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.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
,
p
p
.
105
~
113
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v
9
.
i1
.
pp
1
0
5
-
113
105
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e.
co
m/jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JP
E
DS
M
P
P
T &
P
o
w
e
r F
a
c
to
r C
o
n
tro
l
f
o
r Gr
i
d
C
o
nnected P
V
Sy
s
t
em
s
wi
th
F
uzzy
L
o
g
i
c C
o
n
tro
l
l
e
rs
T
a
o
ufi
k
L
a
a
g
o
ub
i
1
,
M
o
s
t
a
f
a
B
o
uzi
2
,
M
o
ha
m
e
d B
encha
g
ra
3
1,
2
Un
iv
e
rsity
Ha
ss
a
n
1
,
IM
M
II
L
a
b
o
ra
to
ry
,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
,
F
S
T
S
e
tt
a
t,
M
o
ro
c
c
o
3
Un
iv
e
rsit
y
Ha
ss
a
n
1
,
L
a
b
o
ra
to
ire L
IS
ERT
,
Eco
le Na
ti
o
n
a
le d
e
s S
c
ien
c
e
s A
p
p
li
q
u
é
e
s,
ENS
A
Kh
o
u
r
i
b
g
a
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Oct
3
1
,
2
0
1
7
R
ev
i
s
ed
J
an
4
,
2
0
1
8
A
cc
ep
ted
J
an
1
0
,
2
0
1
8
Tw
o
f
u
z
z
y
lo
g
ic
c
o
n
tro
ll
e
rs
a
re
p
ro
p
o
se
d
in
t
h
is
p
a
p
e
r
to
c
o
n
tr
o
l
a
t
h
re
e
p
h
a
se
in
v
e
rter
f
o
r
g
rid
c
o
n
n
e
c
te
d
p
h
o
to
v
o
lt
a
ic
sy
ste
m
.
T
h
e
f
irst
c
o
n
tr
o
ll
e
r
w
a
s
u
se
d
to
p
re
d
ict
th
e
DC
v
o
lt
a
g
e
th
a
t
a
ll
o
w
s
th
e
th
re
e
p
h
a
se
i
n
v
e
rter
to
trac
k
th
e
m
a
x
i
m
u
m
p
o
we
r
p
o
i
n
t
o
f
p
h
o
to
v
o
lt
a
ic
a
rra
y
u
n
d
e
r
d
if
fe
re
n
t
e
n
v
iro
n
m
e
n
tal
c
o
n
d
it
io
n
s
su
c
h
a
s
irrad
ian
c
e
s
a
n
d
tem
p
e
ra
tu
re
.
Th
e
se
c
o
n
d
w
a
s u
se
d
to
c
o
n
tro
l
th
e
a
c
ti
v
e
p
o
w
e
r
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
in
jec
ted
i
n
to
t
h
e
g
rid
in
o
r
d
e
r
to
in
jec
t
t
h
e
m
a
x
i
m
u
m
a
c
ti
v
e
p
o
we
r
p
ro
d
u
c
e
d
b
y
p
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
s
in
to
g
rid
w
it
h
h
ig
h
e
fficie
n
c
y
a
n
d
l
o
w
to
tal
h
a
rm
o
n
ic
d
ist
o
rti
o
n
u
sin
g
th
e
sa
m
e
th
re
e
p
h
a
se
in
v
e
rt
e
r.
T
h
e
s
y
ste
m
c
o
m
p
o
n
e
n
ts
a
re
p
h
o
t
o
v
o
lt
a
ic
a
rra
y
,
DC
li
n
k
v
o
lt
a
g
e
,
th
re
e
-
p
h
a
se
in
v
e
rter,
in
v
e
rter
c
o
n
tr
o
l,
L
C
f
il
ter,
tran
sf
o
r
m
e
r
a
n
d
g
rid
.
T
o
v
e
ri
fy
t
h
e
e
ffe
c
ti
v
n
e
ss
e
o
f
th
e
in
tro
d
u
e
c
e
d
s
y
ste
m
,
m
o
d
e
li
n
g
a
n
d
si
m
u
latio
n
a
re
v
e
rif
ied
in
M
a
tl
a
b
/S
im
u
li
n
k
d
u
e
to
it
s
f
re
q
u
e
n
t
u
se
a
n
d
i
ts eff
e
c
ti
v
e
n
e
ss
.
K
ey
w
o
r
d
:
Fu
zz
y
L
o
g
ic
C
o
n
tr
o
ller
Gr
id
I
n
v
er
ter
MP
PT
P
h
o
to
v
o
ltaic
P
o
w
er
f
ac
to
r
co
n
tr
o
l
Co
p
y
rig
h
t
©
201
8
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
:
T
ao
u
f
ik
L
aa
g
o
u
b
i,
E
n
g
i
n
ee
r
i
n
g
,
Me
c
h
an
ics,
Ma
n
ag
e
m
e
n
t,
I
n
d
u
s
tr
ial
a
n
d
I
n
o
v
at
io
n
L
ab
o
r
ato
r
y
Hass
a
n
1
Un
i
v
er
s
it
y
,
Facu
lt
y
o
f
Sc
ien
ce
s
an
d
T
ec
h
n
o
lo
g
y
B
P
5
7
7
,
2
6
0
0
0
,
Settat,
Mo
r
o
cc
o
.
E
m
ail:
laa
g
o
u
b
i.ta
o
u
f
i
k
@
g
m
a
il.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t
y
ea
r
s
,
h
o
w
e
v
er
,
th
e
n
u
m
b
er
o
f
s
o
lar
p
o
w
er
ed
h
o
m
es
co
n
n
ec
ted
to
t
h
e
lo
ca
l
elec
t
r
icit
y
g
r
id
h
as
i
n
cr
ea
s
ed
d
r
am
a
ticall
y
.
T
h
ese
g
r
id
co
n
n
ec
ted
p
h
o
to
v
o
l
taic
(
P
V)
s
y
s
te
m
s
h
a
v
e
s
o
lar
p
an
els
th
a
t
p
r
o
v
id
e
s
o
m
e
o
r
ev
e
n
m
o
s
t o
f
t
h
eir
p
o
w
er
n
ee
d
s
d
u
r
i
n
g
th
e
d
a
y
ti
m
e
,
w
h
ile
s
till
b
ei
n
g
co
n
n
ec
ted
t
o
th
e
lo
ca
l e
lectr
ical
g
r
id
n
et
w
o
r
k
d
u
r
i
n
g
th
e
n
i
g
h
t
ti
m
e.
So
lar
p
o
w
er
ed
P
V
s
y
s
te
m
s
ca
n
s
o
m
eti
m
es
p
r
o
d
u
ce
m
o
r
e
elec
tr
icity
t
h
a
n
is
ac
tu
all
y
n
ee
d
ed
o
r
c
o
n
s
u
m
ed
,
esp
ec
iall
y
d
u
r
i
n
g
th
e
l
o
n
g
h
o
t
s
u
m
m
er
m
o
n
th
s
.
T
h
is
ex
tr
a
o
r
s
u
r
p
lu
s
elec
tr
icit
y
i
s
eith
er
s
to
r
ed
in
b
atter
ies
o
r
as
in
m
o
s
t
g
r
id
co
n
n
ec
ted
P
V
s
y
s
te
m
s
,
f
ed
d
ir
ec
tl
y
b
ac
k
i
n
to
th
e
elec
tr
ical
g
r
id
n
et
w
o
r
k
.
Go
v
er
n
m
e
n
t
s
an
d
u
tili
t
y
co
m
p
a
n
ie
s
s
u
p
p
o
r
t
p
r
o
g
r
am
s
w
h
ich
f
o
c
u
s
o
n
g
r
id
co
n
n
ec
ted
P
V
s
y
s
te
m
s
.
So
,
th
e
n
u
m
b
er
o
f
P
V
in
s
ta
llatio
n
h
as a
n
ex
p
o
n
en
tial
g
r
o
w
t
h
.
P
V
en
er
g
y
i
s
a
g
r
ee
n
r
en
e
w
ab
l
e
s
o
u
r
ce
.
P
V
ce
ll is
th
e
m
o
s
t b
asic o
f
P
V
m
o
d
u
le
s
.
I
t c
o
n
s
i
s
t
s
o
f
a
P
-
N
j
u
n
ctio
n
f
ab
r
icate
d
in
a
la
y
er
s
e
m
ico
n
d
u
cto
r
.
T
h
e
cu
r
r
en
t
-
v
o
ltag
e
(
I
-
V)
an
d
p
o
w
er
–
v
o
lt
ag
e
(
P
-
V)
o
u
tp
u
ts
ch
ar
ac
ter
is
tic
s
o
f
s
o
lar
ce
ll
ar
e
s
i
m
ilar
to
t
h
at
o
f
a
d
io
d
e
[
1
]
.
Un
d
er
s
u
n
,
p
h
o
to
n
s
w
it
h
en
er
g
y
g
r
ea
ter
t
h
a
n
t
h
e
b
an
d
g
ap
en
er
g
y
o
f
t
h
e
s
e
m
i
co
n
d
u
cto
r
ar
e
ab
s
o
r
b
ed
an
d
cr
ea
te
an
elec
tr
o
n
–
h
o
le
p
air
th
at
cr
ea
tes
a
cu
r
r
en
t
p
r
o
p
o
r
tio
n
al
to
th
e
ir
r
ad
iatio
n
.
I
t
is
th
e
in
ter
f
ac
e
w
h
ic
h
co
n
v
er
ts
li
g
h
t
in
to
elec
tr
icit
y
.
M
o
d
elin
g
t
h
is
d
ev
ice
r
eq
u
ir
es
tak
i
n
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
(
ir
r
ad
ian
ce
an
d
te
m
p
er
at
u
r
e)
as
in
p
u
t
v
ar
iab
le
s
an
d
cu
r
r
en
t,
v
o
lta
g
e
o
r
p
o
w
er
as
o
u
tp
u
ts
.
An
y
c
h
an
g
e
i
n
t
h
e
in
p
u
ts
i
m
m
ed
iate
l
y
i
m
p
lies
c
h
an
g
es
i
n
o
u
tp
u
ts
.
C
o
n
s
eq
u
e
n
tl
y
,
to
ex
tr
ac
t
t
h
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
f
r
o
m
t
h
e
P
V
ar
r
a
y
u
n
d
er
d
if
f
er
e
n
t
i
n
p
u
te
s
w
e
u
s
e
a
M
P
PT
alg
o
r
ith
m
[
2
]
-
[
6
]
.
I
n
th
is
p
ap
er
,
a
f
u
zz
y
lo
g
i
c
co
n
tr
o
ller
w
as
u
s
ed
in
MP
P
T
f
o
r
a
th
r
ee
p
h
ase
in
v
er
ter
in
o
r
d
r
e
to
p
r
id
ec
t
th
e
DC
li
n
k
v
o
lta
g
e
w
h
ic
h
e
x
tr
ac
t
s
th
e
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
P
V
ar
r
ay
.
Fo
r
th
a
t,
u
s
in
g
a
n
ac
cu
r
ate
m
o
d
el
f
o
r
t
h
e
P
V
m
o
d
u
le
i
s
i
m
p
o
r
ta
n
t
[
2
]
,
[
7
]
.
I
t
is
a
s
in
g
le
d
io
d
e
m
o
d
el
w
it
h
b
o
th
s
er
ie
s
an
d
p
ar
allel
r
esis
to
r
s
f
o
r
g
r
ea
ter
ac
cu
r
ac
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
105
–
1
1
3
106
I
n
g
r
id
co
n
n
ec
ted
P
V
s
y
s
te
m
s
,
th
e
i
n
v
er
te
r
w
h
ic
h
co
n
v
er
ts
t
h
e
o
u
tp
u
t d
ir
ec
t c
u
r
r
en
t (
DC
)
o
f
th
e
s
o
lar
m
o
d
u
les
to
th
e
alter
n
ate
c
u
r
r
en
t
(
A
C
)
i
s
r
ec
eiv
i
n
g
i
n
cr
ea
s
ed
in
ter
est
i
n
o
r
d
er
to
g
en
er
a
te
p
o
w
er
to
u
til
it
y
.
Ma
n
y
to
p
o
lo
g
ie
s
ar
e
u
s
ed
to
th
is
p
u
r
p
o
s
e
[
8
]
-
[
1
3
]
.
T
h
is
p
ap
er
p
r
esen
t
t
w
o
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
u
s
in
g
a
th
r
ee
p
h
ase
in
v
er
ter
,
f
ir
s
t
o
n
e
tr
ac
k
th
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
o
f
P
V
ar
r
ay
an
d
t
h
e
s
ec
o
n
d
o
n
e
f
o
r
cu
r
r
en
t
r
eg
u
lato
r
.
B
a
s
ed
o
n
th
e
cu
r
r
en
t
r
ef
er
en
ce
s
(
d
ir
ec
t
cu
r
r
en
t)
an
d
(
q
u
ad
r
atic
cu
r
r
en
t)
,
th
e
r
eg
u
lato
r
d
eter
m
in
e
s
th
e
r
eq
u
ir
ed
r
ef
er
en
c
e
v
o
ltag
es
f
o
r
th
e
in
v
er
ter
.
T
h
e
r
ef
er
en
ce
is
s
e
t
t
o
ze
r
o
.
I
n
f
ir
s
t
s
ec
tio
n
,
p
h
o
to
v
o
ltaic
w
as
d
escr
ib
ed
.
T
h
e
s
ec
o
n
d
s
ec
tio
n
p
r
esen
ts
a
f
u
zz
y
lo
g
ic
co
n
tr
o
l
to
tr
a
ck
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
i
n
t
ar
r
a
y
u
n
d
er
d
if
f
er
en
t
co
n
d
itio
n
s
(
ir
r
ad
ian
ce
,
te
m
p
er
atu
r
e
a
n
d
lo
ad
)
.
I
n
t
h
e
n
e
x
t
s
ec
tio
n
,
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
f
o
r
c
u
r
r
en
t
co
n
tr
o
l
was
d
escr
ib
ed
w
it
h
a
P
h
ase
L
o
c
k
ed
L
o
o
p
to
s
y
n
c
h
r
o
n
ize
t
h
e
P
ar
k
f
r
a
m
to
g
r
id
v
o
ltag
e.
I
n
t
h
e
f
o
r
t
h
s
ec
ti
o
n
,
s
i
m
u
latio
n
s
i
n
Ma
tlab
/Si
m
u
l
in
k
o
f
g
r
id
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
te
m
s
ar
e
p
r
esen
ted
an
d
an
al
y
ze
d
.
T
h
e
last
s
ec
tio
n
is
a
g
lo
b
al
co
n
clu
s
io
n
ab
o
u
t t
h
is
wo
r
k
.
2.
G
RI
D
CO
NNE
CT
E
D
P
V
S
YST
E
M
S
Fig
u
r
e
1
s
h
o
w
s
a
d
etailed
m
o
d
el
o
f
a
2
5
0
-
k
W
P
V
ar
r
a
y
co
n
n
ec
ted
to
a
2
5
-
k
V
g
r
id
v
ia
a
t
h
r
ee
-
p
h
a
s
e
in
v
er
ter
.
T
h
is
m
o
d
el
i
s
d
escr
ib
ed
as f
o
llo
w
:
P
V
A
r
r
a
y
:
it
co
n
s
is
t
s
o
f
8
6
p
ar
allel
s
tr
i
n
g
s
.
E
ac
h
s
tr
in
g
h
a
s
7
m
o
d
u
les
co
n
n
ec
ted
i
n
s
er
i
es.
T
h
r
ee
-
p
h
ase
in
v
er
ter
:
it
is
m
o
d
eled
u
s
i
n
g
a
3
-
lev
el
I
GB
T
b
r
i
d
g
e
P
W
M
-
co
n
tr
o
lled
.
T
h
e
in
v
er
te
r
ch
o
k
es
R
L
an
d
a
s
m
al
l
h
ar
m
o
n
ics
f
ilter
C
ar
e
u
s
ed
to
f
il
ter
th
e
h
ar
m
o
n
ic
s
g
e
n
er
ated
b
y
th
e
I
GB
T
B
r
id
g
e.
A
2
5
0
-
k
V
A
2
5
0
V/2
5
k
V
th
r
ee
-
p
h
ase
tr
a
n
s
f
o
r
m
er
is
u
s
ed
to
co
n
n
ec
t
t
h
e
i
n
v
er
ter
to
th
e
u
tili
t
y
g
r
id
.
I
n
v
er
ter
C
o
n
tr
o
l:
T
h
e
co
n
tr
o
l
s
y
s
te
m
co
n
tai
n
s
s
ex
m
aj
o
r
s
u
b
s
y
s
te
m
s
.
Uti
lit
y
g
r
i
d
:
it
in
cl
u
d
ed
t
w
o
2
5
-
k
V
f
ee
d
er
s
,
lo
ad
s
,
g
r
o
u
n
d
i
n
g
tr
an
s
f
o
r
m
er
an
d
an
eq
u
iv
a
len
t
1
2
0
-
k
V
tr
an
s
m
i
s
s
io
n
s
y
s
te
m
.
Fig
u
r
e
1
.
Gr
id
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
te
m
I
n
v
er
ter
C
o
n
tr
o
l su
b
s
y
s
te
m
s
a
r
e:
MP
PT
C
o
n
tr
o
ller
:
th
e
Ma
x
i
m
u
m
P
o
w
er
P
o
in
t
T
r
ac
k
in
g
(
M
P
PT)
b
ased
o
n
th
e
F
u
zz
y
lo
g
i
c
co
n
tr
o
l.
T
h
is
MP
PT
s
y
s
te
m
a
u
to
m
at
icall
y
v
ar
ies
th
e
VD
C
r
ef
er
e
n
ce
s
ig
n
al
o
f
t
h
e
i
n
v
er
ter
VD
C
r
e
g
u
l
ato
r
in
o
r
d
er
to
o
b
tain
a
DC
v
o
lta
g
e
w
h
ich
w
i
l
l e
x
tr
ac
t
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
th
e
P
V
ar
r
a
y
.
V
DC
R
e
g
u
lato
r
: d
eter
m
i
n
e
t
h
e
r
eq
u
ir
ed
I
d
r
ef
er
en
ce
f
o
r
th
e
cu
r
r
en
t r
eg
u
la
to
r
.
T
h
e
VSC
co
n
v
er
ts
t
h
e
5
0
0
V
DC
li
n
k
v
o
lta
g
e
(
VD
C
)
to
2
6
0
V
A
C
a
n
d
k
ee
p
s
u
n
it
y
p
o
w
er
f
ac
to
r
.
T
h
e
VSC
co
n
tr
o
l
s
y
s
te
m
u
s
es
t
w
o
co
n
tr
o
l
lo
o
p
s
:
an
ex
ter
n
a
l
co
n
tr
o
l
lo
o
p
w
h
ich
r
e
g
u
lates
D
C
lin
k
v
o
lta
g
e
to
+/
-
2
5
0
V
an
d
a
n
i
n
ter
n
al
co
n
t
r
o
l
lo
o
p
w
h
ic
h
r
eg
u
late
s
I
d
an
d
I
q
g
r
id
cu
r
r
en
t
s
.
I
d
cu
r
r
en
t
r
ef
er
en
ce
i
s
t
h
e
o
u
tp
u
t
o
f
t
h
e
D
C
v
o
lta
g
e
e
x
te
r
n
al
co
n
tr
o
ller
.
I
q
cu
r
r
en
t
r
ef
er
en
ce
is
s
et
to
ze
r
o
in
o
r
d
er
to
m
ai
n
tai
n
u
n
it
y
p
o
w
er
f
ac
to
r
.
V
d
an
d
V
q
v
o
lt
ag
e
o
u
tp
u
t
s
o
f
th
e
cu
r
r
en
t
co
n
tr
o
ller
ar
e
co
n
v
er
ted
to
th
r
ee
m
o
d
u
lat
in
g
s
ig
n
al
s
U
abc
-
ref
u
s
ed
b
y
t
h
e
P
W
M
Gen
er
ato
r
.
T
h
e
co
n
tr
o
l
s
y
s
te
m
u
s
e
s
a
s
a
m
p
le
ti
m
e
f
o
r
v
o
ltag
e
an
d
cu
r
r
en
t
co
n
tr
o
ller
s
as
w
ell
as
f
o
r
th
e
P
L
L
s
y
n
c
h
r
o
n
izat
io
n
u
n
it.
P
u
ls
e
g
en
er
ato
r
s
o
f
VS
C
co
n
v
er
ter
s
u
s
e
a
f
ast
s
a
m
p
le
ti
m
e
i
n
o
r
d
er
to
g
et
an
ap
p
r
o
p
r
iate
r
eso
lu
tio
n
o
f
P
W
M
w
a
v
e
f
o
r
m
s
.
C
u
r
r
en
t
r
eg
u
lato
r
:
b
ased
o
n
th
e
c
u
r
r
en
t
r
ef
er
e
n
ce
s
I
d
a
n
d
I
q
,
th
e
r
eg
u
lato
r
d
eter
m
i
n
es
th
e
r
eq
u
ir
ed
r
ef
er
en
ce
v
o
lta
g
es
f
o
r
th
e
i
n
v
e
r
ter
.
A
s
ec
o
n
d
F
u
zz
y
lo
g
ic
co
n
tr
o
ller
w
as
u
s
ed
f
o
r
cu
r
r
en
t r
e
g
u
la
to
r
.
P
L
L
: r
eq
u
ir
ed
f
o
r
s
y
n
c
h
r
o
n
iza
tio
n
an
d
v
o
lta
g
e/c
u
r
r
en
t
m
ea
s
u
r
e
m
e
n
ts
.
P
W
M
Gen
er
ato
r
: g
en
er
ate
f
ir
i
n
g
s
ig
n
al
s
to
th
e
I
GB
T
s
b
ased
o
n
th
e
r
eq
u
ir
ed
r
ef
er
en
ce
v
o
lta
g
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
MPP
T
&
P
o
w
e
r
F
a
cto
r
C
o
n
tr
o
l
fo
r
Gri
d
C
o
n
n
ec
ted
P
V
S
ys
t
ems wi
th
F
u
z
z
y
Lo
g
ic…
(
Ta
o
u
fik
La
a
g
o
u
b
i
)
107
2
.
1
.
P
V
Sy
s
t
em
T
h
e
P
V
cir
cu
it m
o
d
el
is
b
ased
o
n
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
0
e
x
p
1
p
v
p
v
s
p
v
p
v
s
p
v
p
v
b
sh
s
V
I
R
V
I
R
I
i
I
KT
R
N
e
(
1
)
I
n
o
r
d
er
to
a
p
p
ly
th
i
s
m
o
d
el
i
n
s
i
m
u
latio
n
,
th
e
k
e
y
s
p
ec
if
icat
i
o
n
s
ar
e
g
i
v
en
i
n
T
ab
le
1
.
T
ab
le
1
.
P
h
o
to
v
o
ltaic
P
ar
am
et
er
s
A
t
Te
mp
e
r
a
t
u
r
e
T
25
°C
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
oc
V
5
9
7
.
1
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
sc
I
5
3
5
.
9
A
V
o
l
t
a
g
e
,
max
i
mu
m
p
o
w
e
r
m
a
x
p
V
5
1
0
.
3
V
C
u
r
r
e
n
t
,
m
a
x
i
mu
m
p
o
w
e
r
m
a
x
p
I
5
0
0
.
7
A
M
a
x
i
m
u
m
p
o
w
e
r
m
a
x
P
2
5
5
5
0
0
W
As
t
h
e
s
o
lar
ir
r
ad
ian
ce
v
ar
ies
o
v
er
ti
m
e
a
n
d
d
ep
en
d
in
g
o
n
t
h
e
cli
m
atic
co
n
d
itio
n
s
,
t
h
e
p
o
w
er
o
u
tp
u
t
also
v
ar
ies.
T
h
e
p
er
f
o
r
m
an
ce
o
f
a
p
h
o
to
v
o
ltaic
ce
ll
is
u
s
u
al
l
y
p
r
ese
n
ted
b
y
it
s
I
(
V)
an
d
P
(
V)
cu
r
v
es
w
h
ich
ar
e
p
r
o
d
u
ce
d
f
o
r
s
ev
er
al
ir
r
ad
ian
ce
lev
els
a
n
d
s
e
v
er
al
ce
ll
te
m
p
er
atu
r
e
lev
els.
T
h
e
v
ar
iatio
n
o
f
cu
r
r
en
t
an
d
p
o
w
er
v
er
s
u
s
v
o
ltag
e
c
u
r
v
e
u
n
d
er
v
a
r
io
u
s
ir
r
ad
iatio
n
le
v
els a
n
d
te
m
p
er
at
u
r
es a
r
e
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
We
ca
n
o
b
s
er
v
e
th
at
t
h
e
w
ea
k
s
u
n
li
g
h
t a
n
d
r
ais
in
g
t
h
e
ce
ll te
m
p
er
atu
r
e
w
il
l r
ed
u
ce
th
e
p
o
w
er
co
n
v
er
s
io
n
ca
p
ac
it
y
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
2
.
Var
iatio
n
o
f
cu
r
r
en
t a
n
d
p
o
w
er
v
er
s
u
s
v
o
ltag
e
c
u
r
v
e
u
n
d
er
v
ar
io
u
s
ir
r
ad
iatio
n
lev
els an
d
te
m
p
er
atu
r
es.
(
a)
.
C
u
r
r
e
n
t
–
Vo
ltag
e
at
1
k
W
.
m
²
a
n
d
s
p
ec
if
ied
te
m
p
er
atu
r
es
.
(
b
)
.
P
o
w
er
–
Vo
lt
ag
e
at
1
k
W
.
m
²
an
d
s
p
ec
if
ied
te
m
p
er
at
u
r
es
.
(
c
)
.
C
u
r
r
en
t
–
Vo
ltag
e
at
2
5
°
C
an
d
s
p
ec
if
ied
I
r
r
ad
ian
ce
s
.
(
d
)
.
P
o
w
er
–
Vo
ltag
e
at
2
5
°C
an
d
s
p
ec
if
ied
I
r
r
ad
ian
ce
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
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
105
–
1
1
3
108
3
.
1
.
M
P
P
T
w
it
h
F
uzzy
L
o
g
ic
Co
ntr
o
ller
T
h
e
Ma
x
i
m
u
m
P
o
w
er
P
o
in
t
T
r
ac
k
in
g
(
MP
PT
)
co
n
tr
o
ller
i
s
b
ased
o
n
th
e
Fu
zz
y
lo
g
ic
c
o
n
tr
o
l.
T
h
is
MP
PT
s
y
s
te
m
a
u
to
m
atica
ll
y
v
ar
ies
th
e
V
DC
r
ef
er
en
ce
s
i
g
n
al
o
f
t
h
e
i
n
v
er
ter
V
DC
r
e
g
u
la
to
r
in
o
r
d
er
to
o
b
tain
a
DC
v
o
lta
g
e
w
h
ich
w
i
ll e
x
tr
ac
t
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
th
e
P
V
ar
r
ay
.
Fu
zz
y
lo
g
ic
co
n
tr
o
ller
h
a
s
t
h
e
ad
v
an
ta
g
e
to
w
o
r
k
i
n
g
w
it
h
i
m
p
r
ec
i
s
e
i
n
p
u
t
s
,
n
o
t
n
ee
d
in
g
an
ac
cu
r
ate
m
at
h
e
m
a
tical
m
o
d
el,
a
n
d
h
a
n
d
lin
g
n
o
n
lin
ea
r
it
y
.
Ge
n
er
all
y
,
it c
o
n
s
i
s
ts
o
f
t
h
r
ee
s
ta
g
es:
f
u
zz
if
icatio
n
,
r
u
le
s
b
ase
tab
le
lo
o
k
u
p
,
an
d
d
ef
u
zz
i
f
icati
o
n
.
Du
r
i
n
g
f
u
zz
i
f
icatio
n
,
n
u
m
er
ical
in
p
u
t
v
ar
iab
les ar
e
co
n
v
er
ted
in
to
lin
g
u
is
t
ic
b
ased
o
n
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
i
m
ilar
to
Fig
u
r
e
3
.
I
n
th
is
ca
s
e
f
i
v
e
f
u
zz
y
le
v
els
ar
e
u
s
ed
:
NB
(
Neg
ativ
e
B
ig
)
,
NS (
Neg
ati
v
e
S
m
all)
,
Z
E
(
Z
er
o
)
,
P
S (
Po
s
itiv
e
S
m
all)
a
n
d
PB
(
Po
s
itiv
e
B
ig
)
.
Fig
u
r
e
3
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
f
o
r
in
p
u
ts
a
n
d
o
u
tp
u
t o
f
f
u
zz
y
co
n
tr
o
ller
T
h
e
in
p
u
ts
to
a
MP
PT
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
ar
e
u
s
u
a
ll
y
a
n
er
r
o
r
E
an
d
a
ch
an
g
in
g
er
r
o
r
CE
.
(
)
(
1
)
()
(
)
(
1
)
p
v
p
v
p
v
p
v
P
n
P
n
En
V
n
V
n
(
2
)
(
)
(
)
(
1
)
C
E
n
E
n
E
n
(
3
)
T
h
e
o
u
tp
u
t o
f
MP
PT
f
u
zz
y
co
n
tr
o
ller
is
a
d
esire
d
DC
v
o
lta
g
e.
T
ab
le
2
s
h
o
w
s
t
h
e
r
u
les
tab
le
o
f
f
u
zz
y
co
n
tr
o
ller
;
w
h
er
e
al
l
th
e
en
tr
ies
o
f
m
atr
i
x
ar
e
f
u
z
z
y
s
ets
o
f
er
r
o
r
,
ch
an
g
in
g
er
r
o
r
an
d
d
esire
d
DC
v
o
ltag
e.
T
ab
le
2
.
Fu
zz
y
R
u
les B
ase
T
ab
le
E/
C
E
NB
NS
ZE
PS
PB
NB
ZE
ZE
NB
NB
NS
NS
ZE
ZE
NS
NS
NS
ZE
NS
ZE
ZE
ZE
PS
PS
PS
PS
PS
ZE
ZE
PB
PB
PB
PB
ZE
ZE
I
f
,
f
o
r
ex
a
m
p
le,
th
e
o
p
er
atin
g
p
o
in
t
is
f
ar
to
th
e
lef
t
to
th
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
(
MP
P
)
t
h
at
is
E
is
P
B
an
d
CE
is
Z
E
,
th
en
w
e
n
ee
d
to
lar
g
el
y
in
cr
ea
s
e
th
e
D
C
v
o
ltag
e,
th
at
d
c
r
e
f
V
s
h
o
u
ld
b
e
P
B
to
r
ea
ch
th
e
MP
P
.
Fig
u
r
e
4
s
h
o
w
s
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
al
g
o
r
ith
m
.
Fig
u
r
e
4
.
A
l
g
o
r
ith
m
f
o
r
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
I
n
Si
m
u
l
in
k
w
e
u
s
e
t
h
e
b
lo
c
s
h
o
w
n
i
n
Fi
g
u
r
e
5
NB
NS
Z
P
S
P
B
-
b
-
a
0
a
b
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
MPP
T
&
P
o
w
e
r
F
a
cto
r
C
o
n
tr
o
l
fo
r
Gri
d
C
o
n
n
ec
ted
P
V
S
ys
t
ems wi
th
F
u
z
z
y
Lo
g
ic…
(
Ta
o
u
fik
La
a
g
o
u
b
i
)
109
Fig
u
r
e
5
.
Si
m
u
li
n
k
b
lo
c
f
o
r
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
3.
CURR
E
NT
CO
N
T
RO
L
W
I
T
H
F
U
Z
Z
Y
L
O
G
I
C
CO
N
T
RO
L
L
E
R
T
h
e
v
o
ltag
e
an
d
cu
r
r
e
n
t e
q
u
ati
o
n
s
o
f
t
h
e
g
r
id
u
s
i
n
g
a
b
c
d
q
tr
an
s
f
o
r
m
atio
n
s
ar
e
g
i
v
en
b
y
:
c
o
s
(
)
s
i
n
(
)
.
s
i
n
(
)
c
o
s
(
)
d
w
t
w
t
q
w
t
w
t
(4
)
11
1
22
2
.
3
33
0
22
a
b
c
(5
)
dq
abc
ar
e
r
ep
lace
d
b
y
dq
abc
V
V
V
f
o
r
v
o
ltag
e
o
r
b
y
dq
abc
I
I
I
f
o
r
cu
r
r
en
t
m
ea
s
u
r
e
m
e
n
t.
T
h
e
r
o
tatin
g
r
ef
er
en
ce
f
r
a
m
e
at
th
e
g
r
id
f
r
eq
u
en
c
y
g
i
v
es:
V
=V
+RI
L
V
=V
+RI
L
+
+
d
d
G
rid
d
G
rid
q
q
G
rid
q
G
rid
d
G
r
id
q
G
r
id
q
G
r
id
d
G
r
id
dI
LI
dt
dI
LI
dt
(6
)
Usi
n
g
dq
tr
an
s
f
o
r
m
atio
n
,
t
h
e
ac
ti
v
e
an
d
r
e
ac
tiv
e
p
o
w
er
s
(
,
PQ
)
ar
e
g
iv
e
n
b
y
:
3
2
3
2
d
d
q
q
q
d
d
q
P
V
I
V
I
Q
V
I
V
I
(7
)
T
h
er
ef
o
r
e,
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
ca
n
b
e
co
n
tr
o
lled
b
y
c
o
n
tr
o
llin
g
d
ir
ec
t
an
d
q
u
ad
r
atu
r
e
cu
r
r
en
t
co
m
p
o
n
e
n
t
s
d
g
r
e
f
i
,
q
g
r
e
f
i
,
w
h
ic
h
is
g
iv
e
n
as:
22
22
2
3
2
3
dq
d
dq
qd
q
dq
P
V
Q
V
I
VV
P
V
Q
V
I
VV
(8
)
T
h
e
s
ec
o
n
d
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
w
a
s
u
s
ed
to
co
n
tr
o
l
d
ir
e
ct
an
d
q
u
ad
r
atu
r
e
c
u
r
r
en
ts
.
An
d
a
P
h
a
s
e
L
o
ck
ed
L
o
o
p
(
P
L
L
)
i
s
u
s
ed
t
o
s
y
n
ch
r
o
n
ize
t
h
e
P
ar
k
tr
an
s
f
o
r
m
at
io
n
to
t
h
e
p
u
ls
atio
n
o
f
t
h
e
m
ea
s
u
r
ed
v
o
lta
g
e
ac
r
o
s
s
th
e
g
r
id
.
T
h
u
s
,
w
h
e
n
th
e
s
y
s
te
m
is
i
n
an
estab
li
s
h
ed
r
eg
i
m
e,
th
e
d
ir
ec
t
co
m
p
o
n
e
n
t
d
V
at
th
e
o
u
tp
u
t
o
f
th
e
P
ar
k
tr
a
n
s
f
o
r
m
atio
n
i
s
an
i
m
a
g
e
o
f
th
e
a
m
p
li
tu
d
e
o
f
t
h
e
m
ea
s
u
r
ed
v
o
lta
g
e
a
n
d
t
h
e
q
u
ad
r
atic
co
m
p
o
n
e
n
t
q
V
is
ze
r
o
.
T
h
u
s
,
t
h
e
eq
u
atio
n
s
(
8
)
s
h
o
w
d
I
as
a
d
ir
ec
t
i
m
a
g
e
o
f
th
e
ac
t
iv
e
p
o
w
er
a
n
d
q
I
as
a
n
i
m
ag
e
o
f
t
h
e
r
ea
ctiv
e
p
o
w
er
.
Fi
g
u
r
e
.
6
s
h
o
w
s
th
e
p
r
o
p
o
s
ed
in
v
er
ter
co
n
tr
o
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
105
–
1
1
3
110
Fig
u
r
e
6
.
P
r
o
p
o
s
ed
in
v
er
ter
co
n
tr
o
l
w
ith
t
w
o
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
4.
SI
M
UL
AT
I
O
N
A
ND
RE
SU
L
T
S
T
h
e
o
p
er
atin
g
te
m
p
er
at
u
r
e
is
4
5
d
eg
.
C
.
W
h
en
s
tead
y
-
s
tate
is
r
ea
ch
ed
,
w
e
g
e
t
a
P
V
v
o
lta
g
e
an
d
t
h
e
p
o
w
er
ex
tr
ac
ted
f
r
o
m
th
e
ar
r
ay
.
T
h
ese
v
al
u
es
co
r
r
esp
o
n
d
to
th
e
ex
p
ec
ted
v
al
u
es
f
r
o
m
t
h
e
P
V
m
o
d
u
le
m
an
u
f
ac
t
u
r
er
s
p
ec
if
icatio
n
s
.
F
ig
u
r
e
7
s
h
o
w
s
v
ar
iatio
n
o
f
c
u
r
r
en
t,
v
o
lta
g
e
a
n
d
p
o
w
er
v
er
s
u
s
ti
m
e
c
u
r
v
e
u
n
d
er
v
ar
io
u
s
ir
r
ad
ian
ce
le
v
el
s
.
Su
n
ir
r
ad
ian
ce
is
r
ap
id
l
y
r
a
m
p
ed
d
o
w
n
.
D
u
e
to
t
h
e
MP
P
T
o
p
er
atio
n
,
th
e
co
n
tr
o
l
s
y
s
te
m
r
ed
u
ce
s
t
h
e
VDC r
ef
er
e
n
ce
in
o
r
d
er
to
ex
tr
ac
t
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
th
e
P
V
ar
r
ay
.
As
it
ca
n
b
e
s
ee
n
,
Ma
x
i
m
u
P
o
w
er
P
o
in
t
w
a
s
r
ea
h
ed
u
n
d
er
ir
r
ad
ian
ce
ch
a
n
g
e
s
.
A
ls
o
,
t
h
e
v
a
lu
e
o
f
th
e
v
o
ltag
e
in
j
ec
ted
in
to
g
r
id
i
s
s
t
ab
le
an
d
eq
u
al
to
th
a
t
o
f
th
e
g
r
id
.
T
h
e
t
h
ir
d
r
esu
t
is
th
at
v
o
lt
ag
e
a
n
d
cu
r
r
en
t
ar
e
in
p
h
ase
w
h
ich
p
r
o
v
es
t
h
at
th
e
r
ea
ctiv
e
p
o
w
er
i
n
j
ec
ted
in
to
g
r
id
is
ze
r
o
.
So
w
e
o
b
tain
ed
th
e
o
b
j
ec
tiv
es
o
f
t
w
o
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
.
Fi
g
u
r
e
8
s
h
o
w
P
h
a
s
e
d
if
f
er
en
ce
b
e
t
w
ee
n
v
o
ltag
e
a
n
d
cu
r
r
en
t
o
f
g
r
id
u
n
d
er
v
ar
i
o
u
s
ir
r
ad
iatio
n
lev
els
(
a)
(
b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
MPP
T
&
P
o
w
e
r
F
a
cto
r
C
o
n
tr
o
l
fo
r
Gri
d
C
o
n
n
ec
ted
P
V
S
ys
t
ems wi
th
F
u
z
z
y
Lo
g
ic…
(
Ta
o
u
fik
La
a
g
o
u
b
i
)
111
(
c)
(
d
)
Fig
u
r
e
7
.
Var
iatio
n
o
f
cu
r
r
en
t,
v
o
ltag
e
a
n
d
p
o
w
er
v
er
s
u
s
ti
m
e
cu
r
v
e
u
n
d
er
v
ar
io
u
s
ir
r
ad
ian
ce
lev
els.
(
a)
.
I
r
r
ad
ian
ce
.
(
b
)
.
Vo
ltag
e
in
v
er
t
er
o
u
tp
u
t.
(
c)
.
C
u
r
r
en
t i
n
v
er
ter
o
u
tp
u
t.
(
d
)
.
Po
w
er
in
v
er
ter
o
u
tp
u
t
Fig
u
r
e
8
.
P
h
ase
d
if
f
er
e
n
ce
b
etw
ee
n
v
o
lta
g
e
an
d
c
u
r
r
en
t o
f
g
r
id
u
n
d
er
v
ar
io
u
s
ir
r
ad
iatio
n
le
v
els
5.
CO
NCLU
SI
O
N
Usu
el
l
y
a
MP
P
T
tech
n
iq
u
e
is
ap
p
lied
to
a
DC
–
DC
co
n
v
er
t
er
an
d
th
e
n
a
s
ec
o
n
d
P
FC
co
m
m
an
d
e
i
s
ap
p
lied
to
an
in
v
er
ter
.
I
n
t
h
i
s
w
o
r
k
,
t
w
o
f
u
zz
y
lo
g
ic
co
n
tr
o
ll
er
s
ar
e
d
escr
ib
ed
f
o
r
g
r
id
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
te
m
s
u
s
in
g
a
th
r
ee
p
h
ase
in
v
er
ter
w
it
h
o
u
t
DC
–
D
C
co
n
v
er
ter
.
T
h
e
f
ir
s
t
o
n
e
w
a
s
ap
p
lied
to
tr
ac
k
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
an
d
th
e
s
ec
o
n
d
w
a
s
ap
p
lied
to
co
n
tr
o
l
th
e
p
o
w
er
f
ac
to
r
.
T
h
e
f
u
zz
y
lo
g
ic
c
o
n
tr
o
ller
f
o
r
MP
PT
alg
o
r
ith
m
s
tr
ac
k
th
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
u
n
d
er
t
w
o
s
tep
s
in
ir
r
ad
ian
ce
w
it
h
g
o
o
d
s
tab
ilt
y
.
A
v
ec
to
r
co
n
tr
o
l
s
tr
ateg
y
f
o
r
p
h
o
to
v
o
lta
ic
s
id
e
in
v
er
ter
a
n
d
g
r
id
s
id
e
i
n
v
er
ter
u
s
i
n
g
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
g
i
v
e
a
g
o
o
d
p
er
f
o
r
m
a
n
c
es o
f
MP
PT
an
d
Po
w
er
Facto
r
C
o
n
tr
o
l.
NO
M
E
NCLAT
UR
E
e
E
lectr
o
n
ch
ar
g
e
b
K
B
o
ltzm
a
n
n
’
s
co
n
s
tan
t
0
I
R
ev
er
s
e
s
atu
r
at
io
n
cu
r
r
e
n
t
s
N
Nu
m
b
er
o
f
s
o
lar
ce
lls
a
b
c
Gr
i
d
I
Gr
id
th
r
ee
p
h
ase
cu
r
r
en
t
pv
P
Ou
tp
u
t p
o
w
er
o
f
s
o
lar
ce
ll
d
I
Desire
d
d
ir
ec
t c
u
r
r
en
t
s
R
Ser
ies r
esis
ta
n
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
105
–
1
1
3
112
d
r
e
f
I
Gr
id
r
ef
er
en
ce
d
ir
ec
t
cu
r
r
en
t
sh
R
Sh
u
n
t r
esis
ta
n
ce
d
i
Dio
d
e
cu
r
r
en
t
d
G
r
i
d
V
Gr
id
d
ir
ec
t v
o
ltag
e
pv
I
Ou
tp
u
t c
u
r
r
en
t o
f
s
o
lar
ce
ll
d
c
r
e
f
V
DC
v
o
lta
g
e
w
itc
h
ex
tr
ac
t
MP
P
pv
i
P
h
o
to
cu
r
r
en
t
pv
V
Ou
tp
u
t v
o
lta
g
e
o
f
s
o
lar
ce
ll
q
I
Desire
d
q
u
ad
r
atic
cu
r
r
en
t
q
V
Qu
ad
r
atic
v
o
lta
g
e
q
r
e
f
I
Gr
id
r
ef
er
en
ce
q
u
ad
r
atic
cu
r
r
en
t
Dio
d
e
q
u
alit
y
sc
I
Sh
o
r
t c
ir
cu
it c
u
r
r
en
t
sh
i
Sh
u
n
t r
esis
ta
n
ce
cu
r
r
e
n
t
RE
F
E
R
E
NC
E
S
[1
]
V
a
n
d
a
n
a
Kh
a
n
n
a
,
B
ij
o
y
Kish
o
re
Da
s,
Din
e
sh
Bish
t"
M
a
tl
a
b
/S
im
e
lec
tro
n
ics
M
o
d
e
ls
Ba
se
d
S
tu
d
y
o
f
S
o
lar
Ce
ll
s.
"
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Re
n
e
wa
b
le E
n
e
rg
y
Res
e
a
rc
h
V
a
n
d
a
n
a
K
h
a
n
n
a
a
n
d
a
l.
,
V
o
l
.
3
,
No
.
1
,
2
0
1
3
[2
]
T
.
Laa
g
o
u
b
i,
M
.
Bo
u
z
i,
M
.
Be
n
c
h
a
g
ra
,
"
An
a
lys
is
a
n
d
c
o
mp
a
ris
o
n
o
f
M
PP
T
n
o
n
li
n
e
a
r
c
o
n
tro
ll
e
rs
f
o
r
PV
sy
ste
m,
"
IEE
E
Co
n
f
e
re
n
c
e
IRS
EC’1
5
,
3
r
d
In
ter
n
a
ti
o
n
a
l
Re
n
e
w
a
b
le
a
n
d
S
u
sta
in
a
b
le
En
e
rg
y
Co
n
f
e
re
n
c
e
De
c
e
m
b
e
r
1
0
-
1
3
,
2
0
1
5
M
a
rra
k
e
c
h
&
Ou
a
rz
a
z
a
te
,
M
o
r
o
c
c
o
.
[3
]
T
.
L
a
a
g
o
u
b
i,
M
.
Be
n
c
h
a
g
ra
,
M
.
Bo
u
z
i.
"
P
h
o
to
v
o
lt
a
ic
S
y
ste
m
f
o
r
T
h
re
e
P
h
a
se
L
o
a
d
w
it
h
No
n
li
n
e
a
r
Co
n
tro
ll
e
rs"
,
In
ter
n
a
t
io
n
a
l
Rev
iew o
n
M
o
d
e
ll
i
n
g
a
n
d
S
imu
la
ti
o
n
s
(
I.
RE
.
M
O.S
.
),
V
o
l
.
1
0
,
N
.
1
IS
S
N
1
9
7
4
-
9
8
2
1
F
e
b
ru
a
ry
2
0
1
7
[4
]
C.
-
Y.
W
o
n
,
D
.
-
H.
Kim
,
S
.
-
C.
Kim
,
W
.
-
S
.
Kim
,
a
n
d
H.
-
S
.
K
im"
A
n
e
w
ma
x
imu
m
p
o
we
r
p
o
in
t
tra
c
k
e
r
o
f
p
h
o
to
v
o
lt
a
ic
Arra
y
s
Us
in
g
F
u
zz
y
Co
n
tro
ll
e
r,
"
P
ro
c
.
2
5
t
h
A
n
n
u
.
IE
EE
P
o
w
e
r
El
e
c
tro
n
.
S
p
e
c
.
Co
n
f
.
,
1
9
9
4
,
p
p
.
3
9
6
–
4
0
3
.
[5
]
M
.
S
.
Kh
i
re
d
d
i
n
e
,
M
.
T
.
M
a
k
h
lo
u
f
i,
Y.
A
b
d
e
ss
e
m
e
d
,
A
.
Bo
u
tarf
a
"
T
ra
c
k
in
g
p
o
w
e
r
p
h
o
to
v
o
lt
a
ic
sy
st
e
m
w
it
h
a
f
u
z
z
y
lo
g
ic co
n
tr
o
l
stra
teg
y
,
"
Co
mp
u
ter
S
c
ien
c
e
a
n
d
I
n
fo
rm
a
ti
o
n
T
e
c
h
n
o
l
o
g
y
(
CS
IT
),
2
0
1
4
6
t
h
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
.
[6
]
M
o
u
n
ir
De
rri,
M
o
sta
f
a
Bo
u
z
i,
Is
m
a
il
L
a
g
ra
t,
Yo
u
ss
e
f
Ba
b
a
,
M
u
rtaz
a
.
"
F
u
z
z
y
S
li
d
in
g
M
o
d
e
Co
n
tr
o
l
f
o
r
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
"
.
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
t
ro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
),
2
0
1
6
,
V
o
l.
7
,
N
o
3
,
S
e
p
tem
b
re
2
0
1
6
,
p
p
.
9
6
4
~
9
7
3
.
[7
]
O
m
a
r
M
o
h
a
m
m
e
d
Be
n
a
issa
,
S
a
m
ir
Ha
d
jeri,
S
id
A
h
m
e
d
Zi
d
i.
"
M
o
d
e
li
n
g
a
n
d
S
im
u
latio
n
o
f
G
rid
Co
n
n
e
c
ted
P
V
G
e
n
e
r
a
ti
o
n
S
y
ste
m
Us
in
g
M
a
tl
a
b
/S
im
u
li
n
k
"
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
st
e
m
(
IJ
PE
DS
)
.
V
o
l
.
8
,
No
.
1
,
M
a
rc
h
2
0
1
7
,
p
p
.
3
9
2
-
4
0
1
.
IS
S
N:
2
0
8
8
-
8
6
9
4
.
[8
]
Bo
u
c
e
tt
a
A
b
d
A
ll
a
h
,
Lab
e
d
Dja
m
e
l.
"
Co
n
tro
l
o
f
P
o
w
e
r
a
n
d
V
o
lt
a
g
e
o
f
S
o
lar
G
rid
Co
n
n
e
c
ted
"
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
).
V
o
l.
6
,
No
.
1
,
F
e
b
ru
a
ry
2
0
1
6
,
p
p
.
2
6
-
3
3
.
IS
S
N:
2
0
8
8
-
8
7
0
8
,
[9
]
Re
n
u
g
a
V
e
ra
y
iah
,
A
n
u
siy
a
I
y
a
d
u
ra
i.
"
A
Co
m
p
a
riso
n
S
tu
d
y
o
n
Ty
p
e
s
o
f
P
V
f
o
r
G
rid
Co
n
n
e
c
ted
P
h
o
t
o
v
o
lt
a
i
c
P
o
w
e
r"
.
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
E
lec
trica
l
En
g
i
n
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
.
V
o
l
.
6
,
N
o
.
2
,
M
a
y
2
0
1
7
,
p
p
.
3
4
9
-
3
5
6
.
[1
0
]
Ch
a
n
d
a
n
i
S
h
a
rm
a
,
A
n
a
m
ik
a
Ja
in
,
"
P
e
rf
o
rm
a
n
c
e
Co
m
p
a
riso
n
o
f
P
I
D
a
n
d
F
u
z
z
y
Co
n
tro
ll
e
rs
in
Distr
ib
u
te
d
M
P
P
T
"
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
I
J
PE
DS
)
,
V
o
l
.
6
,
No
.
3
,
S
e
p
tem
b
e
r
2
0
1
5
,
p
p
.
6
2
5
~
6
3
5
IS
S
N:
2
0
8
8
-
8
6
9
4
.
[1
1
]
L
.
Ha
s
sa
in
e
,
E.
OL
ias
,
J.Qu
in
tero
,
V
.
S
a
las
,
"
Ov
e
rv
ie
w
o
f
p
o
we
r
in
v
e
rter
to
p
o
l
o
g
ies
a
n
d
c
o
n
tr
o
l
str
u
c
tu
re
s
f
o
r
g
rid
c
o
n
n
e
c
ted
p
h
o
to
v
o
lt
a
ic sy
ste
m
s,
"
Ren
e
wa
b
le
a
n
d
S
u
st
a
in
a
b
le
En
e
r
g
y
Rev
iews
3
0
(
2
0
1
4
)
7
9
6
–
8
0
7
.
[1
2
]
M
.
Be
n
c
h
a
g
ra
1
,
M
.
Hilal,
Y.
Err
a
m
i,
M
.
Ou
a
ss
a
id
,
M
.
M
a
a
ro
u
f
i,
"
M
o
d
e
li
n
g
a
n
d
Co
n
tro
l
o
f
S
CIG
b
a
se
d
v
a
riab
le
-
S
p
e
e
d
w
it
h
P
o
w
e
r
F
a
c
to
r
Co
n
tro
l
"
,
In
ter
n
a
ti
o
n
a
l
Rev
iew
o
n
M
o
d
e
ll
in
g
a
n
d
S
imu
l
a
ti
o
n
s
(
I.
RE
.
M
O.S
.
)
,
V
o
l
.
4
,
N.
3
IS
S
N 1
9
7
4
-
9
8
2
1
A
p
ril
2
0
1
1
.
[1
3
]
M
.
V
e
n
k
a
tes
a
n
1
,
R.
Ra
jes
h
w
a
ri
,
N.
De
v
e
ra
jan
,
M
.
Ka
li
y
a
m
o
o
rth
y
,
"
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
f
T
h
re
e
P
h
a
se
G
rid
Co
n
n
e
c
ted
P
h
o
to
v
o
lt
a
ic
In
v
e
rter
Us
in
g
P
I
a
n
d
F
u
z
z
y
L
o
g
ic
C
o
n
tr
o
ll
e
r
w
it
h
S
w
it
c
h
in
g
L
o
ss
e
s
Ca
lcu
latio
n
"
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
I
J
PE
DS
)
,
Vo
l.
7
,
No
.
2
,
Ju
n
e
2
0
1
6
,
p
p
.
5
4
3
~
5
50
IS
S
N
2
0
8
8
-
8
6
9
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
MPP
T
&
P
o
w
e
r
F
a
cto
r
C
o
n
tr
o
l
fo
r
Gri
d
C
o
n
n
ec
ted
P
V
S
ys
t
ems wi
th
F
u
z
z
y
Lo
g
ic…
(
Ta
o
u
fik
La
a
g
o
u
b
i
)
113
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
T
a
o
u
f
ik
L
a
a
g
o
u
b
i
w
a
s b
o
rn
i
n
Be
n
i
-
M
e
ll
a
l,
M
o
r
o
c
c
o
,
i
n
1
9
7
9
.
He
re
c
e
iv
e
d
T
h
e
DES
A
in
a
u
to
m
a
ti
c
c
o
n
tro
l
f
ro
m
th
e
f
a
c
u
lt
y
o
f
sc
ien
c
e
s S
e
m
l
a
li
a
,
Ca
d
i
Ay
y
a
d
Un
iv
e
rsity
,
M
a
rra
k
e
c
h
,
M
o
ro
c
c
o
.
He
p
u
rsu
e
s h
is
d
o
c
t
o
ra
l
p
ro
g
ra
m
a
t
Ha
ss
a
n
1
Un
iv
e
rsity
.
His res
e
a
rc
h
in
tere
sts a
re
a
u
to
m
a
ti
c
c
o
n
tro
l,
p
o
w
e
r
e
lec
tro
n
ics
a
n
d
re
n
e
w
a
b
le en
e
rg
y
.
M
o
h
a
m
e
d
Be
n
c
h
a
g
ra
wa
s b
o
rn
i
n
Be
n
i
-
M
e
ll
a
l,
M
o
r
o
c
c
o
,
i
n
1
9
8
2
.
He
re
c
e
iv
e
d
th
e
P
h
.
D
d
e
g
re
e
s,
in
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
f
ro
m
Eco
le M
o
h
a
m
m
a
d
ia d
’In
g
é
n
ieu
rs,
U
n
iv
e
rsité M
o
h
a
m
e
d
V
,
Ra
b
a
t,
M
o
ro
c
c
o
,
in
2
0
1
3
.
He
i
s c
u
rre
n
tl
y
a
n
A
s
sista
n
t
P
ro
f
e
ss
o
r
a
t
th
e
Na
ti
o
n
a
l
S
c
h
o
o
l
o
f
A
p
p
li
c
a
ti
o
n
S
c
ien
c
e
s (E
NSA
Kh
o
u
rib
g
a
)
Ha
ss
a
n
1
e
r
Un
iv
e
rsity
,
M
o
ro
c
c
o
.
His
re
se
a
rc
h
in
tere
sts
a
re
e
lec
tri
c
m
a
c
h
in
e
s,
p
o
w
e
r
e
lec
t
ro
n
ics
,
p
o
w
e
r
s
y
ste
m
s a
n
d
re
n
e
wa
b
le en
e
rg
y
.
Dr.
Be
n
c
h
a
g
ra
is
a
m
e
m
b
e
r
o
f
th
e
IEE
E.
M
o
sta
f
a
Bo
u
z
i
w
a
s b
o
rn
i
n
Ca
sa
b
lan
c
a
,
M
o
r
o
c
c
o
;
He
is a
P
r
o
f
e
ss
o
r
a
t
th
e
El
e
c
tri
c
a
l
E
n
g
in
e
e
rin
g
De
p
a
rtme
n
t
o
f
th
e
S
c
ien
c
e
a
n
d
tec
h
n
o
l
o
g
y
f
a
c
u
lt
y
,
Ha
ss
a
n
1
u
n
iv
e
rsity
.
He
re
c
e
iv
e
d
th
e
En
g
in
e
e
rin
g
d
e
g
re
e
in
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
f
ro
m
th
e
En
g
in
e
e
r
sc
h
o
o
l
o
f
L
il
le i
n
F
ra
n
c
e
,
o
b
tai
n
e
d
t
h
e
P
h
D
d
e
g
re
e
in
p
h
o
t
o
v
o
lt
a
ic s
y
ste
m
c
o
n
tro
l
a
t
u
n
iv
e
rsity
H
a
ss
a
n
1
a
n
d
g
o
t
h
is
h
a
b
il
it
a
ti
o
n
to
su
p
e
rv
ise
re
se
a
rc
h
a
t
Ha
ss
a
n
1
u
n
iv
e
rsity
.
His c
u
rre
n
t
re
se
a
rc
h
a
c
ti
v
it
ies
a
re
in
th
e
fi
e
ld
s o
f
e
lec
tri
c
a
l
s
y
ste
m
s,
re
n
e
wa
b
le en
e
rg
y
c
o
n
v
e
rsio
n
s
y
ste
m
s a
n
d
n
o
n
li
n
e
a
r
c
o
n
tr
o
l
sy
ste
m
s.
Evaluation Warning : The document was created with Spire.PDF for Python.