I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
,
p
p
.
8
2
6
~
8
4
1
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
0
.
1
1
5
9
1
/ijap
e
.
v
14
.
i
4
.
pp
826
-
841
826
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//
ija
p
e.
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m/
O
ptima
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ceme
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nd sizi
ng
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and
DSTAT
C
O
M
in
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to mitig
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w
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trica
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tion sy
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Sm
rut
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a
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y:
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2
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Acc
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Th
e
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m
p
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sis
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w
s
h
ift
i
n
g
a
wa
y
fro
m
c
o
n
v
e
n
t
io
n
a
l
m
e
th
o
d
s
o
f
p
o
we
r
g
e
n
e
ra
ti
o
n
a
n
d
t
o
wa
rd
s
u
n
c
o
n
v
e
n
ti
o
n
a
l
d
istri
b
u
ted
e
n
e
r
g
y
re
so
u
rc
e
s
(
DERs
)
lo
c
a
ted
a
t
d
istri
b
u
ti
o
n
v
o
lt
a
g
e
lev
e
l
d
u
e
t
o
th
e
ra
p
i
d
d
e
p
letio
n
o
f
fo
ss
il
fu
e
l
su
p
p
l
ies
a
n
d
si
g
n
ifi
c
a
n
t
e
n
v
iro
n
m
e
n
tal
p
o
l
lu
ti
o
n
.
Emp
h
a
sis
o
n
re
se
a
rc
h
in
to
th
e
a
p
p
l
ica
ti
o
n
s
o
f
DERs
fo
u
n
d
sc
o
p
e
in
m
icro
g
rid
s
a
n
d
a
c
ti
v
e
d
istri
b
u
t
io
n
n
e
two
rk
s.
T
h
e
p
lac
e
m
e
n
t
o
f
DE
Rs
c
lo
se
t
o
lo
a
d
c
e
n
ters
a
i
d
s
wit
h
p
ro
v
id
in
g
c
lea
n
,
re
li
a
b
le
p
o
we
r
t
o
a
d
d
it
i
o
n
a
l
c
u
st
o
m
e
rs,
re
d
u
c
e
e
lec
tri
c
it
y
lo
s
se
s
a
lo
n
g
tran
sm
issio
n
a
n
d
d
istri
b
u
ti
o
n
li
n
e
s
a
n
d
in
e
v
e
n
t
o
f
fa
u
lt
s
it
a
ll
o
ws
t
o
o
p
e
ra
te
in
islan
d
e
d
m
o
d
e
.
Th
is
m
a
n
u
sc
rip
t
fo
c
u
se
s
o
n
p
o
we
r
sm
o
o
th
i
n
g
,
w
h
ic
h
imp
li
e
s
re
d
u
c
ti
o
n
o
f
p
o
we
r
l
o
ss
,
imp
ro
v
e
d
v
o
lt
a
g
e
lev
e
ls,
a
n
d
v
o
lt
a
g
e
sta
b
il
it
y
.
Th
is
stu
d
y
a
ims
to
o
p
ti
m
ize
th
e
c
a
p
a
c
it
ies
a
n
d
p
lac
e
m
e
n
ts
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
s
(
DG
s
)
a
n
d
d
istri
b
u
ti
o
n
sta
ti
c
c
o
m
p
e
n
sa
to
rs
(
DST
ATCOMs
)
in
o
rd
e
r
t
o
re
d
u
c
e
re
a
l
p
o
we
r
lo
ss
a
n
d
imp
r
o
v
e
t
h
e
v
o
l
tag
e
p
ro
fil
e
.
T
h
e
p
r
o
b
lem
o
f
v
o
lt
a
g
e
fr
o
m
u
n
d
istr
ib
u
ted
e
n
e
rg
y
re
so
u
rc
e
s
c
a
n
b
e
s
t
b
e
so
l
v
e
d
b
y
DST
ATCOM
.
T
h
e
g
o
a
l
fu
n
c
ti
o
n
o
f
t
h
e
d
irec
t
l
o
a
d
fl
o
w
tec
h
n
iq
u
e
,
w
h
ich
a
lso
m
a
k
e
s
u
se
o
f
v
o
l
tag
e
d
e
v
iati
o
n
a
n
d
t
h
e
lo
ss
se
n
siti
v
it
y
fa
c
to
r,
is
u
se
d
in
th
is
stu
d
y
t
o
p
i
n
p
o
in
t
t
h
e
id
e
a
l
p
lac
e
m
e
n
t
fo
r
t
h
e
DG
a
n
d
DST
ATCOM
o
n
th
e
M
ATLAB
p
latfo
rm
.
T
h
e
m
e
th
o
d
is
tes
ted
u
si
n
g
th
e
3
3
a
n
d
6
9
b
u
s
ro
u
tes
.
W
h
e
n
t
h
e
re
su
lt
s
a
re
c
o
m
p
a
re
d
to
re
c
e
n
t
m
e
th
o
d
o
lo
g
ies
,
th
e
y
sh
o
w en
c
o
u
ra
g
i
n
g
re
su
lt
s.
K
ey
w
o
r
d
s
:
Activ
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
Dis
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
DSTA
T
C
OM
Op
tim
al
DG
p
lace
m
en
t
Vo
ltag
e
p
r
o
f
ile
i
m
p
r
o
v
em
en
t
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
:
Sm
r
u
tire
k
h
a
Ma
h
a
n
ta
Sch
o
o
l o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
,
KI
I
T
Dee
m
ed
to
b
e
Un
iv
e
r
s
ity
B
h
u
b
an
eswar
,
Od
is
h
a,
I
n
d
ia
E
m
ail:
m
.
s
m
r
u
tire
k
h
a
8
8
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
C
lim
ate
ch
an
g
e,
en
e
r
g
y
s
ec
u
r
ity
,
an
d
th
e
r
ap
id
d
ep
letio
n
o
f
f
o
s
s
il
f
u
el
s
o
u
r
ce
s
[
1
]
h
a
v
e
p
u
t
th
e
g
lo
b
a
l
en
e
r
g
y
s
ec
to
r
in
a
c
r
is
is
.
T
h
is
ch
an
g
e
f
r
o
m
ce
n
tr
alize
d
p
o
wer
g
en
e
r
atio
n
t
o
d
is
tr
ib
u
ted
en
e
r
g
y
r
eso
u
r
ce
s
(
DE
R
s
)
th
at
ar
e
s
tr
ateg
ically
p
lace
d
at
d
is
tr
ib
u
tio
n
v
o
ltag
e
lev
els
h
as
b
ee
n
v
e
r
y
im
p
o
r
ta
n
t
[
2
]
.
As
g
o
v
er
n
m
en
ts
all
o
v
er
t
h
e
wo
r
ld
s
et
s
tr
ict
g
o
als
f
o
r
ca
r
b
o
n
n
eu
tr
ality
an
d
r
e
n
ewa
b
le
e
n
er
g
y
,
th
e
n
u
m
b
er
o
f
s
o
lar
s
y
s
tem
s
an
d
win
d
g
e
n
er
ato
r
s
h
as
g
r
o
wn
at
an
u
n
p
r
ec
e
d
en
ted
r
ate
[
3
]
.
T
h
e
way
elec
tr
icity
is
d
is
tr
ib
u
ted
to
d
ay
is
ch
an
g
in
g
a
lo
t.
Po
we
r
ca
n
n
o
w
f
lo
w
in
b
o
th
d
ir
ec
ti
o
n
s
,
wh
ich
m
a
k
es
m
an
ag
i
n
g
v
o
ltag
e
h
a
r
d
er
,
an
d
th
e
s
y
s
tem
n
ee
d
s
to
b
e
m
o
r
e
f
lex
ib
le
[
4
]
.
E
lectr
ic
ca
r
s
,
h
ea
t p
u
m
p
s
,
an
d
o
th
er
tec
h
n
o
lo
g
ies
th
at
u
s
e
elec
tr
icity
h
av
e
ch
an
g
ed
th
e
way
p
e
o
p
le
u
s
e
p
o
wer
,
m
a
k
in
g
it
h
a
r
d
t
o
p
lan
f
o
r
d
is
tr
ib
u
tio
n
.
New
i
d
ea
s
ar
e
n
ee
d
ed
to
k
ee
p
th
e
s
y
s
te
m
r
eliab
le
a
n
d
e
f
f
icien
t [
5
]
.
T
h
is
ch
an
g
i
n
g
en
v
ir
o
n
m
en
t
m
ak
es
it
p
o
s
s
ib
le
f
o
r
d
is
tr
ib
u
ted
g
en
e
r
atio
n
(
DG)
a
n
d
d
is
tr
ib
u
t
io
n
s
tatic
co
m
p
en
s
ato
r
s
(
D
-
STAT
C
OM
)
to
m
a
k
e
s
y
s
tem
s
wo
r
k
b
etter
an
d
s
u
p
p
o
r
t
en
er
g
y
s
y
s
tem
s
th
at
a
r
e
g
o
o
d
f
o
r
th
e
en
v
ir
o
n
m
en
t.
W
in
d
tu
r
b
in
es,
s
m
all
-
s
ca
le
co
m
b
in
ed
h
ea
t
an
d
p
o
wer
p
lan
ts
,
an
d
s
o
lar
p
h
o
to
v
o
ltaic
s
y
s
tem
s
ar
e
all
ex
am
p
les
o
f
d
is
p
er
s
ed
g
en
er
atio
n
u
n
its
.
T
h
ese
u
n
its
[
6
]
ar
e
n
ee
d
ed
to
m
o
d
e
r
n
ize
d
is
tr
ib
u
tio
n
n
etwo
r
k
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
Op
tima
l p
la
ce
men
t a
n
d
s
iz
in
g
o
f
DG
a
n
d
DS
TATC
OM in
o
r
d
er to
mitig
a
te
…
(
S
mru
tir
ek
h
a
Ma
h
a
n
t
a
)
827
T
h
ese
s
y
s
tem
s
m
ak
e
elec
tr
icit
y
clo
s
e
to
wh
er
e
it
is
u
s
ed
,
w
h
ich
cu
ts
d
o
wn
o
n
tr
a
n
s
m
is
s
io
n
lo
s
s
es
an
d
m
ak
es
th
e
s
y
s
tem
wo
r
k
b
etter
[
7
]
.
Pu
ttin
g
DG
u
n
its
in
th
e
r
ig
h
t
p
lace
s
h
elp
s
th
e
en
v
ir
o
n
m
en
t
a
n
d
m
ak
es
th
e
g
r
id
s
tr
o
n
g
er
b
y
lettin
g
it
r
u
n
o
n
its
o
wn
wh
e
n
th
er
e
ar
e
p
r
o
b
lem
s
with
th
e
g
r
id
an
d
lo
w
er
in
g
th
e
n
ee
d
f
o
r
ce
n
tr
alize
d
g
en
e
r
atio
n
[
8
]
.
DG
u
n
its
p
r
o
v
i
d
e
ac
tiv
e
p
o
w
er
,
wh
ile
d
is
tr
ib
u
tio
n
s
tatic
co
m
p
en
s
ato
r
s
(
D
-
STAT
C
OM
)
h
elp
with
r
ea
ctiv
e
p
o
wer
a
n
d
v
o
ltag
e
m
an
ag
em
en
t
t
o
k
ee
p
th
e
p
o
wer
q
u
ality
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
h
ig
h
[
9
]
.
D
-
STAT
C
OM
d
ev
ices
u
s
e
v
o
l
tag
e
s
o
u
r
ce
co
n
v
er
ter
tech
n
o
lo
g
y
to
m
a
n
ag
e
v
o
ltag
e
in
r
ea
l
tim
e,
f
ix
th
e
p
o
we
r
f
ac
to
r
,
a
n
d
r
ed
u
c
e
h
a
r
m
o
n
ics
[
1
0
]
.
DG
an
d
D
-
STAT
C
OM
wo
r
k
to
g
eth
er
to
s
o
lv
e
p
r
o
b
le
m
s
with
m
an
ag
i
n
g
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
in
m
o
d
er
n
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
[
1
1
]
.
Pu
ttin
g
DG
an
d
D
-
STAT
C
OM
s
y
s
tem
s
to
g
eth
er
ca
n
m
a
k
e
m
an
y
p
ar
ts
o
f
th
e
d
is
tr
ib
u
t
io
n
s
y
s
tem
wo
r
k
b
etter
[
1
2
]
.
Nu
m
er
o
u
s
s
tu
d
ies
h
av
e
d
em
o
n
s
tr
ated
th
at
t
h
e
s
im
u
ltan
eo
u
s
im
p
lem
en
tatio
n
o
f
th
ese
tech
n
o
lo
g
ies
d
im
in
is
h
es
s
y
s
tem
lo
s
s
es
an
d
en
h
an
ce
s
v
o
ltag
e
p
r
o
f
iles
,
p
o
wer
q
u
ality
,
an
d
t
h
e
h
o
s
tin
g
c
ap
ac
ity
f
o
r
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
1
3
]
.
Sm
ar
t
g
r
id
tech
n
o
lo
g
ies
an
d
b
etter
co
n
tr
o
l
s
y
s
tem
s
m
ak
e
it
ea
s
i
er
to
co
o
r
d
in
ate
t
h
e
in
s
tallat
io
n
o
f
DG
an
d
D
-
STAT
C
OM
[
1
4
]
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
DG
an
d
D
-
STAT
C
OM
in
teg
r
atio
n
d
ep
en
d
s
o
n
h
o
w
well
th
e
s
tr
ateg
ic
d
is
tr
ib
u
tio
n
n
etwo
r
k
is
laid
o
u
t a
n
d
s
ized
[
1
5
]
.
I
f
th
ese
d
ev
ic
es a
r
e
n
o
t p
u
t i
n
th
e
r
ig
h
t p
lac
e
o
r
s
ized
co
r
r
ec
tly
,
th
ey
co
u
ld
ca
u
s
e
m
o
r
e
lo
s
s
es,
v
o
ltag
e
in
s
tab
ilit
y
,
o
r
p
r
o
b
le
m
s
with
p
r
o
tectio
n
co
o
r
d
in
ati
o
n
[
1
6
]
.
Fin
d
in
g
th
e
b
est
s
ize
an
d
lo
ca
tio
n
f
o
r
DG
an
d
D
-
STAT
C
OM
u
n
its
i
s
a
m
u
lti
-
d
im
en
s
io
n
al
o
p
tim
izatio
n
p
r
o
b
lem
th
at
m
u
s
t
tak
e
in
to
ac
c
o
u
n
t
tec
h
n
o
lo
g
ic
al,
ec
o
n
o
m
ic
,
an
d
o
p
e
r
atio
n
al
lim
its
[
1
7
]
.
W
h
en
p
lacin
g
th
in
g
s
,
th
e
elec
tr
ical
p
r
o
p
er
ties
o
f
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
,
th
e
p
atter
n
s
o
f
lo
a
d
,
th
e
p
r
o
f
iles
o
f
g
en
er
atio
n
,
an
d
th
e
co
n
d
itio
n
s
u
n
d
er
wh
ich
th
e
s
y
s
tem
r
u
n
s
ar
e
all
tak
en
in
to
ac
co
u
n
t
[
1
8
]
.
L
o
s
s
s
en
s
itiv
ity
f
ac
to
r
s
a
n
d
v
o
ltag
e
s
tab
ilit
y
in
d
ices
ar
e
n
ec
ess
ar
y
f
o
r
p
in
p
o
in
tin
g
ar
ea
s
wh
e
r
e
th
e
s
y
s
te
m
ca
n
b
e
im
p
r
o
v
ed
[
1
9
]
.
Sizin
g
o
p
tim
izatio
n
m
u
s
t
f
in
d
a
b
ala
n
ce
b
etwe
en
th
e
c
o
s
ts
o
f
in
v
estme
n
t,
th
e
b
e
n
ef
i
ts
o
f
o
p
er
atio
n
,
an
d
th
e
lim
its
o
f
tech
n
o
lo
g
y
,
all
wh
ile
s
tay
in
g
with
in
v
o
ltag
e
li
m
its
,
tem
p
er
atu
r
e
r
atin
g
s
,
an
d
s
af
ety
s
tan
d
ar
d
s
[
2
0
]
.
R
ec
en
t
s
tu
d
ies
h
av
e
s
h
o
wn
th
at
it
is
b
etter
to
o
p
tim
ize
t
h
e
p
o
s
itio
n
in
g
an
d
s
izin
g
o
f
DG
an
d
D
-
STAT
C
OM
at
th
e
s
am
e
tim
e
th
an
to
d
o
th
em
s
ep
a
r
ately
[
2
1
]
.
T
h
is
in
teg
r
ated
ap
p
r
o
ac
h
s
ee
s
th
e
co
n
n
ec
tio
n
s
b
etwe
en
m
a
n
ag
in
g
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
,
wh
ich
h
elp
s
f
in
d
s
o
lu
tio
n
s
th
at
m
ak
e
th
e
s
y
s
tem
wo
r
k
b
etter
[
2
2
]
.
B
ec
au
s
e
o
f
c
h
an
g
es
in
r
en
ewa
b
le
en
er
g
y
p
r
o
d
u
ctio
n
a
n
d
lo
a
d
d
em
an
d
,
b
e
tter
p
lace
m
en
t
an
d
s
izin
g
s
tr
ateg
ies
ar
e
n
ee
d
ed
[
2
3
]
.
T
h
e
b
est
way
to
co
n
n
ec
t
D
G
an
d
D
-
STAT
C
OM
in
d
is
tr
ib
u
tio
n
s
y
s
tem
s
cu
ts
d
o
wn
o
n
p
o
wer
lo
s
s
[
2
4
]
.
Usu
ally
,
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
lo
s
e
b
etwe
en
8
an
d
1
5
%
o
f
th
eir
en
er
g
y
.
T
h
is
c
o
s
ts
th
e
ec
o
n
o
m
y
an
d
en
v
ir
o
n
m
e
n
t
a
lo
t,
b
u
t
p
lan
n
ed
DE
R
u
s
e
ca
n
cu
t
it
d
o
wn
[
2
5
]
.
I
n
t
eg
r
atin
g
d
is
tr
ib
u
ted
g
en
er
atio
n
(
DG)
in
to
th
e
g
r
id
lo
wer
s
p
o
wer
lo
s
s
b
y
m
ee
tin
g
lo
ca
l
lo
ad
d
em
a
n
d
an
d
lo
wer
in
g
th
e
f
lo
w
o
f
cu
r
r
en
t
i
n
d
is
tr
ib
u
tio
n
l
in
es
[
2
6
]
.
T
h
er
e
ar
e
m
an
y
way
s
th
at
co
o
r
d
in
atin
g
DG
a
n
d
D
-
STAT
C
OM
cu
ts
d
o
wn
o
n
lo
s
s
es
[
2
7
]
.
DG
u
n
its
cu
t
d
o
wn
o
n
ac
tiv
e
p
o
wer
lo
s
s
es
b
y
lo
wer
in
g
th
e
n
et
p
o
we
r
f
lo
w
at
s
u
b
s
tatio
n
s
.
D
-
STAT
C
OM
d
ev
ices,
o
n
th
e
o
th
er
h
an
d
,
h
elp
r
ed
u
ce
lo
s
s
es
b
y
s
u
p
p
o
r
tin
g
r
ea
ctiv
e
p
o
wer
lo
ca
lly
.
T
h
is
lo
wer
s
r
ea
ctiv
e
cu
r
r
en
t
o
n
d
is
tr
ib
u
tio
n
lin
es
[
2
8
]
.
B
y
o
p
tim
izin
g
b
o
th
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
f
l
o
ws
at
th
e
s
am
e
tim
e,
it is
p
o
s
s
ib
le
to
f
in
d
o
p
er
atio
n
al
p
o
i
n
ts
with
th
e
least lo
s
s
th
at
n
eith
er
tech
n
o
lo
g
y
co
u
l
d
f
in
d
[
2
9
]
.
C
h
an
g
in
g
th
e
p
atter
n
s
o
f
lo
a
d
an
d
g
en
er
atio
n
is
o
n
e
o
f
t
h
e
n
ew
way
s
to
r
ed
u
ce
lo
s
s
es.
T
h
is
lets
d
y
n
am
ic
o
p
tim
izatio
n
m
eth
o
d
s
ch
an
g
e
to
f
it
th
e
s
y
s
tem
[
3
0
]
.
T
o
d
ea
l
with
th
e
m
u
lti
-
d
im
e
n
s
io
n
al,
n
o
n
-
lin
ea
r
,
an
d
o
f
ten
n
o
n
-
co
n
v
ex
n
atu
r
e
o
f
co
n
c
u
r
r
e
n
t
DG
a
n
d
D
-
STAT
C
OM
o
p
tim
izatio
n
,
we
n
ee
d
ad
v
a
n
ce
d
co
m
p
u
tatio
n
al
m
eth
o
d
s
[
1
0
]
.
Me
tah
eu
r
is
tic
o
p
tim
izatio
n
al
g
o
r
ith
m
s
th
at
lo
o
k
t
h
r
o
u
g
h
h
u
g
e
s
o
lu
tio
n
s
p
ac
es
f
o
r
p
r
ac
tical
n
ea
r
-
o
p
tim
al
s
o
lu
tio
n
s
h
av
e
r
e
p
lace
d
m
o
s
t
an
aly
tical
m
eth
o
d
s
[
1
1
]
.
Ge
n
etic
a
lg
o
r
ith
m
s
,
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
,
wh
ale
o
p
tim
izatio
n
,
ar
tific
ial
b
ee
c
o
lo
n
y
,
an
d
n
ewe
r
i
d
ea
s
lik
e
a
r
tific
ial
r
ab
b
it
an
d
b
lack
wid
o
w
o
p
t
im
izatio
n
ar
e
well
-
k
n
o
wn
[
1
2
]
.
M
ix
ed
-
in
teg
e
r
lin
ea
r
p
r
o
g
r
am
m
in
g
(
MI
L
P
)
an
d
m
ix
ed
-
i
n
teg
e
r
nonl
in
ea
r
p
r
o
g
r
a
m
m
in
g
(
MI
NL
P
)
f
o
r
m
u
latio
n
s
ar
e
m
o
r
e
wid
ely
u
s
ed
b
ec
au
s
e
th
e
y
ca
n
h
a
n
d
le
d
is
cr
ete
d
ec
is
io
n
f
ac
to
r
s
th
at
h
av
e
to
d
o
with
ch
o
o
s
in
g
a
n
d
p
lacin
g
d
ev
ices
wh
ile
s
til
l
b
ein
g
m
ath
em
atica
lly
co
r
r
ec
t
[
1
3
]
.
T
h
ese
m
eth
o
d
s
allo
w
f
o
r
co
m
p
licated
o
p
er
atio
n
al
lim
it
s
an
d
g
o
al
f
u
n
ctio
n
s
wh
ile
s
till
en
s
u
r
in
g
th
e
b
est
p
o
s
s
ib
le
s
o
lu
tio
n
o
r
q
u
ality
[
1
4
]
.
T
h
ese
m
eth
o
d
s
ar
e
m
o
r
e
u
s
ef
u
l
in
th
e
r
ea
l
wo
r
ld
b
ec
au
s
e
th
ey
m
ea
s
u
r
e
u
n
ce
r
tain
ty
[
1
5
]
.
Mu
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
f
r
am
ewo
r
k
s
h
av
e
b
ec
o
m
e
p
o
p
u
lar
b
ec
a
u
s
e
th
ey
ca
n
tak
e
in
to
ac
co
u
n
t
co
n
f
lictin
g
g
o
als
lik
e
lo
wer
in
g
co
s
ts
,
lo
wer
in
g
lo
s
s
es,
r
ai
s
in
g
v
o
ltag
e,
an
d
p
r
o
tectin
g
th
e
en
v
ir
o
n
m
en
t
all
at
o
n
ce
[
1
6
]
.
T
h
er
e
ar
e
m
an
y
tr
ad
e
-
o
f
f
s
i
n
Par
eto
-
o
p
tim
al
s
o
lu
tio
n
s
ets,
d
ep
en
d
in
g
o
n
th
e
n
ee
d
s
an
d
lim
its
o
f
th
e
s
y
s
t
em
[
1
7
]
.
Hy
b
r
id
o
p
tim
izatio
n
m
eth
o
d
s
th
at
u
s
e
th
e
b
est
alg
o
r
ith
m
s
f
o
r
b
ig
d
is
tr
ib
u
tio
n
s
y
s
tem
o
p
tim
izati
o
n
p
r
o
b
lem
s
ar
e
p
r
o
m
is
in
g
[
1
8
]
.
T
h
is
s
tu
d
y
aim
s
to
o
p
tim
ize
t
h
e
ca
p
ac
ities
an
d
p
lace
m
en
ts
o
f
DGs
an
d
DSTA
T
C
OM
s
i
n
o
r
d
er
to
r
ed
u
ce
r
ea
l
p
o
wer
lo
s
s
an
d
im
p
r
o
v
e
th
e
v
o
ltag
e
p
r
o
f
ile.
T
h
e
p
r
o
b
lem
o
f
v
o
ltag
e
f
r
o
m
u
n
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
ca
n
b
est
b
e
s
o
lv
ed
b
y
DSTA
T
C
OM
.
T
h
e
g
o
al
f
u
n
ctio
n
o
f
t
h
e
d
ir
ec
t
lo
ad
f
lo
w
tech
n
iq
u
e,
wh
ich
also
m
ak
es
u
s
e
o
f
v
o
ltag
e
d
ev
iatio
n
an
d
t
h
e
lo
s
s
s
en
s
itiv
ity
f
ac
to
r
,
is
u
s
ed
i
n
th
is
s
tu
d
y
t
o
p
in
p
o
i
n
t
th
e
id
ea
l
p
lace
m
en
t f
o
r
th
e
DG
an
d
DSTA
T
C
OM
.
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.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
8
2
6
-
841
828
2.
DIS
T
RI
B
U
T
I
O
N
S
T
A
T
I
C
CO
M
P
E
N
SAT
O
R
I
n
h
i
g
h
v
o
ltag
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
s
,
s
h
u
n
t
FAC
T
S
d
ev
ices,
s
u
c
h
as
s
tatic
s
y
n
ch
r
o
n
o
u
s
co
m
p
en
s
ato
r
(
STAT
C
OM
)
,
ar
e
co
m
m
o
n
ly
u
tili
ze
d
.
W
h
en
d
ep
lo
y
ed
in
lo
w
-
v
o
ltag
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
,
it is
r
ef
er
r
ed
to
as
DSTA
T
C
OM
.
T
h
is
s
h
u
n
t
d
ev
ice,
DSTA
T
C
OM
,
is
ca
p
ab
le
o
f
in
jectin
g
a
n
d
ab
s
o
r
b
in
g
r
ea
l
o
r
r
ea
ctiv
e
p
o
wer
at
th
e
b
u
s
,
e
f
f
ec
tiv
ely
r
e
d
u
cin
g
b
u
s
v
o
lta
g
e
s
ag
.
C
o
n
n
ec
tin
g
to
t
h
e
d
i
s
tr
ib
u
tio
n
n
etwo
r
k
r
eq
u
ir
es
a
c
o
u
p
lin
g
tr
a
n
s
f
o
r
m
er
,
wh
ile
a
DC
en
er
g
y
s
to
r
ag
e
d
e
v
ice,
s
p
ec
if
ically
a
D
C
lin
k
ca
p
ac
ito
r
,
is
em
p
lo
y
ed
to
m
ain
tain
a
co
n
s
tan
t
DC
-
lin
k
v
o
ltag
e.
Actin
g
a
s
a
s
y
n
ch
r
o
n
o
u
s
v
o
ltag
e
s
o
u
r
c
e,
DSTA
T
C
OM
is
r
esp
o
n
s
ib
le
f
o
r
r
e
g
u
latin
g
a
n
d
co
r
r
ec
tin
g
th
e
b
u
s
v
o
ltag
e
an
d
p
o
wer
f
ac
to
r
.
W
h
en
f
ac
ed
w
ith
h
ig
h
lo
ad
lev
els
o
r
s
h
o
r
t
cir
cu
its
,
DSTA
T
C
OM
s
u
p
p
lies
o
r
i
n
jects
th
e
n
ec
e
s
s
ar
y
cu
r
r
en
t
at
th
e
c
o
n
n
ec
tio
n
p
o
i
n
t
to
ele
v
ate
th
e
v
o
ltag
e
p
r
o
f
ile
at
th
e
co
n
n
e
cted
lo
ad
b
u
s
an
d
en
s
u
r
e
r
eg
u
latio
n
t
o
th
e
d
esire
d
r
ef
er
en
ce
v
alu
e.
T
h
e
s
im
u
ltan
eo
u
s
ex
ch
an
g
e
o
f
r
e
ac
tiv
e
an
d
r
ea
l
p
o
wer
is
en
a
b
led
b
y
DSTA
T
C
OM
.
T
h
e
t
y
p
e
an
d
q
u
a
n
tity
o
f
en
er
g
y
s
o
u
r
ce
u
tili
ze
d
d
eter
m
in
e
th
e
ac
tu
al
p
o
wer
ex
c
h
an
g
ed
.
Vo
ltag
e
f
lu
ctu
atio
n
s
ar
e
m
itig
ated
b
y
DSTA
T
C
OM
th
r
o
u
g
h
a
co
m
p
ar
is
o
n
o
f
th
e
li
n
e
wav
ef
o
r
m
with
a
r
ef
e
r
en
ce
s
ig
n
al
an
d
s
u
b
s
eq
u
en
t
a
d
ju
s
tm
en
ts
as
n
ec
ess
ar
y
.
R
ea
ctiv
e
cu
r
r
en
t
is
in
jecte
d
o
r
ab
s
o
r
b
ed
b
y
DSTA
T
C
OM
to
r
ec
tify
an
y
v
o
ltag
e
er
r
o
r
s
.
T
h
e
m
ain
co
m
p
o
n
en
ts
o
f
DSTA
T
C
OM
co
m
p
r
is
e
a
co
u
p
lin
g
tr
an
s
f
o
r
m
er
,
PW
M,
co
n
tr
o
l
s
ch
em
e,
DC
-
lin
k
ca
p
ac
ito
r
,
in
v
e
r
ter
m
o
d
u
les,
a
n
d
an
AC
f
ilter
.
T
h
e
d
ir
ec
tio
n
an
d
m
ag
n
itu
d
e
o
f
th
e
r
ea
ctiv
e
cu
r
r
en
t
d
e
p
en
d
o
n
th
e
v
o
ltag
e
s
o
u
r
ce
s
em
p
lo
y
e
d
in
DSTA
T
C
OM
.
W
h
en
th
e
v
o
ltag
e
at
th
e
co
n
n
ec
tio
n
p
o
in
t
ex
ce
ed
s
th
at
o
f
th
e
v
o
ltag
e
s
o
u
r
ce
,
DSTA
T
C
OM
ac
ts
as
a
r
ea
cto
r
an
d
a
b
s
o
r
b
s
ex
ce
s
s
iv
e
r
ea
ctiv
e
p
o
wer
.
C
o
n
v
er
s
ely
,
w
h
en
th
e
v
o
ltag
e
is
lo
wer
th
an
th
at
o
f
t
h
e
v
o
ltag
e
s
o
u
r
ce
,
DSTA
T
C
O
M
o
p
er
ates
as
a
v
ar
iab
le
ca
p
a
cito
r
an
d
in
jects
th
e
r
eq
u
ir
ed
r
ea
ctiv
e
p
o
wer
.
3.
M
AT
H
E
M
AT
I
CA
L
M
O
D
E
L
I
NG
O
F
DS
T
AT
CO
M
Fig
u
r
e
1
s
h
o
ws
th
e
in
s
tallati
o
n
o
f
DSTA
T
C
OM
in
an
I
E
E
E
b
u
s
s
y
s
tem
.
T
h
e
lin
e
r
esi
s
tan
ce
an
d
r
ea
ctan
ce
b
etwe
en
in
ter
c
h
an
g
e
node
s
ar
e
r
e
p
r
esen
ted
b
y
an
d
r
esp
ec
tiv
ely
.
T
h
e
v
o
ltag
e
an
d
lo
ca
l
lo
ad
s
co
n
n
ec
ted
to
an
d
n
o
d
es
ar
e
d
en
o
ted
b
y
,
,
+
an
d
+
r
esp
ec
tiv
ely
.
T
h
e
p
h
ase
a
n
g
le
o
f
is
α
.
T
h
e
v
o
ltag
e
is
co
n
s
id
er
e
d
to
h
av
e
m
ag
n
itu
d
e
less
th
an
1
.
0
p
.
u
.
s
u
ch
th
at
DSTA
T
C
OM
ca
n
b
e
u
tili
ze
d
to
im
p
r
o
v
e
its
v
o
ltag
e
p
r
o
f
il
e.
DSTA
T
C
OM
in
ject
s
r
ea
ct
iv
e
p
o
wer
to
th
e
s
y
s
tem
;
co
n
s
eq
u
en
tly
cu
r
r
en
t
in
jecte
d
b
y
th
e
DSTA
T
C
OM
(
)
is
in
q
u
ad
r
atu
r
e
with
v
o
ltag
e
o
f
th
e
s
y
s
tem
.
Af
ter
th
e
ap
p
licatio
n
o
f
DSTA
T
C
OM
,
th
e
v
o
ltag
e
ch
a
n
g
es to
.
I
n
o
r
d
er
to
m
ak
e
th
e
ca
lcu
latio
n
s
s
im
p
ler
,
th
e
an
g
le
o
f
v
o
ltag
e
is
ass
u
m
ed
t
o
b
e
ze
r
o
.
V
o
l
t
a
g
e
S
o
u
r
c
e
C
o
n
v
e
r
t
e
r
D
C
S
o
u
r
c
e
o
v
n
v
r
p
p
x
p
+
jq
nn
p
+
jq
oo
Ip
ds
tat
I
Fig
u
r
e
1
.
DSTA
T
C
OM
m
o
d
el
Fig
u
r
e
1
illu
s
tr
ates
th
e
s
ch
e
m
atic
r
ep
r
esen
tatio
n
o
f
a
d
is
tr
ib
u
tio
n
s
tatic
s
y
n
ch
r
o
n
o
u
s
c
o
m
p
en
s
ato
r
(
DSTA
T
C
OM
)
,
wh
ich
is
p
r
i
m
ar
ily
u
s
ed
f
o
r
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
an
d
v
o
lta
g
e
r
eg
u
latio
n
at
th
e
d
is
tr
ib
u
tio
n
lev
el.
T
h
e
co
r
e
c
o
m
p
o
n
en
t
o
f
th
e
DSTA
T
C
O
M
is
a
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
,
wh
ich
is
co
n
n
ec
ted
to
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
t
h
r
o
u
g
h
a
co
u
p
lin
g
tr
an
s
f
o
r
m
er
.
T
h
e
VSC
co
n
v
er
ts
DC
v
o
ltag
e
f
r
o
m
a
DC
s
o
u
r
ce
in
to
a
co
n
tr
o
llab
le
AC
v
o
ltag
e,
allo
win
g
it
to
i
n
ject
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
we
r
d
ep
en
d
in
g
o
n
th
e
s
y
s
tem
r
eq
u
ir
em
en
ts
.
T
h
e
co
u
p
lin
g
in
d
u
cto
r
(
o
r
in
ter
f
ac
in
g
in
d
u
cto
r
)
h
elp
s
in
f
ilter
in
g
o
u
t
h
ig
h
-
f
r
eq
u
e
n
cy
s
witch
in
g
h
ar
m
o
n
ics
an
d
r
eg
u
lates
th
e
p
o
wer
ex
ch
an
g
e
b
e
twee
n
th
e
VS
C
an
d
th
e
g
r
id
.
T
h
e
DSTA
T
C
O
M
o
p
er
ates
b
y
ad
ju
s
tin
g
th
e
m
a
g
n
itu
d
e
an
d
p
h
ase
o
f
th
e
o
u
t
p
u
t
v
o
ltag
e
o
f
th
e
VSC
r
elativ
e
to
th
e
g
r
id
v
o
ltag
e
.
W
h
en
th
e
VSC
o
u
tp
u
t
v
o
ltag
e
is
h
ig
h
er
th
an
th
e
g
r
id
v
o
lta
g
e,
it
s
u
p
p
lies
r
ea
ctiv
e
p
o
wer
(
ca
p
ac
itiv
e
m
o
d
e)
,
an
d
wh
en
it
is
lo
wer
,
it
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
wer
(
in
d
u
ctiv
e
m
o
d
e)
.
T
h
is
d
y
n
am
ic
co
n
tr
o
l
ca
p
ab
ilit
y
en
ab
les
th
e
DSTA
T
C
OM
to
p
r
o
v
id
e
f
ast
v
o
ltag
e
s
u
p
p
o
r
t,
m
itig
ate
v
o
ltag
e
s
ag
s
an
d
s
well
s
,
an
d
im
p
r
o
v
e
p
o
wer
q
u
ality
in
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d
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iz
in
g
o
f
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n
d
DS
TATC
OM in
o
r
d
er to
mitig
a
te
…
(
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mru
tir
ek
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a
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h
a
n
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d
is
tr
ib
u
tio
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ts
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m
p
ac
t
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esig
n
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h
ig
h
r
eliab
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y
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r
ap
id
r
esp
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ak
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h
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ilit
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o
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ac
tiv
e
d
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u
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n
etwo
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,
esp
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ially
th
o
s
e
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teg
r
ated
with
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
(
DE
R
s
)
.
(
)
(
)
=
o
n
e
w
n
e
w
n
p
p
p
p
p
d
s
t
a
t
n
e
w
π
v
α
v
δ
-
r
+
jx
I
θ
-
r
+
jx
I
α
+
2
(
1
)
T
h
e
(2
)
an
d
(
3
)
a
r
e
o
b
tain
ed
b
y
eq
u
atin
g
r
ea
l a
n
d
im
ag
in
a
r
y
p
ar
ts
o
f
(
1
)
.
(
)
(
)
on
e
w
ne
w
n
p
p
p
dstat
ne
w
p
dstat
ne
w
ππ
v
c
os
α
=
Re
v
δ
-
Re
r
I
θ
+
x
I
si
n
α
+
-
r
I
c
os
α
+
22
(
2
)
(
)
(
)
on
e
w
ne
w
n
p
p
p
dstat
ne
w
p
dstat
ne
w
ππ
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si
n
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m
v
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I
m
r
I
θ
-
x
I
c
os
α
+
-
r
I
si
n
α
+
22
(
3
)
Simp
lify
in
g
in
(2
)
an
d
(
3
)
,
(
)
(
)
n
p
p
a
=
Re
v
δ
-
Re
r
I
θ
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(
)
(
)
n
p
p
v
b
=
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m
v
δ
-
I
m
r
I
θ
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1
=
−
,
2
=
−
,
=
,
1
=
,
an
d
2
=
.
T
h
e
(2
)
a
n
d
(
3
)
ca
n
b
e
r
ewr
itten
as
in
(4
)
an
d
(
5
)
.
2
=
−
1
1
1
−
2
1
2
(
4
)
2
=
−
2
1
2
+
1
1
2
2
(
5
)
T
h
e
v
alu
es f
o
r
1
an
d
2
as o
b
tain
ed
f
r
o
m
(
4
)
an
d
(
5)
a
r
e
ex
p
r
ess
ed
in
(
6
)
.
1
=
2
−
−
1
2
−
2
2
;
1
=
2
−
−
2
2
+
1
2
(
6
)
T
h
e
(
7
)
is
o
b
tain
ed
b
y
e
q
u
atin
g
1
=
1
2
−
2
1
,
=
2
,
2
=
1
1
+
2
2
an
d
s
u
b
s
titu
tin
g
i
n
(
6
)
.
(
1
2
+
2
2
)
2
+
(
2
1
1
)
+
(
2
1
2
−
2
2
)
=
0
(
7
)
T
h
e
s
o
lu
tio
n
o
f
(
7
)
ca
n
b
e
ex
p
r
ess
ed
b
y
(
8
)
an
d
(
9
)
.
=
2
1
1
±
√
(
2
1
1
)
2
−
4
(
1
2
+
2
2
)
(
1
2
−
2
2
)
2
(
1
2
+
2
2
)
(
8
)
=
2
=
−
1
(
9
)
No
w
th
e
in
jecte
d
r
ea
ctiv
e
p
o
wer
(
)
,
cu
r
r
en
t
an
d
v
o
ltag
e
w
h
er
e
DSTA
T
C
OM
is
in
s
ta
lle
d
is
g
iv
en
b
y
(
1
0
)
-
(
1
2
)
.
o
n
e
w
o
n
e
w
n
e
w
v
=
v
α
(
1
0
)
d
s
ta
t
d
s
ta
t
n
e
w
π
I
=
I
α+
2
(
1
1
)
=
∗
(
1
2
)
T
h
e
f
o
r
m
u
latio
n
o
f
DSTA
T
C
OM
aim
s
to
s
e
t
th
e
v
o
ltag
e
m
ag
n
itu
d
e
n
o
d
e
at
th
e
DS
T
AT
C
OM
'
s
lo
ca
tio
n
to
a
v
alu
e
o
f
1
p
er
u
n
it
(
p
.
u
.
)
.
T
h
e
p
h
ase
an
g
le
o
f
th
e
DSTA
T
C
OM
'
s
n
o
d
e
is
d
eter
m
in
ed
u
s
in
g
in
(
9
)
,
wh
ile
in
(
1
1
)
is
em
p
lo
y
ed
t
o
ca
lcu
late
th
e
I
d
s
tat.
L
astl
y
,
th
e
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
in
jecte
d
b
y
th
e
DSTA
T
C
OM
is
ev
alu
ated
b
y
im
p
lem
en
tin
g
in
(
1
2
)
.
T
h
e
th
r
ee
p
r
im
ar
y
c
o
m
p
o
n
en
ts
o
f
th
e
p
o
wer
s
y
s
tem
ar
e
g
en
er
atio
n
,
t
r
an
s
m
is
s
io
n
,
an
d
d
is
tr
ib
u
tio
n
.
Po
wer
f
o
r
en
d
u
s
er
s
is
p
r
o
v
id
ed
b
y
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
Dis
tr
ib
u
tio
n
s
y
s
tem
ty
p
es
in
clu
d
e
r
a
d
ial,
r
in
g
,
a
n
d
d
o
u
b
l
y
f
ed
co
n
f
ig
u
r
atio
n
s
f
o
r
th
e
d
is
tr
ib
u
tio
n
lin
es.
B
ec
au
s
e
o
f
its
d
u
r
ab
ilit
y
a
n
d
af
f
o
r
d
ab
ilit
y
,
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
s
ar
e
o
n
e
o
f
th
e
m
o
s
t
p
o
p
u
lar
co
n
f
ig
u
r
atio
n
s
.
Vo
ltag
e
s
ag
a
n
d
s
tab
ilit
y
is
s
u
e
ca
u
s
e
h
ig
h
lo
s
s
es
in
th
e
r
ad
ial
d
is
tr
ib
u
ti
o
n
n
etwo
r
k
.
T
h
ese
d
is
tr
ib
u
tio
n
lo
s
s
es
in
I
n
d
ia
r
an
g
e
f
r
o
m
1
3
%
to
1
4
%
o
f
th
e
n
atio
n
'
s
to
tal
p
o
wer
o
u
tp
u
t.
T
o
m
in
im
ize
lo
s
s
es
in
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
,
a
s
tr
ateg
ic
ap
p
r
o
ac
h
in
v
o
l
v
es
th
e
p
lace
m
en
t
o
f
d
is
tr
ib
u
ted
g
e
n
er
atio
n
(
DG)
an
d
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.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
8
2
6
-
841
830
d
is
tr
ib
u
tio
n
STAT
C
OM
(
DSTA
T
C
OM
)
at
wea
k
b
u
s
es.
C
o
n
v
en
tio
n
al
lo
ad
f
lo
w
m
o
d
els
lik
e
New
to
n
-
R
ap
h
s
o
n
,
Gau
s
s
-
Seid
el
,
an
d
f
ast
-
d
ec
o
u
p
led
m
eth
o
d
s
ar
e
co
n
s
id
er
ed
u
n
s
u
itab
le
f
o
r
lo
ad
f
lo
w
s
tu
d
ies
i
n
d
is
tr
ib
u
tio
n
s
y
s
tem
s
d
u
e
to
th
eir
h
ig
h
R
/X
r
atio
.
T
h
ese
m
et
h
o
d
s
d
o
n
o
t
ac
cu
r
ately
d
eter
m
in
e
lin
e
f
lo
ws
an
d
lin
e
v
o
ltag
es
with
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
T
o
tac
k
le
th
is
is
s
u
e,
ad
v
an
ce
d
n
u
m
er
ic
al
alg
o
r
ith
m
s
an
d
tech
n
iq
u
es
ar
e
em
p
lo
y
ed
in
th
is
m
an
u
s
cr
ip
t
to
an
aly
ze
th
e
lo
ad
f
lo
w.
Sp
ec
if
ically
,
th
e
m
e
th
o
d
o
lo
g
y
b
ased
o
n
d
ir
ec
t
lo
ad
f
lo
w
(
DL
F)
a
n
aly
s
is
is
u
tili
ze
d
in
th
is
p
ap
er
f
o
r
p
er
f
o
r
m
in
g
lo
a
d
f
lo
w
ca
lcu
lat
io
n
s
.
T
h
e
co
m
p
lex
lo
ad
(
)
f
o
r
o
th
b
u
s
in
a
n
I
E
E
E
b
u
s
s
y
s
tem
is
r
ep
r
esen
ted
b
y
(
1
3
)
.
=
+
(
1
3
)
W
h
er
e
,
an
d
r
ep
r
esen
ts
th
e
r
ea
l
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
at
o
th
b
u
s
.
T
h
e
(
1
4
)
r
ep
r
esen
ts
th
e
cu
r
r
en
t
in
jecte
d
at
th
e
o
th
b
u
s
.
=
(
)
∗
(
1
4
)
W
h
er
e
,
r
ep
r
esen
ts
th
e
v
o
ltag
e
at
th
e
o
th
b
u
s
.
T
h
e
r
elatio
n
s
h
ip
m
atr
ix
is
d
e
v
elo
p
e
d
b
y
u
s
in
g
th
e
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
T
h
e
(
1
4
)
is
u
tili
ze
d
to
ca
lcu
late
th
e
cu
r
r
en
t
in
jectio
n
m
atr
ix
f
r
o
m
th
e
p
o
wer
in
jectio
n
v
alu
es.
Kir
ch
h
o
f
f
’
s
cu
r
r
en
t
law
is
u
tili
ze
d
to
estab
lis
h
co
r
r
elatio
n
b
etwe
en
th
e
b
r
an
ch
c
u
r
r
en
t
a
n
d
b
u
s
cu
r
r
en
t
o
f
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
T
h
e
(
1
5
)
r
ep
r
esen
ts
th
e
co
r
r
elatio
n
b
etwe
en
th
e
b
r
an
ch
cu
r
r
en
t (
)
an
d
b
u
s
cu
r
r
en
t in
je
ctio
n
s
(
)
f
o
r
th
e
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
=
[
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
]
(
1
5
)
T
h
e
(
1
6
)
r
ep
r
esen
ts
th
e
c
o
r
r
e
latio
n
b
etwe
en
th
e
an
d
b
u
s
v
o
ltag
es
(
)
f
o
r
t
h
e
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
=
[
]
(
1
6
)
W
h
er
e
,
is
th
e
b
r
an
ch
cu
r
r
e
n
t
b
u
s
v
o
ltag
e
m
atr
ix
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
an
d
is
ex
p
r
ess
ed
b
y
(
1
7
)
.
=
[
]
×
(
1
7
)
W
h
er
e
,
is
th
e
d
iag
o
n
al
b
u
s
im
p
ed
an
ce
m
atr
ix
.
T
h
e
co
r
r
elatio
n
b
etwe
en
an
d
is
est
ab
lis
h
ed
b
y
(
1
8
)
.
=
[
]
[
]
[
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
]
(
1
8
)
T
h
e
lo
ad
f
lo
w
s
o
lu
tio
n
in
a
r
a
d
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
ca
n
b
e
attain
ed
b
y
iter
ativ
el
y
s
o
lv
in
g
in
(
1
9
)
,
(
2
0
)
.
=
(
)
∗
(
1
9
)
+
1
=
[
]
(
2
0
)
W
h
er
e
,
[
]
=
[
]
[
]
,
is
cu
r
r
en
t
iter
atio
n
,
=
[
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
]
,
+
1
=
[
]
[
+
1
]
,
an
d
is
th
e
r
ef
er
en
ce
v
o
ltag
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
Op
tima
l p
la
ce
men
t a
n
d
s
iz
in
g
o
f
DG
a
n
d
DS
TATC
OM in
o
r
d
er to
mitig
a
te
…
(
S
mru
tir
ek
h
a
Ma
h
a
n
t
a
)
831
T
h
is
s
ec
tio
n
elab
o
r
ates
o
n
th
e
o
p
tim
u
m
lo
ca
tio
n
an
d
s
izin
g
o
f
DGs
an
d
STAT
C
OM
.
On
e
o
f
th
e
f
ac
to
r
s
u
s
ed
t
o
d
ete
r
m
in
e
wh
er
e
to
p
lace
DGs
in
a
g
iv
e
n
d
is
tr
ib
u
tio
n
n
etwo
r
k
is
th
e
lo
s
s
s
en
s
itiv
ity
f
ac
to
r
(
L
SF
)
.
T
h
e
ch
o
ice
o
f
L
SF
is
b
ec
au
s
e
L
SF
s
h
r
in
k
s
th
e
s
ea
r
ch
s
p
ac
e,
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
ca
n
b
e
ca
lcu
lated
m
o
r
e
q
u
ick
ly
.
T
h
e
r
ea
l
(
(
)
)
an
d
r
ea
ctiv
e
p
o
we
r
lo
s
s
(
(
)
)
f
o
r
t
h
e
lin
e
is
e
x
p
r
ess
ed
m
ath
em
atica
lly
b
y
(
2
1
)
an
d
(
2
2
)
.
(
)
=
(
(
×
)
2
+
(
×
)
2
)
×
2
(
2
1
)
(
)
=
(
(
×
)
2
+
(
×
)
2
)
×
2
(
2
2
)
W
h
er
e,
an
d
r
ep
r
esen
ts
th
e
to
tal
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
s
u
p
p
lied
ah
ea
d
o
f
n
o
d
e
o
.
T
h
e
L
SF
(
an
d
)
is
o
b
tain
ed
b
y
p
er
f
o
r
m
in
g
p
ar
tial
f
r
ac
tio
n
o
f
(
)
w
ith
r
esp
ec
t
to
an
d
r
esp
ec
tiv
ely
.
L
SF
is
ex
p
r
ess
ed
m
ath
em
atica
lly
b
y
(
2
3
)
an
d
(
2
4
)
.
=
(
)
=
(
2
×
(
×
)
)
×
2
(
2
3
)
=
(
)
=
(
2
×
(
×
)
)
×
2
(
2
4
)
T
h
e
b
est
b
u
s
es
f
o
r
DG
p
lace
m
en
t
ar
e
th
o
s
e
with
th
e
h
ig
h
est
L
SF
v
alu
es.
Her
e,
th
e
v
o
ltag
e
d
ev
iatio
n
f
r
o
m
th
e
allo
wab
le
lim
it
an
d
b
o
th
th
e
r
ea
l
a
n
d
r
ea
ctiv
e
p
o
wer
L
SF
s
ar
e
u
s
ed
to
d
eter
m
in
e
wh
er
e
th
e
DG
s
h
o
u
ld
b
e
p
lace
d
.
T
h
e
(
2
5
)
d
escr
ib
es th
e
o
b
jectiv
e
f
u
n
ctio
n
(
1
)
f
o
r
ch
o
o
s
in
g
t
h
e
b
est DG
lo
ca
tio
n
.
(
1
)
=
1
+
+
2
×
−
3
×
[
∑
{
(
−
)
2
+
(
−
)
2
}
=
1
]
(
2
5
)
W
h
er
e
1
,
2
,
an
d
3
ar
e
th
e
weig
h
i
n
g
f
ac
to
r
s
,
to
tal
n
u
m
b
er
o
f
b
u
s
es
an
d
th
e
v
alu
es
o
f
an
d
is
0
.
9
5
a
n
d
1
.
0
5
p
.
u.
4.
O
P
T
I
M
AL
P
L
ACE
M
E
NT
O
F
DST
AT
CO
M
T
h
e
r
ed
u
cti
o
n
o
f
o
v
e
r
all
n
etwo
r
k
lo
s
s
es
an
d
th
e
en
h
an
ce
m
e
n
t
o
f
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
'
s
o
v
er
all
v
o
ltag
e
p
r
o
f
ile
ar
e
g
o
als
b
eh
in
d
t
h
e
ca
lcu
latio
n
o
f
D
STAT
C
OM
's
o
p
tim
al
lo
ca
ti
o
n
.
Af
te
r
in
s
tallin
g
DSTA
T
C
OM
,
all
o
f
th
e
b
u
s
es'
v
o
ltag
es
s
h
o
u
ld
b
e
with
in
th
e
p
er
m
itted
d
ev
iatio
n
r
a
n
g
e
(
0
.
9
5
to
1
.
0
5
p
.
u
.
)
.
T
h
e
p
lace
m
en
t
o
f
DSTA
T
C
O
M
m
u
s
t
tak
e
in
to
ac
co
u
n
t
an
d
v
alid
ate
all
o
p
er
atio
n
al
an
d
s
y
s
tem
co
n
s
tr
ain
ts
.
T
h
e
ac
ce
p
tab
le
r
an
g
e
o
f
v
o
ltag
e
d
ev
iatio
n
an
d
o
v
e
r
all
s
y
s
tem
lo
s
s
es
d
eter
m
in
e
th
e
b
est
lo
ca
tio
n
f
o
r
DSTA
T
C
OM
.
C
o
n
s
eq
u
en
t
ly
,
th
e
o
b
jectiv
e
f
u
n
ctio
n
(
2
)
is
b
ein
g
f
o
r
m
u
lated
as
ex
p
r
ess
ed
m
ath
em
atica
lly
b
y
(
2
6
)
.
(
2
)
=
′
×
0
.
01
×
[
∑
{
(
−
)
2
+
(
−
)
2
}
=
1
]
(
2
6
)
W
h
er
e,
′
an
d
in
d
icate
th
e
lo
s
s
af
ter
an
d
b
ef
o
r
e
th
e
in
s
tallatio
n
o
f
DSTA
T
C
OM
.
T
h
e
o
p
tim
al
s
ize
o
f
DSTA
T
C
OM
an
d
DG
is
d
eter
m
i
n
ed
b
y
co
n
s
id
er
in
g
th
e
v
ar
iab
les
k
VAR
an
d
k
W
,
r
esp
ec
tiv
ely
.
T
h
e
ca
lcu
latio
n
o
f
th
e
o
p
tim
al
s
ize
f
o
cu
s
es
o
n
en
h
an
cin
g
th
e
o
v
er
all
v
o
ltag
e
p
r
o
f
ile,
m
in
im
izin
g
n
etwo
r
k
lo
s
s
es,
an
d
r
e
d
u
cin
g
en
e
r
g
y
co
s
ts
.
T
h
e
(
2
7
)
r
e
p
r
esen
ts
th
e
e
x
p
r
ess
io
n
u
s
ed
to
d
eter
m
in
e
th
e
o
p
tim
al
s
ize
o
f
DSTA
T
C
OM
.
=
∗
(
2
7
)
T
h
e
o
p
tim
u
m
s
ize
o
f
DG
(
P
DG
)
is
ex
p
r
ess
ed
b
y
(
2
8
)
.
3
=
×
×
8760
−
×
×
(
2
8
)
W
h
er
e,
3
,
,
,
,
an
d
r
ep
r
esen
ts
th
e
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
DG
an
d
DSTA
T
C
OM
s
ize,
co
s
t
o
f
th
e
en
er
g
y
(
I
NR
/k
W
h
)
,
p
o
wer
lo
s
s
r
ed
u
ctio
n
af
ter
th
e
in
s
tallatio
n
o
f
DG,
ca
p
ital
co
s
t
o
f
th
e
DG
(
p
er
k
W
)
,
an
d
an
n
u
al
r
ate
o
f
d
ep
r
ec
iatio
n
a
n
d
in
ter
est
ch
ar
g
es
r
esp
ec
tiv
ely
.
T
h
e
s
ize
o
f
th
e
DG
wil
l
b
e
o
p
tim
u
m
an
d
m
ax
im
u
m
w
h
en
th
e
f
u
n
ctio
n
F
3
will
h
av
e
th
e
m
a
x
im
u
m
v
alu
e.
T
h
e
(
2
8
)
an
d
(
2
5
)
is
u
s
ed
f
o
r
lo
ca
tio
n
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.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
8
2
6
-
841
832
f
in
aliza
tio
n
an
d
s
izin
g
r
esp
e
ctiv
ely
.
Vo
ltag
e
v
io
latio
n
s
er
v
es
as
th
e
p
r
im
ar
y
cr
iter
io
n
f
o
r
DSTA
T
C
OM
p
lace
m
en
t
an
d
s
izin
g
.
As
a
r
esu
lt,
DSTA
T
C
OM
wil
l
b
e
p
o
s
itio
n
ed
in
ac
co
r
d
an
ce
with
(
2
6
)
an
d
its
s
ize
will
b
e
d
eter
m
in
e
d
u
s
in
g
(
2
7
)
if
th
er
e
is
a
v
o
ltag
e
v
i
o
latio
n
in
th
e
n
etwo
r
k
.
5.
RE
SU
L
T
ANAL
YSI
S
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
allo
ca
tin
g
DGs
an
d
DSTA
T
C
OM
s
tech
n
iq
u
e
is
ev
alu
ated
b
y
co
n
d
u
ctin
g
test
s
o
n
two
co
m
m
o
n
ly
u
s
ed
d
is
tr
ib
u
tio
n
s
y
s
tem
s
:
a
3
3
-
b
u
s
s
y
s
tem
an
d
a
6
9
-
b
u
s
s
y
s
tem
.
T
o
v
alid
ate
th
e
m
eth
o
d
'
s
ef
f
icac
y
,
th
r
ee
d
is
tin
ct
s
ce
n
ar
io
s
ar
e
e
x
am
in
ed
.
I
n
th
e
f
ir
s
t
s
ce
n
ar
io
,
o
n
ly
o
n
e
DGs
an
d
D
-
STAT
C
OM
s
is
in
s
talled
.
I
n
th
e
s
ec
o
n
d
an
d
th
ir
d
s
ce
n
ar
io
s
,
two
an
d
th
r
ee
DGs
an
d
D
-
STAT
C
OM
s
ar
e
r
esp
ec
tiv
ely
co
n
s
id
er
ed
.
T
h
e
b
est
o
u
tco
m
e
f
r
o
m
te
n
s
ep
ar
ate
alg
o
r
ith
m
r
u
n
s
is
r
ep
o
r
te
d
f
o
r
ea
c
h
s
ce
n
ar
io
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
ex
ec
u
ted
o
n
a
n
AM
D
R
y
ze
n
9
7
9
5
0
X
C
PU
o
p
er
atin
g
at
5
.
7
0
GHz
with
3
2
GB
o
f
R
AM
u
s
in
g
th
e
MA
T
L
AB
en
v
ir
o
n
m
e
n
t.
5
.
1
.
3
3
bu
s
s
y
s
t
em
T
h
e
I
E
E
E
3
3
b
u
s
test
s
y
s
tem
h
as
a
co
m
b
in
ed
lo
ad
o
f
3
7
1
5
+
j
2
3
0
0
k
VA.
T
h
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
is
s
u
b
jecte
d
to
lo
ad
f
lo
w
an
al
y
s
is
with
an
d
with
o
u
t
th
e
p
r
e
s
en
ce
o
f
DSTA
T
C
OM
.
T
h
e
r
esu
lts
o
f
wh
ich
ar
e
p
r
esen
ted
in
T
a
b
le
s
1
an
d
2.
As
s
h
o
wn
in
T
ab
le
1
,
th
e
s
y
s
tem
ex
h
ib
its
p
o
o
r
p
e
r
f
o
r
m
an
c
e
with
a
s
in
g
le
DG
allo
ca
tio
n
in
9
th
n
o
d
e
,
c
h
ar
ac
t
er
ized
b
y
a
r
ea
l
p
o
wer
lo
s
s
o
f
1
1
7
.
6
4
k
W
,
r
ea
ctiv
e
p
o
wer
l
o
s
s
7
9
.
5
7
4
9
k
VAR,
s
tab
ilit
y
in
d
ex
o
f
0
.
7
7
8
p
.
u
.
with
a
lo
w
v
o
ltag
e
m
ag
n
itu
d
e
o
f
0
.
9
3
9
1
p
.
u
.
f
o
r
co
n
s
tan
t
p
o
wer
lo
a
d
m
o
d
el.
T
h
er
e
is
an
im
p
r
o
v
em
e
n
t
in
t
h
e
p
o
wer
lo
s
s
as
well
as
v
o
ltag
e
p
r
o
f
ile
wh
en
two
an
d
th
r
ee
n
u
m
b
er
s
o
f
DGs
ar
e
p
lace
d
,
in
all
ty
p
es o
f
lo
a
d
m
o
d
els.
T
ab
le
1
.
E
f
f
ec
t o
f
DG
allo
ca
ti
o
n
o
n
3
3
b
u
s
s
y
s
tem
DGs
Ty
p
e
o
f
l
o
a
d
Lo
c
a
t
i
o
n
S
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z
e
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n
k
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l
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n
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n
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r
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.
M
i
n
(
a
b
s(
V
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)
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.
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0
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4
7
9
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.
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f
f
ec
t o
f
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a
n
d
DS
T
AT
C
OM
allo
ca
tio
n
o
n
3
3
b
u
s
s
y
s
tem
DGs
S
TA
TC
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M
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.
4
6
2
6
,
6
0
1
.
7
1
8
3
7
4
.
5
6
7
1
5
7
.
5
3
1
2
0
.
9
6
4
1
0
.
9
9
0
9
1
1
CI
12
30
1
3
4
8
1
0
0
0
6
3
.
3
6
6
8
4
2
.
5
7
7
8
0
.
8
6
2
4
0
.
9
6
3
7
2
2
CI
3
1
,
13
8,
30
1
0
9
1
.
1
,
1
2
9
6
7
8
4
.
3
3
2
4
,
9
4
5
.
5
0
1
4
3
9
.
9
4
4
7
2
9
.
3
4
3
6
0
.
9
3
3
1
0
.
9
8
2
9
3
3
CI
2
5
,
2
9
,
14
3
0
,
7,
24
8
8
9
.
8
9
0
7
,
1
2
9
4
.
6
,
1
0
8
3
.
4
6
7
5
.
4
8
1
9
,
8
8
8
.
4
5
1
2
,
6
4
6
.
4
5
0
2
2
4
.
5
2
5
8
1
9
.
6
2
4
1
0
.
9
7
7
5
0
.
9
9
4
3
T
ab
le
2
s
h
o
ws,
with
th
e
in
clu
s
io
n
o
f
D
-
STAT
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OM
(
s
)
,
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er
e
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a
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ig
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if
ican
t
im
p
r
o
v
em
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i
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e
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ea
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o
wer
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s
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o
f
th
e
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y
s
tem
.
W
it
h
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n
e
D
-
STAT
C
OM
,
th
e
r
ea
l
p
o
wer
lo
s
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is
8
4
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3
9
1
5
k
W
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d
r
ea
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e
p
o
er
l
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s
s
is
5
6
.
2
2
1
k
VAR,
with
two
D
-
STAT
C
OM
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it
is
3
6
.
1
7
3
7
k
W
an
d
2
6
.
2
3
1
3
k
VAR
,
an
d
with
th
r
ee
D
-
STAT
C
OM
s
it
is
r
ed
u
ce
d
to
1
6
.
4
0
85
kW
an
d
1
3
.
0
9
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7
k
VAR
f
o
r
C
P
lo
a
d
m
o
d
el
.
B
ased
o
n
th
e
r
esu
lts
,
it
ca
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
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SS
N:
2252
-
8
7
9
2
Op
tima
l p
la
ce
men
t a
n
d
s
iz
in
g
o
f
DG
a
n
d
DS
TATC
OM in
o
r
d
er to
mitig
a
te
…
(
S
mru
tir
ek
h
a
Ma
h
a
n
t
a
)
833
b
e
s
aid
th
at
b
y
u
s
in
g
th
r
ee
DGs a
n
d
DSTA
T
C
OM
s
s
im
u
ltan
eo
u
s
ly
,
th
e
s
y
s
tem
p
er
f
o
r
m
s
b
etter
th
an
u
s
in
g
o
n
e
o
r
two
.
T
o
f
u
r
t
h
er
s
u
p
p
o
r
t
th
i
s
co
n
clu
s
io
n
,
Fig
u
r
es
2
(
a
)
-
2(
c
)
,
Fig
u
r
es
3
(
a
)
-
3(
c)
,
an
d
Fig
u
r
es
4
(
a
)
-
4(
c
)
d
is
p
lay
th
e
v
o
ltag
e
p
r
o
f
ile,
b
r
an
c
h
c
u
r
r
en
t
p
r
o
f
ile,
a
n
d
a
m
u
lti
o
b
jectiv
e
f
u
n
ctio
n
-
b
ased
p
o
we
r
lo
s
s
p
r
o
f
ile
f
o
r
a
v
ar
y
in
g
n
u
m
b
er
o
f
DGs
allo
c
atio
n
s
,
f
o
r
co
n
s
tan
t
p
o
wer
,
c
o
n
s
tan
t
cu
r
r
en
t
,
an
d
co
n
s
tan
t
i
m
p
ed
an
ce
lo
ad
t
y
p
es
r
esp
ec
tiv
ely
.
Fig
u
r
es
5
(
a
)
-
5(
c
)
,
Fig
u
r
es
6
(
a
)
-
6
(
c)
,
a
n
d
Fig
u
r
es
7
(
a
)
-
7
(
c)
d
is
p
lay
th
e
v
o
lt
ag
e
p
r
o
f
ile,
b
r
an
ch
cu
r
r
en
t
p
r
o
f
ile,
a
n
d
a
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
-
b
ased
p
o
wer
l
o
s
s
p
r
o
f
ile
f
o
r
all
th
e
ab
o
v
e
ty
p
es
o
f
lo
ad
m
o
d
els
f
o
r
s
im
u
ltan
eo
u
s
DGs a
n
d
DSTA
T
C
OM
s
p
lace
m
en
t.
Fig
u
r
e
2
p
r
esen
ts
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
with
co
n
s
tan
t
p
o
wer
(
C
P)
lo
ad
ty
p
e
u
n
d
er
d
if
f
er
en
t
d
is
tr
ib
u
ted
g
en
er
atio
n
(
DG)
s
ce
n
ar
io
s
.
Fig
u
r
e
2
(
a)
s
h
o
ws
th
e
v
o
ltag
e
p
r
o
f
i
le
ac
r
o
s
s
th
e
b
u
s
es,
wh
er
e
th
e
o
p
tim
al
DG
p
lac
em
en
t
s
ce
n
ar
io
s
ig
n
if
ican
tly
im
p
r
o
v
es
v
o
ltag
e
s
tab
ilit
y
b
y
m
ain
tain
i
n
g
b
u
s
v
o
ltag
es
clo
s
er
to
th
e
n
o
m
in
al
1
p
.
u
.
Fig
u
r
e
2
(
b
)
d
is
p
lay
s
th
e
b
r
an
ch
cu
r
r
e
n
t
p
r
o
f
iles
,
h
ig
h
lig
h
tin
g
a
r
e
d
u
ctio
n
in
cu
r
r
e
n
t
m
ag
n
itu
d
es
wh
e
n
DG
is
ap
p
r
o
p
r
iately
in
teg
r
ated
,
wh
ich
h
elp
s
in
r
eliev
in
g
s
tr
ess
o
n
d
is
tr
ib
u
tio
n
lin
es.
Fig
u
r
e
2
(
c)
illu
s
tr
ates
th
e
m
in
im
izatio
n
o
f
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
(
Mo
F)
u
n
d
e
r
th
e
o
p
tim
al
DG
co
n
f
ig
u
r
atio
n
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
at
u
n
d
e
r
C
P
lo
ad
co
n
d
itio
n
s
,
p
r
o
p
e
r
DG
p
la
ce
m
en
t
ef
f
ec
tiv
ely
en
h
an
ce
s
v
o
ltag
e
r
eg
u
latio
n
,
r
ed
u
ce
s
b
r
an
c
h
cu
r
r
en
t lo
ad
i
n
g
,
an
d
m
in
im
izes r
ea
l p
o
wer
lo
s
s
es,
co
n
tr
ib
u
tin
g
to
a
m
o
r
e
ef
f
icien
t a
n
d
r
eliab
le
o
p
er
atio
n
o
f
th
e
d
is
tr
ib
u
tio
n
n
et
wo
r
k
.
Fig
u
r
e
3
s
h
o
ws
wh
at
h
ap
p
e
n
e
d
wh
en
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
r
an
with
a
co
n
s
tan
t
c
u
r
r
en
t
(
C
C
)
lo
ad
ty
p
e
an
d
d
if
f
er
en
t
d
is
tr
ib
u
ted
g
en
er
atio
n
(
DG)
s
ce
n
ar
io
s
.
Fig
u
r
e
3
(
a
)
s
h
o
ws
th
e
v
o
ltag
e
p
r
o
f
ile
ac
r
o
s
s
th
e
b
u
s
es.
T
h
e
b
est
DG
p
lace
m
en
t
s
ce
n
ar
io
g
ets
b
etter
v
o
ltag
e
lev
els,
k
ee
p
in
g
v
alu
es
clo
s
er
to
1
p
.
u
.
th
a
n
o
th
er
s
etu
p
s
,
wh
ich
m
a
k
es
v
o
ltag
e
s
tab
ilit
y
b
etter
.
Fi
g
u
r
e
3
(
b
)
s
h
o
ws
th
e
b
r
a
n
ch
cu
r
r
en
t
p
r
o
f
ile
s
,
wh
ich
s
h
o
w
th
at
th
e
b
est
way
to
in
teg
r
ate
DG
lead
s
to
a
b
ig
d
r
o
p
in
cu
r
r
e
n
t
m
ag
n
itu
d
es
ac
r
o
s
s
s
ev
er
al
b
r
an
ch
es.
T
h
is
h
elp
s
with
b
etter
lo
ad
d
is
tr
ib
u
tio
n
a
n
d
less
lin
e
lo
ad
in
g
.
W
h
en
DG
is
p
u
t
in
th
e
b
est
p
lace
,
Fig
u
r
e
3
(
c
)
s
h
o
ws
h
o
w
to
m
in
im
ize
th
e
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
(
Mo
F).
T
h
ese
r
esu
lts
all
s
h
o
w
th
at
s
tr
ateg
icall
y
p
lacin
g
DG
u
n
d
er
C
C
lo
ad
co
n
d
itio
n
s
g
r
ea
tly
i
m
p
r
o
v
es
v
o
ltag
e
r
eg
u
latio
n
,
lo
wer
s
cu
r
r
en
t
f
lo
w
in
th
e
n
et
wo
r
k
,
an
d
m
a
k
es
th
e
wh
o
le
s
y
s
tem
m
o
r
e
ef
f
icien
t
.
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
R
esu
lts
f
o
r
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
with
C
P lo
ad
ty
p
e
u
n
d
er
v
ar
y
in
g
D
G
s
ce
n
ar
i
o
s
:
(
a)
v
o
ltag
e
p
r
o
f
ile
,
(
b
)
b
r
a
n
ch
cu
r
r
en
t
p
r
o
f
ile
,
a
n
d
(
c
)
p
o
wer
lo
s
s
p
lo
t
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
R
esu
lts
f
o
r
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
with
C
C
lo
ad
ty
p
e
u
n
d
er
v
ar
y
in
g
D
G
s
ce
n
ar
i
o
s
:
(
a)
v
o
ltag
e
p
r
o
f
ile
,
(
b
)
b
r
a
n
ch
cu
r
r
en
t
p
r
o
f
ile
,
a
n
d
(
c
)
p
o
wer
lo
s
s
p
lo
t
Fig
u
r
e
4
s
h
o
ws
th
e
s
im
u
latio
n
r
esu
lts
f
o
r
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
with
a
co
n
s
tan
t
im
p
e
d
an
ce
(
C
I
)
lo
ad
ty
p
e
in
d
if
f
er
en
t
d
is
tr
ib
u
ted
g
e
n
er
atio
n
(
DG)
s
ce
n
ar
i
o
s
.
Fig
u
r
e
4
(
a)
s
h
o
ws
th
e
v
o
ltag
e
p
r
o
f
iles
.
T
h
e
in
teg
r
atio
n
o
f
DG
u
n
its
,
esp
e
cially
wh
en
t
h
ey
ar
e
p
lace
d
i
n
th
e
b
est
way
,
r
aises
v
o
ltag
e
lev
els
ac
r
o
s
s
th
e
b
u
s
es
s
ig
n
if
ican
tly
,
k
ee
p
in
g
t
h
em
clo
s
er
to
th
e
n
o
m
in
al
1
p
.
u
.
Fig
u
r
e
4
(
b
)
s
h
o
ws
th
e
b
r
an
ch
cu
r
r
e
n
t
p
r
o
f
iles
,
wh
ich
s
h
o
w
th
at
ad
d
in
g
DG
lo
wer
s
th
e
cu
r
r
en
t
in
s
ev
er
al
b
r
an
ch
es.
T
h
is
lo
wer
s
th
e
s
tr
ess
o
n
th
e
n
etwo
r
k
an
d
im
p
r
o
v
es
th
e
f
lo
w
o
f
c
u
r
r
en
t.
F
ig
u
r
e
4
(
c
)
s
h
o
ws
h
o
w
th
e
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
(
Mo
F)
is
m
in
im
ized
,
w
h
ich
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.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
8
2
6
-
841
834
s
h
o
ws
h
o
w
well
DG
wo
r
k
s
to
m
ak
e
th
e
s
y
s
tem
m
o
r
e
ef
f
icien
t.
Ov
er
all,
th
e
r
esu
lts
s
h
o
w
th
at
p
u
ttin
g
DG
in
th
e
r
ig
h
t
p
lace
u
n
d
er
C
I
lo
a
d
co
n
d
itio
n
s
im
p
r
o
v
es
v
o
ltag
e
r
eg
u
latio
n
,
lo
we
r
s
b
r
an
c
h
cu
r
r
en
ts
,
an
d
cu
ts
d
o
wn
o
n
p
o
we
r
lo
s
s
es in
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
Fig
u
r
e
5
s
h
o
ws
th
e
r
esu
lts
f
o
r
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
wi
th
a
co
n
s
tan
t
p
o
wer
(
C
P)
lo
a
d
ty
p
e
i
n
d
if
f
er
en
t
DG
-
STAT
C
OM
s
itu
atio
n
s
.
Fig
u
r
e
5
(
a)
s
h
o
ws
th
e
v
o
ltag
e
lev
els
ac
r
o
s
s
th
e
b
u
s
e
s
.
I
t
s
h
o
ws
th
at
th
e
DGStat3
-
C
P
s
e
tu
p
g
iv
es
th
e
h
ig
h
est
an
d
m
o
s
t
s
tab
le
v
o
lta
g
e
lev
els,
k
ee
p
in
g
th
e
m
clo
s
e
to
th
e
n
o
m
i
n
al
1
p
.
u
.
lev
el
co
m
p
ar
ed
to
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C
P
an
d
DGStat2
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C
P.
F
ig
u
r
e
5
(
b
)
s
h
o
ws
th
e
b
r
an
ch
cu
r
r
en
t
p
r
o
f
iles
.
Un
d
er
th
e
DGStat3
-
C
P
s
ce
n
ar
io
,
th
e
cu
r
r
en
t
m
a
g
n
itu
d
es
d
r
o
p
s
ig
n
if
ican
tly
,
wh
ich
m
ea
n
s
th
at
th
e
lo
ad
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b
etter
d
is
tr
ib
u
ted
an
d
th
e
lin
es a
r
e
le
s
s
cr
o
wd
ed
.
F
ig
u
r
e
5
(
c
)
s
h
o
ws h
o
w
to
m
ak
e
th
e
m
u
lti
-
o
b
ject
iv
e
f
u
n
ctio
n
(
Mo
F)
as
s
m
all
as
p
o
s
s
ib
le.
T
h
ese
r
esu
lts
s
h
o
w
th
at
th
e
b
est
way
to
co
o
r
d
in
ate
DG
an
d
STAT
C
OM
u
n
d
er
C
P
lo
ad
co
n
d
itio
n
s
g
r
ea
tly
im
p
r
o
v
es
v
o
ltag
e
s
tab
ilit
y
,
r
ed
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ce
s
cu
r
r
e
n
t
f
lo
w,
an
d
lo
wer
s
o
v
e
r
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y
s
tem
lo
s
s
es.
T
h
is
m
ak
es th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
wo
r
k
m
o
r
e
e
f
f
icien
tly
.
Fig
u
r
e
6
s
h
o
ws
th
e
r
esu
lts
o
f
th
e
s
im
u
latio
n
f
o
r
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
with
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co
n
s
ta
n
t
cu
r
r
en
t
(
C
C
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lo
ad
ty
p
e
in
d
if
f
e
r
en
t
s
ce
n
ar
io
s
f
o
r
d
ep
lo
y
i
n
g
DG
-
S
T
AT
C
OM
.
Fig
u
r
e
6
(
a)
s
h
o
ws
th
e
v
o
ltag
e
p
r
o
f
ile
ac
r
o
s
s
th
e
b
u
s
es.
T
h
e
DGStat3
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C
C
co
n
f
ig
u
r
atio
n
d
o
es
th
e
b
est
jo
b
o
f
k
ee
p
in
g
v
o
ltag
es
clo
s
e
to
1
p
.
u
.
,
wh
ile
th
e
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-
C
C
an
d
DGStat
2
-
C
C
co
n
f
ig
u
r
atio
n
s
d
o
n
o
t.
F
ig
u
r
e
6
(
b
)
s
h
o
ws
th
e
b
r
an
c
h
cu
r
r
en
t
p
r
o
f
iles
,
wh
ich
s
h
o
w
th
at
th
e
DGStat3
-
C
C
s
ce
n
ar
io
ca
u
s
es th
e
cu
r
r
en
t to
b
e
lo
wer
in
s
ev
e
r
al
b
r
an
c
h
es.
T
h
is
m
ea
n
s
th
at
lo
ad
b
alan
cin
g
is
b
etter
an
d
li
n
e
co
n
g
esti
o
n
is
lo
wer
.
F
ig
u
r
e
6
(
c)
s
h
o
ws
h
o
w
to
m
in
im
ize
th
e
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
(
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F),
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ich
s
h
o
ws
th
e
ad
v
a
n
tag
es
o
f
p
laci
n
g
DG
an
d
STAT
C
OM
in
th
e
b
est
p
lace
s
.
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e
r
all,
th
e
r
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lts
s
h
o
w
th
at
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u
ttin
g
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th
e
r
ig
h
t
p
lace
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er
g
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ea
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im
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ilit
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s
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r
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ch
c
u
r
r
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n
t,
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t
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o
n
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o
wer
l
o
s
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es in
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e
d
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ib
u
tio
n
s
y
s
tem
wh
en
th
e
r
e
is
a
C
C
lo
ad
.
Fig
u
r
e
7
d
is
p
lay
s
th
e
p
er
f
o
r
m
an
ce
r
esu
lts
o
f
th
e
I
E
E
E
-
3
3
b
u
s
s
y
s
tem
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th
a
co
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s
tan
t im
p
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ce
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I
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ad
ty
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e
u
n
d
e
r
v
ar
i
o
u
s
DG
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STAT
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OM
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ce
n
ar
io
s
.
F
ig
u
r
e
7
(
a)
s
h
o
ws
th
e
v
o
ltag
e
p
r
o
f
ile
ac
r
o
s
s
th
e
b
u
s
es,
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er
e
th
e
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I
co
n
f
i
g
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r
atio
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r
o
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id
es
th
e
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o
s
t
im
p
r
o
v
e
d
an
d
s
tab
le
v
o
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e
lev
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in
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icatin
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ef
f
ec
tiv
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o
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e
r
eg
u
latio
n
d
u
e
to
o
p
tim
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o
r
d
i
n
atio
n
o
f
DG
an
d
STAT
C
OM
.
F
ig
u
r
e
7
(
b
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p
r
esen
ts
th
e
b
r
an
ch
c
u
r
r
en
t
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r
o
f
iles
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em
o
n
s
tr
atin
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th
at
th
e
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I
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io
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u
r
r
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ag
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ig
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r
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7
(
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illu
s
tr
ates
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m
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o
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m
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ti
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u
n
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e
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at
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ateg
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Fig
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r
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R
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o
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3
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.
3
,
8
7
0
.
7
7
3
7
7
6
7
5
.
8
0
4
6
3
7
.
1
0
5
2
0
.
9
4
7
3
0
.
9
8
6
6
1
CI
61
1
5
0
0
7
8
.
6
4
7
3
3
8
.
9
5
3
7
0
.
8
7
7
5
0
.
9
6
7
9
2
CI
1
5
,
61
6
4
6
.
2
7
8
1
,
1
4
9
2
6
8
.
1
4
6
5
3
4
.
2
9
6
6
0
.
8
8
9
2
0
.
9
7
1
1
3
CI
1
7
,
6
0
,
61
6
7
4
.
0
8
6
3
,
7
0
4
.
2
5
7
9
,
1
2
3
5
.
2
7
0
.
0
6
1
3
3
4
.
8
2
0
3
0
.
9
3
5
7
0
.
9
8
3
5
I
n
T
ab
le
4
,
we
ca
n
s
ee
th
at
,
with
th
e
in
clu
s
io
n
o
f
D
-
STAT
C
OM
(
s
)
,
ag
ain
th
er
e
is
a
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
in
th
e
s
y
s
tem
p
ar
am
eter
s
.
Fo
r
c
o
n
s
tan
t
p
o
wer
lo
ad
m
o
d
el,
w
ith
o
n
e
D
-
ST
AT
C
OM
,
th
e
r
ea
l
p
o
wer
lo
s
s
is
3
0
.
8
1
5
2
k
W
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
is
1
8
.
4
2
1
9
k
VAR,
with
two
D
-
STAT
C
OM
s
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
ar
e
3
0
.
3
0
3
7
kW
an
d
1
6
.
8
0
5
1
k
VAR
,
an
d
with
th
r
ee
D
-
STAT
C
OM
s
it
is
5
6
.
8
8
kW
an
d
2
7
.
0
4
6
7
k
VAR,
r
esp
ec
tiv
ely
.
B
ased
o
n
th
e
r
esu
lts
s
h
o
wn
,
it
ca
n
b
e
s
aid
th
at
b
y
allo
ca
t
in
g
two
DGs
a
n
d
two
DSTA
T
C
OM
s
s
im
u
ltan
eo
u
s
ly
,
th
e
s
y
s
tem
p
er
f
o
r
m
s
b
ett
er
th
an
u
s
in
g
o
n
e
o
r
th
r
ee
.
Fig
u
r
es
8
(
a
)
-
8(
c
)
,
Fig
u
r
es
9
(
a
)
-
9(
c)
,
an
d
Fig
u
r
e
s
1
0
(
a
)
-
10
(
c)
d
is
p
lay
th
e
v
o
lt
ag
e
p
r
o
f
ile,
b
r
an
c
h
cu
r
r
en
t
p
r
o
f
ile,
an
d
a
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
-
b
ased
p
o
w
er
lo
s
s
p
r
o
f
ile
f
o
r
v
a
r
y
in
g
n
u
m
b
er
s
o
f
DGs
allo
ca
tio
n
s
f
o
r
co
n
s
tan
t
p
o
wer
,
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