Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
3, N
o
. 4
,
A
ugu
st
2013
, pp
. 56
8
~
57
6
I
S
SN
: 208
8-8
7
0
8
5
68
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Modeling and Simulation of A
S
o
l
a
r Power Sou
r
ce for a Cl
ean
Energy without Pollution
Mo
ha
med L
o
uz
az
ni
*, E
l
H
a
ss
an
Ar
oud
a
m*,
H
a
n
a
ne
Y
a
ti
mi
*
* Modeling
and
simulation of
Mechan
ical S
y
s
t
ems Laborator
y
,
F
acult
y
of S
c
i
e
n
ces
, Univ
ers
i
t
y
Abdelm
alek
Es
s
aadi
Av
de Sebta, Mhann
ech II
93002 BP
2121, Tetou
a
n,
Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 26, 2013
Rev
i
sed
Ju
l 6
,
2
013
Accepte
d
J
u
l 16, 2013
Pho
t
ov
o
ltaic cell g
e
n
e
ration
is th
e tech
n
i
qu
e wh
ich
u
s
es pho
tov
o
ltaic
cell to
co
nv
ert
so
lar en
erg
y
into
elect
rical energy.
Now a days ,the
ph
ot
o
v
o
l
t
a
i
c
gene
rat
i
o
n i
s
de
vel
o
pi
n
g
i
n
creasi
ngl
y
fast
as a
rene
wa
ble energy source.
The func
tio
n
i
ng
of a ph
o
t
o
voltaic cel
l as
th
e power
g
e
nerato
r is equ
i
valen
t
to
a
n
electric circuit containing
a
cur
r
ent
gene
ra
t
o
r,
di
o
d
e, se
ri
es and s
h
un
t
resi
st
ance. Thi
s
pa
pe
r
prese
n
t
s
a m
odel
i
n
g a
nd
sim
u
l
a
t
i
on of
a ph
ot
o
v
o
l
t
a
i
c
sy
st
em
co
nstitu
tes of a g
e
n
e
rator
p
h
o
t
ovo
ltaic (PVG), DC
-DC con
v
e
rter
(boo
st chop
p
e
r) to
tran
sfer the
m
a
x
i
m
u
m
p
o
w
er t
o
a
b
a
se t
r
an
sm
itter
statio
n
.
Th
e tem
p
erature an
d irrad
i
ance effects on
t
h
e PVG
will be
st
udi
e
d
, pa
rt
i
c
ul
arl
y
on t
h
e v
a
ri
abl
e
s
such a
s
the short circ
uit current
I
cc
, th
e op
en
ci
rcu
it
v
o
ltag
e
V
oc
. De
pen
d
i
n
g
on
t
h
e l
o
ad
(B
TS,
I=6
0
A
,
V=48V)
profile and
clim
at
ic facto
r
s in
fl
ue
n
c
i
ng,
we
can
fi
nd
a
hi
g
h
l
y
gap
bet
w
ee
n t
h
e m
a
xim
u
m
po
we
r su
ppl
i
e
d by
t
h
e P
V
G an
d t
h
at
actu
a
lly tran
sferred
t
o
th
e
BTS.
A m
a
x
i
m
u
m
p
o
w
er
po
in
t track
e
r
(M
PPT
) base
d
on a b
oost
c
o
n
v
e
r
t
e
r com
m
a
nded
by
a Pul
s
e
W
i
dt
h
M
o
d
u
l
a
t
i
on
(P
WM
) i
s
use
d
f
o
r e
x
t
r
act
i
n
g t
h
e m
a
xim
u
m
powe
r
f
r
om
the PVG. T
h
us, a
real time track
i
ng
of t
h
e o
p
t
i
m
al
poi
nt
of
functioning
is neces
sary to opti
m
i
ze the efficiency
on t
h
e system
.
The m
odel
i
ng and si
m
u
l
a
t
i
on of t
h
e sy
st
em
(PV
G
, b
o
o
st
con
v
e
r
t
e
r
,
P
W
M
a
nd M
P
PT al
g
o
ri
t
h
m
of Pert
ur
bat
i
o
n
and
O
b
ser
v
at
i
o
n P&
O
)
i
s
th
en
m
a
d
e
wit
h
Matlab
/
Sim
u
lin
k
so
ft
ware.
Keyword:
Pho
t
ov
o
ltaic
Gene
rato
r
B
oost
C
o
nve
rt
er
PW
M
MPPT
P&O
Copyright ©
201
3 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Moaham
ed LOUZAZNI,
Facu
lty of Scien
ces, Un
iv
ersity Abd
e
lm
alek
Essaad
i,
Av
de
Se
bt
a,
M
h
an
nec
h
I
I
B
P
2
1
2
1
,
Tet
oua
n, M
o
r
o
cc
o.
Em
a
il: louzazni@m
s
n.com
1.
INTRODUCTION
For t
w
o ce
nt
ur
i
e
s, t
h
e wo
rl
d
has use
d
i
t
s
en
ergy
al
m
o
st exclusively from
th
e com
bustion of coal, oil
and
g
a
s
rep
r
es
ent
t
o
day
80
%
o
f
gl
o
b
al
e
n
er
gy
co
ns
um
p
tio
n
m
a
rk
eted
. B
u
t co
al,
o
il
and gas
are
fossil
energy
t
h
at
are
not
re
n
e
wed
.
T
h
i
s
e
n
e
r
gy
i
s
t
h
e p
r
i
n
c
i
pal
cause
o
f
gl
obal
warm
i
ng,
i
s
no
w a
m
a
jor
en
vi
ro
nm
ent
a
l
an
d
econ
o
m
i
c pro
b
l
em
affect
i
ng t
h
e
pers
pect
i
v
e
s
o
f
s
u
st
ai
na
bl
e de
vel
o
pm
ent
.
The
use
o
f
s
o
l
a
r en
er
gy
t
o
pr
od
uc
e
el
ect
ri
ci
t
y
by
a ph
ot
o
v
o
l
t
a
i
c
panel
req
u
i
r
es
no
f
u
el
. S
o
t
h
ere i
s
n
o
i
s
s
u
e
or
pr
o
duci
n
g
t
oxi
c ga
ses f
r
o
m
t
h
e
com
bustion
of
coal whic
h has
the effect of increasi
ng th
e t
e
m
p
erature of t
h
e earth by gre
e
nhouse gases
.
Solar
en
erg
y
is a cle
a
n
and
in
exh
a
ustib
le ex
cellen
t
altern
ativ
e.
In
ad
d
ition
,
th
ere is n
o
waste from th
is
tech
n
i
qu
e of
en
erg
y
pro
d
u
c
tio
n
an
d no
t rej
ect po
llu
ting and
tox
i
c su
bstan
ces in th
e so
il.
In
t
h
is stu
d
y
,
we m
o
del and
opt
i
m
i
ze a sy
stem
com
p
ri
si
ng
a p
hot
ov
ol
t
a
i
c
gen
e
rat
o
r c
o
nnected t
o
a
boost converte
r fo
r
a
b
e
st tr
an
sfer
th
e
po
we
r
dra
w
n
f
r
om
t
h
e su
n a
n
d c
o
n
v
e
r
t
e
d i
n
t
o
el
ect
ri
ci
t
y
, w
i
t
hout
b
u
r
n
i
n
g
coal
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
o
n
of
a
sol
a
r
pow
er
s
our
ce f
o
r
a
cl
ean
ene
r
gy
w
i
t
hout
p
o
l
l
u
t
i
o
n (
M
o
h
a
m
e
d
L
o
u
z
az
ni
)
56
9
2.
SYSTE
M
MO
DELING
The system
studie
d
is the associ
atio
n
o
f
a set o
f
in
terconn
ected
sub
s
yst
e
m
s
wh
ich
are: th
e GPV,
rep
r
ese
n
t
s
t
h
e sol
a
r m
odul
e as a source o
f
cur
r
ent
i
n
pa
ral
l
e
l
wi
t
h
a di
ode
, a resi
st
or i
n
seri
es rep
r
esent
s
t
h
e
cont
act
resi
st
a
n
ce, an
d an
ot
h
e
r so-cal
l
e
d pa
ral
l
e
l
by
pass or
shunt resistance, represe
n
ts
the curre
n
ts of l
eaks, a
q
u
a
drupo
le
of ad
ap
tation
,
which
is
a p
o
wer DC-DC
conv
erter. Th
e
DC-DC co
nv
erter is
co
n
t
ro
lled b
y
a sig
n
a
l
pul
se
wi
dt
h m
o
d
u
l
a
t
i
on
wi
t
h
a researc
h
st
rat
e
gy
o
f
M
PPT.
The M
P
P
T
co
nt
r
o
l
fol
l
o
ws t
h
e p
o
i
n
t
of m
a
xi
m
u
m
powe
r at eac
h i
n
stant. This
co
nt
r
o
l
,
act
s
di
re
ct
l
y
on t
h
e
dut
y cycle of t
h
e c
o
nve
r
ter.
2.
1
Modeling
of a
Photovo
lta
i
c Cell
In
t
h
e id
eally a p
h
o
t
o
v
o
ltaic cell (PV) can b
e
su
m
m
ari
z
ed by
a
n
i
d
e
a
l
cur
r
ent
s
o
urce
pr
o
duce
s
a
cur
r
ent
pr
o
p
o
r
t
i
onal
t
o
t
h
e I
p
h i
n
ci
dent
l
i
g
ht
po
we
r, i
n
p
a
rallel with
a d
i
ode. If we con
n
ect a resistiv
e load
to
th
e termin
als o
f
th
e GPV, latter is d
e
liv
ers a p
o
r
ti
o
n
o
f
cu
rrent I and the rest Id, curre
n
t
in
th
e d
i
od
e. Fo
r an
id
eal GPV, th
e vo
ltag
e
at th
e
termin
als o
f
t
h
e resistan
ce is
equal t
o
that at
the term
inals of t
h
e led:
V=
Vd and
th
e non
lin
ear dio
d
e
I-V ch
aracteristic is g
i
v
e
n
b
y
th
e
relation
.
I =
I
1
d
T
V
nV
ds
e
(1
)
Th
e cu
rren
t sup
p
lied wou
l
d
be:
d
T
V
nV
ph
d
p
h
s
I
=
I-
I
=
I-
I
e
-
1
(2
)
In the
real case
in m
odels los
s
of
voltage
and leakage
by t
w
o
resistance i
n
parallel Rp and Rs series
. T
h
e
m
odel
of t
h
e c
e
l
l
i
s
sho
w
n i
n
Fi
gu
re
1:
Fig
u
re
1
.
Model o
f
PV cell with
in
clu
s
i
o
n of vo
ltag
e
loss an
d leak
ag
e cu
rren
t
Accord
ing
th
e law
of Kirch
hofff, we h
a
v
e
:
p
hdp
II
I
I
(3
)
.
ds
p
pp
VV
I
R
I
RR
(4
)
.
.
.
1
s
T
VI
R
nV
s
ph
s
p
VI
R
II
I
e
R
(5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
I
J
ECE
Vo
l. 3
,
N
o
. 4
,
Aug
u
s
t 2
013
:
56
8
–
57
6
57
0
In
th
e i
d
eal, Rs ten
d
s
towards 0
and
Rp
to
i
n
fi
n
ity. An
d in the real, these
resistor
s
provide an asse
ssm
ent of
th
e im
p
e
rfection
s
o
f
th
e
d
i
od
e; co
ns
ideri
n
g t
h
at the
resistance Rs ha
s a
l
o
w
value. Using a num
e
rical
method
(t
he m
e
t
hod
o
f
Ne
wt
o
n
-R
a
p
h
s
on
f
o
r e
x
am
pl
e) an
d
u
nde
r i
l
l
u
m
i
nat
i
on, t
h
e sl
o
p
es
of
t
h
e
I-
V c
h
a
r
act
eri
s
t
i
c
s
are calculated at I=0 open circuit and s
h
ort circuit V=0
a
n
d res
p
ectively give the invers
e of series and shunt
resistance values.
2.
2
Influence
of L
i
ght an
d Tem
p
eratu
re
on the Char
ac
teristic I(V)
The res
p
onse of a PV cell at differe
nt
l
i
ght
ener
gy
fi
g
u
re (
2
). Sh
o
w
s t
h
at
i
rra
di
at
i
on ha
s a si
gni
fi
cant
effect
on t
h
e c
u
rrent
open-circuit. Th
at is the curve
of the
I-V c
h
aracter
istic an
d
relativ
ely h
o
r
izo
n
t
al,
wh
ile
the effect
on the
voltage in open circ
u
it, i.e. th
e sl
o
p
e
of t
h
e I-V curv
e and
relativ
ely v
e
rtical, wh
ich
is qu
ite
lo
w.
W
i
t
h
regard
to
th
e m
a
x
i
m
u
m
p
o
w
er of a p
h
o
t
ov
o
ltai
c
cell, wh
en
th
e illu
m
i
n
a
tio
n
is h
i
g
h
e
st, th
e cell
gene
rat
e
s m
o
re po
wer
.
The t
e
m
p
erat
ur
e ha
s a very
i
m
por
t
a
nt
effect
o
n
t
h
e o
p
e
n
ci
rcui
t
vol
t
a
ge a
n
d a no
n-
rem
a
rkable effect on the
shor
t
circuit of cell
fig
u
re (
3
).
0
5
10
15
20
25
30
35
0
2
4
6
8
10
12
14
16
T
e
ns
i
o
n o
n
v
o
l
t
C
o
u
r
an
t
on
am
p
10
00
W
/
s
80
0 W
/
S
60
0 W
/
S
40
0 W
/
S
20
0 W
/
S
Fi
gu
re 2.
C
u
rre
nt
-
vol
t
a
ge
cha
r
act
eri
s
t
i
c
fo
r di
ffe
rent
val
u
es
of
ra
di
at
i
o
n
0
10
20
30
40
50
60
70
0
5
10
15
T
e
ns
i
o
n
on
v
o
l
t
C
o
ura
n
t
on
a
m
p
1
00°C
90
°
C
75
°
C
25
°
C
0°
C
Fi
gu
re
3.
C
u
rre
nt
-
vol
t
a
ge
cha
r
act
eristic in
d
i
fferen
t tem
p
eratu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
o
n
of
a
sol
a
r
pow
er
s
our
ce f
o
r
a
cl
ean
ene
r
gy
w
i
t
hout
p
o
l
l
u
t
i
o
n (
M
o
h
a
m
e
d
L
o
u
z
az
ni
)
57
1
2.
3
Mo
del
i
n
g
o
f
t
h
e Ph
ot
o
vol
tai
c
Gener
a
t
o
r
Because of its low thic
knes
s
,
a photovoltaic
cell pr
oduce
s
a very low elect
ri
cal
power of the
orde
r
1
to 3
W. So to increase the
powe
r,
on
asse
m
b
les th
ese cells eith
er in
series or in
p
a
rallel for form
ed
a
p
h
o
t
ovo
ltaic
mo
du
le and
ach
i
e
v
e
th
e d
e
sired p
o
wer fo
r supp
lyin
g
a BTS.
An
asso
ciatio
n o
f
cells in
series to
in
crease th
e ten
s
ion
of th
e GPV,
wh
ile an
N
s
conn
ection
in
p
a
rallel allo
ws in
creasing
th
e o
u
t
p
u
t
curren
t of
t
h
e
ge
ne
rat
o
r. The
e
q
ui
val
e
nt
ci
rcui
t
of
t
h
e PV ge
nerat
o
r b
ecom
e
s:
Fi
gu
re
4.
M
o
d
e
l
of
t
h
e
p
hot
o
vol
t
a
i
c
g
e
ne
rat
o
r
Th
e equ
a
tio
n of th
e term
in
al fo
r th
e cu
rren
t an
d th
e
vo
ltag
e
is as fo
llows:
pG
P
V
s
s
G
P
V
sP
T
N.
V
+
N
.
R
.
I
N.
N
.
V
p
GP
V
s
s
G
P
V
GPV
p
ph
p
s
sp
N.
V
+
N
.
R
.
I
I=
N
I
-
N
I
e
-
1
-
N.
R
(6
)
In
fact, t
h
e ph
o
t
o
v
o
ltaic efficien
cy is sen
s
itiv
e to
s
m
all
ch
ang
e
s in
resistan
ce Rs, bu
t in
sen
s
itiv
e
to
th
e
vari
at
i
o
n o
f
R
p
f
o
r a P
V
m
o
d
u
l
e
o
r
a ge
n
e
rat
o
r
,
t
h
e se
ri
es resi
st
ance i
s
appa
re
nt
l
y
im
port
a
nt
an
d paral
l
e
l
resi
st
ance t
e
nd
s t
o
i
n
fi
ni
t
y
i
s
repl
ace
d
by
a
n
ope
n ci
rc
ui
t
.
The m
a
t
h
em
at
i
cal
equat
i
o
n
of t
h
e
gene
ral
i
zed
m
o
d
e
l can
be
written
as:
pG
P
V
s
s
G
P
V
sP
T
N.
V
+
N
.
R
.
I
N.
N
.
V
GPV
p
ph
p
s
I=
N
I
-
N
I
e
-
1
(7
)
pp
h
G
P
V
s
GP
V
s
t
s
G
P
V
ps
p
NI
-
I
N
V=
N
n
V
l
n
1
+
-
R
I
NI
N
(8
)
2.
4
Mo
del
i
n
g
o
f
B
oos
t c
h
o
pper
A
DC/DC conv
erter is a chop
p
e
r tran
sist
o
r
typ
e
p
a
rallel vo
ltag
e
bo
o
s
ter
u
s
ed
to in
crease th
e
ou
tpu
t
v
o
ltag
e
fro
m
th
e sou
r
ce, th
e
sch
e
m
a
tic d
i
ag
ram
is sh
own in
figu
re
(5
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8-8
7
0
8
I
J
ECE
Vo
l. 3
,
N
o
. 4
,
Aug
u
s
t 2
013
:
56
8
–
57
6
57
2
Fi
gu
re
5.
M
o
d
e
l
of
a
DC
/
D
C
cho
p
p
er
It
i
s
si
zed for
a 3 k
W
po
we
r
t
h
at
corres
p
o
nds t
o
t
h
e val
u
es n
o
m
i
nal
I
=
17
0,
V=1
7
.
6
4 V,
on t
h
e si
de o
f
t
h
e
g
e
n
e
rator, and
Vs=50V,
Is=60
A, lo
ad
sid
e
. His transfo
r
m
a
tio
n
ratio
is t
h
e du
ty cycle (ratio
o
f
tim
e
d
u
ring
wh
ich
th
e tran
sisto
r
is cl
o
s
ed,
th
e p
e
riod
h
a
sh as
α
<<
1):
a
n
d
V1
s
=
V1
-
α
The c
h
op
per
f
o
rces t
h
e
G
P
V t
o
ope
rat
e
at
m
a
xi
m
u
m
powe
r
,
wh
atev
er th
e il
lu
min
a
tio
n
an
d tran
sfer to
t
h
e
lo
ad
fo
r a dut
y
cy
cle defi
ne
d. T
h
i
s
cho
ppe
r has f
o
u
r
com
pone
nt
s:
An i
n
d
u
ct
an
ce L, a di
ode,
a capaci
t
o
r C
and
a
switch
th
at takes two
states,
S=1
an
d
S=0
.
Wh
en
th
e switc
h
S is clo
s
ed
, th
e d
i
od
e D is p
o
l
arized
in
op
po
site
th
e lo
ad
is t
h
erefo
r
e iso
l
ated. Th
e so
ur
ce
pr
ov
id
ed
en
ergy to
th
e i
n
du
c
t
ance.
If t
h
e s
w
itch S is ope
n
, t
h
e
out
put
st
age
re
cei
ves e
n
er
gy
f
r
om
t
h
e s
o
urce
and i
n
ductor
whe
r
e a
n
i
n
cre
a
se
in
t
h
e
ou
tpu
t
vo
ltag
e
. Id
eally, all
com
pone
nt
s ar
e i
d
eal
;
t
h
e
b
o
o
s
t
ch
op
per
can
be m
odel
e
d
usi
n
g
t
h
e
f
o
l
l
o
wi
n
g
or
di
na
ry
di
ff
erent
i
a
l
eq
uat
i
ons:
cc
L0
dV
V
C=
1
-
s
i
-
-
i
dt
R
(9
)
L
ic
di
L=
V
-
1
-
s
V
dt
(1
0)
And
0
.
VR
i
We a
dde
d t
o
t
h
e p
r
evi
ous
m
odel
a
resi
st
ance
R
L
in
tern
al ind
u
c
tan
ce and
resist
ance Rc internal ca
pacity, so
the (9) and
(10)
becom
e
:
c0
L0
dV
V
C=
1
-
s
i
-
-
i
dt
R
(1
1)
L
i0
L
L
di
L=
V
-
1
-
s
V
-
R
i
dt
(1
2)
C
0C
C
.
dV
V=
V
+
R
C
.
dt
(1
3)
Inse
rt
i
n
g 13
i
n
11:
CC
C
0C
L
C
0
CC
C
RR
R
R
R
V=
V
+
1
-
s
i
-
V
-
i
R+
R
R
+
R
R+
R
(1
4)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
o
n
of
a
sol
a
r
pow
er
s
our
ce f
o
r
a
cl
ean
ene
r
gy
w
i
t
hout
p
o
l
l
u
t
i
o
n (
M
o
h
a
m
e
d
L
o
u
z
az
ni
)
57
3
B
y
devel
opi
ng
t
h
e ex
p
r
essi
o
n
of
V
0
i
n
(15) becom
e
s:
CC
C
0C
L
C
0
CC
C
RR
R
R
R
V=
V
+
1
-
s
i
-
V
-
i
R+
R
R
+
R
R+
R
(1
5)
Devel
opi
ng
t
h
e
ex
pres
si
o
n
of
V
0
we get
:
C
0C
L
0
CC
RR
R
V=
V
+
1
-
s
i
-
i
R+
R
R
+
R
(1
6)
The
1
1
e
x
p
r
ess
i
on
bec
o
m
e
s:
Li
0
L
L
1
iV
1
s
V
R
i
d
t
L
(1
7)
U
s
ing
(1
6)
and
(
1
7
)
, it sets t
h
e
p
a
tter
n
of
t
h
e bo
oster
D
C
-D
C r
eal cho
pper
,
f
i
gu
r
e
6.
Fi
gu
re
6.
R
eal
cho
p
p
er
B
o
ost
i
n
Si
m
u
l
i
nk
3.
MODELING OF
THE COMMANDS
3.
1. C
o
ntr
o
l
A
l
gori
t
hm "Di
s
turb
ance
a
nd Obser
v
a
t
i
o
n
"
The be
havi
or
of
a GPV
is
nonlinear
because its
power depe
nds on
the
temperat
ure
and illum
i
nation.
Whe
r
e t
h
e
G
P
V
fee
d
s a
n
e
t
w
o
r
k
,
i
t
w
o
rki
n
g
at
t
h
e
poi
nt
of m
a
xi
m
u
m
power
M
PPT t
o
m
a
xi
m
i
ze
per
f
o
r
m
a
nce. Thi
s
M
PPT al
way
s
vari
es depe
n
d
i
n
g
on the irradiation, the tem
p
erature…
,
W
e
use an
al
go
ri
t
h
m
of Di
st
ur
ba
nce a
nd
O
b
ser
v
at
i
o
n t
o
fi
nd t
h
i
s
i
t
e
m
i
n
real
t
i
m
e
. It
i
s
t
h
e al
gori
t
hm
based
o
n
di
st
ur
ba
nce o
f
t
h
e sy
st
em
by
t
h
e i
n
crease or
decrease of Vi
where by
ac
t
i
ng
di
rect
l
y
on
t
h
e dut
y
cy
cl
e of t
h
e
DC
-
DC
co
nv
ert
e
r, t
h
e
n
t
h
e
obs
er
vat
i
on
o
f
t
h
e effect
on t
h
e out
put
po
we
r
of t
h
e
Panel
.
I
f
t
h
e v
a
l
u
e
of
p
o
we
r
cu
rren
t P(k
)
o
f
th
e Pan
e
l is larg
er th
an
th
e
prev
i
o
u
s
P(
k-1) value
t
h
en we keep
t
h
e
sam
e
di
rect
i
o
n o
f
pr
evi
o
us
d
i
stu
r
b
a
n
ce
o
t
h
e
rw
ise you r
e
v
e
r
s
e th
e d
i
sr
up
tio
n of
t
h
e
p
r
ev
iou
s
cycle.
A
r
e m
o
d
e
l un
der
Sim
u
lin
k
is
g
i
v
e
n
by
fig
u
re 7.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
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8
I
J
ECE
Vo
l. 3
,
N
o
. 4
,
Aug
u
s
t 2
013
:
56
8
–
57
6
57
4
Fi
gu
re
7.
Si
m
u
l
i
nk m
odel
of t
h
e P
&
O al
go
r
i
t
h
m
3.
2.
Contr
o
l
b
y
P
u
lse Wid
t
h
Modul
ati
o
n
(PWM)
The P
W
M
co
n
t
rol
i
s
t
o
cut
t
h
e out
p
u
t
vol
t
a
g
e
generat
e
d by
t
h
e conve
rt
er i
n
t
o
a seri
es of
el
em
ent
a
ry
p
a
ttern
s with
l
o
w
p
e
riod
, and
variab
le
du
ty cycle in
time. The
tem
poral change
of t
h
e
duty cycle of ea
c
h
swi
t
c
h i
s
t
h
e
n
det
e
rm
i
n
ed b
y
a
m
odul
at
i
n
g si
g
n
al
w
h
i
c
h i
s
sel
ect
ed
gene
ral
l
y
si
nu
soi
d
al
. T
h
e c
ont
rol
commands of each
cell
are gene
rated by
t
h
e
intersectio
n betwee
n a t
r
iangular ca
rrie
r
and the m
o
dulating
sig
n
a
l. Accordin
g
to
th
e strateg
y
, it can
b
e
sa
m
p
led
sy
nchr
o
n
o
u
sl
y
wi
t
h
t
h
e t
r
i
a
ng
ul
a
r
carri
er
, or
di
rect
l
y
com
p
ared. Eac
h
s
w
itch is
swi
t
ched
at
a rate i
m
posed
by the
carrier.
Th
e
fo
llowing
figu
re illu
st
rates th
e m
o
d
e
ling
o
f
th
e
PW
M comman
d
in
Mat
l
ab
/Si
m
u
lin
k
.
Fi
gu
re
8.
Si
m
u
l
i
nk m
odel
of t
h
e P
W
M
c
o
nt
r
o
l
4.
RESULTS
To
realize the s
i
m
u
lation cons
idering t
h
e BT
S as a
resistive
load. T
h
e
figure (9) s
h
ows t
h
e evolution
of
t
h
e o
p
erat
i
n
g poi
nt
o
n
t
h
e po
we
r-
vol
t
a
ge
charact
e
r
i
s
t
i
c
fo
r d
i
fferen
t levels o
f
su
n
ligh
t
an
d th
e
figu
re (1
0)
the power-voltage c
h
aracte
r
istic for di
ffe
rent
te
m
p
eratur
es.
For a
duty cycle of
0.
5, o
n
at
m
a
xim
u
m
pow
er
and
fi
gu
re
(1
1)
sh
ow
s t
h
e
rel
a
t
i
ons
hi
p
bet
w
e
e
n t
h
e
o
u
t
p
ut
p
o
we
r
of
t
h
e i
n
v
e
rt
er a
n
d
i
t
s
d
u
t
y
cy
cl
e. Fi
gu
r
e
(12
)
shows t
h
at th
e power of t
h
e inv
e
rter
o
u
t
p
u
t
is equ
a
l to
th
e lo
ad
o
f
th
e
BTS.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
Mo
del
i
n
g
a
n
d
si
mul
a
t
i
o
n
of
a
sol
a
r
pow
er
s
our
ce f
o
r
a
cl
ean
ene
r
gy
w
i
t
hout
p
o
l
l
u
t
i
o
n (
M
o
h
a
m
e
d
L
o
u
z
az
ni
)
57
5
0
5
10
15
20
25
30
35
40
0
100
200
300
400
T
e
ns
i
o
n o
n
v
o
l
t
P
u
i
s
s
anc
e onn w
a
t
t
10
00 W
/
S
80
0 W
/
S
60
0 W
/
S
40
0 W
/
S
20
0 W
/
S
Fi
gu
re
9.
P
o
we
r-
vol
t
a
ge
ch
ara
c
t
e
ri
st
i
c
fo
r l
e
v
e
l
s
of
s
uns
hi
ne
0
10
20
30
40
50
60
70
0
20
0
40
0
60
0
80
0
T
e
ns
i
o
n
on
v
o
l
t
P
u
i
s
s
a
nc
e onn w
a
t
t
10
0°C
90
°C
75
°C
50
°C
25
°C
Figu
re 1
0
. Po
w
e
r-
voltage
c
h
ar
acteristic
fo
r diffe
rent
tem
p
era
t
ures
Fi
gu
re 1
1
. Po
w
e
r
c
u
r
v
e depe
n
d
i
n
g on
t
h
e rat
i
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
I
J
ECE
Vo
l. 3
,
N
o
. 4
,
Aug
u
s
t 2
013
:
56
8
–
57
6
57
6
Figure 12. I-V characte
r
istic
at the output
of
conve
r
ter
5.
CO
NCL
USI
O
N
The c
o
n
s
um
pt
i
on
o
f
f
o
ssi
l
en
ergy
i
s
a m
a
jor
so
urce
of
en
vi
ro
nm
ent
a
l
degr
adat
i
o
n
.
T
h
e P
hot
ov
ol
t
a
i
c
can
be
use
d
i
n
vari
ous
ap
pl
i
c
a
t
i
ons.
Thi
s
t
y
p
e
o
f
a
ppl
i
cat
i
o
n ca
n
be i
n
st
al
l
e
d
on
t
h
e
r
o
o
f
of
p
r
i
v
at
e
hom
es (a
n
avera
g
e of 3
kW). The
r
e are
also sy
ste
m
s
o
f
larg
er size,
u
p
t
o
sev
e
ral meg
a
watts. And
to
ob
tain
th
e b
e
st
po
we
r t
r
a
n
sfe
r
bet
w
ee
n t
h
e
PV
gen
e
rat
o
r
GP
V an
d t
h
e
lo
ad
, we m
o
deled
th
e en
tire con
v
e
rsion
ch
ain
i
n
M
a
t
l
a
b an
d t
h
e sea
r
ch
al
g
o
ri
t
h
m
of m
a
xi
m
u
m
powe
r
p
o
i
n
t
t
r
ac
ki
n
g
(M
PPT
)
ha
s bee
n
desi
g
n
e
d a
n
d
si
m
u
lated
.
It forces th
e GPV t
o
wo
rk
at its Max
i
m
u
m Po
wer Po
in
t (M
PP), lead
i
n
g
t
o
an
ov
erall im
p
r
o
v
e
m
e
n
t
of pe
rform
a
nce of electrical conversi
on s
y
ste
m
. A
l
t
hou
gh sat
i
s
fact
ory
for di
rect
G
P
V-B
T
S co
nn
ect
i
on,
i
m
p
r
ov
ed P
&
O
algor
ith
m
may b
e
n
ece
ssa
ry in the ca
se
of sudden cha
n
g
e
s o
f
t
e
m
p
erat
ure
an
d i
n
sol
a
t
i
on.
REFERE
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