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~
1
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I
SS
N:
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8
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118
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a
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P
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).
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o
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ims
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ro
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s
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C
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r
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en
t v
ec
to
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DC
b
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t
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v
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ter
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lectr
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g
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id
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ax
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t tr
ac
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Ph
o
to
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ltaic
s
y
s
tem
Seco
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d
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s
lid
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g
m
o
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e
co
n
tr
o
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T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
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r th
e
CC B
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SA
li
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se
.
C
o
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s
p
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nd
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A
uth
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r
:
No
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d
i
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e
E
ch
-
c
h
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k
i
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ab
o
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ato
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y
: E
lectr
o
n
ics,
I
n
s
tr
u
m
en
tatio
n
a
n
d
E
n
e
r
g
y
(
L
E
I
E
)
,
Facu
lty
o
f
Scien
ce
C
h
o
u
aib
Do
u
k
k
ali
Un
iv
er
s
ity
E
l Jad
id
a
,
Mo
r
o
cc
o
E
m
ail:
ch
er
k
i.u
c
d
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t
y
ea
r
s
,
th
e
ad
v
an
ce
m
en
t
in
r
en
ewa
b
le
a
n
d
g
r
ee
n
en
er
g
y
u
tili
za
tio
n
h
as
em
er
g
ed
as
a
k
ey
s
o
lu
tio
n
to
en
v
ir
o
n
m
en
tal
p
o
llu
tio
n
ca
u
s
ed
b
y
f
o
s
s
il
f
u
els
an
d
th
e
d
ec
lin
e
in
en
er
g
y
p
r
o
d
u
ctio
n
[
1
]
.
R
en
ewa
b
le
en
er
g
y
-
b
ased
p
o
w
er
g
en
e
r
atio
n
s
y
s
tem
s
ar
e
n
o
w
cr
u
cial
i
n
g
l
o
b
al
e
n
er
g
y
p
r
o
d
u
ctio
n
.
Am
o
n
g
th
e
av
ailab
le
r
en
ewa
b
le
s
o
u
r
ce
s
,
p
h
o
to
v
o
ltaic
(
PV)
e
n
er
g
y
s
tan
d
s
o
u
t
as
th
e
m
o
s
t
f
av
o
r
ab
l
e
o
p
tio
n
d
u
e
to
its
wid
esp
r
ea
d
av
ailab
ilit
y
,
en
v
ir
o
n
m
en
tal
b
en
e
f
its
,
an
d
co
s
t
-
f
r
ee
n
atu
r
e
[
2
]
.
C
o
m
p
ar
ed
to
o
t
h
er
en
er
g
y
s
o
u
r
ce
s
,
PV
s
y
s
tem
s
ar
e
h
ig
h
ly
r
eg
ar
d
ed
f
o
r
th
eir
d
u
r
a
b
ilit
y
an
d
e
f
f
icien
cy
,
estab
lis
h
in
g
PV
as
a
r
ap
id
ly
g
r
o
win
g
en
er
g
y
s
o
u
r
ce
wo
r
ld
wid
e
.
PV
s
y
s
tem
s
ar
e
ex
p
ec
ted
to
g
r
o
w
b
y
1
5
%
b
etwe
en
2
0
2
0
an
d
2
0
4
0
an
d
h
av
e
th
e
p
o
ten
tial
to
g
e
n
er
ate
9
0
0
0
T
W
h
,
r
ep
r
esen
tin
g
2
6
%
o
f
p
r
o
j
ec
ted
g
lo
b
al
d
em
an
d
[
3
]
.
T
h
is
tr
en
d
r
e
q
u
ir
es
m
o
s
t
p
h
o
to
v
o
ltaic
p
o
wer
g
en
er
atio
n
p
lan
ts
to
m
a
k
e
s
u
b
s
tan
tial
ch
an
g
es
to
th
eir
o
p
e
r
atio
n
al
an
d
co
n
tr
o
l
s
tr
u
ctu
r
es
.
C
o
n
s
eq
u
en
tly
,
m
a
n
y
r
esear
c
h
er
s
h
av
e
p
r
o
p
o
s
ed
v
ar
io
u
s
co
n
tr
o
l
co
n
f
ig
u
r
ati
o
n
s
to
i
m
p
r
o
v
e
th
e
d
esire
d
o
p
er
atio
n
al
c
h
ar
ac
ter
is
tics
[
4
]
.
I
n
th
e
liter
atu
r
e
,
m
o
s
t
ar
ticles
o
n
g
r
id
-
c
o
n
n
ec
te
d
PV
s
y
s
tem
s
co
n
ce
n
tr
ate
o
n
in
v
er
ter
co
n
tr
o
l.
T
h
ese
m
eth
o
d
s
ty
p
ically
em
p
lo
y
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
(
PI)
co
n
t
r
o
ller
s
to
r
eg
u
late
th
e
V
dc
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Hig
h
o
r
d
er sl
id
in
g
mo
d
e
c
o
n
tr
o
l fo
r
g
r
id
in
teg
r
a
tio
n
o
f p
h
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to
vo
lta
ic
s
ystems
(
N
o
u
r
ed
d
in
e
E
ch
-
ch
erki
)
119
th
e
cu
r
r
e
n
t
s
u
p
p
lied
to
th
e
g
r
id
,
en
s
u
r
in
g
m
ax
im
u
m
ac
tiv
e
p
o
we
r
tr
a
n
s
f
er
(
P).
Fo
r
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT
)
co
n
tr
o
l,
t
h
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O
)
te
ch
n
iq
u
e
is
co
m
m
o
n
l
y
u
s
ed
d
u
e
to
its
s
im
p
licity
an
d
s
atis
f
ac
to
r
y
r
esu
lts
[
5
]
.
H
o
wev
er
,
it
is
im
p
o
r
tan
t
t
o
n
o
t
e
th
at
th
is
tech
n
iq
u
e
ex
h
ib
its
f
lu
ctu
atio
n
s
ar
o
u
n
d
th
e
o
p
er
atin
g
p
o
in
t
an
d
ca
n
l
o
s
e
th
is
p
o
in
t
d
u
r
in
g
r
ap
id
c
h
an
g
es
i
n
ir
r
ad
iatio
n
,
s
o
f
o
r
h
ig
h
-
q
u
ality
en
er
g
y
tr
an
s
f
er
,
an
alter
n
ativ
e
m
eth
o
d
f
o
r
MPPT
is
r
eq
u
ir
e
d
[
6
]
.
O
n
e
m
eth
o
d
th
at
f
u
lf
ills
th
is
r
eq
u
ir
em
en
t
is
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
,
p
ar
ticu
lar
ly
h
ig
h
-
o
r
d
e
r
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
HOSMC).
SMC
is
v
alu
ed
f
o
r
it
s
r
o
b
u
s
tn
ess
ag
ain
s
t
clim
atic
f
lu
ctu
atio
n
s
.
HOSMC
is
in
tr
o
d
u
ce
d
to
o
v
er
c
o
m
e
th
e
c
h
allen
g
es
ass
o
ciate
d
with
f
ir
s
t
-
o
r
d
er
SMC
,
esp
ec
ially
th
e
s
ig
n
if
ican
t
is
s
u
e
o
f
c
h
at
ter
in
g
ar
o
u
n
d
th
e
s
lid
in
g
s
u
r
f
ac
e
(
σ
)
[
7
]
.
T
h
e
d
ev
elo
p
m
e
n
t
o
f
g
r
i
d
-
co
n
n
ec
te
d
PV
s
y
s
tem
s
h
as
led
m
an
y
r
esear
ch
er
s
to
s
tu
d
y
th
eir
r
o
b
u
s
tn
ess
an
d
s
tab
ilit
y
.
Fo
r
in
s
tan
ce
,
De
b
d
o
u
ch
e
et
a
l
.
[
8
]
p
r
o
p
o
s
e
a
co
n
tr
o
l
s
tr
a
teg
y
f
o
r
g
r
id
-
c
o
n
n
ec
te
d
in
v
er
ter
s
th
at
co
m
b
in
e
s
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
with
in
te
g
r
al
s
lid
in
g
m
o
d
e
co
n
tr
o
l
.
Ali
et
a
l
.
[
9
]
s
h
o
w
t
h
at
co
m
b
in
in
g
f
u
zz
y
lo
g
ic
co
n
tr
o
l
(
FLC)
with
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
s
en
h
an
ce
s
MPPT
c
o
m
p
ar
ed
t
o
P&
O
m
eth
o
d
s
.
W
h
ile
th
is
tech
n
iq
u
e
o
f
f
er
s
r
o
b
u
s
t
p
er
f
o
r
m
an
ce
in
m
in
im
izin
g
r
esp
o
n
s
e
tim
e,
it
is
co
m
p
lex
to
im
p
lem
en
t.
An
o
t
h
er
MPPT
m
eth
o
d
,
in
t
r
o
d
u
ce
d
in
[
1
0
]
,
em
p
lo
y
s
n
eu
r
o
-
f
u
zz
y
lo
g
ic
(
NFL
)
to
im
p
r
o
v
e
o
u
tp
u
t
p
o
wer
an
d
r
esp
o
n
s
e
tim
e
u
n
d
er
v
ar
y
i
n
g
clim
atic
co
n
d
itio
n
s
.
Z
h
en
g
et
a
l
.
[
1
1
]
d
escr
ib
e
an
MPPT
s
tr
ateg
y
u
s
in
g
a
f
i
r
s
t
-
o
r
d
er
p
lu
s
in
te
g
r
al
p
lu
s
d
er
iv
ativ
e
(
FOPID)
co
n
tr
o
ller
to
elim
in
ate
d
is
tu
r
b
a
n
ce
s
af
f
e
ctin
g
o
u
tp
u
t
v
o
ltag
e,
d
em
o
n
s
tr
atin
g
en
h
a
n
ce
d
p
er
f
o
r
m
an
ce
an
d
d
y
n
a
m
ic
r
esp
o
n
s
e
co
m
p
ar
e
d
to
tr
ad
i
tio
n
al
m
eth
o
d
s
.
I
n
[
1
2
]
,
an
ad
a
p
tiv
e
p
e
r
tu
r
b
in
g
f
u
z
zy
T
a
k
ag
i
-
Su
g
e
n
o
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
Fu
zz
y
T
-
S
SMC
)
ap
p
r
o
ac
h
is
d
ev
elo
p
e
d
f
o
r
ac
c
u
r
ate
MPPT
tr
ac
k
in
g
an
d
r
ed
u
ci
n
g
o
s
c
ill
atio
n
s
ar
o
u
n
d
th
e
MPP.
Sh
ah
d
ad
i
et
a
l
.
[
1
3
]
p
r
esen
t
SMC
co
n
tr
o
l
f
o
r
a
S
E
PIC
b
o
o
s
t
co
n
v
er
ter
,
ac
h
iev
in
g
p
r
ec
is
e
MPP
tr
ac
k
in
g
an
d
in
cr
ea
s
ed
s
y
s
tem
r
o
b
u
s
tn
ess
.
Gu
o
et
a
l
.
[
1
4
]
s
u
g
g
est
u
s
in
g
a
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
m
o
d
e
co
n
t
r
o
l
(
SOSMC
)
co
n
f
ig
u
r
atio
n
f
o
r
a
PV
s
y
s
tem
with
a
s
in
g
le
p
o
wer
co
n
v
er
ter
,
aim
in
g
to
g
en
er
ate
s
in
u
s
o
id
al
cu
r
r
en
t
f
o
r
t
h
e
g
r
i
d
an
d
r
ed
u
ce
h
ar
m
o
n
ics,
th
u
s
im
p
r
o
v
in
g
r
o
b
u
s
tn
ess
ag
ain
s
t
s
o
lar
ir
r
ad
ian
ce
f
lu
ctu
atio
n
s
.
B
en
is
s
et
a
l
.
[
1
5
]
d
is
cu
s
s
f
r
ac
tio
n
al
o
r
d
er
SMC
(
FOSMC
)
to
o
p
tim
ize
p
o
we
r
d
eliv
er
y
an
d
r
eg
u
late
DC
v
o
ltag
e
in
p
er
m
an
e
n
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
ato
r
s
(
PMSG)
,
s
h
o
win
g
f
ast
r
esp
o
n
s
e
u
n
d
er
v
a
r
iab
le
win
d
co
n
d
itio
n
s
.
No
n
lin
ea
r
i
n
teg
r
al
b
ac
k
s
tep
p
in
g
(
NI
B
)
f
o
r
PV
s
y
s
tem
s
,
as
p
r
esen
ted
in
[
1
6
]
,
p
r
o
v
ed
ef
f
icien
t,
t
h
o
u
g
h
co
m
p
lex
ity
is
s
u
es
ca
n
lead
to
h
ig
h
er
e
n
er
g
y
co
s
ts
.
An
in
tellig
en
t
MPPT
ap
p
r
o
ac
h
co
m
b
in
in
g
n
e
u
r
al
n
etwo
r
k
s
an
d
f
u
zz
y
l
o
g
ic
(
NN
-
FL)
f
o
r
PV
co
n
tr
o
l
is
d
etailed
in
[
1
7
]
,
o
f
f
er
i
n
g
in
cr
ea
s
ed
r
o
b
u
s
tn
ess
an
d
r
ap
id
d
y
n
a
m
ic
r
esp
o
n
s
e
co
m
p
a
r
ed
to
co
n
v
en
tio
n
al
m
eth
o
d
s
.
R
o
y
et
a
l
.
[
1
8
]
in
tr
o
d
u
ce
an
SMC
co
n
tr
o
ller
u
s
in
g
a
two
-
p
o
wer
-
l
aw
co
n
tr
o
l
m
eth
o
d
f
o
r
PV
s
y
s
tem
s
an
d
b
atter
y
-
p
o
wer
ed
DC
m
icr
o
g
r
id
s
,
alth
o
u
g
h
ch
atter
in
g
r
em
ain
s
a
m
ajo
r
d
r
awb
ac
k
.
Var
io
u
s
im
p
r
o
v
em
e
n
t
m
eth
o
d
s
,
in
clu
d
in
g
th
e
t
er
m
in
al
SMC
(
T
SMC
)
tech
n
iq
u
e
cited
in
[
1
9
]
,
c
o
n
tin
u
o
u
s
n
o
n
lin
ea
r
p
r
ed
ictiv
e
co
n
tr
o
l
with
i
n
teg
r
al
SMC
(
I
SMC
)
d
escr
ib
ed
in
[
2
0
]
,
an
d
f
u
zz
y
SMC
(
FS
M
C
)
p
r
esen
ted
in
[
2
1
]
,
ex
p
lo
r
e
d
if
f
e
r
en
t
s
tr
ateg
ies
to
en
h
a
n
ce
p
e
r
f
o
r
m
an
ce
.
W
h
ile
th
ese
s
tr
ateg
ies
p
r
o
v
id
e
n
u
m
er
o
u
s
b
e
n
ef
its
,
th
ey
also
co
m
e
with
d
r
awb
ac
k
s
,
s
u
ch
as
p
o
wer
f
lu
ctu
atio
n
s
an
d
h
ig
h
lev
el
s
o
f
T
HD
,
wh
ich
n
eg
ativ
ely
im
p
ac
t
o
v
er
all
p
o
we
r
q
u
ality
.
T
ab
le
1
s
u
m
m
ar
izes th
e
ad
v
a
n
tag
es a
n
d
d
is
ad
v
a
n
tag
es o
f
s
o
m
e
o
f
t
h
ese
s
tr
ateg
ies.
I
n
th
is
co
n
tex
t,
th
e
SOSTM
an
d
MPPT
-
SOSMC
co
n
tr
o
ll
er
s
ar
e
th
e
m
a
jo
r
co
n
tr
ib
u
tio
n
s
o
f
th
is
p
ap
er
.
T
h
e
r
esu
lts
ar
e
co
m
p
ar
ed
with
th
e
co
n
v
en
tio
n
al
tech
n
iq
u
e
r
eg
ar
d
i
n
g
d
y
n
a
m
ic
r
esp
o
n
s
e,
o
v
e
r
s
h
o
o
t
an
d
T
HD
u
n
d
er
two
d
if
f
e
r
en
t
ir
r
a
d
iatio
n
p
r
o
f
iles
.
Simu
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
its
ef
f
ec
tiv
en
ess
co
m
p
ar
ed
t
o
co
n
v
en
tio
n
al
co
n
tr
o
l m
eth
o
d
s
.
T
h
er
ef
o
r
e,
th
e
p
r
in
cip
al
c
o
n
tr
ib
u
tio
n
s
o
f
t
h
is
wo
r
k
ar
e
as f
o
l
lo
ws:
-
T
h
e
SOSMC
m
eth
o
d
r
ed
u
ce
s
t
h
e
ch
atter
in
g
e
f
f
ec
ts
of
tr
a
d
itio
n
al
SMC
;
-
T
h
e
MPPT
-
SOSMC
m
eth
o
d
r
ep
lace
s
th
e
P&
O
to
im
p
r
o
v
e
MPPT
;
-
T
h
e
d
ev
elo
p
ed
SOSMC
m
eth
o
d
r
ed
u
ce
s
th
e
T
HD
of
t
h
e
cu
r
r
en
t
in
jecte
d
to
t
h
e
g
r
id
;
a
n
d
-
R
ed
u
ce
P
an
d
Q
o
v
er
s
h
o
o
ts
an
d
s
tead
y
-
s
tate
er
r
o
r
s
.
T
h
e
s
tr
u
ctu
r
e
of
th
is
ar
ticle
is
:
t
he
f
ir
s
t
s
ec
tio
n
p
r
esen
ts
t
h
e
in
tr
o
d
u
ctio
n
to
t
h
is
wo
r
k
.
T
h
e
s
ec
o
n
d
s
ec
tio
n
d
escr
ib
es
th
e
p
h
o
to
v
o
ltaic
g
en
er
ato
r
(
PVG
)
m
o
d
el,
th
e
DC
-
D
C
,
DC
-
AC
co
n
v
er
ter
an
d
its
SO
SM
C
co
n
tr
o
l.
T
h
e
th
ir
d
s
ec
tio
n
d
e
tails
th
e
s
im
u
latio
n
r
esu
lts
a
n
d
an
aly
s
is
of
th
e
p
r
o
p
o
s
ed
SOSM
C
m
eth
o
d
,
in
clu
d
in
g
a
co
m
p
a
r
is
o
n
with
th
e
co
n
v
en
tio
n
al
v
ec
to
r
co
n
tr
o
l
(
C
VC
)
tech
n
iq
u
e,
wh
ile
th
e
f
o
u
r
th
s
ec
tio
n
p
r
esen
ts
a
g
en
er
al
c
o
n
clu
s
io
n
of
th
is
s
tu
d
y
.
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
o
f
s
o
m
e
s
tr
ateg
ies u
s
ed
in
PV sy
s
tem
c
o
n
tr
o
l
S
t
r
a
t
e
g
y
N
a
me
A
d
v
a
n
t
a
g
e
D
i
sad
v
a
n
t
a
g
e
F
LC
a
n
d
P
S
O
[
9
]
R
o
b
u
st
f
o
r
m
i
n
i
mi
z
i
n
g
r
e
s
p
o
n
s
e
t
i
me
C
o
m
p
l
e
x
h
a
r
d
w
a
r
e
a
n
d
p
r
o
g
r
a
m
mi
n
g
r
e
q
u
i
r
e
d
N
F
L
[
1
0
]
R
a
p
i
d
c
o
n
v
e
r
g
e
n
c
e
O
sci
l
l
a
t
i
o
n
n
e
a
r
t
h
e
o
p
e
r
a
t
i
n
g
p
o
i
n
t
F
O
P
I
D
[
1
1
]
R
a
p
i
d
d
y
n
a
mi
c
r
e
s
p
o
n
s
e
La
r
g
e
o
v
e
r
r
u
n
S
M
C
[
1
3
]
S
i
mp
l
e
a
n
d
i
n
e
x
p
e
n
s
i
v
e
C
h
a
t
t
e
r
i
n
g
N
I
B
[
1
6
]
G
o
o
d
p
e
r
f
o
r
ma
n
c
e
H
i
g
h
e
r
c
o
n
st
r
u
c
t
i
o
n
c
o
s
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
18
-
1
26
120
2.
P
RO
P
O
SE
D
SYS
T
E
M
Fig
u
r
e
1
illu
s
tr
ates a
d
iag
r
am
o
f
a
PV s
y
s
tem
co
n
n
ec
ted
to
a
g
r
id
th
r
o
u
g
h
two
p
o
wer
c
o
n
v
er
ter
s
.
T
h
e
f
ir
s
t
co
n
v
e
r
ter
,
o
p
er
atin
g
as
a
DC
-
DC
co
n
v
er
ter
in
b
o
o
s
t
m
o
d
e,
is
d
esig
n
ed
to
r
eg
u
late
p
o
wer
o
n
th
e
PVG
s
id
e.
T
h
e
s
ec
o
n
d
co
n
v
er
te
r
,
f
u
n
ctio
n
in
g
as
a
DC
-
AC
in
v
er
ter
,
is
p
r
im
ar
ily
r
esp
o
n
s
ib
le
f
o
r
m
ain
tain
i
n
g
a
co
n
s
tan
t V
dc
an
d
en
s
u
r
in
g
a
u
n
ity
p
o
wer
f
ac
t
o
r
(
UPF)
.
2
.
1
.
M
o
delin
g
o
f
t
he
P
V
g
ener
a
t
o
r
T
h
e
PVG
is
co
m
p
o
s
ed
o
f
PV
ce
lls
ar
r
an
g
ed
in
a
s
er
ies
-
p
ar
allel
co
n
f
ig
u
r
atio
n
to
p
r
o
d
u
ce
elec
tr
icity
d
ir
ec
tly
f
r
o
m
s
u
n
lig
h
t.
Fig
u
r
e
1
s
h
o
ws th
e
cir
cu
it d
iag
r
am
o
f
a
s
in
g
le
-
d
io
d
e
PV c
ell.
Fig
u
r
e
2
s
h
o
ws th
e
ef
f
ec
t
o
f
tem
p
er
at
u
r
e
an
d
ir
r
ad
ia
n
ce
o
n
th
e
PVG
p
ar
am
ete
r
s
(P
-
V)
.
T
h
e
PVG
is
m
o
d
eled
u
s
in
g
(
1
)
[
2
1
]
.
pv
=
i
ph
-
i
0
[
E
xp
(
A.k
.T
(
pv
+
i
pv
.
R
)
)
-
1
]
-
(
pv
+
i
pv
.
R
sh
)
(
1
)
T
h
e
p
h
o
to
cu
r
r
en
t
i
ph
,
in
f
l
u
en
c
ed
b
y
t
h
e
ir
r
ad
ia
n
ce
an
d
ce
ll tem
p
er
atu
r
e,
is
g
iv
en
b
y
(
2
)
.
ph
=
[
sc
+
K
.
(
T
-
T
)
]
.
(
)
(
2
)
W
h
er
e:
sc
is
s
h
o
rt
-
cir
cu
it
cu
r
r
e
n
t
,
q
is
th
e
elec
tr
ic
c
h
ar
g
e,
is
th
e
B
o
ltzm
an
n
co
n
s
tan
t,
K
is
th
e
cu
r
r
e
n
t
tem
p
er
atu
r
e
c
o
ef
f
ici
en
t,
is
th
e
ce
ll'
s
id
ea
li
ty
f
ac
to
r
,
is
th
e
i
r
r
ad
ian
ce
,
is
th
e
r
ef
er
e
n
ce
ir
r
ad
ian
ce
,
is
th
e
tem
p
er
atu
r
e
,
T
is
tem
p
er
atu
r
e
r
ef
er
en
ce
,
is
th
e
v
o
ltag
e
in
an
o
p
en
cir
cu
it
,
is
th
e
b
an
d
g
ap
en
er
g
y
,
an
d
ℎ
ar
e
th
e
s
er
ies an
d
s
h
u
n
t r
esis
to
r
s
,
an
d
is
th
e
n
u
m
b
e
r
o
f
s
er
ies ce
lls
.
F
i
g
u
r
e
1
.
T
o
p
o
l
o
g
y
o
f
P
V
S
c
o
n
n
e
c
t
e
d
t
o
g
r
i
d
(
a)
(
b
)
Fig
u
r
e
2
.
P
-
V
ch
a
r
ac
ter
is
tics
o
f
PV
G
ac
co
r
d
in
g
t
o
(
a)
i
r
r
ad
ia
tio
n
an
d
(b
)
tem
p
er
atu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Hig
h
o
r
d
er sl
id
in
g
mo
d
e
c
o
n
tr
o
l fo
r
g
r
id
in
teg
r
a
tio
n
o
f p
h
o
to
vo
lta
ic
s
ystems
(
N
o
u
r
ed
d
in
e
E
ch
-
ch
erki
)
121
2
.
2
.
SO
SM
C
co
ntr
o
ller
des
ig
n
I
n
th
e
SMC
tech
n
iq
u
e,
th
e
s
y
s
tem
tr
ajec
to
r
ies
ar
e
g
u
id
ed
to
war
d
s
a
s
p
ec
if
ic
s
u
r
f
ac
e
k
n
o
wn
as
th
e
s
lid
in
g
s
u
r
f
ac
e
(
σ
)
,
wh
e
r
e
d
esira
b
le
ch
ar
ac
ter
is
tics
ar
e
a
ch
iev
ed
.
T
h
e
co
n
tr
o
ller
e
n
s
u
r
es
th
at
th
e
s
y
s
tem
r
em
ain
s
o
n
th
is
s
u
r
f
ac
e
at
all
tim
es
[
2
2
]
,
[
2
3
]
.
Ho
wev
er
,
th
is
m
eth
o
d
ca
n
lead
to
p
er
s
is
ten
t
o
s
cillatio
n
s
in
th
e
s
tead
y
s
tate,
wh
ich
is
u
n
d
esir
ab
le.
I
n
co
n
tr
ast,
th
e
SOSMC
m
eth
o
d
is
r
eg
ar
d
e
d
as
o
n
e
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
s
tr
ateg
ies f
o
r
r
ed
u
ci
n
g
ch
atter
i
n
g
ef
f
ec
ts
an
d
en
h
a
n
cin
g
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
PV sy
s
tem
[
2
4
]
.
T
h
e
s
u
r
f
ac
e
σ
is
ex
p
r
ess
ed
as
(
3
)
.
σ
=
x
re
f
-
x
(3
)
W
h
er
e
x
is
th
e
p
ar
a
m
eter
to
b
e
r
eg
u
lated
an
d
x
re
f
its
r
ef
er
en
c
e.
T
h
e
SOSMC
co
n
tr
o
ller
(
)
co
m
p
r
is
es
two
c
o
m
p
o
n
en
ts
: th
e
eq
u
iv
ale
n
t c
o
n
tr
o
l c
o
m
p
o
n
e
n
t (
u
eq
)
an
d
th
e
SO
SMC
alg
o
r
ith
m
ter
m
(
u
SO
)
[
2
4
]
.
=
u
eq
+
u
SO
(4
)
T
h
e
ter
m
u
eq
is
d
eter
m
in
ed
b
y
(
5
)
.
d
σ
dt
=
0
(5
)
T
h
e
u
SO
ter
m
en
s
u
r
es
th
at
th
e
PV
s
y
s
tem
r
em
ain
s
o
n
th
e
σ
d
esp
ite
p
ar
am
eter
v
ar
iatio
n
s
an
d
ir
r
a
d
iatio
n
ch
an
g
es
.
T
h
e
ex
p
r
ess
io
n
f
o
r
u
SO
is
g
iv
en
b
y
(
6
)
.
SO
=
u
1
+
u
2
(6
)
W
h
er
e:
{
1
=
β
1
|
|
0.5
.
s
ign
(
)
2
=
β
2
∫
s
ign
(
)
.dt
(7
)
W
h
er
e
β1
an
d
β2
ar
e
th
e
SOSMC
g
ain
s
.
2
.
3
.
M
o
delin
g
a
nd
co
ntr
o
l d
esig
n o
f
t
he
bo
o
s
t
co
nv
er
t
er
T
h
e
b
o
o
s
t
c
o
n
v
er
ter
is
u
s
ed
to
ad
ju
s
t
th
e
v
o
ltag
e
b
etwe
en
th
e
PVG
an
d
th
e
in
v
er
ter
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
o
b
jectiv
es
ar
e
to
m
ain
tain
MPP
an
d
in
cr
ea
s
e
o
u
tp
u
t
v
o
ltag
e
[
2
5
]
.
T
h
e
d
iag
r
a
m
o
f
t
h
e
b
o
o
s
t
co
n
v
er
te
r
u
s
ed
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
ch
ar
ac
ter
is
tic
eq
u
atio
n
s
o
f
th
e
b
o
o
s
t c
o
n
v
er
ter
a
r
e
g
iv
e
n
b
y
(
8
)
.
{
d
i
pv
dt
=
1
.
[
pv
-
(
1
-
α
)
.
V
dc
]
d
V
dc
dt
=
1
0
.
[
(
1
-
α
)
.
i
−
dc
]
(
8
)
W
h
er
e
α
is
th
e
d
u
ty
cy
cle
α
.
B
ased
o
n
th
e
P
-
V
an
d
I
-
V
p
r
o
f
iles
o
f
t
h
e
PVG
p
r
esen
ted
i
n
Fig
u
r
e
2
,
it
ca
n
b
e
d
ed
u
ce
d
th
at
wh
e
n
o
p
er
atin
g
at
MPP
:
d
P
pv
d
V
pv
=
(
pv
.
i
pv
)
d
V
pv
=
i
pv
+
V
pv
⋅
d
i
pv
d
V
pv
=
0
(
9
)
t
h
e
s
u
r
f
ac
e
σ
is
d
ete
r
m
i
n
ed
ac
co
r
d
in
g
to
(
1
0
)
to
r
ea
ch
t
h
e
M
PP
[
2
6
].
σ
=
d
P
pv
d
V
pv
(
1
0
)
T
h
e
eq
u
iv
ale
n
t c
o
n
tr
o
l te
r
m
eq
o
f
th
e
SOSMC
co
n
tr
o
ller
is
d
eter
m
in
ed
b
y
(
1
0
)
.
eq
=
1
-
pv
dc
(
1
1
)
F
r
o
m
th
e
(
4
)
,
(
6
)
,
(
7
)
,
a
n
d
(
1
1
)
,
th
e
f
in
al
ex
p
r
ess
io
n
f
o
r
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l sig
n
al
is
g
iv
en
b
y
(
1
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
18
-
1
26
122
=
1
-
pv
dc
+
1
×
|
|
0.5
×
s
ign
(
)
+
2
×
∫
s
ign
(
)
×
dt
(
12
)
2
.
4
.
M
o
delin
g
a
nd
co
ntr
o
l d
esig
n o
n t
he
g
rid sid
e
wit
h
S
O
SM
C
T
h
e
in
v
er
te
r
'
s
r
o
le
is
to
m
ain
tain
a
co
n
s
tan
t
V
dc
an
d
r
e
g
u
lat
e
th
e
P
an
d
Q
in
jecte
d
in
to
th
e
g
r
id
to
en
s
u
r
e
a
UPF
.
I
n
th
is
s
tu
d
y
,
a
two
-
lo
o
p
co
n
tr
o
l
s
ch
em
e
is
u
s
ed
:
th
e
in
ter
n
al
lo
o
p
s
r
eg
u
late
th
e
q
u
ad
r
atu
r
e
(
i
q
)
an
d
d
i
r
ec
t
(
i
d
)
cu
r
r
e
n
ts
,
wh
ile
th
e
ex
t
e
r
n
al
lo
o
p
c
o
n
tr
o
ls
V
dc
an
d
g
en
er
ates
t
h
e
r
e
f
er
en
ce
cu
r
r
en
t
(
i
d
-
ref
)
.
T
h
e
cir
cu
it
d
iag
r
am
o
f
th
e
in
v
er
ter
co
n
n
ec
ted
to
th
e
g
r
id
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
Par
k
tr
an
s
f
o
r
m
a
tio
n
is
ap
p
lie
d
to
co
n
v
e
r
t th
e
in
v
e
r
ter
'
s
th
r
ee
-
p
h
ase
co
o
r
d
in
ates in
to
two
s
y
n
ch
r
o
n
o
u
s
d
-
q
r
o
tatio
n
al
co
o
r
d
in
ates [
2
7
]
.
{
d
i
dt
=
1
⋅
(
-
R
.
i
-
e
)
+
L
ω
i
d
i
dt
=
1
⋅
(
-
R
.
i
-
e
)
-
L
ω
i
(
1
3
)
W
h
en
th
e
ten
s
io
n
v
ec
to
r
is
alig
n
ed
o
n
th
e
d
-
ax
is
,
th
e
P a
n
d
Q
ar
e
g
iv
en
with
:
{
P
=
3
2
.
V.
i
Q
=
3
2
.
V.
i
(
14
)
P
an
d
Q
ca
n
th
er
ef
o
r
e
b
e
c
o
n
tr
o
lled
b
y
r
e
g
u
latin
g
i
q
an
d
i
d
.
T
h
u
s
,
th
e
i
q
r
ef
er
e
n
ce
(
i
q_ref
)
is
k
ep
t
at
ze
r
o
to
ac
h
iev
e
UPF,
wh
ile
i
d
r
e
f
er
en
ce
(
i
d_ref
)
is
d
eter
m
in
e
d
b
y
th
e
V
dc
co
n
tr
o
ller
.
T
h
e
o
b
jectiv
e
o
f
SOSMC
in
v
er
ter
co
n
tr
o
l
is
t
o
elim
in
ate
th
e
c
h
a
tter
in
g
p
h
en
o
m
en
o
n
b
y
a
d
d
in
g
an
in
teg
r
al
ter
m
to
th
e
cu
r
r
e
n
t
er
r
o
r
.
T
h
e
σ
ca
n
b
e
d
escr
ib
ed
as
(
1
5
)
[
1
5
]
.
dq
=
i
dq
-
re
f
-
i
dq
(
1
5
)
u
eq
is
d
eter
m
in
ed
f
r
o
m
th
e
(
5
)
,
(
1
3
)
,
a
n
d
(
1
5
)
as
(
1
6
)
.
{
d
-
eq
=
d
i
d
-
r
e
f
dt
+
R
.
i
-
L
ω
i
+
e
q
-
eq
=
R
.
i
+
L
ω
i
+
e
(
1
6
)
T
h
e
f
in
al
ex
p
r
ess
io
n
s
o
f
th
e
p
r
o
p
o
s
ed
co
m
m
an
d
s
ar
e
g
iv
en
a
s
(
1
7
)
.
{
=
d
i
d
-
r
e
f
dt
+
R
×
i
-
L
ω
i
+
e
-
λ
1
×
|
|
0.5
×
s
ign
(
)
-
λ
2
×
∫
s
ign
(
)
×
dt
=
R
×
i
+
L
ω
i
+
e
−
λ
3
×
|
|
0.5
×
s
ign
(
)
-
λ
4
×
∫
s
ign
(
)
×
dt
(
1
7
)
3.
T
H
E
R
E
SU
L
T
S AN
D
D
I
SC
USSI
O
N
I
n
th
is
s
tu
d
y
,
th
e
PVG
u
s
e
d
p
r
o
v
i
d
es
a
m
ax
im
u
m
p
o
wer
o
f
1
6
0
k
W
at
G=
1
0
0
0
W
/m
2
.
A
co
m
p
ar
ativ
e
an
aly
s
is
b
etwe
en
SOSMC
an
d
co
n
v
en
tio
n
al
C
VC
is
co
n
d
u
cted
to
d
em
o
n
s
tr
a
te
th
e
e
f
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
tech
n
i
q
u
e.
T
h
e
ir
r
ad
iatio
n
p
r
o
f
ile
u
tili
ze
d
is
d
ep
icted
in
Fig
u
r
es
3
(
a)
an
d
3
(
b
)
.
T
h
e
s
im
u
latio
n
re
s
u
lts
ar
e
p
r
esen
ted
in
Fig
u
r
e
s
3
th
r
o
u
g
h
7
.
T
ab
le
2
g
iv
es th
e
PVS p
ar
am
eter
s
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
P
an
d
Q
in
jecte
d
in
to
th
e
g
r
id
u
s
i
n
g
b
o
th
th
e
SOSMC
co
n
tr
o
l
an
d
C
V
C
m
eth
o
d
f
o
r
s
tep
(
Fig
u
r
e
4
(
a)
)
an
d
r
ea
l
(
Fig
u
r
e
4
(
b
)
)
ir
r
a
d
iatio
n
ch
a
n
g
es.
I
t
is
ev
i
d
en
t
th
at
P
q
u
ick
ly
c
o
n
v
e
r
g
es
to
its
MP
P
with
h
ig
h
p
r
ec
is
io
n
d
u
r
in
g
ir
r
ad
iatio
n
v
a
r
iatio
n
s
.
At
G=
1
0
0
0
W
/m
2
,
P
r
ea
ch
es
its
m
ax
im
u
m
v
alu
e
o
f
1
6
0
k
W
s
u
p
p
lied
b
y
th
e
PVG,
with
th
e
o
v
er
s
h
o
o
t r
ed
u
ce
d
to
ze
r
o
,
wh
ile
Q
r
em
ain
s
at
ze
r
o
.
Fig
u
r
e
5
s
h
o
ws
th
e
d
y
n
am
ics
o
f
V
dc
,
d
em
o
n
s
tr
atin
g
th
at
it
cl
o
s
e
ly
f
o
llo
ws
its
r
ef
er
en
ce
v
alu
e
in
a
v
e
r
y
s
h
o
r
t
tim
e,
with
m
in
im
al
s
tead
y
-
s
tate
er
r
o
r
f
o
r
th
e
SOSMC
co
n
tr
o
ller
.
Fig
u
r
e
6
p
r
esen
ts
th
e
cu
r
r
en
t
i
n
jecte
d
in
to
th
e
g
r
id
d
u
r
in
g
t
h
e
f
ir
s
t
p
h
ase,
wh
ich
h
as
a
s
in
u
s
o
id
al
wav
ef
o
r
m
at
5
0
Hz,
in
d
icatin
g
a
lo
w
r
ate
o
f
cu
r
r
en
t
h
a
r
m
o
n
ics.
T
h
is
f
ig
u
r
e
also
s
h
o
ws
th
at
t
h
e
g
r
id
v
o
ltag
es
an
d
cu
r
r
en
ts
ar
e
in
p
h
ase,
co
n
f
ir
m
in
g
th
e
ab
s
en
ce
o
f
r
ea
ctiv
e
p
o
wer
in
jectio
n
a
n
d
en
s
u
r
i
n
g
a
UPF.
Fig
u
r
e
7
d
is
p
lay
s
th
e
T
HD
o
f
th
e
f
ir
s
t
-
p
h
ase
cu
r
r
en
t
co
n
n
ec
ted
to
t
h
e
g
r
id
f
o
r
b
o
th
C
VC
(
Fig
u
r
e
7
(
a
)
)
an
d
SOSMC
(
F
ig
u
r
e
7
(
b
)
)
co
n
tr
o
ller
s
.
T
h
e
T
HD
f
o
r
SOSMC
i
s
r
ed
u
ce
d
to
1
.
1
9
%,
c
o
m
p
a
r
ed
t
o
2
.
2
8
%
f
o
r
C
VC
,
in
d
icatin
g
th
at
th
e
C
VC
tech
n
iq
u
e
is
m
o
r
e
af
f
e
cted
b
y
ir
r
a
d
iatio
n
v
ar
iatio
n
s
.
T
h
e
d
ev
elo
p
e
d
m
eth
o
d
s
ig
n
if
ican
tly
r
ed
u
ce
s
r
ip
p
le,
d
em
o
n
s
t
r
atin
g
its
r
o
b
u
s
tn
ess
u
n
d
er
f
l
u
ctu
atin
g
clim
atic
co
n
d
itio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Hig
h
o
r
d
er sl
id
in
g
mo
d
e
c
o
n
tr
o
l fo
r
g
r
id
in
teg
r
a
tio
n
o
f p
h
o
to
vo
lta
ic
s
ystems
(
N
o
u
r
ed
d
in
e
E
ch
-
ch
erki
)
123
T
ab
le
2
.
T
h
e
PVS p
ar
am
eter
s
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
C
a
p
a
c
i
t
o
r
f
o
r
D
C
b
u
s (μF
)
C
O
2
0
0
0
I
n
p
u
t
c
a
p
a
c
i
t
o
r
(
μF)
C
in
1
0
0
0
I
n
d
u
c
t
a
n
c
e
o
f
t
h
e
b
o
o
st
(
mH
)
L
3
.
5
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
(
k
H
z
)
Fs
5
I
n
v
e
r
t
e
r
i
n
d
u
c
t
a
n
c
e
(
mH
)
L
f
3
I
n
v
e
r
t
e
r
sw
i
t
c
h
i
n
g
r
a
t
e
(
k
H
z
)
F
sh
5
D
C
b
u
s
v
o
l
t
a
g
e
r
e
f
e
r
e
n
c
e
(
V
)
V
dc
_re
f
7
0
0
(
a)
(
b
)
Fig
u
r
e
3
.
I
r
r
ad
iatio
n
v
ar
iatio
n
s
in
W
/m
2
:
(
a)
s
tep
p
ed
p
r
o
f
ile
a
n
d
(
b
)
r
ea
l p
r
o
f
ile
(
a)
(
b
)
Fig
u
r
e
4
.
Activ
e
a
n
d
r
ea
ctiv
e
p
o
wer
f
o
r
(a
)
s
tep
ir
r
ad
iatio
n
a
n
d
(
b
)
r
ee
l i
r
r
a
d
iatio
n
Fig
u
r
e
5
. V
dc
r
esp
o
n
s
es
with
SOSMC
an
d
C
V
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
20
2
5
:
1
18
-
1
26
124
Fig
u
r
e
6
.
C
u
r
r
e
n
t in
jecte
d
in
t
o
g
r
id
f
o
r
th
e
f
ir
s
t p
h
ase
(
a)
(
b
)
Fig
u
r
e
7
.
T
HD
o
f
th
e
c
u
r
r
en
t
with
(
a)
C
VC
an
d
(
b
)
SOSMC
4.
CO
NCLU
SI
O
N
T
h
is
ar
ticle
in
tr
o
d
u
ce
s
a
n
o
v
el
SOSM
C
co
n
tr
o
ller
f
o
r
r
eg
u
la
tin
g
a
PV
s
y
s
tem
in
two
d
is
ti
n
ct
s
tag
es.
I
n
itially
,
o
n
th
e
d
ir
ec
t
cu
r
r
e
n
t
s
id
e,
th
e
co
n
tr
o
ller
f
o
cu
s
es
o
n
m
ax
im
izin
g
th
e
p
o
wer
g
en
e
r
ated
b
y
th
e
PVG.
Su
b
s
eq
u
en
tly
,
o
n
th
e
alter
n
ati
n
g
c
u
r
r
en
t
s
id
e,
t
h
e
g
o
al
is
to
tr
an
s
f
er
th
is
p
o
wer
to
t
h
e
g
r
id
with
a
u
n
ity
p
o
wer
f
ac
to
r
.
T
h
e
SOSMC
-
b
ased
s
tr
ateg
y
is
d
esig
n
ed
to
e
n
h
an
ce
PV
s
y
s
tem
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
to
tr
a
d
itio
n
al
SMC
b
y
m
in
im
izin
g
r
ip
p
les
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
.
C
o
m
p
ar
ativ
e
r
esu
lts
b
etwe
en
th
e
S
OSMC
an
d
co
n
v
en
tio
n
al
C
VC
s
h
o
w
a
1
0
0
%
r
ed
u
ctio
n
i
n
ac
tiv
e
p
o
wer
o
v
er
s
h
o
o
t
d
u
r
in
g
s
u
d
d
en
ir
r
ad
ian
ce
ch
a
n
g
es,
wit
h
m
in
im
ized
r
esp
o
n
s
e
tim
e.
Ad
d
itio
n
ally
,
th
e
T
HD
o
f
th
e
cu
r
r
en
t
is
r
ed
u
ce
d
to
1
.
1
9
%
with
SOSM
C
,
co
m
p
ar
ed
to
2
.
2
8
%
with
C
VC
.
T
h
u
s
,
th
e
SOSMC
s
tr
at
eg
y
d
em
o
n
s
tr
a
tes
s
ig
n
if
ican
t
p
r
o
m
is
e
f
o
r
im
p
r
o
v
in
g
th
e
en
er
g
y
ef
f
icien
cy
o
f
g
r
i
d
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
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c
h
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ra
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k
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Ja
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o
r
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c
o
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wa
s
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h
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4
–
2
0
1
7
.
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m
a
in
re
se
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