I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
P
owe
r
E
lec
t
r
on
ics
an
d
Dr
ive
S
ys
t
e
m
s
(
I
JP
E
DS)
Vol.
13
,
No.
1
,
M
a
r
c
h
20
2
2
,
pp.
488
~
499
I
S
S
N:
2088
-
8694,
DO
I
:
10
.
11591/i
jpeds
.
v
13
.i
1
.
pp
488
-
499
488
Jou
r
n
al
h
omepage
:
ht
tp:
//
ij
pe
ds
.
iaes
c
or
e
.
c
om
Im
p
ac
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of
on
-
gr
i
d
sol
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r
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y ge
n
e
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at
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n
syste
m
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l
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vo
ltage
r
id
e
t
h
r
ou
g
h
c
a
p
ab
il
ity
M
oh
am
m
ad
Ah
m
ad
S
h
awqi
1
,
M
ok
h
t
ar
Hu
s
s
ien
Abd
all
ah
2
,
I
b
r
ah
im
Ahm
e
d
Nas
s
ar
3
1
R
e
s
e
a
r
c
h a
nd P
la
nni
ng
D
e
p
a
r
tm
e
nt
, M
in
is
tr
y of
E
le
c
tr
ic
it
y a
nd
R
e
ne
w
a
bl
e
E
ne
r
gy, C
a
ir
o, E
gypt
2
D
e
ve
lo
pi
ng P
e
r
f
or
ma
nc
e
a
nd P
ol
it
ic
a
l
C
omm
uni
c
a
ti
on U
ni
t,
M
in
is
tr
y of
E
le
c
tr
ic
it
y a
nd R
e
ne
w
a
bl
e
E
ne
r
gy, C
a
ir
o,
E
gypt
3
E
le
c
tr
ic
a
l
P
ow
e
r
a
nd M
a
c
hi
ne
s
E
ngi
ne
e
r
in
g D
e
pa
r
tm
e
nt
, A
l
A
z
ha
r
U
ni
ve
r
s
it
y, C
a
ir
o, E
gypt
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
J
ul
14,
2021
R
e
vis
e
d
J
a
n
24
,
2022
Ac
c
e
pted
J
a
n
31
,
2022
T
h
i
s
p
ap
e
r
r
ep
re
s
en
t
ed
a
co
n
t
ro
l
s
t
rat
eg
y
fo
r
p
hotovolta
i
c
(
P
V
)
syste
m
,
t
h
i
s
co
n
t
ro
l
s
t
rat
eg
y
w
as
r
ef
er
red
t
o
as
a
l
o
w
v
o
l
t
ag
e
ri
d
e
t
h
ro
u
g
h
(
L
V
RT
)
,
i
t
h
ad
b
een
ach
i
ev
ed
b
y
u
s
i
n
g
t
h
r
ee
p
h
a
s
e
(3
-
PH
)
(P
V
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g
ri
d
-
co
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ect
ed
s
y
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t
em
,
w
h
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t
h
i
s
p
ap
e
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d
i
s
cu
s
s
ed
t
h
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w
ay
t
o
a
ch
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ev
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max
i
mu
m
o
u
t
p
u
t
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ct
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v
e
p
o
w
er
fro
m
t
h
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s
o
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r
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t
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m,
w
h
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h
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l
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r
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t
em
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mai
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n
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w
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ag
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ch
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ch
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ari
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ed
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n
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T
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n
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ag
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eg
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t
r
at
eg
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ep
en
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n
t
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ri
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v
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ag
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ro
p
a
mo
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t
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M
A
T
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A
B
s
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mu
l
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o
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ad
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e
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u
s
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at
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men
t
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ed
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o
v
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ed
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o
p
res
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t
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ari
o
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s
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o
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ch
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p
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p
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al
i
n
t
eg
ral
(
PI)
co
n
t
ro
l
o
f
t
h
e
i
n
v
e
rt
e
r.
Fi
n
al
l
y
,
an
o
t
h
e
r
co
n
t
ro
l
m
et
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o
d
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ch
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t
eg
ral
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en
et
i
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al
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o
ri
t
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m
(
PI
-
G
A
),
h
ad
b
e
en
u
s
ed
t
o
i
mp
ro
v
e
v
al
u
e
o
f
t
h
e
g
en
e
rat
ed
o
u
t
p
u
t
act
i
v
e
p
o
w
er
.
K
e
y
w
o
r
d
s
:
G
e
ne
ti
c
a
lgor
it
hm
Gr
id
c
onne
c
ted
L
ow
volt
a
ge
r
ide
thr
ough
M
AT
L
AB
s
im
ulation
S
olar
e
ne
r
gy
ge
ne
r
a
ti
on
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
M
oha
mm
a
d
Ahma
d
S
ha
wqi
R
e
s
e
a
r
c
h
a
nd
P
lanning
De
pa
r
tm
e
nt
,
M
ini
s
tr
y
of
E
l
e
c
tr
icity
a
nd
R
e
ne
wa
ble
E
ne
r
gy
Abba
s
ia
S
qua
r
e
,
C
a
ir
o,
E
gypt
E
mail:
wild_s
ha
ks
ha
k@ya
hoo.
c
om
1.
I
NT
RODU
C
T
I
ON
R
e
c
e
ntl
y,
the
lac
k
of
c
onve
nti
ona
l
f
ue
ls
a
nd
poll
uti
on
ha
s
be
c
ome
a
n
im
po
r
tant
is
s
ue
be
c
a
us
e
it
c
a
us
e
s
global
c
li
mate
c
ha
nge
a
nd
a
s
hor
tage
of
e
ne
r
gy
r
e
s
our
c
e
s
[
1]
,
[2
]
.
C
ons
e
que
ntl
y,
the
global
dir
e
c
ted
towa
r
ds
us
ing
g
r
e
e
n
e
ne
r
gy
r
e
s
our
c
e
s
[
3
]
,
s
uc
h
a
s
wind,
s
olar
,
ge
other
mal
a
nd
biom
a
s
s
[
4]
,
[5
]
.
T
o
a
c
hieve
the
ne
e
de
d
r
e
quir
e
ment
a
nd
de
c
r
e
a
s
e
the
pr
oble
ms
a
tt
a
c
he
d
with
the
lac
k
o
f
c
onve
nti
ona
l
f
ue
ls
a
nd
the
poll
uted
a
tm
o
s
phe
r
e
a
nd
many
s
tudi
e
s
ha
ve
be
e
n
p
e
r
f
or
med
f
or
r
e
ne
wa
ble
e
ne
r
gy
de
ve
lopm
e
nt
[
6]
,
[7
]
.
T
he
r
e
is
a
big
pr
oblem
f
a
c
e
s
the
r
e
gulator
y
e
nti
ti
e
s
whic
h
is
the
ba
d
im
pa
c
t
on
the
gr
id
while
c
onne
c
ti
ng
ge
ne
r
a
ti
on
s
ys
tems
e
s
pe
c
ially
whe
n
the
c
onne
c
ted
s
ys
tems
be
c
om
e
lar
ge
[
8]
,
[9
]
.
T
he
r
e
f
or
e
,
many
c
ountr
ies
r
e
gulate
a
c
ode
f
o
r
the
gr
id
to
q
ua
li
f
y
thi
s
ne
ga
ti
ve
im
pa
c
t.
T
he
s
e
r
e
gulations
va
r
y
f
r
om
c
ountr
y
to
c
ountr
y
[
10]
,
[
11
]
.
Ge
ne
r
a
ll
y,
thes
e
r
e
gulations
c
lar
if
y
that
photovol
taic
(
P
V)
s
ys
tems
mus
t
r
e
main
c
onne
c
ted
a
nd
ope
r
a
ted
f
o
r
a
s
pe
c
if
ic
ti
me
while
c
a
s
e
s
of
volt
a
ge
dr
op
in
the
g
r
id
[
12
]
,
a
nd
s
uppor
ti
ng
thi
s
gr
id
with
the
r
e
quir
e
d
r
e
a
c
ti
ve
c
ur
r
e
nt
[
13]
,
[
14
]
.
T
he
de
f
ini
ti
on
of
thi
s
r
e
quir
e
ment
,
c
a
ll
e
d
low
volt
a
ge
r
ide
thr
ough
(
L
VR
T
)
,
it
is
ve
r
y
im
por
tant
to
a
void
the
blac
kouts
of
the
gr
id
[
15
]
,
[
16
].
De
pe
nding
on
the
volt
a
ge
dr
op
va
lue,
the
r
e
quir
e
m
e
nts
of
L
VR
T
a
r
e
dif
f
e
r
e
nt
r
e
ga
r
ding
the
du
r
a
ti
on
of
the
f
a
ult
a
nd
the
qua
nti
ty
o
f
the
r
e
a
c
ti
ve
powe
r
inj
e
c
ted
[
17]
,
[
18
]
.
T
he
s
e
r
e
quir
e
ments
to
e
ns
ur
e
the
P
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mpac
t
of
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
ati
on
s
y
s
te
m
on
…
(
M
ohamm
ad
A
hmad
Shaw
qi
)
489
s
ys
tem
r
e
m
a
ins
c
onne
c
ted
to
the
gr
id
a
nd
ope
r
a
te
d
whe
n
the
gr
id's
volt
a
ge
de
c
r
e
a
s
e
s
by
s
upplyi
ng
the
gr
id
with
the
r
e
quir
e
d
r
e
a
c
ti
ve
c
ur
r
e
nt
in
the
s
pe
c
if
i
e
d
volt
a
ge
r
a
nge
a
nd
s
uppor
ti
ng
the
gr
id
a
ls
o
with
the
maximum
output
powe
r
ge
ne
r
a
ti
on
[
19]
−
[
22
]
,
I
t
mea
ns
,
in
c
a
s
e
ther
e
is
a
dr
op
in
the
vo
lt
a
ge
of
the
gr
id,
the
L
VR
T
s
tr
a
tegy
de
ter
mi
ne
s
the
r
e
quir
e
d
inj
e
c
ted
r
e
a
c
ti
ve
c
ur
r
e
nts
a
c
c
or
ding
to
the
a
mount
o
f
volt
a
ge
de
c
r
e
a
s
ing
of
the
thr
e
e
-
pha
s
e
gr
id.
W
he
r
e
,
the
c
ont
r
ol
box
of
(
P
V
)
inver
ter
ha
s
the
main
r
ole
in
e
nha
n
c
ing
the
s
ys
tem
pe
r
f
or
manc
e
[
23
]
.
I
t
is
ve
r
y
ne
c
e
s
s
a
r
y
f
o
r
put
gr
id
-
c
ode
r
e
gulations
,
de
te
r
mi
ning
T
h
e
L
VR
T
r
e
quir
e
ment
[
24
]
−
[
26]
.
T
he
a
dva
nc
e
d
g
r
owth
in
r
e
ne
wa
ble
e
ne
r
gy
s
our
c
e
s
pus
he
s
the
dis
tr
ibut
ion
e
nti
ti
e
s
to
put
a
nd
upda
te
the
r
e
ne
wa
ble
e
ne
r
gy
g
r
id
c
onne
c
ted
c
ode
to
ge
t
t
he
maximum
output
powe
r
ge
ne
r
a
ted
f
r
om
it
with
out
a
ny
ba
d
im
pa
c
t
on
the
g
r
id.
E
gypt
is
one
of
the
c
ountr
i
e
s
that
diver
s
if
y
va
r
ious
tec
hniques
to
int
r
oduc
e
r
e
ne
wa
ble
e
ne
r
gy
tec
hnologi
e
s
a
nd
upda
te
the
gr
id
ge
ne
r
a
ti
o
n,
whe
r
e
,
a
big
plan
wa
s
made
to
s
pr
e
a
d
g
r
id
c
onn
e
c
ted
P
V
s
mall
s
c
a
ll
s
ys
tems
,
thi
s
plan
tar
ge
ted
one
thous
a
nd
r
oof
top
s
ys
tem
in
it
s
f
ir
s
t
pha
s
e
[
27
]
.
I
n
thi
s
p
a
pe
r
,
the
va
lues
of
the
s
olar
s
ys
tem
a
c
ti
ve
powe
r
,
r
e
a
c
ti
ve
powe
r
,
a
c
ti
ve
c
ur
r
e
nc
t,
r
e
a
c
ti
ve
c
ur
r
e
nt
a
nd
the
pe
r
c
e
ntage
of
tot
a
l
ha
r
moni
c
dis
tor
ti
on
(
T
HD
%
)
f
or
c
ur
r
e
nt
ha
d
be
e
n
c
he
c
ke
d.
F
inally,
we
c
onc
luded
that
th
e
r
e
is
a
n
im
pa
c
t
of
g
r
id
c
onne
c
ted
s
olar
e
ne
r
gy
ge
ne
r
a
ti
on
s
ys
tem
on
L
VR
T
c
a
pa
bil
it
y.
2.
RE
S
E
AR
CH
M
E
T
HO
D
2.
1.
3
-
P
H
ON
-
GRI
D
S
OL
AR
E
NE
RGY
S
YST
E
M
Fi
g
ur
e
1
r
e
pr
e
s
e
nts
3
-
PH
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
a
ti
on
s
ys
tem
c
onf
igu
r
a
ti
on,
the
P
V
s
ys
tem
pe
r
f
or
manc
e
wa
s
s
tudi
e
d
while
c
ontr
oll
e
d
it
by
c
onve
nti
ona
l
P
I
c
ontr
ol
with
va
r
ious
s
olar
ir
r
a
dianc
e
.
T
he
s
olar
s
ys
tem
c
ons
is
ts
of
s
olar
a
r
r
a
y
,
c
onve
r
ter
,
DC
c
onne
c
ti
on
,
inver
ter
a
nd
f
il
te
r
.
T
he
c
onve
r
ter
wa
s
a
djus
ted
with
maximum
powe
r
point
t
r
a
c
king
(
M
P
P
T
)
s
tr
a
tegy
to
e
ns
ur
e
that
the
P
V
s
ys
tem
ge
ne
r
a
tes
m
a
xim
um
powe
r
a
t
a
ll
ti
mes
.
a
nd
the
inver
ter
t
r
a
ns
f
e
r
s
the
p
r
oduc
e
d
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
powe
r
to
the
gr
id
a
nd
the
P
V
s
ys
tem
c
onne
c
ted
to
(
I
E
E
E
9
B
us
e
s
)
f
r
om
B
us
2
a
nd
F
igur
e
2
r
e
pr
e
s
e
nts
the
thr
e
e
-
pha
s
e
gr
id
.
T
a
ble
1
r
e
pr
e
s
e
nts
the
pa
r
a
mete
r
s
of
the
3
-
P
H
on
-
gr
id
s
olar
e
ne
r
gy
s
ys
tem.
F
igur
e
3
r
e
pr
e
s
e
nts
the
powe
r
c
ha
r
a
c
ter
is
ti
c
s
of
the
s
ola
r
a
r
r
a
y
F
igur
e
1.
3
-
P
H
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
a
ti
on
s
ys
tem
F
igur
e
2
.
(
I
E
E
E
9
B
us
e
s
)
thr
e
e
-
pha
s
e
gr
id
T
a
ble
1.
3
-
P
H
on
-
gr
id
s
olar
e
ne
r
gy
s
ys
tem
pa
r
a
mete
r
s
P
a
r
a
me
te
r
M
a
gni
tu
de
G
r
id
'
s
F
r
e
que
nc
y
50 H
z
S
w
it
c
hi
ng f
r
e
que
nc
y of
t
he
c
onve
r
te
r
a
nd t
he
i
nve
r
te
r
5
KHz
I
nduc
ta
nc
e
of
(
s
ol
a
r
s
ys
te
m r
e
a
c
to
r
-
f
il
te
r
r
e
a
c
to
r
)
(
0.1
–
10)
mH
C
a
pa
c
it
a
nc
e
of
(
s
ol
a
r
s
ys
te
m c
a
pa
c
it
or
-
D
C
c
onne
c
ti
on c
a
pa
c
it
or
)
(
100
–
200)
μ
F
Evaluation Warning : The document was created with Spire.PDF for Python.
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S
S
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:
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I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
488
-
499
490
T
he
model
c
ons
is
ts
of
20
modul
e
s
e
a
c
h
modul
e
a
c
ti
ve
powe
r
is
305
W
a
nd
the
modul
e
is
c
a
ll
e
d
s
unpowe
r
(
Ame
r
ica
n
b
r
a
nd
with
e
f
f
icie
nc
y
22
%
)
.
T
h
e
s
ol
a
r
a
r
r
a
y
c
on
ta
ins
tw
o
s
t
r
i
ngs
,
e
a
c
h
s
t
r
i
ng
c
ont
a
ins
te
n
m
o
du
les
in
s
e
r
i
e
s
c
on
ne
c
ti
on
a
n
d
the
t
wo
s
t
r
i
ngs
a
r
e
i
n
p
a
r
a
l
le
l
c
on
ne
c
t
io
n
w
i
th
to
ta
l
a
c
t
iv
e
p
owe
r
6
.
1
kW
.
T
a
ble
2
r
e
pr
e
s
e
nts
the
s
pe
c
if
ica
ti
ons
f
or
1
modul
e
of
the
s
olar
a
r
r
a
y.
F
igur
e
3.
P
owe
r
c
ha
r
a
c
ter
is
ti
c
s
of
the
s
olar
a
r
r
a
y
T
a
ble
2.
S
pe
c
if
ica
ti
ons
f
o
r
1
modul
e
o
f
the
s
olar
a
r
r
a
y
S
pe
c
if
ic
a
ti
ons
M
a
gni
tu
de
c
e
ll
s
c
onne
c
t
e
d i
n s
e
r
ie
s
96
vol
ta
ge
of
ma
xi
mum
pow
e
r
poi
nt
54 V
ol
t
c
ur
r
e
nt
of
ma
xi
mum
pow
e
r
poi
nt
5.6 Amp
ope
n c
ir
c
ui
t
vol
ta
ge
64 V
ol
t
s
hor
t
c
ir
c
ui
t
c
ur
r
e
nt
6 A
mp
2.
2
.
L
ow
volt
age
r
id
e
t
h
r
ou
gh
c
on
t
r
ol
s
t
r
at
e
gy
T
he
L
VR
T
c
ont
r
ol
s
tr
a
tegy
a
ppe
a
r
s
whe
n
the
vo
lt
a
ge
of
the
g
r
id
de
c
r
e
a
s
e
s
,
then
r
e
a
c
ti
ve
powe
r
inj
e
c
ts
in
the
gr
id
s
ide
a
s
a
r
e
a
c
t
of
the
L
VR
T
c
on
tr
ol
s
tr
a
tegy,
the
r
e
a
c
ti
ve
c
ur
r
e
nt
(
I
d
)
r
e
quir
e
d
f
o
r
i
njec
ti
ng
r
e
a
c
ti
ve
powe
r
int
o
the
gr
id
s
ide
is
de
ter
mi
ne
d
a
c
c
or
ding
to
the
L
VR
T
r
e
quir
e
ment
de
pe
nding
on
r
a
te
of
the
de
c
r
e
a
s
e
d
volt
a
ge
.
I
n
a
ddit
ion
,
maximum
powe
r
tr
a
ns
f
e
r
s
f
r
o
m
s
olar
a
r
r
a
ys
to
the
gr
id
dur
ing
the
volt
a
ge
d
e
c
r
e
a
s
i
n
g
p
e
r
i
o
d
a
n
d
t
h
e
a
c
t
i
v
e
c
u
r
r
e
n
t
w
h
i
c
h
r
e
s
p
o
n
s
i
b
l
e
t
o
p
r
o
d
u
c
e
m
a
x
i
m
u
m
a
c
t
i
v
e
p
o
w
e
r
i
s
c
a
l
c
u
l
a
t
e
d
b
y
(
1
)
.
I
q
=
√
(
I
2
r
a
t
i
ng
−
I
2
d
)
(
1)
W
he
r
e
:
(
I
d
)
is
the
r
e
a
c
ti
ve
c
u
r
r
e
nt
of
the
s
olar
s
ys
tem
,
(
I
q
)
is
a
c
ti
ve
c
ur
r
e
nt
o
f
the
s
olar
s
ys
tem
a
nd
I
r
a
t
i
n
g
is
the
r
a
ted
c
ur
r
e
nt
ge
ne
r
a
ted
by
s
olar
s
ys
tem.
2.
2
.
I
n
ve
r
t
e
r
c
on
t
r
ol
T
he
c
ontr
ol
of
the
inver
ter
c
ons
is
ts
of
two
c
yc
les
(
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nt
–
DC
volt
a
ge
)
.
T
he
f
ir
s
t
one
is
the
int
e
r
na
l
c
yc
le
that
c
ontr
ols
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nts
a
mount
a
s
s
hown
in
F
ig
u
r
e
4
.
T
h
e
s
e
c
ond
one
is
the
e
xter
na
l
c
yc
le
that
c
ontr
ols
DC
vol
tage
o
f
the
inve
r
ter
a
s
s
hown
in
F
ig
ur
e
5.
F
igur
e
4.
Ac
ti
ve
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nt
c
ontr
oll
e
r
F
igur
e
5
.
DC
volt
a
ge
c
ont
r
oll
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mpac
t
of
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
ati
on
s
y
s
te
m
on
…
(
M
ohamm
ad
A
hmad
Shaw
qi
)
491
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ONS
M
a
tl
a
b
s
im
ulation
s
of
twa
r
e
ha
s
b
e
e
n
us
e
d
in
thi
s
pa
pe
r
a
s
s
hown
in
F
ig
ur
e
6,
T
he
s
im
ulation
wa
s
done
withi
n
c
ha
nge
s
of
the
s
olar
s
y
s
tem
s
un
ir
r
a
dianc
e
to
tes
t
the
s
y
s
tem
r
e
s
pons
e
,
K
P
&
K
i
of
P
I
c
ur
r
e
nt
r
e
gulator
a
r
e
9.
7
a
nd
2405
r
e
s
pe
c
ti
ve
ly,
K
P
&
K
i
of
P
I
DC
volt
a
ge
c
ont
r
oll
e
r
a
r
e
7
a
nd
800
r
e
s
pe
c
ti
ve
ly,
DC
volt
a
ge
is
620
V,
an
a
lys
is
o
f
t
he
r
e
s
ul
ts
wa
s
ma
de
b
y
c
h
a
n
gi
ng
the
no
mi
na
l
v
ol
ta
ge
o
f
t
he
P
V
s
y
s
tem
wi
th
i
n
(0
-
3
)
s
e
c
o
nd
a
n
d
t
he
s
t
ud
yi
ng
s
t
r
a
te
gy
i
n
th
is
s
e
c
t
ion
is
t
o
f
o
l
lo
w
u
p
th
e
o
ut
pu
t
a
c
ti
ve
a
n
d
r
e
a
c
t
iv
e
powe
r
,
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
c
u
r
r
e
nt
a
n
d
(
T
HD
%
f
o
r
c
u
r
r
e
nt
)
c
u
r
v
e
s
w
h
il
e
c
h
a
n
gi
ng
(
de
c
r
e
a
s
i
ng
)
t
he
v
ol
ta
ge
o
f
t
he
th
r
e
e
-
ph
a
s
e
g
r
id
.
F
i
gu
r
e
7
s
ho
ws
th
e
i
r
r
a
d
ia
nc
e
o
f
o
u
r
s
im
ul
a
t
io
n
,
wh
e
r
e
i
t
c
ha
ng
e
s
f
r
o
m
1
00
0
W
/
m
2
t
o
50
0
W
/
m
2
a
t
then
ba
c
k
a
ga
in
to
1000
W
/m
2
.
F
igur
e
6
.
On
-
gr
id
s
olar
e
ne
r
gy
s
ys
tem
M
AT
L
AB
s
im
ulation
F
ig
ur
e
7
.
Us
e
d
ir
r
a
dianc
e
(
w/
m
2
)
3.
1
.
Ou
t
p
u
t
r
e
s
u
lt
s
at
3
-
P
H
volt
age
e
q
u
al
1
P
.
U
F
igur
e
s
8,
9,
10
a
nd
11
s
hows
the
output
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
powe
r
,
output
a
c
ti
ve
c
ur
r
e
nt
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nt
a
nd
(
T
HD
%
f
or
c
ur
r
e
nt)
of
the
on
-
gr
id
s
olar
s
ys
tem.
I
t
wa
s
noted
that
magnitud
e
of
the
output
a
c
ti
ve
powe
r
ge
ne
r
a
ted
f
r
om
the
s
olar
s
ys
tem
a
t
maximum
va
lue
of
ir
r
a
dianc
e
is
5
.
9
kW
a
nd
the
output
r
e
a
c
ti
ve
powe
r
is
z
e
r
o
KV
AR
{r
e
a
c
ti
ve
c
ur
r
e
nt
(
I
d
)
is
z
e
r
o}
a
nd
(
T
HD
%
f
or
c
u
r
r
e
nt)
withi
n
li
mi
t
(
les
s
than
0.
5%
)
.
F
igur
e
8.
Output
a
c
ti
ve
powe
r
(
k
W)
Output
a
c
ti
ve
powe
r
(
KW
)
T
im
e
(
S
e
c
.
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
488
-
499
492
F
igur
e
9.
output
r
e
a
c
ti
ve
powe
r
(
KV
AR
)
F
igur
e
10.
Output
I
q
(
a
c
ti
ve
c
ur
r
e
nt)
&
I
d
(
r
e
a
c
ti
ve
c
ur
r
e
nt
F
igur
e
11.
T
HD
%
f
or
c
ur
r
e
nt
3.
2.
Ou
t
p
u
t
r
e
s
u
lt
s
at
3
-
P
H
volt
age
e
q
u
al
0.
8
P
.
U
F
igur
e
s
12,
13
,
14
a
nd
15
s
hows
the
output
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
powe
r
,
output
a
c
ti
ve
c
u
r
r
e
nt
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nt
a
nd
(
T
HD
%
f
or
c
ur
r
e
nt)
of
the
on
-
gr
id
s
olar
s
ys
tem.
I
t
wa
s
noted
that
magnitud
e
of
the
output
a
c
ti
ve
powe
r
ge
ne
r
a
ted
f
r
om
the
s
olar
s
ys
tem
a
t
maximum
va
lue
of
ir
r
a
dianc
e
is
5
.
9
kW
a
nd
the
output
r
e
a
c
ti
ve
c
ur
r
e
nt
(
I
d
)
incr
e
a
s
e
d
c
ompar
ing
to
the
pr
e
vious
c
a
s
e
whic
h
lea
d
t
o
a
n
incr
e
a
s
e
i
n
output
r
e
a
c
ti
ve
powe
r
c
ur
ve
c
ompar
ing
to
the
pr
e
vious
c
a
s
e
,
a
nd
(
T
HD
%
f
or
c
ur
r
e
nt
)
withi
n
li
mi
t
(
les
s
than
0.
5%
)
.
Output
r
e
a
c
ti
ve
powe
r
(
KV
AR
)
T
im
e
(
S
e
c
.
)
Output
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nt
(
Amp.
)
T
im
e
(
S
e
c
.
)
T
H
D
%
T
H
D
%
w
i
t
h
i
n
l
i
m
i
t
(l
es
s
t
h
a
n
0
.
5
%
)
T
i
m
e
(
S
e
c
.
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mpac
t
of
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
ati
on
s
y
s
te
m
on
…
(
M
ohamm
ad
A
hmad
Shaw
qi
)
493
F
igur
e
12.
Output
a
c
ti
ve
powe
r
F
igur
e
13.
Output
r
e
a
c
ti
ve
powe
r
F
igur
e
14.
Output
I
q
(
a
c
ti
ve
c
ur
r
e
nt)
&
I
d
(
r
e
a
c
ti
ve
c
ur
r
e
nt)
Output
a
c
ti
ve
powe
r
(K
W
)
T
im
e
(
S
e
c
.
)
I
nc
r
e
a
s
in
g
in
t
he
out
put
r
e
a
c
ti
ve
pow
e
r
c
ompa
r
in
g
to
t
he
pr
e
vi
ous
c
a
s
e
O
ut
put
re
a
c
t
i
ve
pow
e
r
(K
V
A
R)
T
i
m
e
(S
e
c
.
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
488
-
499
494
F
igur
e
15.
T
HD
%
f
or
c
ur
r
e
nt
3.
3.
Ou
t
p
u
t
r
e
s
u
lt
s
at
3
-
P
H
volt
age
e
q
u
al
0.
5
P
.
U.
F
igur
e
s
16,
17
,
18
a
nd
19
s
hows
the
output
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
powe
r
,
output
a
c
ti
ve
c
u
r
r
e
nt
a
nd
r
e
a
c
ti
ve
c
ur
r
e
nt
a
nd
(
T
HD
%
f
or
c
ur
r
e
nt)
of
the
on
-
gr
id
s
olar
s
ys
tem.
I
t
wa
s
noted
that
magnitud
e
of
the
output
a
c
ti
ve
powe
r
ge
ne
r
a
ted
f
r
om
the
s
olar
s
ys
tem
a
t
maximum
va
lue
of
ir
r
a
dianc
e
is
mor
e
than
the
pr
e
vious
c
a
s
e
s
6
kW
a
nd
the
out
r
e
a
c
ti
ve
c
ur
r
e
nt
(
I
d
)
is
incr
e
a
s
e
mor
e
than
the
pr
e
vious
c
a
s
e
too,
wh
ich
lea
d
to
a
n
incr
e
a
s
e
in
the
outpu
t
r
e
a
c
ti
ve
powe
r
c
ur
ve
c
ompar
ing
to
the
pr
e
vious
c
a
s
e
,
a
n
d
(
T
HD
%
f
o
r
c
ur
r
e
nt)
withi
n
li
mi
t
(
0
.
5%
)
.
F
igur
e
16.
Output
a
c
ti
ve
powe
r
F
igur
e
17.
Output
r
e
a
c
ti
ve
powe
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mpac
t
of
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
ati
on
s
y
s
te
m
on
…
(
M
ohamm
ad
A
hmad
Shaw
qi
)
495
F
igur
e
18.
Output
I
q
(
a
c
ti
ve
c
ur
r
e
nt)
&
I
d
(
r
e
a
c
ti
ve
c
ur
r
e
nt)
F
igur
e
19.
T
HD
%
f
or
c
ur
r
e
nt
3.
4.
Ou
t
p
u
t
r
e
s
u
lt
s
at
3
-
P
H
volt
age
e
q
u
al
0.
47
P
.
U.
F
igur
e
s
20
a
nd
21
s
hows
the
output
a
c
ti
ve
pow
e
r
a
nd
(
T
HD
%
f
o
r
c
ur
r
e
nt)
o
f
the
on
-
gr
id
s
olar
s
ys
tem.
I
t
wa
s
noted
that
magnitude
o
f
the
output
a
c
ti
ve
powe
r
a
t
maximum
va
lue
of
ir
r
a
dianc
e
de
c
r
e
a
s
e
d
to
5.
6
kW
a
nd
the
(
T
HD
%
f
o
r
c
ur
r
e
nt)
is
(
0.
6
%
)
,
w
hich
is
mor
e
than
the
a
c
c
e
ptable
li
mi
t
.
F
igur
e
20.
Output
a
c
ti
ve
powe
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
488
-
499
496
F
igur
e
21.
T
HD
%
f
or
c
ur
r
e
nt
3.
5.
Ou
t
p
u
t
r
e
s
u
lt
a
t
3
-
P
H
vo
lt
age
e
q
u
a
l
1
P
.
U.
b
y
u
s
in
g
an
o
t
h
e
r
c
on
t
r
ol
m
e
t
h
od
whi
c
h
is
p
r
op
or
t
ion
al
in
t
e
gr
al
-
g
e
n
e
t
ic
a
lgori
t
h
m
(
P
I
-
GA)
I
n
t
h
i
s
s
e
c
t
i
o
n
,
a
n
o
t
h
e
r
c
o
n
t
r
o
l
m
e
t
h
o
d
w
a
s
a
p
p
l
i
e
d
,
w
h
i
c
h
i
s
p
r
o
p
o
r
t
i
o
n
a
l
i
n
t
e
g
r
a
l
-
g
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
(
P
I
-
G
A
)
,
a
n
d
T
a
b
l
e
3
s
h
o
w
s
t
h
e
v
a
r
i
a
b
l
e
s
u
s
e
d
i
n
t
h
i
s
c
o
n
t
r
o
l
m
e
t
h
o
d
.
As
s
hown
in
F
igur
e
2
2
,
the
f
it
ne
s
s
f
unc
ti
on
of
the
pr
opor
t
ional
int
e
gr
a
l
-
ge
ne
ti
c
a
l
gor
it
hm
(
P
I
-
GA
)
s
e
lec
ted
to
a
c
hieve
maximum
output
a
c
ti
ve
powe
r
ge
ne
r
a
ted
f
r
om
the
P
V
s
ys
tem
,
whe
r
e
the
f
it
ne
s
s
f
unc
ti
on
is
:
E
r
r
o
r
=
P
owe
r
r
e
f
–
P
owe
r
PV
(
2
)
whe
r
e
:
P
owe
r
r
e
f
=
tot
a
l
a
c
ti
ve
powe
r
o
f
the
P
V
a
r
r
a
y
,
whic
h
is
6
.
1
kW
.
P
owe
r
PV
=
maximum
outp
ut
a
c
ti
ve
powe
r
ge
ne
r
a
ted
f
r
om
the
PV
s
ys
tem
.
E
r
r
or
is
c
l
os
e
s
t
va
lue
to
z
e
r
o
.
F
igur
e
23
r
e
pr
e
s
e
nts
the
F
lo
w
c
ha
r
t
o
f
pr
opor
ti
ona
l
int
e
gr
a
l
-
ge
ne
ti
c
a
lgor
it
hm
c
ontr
ol
m
e
thod
(
P
I
-
GA)
.
F
igu
r
e
24
pr
e
s
e
nts
the
output
a
c
ti
v
e
powe
r
of
the
on
-
gr
id
s
olar
s
ys
tem.
I
t
wa
s
no
ted
that
by
us
ing
(
P
I
-
GA
)
,
the
va
lue
of
the
output
a
c
ti
ve
powe
r
ge
ne
r
a
ted
f
r
om
the
s
olar
s
ys
tem
a
t
maximum
ir
r
a
dianc
e
va
lue
is
incr
e
a
s
e
d
to
6.
03
kW
(
highe
r
than
the
va
lue
whic
h
wa
s
a
c
hieve
d
by
us
ing
c
onve
nti
ona
l
P
I
c
ont
r
oll
e
r
a
t
3
-
P
H
volt
a
ge
e
qua
l
1P
.
U)
.
T
a
ble
3.
Va
r
iable
s
us
e
d
in
the
(
P
I
-
GA
)
V
a
r
ia
bl
e
s
M
a
gni
tu
de
P
opul
a
ti
on
14
P
r
oba
bi
li
ty
0.85
N
umbe
r
of
va
r
ia
bl
e
s
4
B
it
s
8
N
o. of
ge
ne
r
a
ti
ons
6
K
P
r
a
te
of
t
he
c
ur
r
e
nt
r
e
gul
a
to
r
K
i
r
a
te
of
t
he
c
ur
r
e
nt
r
e
gul
a
to
r
[
7 12]
[
2350 2500]
K
P
r
a
te
of
th
e
D
C
vol
ta
ge
c
ont
r
ol
le
r
K
i
r
a
te
of
t
he
D
C
vol
ta
ge
c
ont
r
ol
le
r
[
6 11]
[
500 900]
R
a
te
of
mut
a
ti
on
0.08
P
ow
e
r
–
r
e
f
.
(
r
e
f
e
r
e
nc
e
pow
e
r
)
6.1
kW
F
igur
e
22.
G
e
ne
ti
c
a
lgor
it
h
m
f
it
ne
s
s
f
unc
ti
on
t
o
a
c
hieve
ma
xim
um
output
a
c
ti
ve
powe
r
f
r
om
the
P
V
s
ys
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mpac
t
of
on
-
gr
id
s
olar
e
ne
r
gy
ge
ne
r
ati
on
s
y
s
te
m
on
…
(
M
ohamm
ad
A
hmad
Shaw
qi
)
497
F
igur
e
23.
F
low
c
ha
r
t
o
f
p
r
opo
r
ti
ona
l
i
ntegr
a
l
-
g
e
ne
ti
c
a
lgor
it
hm
c
ontr
ol
method
(
P
I
-
GA)
F
igur
e
24.
Ac
ti
ve
powe
r
3.
6.
O
u
t
p
u
t
r
e
s
u
lt
a
t
3
-
P
H
vo
lt
age
(
0.
8
P
.
U.
)
b
y
u
s
in
g
(
P
I
-
GA)
F
igur
e
25
p
r
e
s
e
nts
the
output
a
c
ti
ve
powe
r
of
th
e
on
-
gr
id
s
olar
s
ys
tem
.
I
t
w
a
s
n
o
t
e
d
t
h
a
t
b
y
u
s
i
n
g
(
P
I
-
G
A
)
,
t
h
e
v
a
l
u
e
o
f
t
h
e
o
u
t
p
u
t
a
c
t
i
v
e
p
o
w
e
r
g
e
n
e
r
a
t
e
d
f
r
o
m
t
h
e
s
o
l
a
r
s
y
s
t
e
m
a
t
m
a
x
i
m
u
m
i
r
r
a
d
i
a
n
c
e
v
a
l
u
e
i
s
i
n
c
r
e
a
s
e
d
t
o
6
.
0
5
k
W
(
h
i
g
h
e
r
t
h
a
n
t
h
e
v
a
l
u
e
w
h
i
c
h
w
a
s
a
c
h
i
e
v
e
d
b
y
u
s
i
n
g
c
o
n
v
e
n
t
i
o
n
a
l
P
I
c
o
n
t
r
o
l
l
e
r
a
t
3
-
P
H
v
o
l
t
a
g
e
e
q
u
a
l
0
.
8
P
.
U
.
)
.
F
igur
e
25.
Ac
ti
ve
powe
r
Evaluation Warning : The document was created with Spire.PDF for Python.