ω
.
T
h
ese
p
ar
am
eter
v
al
u
es
wer
e
ch
o
s
en
s
o
th
at
th
e
in
d
u
cto
r
cu
r
r
en
t
r
i
p
p
le
r
em
ain
ed
b
elo
w
1
0
%,
wh
ile
o
u
tp
u
t
v
o
ltag
e
r
ip
p
les
ar
o
u
n
d
its
d
u
e
v
alu
e
d
o
es
n
o
t
ex
ce
e
d
2
%.
T
h
is
en
s
u
r
es
s
tab
le
o
p
er
atio
n
d
u
r
in
g
MPPT
p
er
tu
r
b
atio
n
s
.
Fig
u
r
e
2
d
e
p
icts
th
e
s
y
s
tem
ar
ch
itectu
r
e
test
b
ed
,
co
n
f
ig
u
r
e
d
in
a
s
tan
d
ar
d
c
o
n
f
ig
u
r
atio
n
f
o
u
n
d
in
liter
atu
r
e
as
PV
→
M
PP
T
→
b
o
o
s
t
co
n
v
er
ter
→
lo
ad
,
wh
ich
is
a
co
m
m
o
n
ch
o
ice
d
u
e
to
d
ec
o
u
p
lin
g
o
f
th
e
PV
o
p
er
atin
g
p
o
in
t
f
r
o
m
d
o
wn
s
tr
ea
m
lo
a
d
s
wh
ile
m
ain
tain
in
g
d
y
n
am
ic
in
ter
a
ctio
n
s
r
elev
an
t
f
o
r
b
en
ch
m
ar
k
in
g
[
3
]
.
T
h
is
s
etu
p
allo
ws
f
o
r
s
y
s
tem
atic
test
in
g
o
f
MPPT
alg
o
r
ith
m
s
u
n
d
er
m
u
ltip
le
p
ea
k
P
–
V
ch
ar
ac
ter
is
tics
b
r
o
u
g
h
t
o
n
b
y
p
ar
tial sh
ad
in
g
.
T
ab
le
3
.
Par
am
eter
o
f
th
e
b
o
o
s
t c
o
n
v
er
ter
P
a
r
a
me
t
e
r
V
a
l
u
e
C1
1
1
0
µ
F
C2
1
1
0
µ
F
L
9
3
0
µ
H
F
5
k
H
z
R
1
2
0
Ω
Fig
u
r
e
2
.
Mo
d
elin
g
s
y
s
tem
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.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
4
2
2
-
1
4
3
8
1426
2
.
3
.
M
P
P
T
a
lg
o
rit
h
m
s
T
h
is
r
esear
ch
u
s
in
g
4
MPPT
alg
o
r
ith
m
s
f
o
r
e
v
alu
ated
:
t
h
er
e
was
i)
P&
O,
ii)
I
n
C
,
iii)
PS
O,
an
d
iv
)
FPA
.
P&
O
p
er
tu
r
b
s
th
e
d
u
t
y
cy
cle
an
d
r
ev
er
s
es d
ir
ec
tio
n
wh
en
p
o
wer
d
ec
r
ea
s
es; a
f
ix
ed
s
tep
s
ize
o
f
0
.
0
0
1
was
u
s
ed
to
m
in
im
ize
o
s
cillatio
n
wh
ile
m
ain
tain
in
g
ac
c
ep
tab
le
an
d
c
o
n
v
er
g
en
ce
s
p
ee
d
[
4
]
,
[
2
4
]
.
I
n
C
co
m
p
ar
es
d
/
d
to
−
/
an
d
a
d
ju
s
ts
th
e
r
ef
er
en
ce
v
o
ltag
e
d
y
n
am
ically
;
an
ad
a
p
tiv
e
m
ec
h
an
is
m
co
m
b
in
ed
with
a
b
ase
s
tep
s
ize
o
f
0
.
0
0
1
ac
ce
ler
ates
co
n
v
er
g
e
n
ce
f
ar
f
r
o
m
th
e
MPP
[
5
]
,
[
2
7
]
-
[
2
9
]
.
W
h
ile
PS
O
alg
o
r
ith
m
was
co
n
f
ig
u
r
e
d
with
5
p
ar
ticl
es,
in
er
tia
weig
h
t
=
0
.
5
,
an
d
ac
ce
le
r
atio
n
co
ef
f
icien
ts
1
=
1
.
5
an
d
2
=
1
.
1
.
f
o
r
a
v
o
id
in
g
p
r
em
atu
r
e
co
n
v
er
g
en
ce
a
n
d
f
o
r
th
e
p
r
eser
v
a
tio
n
o
f
s
war
m
d
i
v
er
s
ity
v
elo
city
clam
p
in
g
an
d
in
er
tia
r
ed
u
ctio
n
wer
e
u
s
ed
[
2
5
]
,
[
2
9
]
.
T
o
r
etain
g
lo
b
al
s
ea
r
c
h
ca
p
ab
ilit
y
o
v
er
m
u
ltim
o
d
al
P
-
V
lan
d
s
ca
p
e
[
1
0
]
,
[
3
0
]
,
[
3
1
]
,
FP
A
ap
p
lied
a
s
wit
ch
in
g
p
r
o
b
ab
ilit
y
o
f
0
.
8
an
d
L
ev
y
f
lig
h
t
s
tep
s
ize
o
f
1
.
5
ac
co
r
d
in
g
to
p
r
ev
io
u
s
s
tu
d
ies
th
at
im
p
lem
en
t
d
if
f
e
r
e
n
t
v
ar
ian
ts
o
f
FP
A
-
b
ased
MP
PT
alg
o
r
ith
m
[
2
9
]
,
[
3
0
]
.
All
a
lg
o
r
ith
m
s
th
at
wer
e
f
ix
ed
in
th
e
s
ce
n
ar
io
wer
e
in
i
tialized
to
th
e
s
am
e
v
alu
es
at
th
e
b
eg
in
n
in
g
o
f
ea
ch
s
ce
n
a
r
io
an
d
d
u
t
y
cy
cle
u
p
d
ates c
o
in
cid
e
d
with
th
e
co
n
tr
o
l sam
p
lin
g
p
er
io
d
,
p
r
o
v
id
i
n
g
a
f
air
co
m
p
a
r
is
o
n
.
2
.
3
.
1
.
P
er
t
urb a
nd
o
bs
er
v
e
T
h
e
P&
O
alg
o
r
ith
m
m
eth
o
d
i
s
a
tech
n
iq
u
e
u
s
ed
f
o
r
MPPT
[
2
5
]
.
T
h
e
o
p
er
atio
n
o
f
th
is
te
ch
n
iq
u
e
is
th
at
th
e
v
o
ltag
e
o
r
cu
r
r
en
t
o
f
th
e
PV
s
y
s
tem
is
d
is
tu
r
b
ed
,
an
d
th
e
p
o
wer
d
if
f
e
r
en
ce
g
en
er
ated
f
r
o
m
d
is
tu
r
b
an
ce
will
b
e
m
o
n
ito
r
e
d
.
I
f
in
cr
ea
s
in
g
p
o
wer
,
th
e
p
er
tu
r
b
atio
n
p
r
o
ce
ed
s
as
b
ef
o
r
e;
if
d
ec
r
ea
s
in
g
,
th
e
p
er
tu
r
b
atio
n
r
ev
e
r
s
es.
T
h
e
p
r
o
ce
s
s
will
co
n
tin
u
e
u
n
til
th
e
M
PP
is
ac
h
iev
ed
,
an
d
wh
ic
h
is
wh
en
th
e
PV
s
y
s
tem
o
p
er
ates a
t p
ea
k
e
f
f
icien
cy
[
3
2
]
.
T
h
is
r
elatio
n
s
h
ip
ca
n
b
e
e
x
p
r
ess
ed
m
ath
em
atica
lly
as
(
1
)
a
n
d
(
2
)
.
=
(
)
−
(
−
1
)
(
1
)
=
(
)
−
(
−
1
)
(
2
)
L
et
P
r
ep
r
esen
t th
e
c
h
an
g
e
in
p
o
wer
an
d
V
d
en
o
te
th
e
ch
a
n
g
e
i
n
v
o
ltag
e.
T
h
e
f
l
o
wch
ar
t o
f
th
e
m
eth
o
d
is
d
ep
icted
in
Fig
u
r
e
3
.
Fig
u
r
e
3.
Flo
wch
ar
t
o
f
p
er
tu
r
b
an
d
o
b
s
er
v
e
2
.
3
.
2
.
I
ncre
m
ent
a
l
c
o
nd
uct
a
nce
T
h
e
I
n
C
alg
o
r
ith
m
is
a
p
o
p
u
l
ar
alg
o
r
ith
m
th
at
u
s
ed
f
o
r
o
p
t
im
izin
g
th
e
p
er
f
o
r
m
an
ce
o
f
s
o
lar
p
an
els
b
y
ac
cu
r
ately
d
eter
m
in
in
g
th
e
MPP.
T
h
is
alg
o
r
ith
m
o
p
er
ate
s
b
y
an
aly
zi
n
g
th
e
s
lo
p
e
o
f
th
e
p
o
wer
-
v
o
ltag
e
(
P
-
V)
ch
ar
ac
ter
is
tic
cu
r
v
e
o
f
s
o
la
r
ce
lls
[
1
7
]
,
[
3
3
]
.
T
h
e
o
p
tim
al
o
p
er
atin
g
p
o
in
ts
v
alu
e,
s
p
ec
if
ically
th
e
m
ax
im
u
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
s
tu
d
y
o
f MP
P
T a
lg
o
r
ith
m
o
n
p
h
o
to
vo
lta
ic
s
tr
in
g
u
n
d
er
p
a
r
tia
l sh
a
d
in
g
(
Dikp
r
id
e
Desp
a
)
1427
p
o
wer
v
o
ltag
e
(
V
MPP
)
an
d
cu
r
r
en
t
(
I
MPP
)
,
ar
e
in
f
l
u
en
ce
d
b
y
en
v
ir
o
n
m
en
tal
f
ac
to
r
s
s
u
ch
as
ir
r
ad
ian
ce
an
d
also
th
e
tem
p
er
at
u
r
e
v
alu
e.
T
h
e
M
PP
T
alg
o
r
ith
m
d
y
n
am
ically
a
d
ju
s
ts
th
e
r
ef
e
r
en
ce
v
o
ltag
e
(
V
ref
)
f
o
r
en
s
u
r
i
n
g
th
e
s
o
lar
p
an
el
o
p
er
ates
at
th
eir
m
ax
im
u
m
p
o
we
r
p
o
in
t
[
3
4
]
.
Fig
u
r
e
4
d
escr
ib
es
th
e
f
lo
wch
ar
t
o
f
in
cr
em
e
n
tal
co
n
d
u
cta
n
ce
.
T
h
is
r
elatio
n
s
h
ip
ca
n
b
e
e
x
p
r
ess
ed
m
ath
em
atic
ally
as
(
3
)
.
=
0
(
3
)
L
et
dP
r
ep
r
esen
t
th
e
ch
an
g
e
in
p
o
wer
an
d
dV
d
en
o
te
th
e
ch
an
g
e
in
v
o
ltag
e.
Sin
ce
p
o
wer
P
is
th
e
p
r
o
d
u
ct
o
f
v
o
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e
an
d
cu
r
r
en
t (
i.e
.
,
=
.
)
,
th
e
ab
o
v
e
e
q
u
atio
n
ca
n
b
e
r
ef
o
r
m
u
lated
as f
o
llo
ws:
=
(
×
)
=
+
(
4
)
+
=
0
(
5
)
=
−
(
6
)
L
et
dI
r
ep
r
esen
t
th
e
cu
r
r
e
n
t
ch
an
g
e,
dV
r
ep
r
esen
t
th
e
v
o
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e
ch
an
g
e,
I
r
ep
r
esen
t
th
e
cu
r
r
e
n
t,
an
d
V
r
ep
r
esen
t
th
e
v
o
ltag
e.
T
h
e
f
lo
wc
h
ar
t o
f
th
e
m
eth
o
d
is
d
ep
icted
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
Flo
wch
ar
t
o
f
in
c
r
em
en
tal
co
n
d
u
ctan
ce
2
.
3
.
3
.
P
a
rt
icle
s
wa
rm
o
pti
m
iza
t
io
n
(
P
SO
)
T
h
e
PS
O
is
an
o
p
tim
izatio
n
t
ec
h
n
iq
u
e
t
h
at
was
in
tr
o
d
u
ce
d
b
y
Ken
n
e
d
y
a
n
d
E
b
er
h
a
r
t
[
3
3
]
b
ased
o
n
th
e
f
lo
ck
in
g
b
eh
a
v
io
r
o
f
b
i
r
d
s
in
th
eir
q
u
est
f
o
r
f
o
o
d
.
I
t
is
b
a
s
ed
o
n
an
al
g
o
r
ith
m
th
at
u
s
es
th
e
f
ly
in
g
p
ar
ticles
in
th
e
s
ea
r
ch
d
o
m
ain
,
m
o
v
in
g
b
y
p
r
eser
v
in
g
m
em
o
r
y
o
f
Pb
est
(
in
d
iv
id
u
al
b
est
p
o
s
itio
n
)
an
d
Gb
est
(
g
r
o
u
p
b
est
p
o
s
itio
n
)
.
E
s
s
en
tially
,
d
e
v
ices
s
ea
r
ch
ad
ju
s
t
t
h
eir
p
o
s
itio
n
d
e
p
en
d
i
n
g
o
n
th
eir
o
wn
e
x
p
er
ien
ce
a
n
d
t
h
o
s
e
o
f
o
th
er
p
ar
ticles
s
o
th
at
it
g
iv
es
lo
ca
l
as
well
a
s
g
lo
b
al
s
ea
r
ch
ab
ilit
y
to
f
in
d
b
etter
an
d
ef
f
icien
t
s
o
lu
tio
n
s
[
3
5
]
.
Par
ticu
la
r
ly
,
th
e
f
o
r
m
u
la
e
f
o
r
in
f
o
r
m
atio
n
p
ar
ticles v
el
o
city
u
p
d
ate
ar
e:
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.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
4
2
2
-
1
4
3
8
1428
+
1
=
×
+
1
1
(
)
×
(
−
+
2
×
2
(
)
×
(
−
)
(
7
)
L
et
1
r
ep
r
esen
t
th
e
co
g
n
itio
n
-
o
n
ly
lear
n
in
g
f
ac
to
r
,
2
r
ep
r
esen
t
th
e
s
o
cial
-
o
n
ly
lear
n
in
g
f
ac
to
r
,
an
d
r
ep
r
esen
t
th
e
in
er
tia
weig
h
t.
T
h
e
v
ar
iab
le
s
p
ee
d
o
f
m
o
v
e
m
en
t
o
f
th
e
i
-
th
p
ar
ticles
d
u
r
in
g
th
e
j
-
th
iter
atio
n
i
s
d
en
o
ted
as
j
i
V
an
d
th
e
v
ar
iab
le
p
o
s
itio
n
o
f
th
e
i
-
th
p
ar
ticle
d
u
r
in
g
th
e
j
-
th
iter
atio
n
is
d
en
o
ted
as
,
T
h
e
f
u
n
ctio
n
r
a
n
d1
(
∙
)
g
en
er
ates
a
v
ar
iab
le
v
alu
e
b
etwe
en
0
an
d
1
f
r
o
m
th
e
f
ir
s
t
r
an
d
o
m
n
u
m
b
er
g
e
n
e
r
ato
r
,
an
d
r
a
n
d2
(
∙
)
g
en
e
r
ates
a
v
ar
iab
le
v
alu
e
b
e
twee
n
0
an
d
1
f
r
o
m
t
h
e
s
ec
o
n
d
r
an
d
o
m
n
u
m
b
e
r
g
en
er
ato
r
.
T
h
e
ter
m
P
best
is
in
d
icate
s
th
e
b
est p
o
s
itio
n
o
f
th
e
i
-
th
p
ar
ticle,
wh
ile
G
best
in
d
icatin
g
th
e
b
est p
o
s
itio
n
f
o
r
all
p
a
r
ticles.
+
1
=
+
1
+
(
8
)
W
h
er
e
+
1
is
th
e
p
o
s
itio
n
v
ar
iab
le
o
f
th
e
i
-
th
u
p
d
ate
d
p
ar
ticle
d
u
r
in
g
th
e
j
-
t
h
iter
atio
n
,
+
1
is
th
e
v
elo
city
v
ar
iab
le
o
f
th
e
i
-
th
u
p
d
ated
p
a
r
ticle
d
u
r
in
g
th
e
j
-
th
iter
atio
n
,
a
n
d
is
th
e
p
o
s
itio
n
v
ar
ia
b
le
o
f
th
e
i
-
th
p
ar
ticle
d
u
r
in
g
th
e
j
-
th
iter
atio
n
.
T
h
e
f
l
o
wch
ar
t o
f
t
h
e
m
eth
o
d
is
d
ep
i
cted
in
Fig
u
r
e
5
.
Fig
u
r
e
5
.
Flo
wch
ar
t
o
f
p
ar
ticle
s
war
m
o
p
tim
izatio
n
2
.
3
.
4
.
F
lo
wer
po
llin
a
t
io
n a
lg
o
rit
hm
Po
llin
atio
n
is
d
iv
id
ed
in
to
ab
io
tic
(
s
elf
-
p
o
llin
atio
n
)
an
d
b
io
tic
(
cr
o
s
s
-
p
o
llin
atio
n
)
ty
p
es.
B
io
tic
p
o
llin
atio
n
,
p
er
f
o
r
m
ed
b
y
ag
e
n
ts
s
u
ch
as
b
ee
s
,
b
ir
d
s
,
an
d
b
ats,
ac
co
u
n
ts
f
o
r
a
p
p
r
o
x
im
ate
ly
9
0
%
o
f
t
h
e
to
tal
p
o
llin
atio
n
p
r
o
ce
s
s
,
wh
ile
ab
i
o
tic
p
o
llin
atio
n
ac
co
u
n
ts
f
o
r
a
b
o
u
t
1
0
%
[
3
6
]
,
[
3
7
]
.
FP
A
em
p
lo
y
s
th
is
p
r
in
ci
p
le
f
o
r
o
p
tim
izatio
n
,
b
alan
cin
g
s
elf
an
d
cr
o
s
s
-
p
o
llin
atio
n
[
3
8
]
th
r
o
u
g
h
p
r
o
b
a
b
ilit
ies
r
an
g
in
g
f
r
o
m
0
t
o
1
.
FP
A
im
p
lem
en
tatio
n
s
ad
h
e
r
e
to
ce
r
tain
r
u
les to
m
im
ic
th
e
p
o
llin
a
tio
n
p
r
o
ce
s
s
ef
f
ec
tiv
ely
[3
9
]
,
[
40
]
.
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
s
tu
d
y
o
f MP
P
T a
lg
o
r
ith
m
o
n
p
h
o
to
vo
lta
ic
s
tr
in
g
u
n
d
er
p
a
r
tia
l sh
a
d
in
g
(
Dikp
r
id
e
Desp
a
)
1429
B
io
tic
p
o
llin
atio
n
,
also
k
n
o
wn
as
cr
o
s
s
-
p
o
llin
atio
n
,
in
v
o
lv
es
th
e
g
lo
b
al
m
o
v
em
en
t
o
f
p
o
llen
f
o
llo
win
g
th
e
p
atter
n
o
f
L
ev
y
f
lig
h
t,
th
e
p
r
im
a
r
y
m
ec
h
an
is
m
f
o
r
p
o
llen
d
is
tr
ib
u
tio
n
.
T
h
i
s
cr
o
s
s
-
p
o
llin
atio
n
p
r
o
ce
s
s
ca
n
b
e
d
escr
ib
ed
b
y
(
9
)
.
+
1
=
+
+
(
−
)
(
9
)
W
h
er
e
+
1
is
th
e
u
p
d
ated
s
o
lu
tio
n
p
o
s
itio
n
i
at
iter
atio
n
k
,
is
s
o
lu
tio
n
p
o
s
itio
n
i
at
iter
atio
n
k
,
G
b
est
is
b
est s
o
lu
tio
n
o
f
p
o
llen
(
)
,
an
d
L
is
th
e
L
ev
y
f
ac
to
r
.
L
ev
y
f
ac
t
o
r
p
lay
s
an
im
p
o
r
ta
n
t r
o
le
in
p
o
llen
m
o
v
em
e
n
t
d
u
r
in
g
th
e
cr
o
s
s
-
p
o
llin
atio
n
p
r
o
ce
s
s
[
3
6
]
.
Sin
ce
th
e
L
ev
y
f
ac
to
r
af
f
ec
ts
h
o
w
p
o
llen
m
o
v
es,
th
e
f
lo
w
o
f
p
o
llen
m
o
v
em
en
t
.
T
h
r
o
u
g
h
th
e
L
ev
y
f
ac
to
r
m
ec
h
a
n
is
m
ca
n
b
e
r
ep
r
e
s
en
ted
b
y
(
1
0
)
.
=
(
)
(
2
)
1
1
+
(
>
>
0
>
0
)
(
1
0
)
T
h
e
lev
y
f
ac
to
r
L
is
d
ef
in
ed
in
th
e
co
n
tex
t
o
f
th
e
s
tan
d
ar
d
g
am
m
a
f
u
n
ctio
n
Γ(
λ
)
,
wh
ich
i
s
v
alid
f
o
r
S
≫
S
0
>0
,
wh
er
e
λ
r
e
p
r
esen
ts
th
e
lam
b
d
a
v
alu
e
b
ased
o
n
th
e
c
o
n
v
e
r
g
en
ce
o
f
1
.
5
.
Ab
io
tic
p
o
llin
atio
n
,
also
r
ef
er
r
ed
to
as
s
elf
-
p
o
llin
atio
n
,
is
a
n
atu
r
al
m
ec
h
an
is
m
in
wh
ich
f
lo
w
er
in
g
p
lan
ts
au
to
n
o
m
o
u
s
ly
f
ac
ilit
ate
th
eir
o
wn
p
o
llin
atio
n
with
in
th
e
s
am
e
p
lan
t,
with
o
u
t
th
e
i
n
v
o
lv
e
m
en
t
o
f
ex
ter
n
al
ag
e
n
ts
.
T
h
is
p
o
ll
in
atio
n
p
r
o
ce
s
s
is
m
ath
em
atica
lly
ex
p
r
ess
ed
in
(
11
).
+
1
=
+
(
−
)
(
1
1
)
W
h
er
e
ar
e
th
e
p
o
s
itio
n
s
o
f
r
a
n
d
o
m
s
o
lu
tio
n
s
a
an
d
b
f
r
o
m
th
e
p
o
p
u
latio
n
at
iter
atio
n
k
,
an
d
is
th
e
lo
ca
l sear
ch
r
ep
r
esen
tatio
n
(
(
0
,
1
)
)
.
T
h
e
f
lo
wch
ar
t
o
f
th
e
m
et
h
o
d
ca
n
b
e
ex
p
lain
e
d
in
Fig
u
r
e
6
.
Fig
u
r
e
6
.
Flo
wch
ar
t
o
f
f
l
o
wer
p
o
llin
atio
n
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.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
4
2
2
-
1
4
3
8
1430
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
T
est
s
ce
na
rio
ca
s
e
T
h
e
P
–
V
ch
a
r
ac
ter
is
tics
o
b
tain
ed
f
r
o
m
s
ix
test
s
to
ex
am
in
e
th
e
p
e
r
f
o
r
m
an
ce
o
f
MPPT
alg
o
r
ith
m
u
n
d
er
ir
r
ad
ian
t
c
o
n
d
itio
n
ar
e
s
h
o
wn
in
Fig
u
r
e
7
.
I
n
a
s
in
g
le
ir
r
ad
ian
ce
(
Scen
ar
io
1
)
,
th
er
e
is
o
n
e
t
y
p
e
o
f
ir
r
ad
ian
ce
,
wh
ich
cr
ea
tes
o
n
l
y
o
n
e
MPP.
Scen
ar
io
s
2
to
6
m
im
ic
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
th
at
cr
ea
te
m
u
ltip
le
p
ea
k
s
in
t
h
e
P
–
V
c
u
r
v
e
with
o
n
e
GM
PP
an
d
f
o
u
r
lo
ca
l
m
a
x
im
a
L
MPPs
.
T
h
e
GM
MI
p
o
s
itio
n
d
iv
er
g
es
b
etwe
en
t
h
e
s
ce
n
ar
io
s
,
s
h
o
win
g
as
th
e
f
if
th
p
ea
k
f
o
r
S
ce
n
ar
io
2
,
an
d
f
o
u
r
th
p
ea
k
f
o
r
Scen
ar
io
3
,
a
n
d
th
ir
d
p
e
ak
f
o
r
S
ce
n
ar
io
4
,
an
d
s
ec
o
n
d
p
ea
k
in
Scen
ar
io
5
b
u
t
o
n
ly
f
ir
s
t
in
Scen
ar
io
6
.
T
h
e
tr
ac
k
in
g
ef
f
icien
cy
ca
n
b
e
ca
lc
u
lated
b
ased
o
n
t
h
e
v
alu
es
in
T
ab
le
4
,
wh
ich
lis
ts
tr
ac
k
ed
GM
PP
p
o
wer
an
d
v
o
ltag
e
f
o
r
all
s
ce
n
ar
io
s
.
Su
ch
s
ce
n
a
r
io
s
o
f
f
er
a
s
tr
in
g
en
t
f
r
am
ew
o
r
k
f
o
r
t
h
e
ev
al
u
atio
n
o
f
alg
o
r
i
th
m
s
in
ter
m
s
o
f
co
n
v
er
g
en
ce
r
ate,
s
tead
y
s
tate
,
an
d
lo
ca
l
o
p
tim
u
m
r
o
b
u
s
tn
ess
.
Fig
u
r
e
7
. P
-
V
cu
r
v
e
u
n
d
er
v
ar
i
o
u
s
test
s
ce
n
ar
io
s
T
ab
le
4
. P
–
V
cu
r
v
e
d
ata
u
n
d
er
d
if
f
er
en
t scen
a
r
io
s
N
o
.
C
a
se
P
o
w
e
r
V
o
l
t
a
g
e
(W)
(V)
1
S
c
e
n
a
r
i
o
1
3
,
0
0
0
.
3
5
2
0
6
.
4
8
2
S
c
e
n
a
r
i
o
2
1
,
9
7
6
.
0
7
2
1
8
.
4
1
3
S
c
e
n
a
r
i
o
3
1
,
4
4
3
.
3
5
1
7
4
.
5
1
4
S
c
e
n
a
r
i
o
4
1
,
1
5
6
.
6
3
1
2
8
.
7
7
5
S
c
e
n
a
r
i
o
5
7
4
5
.
1
3
8
3
.
3
8
6
S
c
e
n
a
r
i
o
6
5
2
5
.
6
8
3
8
.
1
7
3
.
2
.
P
er
f
o
r
m
a
nce
a
na
ly
s
is
o
f
M
P
P
T
a
lg
o
rit
hm
s
T
h
e
P&
O,
I
C
,
PS
O,
an
d
F
PA
alg
o
r
ith
m
s
ar
e
em
p
lo
y
e
d
to
t
r
ac
k
MPP
u
n
d
er
v
ar
io
u
s
s
h
ad
in
g
co
n
d
itio
n
s
[
1
6
]
,
[
4
1
]
.
T
h
e
tr
ac
k
in
g
r
esu
lts
in
clu
d
e
p
o
wer
,
v
o
ltag
e,
an
d
tr
ac
k
in
g
tim
e
v
alu
es
,
wh
ich
ar
e
u
s
ed
to
ca
lcu
late
th
e
alg
o
r
ith
m
'
s
ef
f
icien
cy
.
T
h
e
r
esu
ltin
g
v
o
ltag
e
i
s
s
en
t
b
y
th
e
MPPT
to
th
e
co
m
p
ar
ato
r
,
wh
ile
th
e
p
o
wer
an
d
tr
ac
k
in
g
tim
e
in
d
icate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
alg
o
r
ith
m
in
f
in
d
in
g
th
e
MPP.
T
h
e
ef
f
icien
cy
o
f
t
h
e
alg
o
r
ith
m
is
ca
lcu
lated
f
r
o
m
t
h
e
r
atio
o
f
th
e
tr
ac
k
e
d
p
o
wer
t
o
th
e
ac
tu
al
MPP to
co
m
p
ar
e
t
h
e
m
eth
o
d
s
u
s
ed
.
Un
d
er
u
n
if
o
r
m
ir
r
ad
ian
ce
(
Sc
en
ar
io
1
)
,
Fig
u
r
e
8
a
n
d
T
ab
le
5
s
h
o
w
th
at
FP
A
an
d
PS
O
a
ch
iev
e
th
e
h
ig
h
est tr
ac
k
ed
p
o
wer
o
f
2
9
8
5
.
1
7
W
at
2
0
9
.
3
0
V,
co
r
r
esp
o
n
d
in
g
to
an
ef
f
icien
c
y
o
f
9
9
.
4
9
4
%.
Ho
wev
er
,
th
ese
alg
o
r
ith
m
s
r
eq
u
ir
e
lo
n
g
er
f
o
r
s
ettlin
g
tim
es (
0
.
7
5
3
s
an
d
0
.
9
3
7
s
)
an
d
ex
h
ib
it si
g
n
if
ican
t o
s
cillatio
n
s
,
in
p
o
wer
an
d
v
o
ltag
e
p
r
o
f
iles
.
I
n
co
n
tr
a
s
t,
I
n
C
an
d
P&
O
c
o
n
v
e
r
g
e
r
a
p
id
ly
with
in
0
.
0
4
9
s
to
ap
p
r
o
x
im
ately
to
2
9
7
7
.
9
9
W
an
d
2
0
1
.
6
6
V
with
m
in
im
al
o
s
cillatio
n
,
alth
o
u
g
h
t
h
eir
e
f
f
icien
cy
ca
p
ab
ilit
y
is
s
lig
h
tly
lo
wer
at
9
9
.
2
5
5
%.
T
h
ese
r
esu
lts
in
d
icate
th
at
I
n
C
an
d
P&
O
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
in
d
y
n
am
ic
r
esp
o
n
s
e
an
d
s
tab
ilit
y
,
wh
ile
FP
A
an
d
PS
O
alg
o
r
ith
m
o
f
f
er
m
ar
g
in
ally
b
etter
ef
f
icien
c
y
at
th
e
e
x
p
en
s
e
o
f
s
lo
wer
c
o
n
v
e
r
g
en
ce
.
T
ab
le
5.
T
est
r
esu
lts
o
f
MPPT
alg
o
r
ith
m
s
u
n
d
er
S
ce
n
a
r
io
1
A
l
g
o
r
i
t
h
m
Ti
me
(
s)
P
o
w
e
r
(
W
)
V
o
l
t
a
g
e
(
V
)
Ef
f
i
c
i
e
n
c
y
(
%)
FPA
0
.
7
5
3
2
9
8
5
.
1
7
0
2
0
9
.
2
9
5
9
9
.
4
9
4
PSO
0
.
9
3
7
2
9
8
5
.
1
7
0
2
0
9
.
2
9
5
9
9
.
4
9
4
I
n
C
0
.
0
4
9
2
9
7
7
.
9
9
0
2
0
1
.
6
6
1
9
9
.
2
5
5
P
&O
0
.
0
4
9
2
9
7
7
.
9
9
0
2
0
1
.
6
6
1
9
9
.
2
5
5
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
s
tu
d
y
o
f MP
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1431
(
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Fig
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.
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ar
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Fig
u
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6
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ile
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Fig
u
r
e
1
0
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d
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ar
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.
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h
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ig
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.
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est
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ith
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s
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