Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
No.
3
,
Septem
be
r 2021
, pp.
176
4
~
177
1
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v12.i
3
.
pp
176
4
-
177
1
1764
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Short a
nd ope
n ci
rcuit fa
ults st
udy
in the P
V syste
m inve
rter
Moham
med B
ou
zi
di
1
,
Ab
d
el
ka
der
H
arrou
z
2
,
Tad
j
M
oha
mmed
3
, Smail
Mans
ou
ri
4
1
,2
Sus
ta
ina
ble D
eve
lop
me
nt
and
Comput
er
Scie
n
ce
La
bor
at
ory
,
F
ac
ul
ty
of
Scie
n
c
es
and Technolo
gy,
Univer
si
ty
of
Ahmed
Drai
a, A
dra
r, Alge
ri
a
3
Analysis
and co
ntrol
of
e
le
c
tro
-
e
ner
gy
and
ren
ew
abl
e
en
erg
y
sys
t
em
s,
Univ
ersit
y
Cent
er
of
Ta
m
an
rasset
,
Alg
eria
4
Ene
rgy, Env
iro
nme
nt
and
Infor
ma
ti
on
Sys
te
ms
La
bora
tory, Faculty
of
Scie
n
ce
s
and
T
ec
hnolo
gy,
Univer
sity
of
A
hme
d
Draia
,
Adrar
,
Al
ger
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Feb
1
8
, 20
21
Re
vised
A
pr
6
,
20
21
Accepte
d
J
ul
1
3
, 2
0
21
The
inve
rt
er
is
the
principal
par
t
of
the
p
ho
tovol
taic
(
PV
)
sys
te
ms
tha
t
assures
the
dir
ect
cur
r
ent
/
alter
n
ating
cur
r
ent
(
DC/
AC
)
conve
rsion
(PV
arr
ay
is
conn
ec
t
ed
d
ir
ec
t
ly
to
an
inve
r
te
r
that
conve
r
ts
the
DC
ene
rgy
produc
ed
by
the
PV
a
rra
y
into
AC
en
erg
y
th
a
t
i
s
d
irectl
y
conn
ec
t
ed
to
th
e
el
e
c
tri
c
utilit
y)
.
In
thi
s
p
ape
r
,
w
e
pre
sen
t
a
simp
le
m
et
hod
for
d
et
e
ct
ing
fau
l
ts
t
hat
o
cc
urr
ed
during
the
oper
a
ti
on
of
the
inve
r
te
r.
The
se
typ
es
of
fau
lt
s
or
fau
lts
aff
ect
th
e
eff
icienc
y
and
c
ost
-
eff
ective
n
ess
of
the
photovolta
i
c
sys
te
m
,
esp
ec
i
al
ly
the
inve
rt
er,
which
i
s
the
ma
in
co
mp
onent
r
esponsibl
e
for
the
convers
ion.
Hen
ce,
we
hav
e
show
n
first
th
e
f
aults
obt
ai
ned
in
th
e
ca
se
of
the
s
hort
ci
rcu
it.
Second,
the
op
en
ci
rcu
it
fa
il
ur
e
is
studi
ed.
T
he
r
esult
s
d
emons
tra
te
th
e
eff
ica
cy
of
the
p
roposed
me
thod
.
Good
moni
tori
n
g
and
detec
ti
on
of
fau
lt
s
in
the
inv
ert
e
r
c
an
inc
re
ase
th
e
sys
te
m's
reliab
i
li
ty
a
nd
dec
r
ea
se
th
e
undesira
bl
e
fau
lt
s
that
appe
a
red
in
th
e
PV
sys
te
m.
Th
e
sys
t
em
b
eha
v
ior
is
t
este
d
und
e
r
var
ia
b
le
p
arame
t
ers
and
conditi
o
ns using
MA
TLA
B
/Sim
uli
nk.
Ke
yw
or
d
s
:
DC/DC c
onve
r
te
r
I
nverte
r
fail
ur
e
O
pe
n
ci
rcu
it
PV
s
ys
te
m
S
hort circ
uit
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Bou
zi
di Mo
ha
mmed
Su
sta
ina
ble
De
velo
pm
e
nt a
nd Com
pute
r
Sci
ence La
borat
ory
Faculty
of Scie
nces a
nd Tec
hnol
ogy
Dep
a
rtme
nt of
Ele
ct
rical
Eng
i
neer
i
ng
Ahmed
Drai
a,
Un
i
ver
sit
y o
f Adrar
,
Aoulef
PB 38
Adra
r
-
A
lgeria
Emai
l:
bouzidi
@univ
-
ad
rar.e
du.d
z
,
m
ohbo
uz
idi81@
yaho
o.fr
1.
INTROD
U
CTION
Photo
vo
lt
ai
c
s
ys
te
ms
hav
e
be
come
a
n
en
vi
ronme
ntall
y
f
r
ie
nd
ly
s
ol
ution
to
ge
ner
at
e
el
ect
rici
ty
in
our
mode
rn
li
f
e.
T
hey
on
l
y
de
pend
on
so
la
r
ra
diati
on
ene
r
gy,
w
hich
is
a
so
urce
of
e
ne
r
gy
ins
pire
d
by
natu
re
and
c
on
si
der
e
d
a
s
ource
of
su
sta
ina
ble
e
ne
rgy.
Se
ver
al
t
yp
e
s
of
resea
r
ch
i
n
the
fiel
d
of
s
olar
ene
r
gy
ha
ve
been
el
a
borate
d
in
the
la
st
t
wo
deca
des
by
st
udying
the
i
ncr
easi
ng
t
he
eff
ic
ie
nc
y
of
t
he
P
V
syst
ems
wh
il
e
ens
ur
in
g
t
he
m
inimum
cost
of
instal
la
ti
on
[
1]
,
[
2
]
.
The
e
ff
ic
ie
nc
y
is
de
pe
nd
e
nt
on
the
c
omp
onents
of
the
P
V
s
ys
te
ms
,
na
mely
on
the
e
ff
ic
ie
nc
y
of
pan
el
s
,
batte
ries,
a
nd
in
ver
te
r
s.
Also
,
bette
r
mo
nitor
i
ng
le
ads
t
o
a
n
a
dequ
at
e
PV
sy
ste
m.
H
ow
e
ve
r,
fau
l
ts
ca
n
decr
ease
a
nd
e
ven
blo
c
k
t
he
well
-
f
un
ct
io
ni
ng
of
the
P
V
s
ys
te
m
[
3]
-
[
7]
.
A
s
ha
de
d
or
brok
e
n
pa
nel,
ba
tt
eries
fail
an
d
in
ve
rter
dy
s
f
un
ct
io
ns
cause
los
ses
in
the
pro
duce
d
e
nerg
y
as
w
el
l
as
the
ec
on
om
ic
e
ff
ect
of
the
P
V
sy
ste
m.
The
i
nverter
s
re
pr
ese
nt
the
inter
me
diar
y
de
vice
be
tween
DC
an
d
AC
si
des.
T
hey
a
re
us
ed
t
o
sup
ply
the
AC
l
oads.
It's
base
d
on
the
c
omm
utati
on
betw
een
it
s
switc
hers
sit
ua
te
d
i
n
it
s
ar
ms
.
T
his
co
mm
utati
on
delivers
the
si
nu
s
oi
dal
s
h
ape
of
t
he
outp
ut
current
that
fe
ds
t
he
AC
l
oa
ds
[
6]
,
[8],
[
9].
The
s
witc
hes
are
t
he
pr
i
ncipal
el
em
ent
in
the
c
onver
si
on
operat
ion
a
nd
a
ny
f
ai
lure
in
their
work
br
e
aks
the
inv
e
rter
outp
uts.
Hen
ce
,
fau
lt
s
i
n
the
in
ver
te
r
are
known
as
a
big
pr
ob
le
m
that
cau
s
es
da
mages
to
t
he
functi
onal
it
y
of
t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri
S
ys
t
IS
S
N: 20
88
-
8
694
Shor
t
and o
pe
n ci
rcuit f
ault
s s
tud
y i
n
the
PV
syste
m
inve
rte
r
(
M
ohamme
d Bo
uz
idi
)
1765
DC/AC
c
onve
r
te
r,
AC
l
oad
s
,
or
ot
her
P
V
syst
em
pa
rts.
F
or
that,
in
ver
te
r
monit
or
i
ng
is
an
es
sentia
l
ta
s
k
fo
r
al
l
PV
sy
ste
m
s
functi
onin
g.
In
[
10
]
t
he
y
ha
ve
stu
died
t
he
increasin
g
of
the
veh
ic
le
powe
r
trai
n
reli
abili
ty
reg
a
rd
i
ng
ins
ul
at
ed
gate
bipolar
tr
ansist
or
(
I
GBT
)
op
e
n
-
ci
rcu
it
fail
ur
e
s,
4
-
wire
,
an
d
4
-
le
g
pulse
width
modu
la
ti
on
(
P
W
M
)
in
ver
te
r
topolo
gies
in
ve
sti
gated
an
d
their
pe
rfo
rma
nc
es
discusse
d
in
a
veh
ic
le
c
on
te
xt
[4].
I
n
[
11
]
it
ha
s b
ee
n
in
vesti
gate
d o
n
f
aults
that may
o
cc
ur
on th
e
D
C l
in
k of
a
n
i
nv
e
rter
f
ed
in
du
ct
i
on
mo
to
r
and the e
ff
ect
of
t
he
ca
pacit
or s
hort circ
uit. I
t al
so
deals
with the e
ff
ect
s
of the s
hort
-
ci
rc
uited ca
pacit
or on th
e
fr
ee
wh
eel
in
g
di
od
e.
And,
i
n
[
1
2
]
,
[
13
]
the
y
hav
e
determi
ne
d
t
he
l
ocati
on
of
t
he
fau
lt
,
the
rati
o
betwe
en
D
C
and
AC
powe
r.
The
y
ha
ve
dev
el
op
e
d
a
s
of
t
war
e
to
ol
t
o
i
den
ti
f
y
dif
f
eren
t
ty
pes
of
fa
ults
li
ke
fa
ult
in
a
photov
oltai
c
m
odule,
fa
ult
in
a
phot
ovoltai
c
string,
fau
lt
in
an
in
ve
rter,
an
d
a
ge
ner
al
fa
ul
t
that
may
i
nc
lud
e
par
ti
al
s
ha
ding
,
P
V
a
ging,
or
ma
xim
um
po
wer
po
i
nt
trac
king
(
M
PP
T
)
error.
In
[5],
[
1
4
]
,
[
15
]
th
ey
ha
ve
carried
ou
t
t
he
fiel
d
meas
ur
e
ment
for
c
urre
nt
ha
rm
onic
s.
In
pa
rtic
ular,
f
or
a
tw
o
-
sta
ge
inv
e
rter
t
hat
as
su
mes
the
DC
-
li
nk
volt
age
is
c
onsta
nt,
the
DC
-
li
nk
volt
age
rip
ple
is
ide
ntifie
d
as
t
he
s
ourc
e
of
a
se
ries
of
od
d
harmo
nics.
A
new
per
i
od
ic
ti
me
-
varyin
g
m
od
el
is
pro
pos
ed
by
i
nclu
ding
t
he
DC
-
li
nk
vo
lt
age
rip
ple
into
t
he
conve
ntion
al
c
urren
t
c
ontr
ol
loop
m
odel
.
In
[1
6
]
-
[
18
]
have
f
ocu
se
d
on
t
he
in
ve
rter
of
photov
oltai
c
sy
ste
ms
and
t
heir
c
har
a
ct
erizat
ion
.
T
he
y
ha
ve
obta
in
ed
a
m
odel
fro
m
a
detai
le
d
st
udy
of
main
lo
ss
proces
ses
in
small
-
siz
e
PV
in
ver
t
ers
i
n
the
ma
rket
.
The
mai
n
a
dv
a
ntage
of
th
e
us
e
d
meth
od
is
to
obta
in
a
model
that
co
mprise
s
two
a
nt
a
gonisti
c
featu
res
si
nc
e
both
are
sim
ple,
eas
y
t
o
c
omp
ute
a
nd
ap
pl
y,
a
nd
acc
ur
at
e.
H
oweve
r,
no
one o
f
these
pa
pers
stud
ie
d
the
fau
lt
s
that
occ
urred
in
the
str
uctu
r
e
of
t
he
P
V
syst
em
inv
e
rters
.
Hen
ce
,
this
pa
per
trie
s
to
e
xpla
in
the
in
ve
rter
fa
ults
ef
fects
a
nd
giv
es
a
gen
e
ral
idea
of
the
beh
a
vior
a
nd
t
he
c
hanges
in
t
he
P
V
sy
ste
m
outp
uts
.
It
is
base
d
on
the
stu
dyin
g
of
the
PV
syst
em
f
un
ct
i
on
i
ng
in
the
norm
al
op
e
rati
on
a
nd
unde
r
fau
lt
s
in
th
e
in
ver
te
r
.
F
or
t
hat,
we
hav
e
pro
pose
d
in
this
pa
per
a
meth
od
t
hat
can
detect
sh
ort
an
d
op
e
n
ci
rcu
it
fau
lt
s in
the
in
ver
te
r
.
Firstl
y,
we
trie
d
to
stu
dy
the
sh
ort
ci
rcu
it
fa
ult
in
the
in
vert
er
that
is
the
mo
st
kn
own
prob
le
m
i
n
th
e
PV
s
ys
te
m
po
wer
co
nversi
on.
The
sho
rt
ci
rcu
it
fa
ult
is
de
pende
nt
on
th
e
inv
e
rter
swit
ch
c
ommutat
io
n
a
nd
influ
e
nces
t
he
PV
s
ys
te
m
outp
uts
by
decre
asi
ng
t
he
DC/AC
co
nv
e
rter
par
a
mete
rs
w
hich
reduce
t
he
PV
sy
ste
m
e
ff
ic
ie
ncy.
Sec
ondly,
we
prese
nted
the
open
ci
rc
uit
fail
ur
e
,
w
he
n
one
of
t
he
inv
e
rter
s
witc
hes
is
op
e
ne
d
a
nd
sta
ys
bl
ock
e
d
in
it
s
posit
ion.
Th
i
s
ki
nd
of
fa
ult
af
fects
t
he
PV
s
ys
te
m
co
ntin
uity
a
nd
break
s
t
he
AC loa
ds
sup
pl
ie
s.
The
rest
of
thi
s
pa
per
is
orga
nized
is
be
in
g
as
.
Sect
io
n
2
s
hows
the
PV
s
ys
te
m
de
vice
modeli
ng.
In
S
ect
ion
3,
w
e
pr
ese
nt
th
e
me
thodo
l
ogy
us
e
d
in
this
w
ork
to
stu
dy
the
fa
il
u
res
in
the
P
V
s
ys
te
m
i
nv
e
rter.
I
n
S
ect
ion
4,
we
hav
e
simulat
e
d
the
res
ults
obta
ined
f
rom
the
pr
opos
e
d
a
ppr
oach
i
n
the
case
of
ab
sen
ce
an
d
pr
ese
nce
of
fai
lure
in
the
P
V
sy
ste
m
i
nv
e
rter.
T
he
la
st
sect
ion
is
de
dicat
ed
to
t
he
c
on
cl
usi
on
a
nd
per
s
pe
ct
ive
the fut
ure
wor
k.
2.
METHO
DOL
OGY
The
m
on
it
ori
ng
of
P
V
s
ys
te
m
dev
ic
es
is
a
n
im
porta
nt
pa
rt
to
ge
ne
rate
t
he
powe
r
pro
duced
by
the
se
sy
ste
ms
.
F
or
t
hat,
the
in
ver
t
er
is
pr
ese
nted
as
an
inter
me
diate
betwee
n
the
DC
a
nd
th
e
AC
si
de,
a
nd
it
s
functi
onin
g
s
houl
d
be
in
th
e
co
rr
ect
wa
y
to
ens
ure
t
he
opti
mum
e
ff
i
ci
ency
.
In
this
re
gard,
a
pr
opose
d
simulat
ion
met
hod
has
bee
n
c
reated
base
d
on
the
M
AT
LA
B
/Si
mu
li
nk
en
vir
onment
t
o
s
tudy
a
nd
treat
fau
lt
s
in
the
in
ver
te
r.
I
n
t
his
w
ork,
we
are
interest
e
d
to
stu
dy
t
he
be
hav
i
or
o
f
the
i
nv
e
rter u
nde
r
s
om
e
s
pecific
fa
ults;
pr
eci
sel
y
t
he
s
hort
ci
rcu
it
an
d
the
open
ci
rc
ui
t
fau
lt
s.
Firstl
y,
the
c
omp
onents
of
the
P
V
sy
ste
m
ar
e
intr
oduce
d
by
relyi
ng
on
t
he
diode
photovo
lt
ai
c
cel
l
model.
Sec
ondl
y,
a
three
-
phase
i
nv
e
rter
is
mod
el
ed
w
he
re
the
tw
o
typ
es
of
f
aults
(shor
t
ci
rc
u
it
a
nd
open
ci
rc
uit)
t
o
stu
dy
th
e
be
hav
i
or
a
re
i
ntrod
uced.
The
pro
posed
str
uct
ur
e
is
sh
ow
n
in
Fi
gur
e
1.
Figure
1. Flo
w
char
t
of the
pro
po
s
ed
meth
odol
ogy
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
3
,
Se
ptembe
r
2021
:
176
4
–
177
2
1766
2.1.
Des
cri
pt
i
on
of P
V
syste
m de
vices
The
PV
syst
em
us
e
d
i
n
this
w
ork
c
onsist
s
of
ei
gh
t
YL
80P
-
17b
2/
3
po
l
ycry
sta
ll
ine
so
la
r
pa
nels.
T
he
y
are
c
onnected
in
par
al
le
l
a
nd
their
pa
ra
mete
rs
a
re
s
ummari
ze
d
in
Table
1.
T
he
Fo
s
han
Ta
nfo
n
e
nerg
y
te
chn
ology i
nv
erter is
us
e
d
in
this stu
dy and i
ts characte
risti
cs are
de
velo
pe
d
in
Ta
ble 2.
Table
1
.
T
he
Y
L8
0P
-
17b 2/
3 pan
el
pa
ramete
rs
Techn
o
lo
g
y
Po
ly
crys
tallin
e Si
Peak
po
wer
80W
Op
en
cir
cu
it vo
lta
g
e
22V
Sh
o
rt
circuit cur
re
n
t
5
.04
A
Peak
vo
ltag
e
17V
Peak
curre
n
t
4
.71
A
Max sy
stem
v
o
ltag
e
50V
Table
2
.
Fo
s
ha
n
ta
nf
on
ene
rgy
te
ch
nolo
gy i
nv
e
rter
char
act
e
risti
cs
Featu
res
Valu
es
Ou
tp
u
t po
wer
1
KW
-
1
0
0
KW
No
m
in
al vo
ltag
e
3
8
0
V/4
1
5
V/4
4
0
V.
Maximu
m
ef
ficien
cy
>8
5
%
Maximu
m
DC vo
lt
ag
e
384V
No
m
in
al DC
cu
rr
e
n
t
156A
2.2.
M
od
el
in
g o
f
P
V array
As
presente
d
i
n
a
pre
vious
pa
per
pu
blishe
d
by
[
6
]
,
[
1
8
]
,
[
19
]
,
[
2
0],
t
he
D
C
outp
ut
powe
rs,
the
outp
ut
currents
,
a
nd
volt
ages
of
the
PV
a
rr
a
y
ha
ve
been
cal
culat
e
d
us
in
g
a
do
uble
diode
PV
ce
ll
mo
de
l
as
e
xpress
ed
in (1) [
14
]
,
[
18
].
=
ℎ
−
01
(
(
+
1
−
1
)
)
−
02
(
(
+
2
−
1
)
)
−
+
ℎ
(1)
wh
e
re
I
ph
is
th
e
cu
rrent
ge
ne
r
at
ed
by
t
he
i
nc
ident
li
gh
t.
I
01
,
I
02
is
the
re
verse
sat
urat
io
n
c
urren
ts
of
the
diodes
D1
a
nd
D
2
res
pecti
vely
.
Vt
i
s
the
the
rmal
volt
age.
n
1
,
n
2
a
re
the
ideal
it
y
factors
of
diod
es
D
1
an
d
D
2
.
Rs
and
Rsh
are
t
he
se
ries
an
d
s
hunt
resist
ance
respec
ti
vely.
V
an
d
I
a
re
the
out
pu
t
P
V
mod
ule
vo
lt
a
ge
an
d
curren
t
resp
ect
ivel
y.
2.3.
M
od
el
in
g o
f
t
he in
vert
e
r
To
obta
in
the
eff
ic
ie
nc
y
of
the
DC
c
urren
t
and
volt
age
co
nv
e
rters
int
o
the
AC
c
urren
t
and
volt
age
,
we
ha
ve
m
od
el
ed
t
his
i
nv
e
rter
with
t
he
sta
ndard
met
hod
gi
ve
n
by
t
he
ne
xt eq
uatio
n.
T
his
model
e
xpress
es
the
eff
ic
ie
nc
y
as
a
functi
on
of
t
he i
nput po
wer
P
in
[
6
]
,
[
2
1
],
[
2
2
]
.
/
=
0
+
1
(
1
−
(
−
2
×
)
)
+
3
(
1
−
(
−
4
×
)
)
(2)
The
par
a
merte
rsy
0,
c1
,
c
2,
c
3,
a
nd
c
4
are
s
how
n
in
Table
3,
t
hese
par
a
m
et
ers
can
be
ob
ta
ined
us
in
g
th
e
le
ast
sq
ua
re al
gorith
m,
mi
nimizi
ng
the qua
dr
at
ic
f
un
ct
io
n:
(
)
=
∑
(
−
(
,
)
)
2
=
1
(3)
Table
3.
E
sti
mate
d
pa
ramete
r
s u
si
ng least
squar
e
alg
or
it
hm
[10]
Para
m
eters
y
0
c
1
c
2
c
3
c
4
v
alu
es
1
.07
3
3
1
.68
1
7
0
.07
2
1
-
1
.84
4
0
0
.40
6
9
3.
INV
E
RTER
F
AU
LT
S
STU
DY
The
DC/
AC
co
nv
e
rter
re
prese
nts
a
pr
i
nciple
dev
ic
e
in
t
he
P
V
sy
ste
m
due
to
it
s
mo
st
imp
or
ta
nt
wor
k
in
the
pro
duct
ion
li
ne
,
w
he
n,
it
ensu
res
t
o
supp
l
y
the
loa
d
by
the
AC
powe
r
co
nv
e
rted
fro
m
the
DC
on
e
[
2
3
]
,
[
2
4
]
.
The
i
nv
e
r
te
r
reli
abili
ty
de
pends
on
good
e
ff
ic
ie
ncy,
w
her
e
it
ca
nnot
be
obta
ine
d
i
f
this
c
onve
rter
is
no
t
well
functi
oning.
T
hu
s
,
in
t
his
stu
dy
;
we
hav
e
t
ried
t
o
monit
or
t
he
in
ver
te
r
be
ha
vior
in
the
case
of
good
functi
onin
g
an
d
ot
her
ca
ses
wh
e
n
we
ha
ve
introd
uced
some
fa
ults
(w
e
are
interest
e
d
i
n
this
a
ppr
oac
h
in
t
he
sh
ort
circ
uit o
f on
e
of t
he
in
ve
rter a
rms
a
nd t
he op
e
n
ci
rcu
it
at the sa
me c
onve
rter a
rm
)
[
14
]
,
[
2
5
]
,
[
2
6
]
,
[
2
7
]
.
3.1
.
Sh
or
t
ci
r
cuit faul
t
The
s
hort
ci
rc
uit
is
the
m
os
t
cu
rr
e
nt
prob
l
em
in
the
PV
sy
ste
m
c
onve
r
te
rs,
a
nd
it
ha
s
cause
d
bi
g
dama
ges
in
th
e
ph
otovo
lt
ai
c
instal
la
ti
on
s
.
Howe
ver,
st
udying
t
he
co
ns
e
qu
e
nces
a
nd
t
he
res
ults
of
t
his
fau
lt
pro
vid
es
t
he
knowle
dge
of
how
this
e
ve
nt
occurre
d
[
2
2
]
,
[
2
8
],
[
2
9
]
.
T
he
nor
mal
f
unct
ion
i
ng
of
t
he
i
nverter
is
sta
rted
w
hen
the
first
s
witc
h
S1
of
t
he
first
arm
A
1
is
cl
ose
d,
w
hich
mea
ns
t
he
c
urre
nt
passes
th
rou
ghou
t
S
1
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri
S
ys
t
IS
S
N: 20
88
-
8
694
Shor
t
and o
pe
n ci
rcuit f
ault
s s
tud
y i
n
the
PV
syste
m
inve
rte
r
(
M
ohamme
d Bo
uz
idi
)
1767
and
S
4.
And
t
he
seco
nd
ste
p
is
w
hen
S
3
is
cl
os
e
d,
the
n
t
he
c
urre
nt
will
be
passe
d
ont
o
S3
a
nd
S6.
And
the
la
st
ste
p
is
when
S
5
is
tur
ne
d
on,
w
hich
m
eans
the
c
urre
nt
will
pass
be
tween
S
5
a
nd
S2
as
dem
onstrat
ed
in
F
igure
2.
Figure
2
.
Flo
w
char
t
of the
us
e
d
in
ve
rter in t
he
prop
os
ed
met
hodolo
gy
3.2.
Ope
n cir
cuit faul
t
The
ope
n
-
ci
rc
uit
re
pr
ese
nts
a
ha
rmful
fau
l
t
that
ap
pears
in
the
DC/AC
co
nv
e
rter
le
ve
l
and
it
has
influ
e
nce
d
the
PV
s
ys
te
m
ef
fici
ency
.
He
nce,
the
in
ver
te
r
f
un
ct
io
ning
be
ha
vior
will
be
c
hange
d
in
this
case.
This
kind
of f
a
ult de
pends
on t
he
in
ver
te
r
s
w
it
ches
co
mm
utati
on
a
nd their
mode c
on
t
ro
l.
The
ope
n
-
ci
rc
uit
fa
ult
is
ha
ppeni
ng
in
t
he
DC/AC
c
onve
r
te
r
w
he
n
al
l
of
it
s
switc
hes
are
op
e
ne
d.
This
cas
e
c
ou
l
d
be
ar
riving
if
on
e
or
m
or
e
switc
hes
are
opene
d
an
d
sta
y
bl
ock
e
d.
T
he
exam
ple
to
ok
i
n
t
hi
s
method
ology
i
s
wh
e
n
the
s
w
it
ch
S
1
an
d
S
4
are
op
e
ne
d
an
d
t
he
switc
h
S
1
sta
y
ope
ned,
but
the
pr
ob
le
m
is
wh
e
n
t
he
s
witc
hes
S
5
a
nd
S
2
become
op
e
ne
d.
In
this
sta
te
,
the
op
e
n
ci
rc
ui
t
fau
lt
is
ap
pe
ared
i
n
the
swi
tc
hes
S1
a
nd
S2,
an
d
al
so
t
he
swit
ches
S
5
a
nd
S
6.
T
his
mea
ns
that
the
arm
A
1
an
d
A3
a
re
i
n
case
of
open
-
ci
rcu
it
fail
ur
e.
T
hus,
the
P
V
sy
ste
m
ef
fici
ency
is
automatic
al
ly
i
nf
l
uen
ce
d
by
t
he
a
ppeara
nce
of
t
his
in
the
so
la
r
inv
e
rter
[1
9
]
,
[
27
],
[
30
]
.
4.
SIMULATI
O
N RESULTS
AND DIS
C
USSION
The
obje
ct
ive
of
the
prese
nt
work
is
t
o
st
ud
y
t
he
i
nv
e
rter
i
n
normal
an
d
unde
r
fa
ults
f
un
ct
ion
in
g.
F
or
that,
we
hav
e
use
d
ei
ght
YL
80P
-
17b
2/3
polycr
ys
ta
ll
ine
so
l
ar
pa
nels
co
nn
ect
ed
in
pa
rall
el
to
get
more
ou
t
pu
t
vo
lt
age
a
nd
th
ey
s
uppl
y
t
he
PV
sy
ste
m
by
55
0
Wp,
t
he
PV
m
odule
pa
rameters
are
gi
ven
in
Table
1.
The
inv
e
rter
us
e
d
i
n
this
stu
dy
is
a
th
ree
-
phase
Fosha
n
Tan
f
on
en
er
gy
te
c
hnolog
y
a
nd
i
ts
cha
racteri
sti
cs
are
mentio
ned
i
n
Table
2.
In
al
l
fig
ur
es
,
t
he
blue
li
ne
re
pr
ese
nt
s
the
in
ver
te
r
ou
t
pu
ts
with
nor
mal
f
unct
io
ni
ng
an
d
the
gr
ee
n
li
ne
sho
w
t
he
DC
/AC
co
nverter
outp
uts
with
diff
e
re
nt
ki
nds
of
fail
ur
es
under
stu
dy
(the
short
ci
rcu
it
and t
he op
e
n
ci
rcu
it
)
.
4.1.
P
V
syste
m inver
ter
functio
ning
w
it
h
ou
t
fail
ure
Figure
3
ex
pla
ins
the
a
ver
a
ge
outp
ut
powe
r
in
ve
rter
with
good
oper
at
io
n
wh
e
n
this
powe
r
is
in
const
ant
val
ue
du
e
t
o
a
c
onsta
nt
so
la
r
ra
diati
on
P
V
a
rr
a
y
i
nput
a
nd
no
pr
ob
le
m
in
the
i
nv
e
rter
c
omm
utati
on
switc
hes.
He
nc
e,
the
i
nverter
ou
t
pu
t
powe
r
r
epr
ese
nts
t
he
PV
s
y
ste
m
ef
fici
ency
rate;
in
this
case
of
nor
mal
functi
onin
g
wi
thout
fa
ults,
th
e
PV
s
ys
te
m
e
ff
ic
ie
nc
y
is
in
the
highest
value.
In
F
ig
ur
e
4
an
d
F
i
gure
5,
the
curves
represe
nt
the
ou
t
pu
ts
inv
e
rter
vo
lt
a
ge
an
d
c
urre
nt
resp
ect
ivel
y
of
t
he
first
ph
ase
of
t
he
D
C/
A
C
conve
rter
us
e
d
unde
r
st
udy.
H
ow
e
ve
r,
both
fi
gures
are
in
a
s
inu
s
oid
al
f
orm
and
the
c
urre
nt
cu
r
ve
is
the
i
mage
of
t
he
volt
age
curve.
T
hus,
we
ta
ke
the
se
curves
as
a
refe
ren
ce
t
o
co
m
par
e
t
hem
with
th
os
e
of
the
fail
ur
e
inv
e
rter
functi
on
i
ng.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
3
,
Se
ptembe
r
2021
:
176
4
–
177
2
1768
Figure
3. P
V
s
ys
te
m
outp
ut pow
e
r wit
h n
ormal
fun
ct
io
ning
(w
it
ho
ut f
a
ults)
Figure
4. P
V
s
ys
te
m
outp
ut volt
age
with
nor
mal
functi
onin
g
(
w
it
ho
ut
fa
ults)
Figure
5.
P
V
s
ys
te
m
outp
ut c
urren
t
with
nor
mal
functi
onin
g
(
w
it
ho
ut
fa
ults)
4.2.
P
V
syste
m inver
ter
functio
ning
w
it
h
sho
r
t
ci
rcui
t
f
au
lt
:
Fig
ures
6
-
8
show
the
e
ff
ect
of
t
he
short
ci
rc
uit
in
the
P
V
s
ys
te
m
in
ver
te
r
by
the
c
urves
of
t
he
powe
r,
the
vo
lt
a
ge
,
an
d
t
he
cu
rr
e
nt
r
especti
vely
.
Fig
ure
6
e
xp
la
in
s
a
co
ns
ide
ra
ble
re
duct
ion
in
the
ou
t
pu
t
pow
er
a
n
d
no
st
abili
ty
in
i
ts
sign
al
that
c
ou
l
d
dama
ge
t
he
dev
ic
e
un
de
rstudy
or
t
he
l
oad
s
upplied
by
this
po
wer.
F
ig
ure
s
7
a
nd
8
a
re
t
he
out
pu
t
volt
age
an
d
the
c
urren
t
of
phase
1
of
t
he
in
ver
t
er.
H
oweve
r,
t
he
cu
rr
e
nt
c
ur
ve
is
th
e
image
of
t
he
volt
age
c
urve.
We
ob
se
r
ve
ju
st
the
ne
gative
par
t
of
t
he
c
urre
nt
phase
i
n
the
short
ci
rcui
t
case
com
par
i
ng
with
the
normal
f
un
ct
io
ning
that
means
the
re
is
a
rev
e
rse
cu
rrent
in
the
P
V
s
ys
te
m
in
ver
te
r
wh
e
n
the
arm
A
1
is
short
-
ci
rcu
it
e
d.
For
that,
it
ap
pear
s
j
us
t
t
he
neg
at
ive
c
urren
t
a
nd
vo
l
ta
ge
f
orm.
T
he
three
par
a
mete
rs
(
power,
vo
lt
a
ge
,
a
nd
c
urren
t
)
a
re
li
nk
e
d
bet
wee
n
t
hem,
the
n
one
of
the
m
c
ha
ng
e
s
al
l
of
th
e
rest
div
e
rg
e
.
Figure
6.
P
V
s
ys
te
m
outp
ut pow
e
r u
nd
e
r
s
hort circ
uit fa
ult i
n
the
in
ver
te
r a
rm
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
100
200
300
400
500
600
T
i
m
e
(
s
e
c
o
n
d
s
)
O
u
t
p
u
t
p
o
w
e
r
(
W
a
t
t
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-
2
0
0
-
1
5
0
-
1
0
0
-
5
0
0
50
100
150
200
T
i
m
e
(
s
e
c
o
n
d
s
)
O
u
t
p
u
t
v
o
l
t
a
g
e
(
V
o
l
t
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-4
-3
-2
-1
0
1
2
3
4
T
i
m
e
(
s
e
c
o
n
d
s
)
O
u
t
p
u
t
c
u
r
r
e
n
t
(
A
m
p
e
r
e
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
100
200
300
400
500
600
T
i
m
e
(
S
e
c
o
n
d
s
)
O
u
t
p
u
t
p
o
w
e
r
(
Wa
t
t
)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri
S
ys
t
IS
S
N: 20
88
-
8
694
Shor
t
and o
pe
n ci
rcuit f
ault
s s
tud
y i
n
the
PV
syste
m
inve
rte
r
(
M
ohamme
d Bo
uz
idi
)
1769
Figure
7.
P
V
s
ys
te
m
outp
ut volt
age
of the
fi
rst phase
unde
r
s
hort cir
cuit fa
ult i
n
the
inv
e
rter a
rm
Figure
8.
P
V
s
ys
te
m
outp
ut c
urren
t
of the
f
ir
st p
hase
unde
r
s
hort cir
cuit fa
ult i
n
the
inv
e
rter a
rm
4.3.
P
V
syste
m inver
ter
functio
ning
w
it
h
o
pe
n
-
ci
rcui
t
fault
In
this
kind
of
fau
lt
,
we
co
uld
no
ti
ce
that
in
F
ig
ure
9
t
he
outp
ut
powe
r
c
urve
dro
ps
it
s
va
lues
w
he
n
the
op
e
n
ci
rc
uit
fa
ult
is
a
pp
li
ed
a
nd
it
s
al
lu
re
si
gn
al
sti
ll
f
loati
ng
.
T
he
ef
fect
of
the
ope
n
-
ci
rc
uit
fau
lt
is
the
decr
ease
of
t
he
total
PV
s
yst
em
e
ff
ic
ie
nc
y,
w
hic
h
ca
use
s
a
no
t
her
deformat
ion
in
t
he
in
ver
te
r
struc
ture.
Fig
ure
s
1
0
a
nd
11
e
xpla
in
the
outp
ut
vo
lt
age
an
d
c
urre
nt
re
sp
ect
ively
of
t
he
first
ph
a
se
of
the
outp
ut
i
nverter
.
The
s
ha
pe
of
c
urves
s
hows
th
e
profo
und
e
ffec
t
of
t
he
ope
n
ci
rcu
it
fa
ults
in
th
e
si
nuso
i
da
l
fo
r
m
of
t
he
volt
age
and
the
c
urre
nt
res
ults.
Be
si
des
,
the
op
e
n
-
ci
rcu
it
fau
lt
is
intr
oduce
d
by
ope
ning
t
wo
switc
hes
in
th
e
same
inv
e
rter
a
rm
that
c
hanges
th
e
volt
age
an
d
the
c
urre
nt
al
lures.
T
he
c
urren
t
bec
om
es
zero
at
the
m
om
e
nt
betwee
n
0.0
6
a
nd
0.08
sec
on
d
s
.
At
this
m
ome
nt,
the
first
op
e
n
ci
rc
uit
is
introd
uced
a
nd
it
af
fects
the
r
est
of
the sig
nal all
ur
e. T
he
same
thi
ng in
t
he vo
lt
a
ge
c
urve,
whic
h remai
ns co
nst
ant at t
his m
ome
nt.
Figure
9. P
V
s
ys
te
m
outp
ut pow
e
r u
nd
e
r ope
n
ci
rc
uit
fa
ult
in the i
nv
e
rter
arms
Figure
10.
PV
sy
ste
m
outp
ut
vo
lt
age
of t
he f
irst
ph
a
se
under o
pe
n
ci
rc
uit fa
ult
in the i
nv
e
rter
arms
Figure
11.
PV
sy
ste
m
outp
ut
current
of the
fi
rst phase
unde
r op
e
n
-
ci
r
cuit fa
ult i
n
the
inv
e
rter a
rms
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-
2
0
0
-
1
5
0
-
1
0
0
-
5
0
0
50
100
150
200
T
i
m
e
(
S
e
c
o
n
d
s
)
O
u
t
p
u
t
v
o
l
t
a
g
e
(
V
o
l
t
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-4
-3
-2
-1
0
1
2
3
4
T
i
m
e
(
S
e
c
o
n
d
s
)
O
u
t
p
u
t
c
u
r
r
e
n
t
(
A
m
p
e
r
e
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-
1
0
0
0
100
200
300
400
500
600
T
i
m
e
(
S
e
c
o
n
d
s
)
O
u
t
p
u
t
p
o
w
e
r
(
W
a
t
t
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
3
,
Se
ptembe
r
2021
:
176
4
–
177
2
1770
5.
CONCL
US
I
O
N
In
this
pa
per,
we
ha
ve
st
ud
ie
d
fau
lt
s
t
hat
oc
curred
in
the
inv
e
rter
es
peci
al
ly
fa
ults
of
the
s
hort
a
nd
op
e
n
ci
rcu
it
of
s
witc
her
s
of
the
in
ve
rter.
The
meth
odol
ogy
c
onsist
s
of
m
odel
ing
al
l
the
par
ts
of
t
he
P
V
sy
ste
m,
namel
y
the
pa
nels
a
nd
t
he
inv
e
rter
.
The
n,
a
de
sc
riptio
n
of
the
inv
e
rter
with
a
nd
with
ou
t
fa
ul
ts
is
pr
ese
nted
.
T
he
simulat
ion
res
ults
ha
ve
s
how
n
that
a
cl
ose
d
blo
c
ke
d
switc
h
of
on
e
a
rm
of
the
in
ve
rter
c
auses
the
short
ci
rc
ui
t
fau
lt
that
le
ad
s
to
a
dec
reasi
ng
of
the
ou
t
put
power
with
a
deformat
ion
of
the
sin
usoidal
form
of
the
c
urre
nt
and
volt
age
ou
tpu
ts.
On
t
he
oth
e
r
ha
nd,
an
op
e
n
ci
rc
uit
f
ault
wh
ic
h
occ
ur
s
w
hen
a
s
w
it
ch
of
on
e
a
rm
of
th
e
in
ver
te
r
is
open
a
nd
sta
y
s
blo
c
ked
i
n
it
s
po
sit
io
n
cau
se
s
a
zer
o
cu
rr
e
nt
value
.
Thes
e
fa
ults
influ
e
nce
dec
r
easi
ng
l
y
t
he
P
V
sy
ste
m
glob
al
ef
fici
ency.
The
obta
ine
d
resu
lt
s
sho
wed
the
ef
ficacy
of
the
pro
po
se
d met
hod t
hat lea
ds
to
opti
mal f
un
ct
i
on
i
ng of t
he
P
V
s
ys
te
m
.
ACKN
OWLE
DGE
MENTS
The
a
uthor
s
w
ou
l
d
li
ke
t
o
th
ank
the
U
niv
er
sit
y
of
Ahmed
Dr
ai
a
of
A
dr
a
r
for
t
he
fi
nan
ci
al
aspect
of
the prese
nt wo
rk.
REFERE
NCE
S
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li
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,
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A
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ma
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aul
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n
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fer
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t
c
li
matic
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ti
o
ns,
”
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urnal
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n
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,
and
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“
Forec
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ng
of
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r
a
dia
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on
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an
em
pirica
l
model
,
”
Al
gerian
Journal
of
Re
newab
le
Ene
rgy
and
Sust
ainabl
e
Dev
el
op
ment
,
vol
.
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Coronado
-
M
endoz
a
and
J.
A.
Domínguez
-
Nava
rro,
“
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mi
c
ph
asors
m
odel
ing
o
f
inv
e
rte
r
f
ed
indu
cti
on
gene
ra
tor,
”
El
e
ctr
ic
Pow
er
Syst
e
ms
Re
search
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vo
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