I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
1
6
,
No
.
2
,
A
p
r
il
20
2
6
,
p
p
.
651
~
662
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
1
6
i
2
.
pp
6
5
1
-
6
6
2
651
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
Sing
le
-
sta
g
e sing
l
e
-
pha
se g
rid
co
nn
ecte
d i
nv
erte
r
pro
po
rtiona
l
reso
na
nt
a
nd ma
x
imum
power
poin
t
tracki
ng
contro
l
lers for
enha
nced p
ho
tov
o
ltaic sy
stem per
f
o
rma
nce
Abdela
ziz
K
a
bb
a
,
Abdella
h
L
a
s
s
io
ui,
H
a
s
s
a
n
E
l F
a
dil
A
S
E
-
La
b
o
r
a
t
o
r
y
,
EN
S
A
,
I
b
n
To
f
a
i
l
U
n
i
v
e
r
s
i
t
y
,
K
e
n
i
t
r
a
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
l 3
1
,
2
0
2
4
R
ev
is
ed
J
an
3
,
2
0
2
6
Acc
ep
ted
J
an
1
6
,
2
0
2
6
Th
e
p
a
p
e
r
d
e
v
e
l
o
p
s
a
c
u
rre
n
t
c
o
n
tro
l
m
e
th
o
d
o
lo
g
y
f
o
r
a
sin
g
le
-
p
h
a
se
g
rid
-
ti
e
d
DC/AC
in
v
e
rter
a
p
p
li
e
d
t
o
p
h
o
t
o
v
o
lt
a
ic
(P
V)
e
n
e
rg
y
c
o
n
v
e
rsi
o
n
sy
ste
m
s.
It
in
c
o
r
p
o
ra
tes
a
n
a
lg
o
rit
h
m
fo
r
fin
d
in
g
t
h
e
o
p
ti
m
a
l
v
o
lt
a
g
e
a
n
d
c
u
rre
n
t
p
o
in
ts t
o
o
b
tai
n
m
a
x
imu
m
p
o
we
r
p
o
in
t
trac
k
in
g
(M
P
P
T),
t
h
e
p
u
rp
o
se
o
f
wh
ich
is
to
e
n
s
u
re
b
e
tt
e
r
e
n
e
rg
y
e
x
trac
ti
o
n
.
Th
is
is
fo
ll
o
we
d
b
y
a
p
ro
p
o
rti
o
n
a
l
-
i
n
teg
ra
l
(P
I)
c
o
n
tro
ll
e
r
to
g
e
n
e
ra
te
th
e
re
fe
re
n
c
e
c
u
rre
n
t.
In
a
d
d
it
i
o
n
,
a
p
r
o
p
o
rti
o
n
a
l
-
re
so
n
a
n
t
(P
R)
c
o
n
tr
o
ll
e
r
is
u
se
d
to
i
n
fin
it
e
l
y
a
m
p
li
f
y
th
e
fu
n
d
a
m
e
n
tal
fre
q
u
e
n
c
y
sig
n
a
l,
wh
ich
m
a
k
e
s
it
p
o
ss
ib
le
to
e
li
m
in
a
te
th
e
ste
a
d
y
-
sta
te
e
rro
r.
Th
e
a
n
a
ly
ti
c
a
l
fo
u
n
d
a
ti
o
n
s
o
f
th
e
P
R
c
o
n
t
ro
ll
e
r
a
re
p
re
se
n
ted
a
n
d
su
b
sta
n
ti
a
ted
t
h
r
o
u
g
h
sim
u
lati
o
n
stu
d
ies
imp
le
m
e
n
ted
in
M
ATLAB/S
imu
li
n
k
.
Th
e
p
h
a
se
-
lo
c
k
e
d
lo
o
p
(
P
LL
)
is
u
se
d
fo
r
sy
n
c
h
r
o
n
iza
ti
o
n
,
e
n
a
b
l
in
g
a
c
c
u
ra
te
p
h
a
se
d
e
tec
ti
o
n
o
f
th
e
g
ri
d
v
o
lt
a
g
e
f
o
r
e
ffe
c
ti
v
e
p
o
we
r
in
jec
ti
o
n
.
An
L
CL
fil
ter
is
a
lso
imp
lem
e
n
ted
b
e
twe
e
n
th
e
in
v
e
rter
a
n
d
th
e
g
rid
.
T
h
e
re
su
lt
s
p
ro
v
id
e
d
b
y
t
h
e
d
e
d
ica
ted
s
o
ftwa
re
c
o
n
firm
th
e
e
ffe
c
t
iv
e
n
e
ss
o
f
t
h
e
p
r
o
p
o
se
d
c
o
n
tro
l
sy
ste
m
.
K
ey
w
o
r
d
s
:
L
y
ap
u
n
o
v
s
tab
ilit
y
Ma
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
er
Ph
ase
lo
ck
ed
lo
o
p
Ph
o
to
v
o
ltaic
Po
wer
f
ac
to
r
co
n
tr
o
ller
Pro
p
o
r
tio
n
al
r
eso
n
an
t c
o
n
tr
o
ll
er
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ab
d
elaz
iz
Kab
b
a
ASE
-
L
ab
o
r
ato
r
y
,
E
NSA,
I
b
n
T
o
f
ail
Un
iv
er
s
ity
4
4
L
o
t
Alo
th
m
an
ia
T
r
3
Me
k
n
es,
5
0
0
0
0
,
Mo
r
o
cc
o
E
m
ail: k
ab
b
az
iz.
7
0
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
R
en
ewa
b
le
en
er
g
ies
r
ep
r
esen
t
a
v
iab
le
p
ath
way
to
war
d
lo
wer
in
g
p
o
llu
tio
n
lev
els.
I
n
p
a
r
ticu
lar
,
I
n
r
ec
en
t
y
ea
r
s
,
p
h
o
t
o
v
o
ltaic
(
P
V)
s
o
lar
en
er
g
y
h
as
u
n
d
e
r
g
o
n
e
s
u
b
s
tan
tial
g
r
o
wth
wo
r
l
d
wid
e,
as
it
is
an
in
ex
h
au
s
tib
le,
en
v
ir
o
n
m
e
n
tally
-
f
r
ien
d
ly
an
d
s
ilen
t
s
o
u
r
ce
[
1
]
,
[
2
]
.
T
h
e
r
a
p
id
d
ev
elo
p
m
e
n
t
o
f
s
o
lar
p
o
wer
is
g
r
ad
u
ally
b
ein
g
im
p
lem
e
n
ted
in
s
m
all
-
s
ca
le
in
s
tallatio
n
s
co
n
n
ec
ted
to
th
e
lo
w
-
v
o
ltag
e
(
L
V)
g
r
id
[
3
]
,
[
4
]
to
s
o
lar
f
ar
m
in
s
tallatio
n
s
d
ir
ec
tly
co
n
n
ec
te
d
to
th
e
m
ed
iu
m
-
v
o
ltag
e
(
MV
)
g
r
i
d
.
Sev
er
al
s
o
l
u
tio
n
s
ar
e
av
ailab
le
to
in
cr
ea
s
e
elec
tr
icity
p
r
o
d
u
cti
o
n
ca
p
ac
ity
,
i
n
clu
d
in
g
th
e
p
er
i
o
d
ic
r
e
m
o
v
al
o
f
d
u
s
t f
r
o
m
p
h
o
to
v
o
ltaic
m
o
d
u
les.
Stu
d
y
[
5
]
p
r
esen
ts
th
e
d
esig
n
an
d
d
e
v
elo
p
m
e
n
t o
f
a
r
o
b
o
t f
o
r
clea
n
in
g
p
h
o
to
v
o
ltaic
m
o
d
u
l
es.
Ho
wev
er
,
th
e
lar
g
e
-
s
ca
le
in
te
g
r
atio
n
o
f
PV
s
o
u
r
ce
s
in
to
th
e
g
r
id
in
tr
o
d
u
ce
s
ad
d
itio
n
al
c
o
m
p
lex
ities
[
6
]
a
n
d
s
o
m
e
ch
alle
n
g
es
th
at
n
ee
d
to
b
e
o
v
er
c
o
m
e
i
n
o
r
d
er
to
en
s
u
r
e
th
e
s
m
o
o
th
in
te
g
r
atio
n
o
f
s
o
lar
p
o
wer
o
n
p
o
wer
g
r
i
d
s
[
7
]
.
T
h
e
m
ain
p
r
o
b
lem
lies
in
m
an
ag
i
n
g
th
e
in
ter
m
itten
cy
o
f
s
o
lar
p
o
wer
g
en
er
atio
n
,
wh
ich
d
ep
en
d
s
o
n
ex
ter
n
al
f
ac
t
o
r
s
s
u
ch
as
in
s
o
latio
n
an
d
tem
p
e
r
a
tu
r
e,
in
f
lu
e
n
cin
g
th
e
m
o
d
if
ica
tio
n
o
f
p
o
wer
f
lo
ws
(
b
id
ir
ec
tio
n
al)
,
o
n
th
e
v
o
ltag
e
p
lan
e,
o
n
th
e
p
r
o
tectio
n
p
l
an
e.
Gr
id
s
tab
ilit
y
ca
n
b
e
af
f
ec
ted
b
y
h
ig
h
s
o
la
r
ir
r
ad
iatio
n
o
r
en
er
g
y
s
h
o
r
tag
es,
wh
ich
ca
n
d
is
r
u
p
t
t
h
e
f
r
eq
u
en
cy
a
n
d
v
o
ltag
e
o
f
th
e
p
o
wer
g
r
i
d
.
T
h
ese
f
lu
ctu
atio
n
s
n
ee
d
t
o
b
e
co
n
tr
o
lled
to
a
v
o
id
o
u
ta
g
es
o
r
d
am
a
g
e
to
n
etwo
r
k
eq
u
ip
m
e
n
t,
wh
i
le
co
m
p
ly
i
n
g
with
tech
n
ical
s
tan
d
ar
d
s
[
8
]
.
T
h
e
o
p
er
atin
g
co
n
d
itio
n
s
d
em
an
d
ed
b
y
r
e
g
u
latio
n
d
e
v
ices,
s
u
ch
as
in
tellig
en
t
in
v
er
ter
s
an
d
e
n
er
g
y
s
to
r
a
g
e
s
y
s
tem
s
(
b
atter
ies),
ar
e
n
ec
ess
a
r
y
to
ad
j
u
s
t
en
er
g
y
p
r
o
d
u
ctio
n
an
d
in
jectio
n
in
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
5
1
-
662
652
th
e
p
o
wer
g
r
id
ac
co
r
d
in
g
to
n
ee
d
s
,
wh
ile
g
u
ar
a
n
teein
g
p
o
wer
q
u
ality
.
T
h
is
o
b
s
er
v
a
tio
n
is
p
r
o
m
p
tin
g
r
esear
ch
er
s
to
p
r
esen
t
n
ew
r
esear
ch
an
d
tec
h
n
o
l
o
g
ical
s
o
lu
tio
n
s
aim
ed
at
s
ec
u
r
e
,
r
eli
ab
le,
an
d
ef
f
icien
t
n
etwo
r
k
co
n
n
ec
tiv
ity
.
I
n
th
e
liter
atu
r
e,
in
g
r
id
-
co
n
n
ec
ted
m
o
d
e
with
a
s
in
g
le
p
h
ase
o
r
m
o
r
e,
a
PV
s
y
s
tem
ca
n
b
e
d
iv
id
ed
in
to
two
s
u
b
s
y
s
tem
s
:
a
p
o
wer
s
u
b
s
y
s
tem
co
n
s
is
tin
g
o
f
PV
p
an
els,
DC
/DC
an
d
DC
/AC
c
o
n
v
er
ter
s
f
o
llo
wed
b
y
an
in
ter
m
ed
iate
f
ilter
[
9
]
wh
er
e
th
e
DC
/A
C
in
v
er
ter
,
is
r
eg
ar
d
ed
as
ce
n
tr
al
co
m
p
o
n
e
n
t
d
u
e
to
its
cr
u
cial
r
o
le
in
g
r
id
-
co
n
n
ec
ted
o
p
er
ati
o
n
[
1
0
]
a
n
d
a
m
a
x
im
u
m
p
o
w
er
p
o
in
t
tr
ac
k
in
g
(
MPPT)
co
n
tr
o
l
s
u
b
s
y
s
tem
an
d
o
th
er
c
o
n
v
e
r
ter
c
o
n
tr
o
l
b
lo
c
k
s
u
s
ed
.
I
n
g
en
er
al,
th
e
f
ir
s
t
s
u
b
s
y
s
tem
is
co
n
tr
o
lled
to
h
av
e
h
ig
h
p
o
wer
,
wh
atev
er
th
e
wea
th
er
co
n
d
iti
o
n
s
,
an
d
en
s
u
r
e
p
o
wer
f
ac
to
r
co
r
r
ec
tio
n
(
PFC
)
to
r
ed
u
c
e
cu
r
r
en
t
h
ar
m
o
n
ics
in
co
n
v
er
ter
s
an
d
o
p
tim
ize
ac
tiv
e
p
o
wer
ex
c
h
an
g
e
d
b
etwe
en
en
er
g
y
s
o
u
r
ce
an
d
g
r
id
[
1
1
]
.
I
n
[
1
2
]
,
n
u
m
er
o
u
s
co
n
tr
o
l m
eth
o
d
s
a
r
e
p
r
o
p
o
s
ed
.
I
n
d
ee
d
,
a
p
ass
iv
e
tech
n
iq
u
e
is
s
tu
d
ied
in
[
1
3
]
,
w
h
ile
co
n
tr
o
ller
s
(
PR
)
an
d
m
u
lti
r
eso
n
an
t
c
o
n
tr
o
l
(
MRC
)
h
av
e
b
ee
n
d
is
cu
s
s
ed
in
[
1
4
]
.
I
n
ad
d
itio
n
to
class
ical
m
eth
o
d
s
,
th
er
e
a
r
e
co
n
tr
o
l
tech
n
iq
u
es
th
at
d
o
n
o
t
r
eq
u
ir
e
m
ath
em
atica
l
m
o
d
els,
s
u
ch
as
g
en
etic
alg
o
r
ith
m
s
,
f
u
zz
y
lo
g
ic
an
d
ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
.
T
y
p
ically
,
cu
r
r
en
t
c
o
n
tr
o
l
is
co
m
m
o
n
ly
ad
o
p
te
d
b
ec
a
u
s
e
it
o
f
f
er
s
ex
ce
llen
t
d
y
n
am
ic
r
esp
o
n
s
e
[
1
5
]
,
[
1
6
]
as
well
as
in
teg
r
ated
o
v
er
cu
r
r
en
t
p
r
o
tectio
n
.
Pre
d
ictiv
e
co
n
tr
o
l
r
el
ies
o
n
an
ac
cu
r
ate
s
y
s
tem
m
o
d
el
an
d
r
ef
e
r
en
ce
cu
r
r
en
t
p
r
ed
ictio
n
[
1
7
]
.
Hy
s
ter
esis
co
n
tr
o
l,
th
o
u
g
h
s
im
p
le
an
d
r
o
b
u
s
t,
s
u
f
f
er
s
f
r
o
m
v
ar
iab
le
s
witch
in
g
r
ates
,
d
o
u
b
led
cu
r
r
en
t
er
r
o
r
s
,
a
n
d
lim
ited
h
ig
h
-
f
r
eq
u
en
cy
o
p
er
atio
n
[
1
8
]
.
Var
io
u
s
MPPT
m
eth
o
d
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
[
1
9
]
.
I
n
s
tu
d
y
[
2
0
]
,
a
r
ec
alib
r
ated
f
r
ac
tio
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
-
d
er
iv
ativ
e
(
FOPID)
co
m
p
en
s
a
to
r
co
n
tr
o
llin
g
th
e
o
u
tp
u
t
v
o
lt
ag
e
er
r
o
r
o
f
an
in
ter
leav
e
d
b
u
ck
–
b
o
o
s
t
co
n
v
er
ter
is
ap
p
lied
f
o
r
MPPT,
wh
ile
[
2
1
]
u
tili
ze
s
a
n
o
n
-
in
v
er
tin
g
b
u
ck
–
b
o
o
s
t
co
n
v
e
r
ter
with
G
GSMC
f
ee
d
b
ac
k
to
tr
ac
k
an
f
ee
d
f
o
r
wa
r
d
n
eu
r
al
n
etwo
r
k
-
g
en
e
r
ated
v
o
ltag
e
r
ef
er
en
ce
a
n
d
e
x
tr
ac
t
th
e
PV
s
y
s
tem
’
s
m
ax
im
u
m
p
o
wer
.
A
s
im
p
le
an
d
c
o
m
m
o
n
ly
u
s
ed
ap
p
r
o
ac
h
is
th
e
p
er
t
u
r
b
atio
n
an
d
o
b
s
er
v
atio
n
(
P&
O
)
m
eth
o
d
,
w
h
ich
in
v
o
lv
es
p
er
t
u
r
b
in
g
th
e
o
p
er
at
in
g
v
o
ltag
e
o
f
t
h
e
p
h
o
to
v
o
ltaic
ar
r
ay
,
ca
u
s
in
g
th
e
s
y
s
tem
to
o
s
cillate
ar
o
u
n
d
th
e
o
p
tim
al
p
o
wer
.
T
h
e
m
ag
n
it
u
d
e
o
f
th
ese
o
s
cillatio
n
s
ca
n
b
e
m
in
im
ized
b
y
r
ed
u
ci
n
g
th
e
d
i
s
tu
r
b
an
ce
s
tep
s
ize,
en
ab
lin
g
t
h
e
r
e
f
er
en
ce
v
o
ltag
e
∗
to
b
e
ac
c
u
r
ately
d
eter
m
in
e
d
d
u
r
in
g
p
er
io
d
ic
o
p
er
atio
n
.
Ad
d
itio
n
ally
,
a
n
H∞
ap
p
r
o
ac
h
was
d
ev
elo
p
e
d
i
n
[
2
2
]
f
o
r
a
two
-
s
tag
e
l
o
w
-
v
o
l
tag
e
to
p
o
lo
g
y
,
ig
n
o
r
in
g
t
h
e
P
V
ar
r
ay
’
s
n
o
n
lin
ea
r
P(V
)
ch
ar
ac
ter
is
tic.
T
h
e
s
am
e
lim
itatio
n
o
cc
u
r
s
in
[
2
3
]
,
w
h
ich
p
r
o
p
o
s
ed
a
n
o
n
lin
ea
r
p
r
ed
i
ctiv
e
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI
)
co
n
tr
o
ller
.
T
h
e
c
o
n
tr
o
l
o
f
th
e
in
ter
m
ed
iate
D
C
b
u
s
h
as
b
ee
n
wid
ely
s
tu
d
i
ed
[
2
4
]
.
T
o
p
r
ev
e
n
t
s
tar
t
-
u
p
s
tallin
g
an
d
g
u
ar
a
n
t
ee
MPP
T
,
th
e
er
r
o
r
s
ig
n
al
=(
-
∗
)
at
th
e
r
eg
u
lato
r
in
p
u
t
is
in
v
er
ted
co
m
p
ar
ed
to
th
e
c
o
n
v
e
n
tio
n
al
co
n
f
ig
u
r
atio
n
.
2.
P
RO
P
O
SE
D
S
T
UDY
T
h
e
ar
ticle
p
r
o
p
o
s
es
a
n
ew
ar
ch
itectu
r
e
f
o
r
co
n
n
ec
tin
g
th
e
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
to
th
e
g
r
id
,
en
ab
lin
g
m
o
r
e
s
tab
le
an
d
ef
f
ic
ien
t
in
teg
r
atio
n
.
I
t
is
b
ased
o
n
th
e
r
eso
n
an
t
p
r
o
p
o
r
tio
n
al
co
n
tr
o
ller
(
PR
)
,
wh
ich
p
lay
s
an
ess
en
tial
r
o
le
in
th
is
co
n
n
ec
tio
n
,
p
ar
ticu
lar
ly
at
th
e
in
v
er
ter
lev
el.
I
t
r
eg
u
lates
th
e
in
jecte
d
cu
r
r
en
t
b
y
f
o
llo
win
g
a
s
in
u
s
o
id
al
r
ef
er
en
ce
(
g
en
er
ally
at
5
0
Hz)
,
s
o
m
et
h
in
g
th
at
co
n
v
e
n
tio
n
al
co
n
t
r
o
l
ler
s
s
u
ch
as
th
e
PI,
h
av
e
d
if
f
icu
lty
ac
h
ie
v
in
g
wit
h
p
r
ec
is
io
n
at
s
tead
y
s
tate.
Desig
n
ed
to
o
f
f
er
h
ig
h
g
ain
at
th
is
f
r
eq
u
en
c
y
,
it
en
s
u
r
es
p
r
ec
is
e
f
o
llo
win
g
o
f
th
e
s
in
u
s
o
id
al
wav
ef
o
r
m
wh
ile
elim
in
atin
g
s
tead
y
-
s
tate
er
r
o
r
.
W
h
at'
s
m
o
r
e,
it
h
elp
s
r
ed
u
ce
h
ar
m
o
n
ics
an
d
s
tab
ilize
th
e
cu
r
r
en
t
wav
ef
o
r
m
,
im
p
r
o
v
i
n
g
g
r
i
d
co
m
p
atib
ilit
y
.
Fin
ally
,
it
o
f
f
er
s
co
m
p
atib
ilit
y
with
r
ea
l
-
tim
e
o
p
er
atio
n
u
n
lik
e
PI
c
o
n
tr
o
lle
r
s
,
th
e
PR
o
p
er
ates
ef
f
icien
tl
y
in
t
h
e
s
tatio
n
ar
y
r
ef
er
en
ce
f
r
a
m
e
(
α
β),
s
im
p
lify
in
g
im
p
lem
en
tatio
n
in
s
in
g
le
-
p
h
ase
o
r
th
r
ee
-
p
h
ase
in
v
er
ter
s
with
o
u
t
co
o
r
d
in
ate
tr
an
s
f
o
r
m
atio
n
.
T
h
e
s
y
s
tem
illu
s
tr
ated
in
Fig
u
r
e
1
h
as
th
e
a
d
v
an
tag
e
o
f
u
s
in
g
a
s
in
g
le
D
C
/A
C
s
tag
e,
with
o
u
t
u
s
in
g
a
tr
an
s
f
o
r
m
er
f
o
r
m
atch
in
g
as
in
[
2
5
]
.
Actin
g
as
a
d
e
co
u
p
lin
g
en
e
r
g
y
r
eser
v
o
ir
,
t
h
e
DC
-
s
id
e
ca
p
ac
ito
r
en
ab
les en
er
g
y
tr
an
s
f
er
t
o
th
e
AC
cir
cu
it.
Fig
u
r
e
1
.
B
asic d
iag
r
am
o
f
PV
s
y
s
tem
co
n
n
ec
ted
g
r
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
in
g
le
-
s
ta
g
e
s
in
g
le
-
p
h
a
s
e
g
r
i
d
co
n
n
ec
ted
in
ve
r
ter p
r
o
p
o
r
tio
n
a
l
…
(
A
b
d
ela
z
iz
K
a
b
b
a
)
653
DC
-
li
n
k
V
o
lt
a
g
e
Co
n
tro
ll
e
r
C
u
rrent
C
o
n
t
r
o
l
l
e
r
G
ri
d
S
y
n
c
h
r
o
n
i
z
a
t
i
o
n
PW
M
Inve
rte
r
T
h
e
AC
ter
m
in
al
f
ilter
o
f
co
n
v
er
ter
s
(
o
n
th
e
g
r
id
s
id
e)
g
en
er
ally
h
as
m
u
c
h
less
s
to
r
ed
en
er
g
y
.
C
o
n
s
eq
u
en
tly
,
its
im
p
ac
t
o
n
p
o
wer
tr
an
s
m
is
s
io
n
ca
n
b
e
co
n
s
id
er
ed
n
eg
lig
ib
le
[
2
6
]
.
Fo
r
s
tab
ilit
y
an
aly
s
is
,
th
e
d
ef
in
ed
L
y
ap
u
n
o
v
f
u
n
ctio
n
o
n
ly
tak
es
i
n
to
ac
c
o
u
n
t
th
e
d
y
n
am
ics
o
f
th
e
en
er
g
y
s
to
r
ed
in
t
h
e
ca
p
ac
ito
r
d
o
wn
s
tr
ea
m
o
f
th
e
PV,
wh
ich
m
u
s
t
b
e
s
u
f
f
icie
n
tly
lar
g
e.
T
h
is
ap
p
r
o
ac
h
is
ad
ap
ted
b
y
th
e
au
th
o
r
s
f
o
r
th
r
ee
-
p
h
ase
PV
in
v
er
ter
s
with
a
l
o
w
-
v
alu
e
co
u
p
lin
g
ca
p
ac
ito
r
,
s
in
ce
th
e
co
n
tin
u
o
u
s
p
o
wer
d
o
es
n
o
t
e
x
h
ib
it
o
s
cillatio
n
s
[
2
7
]
.
I
n
ad
d
itio
n
to
s
y
s
tem
s
tab
ilit
y
,
th
e
s
tu
d
y
also
ad
d
r
ess
es
th
e
f
o
llo
win
g
o
b
j
ec
tiv
es:
i)
to
ap
p
ly
an
MPPT
s
tr
ateg
y
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
PV
m
o
d
u
les,
en
h
an
cin
g
t
h
e
en
er
g
y
ef
f
icien
c
y
o
f
th
e
ar
r
ay
;
ii)
to
im
p
lem
e
n
t
a
PI
co
n
tr
o
ller
f
o
r
th
e
DC
b
u
s
v
o
ltag
e
co
n
s
id
er
in
g
th
e
P
–
V
cu
r
v
e;
an
d
iii)
to
u
s
e
a
PR
co
n
tr
o
ller
to
in
ject
a
s
in
u
s
o
id
a
l c
u
r
r
en
t in
p
h
ase
with
th
e
g
r
i
d
v
o
ltag
e,
with
g
r
id
s
y
n
c
h
r
o
n
i
za
tio
n
en
s
u
r
ed
v
ia
a
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
tr
ac
k
in
g
th
e
v
o
ltag
e
f
u
n
d
am
e
n
tal
[
1
8
]
.
T
h
e
MPPT
b
lo
ck
,
u
s
in
g
a
P&
O
alg
o
r
ith
m
as
illu
s
tr
ated
in
th
e
f
lo
wch
ar
t
in
Fig
u
r
e
2
,
co
m
b
in
ed
with
a
PI
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
v
o
l
tag
e
co
n
tr
o
ller
,
f
o
r
m
s
t
h
e
o
u
t
er
lo
o
p
o
f
th
e
s
y
s
tem
wh
ich
d
eter
m
in
es
th
e
g
r
id
r
ef
er
en
ce
cu
r
r
en
t
r
eq
u
ir
e
d
to
r
eg
u
late
th
e
s
tr
in
g
PV
g
en
er
at
o
r
to
im
p
o
s
e
a
r
e
f
er
en
ce
v
o
lta
g
e
∗
.
As
f
o
r
th
e
in
ter
n
al
lo
o
p
,
it
is
d
esig
n
ed
to
co
n
tr
o
l
th
e
cu
r
r
en
ts
s
u
p
p
l
ied
b
y
th
e
in
v
er
ter
i
inv
an
d
th
o
s
e
in
jecte
d
in
to
th
e
g
r
id
i
g
[
2
8
]
,
a
n
d
Fig
u
r
e
3
illu
s
t
r
ates th
ese
m
ain
d
ev
ices r
eq
u
i
r
ed
f
o
r
th
e
co
n
tr
o
l
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
Fig
u
r
e
2
.
MPPT
alg
o
r
ith
m
f
lo
wch
ar
t
(
P&
O)
Fig
u
r
e
3
.
C
o
n
tr
o
l stru
ctu
r
e
o
f
t
h
e
g
r
id
-
co
n
n
ec
ted
s
in
g
le
-
p
h
ase
PV in
v
er
ter
T
h
e
ar
ticle
is
o
r
g
an
ized
as
f
o
llo
ws:
s
ec
t
io
n
3
ex
am
in
es
th
e
d
if
f
er
en
t
p
o
we
r
s
in
o
r
d
er
to
d
ev
elo
p
th
e
s
y
s
tem
'
s
co
n
tr
o
l
s
tr
ateg
y
.
Sec
tio
n
4
d
is
cu
s
s
es
s
tab
ilit
y
in
r
elatio
n
to
th
e
f
ac
t
th
at
th
e
P(
V)
ch
ar
ac
ter
is
tic
is
n
o
n
lin
ea
r
an
d
af
f
ec
ts
its
ef
f
ec
t
o
n
th
e
in
ter
m
ed
iate
cir
cu
it
v
o
ltag
e.
Sectio
n
5
aim
s
to
v
ali
d
ate
th
e
an
aly
tical
d
em
o
n
s
tr
atio
n
with
MA
T
L
AB
/
Simu
lin
k
s
im
u
latio
n
s
.
Sectio
n
6
co
n
clu
d
es th
e
a
r
ticle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
5
1
-
662
654
3.
CO
NT
RO
L
ST
R
AT
E
G
Y
3
.
1
.
Descript
io
n o
f
t
he
diff
er
ent
po
wer
ra
t
ing
s
I
n
Fig
u
r
e
1
,
th
e
PV
s
y
s
tem
u
s
es
an
in
v
er
te
r
as
a
b
r
id
g
e
to
c
o
n
n
ec
t
to
th
e
g
r
id
.
T
o
s
im
p
lif
y
th
e
s
tu
d
y
,
we
ass
u
m
e
th
at:
i)
T
h
e
in
v
er
ter
,
th
e
co
u
p
lin
g
ca
p
ac
ito
r
with
PV,
an
d
th
e
o
u
tp
u
t
f
ilter
d
o
n
o
t
ex
h
ib
it
p
o
wer
lo
s
s
es.
An
d
ii)
Oth
er
ter
m
s
r
ep
r
esen
tin
g
co
n
d
u
ctio
n
lo
s
s
es c
an
b
e
n
e
g
lecte
d
.
Fo
r
th
e
p
o
wer
b
alan
ce
i
n
th
e
DC
b
u
s
,
we
ca
n
wr
ite:
(
)
=
+
(
1
)
as:
=
.
T
h
e
p
o
wer
in
t
h
e
g
r
i
d
is
g
iv
en
b
y
:
=
(
)
(
)
=
(
1
−
2
)
(
2
)
W
h
er
e
,
ar
e
i
n
s
tan
tan
eo
u
s
g
r
i
d
v
o
ltag
e
a
n
d
g
r
id
cu
r
r
en
t
r
esp
ec
tiv
ely
;
,
ar
e
r
o
o
t
m
ea
n
s
q
u
ar
e
(
R
MS)
o
f
cu
r
r
en
t
an
d
r
esp
ec
tiv
ely
;
an
d
:
g
r
id
p
u
ls
atio
n
.
T
h
e
p
o
we
r
in
jecte
d
i
n
to
th
e
s
in
g
le
-
p
h
ase
g
r
id
,
ca
lcu
lated
in
(
2
)
,
is
s
in
u
s
o
id
al
an
d
h
as
twic
e
th
e
f
r
eq
u
e
n
cy
o
f
th
e
g
r
i
d
.
T
h
e
o
p
er
atio
n
o
f
th
e
PV
g
en
er
at
o
r
at
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
wo
u
ld
b
e
co
m
p
r
o
m
is
ed
if
th
e
p
u
ls
ed
p
o
wer
wer
e
n
o
t
atten
u
ated
u
s
in
g
an
en
er
g
y
s
to
r
ag
e
d
e
v
ice.
T
h
er
ef
o
r
e
,
b
u
s
ca
p
ac
ito
r
s
ar
e
g
en
e
r
ally
u
s
ed
t
o
s
to
r
e
th
is
en
er
g
y
,
an
d
th
eir
i
n
s
tan
tan
eo
u
s
p
o
wer
(
)
is
eq
u
al
to
:
(
)
=
(
3
)
T
h
e
av
er
a
g
e
p
o
wer
o
f
t
h
e
elec
tr
ical
n
etwo
r
k
is
g
iv
en
b
y
:
=
(
4
)
3
.
2
.
P
r
o
po
s
ed
c
o
ntr
o
ller
T
h
e
DC
b
u
s
v
o
ltag
e
co
n
tr
o
ller
is
u
s
ed
to
r
eg
u
late
th
e
D
C
v
o
ltag
e
to
a
d
esire
d
lev
el
in
o
r
d
er
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
p
h
o
to
v
o
ltaic
ar
r
ay
.
T
h
e
n
o
n
-
lin
ea
r
PV
ch
ar
ac
ter
is
tic
m
e
an
s
th
at
ch
an
g
es
in
ir
r
ad
ian
ce
s
h
if
t th
e
o
p
er
atin
g
p
o
in
t,
m
o
d
i
f
y
in
g
th
e
DC
p
o
wer
an
d
,
co
n
s
eq
u
en
tly
,
th
e
MPP.
As th
e
g
r
id
v
o
ltag
e
r
em
ain
s
co
n
s
tan
t,
th
e
p
o
wer
tr
an
s
f
er
r
ed
to
th
e
g
r
i
d
is
co
n
tr
o
l
led
en
tire
ly
b
y
th
e
in
v
er
ter
’
s
o
u
tp
u
t c
u
r
r
en
t.
T
h
e
m
ath
em
atica
l m
o
d
el
d
esc
r
ib
in
g
th
e
d
y
n
a
m
ics o
f
p
o
wer
tr
an
s
f
er
is
g
iv
en
b
y
(
5
)
:
=
=
−
(
5
)
W
h
er
e
∗
,
∗
ar
e
r
ef
e
r
en
ce
g
r
id
p
o
wer
an
d
c
u
r
r
e
n
t
r
esp
ec
ti
v
ely
;
∗
ar
e
cu
r
r
e
n
t
o
f
t
h
e
in
v
er
ter
;
,
ar
e
p
er
i
o
d
ic
s
ig
n
als
h
a
v
in
g
th
e
av
e
r
ag
e
c
o
m
p
o
n
en
ts
̄
,
̄
an
d
th
e
AC
co
m
p
o
n
en
ts
̃
,
̃
;
an
d
=
1
/
(
2
)
ar
e
o
s
cillatio
n
p
er
io
d
.
,
ar
e
d
ef
in
ed
r
esp
ec
tiv
ely
as:
{
=
̄
+
̃
=
̄
+
̃
(
6
)
T
h
e
p
o
wer
in
jecte
d
in
t
o
th
e
Pav
g
r
id
is
co
n
tr
o
lled
ac
co
r
d
in
g
to
(
7
)
,
u
s
in
g
a
ter
m
an
d
a
s
ec
o
n
d
ter
m
k
/
th
at
tak
es in
to
ac
co
u
n
t th
e
s
y
s
tem
d
y
n
am
ics o
f
th
e
p
h
o
to
v
o
ltaic
in
v
er
ter
:
=
=
+
(
7
)
An
d
b
y
s
u
b
s
titu
tin
g
(
8
)
in
to
(
5
)
we
g
et:
=
−
(
8
)
Acc
o
r
d
in
g
to
(
8
)
,
d
P/d
V
d
ep
e
n
d
s
o
n
th
e
d
y
n
am
ics
o
f
ca
p
ac
ito
r
.
T
h
e
alter
n
atin
g
wav
ef
o
r
m
co
m
p
o
n
e
n
ts
th
e
p
o
we
r
PV
̃
an
d
th
e
D
C
b
u
s
v
o
ltag
e
̃
ar
e
esti
m
ated
u
s
in
g
a
q
u
a
d
r
atu
r
e
s
ig
n
al
g
en
er
ato
r
b
ased
o
n
a
g
en
er
alize
d
s
ec
o
n
d
-
o
r
d
er
in
t
eg
r
ato
r
,
f
u
n
ctio
n
i
n
g
as
a
/
2
p
h
ase
s
h
if
ter
(
Fig
u
r
e
3
,
c
lo
s
ed
-
lo
o
p
tr
a
n
s
f
er
f
u
n
ctio
n
i
n
(
9
)
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
in
g
le
-
s
ta
g
e
s
in
g
le
-
p
h
a
s
e
g
r
i
d
co
n
n
ec
ted
in
ve
r
ter p
r
o
p
o
r
tio
n
a
l
…
(
A
b
d
ela
z
iz
K
a
b
b
a
)
655
T
h
e
r
ef
e
r
en
ce
cu
r
r
e
n
t
is
ca
lc
u
lated
f
r
o
m
t
h
e
r
e
f
er
en
ce
PV
p
o
wer
s
u
p
p
lied
b
y
th
e
co
n
tr
o
ller
in
Fig
u
r
e
4
an
d
th
e
ef
f
ec
tiv
e
v
al
u
e
o
f
th
e
g
r
id
v
o
ltag
e.
T
h
e
PLL
ex
tr
ac
ts
th
e
p
h
ase
an
g
le
o
f
th
e
g
r
id
,
wh
ich
is
m
u
ltip
lied
b
y
th
e
am
p
litu
d
e
o
f
th
e
in
v
er
ter
r
ef
er
e
n
ce
cu
r
r
e
n
t.
T
h
e
cu
r
r
en
t
co
n
tr
o
ller
th
en
r
e
g
u
lates
th
e
cu
r
r
en
t
in
jecte
d
in
to
th
e
g
r
id
.
T
h
e
cu
r
r
en
t c
o
n
tr
o
l a
n
d
v
o
ltag
e
c
o
n
tr
o
l lo
o
p
s
ar
e
illu
s
tr
ated
in
Fig
u
r
es 5
an
d
6
.
Fig
u
r
e
4
.
Sh
o
ws th
e
s
tr
u
ctu
r
e
o
f
th
e
co
n
tr
o
ller
s
co
n
tr
o
llin
g
t
h
e
in
v
er
ter
Fig
u
r
e
5
.
MPPT
co
n
tr
o
l
an
d
r
e
f
er
en
ce
cu
r
r
en
t
g
en
er
atio
n
lo
o
p
Fig
u
r
e
6
.
PR
b
ased
co
n
tr
o
l lo
o
p
f
o
r
PW
M
co
m
m
a
n
d
g
e
n
er
ati
o
n
3
.
3
.
Sy
nchro
niza
t
io
n wit
h t
h
e
P
L
L
g
rid
C
o
n
n
ec
tin
g
th
e
PV
s
o
u
r
ce
to
th
e
elec
tr
ical
n
etwo
r
k
th
r
o
u
g
h
th
e
DC
/AC
co
n
v
er
ter
r
eq
u
ir
e
s
s
y
n
ch
r
o
n
izatio
n
o
f
th
e
v
o
ltag
e
p
r
o
d
u
ce
d
with
th
at
o
f
th
e
n
e
two
r
k
,
it
is
t
h
er
ef
o
r
e
ess
en
tial
to
k
n
o
w
t
h
e
p
h
ase
an
d
f
r
eq
u
e
n
cy
o
f
th
e
v
o
ltag
e
g
r
id
.
M
o
s
t
ef
f
icien
t
m
eth
o
d
is
th
e
u
s
e
o
f
a
PLL
,
s
in
g
le
-
p
h
ase
PLL
s
ar
e
s
u
b
jec
t
to
an
a
d
d
itio
n
al
d
if
f
ic
u
lty
th
a
n
in
t
h
r
ee
-
p
h
ase,
b
ec
a
u
s
e
o
f
t
h
e
s
m
aller
in
f
o
r
m
atio
n
f
ield
(
o
n
ly
o
n
e
p
h
ase)
.
T
o
cr
ea
te
two
o
r
th
o
g
o
n
al
s
ig
n
als
in
s
in
g
le
-
p
h
ase,
it
is
n
ec
es
s
a
r
y
to
ad
d
a
“Qu
ad
r
atu
r
e”
d
e
m
o
d
u
latio
n
b
l
o
ck
in
Fig
u
r
e
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
5
1
-
662
656
Fig
u
r
e
7
.
B
asic stru
ctu
r
e
o
f
a
s
in
g
le
-
p
h
ase
PLL
3
.
4
.
T
ra
ns
f
er
f
un
ct
io
n o
f
t
he
re
s
o
na
nt
co
ntr
o
ller
I
n
g
r
id
-
c
o
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
,
th
e
PR
cu
r
r
en
t
co
n
tr
o
ller
is
co
m
m
o
n
l
y
em
p
lo
y
e
d
to
e
n
s
u
r
e
ac
cu
r
ate
tr
ac
k
in
g
o
f
th
e
s
in
u
s
o
id
al
cu
r
r
e
n
t
r
ef
e
r
en
ce
in
jecte
d
I
*
g
,
wh
ile
g
u
ar
an
teei
n
g
ze
r
o
s
tatic
er
r
o
r
at
th
e
f
u
n
d
am
e
n
tal
f
r
e
q
u
en
c
y
an
d
cu
r
r
en
t
q
u
ality
co
m
p
lian
t
with
g
r
id
co
n
n
ec
tio
n
s
tan
d
ar
d
s
.
T
h
e
r
eso
n
an
t
co
n
tr
o
ller
ca
n
b
e
d
escr
ib
e
d
b
y
th
e
f
o
llo
win
g
tr
an
s
f
er
f
u
n
ctio
n
:
(
)
=
2
+
2
+
2
2
+
2
(
9
)
T
h
e
p
r
o
p
o
r
tio
n
al
an
d
r
eso
n
a
n
t
g
ain
s
o
f
th
e
PR
co
n
tr
o
lle
r
ar
e
o
b
tain
ed
t
h
r
o
u
g
h
a
tr
i
al
-
an
d
-
er
r
o
r
tu
n
in
g
m
eth
o
d
,
f
ir
s
t
ad
ju
s
tin
g
th
e
p
r
o
p
o
r
tio
n
al
g
ain
t
o
en
s
u
r
e
s
y
s
t
em
s
tab
ilit
y
an
d
d
y
n
am
ic
p
e
r
f
o
r
m
an
ce
,
th
en
t
h
e
r
eso
n
an
t
g
ain
to
r
ed
u
ce
th
e
e
r
r
o
r
in
s
tatic
m
o
d
e
at
th
e
s
y
n
ch
r
o
n
is
m
f
r
eq
u
en
cy
.
I
n
p
ar
tic
u
lar
,
we
tak
e:
th
e
p
r
o
p
o
r
tio
n
al
c
o
ef
f
icien
t
is
:
=
12
,
t
h
e
in
teg
r
al
co
ef
f
icien
t
is
:
=
200
an
d
th
e
p
u
ls
atio
n
is
:
=
100
.
T
h
e
am
p
litu
d
e
a
n
d
p
h
ase
B
o
d
e
d
iag
r
am
s
ar
e
r
ep
r
esen
ted
b
y
Fig
u
r
e
8
.
Fig
u
r
e
8
.
B
o
d
e
r
esp
o
n
s
e
o
f
th
e
PR
co
n
tr
o
ller
4.
ST
A
B
I
L
I
T
Y
ANA
L
YS
I
S
Sin
ce
th
e
s
y
s
tem
u
n
d
e
r
s
tu
d
y
ex
h
ib
its
n
o
n
lin
ea
r
ity
,
we
d
e
f
i
n
e
a
L
y
a
p
u
n
o
v
f
u
n
ctio
n
(
)
th
at
tak
es
in
to
ac
co
u
n
t
th
e
s
tates
o
f
t
h
e
s
y
s
tem
.
C
o
n
s
eq
u
en
tly
,
(
)
will
b
e
f
o
r
m
ed
b
ased
o
n
th
e
v
ar
ia
tio
n
in
en
er
g
y
s
to
r
ed
in
th
e
in
ter
m
e
d
iate
cir
c
u
it
ca
p
ac
ito
r
,
ass
u
m
in
g
th
at
t
h
e
ef
f
ec
t
o
f
th
e
o
th
er
c
o
m
p
o
n
e
n
ts
is
n
eg
lig
ib
le
an
d
th
er
ef
o
r
e
h
as n
o
e
f
f
ec
t o
n
th
e
s
tab
ilit
y
o
f
th
e
s
y
s
tem
.
T
h
e
ca
n
d
id
ate
f
u
n
ctio
n
ca
n
b
e
wr
itte
n
as:
(
)
=
2
4
(
∗
2
−
2
)
2
(
1
0
)
W
h
er
e:
(
)
>
0
;
is
en
er
g
y
s
to
r
ed
in
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
in
g
le
-
s
ta
g
e
s
in
g
le
-
p
h
a
s
e
g
r
i
d
co
n
n
ec
ted
in
ve
r
ter p
r
o
p
o
r
tio
n
a
l
…
(
A
b
d
ela
z
iz
K
a
b
b
a
)
657
Fig
u
r
e
4
illu
s
tr
ates th
e
MPPT
co
n
tr
o
ller
d
iag
r
am
im
p
lem
en
ti
n
g
th
e
(
P&
O)
alg
o
r
ith
m
.
T
h
is
alg
o
r
ith
m
o
p
er
ates
b
y
s
u
cc
ess
iv
e
p
er
tu
r
b
atio
n
s
ar
o
u
n
d
th
e
m
ea
s
u
r
e
d
v
o
ltag
e
in
o
r
d
er
t
o
g
e
n
er
ate
th
e
o
p
tim
al
r
ef
er
en
ce
v
o
ltag
e
∗
in
Fig
u
r
e
9
(
a)
.
T
h
e
s
tab
le
m
ax
im
u
m
p
o
wer
p
o
in
t
(
PP
)
,
d
ef
i
n
ed
b
y
th
e
co
o
r
d
i
n
ates
(V
MP
=
∗
,
PM)
,
co
r
r
esp
o
n
d
s
to
th
e
m
ax
im
u
m
p
o
wer
ac
h
ie
v
ed
at
th
e
v
o
ltag
e
∗
.
T
h
is
p
o
i
n
t
is
lo
ca
ted
b
etwe
en
th
e
s
tab
le
an
d
u
n
s
tab
le
r
eg
io
n
s
o
f
th
e
P(V
)
ch
a
r
ac
ter
is
tic
cu
r
v
e
t
r
av
er
s
ed
d
u
r
i
n
g
th
e
MPPT
tr
ac
k
in
g
p
r
o
ce
s
s
in
Fig
u
r
e
9
(
b
)
.
I
n
ad
d
itio
n
,
Fig
u
r
e
9
(
c)
s
h
o
ws
th
e
P(V
)
cu
r
v
es
f
o
r
th
e
PV
g
en
er
ato
r
u
s
ed
i
n
th
e
s
im
u
latio
n
,
p
ar
am
eter
ized
b
y
ir
r
ad
ian
ce
lev
els
(
1
0
0
W
/m
²,
5
0
0
W
/m
²,
an
d
1
0
0
0
W
/m
²)
.
Un
d
er
id
e
n
tical
co
n
d
itio
n
s
a
n
d
f
o
llo
win
g
[
2
9
]
,
g
lo
b
al
s
tab
ilit
y
o
f
t
h
e
s
y
s
tem
is
en
s
u
r
ed
if
(
)
s
atis
f
ies
t
h
e
f
o
llo
win
g
co
n
d
itio
n
s
:
(
0
)
=
0
(
1
1
)
(
)
>
0
f
o
r
all
(
)
≠
0
(
1
2
)
(
)
→
∞
as
|
|
→
∞
(
1
3
)
(
)
<
0
f
o
r
all
|
|
≠
0
(
1
4
)
(
a)
(
b
)
(
c)
Fig
u
r
e
9
.
Po
wer
c
u
r
v
e
as a
f
u
n
ctio
n
o
f
v
o
ltag
e
P(V
)
,
(
a)
Sear
ch
f
o
r
r
ef
er
e
n
ce
v
o
ltag
e
∗
,
(
b
)
S
tab
le
p
ea
k
p
o
in
t PP,
an
d
(
c)
Sp
ec
if
icatio
n
s
o
f
th
e
cu
r
v
es o
f
th
e
PV so
u
r
ce
u
s
ed
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
th
e
l
ast
co
n
d
itio
n
en
s
u
r
es
g
l
o
b
al
s
tab
ilit
y
o
f
th
e
s
y
s
tem
wh
en
th
e
s
to
r
e
d
en
er
g
y
is
co
n
tin
u
o
u
s
ly
d
is
s
ip
ated
(
(
)
×
(
)
/
<
0
)
,
wh
ich
im
p
lies
a
co
n
tin
u
o
u
s
co
n
v
e
r
g
en
ce
o
f
th
e
s
y
s
tem
to
war
d
its
eq
u
ilib
r
iu
m
p
o
in
t.
Hen
ce
,
th
e
ad
o
p
ted
L
y
ap
u
n
o
v
f
u
n
ctio
n
s
atis
f
i
es
th
e
r
eq
u
ir
em
en
ts
o
u
tlin
ed
ab
o
v
e,
a
n
d
its
tim
e
d
e
r
iv
ativ
e
(
)
/
i
s
g
iv
en
b
y
(
1
1
)
in
th
e
f
o
llo
win
g
f
o
r
m
:
(
)
=
−
2
(
∗
−
)
(
∗
+
)
(
1
5
)
R
ep
lacin
g
(
1
1
)
with
(
5
)
r
esu
lts
in
:
(
)
=
−
(
−
)
(
∗
−
)
(
∗
+
)
(
1
6
)
I
n
f
ac
t,
o
n
th
e
b
asis
o
f
(
1
7
)
,
as
a
r
esu
lt,
th
e
s
ig
n
o
f
th
e
d
er
iv
ativ
e
o
f
th
e
f
u
n
ctio
n
(
)
ca
n
b
e
id
en
tifie
d
,
an
d
it
ev
id
e
n
tly
d
ep
en
d
s
o
n
th
e
p
o
wer
v
ar
iatio
n
ass
o
ciate
d
with
th
e
v
o
lta
g
e
d
if
f
e
r
en
ce
.
T
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
5
1
-
662
658
co
n
v
er
g
en
ce
o
f
s
y
s
tem
s
tab
ilit
y
is
ev
alu
ated
in
two
ca
s
es,
as
in
[
2
9
]
,
t
h
e
s
y
s
tem
is
s
tab
le.
T
h
e
r
ef
er
e
n
ce
cu
r
r
en
t is g
iv
e
n
b
y
(
1
7
)
:
=
2
+
(
−
∗
+
)
̑
(
1
7
)
5.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
T
h
e
s
y
s
tem
illu
s
tr
ated
in
Fig
u
r
e
1
is
im
p
lem
en
ted
o
n
th
e
MA
T
L
AB
/
S
im
u
lin
k
p
latf
o
r
m
,
Fig
u
r
e
3
p
r
esen
ts
th
e
im
p
lem
en
ted
co
n
tr
o
l
s
tr
ateg
y
.
I
n
p
ar
ticu
lar
,
M
PP
T
co
n
tr
o
ller
b
ased
o
n
th
e
P&
O
alg
o
r
ith
m
an
d
u
s
in
g
th
e
PI
r
eg
u
lato
r
as
s
h
o
wn
in
Fig
u
r
e
5
,
allo
ws
to
o
p
tim
ize
th
e
p
h
o
to
v
o
ltaic
en
er
g
y
p
r
o
d
u
ctio
n
.
On
ce
th
e
m
ax
im
u
m
p
o
wer
is
ex
tr
ac
ted
f
r
o
m
th
e
PV
s
y
s
tem
,
th
is
en
er
g
y
is
co
n
v
er
ted
b
y
th
e
in
v
er
t
er
u
s
ed
.
C
o
n
tr
o
l
is
p
er
f
o
r
m
ed
th
r
o
u
g
h
PW
M,
s
i
g
n
als
g
en
er
ated
ef
f
icien
tly
an
d
ac
cu
r
ately
f
r
o
m
a
PR
co
n
tr
o
ller
in
Fig
u
r
e
6
.
Sy
n
ch
r
o
n
izatio
n
with
th
e
g
r
id
f
r
eq
u
e
n
cy
is
ac
h
iev
ed
b
y
a
PLL
b
ased
cir
cu
it
in
Fig
u
r
e
7
.
T
h
e
ty
p
e
o
f
PV
m
o
d
u
le
u
s
ed
is
Z
y
tech
E
n
g
in
e
er
in
g
T
ec
h
n
o
l
o
g
ie
Z
T
1
9
0
S,
w
h
o
s
e
P(V
)
c
u
r
v
e
f
o
r
1
1
m
o
d
u
l
es
in
s
er
ies
an
d
f
o
r
d
if
f
er
en
t
ir
r
ad
ia
n
ce
v
alu
es
i
s
p
lo
tted
in
Fig
u
r
e
9
(
c)
,
th
e
p
ar
am
eter
s
o
f
th
e
s
im
u
lated
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
ar
e
lis
ted
in
T
ab
le
1
.
T
ab
le
1
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
s
y
s
tem
s
tu
d
y
P
V
mo
d
u
l
e
S
e
r
i
e
s
c
o
n
n
e
c
t
e
d
P
o
w
e
r
(
k
W
)
F
i
l
t
e
r
L
C
L
PWM
G
R
I
D
V
o
c
=
4
4
.
8
6
V
1
1
M
o
d
u
l
e
s
2
k
W
L
1
=
4
mH
f
P
=
1
0
k
H
z
V
max
=
3
2
5
V
I
sc
=
5
.
5
A
C
=
6
.
2
5
µ
F
f
=
5
0
Hz
V
MPP
=
3
7
.
7
3
V
C
d
c
=
6
0
0
µ
F
L
2
=
4
.
3
mH
Fo
r
th
e
s
im
u
latio
n
,
th
e
P&
O
alg
o
r
ith
m
is
co
n
f
ig
u
r
e
d
with
th
e
f
o
llo
win
g
p
ar
am
ete
r
s
:
tr
ac
k
in
g
f
r
eq
u
e
n
cy
s
et
at
=
1
Mh
z,
an
d
th
e
in
cr
em
en
t
v
o
ltag
e
Δ
V
MPPT
=
0
.
5
V,
an
d
th
is
with
th
e
aim
o
f
d
ec
r
ea
s
in
g
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP
an
d
th
u
s
r
ed
u
ci
n
g
s
tead
y
-
s
tate
lo
s
s
es.
T
h
e
cu
r
v
es
b
elo
w
a
r
e
f
o
r
ir
r
ad
iatio
n
o
f
1
0
0
0
W
/m
2
an
d
a
tem
p
e
r
atu
r
e
o
f
2
5
°C
(
STC
co
n
d
itio
n
s
)
.
T
h
e
MPPT
alg
o
r
ith
m
f
o
llo
ws
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
MPP)
o
n
th
e
r
i
g
h
t
s
id
e
o
f
th
e
P(V
)
cu
r
v
e,
as
co
n
f
ir
m
ed
b
y
th
e
g
r
i
d
v
o
ltag
e
in
Fig
u
r
e
1
0
an
d
th
e
DC
b
u
s
s
tar
t
-
u
p
v
o
ltag
e
in
Fig
u
r
e
1
1
.
On
ce
t
h
e
DC
b
u
s
ca
p
ac
ito
r
is
f
u
lly
c
h
ar
g
ed
,
its
v
o
ltag
e
r
ea
ch
es
th
e
v
o
ltag
e
(
Vo
c)
wh
en
it
d
eliv
er
s
ze
r
o
cu
r
r
e
n
t
f
r
o
m
th
e
PV
s
o
u
r
ce
.
T
h
e
m
ea
s
u
r
ed
v
alu
e
is
ap
p
r
o
x
im
ately
4
2
0
V.
T
h
er
ea
f
ter
,
th
e
DC
b
u
s
v
o
ltag
e
s
tab
ilizes,
with
s
l
ig
h
t
f
lu
ctu
atio
n
s
ar
o
u
n
d
th
e
MPP
in
s
tead
y
s
tate,
wi
th
o
u
t
ca
u
s
in
g
d
is
tu
r
b
an
ce
s
.
An
aly
s
is
o
f
th
e
DC
b
u
s
v
o
ltag
e
an
d
g
r
id
cu
r
r
en
t
in
Fig
u
r
e
1
1
s
h
o
ws
th
at
th
e
s
y
s
tem
with
th
e
MPPT
co
n
tr
o
ller
an
d
PI
r
eg
u
lato
r
is
s
tab
le,
with
th
e
PI
r
e
g
u
lato
r
ef
f
ec
tiv
ely
r
ed
u
cin
g
f
lu
ctu
atio
n
s
to
c
o
m
p
en
s
ate
f
o
r
r
ap
id
c
h
an
g
es
i
n
ir
r
ad
ian
ce
o
r
lo
ad
.
T
h
e
an
aly
s
is
o
f
th
e
d
er
iv
ativ
e
o
f
th
e
f
u
n
ctio
n
(
)
,
b
ased
o
n
(
1
6
)
a
n
d
th
e
cu
r
v
e
in
Fig
u
r
e
1
2
,
in
d
icate
s
th
at
af
ter
s
y
s
tem
s
tar
t
-
u
p
,
(
)/
r
em
ain
s
n
eg
ativ
e.
I
t g
r
a
d
u
ally
ap
p
r
o
ac
h
es z
er
o
in
s
tead
y
s
tate,
en
s
u
r
in
g
t
h
e
o
v
er
all
s
tab
ilit
y
o
f
th
e
s
y
s
tem
.
Fig
u
r
e
1
0
.
Vo
ltag
e
an
d
cu
r
r
en
t in
th
e
g
r
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
in
g
le
-
s
ta
g
e
s
in
g
le
-
p
h
a
s
e
g
r
i
d
co
n
n
ec
ted
in
ve
r
ter p
r
o
p
o
r
tio
n
a
l
…
(
A
b
d
ela
z
iz
K
a
b
b
a
)
659
Fig
u
r
e
1
1
.
C
u
r
r
en
t g
r
id
an
d
D
C
lin
k
v
o
ltag
e
Fig
u
r
e
1
2
.
Der
iv
ativ
e
o
f
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
(
)
/
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
co
n
tr
o
l
s
tr
ateg
y
ad
o
p
ted
,
wh
eth
er
b
ased
o
n
MPPT
with
PI
a
n
d
t
h
e
r
eso
n
an
t
p
r
o
p
o
r
tio
n
al
c
o
n
tr
o
ller
(
PR
)
,
is
v
alid
ated
b
y
th
e
s
y
s
tem
'
s
r
esp
o
n
s
e
to
a
v
ar
iab
le
ir
r
ad
ia
n
ce
p
r
o
f
ile
b
etwe
en
3
0
0
W
/m
²
an
d
1
0
0
0
W
/m
²,
u
n
d
er
a
co
n
s
tan
t
tem
p
e
r
atu
r
e
o
f
2
5
°C
.
T
h
is
is
illu
s
tr
ated
in
Fig
u
r
es
1
3
an
d
1
4
,
wh
er
e
th
e
cu
r
r
en
t
in
te
n
s
ity
in
th
e
n
etwo
r
k
,
(
)
,
v
ar
ies
an
d
f
o
llo
ws
th
e
ev
o
lu
tio
n
o
f
th
e
ir
r
a
d
iatio
n
p
r
o
f
ile,
with
ap
p
r
o
p
r
iate
r
esp
o
n
s
e
tim
e
an
d
d
y
n
am
ics.
I
n
ad
d
itio
n
,
th
is
v
o
ltag
e
c
u
r
v
e
h
as
a
r
esp
o
n
s
e
tim
e
o
f
ap
p
r
o
x
im
ately
0
.
2
s
an
d
a
n
o
v
er
s
h
o
o
t o
f
2
5
%.
Fig
u
r
e
1
3
.
Vo
ltag
e
an
d
cu
r
r
en
t g
r
id
f
o
r
a
v
a
r
iab
le
ir
r
a
d
iatio
n
p
r
o
f
ile
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
6
5
1
-
662
660
Fig
u
r
e
1
4
.
v
o
ltag
e
o
f
t
h
e
co
n
n
ec
tio
n
DC
-
lin
k
an
d
cu
r
r
en
t
Gr
id
f
o
r
a
v
ar
iab
le
ir
r
ad
iatio
n
p
r
o
f
ile
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
in
v
esti
g
ated
a
g
r
id
-
co
n
n
ec
ted
s
in
g
le
-
p
h
ase
p
h
o
t
o
v
o
ltaic
s
y
s
tem
eq
u
ip
p
ed
wit
h
a
DC
/AC
in
v
er
ter
,
a
n
MPPT
alg
o
r
ith
m
,
a
PI
co
n
tr
o
ller
f
o
r
DC
b
u
s
v
o
ltag
e
r
eg
u
latio
n
,
a
n
d
a
PR
co
n
tr
o
ller
f
o
r
g
r
i
d
cu
r
r
en
t
in
jectio
n
.
T
h
e
MPPT
en
s
u
r
es
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
f
r
o
m
t
h
e
PV
ar
r
ay
,
wh
i
le
th
e
PI
co
n
tr
o
lle
r
m
ain
tain
s
s
tab
le
DC
b
u
s
v
o
lt
ag
e
u
n
d
er
v
ar
y
i
n
g
ir
r
ad
ian
ce
an
d
l
o
ad
c
o
n
d
itio
n
s
.
T
h
e
PR
co
n
tr
o
ller
allo
ws
ac
cu
r
ate
s
in
u
s
o
id
al
cu
r
r
e
n
t
in
jectio
n
in
to
th
e
g
r
id
,
m
in
im
iz
in
g
s
tead
y
-
s
tate
e
r
r
o
r
an
d
im
p
r
o
v
in
g
d
is
tu
r
b
an
c
e
r
ejec
tio
n
co
m
p
a
r
ed
to
a
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
.
Simu
latio
n
r
esu
lts
co
n
f
ir
m
th
at
th
e
c
o
m
b
in
ed
u
s
e
o
f
th
e
in
v
er
ter
an
d
t
h
ese
co
n
tr
o
l
s
tr
a
teg
ies
g
u
ar
an
tee
o
v
e
r
all
s
y
s
tem
s
tab
ilit
y
an
d
ef
f
icien
t,
r
elia
b
le
o
p
er
atio
n
o
f
th
e
g
r
id
-
co
n
n
ec
ted
PV sy
s
tem
.
Sta
b
ili
ty
is
t
y
p
ica
ll
y
li
m
it
e
d
t
o
t
h
e
r
i
g
h
t
s
i
d
e
o
f
t
h
e
PV
c
u
r
v
e
(
>
)
wit
h
o
u
t
a
v
o
lt
a
g
e
co
n
t
r
o
ll
er
,
wh
i
le
t
h
e
le
f
t
s
i
d
e
(
<
)
r
em
a
in
s
u
n
s
t
ab
le
.
I
n
t
r
o
d
u
ci
n
g
a
PI
co
n
t
r
o
ll
er
to
r
eg
u
l
ate
e
n
e
r
g
y
v
i
a
t
h
e
DC
-
li
n
k
ca
p
ac
it
o
r
en
s
u
r
es
s
y
s
te
m
s
ta
b
i
l
ity
a
c
r
o
s
s
a
ll
o
p
er
ati
n
g
p
o
i
n
ts
.
Usi
n
g
a
L
y
ap
u
n
o
v
f
u
n
cti
o
n
b
a
s
ed
o
n
t
h
e
DC
b
u
s
ca
p
ac
it
o
r
’
s
e
n
e
r
g
y
,
t
h
e
d
e
r
i
v
a
tiv
e
r
e
v
ea
ls
t
h
e
d
y
n
am
ics
o
f
s
to
r
e
d
e
n
e
r
g
y
a
n
d
e
n
s
u
r
es
s
t
a
b
il
it
y
.
A
t
h
e
o
r
eti
ca
l
an
al
y
s
is
was
p
er
f
o
r
m
ed
t
o
o
p
t
i
m
iz
e
th
e
p
e
r
f
o
r
m
a
n
c
e
o
f
a
g
r
i
d
-
c
o
n
n
ec
t
e
d
s
i
n
g
l
e
-
p
h
as
e
DC
/A
C
in
v
er
te
r
.
Sim
u
la
ti
o
n
s
w
e
r
e
c
ar
r
i
ed
o
u
t
a
n
d
v
a
li
d
at
e
d
in
MA
T
L
AB
/
S
im
u
li
n
k
f
o
r
a
2
k
W
s
y
s
te
m
,
d
e
m
o
n
s
tr
ati
n
g
s
atis
f
ac
to
r
y
p
e
r
f
o
r
m
a
n
c
e.
T
h
e
r
es
u
l
ts
i
n
d
ic
at
e
t
h
a
t
a
PR
r
e
g
u
lat
o
r
ca
n
o
v
e
r
c
o
m
e
th
e
l
i
m
it
ati
o
n
s
o
f
t
h
e
P
I
r
e
g
u
la
to
r
,
in
cl
u
d
i
n
g
its
i
n
a
b
il
ity
t
o
t
r
a
c
k
a
s
i
n
u
s
o
id
al
r
e
f
e
r
e
n
c
e
wit
h
o
u
t
s
te
a
d
y
-
s
t
ate
er
r
o
r
a
n
d
its
lim
ite
d
d
is
t
u
r
b
a
n
ce
r
eje
cti
o
n
.
Sta
b
il
it
y
a
n
a
ly
s
is
s
h
o
ws
t
h
at
in
s
ta
b
il
ity
o
r
i
g
i
n
at
es
f
r
o
m
t
h
e
in
v
e
r
s
e
e
r
r
o
r
s
i
g
n
al
at
t
h
e
in
p
u
t
o
f
th
e
DC
v
o
lta
g
e
r
e
g
u
la
to
r
.
T
h
is
r
esear
ch
f
ac
ilit
ates
th
e
in
teg
r
atio
n
o
f
lar
g
e
-
s
ca
le
PV
s
y
s
tem
s
in
to
s
m
ar
t
g
r
id
s
,
th
u
s
co
n
tr
ib
u
tin
g
to
th
e
en
er
g
y
tr
an
s
itio
n
.
T
h
e
s
im
u
lated
s
y
s
tem
ca
n
b
e
in
teg
r
ated
in
to
s
m
ar
t
g
r
id
s
,
en
ab
lin
g
d
y
n
am
i
c
m
an
ag
em
en
t
o
f
lo
ad
,
s
to
r
ag
e
an
d
f
o
r
ec
asti
n
g
o
f
PV
p
r
o
d
u
ctio
n
.
I
t
also
o
f
f
er
s
p
o
te
n
tial
f
o
r
u
s
e
in
u
r
b
a
n
,
r
u
r
a
l
o
r
is
o
lated
ar
ea
s
,
th
an
k
s
to
i
m
p
r
o
v
e
d
g
r
i
d
co
m
p
atib
ilit
y
a
n
d
o
p
tim
ized
e
n
er
g
y
m
an
ag
e
m
en
t.
I
n
p
a
r
ticu
lar
,
it
o
f
f
er
s
an
o
p
p
o
r
tu
n
ity
to
im
p
lem
en
t
s
u
ch
a
g
r
id
-
co
n
n
ec
t
ed
p
h
o
to
v
o
ltaic
s
y
s
tem
u
s
in
g
a
Sem
ik
r
o
n
-
t
y
p
e
ex
p
er
im
en
tal
b
en
c
h
m
ater
ializ
in
g
th
e
in
v
e
r
ter
,
with
s
im
u
lated
co
n
tr
o
ller
s
im
p
lem
e
n
ted
u
s
in
g
a
d
SP
AC
E
1
1
0
4
b
o
ar
d
co
m
b
in
ed
with
MA
T
L
AB
/
Simu
lin
k
.
T
h
is
r
esear
ch
will
p
r
o
v
id
e
a
s
o
lid
b
asis
f
o
r
th
e
r
ea
lizatio
n
o
f
s
in
g
le
-
s
tag
e
th
r
ee
-
p
h
ase
p
h
o
to
v
o
ltaic
s
y
s
tem
s
ass
o
ciate
d
wit
h
a
g
r
id
-
co
n
n
ec
ted
th
r
ee
-
p
h
as
e
in
v
er
ter
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
DATA AV
AI
L
AB
I
L
I
T
Y
Data
a
v
aila
b
i
lit
y
is
n
o
t
a
p
p
li
ca
b
le
t
o
t
h
is
p
ap
er
as
n
o
n
e
w
d
a
t
a
w
er
e
cr
ea
te
d
o
r
an
al
y
z
e
d
i
n
t
h
is
s
t
u
d
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.