I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS
)
Vo
l.
11
,
No
.
1
,
Ma
r
ch
2
0
2
0
,
p
p
.
25
1
~
26
2
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
1
1
.
i1
.
pp
25
1
-
26
2
251
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Co
mpa
ra
tive stu
dy
of new
MPPT
co
ntrol a
ppro
a
ch
es for a
pho
tov
o
ltaic sy
stem
Ahm
ed
H
a
dd
o
u,
No
ur
-
E
dd
i
neT
a
riba
,
Na
im
a
ikk
en,
Abdelh
a
di B
o
uk
na
del,
H
a
f
s
a
E
L
O
m
a
ri,
H
a
m
id E
L
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a
ri
De
p
a
rtme
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t
o
f
t
h
e
P
h
y
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s a
n
d
En
g
in
e
e
rin
g
S
c
ien
c
e
,
La
b
o
ra
t
o
ry
ERE
D,
Ha
ss
a
n
I
Un
iv
e
rsit
y
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
n
2
,
2
0
1
9
R
ev
is
ed
J
u
l 9
,
2
0
1
9
Acc
ep
ted
Au
g
2
,
2
0
1
9
Th
e
o
u
t
p
u
t
c
h
a
ra
c
teristics
o
f
th
e
p
h
o
to
v
o
lt
a
ic
(P
V)
in
sta
ll
a
ti
o
n
n
o
rm
a
ll
y
d
e
p
e
n
d
o
n
s
o
lar
ra
d
iati
o
n
a
n
d
a
m
b
ien
t
tem
p
e
ra
tu
re
,
t
h
e
c
h
a
rg
e
imp
e
d
a
n
c
e
,
it
s
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
(M
P
P
)
is
n
o
t
ste
a
d
y
.
In
e
v
e
ry
sta
te
o
f
th
e
P
V
m
o
d
u
le
h
a
s
a
p
o
in
t
w
h
e
re
it
c
a
n
c
re
a
te
it
s
M
P
P
.
T
h
u
s
,
M
P
P
T
(
m
a
x
imu
m
p
o
in
t
p
o
we
r
m
o
n
it
o
r
in
g
)
p
ro
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e
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c
a
n
b
e
e
m
p
l
o
y
e
d
to
k
e
e
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th
e
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h
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t
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v
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lt
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ic
p
a
n
e
l
ru
n
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i
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it
s
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P
P
.
I
n
th
is
a
rti
c
le,
th
e
o
b
jec
ti
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e
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s
to
d
e
term
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e
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o
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th
e
d
iffere
n
t
m
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m
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o
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t
p
o
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r
m
o
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it
o
ri
n
g
(
M
P
P
T)
tec
h
n
iq
u
e
s
a
p
p
li
e
d
t
o
P
V
sy
ste
m
s
wo
rk
.
T
h
e
re
fo
re
,
two
M
P
P
T
a
lg
o
rit
h
m
s
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d
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o
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n
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e
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l
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a
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o
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o
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tem
p
e
ra
tu
re
a
n
d
ra
d
iatio
n
c
o
n
d
it
io
n
s:
M
RAC
m
e
th
o
d
s
a
n
d
sl
id
i
n
g
m
o
d
e
c
o
n
tro
l
ler
c
o
m
b
in
e
d
with
t
h
e
I
n
c
re
m
e
n
tal
C
o
n
d
u
c
ti
v
it
y
(IC)
a
lg
o
rit
h
m
.
Th
e
y
a
re
o
ften
e
m
p
lo
y
e
d
d
u
e
t
o
th
e
ir
lo
w
p
rice
a
n
d
sim
p
le
u
se
.
Th
e
y
h
a
v
e
b
e
e
n
tes
ted
o
n
t
h
e
ir
p
e
rfo
rm
a
n
c
e
e
m
p
l
o
y
i
n
g
th
e
P
S
I
M
so
ftwa
re
with
d
iffere
n
t
sit
u
a
ti
o
n
s
o
f
tem
p
e
ra
tu
re
a
n
d
so
lar rad
iatio
n
K
ey
w
o
r
d
s
:
B
o
o
s
t Co
n
v
er
ter
I
n
cr
em
en
tal
C
o
n
d
u
ctan
ce
MPPT
MRAC
Sli
d
in
g
m
o
d
e
c
o
n
tr
o
ller
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ah
m
ed
Had
d
o
u
,
Dep
ar
tm
en
t o
f
th
e
Ph
y
s
ics an
d
E
n
g
in
ee
r
i
n
g
Scien
ce
,
Hass
an
I
Un
iv
er
s
ity
,
FS
T
S,
Km
7
,
R
o
ad
C
asab
lan
ca
,
Settat,
Mo
r
o
cc
o
.
E
m
ail: h
ad
d
o
u
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
No
wad
ay
s
,
m
u
ch
o
f
t
h
e
wo
r
l
d
'
s
en
er
g
y
p
r
o
d
u
ctio
n
is
p
r
o
v
id
ed
b
y
f
o
s
s
il
f
u
els,
th
e
co
n
s
u
m
p
tio
n
o
f
th
ese
s
o
u
r
ce
s
r
is
es
th
e
g
r
ee
n
h
o
u
s
e
ef
f
ec
t
a
n
d
th
u
s
,
in
c
r
ea
s
e
p
o
llu
tio
n
.
So
lar
r
e
n
ewa
b
le
en
er
g
y
is
an
im
p
o
r
tan
t
s
o
lu
tio
n
th
at
co
n
tr
ib
u
tes
to
m
in
im
ize
p
o
llu
tio
n
.
T
h
e
p
r
o
d
u
ctio
n
o
f
th
is
en
er
g
y
is
n
o
t
lin
ea
r
b
ec
au
s
e
th
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
(
PV)
d
o
es
n
o
t
alwa
y
s
co
in
cid
e
with
th
e
p
o
i
n
t
o
f
m
ax
im
u
m
p
o
we
r
.
T
o
h
av
e
th
e
b
est p
er
f
o
r
m
an
ce
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
at
all
tim
es,
we
u
s
e
a
m
ax
im
u
m
p
o
in
t r
esear
ch
in
g
an
d
tr
ac
k
in
g
m
ec
h
an
is
m
ca
lled
M
PP
T
[
1
,
2
]
.
As
a
co
n
s
eq
u
en
ce
,
n
u
m
e
r
o
u
s
s
tu
d
ies
h
av
e
co
n
ce
n
tr
ated
o
n
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
T
h
ey
at
tem
p
ted
to
cr
ea
te
alg
o
r
ith
m
s
to
h
av
e
th
e
b
est
en
e
r
g
y
p
e
r
f
o
r
m
an
ce
f
r
o
m
t
h
e
PV
a
n
d
h
av
e
b
etter
y
ield
[
2
,
3
]
.
Hill
C
lim
b
in
g
,
P&
O,
a
n
d
C
o
n
d
u
ct
an
ce
I
n
cr
em
en
t
(
I
NC
)
[
3
]
wa
s
p
r
ec
u
r
s
o
r
in
th
is
d
o
m
ain
.
T
h
er
e
ar
e
also
o
th
er
s
ad
v
an
ce
d
m
eth
o
d
s
b
ased
o
n
f
u
zz
y
lo
g
ic
(
F
L
)
[
4
,
5
]
.
I
n
th
is
a
r
ticle,
th
e
o
b
jectiv
e
w
as
to
s
tu
d
y
th
e
o
p
e
r
atio
n
o
f
v
ar
io
u
s
MPPT
tech
n
iq
u
es
ap
p
lied
to
PV
s
y
s
tem
s
.
T
h
er
ef
o
r
e,
two
MPPT
alg
o
r
ith
m
s
ar
e
p
r
esen
ted
an
d
co
m
p
a
r
ed
u
n
d
er
v
ar
i
o
u
s
tem
p
er
atu
r
e
an
d
r
ad
iatio
n
c
o
n
d
itio
n
s
:
MRAC
m
eth
o
d
s
an
d
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
b
ased
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
.
T
h
ese
alg
o
r
ith
m
s
ar
e
wid
ely
u
s
ed
in
PV
s
y
s
tem
s
b
ec
au
s
e
o
f
th
eir
ea
s
y
im
p
lem
en
tatio
n
an
d
lo
w
co
s
t.
T
h
ese
tech
n
iq
u
es
wer
e
an
aly
ze
d
an
d
th
eir
p
er
f
o
r
m
an
ce
ev
alu
ated
u
s
in
g
th
e
PS
I
M
s
o
f
twar
e
u
n
d
er
d
if
f
er
e
n
t
ty
p
es
o
f
s
o
lar
r
ad
iatio
n
an
d
tem
p
e
r
atu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
Vo
l.
11
,
No
.
1
,
Ma
r
20
20
:
25
1
–
26
2
252
2.
P
H
O
T
O
VO
L
T
A
I
CSY
ST
E
M
Fix
ed
ch
ar
g
e
s
y
s
tem
s
th
at
u
s
e
r
en
ewa
b
le
en
er
g
y
as
a
s
o
u
r
ce
o
f
en
er
g
y
alwa
y
s
n
ee
d
an
in
t
er
m
ed
iate
s
tag
e
b
etwe
en
th
e
p
h
o
t
o
v
o
ltai
c
s
o
u
r
ce
an
d
t
h
e
lo
ad
to
g
et
th
e
m
o
s
t
p
o
wer
av
ailab
le
at
an
y
m
o
m
en
t
[
6
,
7
]
,
th
e
in
ter
m
ed
iate
s
tag
e
u
s
ed
is
a
co
n
v
er
ter
DC
-
DC
as sh
o
wn
b
elo
w
:
Fig
u
r
e
1
.
Diag
r
a
m
o
f
PV
co
n
n
ec
ted
to
a
lo
ad
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
pa
nel
T
h
e
p
h
o
t
o
v
o
ltaic
p
an
el
co
n
s
is
ts
o
f
ce
lls
in
s
er
ies
an
d
in
p
ar
allel
th
at
tr
an
s
f
o
r
m
th
e
s
u
n
lig
h
t
in
to
an
elec
tr
ic
cu
r
r
en
t,
th
e
eq
u
iv
ale
n
t
m
o
d
el
o
f
a
ce
ll
is
a
c
u
r
r
en
t
s
o
u
r
ce
in
p
ar
allel
with
a
d
io
d
e
in
p
a
r
allel
an
d
an
in
ter
n
al
r
esis
tan
ce
th
at
r
ef
lect
s
th
e
in
ter
n
al
h
ea
tin
g
o
f
ea
c
h
ce
ll,
th
e
v
ar
iatio
n
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
with
t
h
e
cu
r
r
en
t
o
f
a
ce
ll is
d
ef
in
e
d
b
y
a
r
esis
to
r
in
s
er
ies with
th
e
cu
r
r
en
t so
u
r
ce
.
Fig
u
r
e
2
.
Fig
u
r
e
2
.
E
lectr
ical
m
o
d
el
o
f
PV
m
o
d
u
le
T
h
e
o
u
tp
u
t c
u
r
r
en
t
-
v
o
ltag
e
(
I
-
V)
ch
ar
ac
ter
is
tics
ca
n
b
e
ca
lcu
lated
b
y
u
s
in
g
th
e
f
o
llo
win
g
e
q
u
atio
n
[
4
]
=
−
(
+
−
1
)
−
−
(
1
)
i
sc
:
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
o
f
PV
ce
ll,
R
p
:
Sh
u
n
t
R
esis
to
r
,
R
s
:
r
esis
to
r
s
er
ies,
i0
is
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t
o
f
th
e
d
io
d
e.
VT
is
th
e
th
er
m
al
v
o
ltag
e;
it
d
e
p
en
d
s
e
x
clu
s
iv
ely
o
n
t
h
e
tem
p
er
atu
r
e.
Ns
n
u
m
b
er
o
f
s
er
ie
ce
ll
,
Np
n
u
m
b
e
r
o
f
p
ar
allel
ce
lls
.
I
n
th
is
s
tu
d
y
,
th
e
SC
HOT
T
POLY
2
4
0
m
o
d
u
le
[
7
]
is
tak
en
in
to
ac
co
u
n
t,
th
e
elec
tr
ical
c
h
a
r
ac
ter
is
tics
o
f
th
e
m
o
d
u
le
a
r
e
s
h
o
wn
in
th
e
T
ab
le
1
:
T
ab
le
1
.
E
lectr
ical
ch
a
r
ac
ter
is
tics
o
f
PV m
o
d
u
le
P
mp
p
(
N
o
m
i
n
a
l
P
o
w
e
r
)
[
W
p
]
≥
240
V
mp
p
(
V
o
l
t
a
g
e
a
t
N
o
mi
n
a
l
P
o
w
e
r
)
[
V
]
3
0
.
4
I
mp
p
(
C
u
r
r
e
n
t
a
t
N
o
mi
n
a
l
P
o
w
e
r
)
[
A
]
7
.
9
0
V
o
c
(
O
p
e
n
-
C
i
r
c
u
i
t
V
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l
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)
[V]
3
7
.
3
I
sc
(
S
h
o
r
t
-
C
i
r
c
u
i
t
C
u
r
r
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n
t
)
[A]
8
.
4
7
Fig
u
r
e
3
s
h
o
ws th
e
v
ar
iatio
n
o
f
GPV
cu
r
r
en
t a
s
a
f
u
n
ctio
n
o
f
GPV
v
o
ltag
e,
wh
ile
F
ig
u
r
e
4
s
h
o
ws th
e
v
ar
iatio
n
o
f
th
e
GPV
p
o
wer
p
r
o
v
id
ed
b
y
th
e
v
o
ltag
e
f
u
n
ctio
n
u
n
d
er
n
o
r
m
al
co
n
d
itio
n
s
[
4
,
5
]
.
T
h
e
ch
a
r
ac
ter
is
tics
I
pv
Vs
V
pv
o
f
th
e
p
an
el
is
a
n
o
n
-
lin
ea
r
f
u
n
ctio
n
,
its
lin
ea
r
izatio
n
is
r
eq
u
ir
ed
to
s
tu
d
y
th
e
d
y
n
a
m
ic
b
e
h
av
io
r
o
f
s
y
s
tem
s
(
PV
+
b
o
o
s
t)
wh
ic
h
s
tr
o
n
g
l
y
d
e
p
en
d
s
o
n
t
h
e
o
p
er
atin
g
p
o
in
t
o
f
th
e
p
h
o
to
v
o
ltaic
g
en
er
at
o
r
,
th
e
lin
ea
r
m
o
d
el
o
f
MPP is g
iv
en
in
Fig
u
r
e
3
.
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:
2
0
8
8
-
8
694
C
o
mp
a
r
a
tive
s
tu
d
y
o
f n
ew MPP
T c
o
n
tr
o
l a
p
p
r
o
a
ch
es fo
r
a
p
h
o
to
vo
lta
ic
s
ystem
(
A
h
med
Ha
d
d
o
u
)
253
T
h
e
m
o
d
el
in
Fig
u
r
e
3
h
as
v
a
lid
ity
at
th
e
lin
ea
r
izatio
n
p
o
in
t,
wh
ich
is
a
s
u
itab
le
ap
p
r
o
x
i
m
atio
n
f
o
r
th
e
s
m
all
s
ig
n
als
an
aly
s
i
s
.
W
h
ile
it
is
d
esira
b
le
to
o
p
er
ate
at
th
e
m
ax
im
u
m
p
o
i
n
t
at
all
ti
m
es,
th
e
GPV
p
an
el
m
ay
ch
an
g
e
th
e
ar
ea
o
f
t
h
e
o
p
er
atin
g
p
o
i
n
t o
f
t
h
e
s
o
u
r
ce
v
o
l
tag
e
o
r
th
e
c
u
r
r
e
n
t
ar
ea
[
6
,
7
]
.
T
h
e
d
y
n
am
ic
b
e
h
av
io
u
r
o
f
th
e
en
tire
s
y
s
tem
,
s
o
lar
p
an
el
a
n
d
p
o
wer
p
lan
t,
d
e
p
en
d
s
s
tr
o
n
g
ly
o
n
th
e
p
an
el'
s
o
p
er
atin
g
p
o
in
t.
Fo
r
t
h
e
p
u
r
p
o
s
e
o
f
d
esig
n
in
g
th
e
co
n
tr
o
l
s
y
s
tem
an
d
en
s
u
r
in
g
th
e
s
tab
ilit
y
u
n
d
er
all
o
p
er
atin
g
co
n
d
itio
n
s
,
th
e
p
h
o
to
v
o
ltaic
m
o
d
u
le
is
also
lin
ea
r
ized
at
b
o
th
cu
r
r
en
t
an
d
v
o
lta
g
e
zo
n
es
b
y
u
s
in
g
(
3
)
an
d
(
4
)
.
T
h
e
d
er
iv
ativ
e
o
f
t
h
e
n
o
n
-
lin
ea
r
f
u
n
ctio
n
I
pv
v
s
V
pv
at
th
e
MPP o
p
er
atin
g
p
o
in
t i
s
g
iv
en
b
elo
w:
|
=
=
=
(
,
)
=
−
0
(
+
−
1
)
−
1
(
2
)
Fig
u
r
e
3
.
C
u
r
r
e
n
t I
p
v
.
v
o
ltag
e
Vp
v
ch
ar
ac
ter
is
tics
Fig
u
r
e
4
.
PV Po
wer
v
s
.
v
o
ltag
e
Vp
v
ch
ar
ac
ter
is
tics
T
h
e
eq
u
atio
n
b
el
o
w
r
ep
r
esen
ts
th
e
lin
ea
r
ized
m
o
d
el
wh
ic
h
is
d
escr
ib
ed
b
y
th
e
tan
g
en
t
o
f
th
e
cu
r
v
e
o
n
th
e
lin
ea
r
izatio
n
p
o
in
t
[
5
]
.
=
(
−
+
)
+
(
3
)
T
h
e
eq
u
iv
ale
n
t T
h
ev
e
n
in
m
o
d
el
[
8
]
is
r
ep
r
esen
te
d
b
elo
w
wit
h
:
=
−
1
/
An
d
=
−
/
(
4
)
Fig
u
r
e
5
.
T
h
ev
en
i
n
m
o
d
el
o
f
P
V
2
.
2
.
B
o
o
s
t
c
o
nv
er
t
er
m
o
dellin
g
An
ad
ap
tatio
n
s
tag
e
(
S
tep
u
p
co
n
v
er
ter
)
is
r
eq
u
ir
ed
to
en
s
u
r
e
th
e
in
ter
f
ac
e
b
etwe
en
GPV
an
d
lo
ad
f
o
r
a
g
o
o
d
o
p
tim
izatio
n
o
f
th
e
s
y
s
tem
’
s
o
p
er
atio
n
,
it
is
ess
en
tial
to
ad
a
p
t
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
o
f
th
e
GPV
to
th
e
co
n
s
u
m
er
’
s
r
eq
u
ir
e
m
en
ts
,
an
d
it
ca
n
also
en
s
u
r
e
th
e
t
r
an
s
f
er
o
f
p
o
wer
b
etwe
en
th
e
GPV
an
d
th
e
lo
ad
,
wh
eth
er
it
is
b
atter
y
,
DC
lo
a
d
o
r
in
v
e
r
ter
.
Fig
u
r
e
6
s
h
o
w
s
th
e
b
o
o
s
t
s
ch
em
e
c
o
r
r
esp
o
n
d
in
g
to
th
e
GPV
T
h
ev
en
in
m
o
d
el
,
T
h
e
S
tep
u
p
co
n
v
er
ter
o
p
er
atin
g
in
c
o
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
[
1
,
2
an
d
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
Vo
l.
11
,
No
.
1
,
Ma
r
20
20
:
25
1
–
26
2
254
Fig
u
r
e
6
.
T
h
ev
en
i
n
m
o
d
el
o
f
P
VG
with
b
o
o
s
t a
d
ap
tiv
e
s
tag
e
T
h
e
elec
tr
ical
cir
cu
it
o
f
th
e
lo
s
s
les
s
PV
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
6
.
T
h
e
d
y
n
am
ic
e
q
u
atio
n
s
ar
e
d
esig
n
ed
to
r
ep
r
esen
t
t
h
e
s
y
s
tem
in
th
e
s
tate
s
p
ac
e
wh
e
r
e
th
e
s
tate
v
ar
iab
les
ar
e
th
e
i
n
d
u
ct
iv
e
cu
r
r
e
n
t
an
d
th
e
v
o
ltag
e
at
th
e
in
p
u
t
ca
p
ac
ito
r
,
wh
ile
th
e
co
n
v
er
ter
in
p
u
t
is
th
e
d
u
t
y
cy
cle,
th
e
GPV
is
r
ep
r
esen
ted
b
y
th
e
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
T
h
e
v
en
in
,
an
d
V
o
is
th
e
B
o
o
s
t
o
u
tp
u
t
v
o
ltag
e,
v
Cin
r
ep
r
esen
ts
th
e
v
o
ltag
e
o
f
th
e
in
p
u
t
ca
p
ac
ito
r
,
i
L
is
th
e
in
d
u
ctiv
e
c
u
r
r
en
t a
n
d
d
is
th
e
d
u
ty
c
y
cle
[
6
,
7
an
d
8
]
.
Av
er
ag
in
g
s
tate
eq
u
atio
n
s
o
v
e
r
a
s
witch
in
g
p
er
io
d
p
e
r
io
d
ar
e
g
iv
en
in
th
e
f
o
llo
win
g
s
et:
−
−
=
0
(
5
)
=
+
(
6
)
=
−
(
1
−
)
(
7
)
=
(
1
−
)
−
(
8
)
C
o
n
tr
o
l to
in
p
u
t v
o
ltag
e
tr
an
s
f
er
f
u
n
ctio
n
:
(
)
=
−
+
+
2
(
9
)
C
o
n
tr
o
l to
in
p
u
t v
o
ltag
e
v
s
s
elf
cu
r
r
e
n
t tr
an
s
f
er
f
u
n
ctio
n
=
−
1
+
3.
M
P
P
T
D
E
SI
G
N
3
.
1
.
I
ncre
m
ent
a
l c
o
nd
uct
a
nce
des
ig
n
T
h
e
in
cr
em
en
tal
co
n
d
u
ctan
c
e
(
I
C
)
alg
o
r
ith
m
u
s
ed
to
ac
h
iev
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
in
g
(
MPPT)
u
s
es
th
e
co
n
ce
p
t
t
h
at
th
e
p
o
wer
d
er
iv
ativ
e
with
r
es
p
ec
t
to
v
o
ltag
e
will
b
e
ze
r
o
at
MPP
an
d
p
o
s
itiv
e
f
o
r
v
o
ltag
es
b
elo
w
MPP
as
w
ell
as
n
eg
ativ
e
f
o
r
v
o
ltag
es
ab
o
v
e
MPP,
wh
ich
is
ac
h
iev
ed
with
o
b
v
io
u
s
ea
s
e
wh
en
v
iewin
g
th
e
en
er
g
y
v
o
ltag
e
cu
r
v
e
[
9
,
1
0
]
,
Po
wer
-
v
o
ltag
e
cu
r
v
e
as sh
o
w
in
Fig
u
r
e
7
.
.
Fig
u
r
e
7
.
Po
wer
-
v
o
ltag
e
c
u
r
v
e
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:
2
0
8
8
-
8
694
C
o
mp
a
r
a
tive
s
tu
d
y
o
f n
ew MPP
T c
o
n
tr
o
l a
p
p
r
o
a
ch
es fo
r
a
p
h
o
to
vo
lta
ic
s
ystem
(
A
h
med
Ha
d
d
o
u
)
255
T
h
e
p
o
wer
d
er
i
v
ativ
e
with
r
e
s
p
ec
t
to
th
e
v
o
ltag
e
ca
n
b
e
e
x
p
r
ess
ed
as
(
1
0
)
s
in
ce
P
=
I
V
an
d
n
ew
co
n
d
itio
n
s
o
n
th
e
v
a
r
iatio
n
o
f
co
n
d
u
cta
n
ce
ar
e
g
i
v
en
(
1
1
)
.
=
(
.
)
=
+
.
≅
+
.
(
1
0
)
−
−
=
−
M
P
P
of
r
i
gh
t
V
I
V
I
M
P
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at
V
I
V
I
M
P
P
of
l
e
f
t
V
I
V
I
PV
PV
PV
PV
PV
PV
PV
PV
PV
PV
PV
PV
(
1
1
)
T
h
e
s
lo
p
/
in
d
icate
s
th
e
m
o
d
if
ied
co
n
d
itio
n
s
f
o
r
th
e
c
h
an
g
e
in
co
n
d
u
ctan
ce
.
T
h
e
co
n
tr
o
l
p
o
in
t
is
lo
ca
ted
at
th
e
lef
t
-
h
an
d
s
id
e
o
f
th
e
MPP
if
th
e
s
lo
p
e
is
g
r
ea
ter
th
a
n
ze
r
o
,
at
th
e
r
ig
h
t
-
h
an
d
s
id
e
o
f
th
e
MPP
th
e
s
lo
p
e
if
th
e
s
lo
p
e
is
less
th
an
ze
r
o
,
an
d
th
e
s
lo
p
e
is
ze
r
o
ex
ac
tly
at
th
e
MP
P.
T
h
er
ef
o
r
e,
th
e
PV
v
o
ltag
e
n
ee
d
s
to
b
e
in
c
r
ea
s
ed
wh
en
th
e
s
lo
p
e
is
p
o
s
itiv
e
an
d
d
ec
r
ea
s
ed
wh
en
t
h
e
s
lo
p
e
is
n
eg
ativ
e.
I
n
th
e
p
r
ev
i
o
u
s
s
ec
tio
n
,
I
n
cr
e
m
en
tal
C
o
n
d
u
ctan
ce
is
ap
p
lie
d
to
d
eter
m
in
e
t
h
e
v
o
ltag
e
V
r
ef
wh
ich
aim
s
to
d
eliv
e
r
th
e
m
a
x
im
u
m
p
o
wer
a
v
ailab
le
in
th
e
s
tab
le
s
tate
[
1
1
,
1
2
]
.
I
t
is
also
d
esira
b
le
th
at
t
h
e
s
y
s
tem
co
n
v
er
g
e
m
o
r
e
q
u
ick
ly
to
th
e
MPP
wh
en
th
e
ir
r
ad
iatio
n
is
ch
an
g
ed
.
T
h
e
p
r
o
p
o
s
ed
ar
c
h
itectu
r
e
o
f
th
e
Mo
d
el
R
ef
er
en
ce
Ad
ap
tiv
e
C
o
n
tr
o
l
(
MRAC
)
is
d
esig
n
ed
to
m
ai
n
tain
a
cr
itical
d
am
p
in
g
b
eh
av
io
u
r
o
f
th
e
GPV
v
o
ltag
e
(
Vp
v
)
[
1
3
,
1
4
]
.
T
h
e
Fi
g
u
r
e
8
s
h
o
ws th
e
b
asic stru
ctu
r
e
o
f
MRAC
co
n
tr
o
ller
.
Fig
u
r
e
8
.
B
asic stru
ctu
r
e
o
f
th
e
ad
ap
tiv
e
co
n
tr
o
l w
ith
th
e
r
ef
er
en
ce
m
o
d
el
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
G
PV v
o
ltag
e
with
r
esp
ec
t to
th
e
cu
r
r
en
t iL
is
g
i
v
en
b
el
o
w:
(
)
=
−
.
+
1
(
1
2
)
I
t
is
a
tr
an
s
f
er
f
u
n
ctio
n
o
f
a
f
ir
s
t
-
o
r
d
er
s
y
s
tem
,
T
h
e
d
esig
n
o
f
MRAC
is
p
er
f
o
r
m
ed
b
y
s
elec
tin
g
a
f
ir
s
t
-
o
r
d
er
r
ef
er
e
n
ce
m
o
d
el
t
o
av
o
i
d
ex
ce
e
d
in
g
t
h
e
GPV
v
o
ltag
e
an
d
h
a
v
e
a
v
er
y
s
h
o
r
t
s
tab
ilizatio
n
tim
e
(
s
ettlin
g
tim
e)
[
1
5
,
1
6
]
.
T
h
e
r
ef
er
e
n
ce
m
o
d
el
is
o
f
th
e
f
o
llo
win
g
f
o
r
m
(
)
=
=
+
(
1
3
)
W
h
er
e
G
ref
is
th
e
f
o
r
m
o
f
th
e
d
esire
d
GPV
v
o
ltag
e,
an
d
V
ref
is
th
e
v
o
ltag
e
ca
lcu
la
ted
b
y
th
e
in
cr
em
en
tal
co
n
d
u
ctan
ce
alg
o
r
ith
m
[
1
7
,
1
8
]
.
T
h
e
er
r
o
r
b
et
wee
n
th
e
d
esire
d
v
o
ltag
e
G
ref
an
d
th
e
m
ea
s
u
r
ed
v
o
ltag
e
V
pv
(
o
r
ac
tu
al)
is
d
ef
in
ed
as f
o
llo
ws:
=
−
(
1
4
)
E
x
p
r
ess
in
g
th
e
e
q
u
atio
n
o
f
th
e
m
o
d
el
(
1
2
)
i
n
th
e
tim
e
d
o
m
ai
n
an
d
s
im
p
lific
atio
n
g
iv
es
=
−
+
(
1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
Vo
l.
11
,
No
.
1
,
Ma
r
20
20
:
25
1
–
26
2
256
with
=
1
,
=
−
1
(
1
6
)
T
h
e
r
ewr
itin
g
o
f
1
7
in
th
e
tim
e
d
o
m
ain
g
iv
es
=
−
+
(
1
7
)
Fro
m
th
e
(
1
7
)
,
it
ca
n
b
e
d
ed
u
c
ed
th
at
a
ze
r
o
-
er
r
o
r
m
ea
n
s
th
at
th
e
r
ate
o
f
c
h
an
g
e
f
o
r
th
ese
s
h
o
u
ld
also
b
e
eq
u
al
in
th
is
ca
s
e.
T
h
u
s
ass
im
ilatin
g
(
1
5
)
an
d
(
1
7
)
an
d
s
im
p
lify
in
g
we
ca
n
r
ea
c
h
:
=
−
(
1
8
)
wh
er
e
X=
a/B
,
an
d
Y=
(a
-
A)
/B
Fo
r
th
e
s
y
s
tem
to
f
o
llo
w
th
e
b
eh
av
io
r
o
f
th
e
f
ir
s
t
-
o
r
d
er
r
ef
er
en
ce
m
o
d
el,
th
e
f
o
llo
win
g
co
n
d
itio
n
s
m
u
s
t b
e
m
et:
•
=
•
−
•
=
0
(
1
9
)
Usi
n
g
(
1
5
)
a
n
d
(
1
7
)
,
an
d
r
ep
la
cin
g
in
(
1
9
)
we
o
b
tain
•
=
−
+
(
+
−
)
+
(
−
)
(
2
0
)
Fo
r
th
e
v
o
ltag
e
V
p
v
t
o
b
e
s
tab
le
an
d
to
f
o
llo
w
th
e
r
ef
er
en
ce
v
o
ltag
e,
t
h
e
er
r
o
r
an
d
th
e
e
r
r
o
r
d
er
iv
ativ
e
b
etwe
en
th
em
m
u
s
t te
n
d
to
war
d
s
ze
r
o
; in
o
d
er
h
a
n
d
,
a
L
y
a
p
u
n
o
v
ca
n
d
id
ate
f
u
n
ctio
n
is
d
ef
in
ed
(
2
1
)
to
s
tu
d
y
th
e
s
tab
ilit
y
o
f
th
e
o
v
er
all
th
e
s
y
s
tem
[
1
3
]
.
(
)
=
1
2
+
2
2
2
(
2
1
)
•
(
,
,
)
=
−
2
+
1
(
−
+
+
)
(
+
•
)
+
1
(
−
)
(
−
•
)
(
2
2
)
Acc
o
r
d
in
g
to
th
e
L
y
a
p
u
n
o
v
c
r
iter
ia,
to
g
u
ar
an
tee
th
e
s
tab
il
ity
o
f
t
h
e
s
y
s
tem
,
th
e
tim
e
d
e
r
iv
ativ
e
o
f
th
e
ca
n
d
i
d
ate
f
u
n
ctio
n
L
y
a
p
u
n
o
v
s
h
o
u
ld
n
e
g
ativ
e
s
em
i
d
ef
i
n
ite
i.e
V(
x
)
<
0
.
T
h
is
eq
u
alit
y
is
tr
u
e
f
o
r
t
h
e
(
2
2
)
an
d
wh
ich
f
u
lf
ils
th
e
f
o
llo
win
g
co
n
d
itio
n
s
.
•
=
(
2
3
)
•
=
−
(
2
4
)
=
∫
+
0
(
2
5
)
=
∫
+
0
(
2
6
)
•
=
−
2
(
2
7
)
T
h
e
(
2
3
)
to
(
2
7
)
r
ep
r
esen
t t
h
e
law
o
f
ad
ap
tatio
n
,
with
X
an
d
Y
b
ein
g
th
e
a
d
ap
tiv
e
g
ain
s
an
d
a
is
th
e
p
o
s
itiv
e
co
n
s
tan
t th
at
m
u
s
t b
e
ad
ju
s
ted
.
T
h
e
ab
o
v
e
eq
u
atio
n
s
h
av
e
b
ee
n
im
p
lem
en
ted
in
th
e
PS
I
M
f
o
r
PV Sy
s
tem
s
to
in
co
r
p
o
r
ate
Mo
d
el
R
ef
er
en
ce
Ad
ap
tiv
e
C
o
n
tr
o
ller
as sh
o
wn
Fig
u
r
e
9.
T
h
e
p
ar
a
m
eter
o
f
th
e
r
ef
er
en
c
e
m
o
d
el
d
ef
in
es
th
e
s
p
ee
d
o
f
t
h
ec
lo
s
ed
-
lo
o
p
r
esp
o
n
s
e.
I
f
we
wan
t
to
d
ec
r
ea
s
e
th
e
clo
s
ed
-
lo
o
p
r
esp
o
n
s
e
we
h
av
e
t
o
in
c
r
ea
s
e
th
e
p
ar
am
eter
o
n
th
e
o
t
h
er
h
a
n
d
if
we
wan
t
to
in
cr
ea
s
e
th
e
clo
s
ed
-
lo
o
p
we
w
ill h
av
e
to
r
ed
u
ce
.
Fro
m
th
e
eq
u
atio
n
s
ab
o
v
e
th
at
p
r
esen
t
th
e
ad
ap
tatio
n
law,
th
e
o
n
ly
co
n
tr
o
l
p
ar
a
m
eter
is
th
e
p
o
s
itiv
e
g
ain
.
Fo
r
th
e
e
f
f
ec
tiv
e
c
o
n
tr
o
l
o
f
th
e
v
ar
iatio
n
in
t
h
e
am
p
litu
d
e
o
f
th
e
r
ef
er
en
ce
s
ig
n
al,
t
h
e
co
n
tr
o
l p
ar
am
eter
p
lay
s
an
im
p
o
r
tan
t
r
o
le.
its
v
alu
e
is
m
ain
tain
ed
h
ig
h
if
th
e
v
ar
iatio
n
o
f
th
e
r
e
f
er
en
ce
s
ig
n
al
is
lar
g
e
an
d
lo
w
if
th
e
v
ar
iatio
n
o
f
th
e
r
ef
er
e
n
c
e
s
ig
n
al
is
s
m
all.
I
n
o
u
r
ca
s
e
=
0
.
0
0
3
an
d
.
a=
7
0
0
0
a
r
e
ch
o
s
en
.
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:
2
0
8
8
-
8
694
C
o
mp
a
r
a
tive
s
tu
d
y
o
f n
ew MPP
T c
o
n
tr
o
l a
p
p
r
o
a
ch
es fo
r
a
p
h
o
to
vo
lta
ic
s
ystem
(
A
h
med
Ha
d
d
o
u
)
257
Fig
u
r
e
9
.
MRAC
co
n
tr
o
l la
w
3
.
3
.
Su
per
T
wis
t
ing
Sli
din
g
Co
ntr
o
l
Su
p
er
-
twis
tin
g
alg
o
r
ith
m
(
ST
A)
is
a
n
o
n
-
lin
ea
r
co
n
tr
o
l
tec
h
n
iq
u
e
an
d
is
o
n
e
o
f
th
e
m
o
s
t
p
o
wer
f
u
l
co
n
tin
u
o
u
s
2
-
o
r
d
er
SMC
s
wh
i
ch
en
s
u
r
es
all
f
u
n
d
am
e
n
tal
p
r
o
p
er
ties
o
f
its
tr
ad
itio
n
al
1
-
o
r
d
er
with
ch
atter
in
g
r
ed
u
ctio
n
ca
p
a
b
ilit
y
[
1
9
,
2
0
]
.
T
h
e
m
ain
ad
v
an
tag
es
o
f
th
e
STA
ar
e
th
e
r
o
b
u
s
tn
ess
ag
ai
n
s
t
v
ar
iatio
n
o
f
th
e
s
y
s
tem
,
an
d
th
e
ab
ilit
y
to
tr
ac
k
th
e
r
ef
er
e
n
ce
with
h
ig
h
ac
c
u
r
ac
y
.
I
t
was
d
ev
elo
p
ed
in
f
ir
s
t
tim
e
b
y
Pro
f
ess
o
r
L
ev
an
t
f
o
r
s
y
s
tem
s
with
a
r
el
ativ
e
d
eg
r
ee
eq
u
al
to
1
[
2
1
,
2
2
]
.
T
h
is
alg
o
r
ith
m
r
eq
u
ir
es
o
n
ly
th
e
k
n
o
wled
g
e
o
f
th
e
s
lid
in
g
v
ar
iab
le
an
d
d
o
es
n
o
t
tak
e
in
to
ac
co
u
n
t
its
tim
e
d
er
iv
ativ
e
.
I
n
th
is
wo
r
k
,
th
e
ST
A
h
as
b
ee
n
ap
p
lied
to
d
r
iv
e
th
e
s
tep
-
u
p
c
o
n
v
e
r
ter
with
th
e
p
u
r
p
o
s
e
o
f
k
ee
p
in
g
th
e
GPV
o
p
er
atin
g
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
T
h
e
co
n
tr
o
l
law,
as
s
h
o
wn
i
n
Fig
u
r
e
1
0
,
is
g
en
e
r
ated
f
r
o
m
a
s
lid
in
g
s
u
r
f
ac
e
t
r
ea
tm
en
t
s
(
x
)
.
T
h
e
co
n
tr
o
l sig
n
al
u
(
t)
r
e
g
u
lates th
e
GPV
v
o
ltag
e
to
o
p
e
r
ate
at
V
m
p
v
o
ltag
e
v
ia
s
witch
S,
it c
an
b
e
wr
itten
as
(
2
8
)
(
2
9
)
wh
er
e
th
e
s
lid
in
g
s
u
r
f
ac
e
is
d
e
f
in
ed
as:
=
+
∫
(
3
0
)
An
d
=
−
(
3
1
)
T
h
e
ab
o
v
e
alg
o
r
ith
m
d
o
es
n
o
t
r
eq
u
i
r
e
th
e
ev
al
u
atio
n
o
f
th
e
s
ig
n
o
f
S.
A
s
ec
o
n
d
o
r
d
er
s
lid
in
g
m
o
d
e
,
ex
p
o
n
e
n
tially
s
tab
le,
ap
p
ea
r
s
if
th
e
co
n
tr
o
l
law
with
r
=
1
is
u
s
ed
.
T
h
e
p
ar
m
eter
ρ
=
0
.
5
g
u
ar
an
tee
th
at
th
e
f
u
lf
ilm
en
t o
f
th
e
s
ec
o
n
d
o
r
d
er
s
lid
in
g
is
ac
h
iev
ed
[
2
3
,
2
4
]
.
T
h
e
co
n
tr
o
l la
w
is
in
th
is
ca
s
e
g
iv
en
b
y
:
=
{
̇
1
=
−
1
(
)
|
|
>
0
2
=
−
2
|
|
0
.
5
(
)
|
|
≤
0
(
3
2
)
T
h
e
s
im
p
licity
o
f
th
e
co
n
tr
o
l
law
s
tr
u
ctu
r
e
is
q
u
ite
o
b
v
io
u
s
with
o
n
ly
f
o
u
r
p
ar
a
m
eter
s
to
b
e
d
eter
m
in
ed
.
C
o
n
v
er
g
e
n
ce
co
n
d
itio
n
s
f
o
r
th
ese
p
ar
am
eter
s
ar
e
[
2
5
]
:
(
3
3
)
T
h
e
s
witch
in
g
c
o
n
tr
o
l
en
s
u
r
e
s
th
e
co
n
v
er
g
e
n
ce
o
f
th
e
en
ti
r
e
s
y
s
tem
b
y
k
ee
p
i
n
g
it
m
o
v
i
n
g
o
n
th
e
s
lid
in
g
s
u
r
f
ac
e
wh
ile
en
s
u
r
in
g
r
o
b
u
s
tn
ess
ag
ain
s
t e
x
ter
n
al
u
n
ce
r
tain
ties
an
d
d
is
tu
r
b
an
ce
.
T
h
er
f
o
r
e
s
h
o
u
ld
b
e
a
h
ig
h
v
alu
e.
T
h
e
o
v
e
r
all
co
n
tr
o
l la
w
is
im
p
lem
en
ted
in
PS
I
M
to
o
ls
as f
o
ll
o
w:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
Vo
l.
11
,
No
.
1
,
Ma
r
20
20
:
25
1
–
26
2
258
Fig
u
r
e
1
0
.
T
h
e
s
y
n
o
p
tic
d
iag
r
am
o
f
th
e
s
u
p
er
-
twis
tin
g
alg
o
r
ith
m
.
4.
SI
M
UL
T
I
O
N
R
E
SU
L
T
S
I
n
o
r
d
er
to
h
av
e
a
p
r
o
p
e
r
ch
ar
ac
ter
izatio
n
o
f
th
e
alg
o
r
ith
m
s
p
r
o
p
o
s
ed
in
th
is
p
ap
e
r
,
s
im
u
la
tio
n
s
wer
e
p
er
f
o
r
m
ed
u
s
in
g
th
e
PS
I
M
s
o
f
twar
e.
I
ts
tak
es
in
to
co
n
s
id
er
at
io
n
th
e
v
ar
io
u
s
o
p
e
r
atin
g
co
n
d
itio
n
s
,
s
tead
y
s
tate
an
d
tr
a
n
s
ien
t
s
tate
d
u
e
to
th
e
v
ar
iatio
n
s
in
s
o
lar
r
a
d
iatio
n
(
f
r
o
m
6
5
0
W
/m
2
to
1
0
0
0
W
/m
2
,
tem
p
er
atu
r
e
(
2
5
°C
to
7
5
°C
)
an
d
c
h
ar
g
e
v
ar
iatio
n
.
T
h
e
f
ig
u
r
e
1
1
(
a)
,
1
1
(
b
)
s
h
o
ws
th
e
s
im
u
latio
n
m
o
d
el
o
f
MR
AC
an
d
SMC
co
n
tr
o
ller
with
PS
I
M.
T
h
e
f
ig
u
r
es
1
2
,
1
3
in
d
icate
th
e
s
im
u
latio
n
r
esu
lto
f
th
e
GPV
o
u
tp
u
t
c
u
r
r
en
t,
v
o
ltag
e
an
d
GPV
p
o
wer
f
o
r
d
if
f
er
en
t
o
p
er
atio
n
c
o
n
d
itio
n
s
.
(
a)
(
b
)
Fig
u
r
e
1
1
.
Simu
latio
n
m
o
d
el
(
a)
MRAC
,
(
b
)
SMC
4
.
1
.
I
n c
a
s
e
o
f
irr
a
dia
t
io
n c
ha
ng
e:
T
h
e
two
p
r
o
p
o
s
ed
m
eth
o
d
is
ef
f
icien
t
an
d
ex
tr
ac
ts
th
e
m
ax
im
u
m
p
o
wer
,
b
u
t
th
e
MR
AC
co
n
tr
o
l
co
m
b
in
ed
with
I
NC
h
as
a
h
ig
h
est
r
is
e
tim
e
co
m
p
ar
e
d
with
SMC
as
it
ca
n
b
e
s
ee
n
in
Fig
u
r
e
1
2
(
a
)
.
W
e
ca
n
s
ee
also
,
in
s
tead
y
s
tate,
th
at
MR
AC
h
av
e
th
e
h
i
g
h
er
o
s
cillatio
n
ar
o
u
n
d
th
e
m
ax
im
u
m
p
o
in
t,
I
n
ad
d
itio
n
;
th
e
GPV
v
o
ltag
e
is
r
eg
u
lated
to
f
o
llo
w
th
e
r
ef
er
en
ce
v
o
ltag
e
Vm
p
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
el
g
en
er
ated
b
y
I
NC
C
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:
2
0
8
8
-
8
694
C
o
mp
a
r
a
tive
s
tu
d
y
o
f n
ew MPP
T c
o
n
tr
o
l a
p
p
r
o
a
ch
es fo
r
a
p
h
o
to
vo
lta
ic
s
ystem
(
A
h
med
Ha
d
d
o
u
)
259
alg
o
r
ith
m
with
less
o
s
cillatio
n
ar
o
u
n
d
it,
in
th
is
ca
s
e,
th
e
MRAC
co
n
tr
o
l
af
f
ec
ts
th
e
v
o
ltag
e
o
f
th
e
GPV,
wh
ich
lead
s
to
o
s
cillatio
n
s
ar
o
u
n
d
Vm
p
p
(
1
6
0
m
V
v
s
4
2
m
V
f
o
r
SMC
)
.
Als
o
,
th
e
r
esu
lts
also
co
n
f
ir
m
th
at
th
e
o
p
tim
al
cu
r
r
en
t
is
d
ir
ec
tly
d
e
p
en
d
u
p
o
n
th
e
s
o
lar
illu
m
in
a
tio
n
an
d
is
s
ig
n
if
ica
n
tly
a
f
f
ec
ted
b
y
th
e
s
u
d
d
e
n
ch
an
g
e
Fig
u
r
e
(
c)
,
in
s
tead
o
f
t
h
e
o
p
tim
al
v
o
ltag
e,
wh
ich
is
s
lig
h
tly
af
f
ec
ted
Fig
u
r
e
1
2
(
b
)
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
2
.
Simu
latio
n
r
esu
lts
with
ir
r
ad
iatio
n
v
a
r
iatio
n
:
a)
O
u
tp
u
t p
o
wer
o
f
GPV;
b
)
o
u
t
p
u
t v
o
ltag
e
o
f
GPV; c
)
C
u
r
r
en
t o
f
GPV,
d
)
L
o
ad
o
u
tp
u
t c
u
r
r
e
n
t.
4
.
2
.
I
n c
a
s
e
o
f
l
o
a
d v
a
ri
a
t
io
n
a
nd
t
em
pera
t
ure
Fig
u
r
e
1
3
s
h
o
ws
th
at
b
o
th
ap
p
r
o
ac
h
es
h
av
e
an
e
f
f
ec
tiv
e
p
er
f
o
r
m
a
n
ce
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
d
esp
ite
th
e
ch
an
g
e
in
te
m
p
er
atu
r
e
an
d
lo
ad
b
u
t
s
till
th
e
S
MC
m
eth
o
d
h
as
a
f
aster
r
esp
o
n
s
e
an
d
a
g
r
ea
ter
ca
p
ac
ity
co
m
p
ar
ed
to
MRAC
to
f
o
llo
w
th
e
r
ef
e
r
en
ce
v
o
ltag
e
Vm
p
o
f
th
e
p
h
o
to
v
o
ltaic
p
a
n
el.
So
,
th
e
MRAC
alg
o
r
ith
m
is
an
ef
f
icien
t
alg
o
r
ith
m
b
u
t
h
as
o
s
cillatio
n
s
ar
o
u
n
d
th
e
o
p
tim
al
v
al
u
e
as
s
h
o
wn
in
Fig
u
r
e
1
3
(
b
)
.
T
h
is
alg
o
r
ith
m
h
as
a
b
ig
i
n
co
n
v
en
ien
ce
wh
ic
h
is
its
p
o
o
r
b
eh
av
io
u
r
af
ter
a
n
ab
r
u
p
t
ch
an
g
e
in
tem
p
er
atu
r
e
an
d
lo
ad
in
g
s
o
f
l
o
ad
s
.
I
n
ad
d
itio
n
,
th
e
SMC
is
ch
ar
ac
ter
ized
b
y
it
s
r
o
b
u
s
tn
ess
,
its
ef
f
icien
cy
an
d
its
s
tab
ilit
y
.
Nev
er
th
eless
,
th
e
s
et
-
u
p
o
f
th
is
k
in
d
o
f
alg
o
r
ith
m
is
m
o
r
e
c
o
m
p
lex
th
an
tr
a
d
itio
n
al
alg
o
r
i
th
m
s
.
W
e
th
er
ef
o
r
e
ev
alu
ated
an
d
co
m
p
ar
ed
th
ese
alg
o
r
ith
m
s
o
f
ea
ch
m
eth
o
d
to
s
h
o
w
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
m
eth
o
d
co
m
p
ar
ed
to
th
e
o
th
er
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
Vo
l.
11
,
No
.
1
,
Ma
r
20
20
:
25
1
–
26
2
260
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
3
.
Dif
f
er
en
ts
s
im
u
latio
n
r
esu
lts
f
o
r
l
o
ad
v
a
r
iatio
n
an
d
tem
p
er
atu
r
e:
(
a)
Ou
t
p
u
t p
o
wer
o
f
GPV;
(
b
)
o
u
tp
u
t v
o
ltag
e
o
f
GPV;
(
c)
C
u
r
r
en
t o
f
GPV,
(
d
)
L
o
ad
o
u
t
p
u
t c
u
r
r
en
t
5.
E
XP
E
R
I
M
E
N
T
A
L
T
E
S
T
A
ND
DIS
C
USS
I
O
N
T
h
e
B
o
o
s
t
co
n
v
er
ter
is
u
s
ed
t
o
tr
an
s
f
er
p
o
wer
f
r
o
m
th
e
in
p
u
t
o
f
th
e
co
n
v
er
ter
to
th
is
o
u
t
p
u
t
,
an
d
to
in
cr
ea
s
e
th
e
lo
w
PV
o
u
tp
u
t
v
o
ltag
e
to
a
h
ig
h
v
o
ltag
e
DC
b
u
s
th
e
B
o
o
s
t
co
n
v
er
ter
is
u
s
ed
as
an
ad
ap
tatio
n
s
tag
e
.
T
h
e
two
s
ig
n
als
u
s
ed
f
o
r
th
e
im
p
lem
en
tatio
n
o
f
th
e
MPPT
alg
o
r
ith
m
an
d
th
e
v
o
lt
ag
e
r
eg
u
latio
n
lo
o
p
ar
e
d
etec
ted
b
y
an
AC
S7
1
1
cu
r
r
en
t
s
en
s
o
r
(
-
1
2
.
5
A
to
+1
2
.
5
A)
f
o
r
I
PV
,
an
d
b
y
a
r
esis
tiv
e
d
iv
id
er
f
o
r
V
PV
an
d
ar
e
in
ter
f
ac
ed
b
y
an
STM
3
2
F4
0
7
Dis
co
v
er
y
b
o
ar
d
v
ia
th
e
ADC
ch
an
n
els
f
o
r
co
n
t
r
o
llin
g
th
e
DC
-
DC
co
n
v
er
ter
.
T
h
e
STM
3
2
co
n
tr
o
ls
th
e
h
ar
d
war
e
p
ar
t
u
s
in
g
a
P
W
M
o
u
tp
u
t
f
o
r
s
witch
in
g
th
e
MO
SF
E
T
tr
an
s
is
to
r
(
SC
H2
0
8
0
KE
)
.
T
h
e
d
escr
ip
tio
n
o
f
th
e
s
o
f
tw
ar
e
an
d
h
a
r
d
war
e
b
l
o
ck
f
o
r
r
u
n
n
in
g
th
e
m
ain
lo
o
p
is
s
h
o
wn
in
th
e
f
o
llo
win
g
Fig
u
r
e
1
4
.
Fig
u
r
e
1
4
.
E
x
p
e
r
im
en
tal
s
y
s
tem
b
lo
c
T
h
e
d
ata
ac
q
u
is
itio
n
o
f
PV v
o
l
tag
e
an
d
c
u
r
r
en
t a
r
e
lo
g
g
in
g
th
r
o
u
g
h
o
u
t th
e
to
o
ls
STM
Stu
d
io
,
th
e
ex
p
er
im
en
tal
r
esu
lts
was
p
lo
tted
in
th
e
Fig
u
r
e
1
5
,
1
6
,
1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.