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Ph
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1.
I
NT
RO
D
UCT
I
O
N
I
n
cr
ea
s
in
g
in
ter
est
in
s
o
lar
p
o
wer
(
SP
V)
f
u
els
d
ev
elo
p
m
en
t
in
s
u
s
tain
ab
le
en
er
g
y
s
o
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s
.
SP
V
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s
v
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f
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r
r
em
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co
m
m
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ities
,
b
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g
r
id
s
b
r
in
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s
p
o
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q
u
ality
(
PQ)
ch
allen
g
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R
ig
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o
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s
test
in
g
an
d
v
alid
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ar
e
n
ec
ess
ar
y
to
ass
e
s
s
th
e
ef
f
ec
tiv
en
ess
o
f
PV
s
o
lar
in
v
er
ter
s
in
m
itig
atin
g
p
o
wer
q
u
ality
is
s
u
es.
T
h
e
g
r
o
win
g
in
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r
atio
n
o
f
en
e
r
g
y
s
o
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r
ce
s
,
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ar
ticu
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ly
s
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-
b
a
s
ed
p
o
wer
,
in
to
th
e
elec
tr
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n
etwo
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k
p
o
s
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ig
n
if
ican
t
tr
ials
allied
t
o
th
e
q
u
ality
o
f
p
o
wer
[
1
]
–
[
5
]
.
Pid
ik
iti
e
t
a
l.
[
6
]
p
r
o
p
o
s
ed
a
cr
o
s
s
o
v
er
f
r
am
ewo
r
k
th
at
all
ev
iates
v
o
ltag
e
d
r
o
o
p
/s
well,
u
n
b
alan
ce
,
an
d
v
o
ltag
e
s
er
ies
in
f
u
s
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wh
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f
ec
ts
win
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-
ass
o
ciate
d
e
n
r
o
l
m
en
t
g
e
n
er
ato
r
s
.
Das
et
a
l
.
[
7
]
p
r
o
p
o
s
ed
a
PV
f
r
a
m
ewo
r
k
th
at
d
y
n
am
ically
p
o
wer
s
an
d
r
ed
u
ce
s
h
a
r
m
o
n
ic
d
is
to
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tio
n
s
u
s
in
g
p
r
e
d
ato
r
-
p
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e
y
-
b
ased
f
ir
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-
f
ly
o
p
tim
izatio
n
,
f
u
zz
y
tr
ac
k
in
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,
a
n
d
ad
ap
tiv
e
p
er
tu
r
b
.
B
en
ab
d
elk
a
d
er
et
a
l
.
[
8
]
p
r
o
p
o
s
ed
an
ef
f
ec
t
iv
e
co
n
tr
o
l a
p
p
r
o
ac
h
f
o
r
a
g
r
id
-
co
n
n
ec
ted
s
i
n
g
le
-
p
h
ase
PV
s
y
s
tem
th
at
im
p
r
o
v
es
p
o
wer
q
u
ality
a
n
d
o
p
er
ates
with
a
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
co
n
tr
o
ller
.
Par
am
asiv
am
et
a
l
.
[
9
]
p
r
o
p
o
s
ed
a
PV
-
d
y
n
a
m
ic
v
o
ltag
e
r
esto
r
er
s
(
DVR
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th
at
r
el
iev
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v
o
ltag
e
h
an
g
an
d
s
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in
ter
f
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en
ce
s
,
an
d
u
n
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lac
k
o
u
ts
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s
in
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a
s
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MO
SF
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T
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witch
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s
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ased
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n
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la
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t
co
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tr
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Ok
wak
o
et
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l
.
[
1
0
]
p
r
o
p
o
s
ed
a
co
u
n
ter
f
eit
b
r
ain
n
etwo
r
k
r
e
g
u
lato
r
th
at
im
p
r
o
v
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co
n
tr
o
l
i
n
tr
icac
y
an
d
r
eliev
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p
o
wer
q
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ality
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s
u
es
u
s
in
g
a
b
r
ain
o
r
g
an
izatio
n
to
c
o
n
tr
o
l
a
s
h
u
n
t
d
y
n
a
m
ic
ch
an
n
el
o
f
th
e
u
n
if
ied
p
o
wer
q
u
ality
co
n
d
iti
o
n
er
(
UPQC
)
[
1
1
]
.
T
h
e
r
esear
ch
aim
s
to
u
n
d
e
r
s
tan
d
h
o
w
PV
s
o
lar
in
v
er
ter
s
ca
n
ef
f
ec
tiv
ely
a
d
d
r
ess
p
o
wer
q
u
ality
is
s
u
es,
en
s
u
r
in
g
a
s
m
o
o
th
in
teg
r
atio
n
o
f
s
o
lar
en
e
r
g
y
i
n
to
ex
is
tin
g
el
ec
tr
ical
f
r
am
ewo
r
k
s
[
1
2
]
,
[
1
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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5
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52
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
36
,
No
.
2
,
No
v
em
b
er
20
24
:
7
1
5
-
7
2
3
716
2.
P
RO
P
O
SE
D
RE
SE
ARCH
M
E
T
H
O
D
T
h
e
co
m
p
r
eh
e
n
s
iv
e
ex
p
e
r
im
e
n
tal
d
esig
n
in
teg
r
ates
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
to
ass
ess
th
e
p
r
esen
tatio
n
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d
ca
p
ab
ilit
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o
f
PV
s
o
lar
i
n
v
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ter
s
in
ad
d
r
ess
in
g
p
o
wer
q
u
ality
ch
allen
g
es.
T
h
is
ap
p
r
o
ac
h
in
v
o
lv
es
u
s
in
g
ad
v
an
ce
d
m
ea
s
u
r
in
g
to
o
ls
to
tr
ac
k
th
e
in
v
er
ter
'
s
im
p
ac
t
o
n
v
ar
io
u
s
p
o
wer
q
u
ality
f
ac
to
r
s
.
T
h
ese
m
ea
s
u
r
em
en
ts
p
r
o
v
id
e
a
th
o
r
o
u
g
h
ass
ess
m
en
t
o
f
th
e
d
e
v
ice'
s
p
er
f
o
r
m
an
ce
,
e
n
s
u
r
in
g
a
n
ac
c
u
r
ate
ev
alu
atio
n
o
f
its
ef
f
ec
tiv
en
ess
.
A
ls
o
,
th
e
d
a
ta
co
llected
f
r
o
m
th
ese
ex
p
er
i
m
en
ts
will
b
e
a
n
aly
ze
d
to
i
d
e
n
tify
an
y
p
o
ten
tial
ar
ea
s
f
o
r
im
p
r
o
v
e
m
en
t
an
d
t
o
v
alid
ate
th
e
in
v
er
ter
'
s
r
elia
b
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y
an
d
ef
f
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u
n
d
er
d
if
f
er
en
t
o
p
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atin
g
co
n
d
itio
n
s
.
2
.
1
.
E
x
perim
ent
a
l set
up
I
n
th
is
ex
p
er
im
e
n
t,
s
o
lar
p
a
n
els
co
n
n
ec
ted
to
th
e
p
o
wer
g
r
id
ar
e
in
v
esti
g
ated
.
T
h
e
s
etu
p
in
clu
d
es
m
o
n
ito
r
in
g
th
e
g
r
id
h
a
n
d
les
alo
n
g
s
id
e
th
e
s
o
lar
en
er
g
y
.
Als
o
,
m
ea
s
u
r
em
en
ts
o
f
v
o
ltag
e,
cu
r
r
en
t,
an
d
p
o
wer
ar
e
co
n
d
u
cte
d
to
an
aly
ze
th
e
s
y
s
tem
'
s
p
er
f
o
r
m
an
ce
.
T
h
i
s
co
m
p
r
eh
en
s
iv
e
ap
p
r
o
ac
h
e
n
s
u
r
es
a
th
o
r
o
u
g
h
ev
alu
atio
n
o
f
th
e
s
o
lar
p
an
els'
in
teg
r
atio
n
with
th
e
p
o
wer
g
r
i
d
.
2
.
2
.
M
ulti
-
o
bje
ct
iv
e
pa
r
t
icle
s
wa
rm
o
ptim
iza
t
io
n
T
h
is
alg
o
r
ith
m
is
d
esig
n
ed
to
s
o
lv
e
p
r
o
b
lem
s
with
m
u
ltip
le
co
n
f
lictin
g
o
b
jectiv
es
,
s
u
ch
as
m
ax
im
izin
g
en
e
r
g
y
p
r
o
d
u
ctio
n
,
m
in
im
izin
g
co
s
ts
,
an
d
r
e
d
u
c
in
g
en
v
ir
o
n
m
e
n
tal
im
p
ac
t in
r
en
ewa
b
le
en
er
g
y
:
{
−
ma
x
(
)
=
[
1
(
)
,
2
(
)
,
…
…
.
.
(
)
]
.
∈
(
1
)
w
h
er
e
V
-
m
ax
d
e
n
o
tes
v
ec
to
r
m
ax
im
izatio
n
;
(
)
(
=
1
,
2
,
…
…
,
d
en
o
tes
th
e
s
u
b
-
o
b
jectiv
e
o
f
th
e
v
ec
to
r
o
b
jectiv
e
f
u
n
ctio
n
f
(
x
)
,
ea
ch
s
u
b
-
o
b
jectiv
e
v
ec
to
r
is
m
ax
im
ized
to
th
e
ex
ten
t
p
o
s
s
ib
le;
x
is
th
e
an
s
wer
to
th
e
p
r
o
b
lem
a
n
d
∈
is
th
e
co
n
s
tr
ain
ts
th
en
b
o
u
n
d
a
r
ies o
f
MO
P
:
(
+
1
)
=
{
(
)
+
1
1
(
)
(
−
(
)
)
3
<
(
)
+
2
2
(
)
(
−
(
)
)
ℎ
(
2
)
w
h
er
e
δ
is
a
p
ar
am
eter
to
co
n
tr
o
l
th
e
ex
p
lo
r
atio
n
-
e
x
p
lo
itatio
n
tr
ad
e
-
o
f
f
,
a
n
d
r
3
is
a
n
u
m
b
er
r
an
d
o
m
ly
ch
o
s
en
f
r
o
m
[
0
,
1
]
.
T
h
en
,
f
o
r
ea
c
h
p
a
r
ticle
,
∈
{1
,
.
.
.
,
n
s
}
in
s
war
m
,
two
p
ar
ticles
r
an
d
o
m
l
y
p
ick
e
d
f
r
o
m
a
n
elite
s
et
o
f
s
ize
γ
an
d
th
e
elite
p
ar
ticle
o
f
o
b
jectiv
e
v
ec
to
r
h
as
a
s
m
aller
an
g
le
with
’
s
o
b
jectiv
e
v
ec
to
r
is
t
h
e
win
n
er
a
n
d
is
th
e
lo
s
er
.
Fo
r
ea
ch
win
n
e
r
-
lo
s
er
p
air
,
th
e
f
o
llo
win
g
eq
u
atio
n
s
ar
e
ap
p
lied
to
c
r
ea
te
a
n
ew
p
ar
ticle
:
′
=
1
+
2
(
−
)
(
3
)
,
=
+
,
(
4
)
w
h
er
e,
1
an
d
2
a
r
e
two
v
ec
to
r
s
r
an
d
o
m
ly
s
elec
ted
f
r
o
m
,
is
th
e
in
d
ex
f
o
r
th
e
win
n
er
(
th
e
s
el
ec
ted
elite
p
ar
ticle)
.
T
h
e
o
r
d
in
ar
y
p
ar
tic
les
ar
e
in
d
ex
e
d
u
s
in
g
i,
i
∈
{1
,
.
.
.
,
}.
T
h
e
p
o
ly
n
o
m
ial
m
u
tatio
n
is
th
e
n
ap
p
lied
to
0
.
2
.
3
.
Co
ntr
o
ller
It
h
elp
s
to
m
an
a
g
e
elec
tr
icity
f
lo
w
in
p
o
wer
g
r
id
s
.
T
h
ey
a
ct
lik
e
s
witch
es
f
o
r
h
ig
h
-
v
o
lt
ag
e
lin
es,
ad
ju
s
tin
g
p
o
wer
f
lo
w
to
m
a
k
e
th
e
g
r
id
m
o
r
e
s
tab
le
an
d
ef
f
ici
en
t.
I
n
ter
lin
e
p
o
wer
f
l
o
w
co
n
t
r
o
ller
s
(
I
PF
C
s
)
ca
n
also
ad
d
r
ess
is
s
u
es lik
e
v
o
ltag
e
f
lu
ctu
atio
n
s
an
d
im
b
alan
ce
s
.
2
.
3
.
1
.
I
nte
rline
po
wer
f
lo
w
co
ntr
o
llers
a
nd
ph
a
s
e
-
lo
ck
ed
lo
o
p
circ
uit
I
PF
C
is
a
m
u
lti
-
ter
m
in
al
FA
C
T
S
an
d
th
e
f
r
am
ewo
r
k
ex
p
l
ain
s
h
o
w
I
PF
C
s
ca
n
im
p
r
o
v
e
th
e
s
o
lid
ity
an
d
co
n
s
is
ten
cy
o
f
p
o
wer
g
r
id
s
.
A
k
ey
I
PF
C
m
o
d
el
is
d
is
p
lay
ed
in
Fig
u
r
e
1
,
I
PF
C
o
f
tw
o
co
n
v
e
r
ter
s
o
f
th
e
ca
lcu
lated
m
o
d
el
is
ex
p
lain
ed
as
:
=
2
−
[
c
os
(
−
)
+
s
in
(
−
)
]
+
[
s
in
(
−
)
−
c
os
(
−
)
]
(
5
)
=
−
2
−
∑
=
,
[
s
in
(
−
)
+
c
os
(
−
)
]
−
∑
=
,
[
s
in
(
−
)
−
c
os
(
−
)
]
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
P
h
o
to
vo
lta
ic
i
n
ve
r
ters
ex
p
eri
men
ta
lly
va
lid
a
te
p
o
w
er q
u
a
lity
…
(
R
a
jen
d
r
a
B
h
imr
a
j Ma
d
a
ke
)
717
=
2
−
[
c
os
(
−
)
+
s
in
(
−
)
]
+
[
s
in
(
−
)
−
c
os
(
−
)
]
(
7
)
=
2
−
[
s
in
(
−
)
+
c
os
(
−
)
]
+
[
s
in
(
−
)
−
c
os
(
−
)
]
(
8
)
As
th
er
e
ar
e
n
o
f
u
n
d
am
en
tal
f
r
am
ewo
r
k
s
,
ex
p
ec
tin
g
a
lo
s
s
le
s
s
co
n
v
er
ter
,
th
e
d
y
n
am
ic
p
o
w
er
p
r
o
v
id
e
d
b
y
o
n
e
co
n
v
er
ter
r
is
es to
th
e
d
y
n
am
ic
p
o
wer
ex
p
ec
ted
b
y
th
e
o
th
er
:
(
∗
+
∗
)
=
0
(
9
)
1
=
1
˪
1
(
1
=i,
j,k
)
a
n
d
1
,
1
is
m
ag
n
itu
d
e
an
d
an
g
le
o
f
1
.
W
h
er
e,
is
th
e
co
m
p
lex
m
a
n
ag
ea
b
le
s
er
ies
-
in
f
u
s
ed
v
o
lta
g
e
s
o
u
r
ce
wh
ic
h
ad
d
r
ess
es th
e
s
er
ies em
o
lu
m
en
t o
f
th
e
c
o
n
v
e
r
ter
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
cir
cu
it
r
ep
r
esen
tatio
n
d
etailin
g
th
e
t
o
p
o
lo
g
y
o
f
th
e
p
h
ase
-
lo
ck
e
d
lo
o
p
(
PLL
)
an
d
th
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
I
PF
C
.
Fig
u
r
e
1
(
a)
s
h
o
wca
s
es
th
e
PLL
'
s
co
n
f
ig
u
r
atio
n
,
cr
u
cial
f
o
r
s
y
n
ch
r
o
n
izi
n
g
s
ig
n
als
in
v
a
r
io
u
s
ap
p
licati
o
n
s
.
Fig
u
r
e
1
(
b
)
d
ep
icts
th
e
I
PF
C
's
m
ath
em
atica
l
f
r
am
ewo
r
k
,
ess
en
tial f
o
r
co
n
tr
o
llin
g
p
o
wer
f
lo
w
in
in
ter
c
o
n
n
ec
ted
AC
tr
an
s
m
is
s
io
n
lin
es.
(
a)
(
b
)
Fig
u
r
e
1
.
R
ep
r
esen
tatio
n
o
f
c
ir
cu
it f
o
r
PLL
a
n
d
I
PF
C
m
ath
e
m
atica
l m
o
d
el
(
a)
t
o
p
o
lo
g
y
o
f
th
e
PLL
[
1
4
]
an
d
(
b
)
I
PF
C
m
ath
em
atica
l m
o
d
el
[
1
5
]
T
h
e
f
r
am
ewo
r
k
ex
p
lain
s
an
is
s
u
e
with
I
PF
C
s
,
d
ev
ices
th
at
m
an
ag
e
elec
tr
icity
f
lo
w
in
p
o
wer
g
r
id
s
th
e
g
r
id
is
s
y
n
ch
r
o
n
ize
d
with
t
h
ese
d
ev
ices,
an
d
a
co
m
m
o
n
t
o
o
l (
PLL
)
f
o
r
th
is
ca
n
ca
u
s
e
in
s
tab
ilit
y
:
−
0
=
(
−
∅
0
)
(
1
0
)
∅
0
=
−
−
1
−
0
(
1
1
)
=
−
(
1
2
)
t
he
Dc
s
ig
n
al
th
at
ch
an
g
es
th
e
VC
O
f
r
eq
u
en
cy
f
r
o
m
its
ce
n
tr
al
v
alu
e
0
to
th
e
in
p
u
t
s
ig
n
al
an
g
u
lar
f
r
eq
u
e
n
cy
,
i.e
:
=
0
+
=
(
1
3
)
a
ls
o
,
r
ep
r
esen
ted
as:
∅
0
=
−
−
1
−
0
(
1
4
)
t
h
e
p
r
o
d
u
ct
=
is
m
en
tio
n
ed
as
t
h
e
lo
o
p
a
g
ai
n
.
W
h
en
th
e
d
i
f
f
e
r
en
ce
|
−
0
|
ex
ce
ed
s
th
e
l
o
o
p
ag
ai
n
in
a
s
in
u
s
o
id
al
ch
ar
ac
te
r
is
tic
f
o
r
th
e
lo
c
k
th
at
ca
n
n
o
lo
n
g
er
m
ain
tain
th
e
lo
o
p
f
alls
o
u
t
o
f
t
h
e
lo
ck
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
36
,
No
.
2
,
No
v
em
b
er
20
24
:
7
1
5
-
7
2
3
718
2
.
3
.
2
.
ST
AT
CO
M
dev
ice
f
o
r
t
he
po
wer
co
ntr
o
ller
STAT
C
OM
s
ar
e
g
u
ar
d
ian
s
o
f
s
tab
le
v
o
ltag
e
in
p
o
wer
g
r
id
s
an
d
ac
t
lik
e
f
ir
s
t
r
e
s
p
o
n
d
e
r
s
,
s
wif
tly
r
ea
ctin
g
to
v
o
ltag
e
f
lu
ctu
atio
n
s
.
STAT
C
OM
s
h
an
d
le
s
in
g
le
-
h
an
d
e
d
ly
lar
g
e
r
v
o
ltag
e
s
win
g
s
o
r
e
m
er
g
en
cies
lik
e
f
au
lts
,
th
ey
ca
ll o
n
b
ac
k
u
p
f
r
o
m
o
th
er
c
o
m
p
en
s
ato
r
s
.
∆
2
=
|
2
−
2
|
=
∆
1
+
∆
2
(
1
5
)
STAT
C
OM
i
s
th
e
ca
p
ac
ity
lim
it
s
itu
atio
n
in
th
e
tar
g
et
v
o
ltag
e
(
2
)
o
f
co
n
tr
o
lled
b
y
o
n
l
y
STAT
C
OM
.
Fig
u
r
e
2
r
ep
r
esen
ts
th
e
p
r
o
p
o
s
ed
w
o
r
k
aim
ed
at
ad
d
r
ess
in
g
p
o
wer
q
u
ality
is
s
u
es
in
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
.
T
h
e
p
r
o
ce
s
s
b
eg
in
s
with
a
s
o
lar
PV
s
y
s
te
m
co
n
n
ec
ted
to
a
C
u
k
co
n
v
e
r
ter
,
m
an
ag
e
d
b
y
a
co
n
tr
o
ller
[
1
6
]
–
[
1
8
]
.
T
h
e
s
y
s
tem
u
tili
ze
s
h
ig
h
-
p
en
etr
atio
n
r
en
ewa
b
le
in
teg
r
atio
n
(
HPR
I
)
an
d
m
u
lti
-
o
b
jectiv
e
m
u
lti
-
v
er
s
e
o
p
tim
izatio
n
(
M
OM
VO)
alg
o
r
ith
m
s
to
en
s
u
r
e
h
ig
h
-
p
en
etr
atio
n
with
o
u
t
lo
s
s
o
f
p
o
wer
q
u
ality
.
Ad
d
itio
n
al
co
m
p
o
n
e
n
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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d
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J
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I
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5
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6
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Fig
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Fig
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
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5
0
2
-
4
7
52
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[
1
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.
[
7
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S
.
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