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d
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tr
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PID
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co
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m
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n
ly
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s
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v
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a
n
d
f
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eq
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cy
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g
u
latio
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a
d
ju
s
tin
g
th
e
o
u
t
p
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t
o
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th
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DG
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s
tem
b
ased
o
n
g
r
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m
e
asu
r
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ts
.
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ch
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izatio
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ith
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s
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ize
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th
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y
s
tem
with
th
e
g
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b
ef
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r
e
co
n
n
ec
tio
n
.
Ph
ase
-
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ed
lo
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p
(
PLL
)
alg
o
r
ith
m
s
ar
e
f
r
eq
u
e
n
tly
u
s
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f
o
r
s
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n
ch
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o
n
izatio
n
,
d
et
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tin
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th
e
p
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ase
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d
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eq
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o
f
th
e
g
r
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d
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d
a
d
ju
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tin
g
t
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e
o
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p
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t
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f
th
e
DG
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s
tem
ac
c
o
r
d
in
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ly
.
A
n
ti
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alg
o
r
ith
m
s
ar
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d
p
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ev
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G
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s
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s
f
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e
wh
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r
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ec
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lo
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[
1
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.
Pas
s
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s
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s
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p
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m
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,
as
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f
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an
ti
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lan
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d
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[
2
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.
Activ
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p
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wer
co
n
tr
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l
alg
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th
m
s
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ab
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DG
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n
d
itio
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s
an
d
c
o
n
tr
o
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s
ig
n
als
[
3
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.
Dr
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co
n
tr
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alg
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ith
m
s
ar
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co
m
m
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tr
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th
e
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u
tp
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t
o
f
th
e
DG
s
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s
tem
in
p
r
o
p
o
r
tio
n
to
f
r
eq
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d
e
v
iatio
n
s
f
r
o
m
th
e
n
o
m
in
al
v
alu
e
[
4
]
,
[
5
]
.
R
ea
ctiv
e
p
o
wer
co
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tr
o
l
alg
o
r
ith
m
s
ar
e
u
s
ed
to
r
eg
u
late
th
e
r
ea
ctiv
e
p
o
wer
o
u
tp
u
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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J
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&
C
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Sci
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Vo
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3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
4
5
9
-
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4
6
6
1460
o
f
DG
s
y
s
tem
s
to
s
u
p
p
o
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u
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to
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co
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[
6
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[
7
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Vo
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ith
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tem
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ased
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ea
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ts
to
m
ain
tain
v
o
ltag
e
with
in
ac
ce
p
tab
le
lim
its
[
8
]
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Activ
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ilter
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ith
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ased
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t o
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[
9
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T
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1
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Po
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an
d
o
t
h
er
d
is
tu
r
b
an
ce
s
[
1
2
]
.
L
o
ad
b
alan
cin
g
a
n
d
d
e
m
an
d
r
esp
o
n
s
e
alg
o
r
ith
m
s
o
p
tim
ize
th
e
o
p
er
atio
n
o
f
DG
s
y
s
tem
s
to
m
atch
g
en
er
atio
n
with
lo
ca
l
d
em
an
d
an
d
g
r
id
c
o
n
d
i
tio
n
s
.
Pre
d
ictiv
e
alg
o
r
ith
m
s
,
m
ac
h
in
e
lear
n
in
g
tech
n
iq
u
es,
an
d
o
p
tim
izatio
n
a
l
g
o
r
i
t
h
m
s
a
r
e
e
m
p
l
o
y
e
d
t
o
f
o
r
e
c
a
s
t
l
o
a
d
d
e
m
a
n
d
a
n
d
a
d
j
u
s
t
t
h
e
o
p
e
r
a
t
i
o
n
o
f
D
G
s
y
s
t
e
m
s
a
c
c
o
r
d
i
n
g
l
y
[
1
3
]
,
[
1
4
]
.
P
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PSO
)
is
o
n
e
o
f
t
h
e
p
o
p
u
lar
o
p
tim
izatio
n
tech
n
iq
u
e
wh
ich
i
s
u
s
ed
f
o
r
o
p
t
im
al
lo
ca
tio
n
an
d
s
ize
o
f
DGs [
1
5
]
,
[
1
6
].
2.
P
SO
AL
G
O
RI
T
H
M
T
h
e
PSO
tech
n
iq
u
e
is
m
o
d
ell
ed
af
ter
th
e
s
o
cial
in
ter
ac
tio
n
s
an
d
d
y
n
a
m
ic
m
o
tio
n
s
o
f
in
s
ec
ts
,
b
ir
d
s
,
an
d
f
is
h
.
A
s
war
m
o
f
ag
en
ts
,
o
r
p
ar
ticles,
is
u
s
ed
in
th
is
m
eth
o
d
to
m
o
v
e
th
r
o
u
g
h
o
u
t
th
e
s
ea
r
ch
s
p
ac
e
in
s
ea
r
ch
o
f
th
e
o
p
tim
al
lo
ca
tio
n
.
B
ased
o
n
b
o
th
its
o
wn
an
d
o
t
h
er
p
ar
ticles
’
f
ly
in
g
ex
p
e
r
ien
c
es,
ev
er
y
p
ar
ticle
in
s
ea
r
ch
s
p
ac
e
m
o
d
if
ies
its
f
lig
h
t
p
ath
.
T
h
e
p
a
r
ticle
with
t
h
e
h
ig
h
est
f
itn
ess
v
alu
e
is
i
n
th
e
b
est
p
o
s
itio
n
g
lo
b
ally
.
Po
s
itio
n
,
v
elo
city
,
a
n
d
p
r
ev
i
o
u
s
b
est
p
o
s
itio
n
ar
e
th
e
th
r
ee
p
ar
am
et
er
s
f
o
r
ev
er
y
p
ar
ticle.
Gath
er
in
g
o
f
f
ly
in
g
p
ar
ticles (
s
war
m
)
-
s
e
ar
ch
f
o
r
ev
o
l
v
in
g
s
o
lu
tio
n
s
.
E
v
er
y
m
e
m
b
er
o
f
th
e
p
o
p
u
l
atio
n
an
d
ass
o
ciate
d
p
ar
ticle
in
PS
O
h
as
a
v
ar
iab
le
v
el
o
city
th
at
d
eter
m
in
es h
o
w
it tr
av
els ar
o
u
n
d
th
e
s
ea
r
ch
s
p
ac
e
in
D
-
d
im
e
n
s
io
n
al
s
p
ac
e,
th
e
‘
i’
th
p
ar
ticl
e
is
(
1
).
=
{
1
,
2
,
…
,
}
(1
)
T
h
e
r
elev
an
t
v
elo
city
is
r
ep
r
esen
ted
b
y
an
o
th
e
r
D
-
d
im
e
n
s
io
n
al
v
ec
to
r
is
g
iv
en
(
2
)
.
+
1
=
∗
+
∗
r
an
d
(
)
∗
(
pbe
s
t
−
)
+
∗
r
an
d
(
)
∗
(
Gbe
s
t
−
)
(2
)
T
h
e
p
o
s
itio
n
o
f
ea
ch
p
ar
ticle
i
s
u
p
d
ated
ev
e
r
y
g
en
er
atio
n
is
g
iv
en
(
3
)
.
+
1
=
+
+
1
(3
)
I
n
th
is
wo
r
k
,
th
e
p
ar
ticle
is
r
ep
r
esen
ted
as DG
lo
ca
tio
n
an
d
s
ize
as sh
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1.
I
n
d
iv
id
u
al
p
ar
ticle
T
h
e
v
ar
iab
le
p
ar
am
eter
s
o
f
th
e
PS
O
alg
o
r
ith
m
ar
e
g
i
v
en
as f
o
llo
ws
:
Ma
x
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
=
1
0
0
Nu
m
b
er
o
f
DG
u
n
its
=
1
0
p
ar
ticle
s
ize=
4
0
=2
=2
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:
2502
-
4
7
5
2
P
erfo
r
ma
n
ce
ev
a
lu
a
tio
n
o
f d
is
tr
ib
u
tio
n
n
etw
o
r
k
w
ith
ch
a
n
g
e
o
f lo
a
d
…
(
S
w
a
th
i S
a
n
ke
p
a
lly
)
1461
W
=
W
m
ax
−
(
W
m
ax
−
W
m
in
i
t
e
r
m
ax
)
∗
ite
r
W
h
er
e
W
max
=0
.
9
an
d
W
min
=
0
.
4
.
3.
WI
ND
P
O
WE
R
G
E
NE
RAT
I
O
N
I
n
th
e
p
r
o
d
u
ctio
n
o
f
win
d
ele
ctr
icity
f
o
r
th
e
win
d
p
o
wer
s
y
s
tem
to
o
p
er
ate
s
af
ely
an
d
s
te
ad
ily
,
it
is
im
p
o
r
tan
t
t
o
p
la
n
a
h
ea
d
a
n
d
c
o
o
r
d
in
ate
th
e
a
ctiv
e
an
d
r
e
ac
tiv
e
p
o
wer
o
f
win
d
f
a
r
m
s
with
th
e
g
r
id
[
1
7
]
,
[
1
8
]
.
Slo
w
m
an
u
al
r
eser
v
es
ca
n
b
e
u
s
ed
to
co
m
p
en
s
ate
f
o
r
th
e
win
d
p
o
wer
lo
s
t
as
a
r
esu
lt
o
f
W
T
s
s
h
u
ttin
g
d
o
wn
d
u
r
in
g
t
h
e
s
to
r
m
[
1
8
]
,
[
1
9
]
.
B
ec
au
s
e
win
d
tu
r
b
in
e
r
o
to
r
s
ar
e
to
tally
d
is
co
n
n
ec
ted
f
r
o
m
th
e
g
r
id
,
th
ey
a
r
e
u
n
ab
le
t
o
ad
a
p
t
to
ch
a
n
g
es
in
s
y
s
tem
f
r
eq
u
en
cy
o
r
tak
e
p
a
r
t
in
p
o
wer
s
y
s
tem
f
r
eq
u
en
c
y
co
n
tr
o
l
[
2
0
]
,
[
2
1
]
.
T
h
e
win
d
g
en
er
at
o
r
’
s
o
u
tp
u
t
p
o
wer
is
ze
r
o
wh
en
th
e
win
d
s
p
ee
d
is
b
elo
w
th
e
cr
itical
s
p
ee
d
.
Usi
n
g
r
ea
lis
ti
c
d
ata,
a
p
o
wer
esti
m
atio
n
m
eth
o
d
b
ased
o
n
Ga
u
s
s
ian
r
eg
r
ess
io
n
ac
cu
r
ately
d
escr
ib
es
v
ar
io
u
s
tu
r
b
in
e
ty
p
es
an
d
lo
ca
tio
n
s
[
2
2
]
,
[
2
3
]
.
a
m
o
d
el
to
d
ep
ict
th
e
co
r
r
elatio
n
b
etwe
en
win
d
s
p
ee
d
an
d
win
d
tu
r
b
in
e
o
u
tag
e
p
r
o
b
a
b
ilit
ies [
2
4
]
,
[
2
5
]
.
4.
RE
SU
L
T
S
AND
ANA
L
YS
I
S
T
h
e
PS
O
m
eth
o
d
h
as
b
ee
n
ap
p
lied
to
a
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
f
o
r
o
p
tim
al
lo
ca
tio
n
an
d
p
o
wer
s
u
p
p
ly
o
f
ten
win
d
DG
.
T
h
e
r
esu
lts
o
f
th
e
s
tu
d
y
o
f
win
d
g
en
er
ato
r
’
s
lo
ca
tio
n
s
an
d
p
o
wer
s
u
p
p
lies
ar
e
p
r
esen
ted
in
a
T
a
b
le
1
.
T
h
e
f
o
llo
win
g
ca
s
e
s
tu
d
ies
ar
e
u
s
e
d
to
ass
ess
an
d
ex
p
lain
th
e
d
i
s
tr
ib
u
tio
n
n
etwo
r
k
’
s
p
er
f
o
r
m
an
ce
.
T
ab
le
1
.
Op
tim
al
lo
ca
tio
n
an
d
p
o
wer
s
u
p
p
l
y
o
f
1
0
win
d
d
is
tr
ib
u
ted
g
e
n
er
ato
r
s
W
i
n
d
g
e
n
e
r
a
t
o
r
s
n
u
m
b
e
r
PSO
B
u
s
N
o
.
S
u
p
p
l
y
p
o
w
e
r
(
k
V
A
)
W
i
n
d
G
e
n
e
r
a
t
o
r
-
1
83
2
9
1
.
2
3
7
W
i
n
d
G
e
n
e
r
a
t
o
r
-
2
53
2
9
7
.
7
3
3
W
i
n
d
G
e
n
e
r
a
t
o
r
-
3
51
2
8
4
.
4
8
3
W
i
n
d
G
e
n
e
r
a
t
o
r
-
4
29
2
7
4
.
2
0
1
W
i
n
d
G
e
n
e
r
a
t
o
r
-
5
85
2
2
1
.
7
0
2
W
i
n
d
G
e
n
e
r
a
t
o
r
-
6
63
2
9
8
.
4
4
7
W
i
n
d
G
e
n
e
r
a
t
o
r
-
7
82
2
8
9
.
0
8
9
W
i
n
d
G
e
n
e
r
a
t
o
r
-
8
29
2
8
6
.
4
7
1
W
i
n
d
G
e
n
e
r
a
t
o
r
-
9
69
1
9
7
.
5
0
8
W
i
n
d
G
e
n
e
r
a
t
o
r
-
10
82
2
7
5
.
4
3
1
4
.
1
.
Ca
s
e
s
t
ud
y
1
:
DN
v
o
lt
a
g
es a
t
1
2
5
%
o
f
f
ull
lo
a
d
W
ith
th
e
ch
an
g
e
in
lo
a
d
,
th
e
v
o
ltag
es
an
d
p
o
wer
lo
s
s
es
in
th
e
DN
ar
e
c
o
m
p
u
te
d
wh
e
n
D
G
u
n
its
ar
e
co
n
n
ec
ted
.
On
ce
DGs
ar
e
co
n
n
ec
ted
in
DN,
th
eir
p
o
s
itio
n
s
s
h
o
u
ld
n
o
t
b
e
c
h
an
g
e
d
.
T
h
e
v
o
ltag
es
an
d
p
o
we
r
lo
s
s
es
ar
e
ca
lcu
lated
wh
en
lo
ad
s
ch
an
g
e.
Fig
u
r
e
2
s
h
o
ws
th
e
DN
v
o
ltag
es
at
1
2
5
%
o
f
f
u
ll
l
o
ad
,
th
e
m
i
n
im
u
m
v
o
ltag
e
is
0
.
9
5
6
p
e
r
u
n
it a
t b
u
s
n
u
m
b
er
7
5
.
Fig
u
r
e
2
.
Vo
ltag
es (
P.U)
o
f
D
N
at
1
2
5
% f
u
ll lo
a
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
3
,
Sep
tem
b
er
20
25
:
1
4
5
9
-
1
4
6
6
1462
4
.
2
.
Ca
s
e
s
t
ud
y
2
:
DN
v
o
lt
a
g
es a
t
1
0
0
%
o
f
f
ull
lo
a
d
T
h
e
v
o
ltag
e
r
esu
lts
ar
e
d
is
p
la
y
ed
in
Fig
u
r
e
3
.
B
u
s
n
u
m
b
er
8
4
h
as
a
m
a
x
im
u
m
d
is
tr
ib
u
tio
n
n
etwo
r
k
v
o
ltag
e
o
f
1
.
0
1
2
p
e
r
u
n
it,
w
h
ile
b
u
s
n
u
m
b
e
r
7
5
h
as
th
e
lo
w
est
v
o
l
tag
e
o
f
0
.
9
8
2
p
er
u
n
it.
All
b
u
s
es
’
v
o
ltag
es
ar
e
with
in
th
e
ac
ce
p
ta
b
le
r
an
g
e
(
0
.
9
5
<
V
<
1
.
0
5
)
.
Fig
u
r
e
3
.
Per
u
n
it v
o
lta
g
es o
f
DN
at
1
0
0
% f
u
ll lo
ad
4
.
3
.
Ca
s
e
s
t
ud
y
3
:
DN
v
o
lt
a
g
es a
t
7
5
%
o
f
f
ull
lo
a
d
T
h
e
v
o
ltag
e
r
esu
lts
at
7
5
%
o
f
th
e
f
u
ll
lo
ad
is
s
h
o
wn
in
Fig
u
r
e
4
.
B
u
s
n
u
m
b
e
r
2
2
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k
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Fig
u
r
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4
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o
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e
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e
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e
T
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le
2
.
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h
e
d
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ib
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le
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en
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ee
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ed
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h
e
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h
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t
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n
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T
h
e
p
o
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s
s
es
r
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ltin
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f
r
o
m
ch
an
g
es
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th
e
lo
ad
ar
e
g
i
v
en
in
T
ab
le
3
.
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:
2502
-
4
7
5
2
P
erfo
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ma
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a
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(
S
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lly
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1463
Fig
u
r
e
5
.
Per
u
n
it
v
o
lta
g
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f
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at
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0
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ab
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2.
Th
e
ch
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ab
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3
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Po
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3
T
h
e
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n
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f
DG
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n
its
with
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ed
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g
e
t
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d
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n
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en
th
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lo
ad
ch
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g
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h
e
f
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o
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n
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d
d
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f
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t
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izes
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n
i
ts
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e
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n
n
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ted
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n
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with
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ad
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h
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g
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s
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O
f
o
r
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d
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g
h
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wer
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u
p
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ly
.
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h
e
f
ix
e
d
lo
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tio
n
s
an
d
d
if
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er
e
n
t
s
izes
o
f
DG
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n
its
with
lo
ad
ch
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g
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e
in
d
icate
d
in
T
ab
le
4
.
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h
e
v
o
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o
f
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f
o
r
d
if
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er
en
t
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izes
o
f
DG
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n
its
with
lo
ad
ch
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n
g
es
ar
e
s
h
o
wn
in
Fig
u
r
e
6
.
T
ab
le
4
.
Var
iab
le
p
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wer
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p
p
l
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n
its
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with
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ch
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ad
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n
u
mb
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r
B
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r
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8
T
ab
le
5
s
h
o
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e
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n
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f
8
5
b
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s
v
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as
well
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e
p
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ce
n
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e
v
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r
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f
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e
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ity
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g
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n
T
a
b
le
6
.
Fig
u
r
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s
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e
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r
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e
ac
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e
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ig
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with
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f
a
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ize
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r
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g
lo
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ch
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g
es c
o
m
p
a
r
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to
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s
o
f
v
ar
iab
le
s
ize.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
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d
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3
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3
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tem
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er
20
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:
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1464
Fig
u
r
e
6
.
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p
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f
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g
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o
r
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T
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le
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.
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h
e
ch
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g
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o
f
v
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4
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8
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u
r
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7
.
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o
m
p
a
r
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n
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f
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tiv
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p
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wer
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es f
o
r
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ize
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n
d
v
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ize
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5.
CO
NCLU
SI
O
N
T
h
e
PS
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d
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e
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n
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le
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ig
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