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.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
,
p
p
.
2
6
2
~
2
7
0
I
SS
N:
2252
-
8
7
9
2
,
DOI
: 1
0
.
1
1
5
9
1
/ijap
e.
v
1
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.
i
3
.
p
p
2
6
2
-
270
262
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
p
e.
ia
esco
r
e.
co
m
A new
method
t
o
inco
rpo
ra
te
th
ree
-
pha
se po
wer
t
ra
nsfo
rmer
mo
del int
o
dis
trib
ution sy
stem lo
a
d
f
lo
w
a
na
ly
sis
Rudy
G
ia
nto
,
P
urwo
ha
rj
o
no
De
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
Un
i
v
e
rsitas
Tan
ju
n
g
p
u
ra
,
In
d
o
n
e
sia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
21
,
2
0
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ev
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r
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2
0
21
Acc
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ted
Ma
y
27
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2
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Th
is
p
a
p
e
r
p
ro
p
o
se
s
a
n
e
w
a
n
d
sim
p
le
m
e
th
o
d
to
in
c
o
r
p
o
ra
te
t
h
re
e
-
p
h
a
se
p
o
we
r
tran
sf
o
rm
e
r
m
o
d
e
l
in
t
o
d
is
tri
b
u
t
io
n
sy
ste
m
l
o
a
d
flo
w
(DSL
F
)
a
n
a
ly
sis.
Th
e
o
b
jec
ti
v
e
o
f
t
h
e
p
re
se
n
t
w
o
r
k
is
t
o
fi
n
d
a
ro
b
u
st
a
n
d
e
fficie
n
t
tec
h
n
i
q
u
e
fo
r
m
o
d
e
li
n
g
a
n
d
i
n
teg
ra
ti
n
g
p
o
we
r
tran
sfo
rm
e
r
in
th
e
DSL
F
a
n
a
ly
sis.
Th
e
p
ro
p
o
se
d
tra
n
sfo
rm
e
r
m
o
d
e
l
is d
e
riv
e
d
b
a
se
d
o
n
n
o
d
a
l
a
d
m
it
tan
c
e
m
a
tri
x
a
n
d
fo
rm
u
late
d
b
y
u
sin
g
t
h
e
sy
m
m
e
tri
c
a
l
c
o
m
p
o
n
e
n
t
t
h
e
o
ry
.
L
o
a
d
fl
o
w
fo
rm
u
latio
n
i
n
term
s
o
f
b
ra
n
c
h
c
u
rre
n
ts
a
n
d
n
o
d
a
l
v
o
lt
a
g
e
s
is
a
lso
p
r
o
p
o
se
d
in
t
h
is
p
a
p
e
r
to
e
n
a
b
le
in
teg
ra
ti
n
g
t
h
e
m
o
d
e
l
i
n
to
t
h
e
DSL
F
a
n
a
ly
sis.
S
in
g
u
larit
y
th
a
t
m
a
k
e
s
th
e
c
a
lcu
latio
n
s
in
f
o
rwa
rd
/
b
a
c
k
wa
rd
sw
e
e
p
(F
BS
)
a
lg
o
rit
h
m
is
d
iffi
c
u
lt
to
b
e
c
a
rrie
d
o
u
t
.
It
c
a
n
b
e
a
v
o
id
e
d
i
n
t
h
e
m
e
th
o
d
.
T
h
e
p
ro
p
o
se
d
m
o
d
e
l
is
v
e
rifi
e
d
b
y
u
si
n
g
t
h
e
sta
n
d
a
rd
IEE
E
tes
t
sy
ste
m
.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
tio
n
s
y
s
tem
F
o
r
war
d
/b
ac
k
war
d
s
wee
p
L
o
ad
f
lo
w
a
n
aly
s
is
S
y
m
m
etr
ical
co
m
p
o
n
en
t th
e
o
r
y
T
h
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
e
r
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
:
R
u
d
y
Gian
to
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
Un
iv
er
s
itas
T
an
ju
n
g
p
u
r
a
Pro
f
.
Dr
.
H.
Had
ar
i N
awa
wi
St.,
Po
n
tian
ak
7
8
1
2
4
,
I
n
d
o
n
esia
E
m
ail: r
u
d
y
g
ian
to
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
r
ee
-
p
h
ase
p
o
wer
tr
an
s
f
o
r
m
er
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
ta
n
t
co
m
p
o
n
e
n
ts
in
m
o
d
er
n
ele
ctr
ic
p
o
wer
s
y
s
tem
.
T
h
e
im
p
o
r
tan
t
o
f
th
i
s
d
ev
ice
co
u
ld
p
r
o
b
ab
ly
b
e
r
an
k
ed
with
th
e
s
y
n
c
h
r
o
n
o
u
s
m
ac
h
in
e
an
d
th
e
tr
an
s
m
is
s
io
n
lin
e.
Gen
e
r
ato
r
tr
an
s
f
o
r
m
er
,
o
n
e
o
f
th
e
ess
en
tia
l
ty
p
es
o
f
p
o
wer
tr
an
s
f
o
r
m
er
,
h
as
th
e
f
u
n
ctio
n
o
f
tr
an
s
f
o
r
m
in
g
s
y
s
tem
v
o
ltag
e
f
r
o
m
g
en
e
r
atio
n
lev
el
to
tr
an
s
m
is
s
io
n
o
r
s
u
b
-
tr
a
n
s
m
is
s
i
o
n
lev
el.
A
n
o
th
er
im
p
o
r
tan
t
ty
p
e
o
f
p
o
wer
tr
an
s
f
o
r
m
er
is
d
is
tr
ib
u
tio
n
s
u
b
s
tatio
n
tr
an
s
f
o
r
m
er
.
T
h
is
d
ev
ice
is
u
s
u
ally
lo
ca
ted
at
lo
ad
ce
n
ter
a
n
d
em
p
lo
y
ed
t
o
tr
an
s
f
o
r
m
th
e
s
y
s
tem
v
o
ltag
e
f
r
o
m
tr
an
s
m
is
s
io
n
lev
el
to
d
is
tr
i
b
u
tio
n
f
ee
d
er
lev
el.
Dis
tr
ib
u
tio
n
tr
an
s
f
o
r
m
e
r
is
th
e
n
u
s
ed
to
p
r
o
v
i
d
e
th
e
f
i
n
al
v
o
lt
ag
e
tr
an
s
f
o
r
m
atio
n
to
t
h
e
cu
s
to
m
er
’
s
lo
ad
.
Dis
tr
ib
u
tio
n
s
y
s
tem
lo
ad
f
lo
w
(
DSLF
)
an
aly
s
is
is
ca
r
r
ie
d
o
u
t
to
in
v
esti
g
ate
th
e
s
tead
y
s
tate
p
er
f
o
r
m
an
ce
s
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
E
lectr
ical
q
u
an
titi
es
s
u
ch
as
n
o
d
al
v
o
ltag
es,
s
u
b
s
tatio
n
p
o
we
r
s
,
d
is
tr
ib
u
tio
n
p
o
we
r
f
lo
ws
an
d
l
o
s
s
es
ca
n
b
e
o
b
tain
ed
b
ased
o
n
th
e
an
aly
s
is
.
DSLF
tech
n
iq
u
es
c
an
b
e
class
if
ied
in
to
two
b
r
o
ad
ca
teg
o
r
ies,
n
a
m
ely
n
o
d
e
-
b
ased
tech
n
iq
u
es
(
i.e
.
New
to
n
-
R
ap
h
s
o
n
-
b
ased
m
eth
o
d
s
)
an
d
b
r
a
n
ch
-
b
ased
tech
n
iq
u
es
(
i.e
.
b
ac
k
war
d
/
f
o
r
war
d
s
weep
in
g
(
FB
S
)
-
b
ased
m
eth
o
d
s
)
.
I
n
New
to
n
-
R
ap
h
s
o
n
-
b
ased
alg
o
r
ith
m
s
[
1
]
-
[
8
]
,
iter
ativ
e
te
ch
n
iq
u
e
s
ar
e
n
o
r
m
all
y
u
s
ed
t
o
o
b
tain
t
h
e
s
o
lu
tio
n
.
T
h
e
alg
o
r
ith
m
will
u
s
u
ally
s
tar
t
with
th
e
i
n
itial
esti
m
atio
n
f
o
r
t
h
e
s
o
lu
tio
n
.
T
h
is
in
itial
esti
m
atio
n
is
th
en
u
p
d
ated
u
n
t
il
th
e
s
o
lu
tio
n
with
d
esire
d
ac
cu
r
ac
y
is
o
b
tain
ed
.
B
ac
k
war
d
/
f
o
r
war
d
s
weep
in
g
-
b
ased
m
eth
o
d
s
a
r
e
s
p
esifica
lly
d
esig
n
ed
to
f
in
d
th
e
s
o
lu
tio
n
o
f
DSLF
p
r
o
b
le
m
s
[
9
]
-
[
1
3
]
.
I
n
s
ea
r
ch
in
g
f
o
r
th
e
s
o
lu
tio
n
,
th
ese
m
eth
o
d
s
ex
p
lo
it
th
e
r
ad
ial
s
tr
u
ctu
r
e
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
Ho
wev
er
,
f
o
r
war
d
/b
ac
k
war
d
s
wee
p
in
g
m
eth
o
d
r
eq
u
ir
es
s
p
ec
ial
tech
n
iq
u
es f
o
r
b
r
a
n
ch
n
u
m
b
e
r
in
g
an
d
b
u
s
o
r
d
er
in
g
o
f
th
e
d
is
t
r
ib
u
tio
n
s
y
s
tem
.
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
A
n
ew me
th
o
d
to
i
n
co
r
p
o
r
a
te
t
h
r
ee
-
p
h
a
s
e
p
o
w
er tr
a
n
s
fo
r
me
r
mo
d
el
in
to
d
is
tr
ib
u
tio
n
…
(
R
u
d
y
Gia
n
to
)
263
T
o
p
r
o
p
er
ly
co
n
d
u
ct
th
e
lo
a
d
f
lo
w
an
al
y
s
is
,
s
tead
y
s
tate
m
o
d
elin
g
o
f
th
e
d
is
tr
ib
u
ti
o
n
s
y
s
tem
co
m
p
o
n
en
ts
(
in
clu
d
in
g
th
e
p
o
wer
tr
an
s
f
o
r
m
er
)
is
n
ec
ess
ar
y
.
Sev
er
al
m
eth
o
d
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
m
o
d
el
an
d
i
n
co
r
p
o
r
ate
th
r
ee
-
p
h
ase
p
o
wer
tr
an
s
f
o
r
m
er
in
to
lo
a
d
f
lo
w
an
aly
s
is
[
1
4]
-
[
2
9
]
.
I
n
[
1
4
]
-
[
24
]
,
tr
an
s
f
o
r
m
e
r
m
o
d
el
b
ased
o
n
n
o
d
al
a
d
m
itt
an
ce
m
atr
ices
h
as
b
ee
n
im
p
le
m
en
ted
to
lo
ad
f
lo
w
s
o
lu
tio
n
m
eth
o
d
s
.
Ho
we
v
er
,
f
o
r
s
o
m
e
tr
a
n
s
f
o
r
m
e
r
co
n
n
ec
t
io
n
ty
p
es,
s
o
lu
tio
n
to
th
e
lo
a
d
f
lo
w
p
r
o
b
lem
h
as
b
ee
n
f
o
u
n
d
to
b
e
d
if
f
icu
lt
to
o
b
tain
.
T
h
is
d
if
f
icu
lt
y
is
m
a
in
ly
ca
u
s
ed
b
y
th
e
m
atr
ix
s
in
g
u
lar
ity
w
h
ich
a
p
p
ea
r
s
o
n
s
o
m
e
tr
an
s
f
o
r
m
er
co
n
n
ec
tio
n
ty
p
es.
I
n
[
2
5
]
-
[
28
]
,
a
t
h
r
ee
-
p
h
ase
p
o
wer
tr
an
s
f
o
r
m
er
m
o
d
el
s
u
itab
l
e
f
o
r
lo
ad
f
lo
w
an
aly
s
is
is
p
r
esen
ted
.
T
h
e
m
o
d
el
h
as
b
ee
n
d
er
i
v
ed
b
ased
o
n
s
eq
u
en
ce
c
o
m
p
o
n
en
ts
.
Ho
wev
er
,
it
h
as
b
ee
n
wid
ely
ac
k
n
o
wled
g
ed
th
at
class
ical
s
eq
u
en
ce
co
m
p
o
n
en
t
s
r
ep
r
esen
tatio
n
lack
s
th
e
ef
f
icien
cy
to
m
o
d
e
l
t
h
e
tr
a
n
s
f
o
r
m
er
p
r
o
p
e
r
ly
s
in
c
e
d
if
f
er
en
t
alg
o
r
ith
m
s
h
a
v
e
to
b
e
u
s
ed
f
o
r
d
if
f
er
en
t
tr
an
s
f
o
r
m
e
r
co
n
n
ec
tio
n
s
.
Mo
r
e
v
e
r
,
in
t
h
e
m
o
d
el
p
r
o
p
o
s
ed
in
[
25]
-
[
2
8
]
,
s
o
m
e
co
m
p
licated
t
r
ea
tm
en
ts
ar
e
n
ee
d
e
d
to
o
v
er
c
o
m
e
th
e
s
in
g
u
lar
ity
p
r
o
b
lem
t
h
at
ap
p
ea
r
s
o
n
s
o
m
e
tr
an
s
f
o
r
m
er
c
o
n
n
ec
tio
n
ty
p
es.
I
n
[
29
]
,
Kir
c
h
h
o
f
f
’
s
v
o
lta
g
e
an
d
cu
r
r
en
t
laws
ar
e
u
s
ed
f
o
r
ea
ch
tr
an
s
f
o
r
m
er
co
n
n
ec
tio
n
f
o
r
r
a
d
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
r
ad
ial
lo
ad
f
lo
w
a
n
aly
s
is
.
T
h
is
tech
n
iq
u
e
r
eq
u
ir
es
a
s
et
o
f
s
ep
ar
ate
eq
u
atio
n
s
f
o
r
ea
ch
tr
an
s
f
o
r
m
er
co
n
n
e
ctio
n
to
b
e
im
p
le
m
en
ted
in
s
id
e
th
e
lo
ad
f
lo
w
s
o
lu
tio
n
p
r
o
ce
s
s
.
T
h
er
ef
o
r
e,
ag
ain
s
t
th
e
ab
o
v
e
b
ac
k
g
r
o
u
n
d
,
th
e
o
b
jectiv
e
o
f
th
e
p
ap
er
is
to
f
in
d
a
r
o
b
u
s
t
an
d
ef
f
icien
t
tech
n
iq
u
e
f
o
r
in
clu
d
in
g
t
h
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
m
o
d
el
in
DSLF
an
aly
s
is
.
I
n
th
e
p
r
esen
t
wo
r
k
,
th
r
ee
-
p
h
ase
p
o
wer
tr
an
s
f
o
r
m
er
m
o
d
el
b
ased
o
n
n
o
d
al
ad
m
ittan
ce
m
atr
ix
f
o
r
v
ar
io
u
s
tr
a
n
s
f
o
r
m
er
co
n
n
ec
ti
o
n
ty
p
es
ar
e
p
r
esen
ted
.
First,
tr
an
s
f
o
r
m
er
m
o
d
el
b
ased
o
n
n
o
d
al
a
d
m
ittan
ce
m
atr
ix
in
ter
m
s
o
f
s
eq
u
en
ce
co
m
p
o
n
en
ts
is
d
e
v
elo
p
e
d
.
Usi
n
g
th
e
s
y
m
m
etr
ical
c
o
m
p
o
n
en
t
th
eo
r
y
,
th
e
s
eq
u
en
ce
co
m
p
o
n
e
n
ts
m
o
d
el
is
th
en
co
n
v
e
r
ted
in
to
its
eq
u
iv
alen
t
p
h
ase
co
m
p
o
n
en
ts
m
o
d
el.
T
o
en
ab
le
in
co
r
p
o
r
atin
g
th
e
m
o
d
el
in
to
DSLF
an
aly
s
is
,
th
e
lo
ad
f
lo
w
f
o
r
m
u
latio
n
in
ter
m
s
o
f
b
r
an
c
h
cu
r
r
en
ts
an
d
n
o
d
al
v
o
ltag
es
is
also
p
r
o
p
o
s
ed
in
th
e
p
r
esen
t
p
ap
er
.
I
n
th
e
f
o
r
m
u
latio
n
,
s
ets
o
f
n
o
n
lin
ea
r
e
q
u
a
tio
n
s
ar
e
d
er
iv
ed
b
y
ex
am
in
in
g
th
e
c
o
n
d
itio
n
s
(
i.e
.
elec
tr
ical
q
u
a
n
titi
es
r
elatio
n
s
h
ip
s
)
at
ev
e
r
y
n
o
d
e
an
d
b
r
an
c
h
in
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
T
h
e
co
m
p
lete
s
et
o
f
n
o
n
lin
ea
r
e
q
u
atio
n
s
is
th
e
n
s
o
lv
ed
to
o
b
tain
th
e
s
o
lu
tio
n
to
t
h
e
lo
a
d
f
lo
w
p
r
o
b
lem
.
I
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
th
e
s
in
g
u
lar
ity
t
h
at
m
ak
es
th
e
ca
lc
u
latio
n
s
in
FB
S
alg
o
r
ith
m
d
if
f
icu
lt
to
b
e
ca
r
r
ied
o
u
t
ca
n
b
e
a
v
o
id
e
d
.
As
a
r
esu
lt,
co
m
p
licated
v
o
l
tag
e
u
p
d
atin
g
p
r
o
ce
d
u
r
es
as
in
th
e
FB
S
-
b
ased
m
eth
o
d
,
ar
e
n
o
t
r
eq
u
ir
e
d
.
Mo
r
eo
v
er
,
th
e
m
eth
o
d
p
r
o
p
o
s
ed
in
th
e
p
r
esen
t
p
ap
er
u
s
es
o
n
ly
o
n
e
alg
o
r
ith
m
f
o
r
d
if
f
er
en
t tr
an
s
f
o
r
m
er
c
o
n
n
ec
ti
o
n
s
(
i.e
.
th
e
s
am
e
alg
o
r
ith
m
ca
n
b
e
ap
p
lied
to
all
tr
an
s
f
o
r
m
er
co
n
n
ec
tio
n
ty
p
es).
T
h
er
ef
o
r
e,
it is
m
o
r
e
ef
f
icie
n
t in
ter
m
s
o
f
v
ar
i
o
u
s
t
r
an
s
f
o
r
m
e
r
co
n
n
ec
tio
n
im
p
lem
e
n
tatio
n
s
.
Ver
if
icatio
n
o
f
th
e
m
eth
o
d
u
s
in
g
s
tan
d
ar
d
I
E
E
E
t
est s
y
s
tem
is
al
s
o
p
r
esen
ted
in
th
e
p
r
esen
t p
a
p
er
.
2.
TH
RE
E
-
P
H
ASE
T
RAN
SFO
RM
E
R
M
O
D
E
L
I
NG
2
.
1
.
T
ra
ns
f
o
rm
er
mo
del in s
equence
co
m
po
nents
T
h
is
s
ec
tio
n
d
is
cu
s
s
e
s
th
e
p
r
o
p
o
s
ed
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
e
r
m
o
d
el
to
b
e
in
teg
r
ated
in
to
d
is
tr
ib
u
tio
n
s
y
s
tem
lo
ad
f
lo
w
a
n
aly
s
is
.
T
h
e
m
o
d
el
is
f
ir
s
t
r
ep
r
esen
ted
in
ter
m
s
o
f
s
eq
u
en
ce
co
m
p
o
n
en
ts
.
T
h
en
,
in
Sectio
n
2
.
2
,
it is
r
ep
r
esen
ted
in
ter
m
s
o
f
p
h
ase
co
m
p
o
n
en
ts
b
y
u
s
in
g
s
y
m
m
etr
ical
co
m
p
o
n
en
t th
e
o
r
y
.
Fig
u
r
e
1
s
h
o
ws a
s
ch
em
atic
d
iag
r
am
o
f
a
th
r
e
e
-
p
h
ase
tr
an
s
f
o
r
m
er
.
I
t
ca
n
b
e
s
h
o
wn
th
at
th
e
m
ath
em
at
ical
m
o
d
el
o
f
t
h
e
tr
an
s
f
o
r
m
er
i
n
Fig
u
r
e
1
is
g
iv
e
n
b
y
(
1
)
.
=
0
1
2
S
0
1
2
P
0
1
2
SS
0
1
2
SP
0
1
2
PS
0
1
2
PP
0
1
2
S
0
1
2
P
V
V
Y
Y
Y
Y
I
I
(
1
)
wh
er
e:
012
S
012
P
I
I
an
d
: tr
an
s
f
o
r
m
er
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
s
eq
u
en
ce
cu
r
r
e
n
ts
0
1
2
S
0
1
2
P
V
V
an
d
: tr
an
s
f
o
r
m
er
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
s
eq
u
en
ce
v
o
ltag
es
012
SS
012
SP
012
PS
012
PP
,
,
,
Y
Y
Y
Y
an
d
: tr
an
s
f
o
r
m
er
s
u
b
-
m
atr
ices
I
t
is
to
b
e
n
o
ted
t
h
at
ea
ch
o
f
tr
an
s
f
o
r
m
er
s
u
b
-
m
atr
ices
in
(
1
)
is
o
f
3
×3
d
im
e
n
s
io
n
a
n
d
its
v
alu
e
d
ep
en
d
s
o
n
th
e
ty
p
e
o
f
t
h
e
tr
an
s
f
o
r
m
er
co
n
n
ec
tio
n
.
T
a
b
l
e
1
s
h
o
ws
th
e
p
r
o
p
o
s
ed
s
u
b
-
m
atr
ix
v
al
u
es
f
o
r
co
m
m
o
n
tr
an
s
f
o
r
m
er
co
n
n
e
ctio
n
s
.
Stan
d
ar
d
30
-
d
eg
r
ee
co
n
n
ec
tio
n
s
a
r
e
ass
u
m
ed
f
o
r
Y
-
D
a
n
d
D
-
Y
co
n
n
ec
tio
n
s
.
T
h
e
f
o
r
m
u
latio
n
s
f
o
r
m
atr
ices
Y
I
,
Y
II
,
Y
III
,
an
d
Y
IV
in
T
ab
le
1
a
r
e
(
2
)
,
(
3
)
,
(
4
)
,
a
n
d
(
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
2
6
2
–
270
264
=
t
t
t
I
y
0
0
0
y
0
0
0
y
Y
(
2
)
=
t
t
II
y
0
0
0
y
0
0
0
0
Y
(
3
)
−
−
−
=
)
30
1
(
y
0
0
0
)
30
1
(
y
0
0
0
0
o
t
o
t
I
I
I
Y
(
4
)
−
=
)
30
1
(
y
0
0
0
)
30
1
(
y
0
0
0
0
o
t
o
t
IV
Y
(
5
)
wh
er
e
y
t
is
th
e
tr
an
s
f
o
r
m
er
lea
k
ag
e
ad
m
ittan
ce
.
Fig
u
r
e
1
.
Sch
em
atic
d
iag
r
am
o
f
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
T
ab
le
1
.
Su
b
-
m
atr
ices f
o
r
co
m
m
o
n
tr
an
s
f
o
r
m
er
c
o
n
n
ec
tio
n
s
C
o
n
n
e
c
t
i
o
n
s
012
PP
Y
012
PS
Y
012
SP
Y
012
SS
Y
GrY
–
GrY
Y
I
-
Y
I
Y
I
-
Y
I
D
–
D
Y
II
-
Y
II
Y
II
-
Y
II
Y
–
D
Y
II
Y
III
Y
IV
-
Y
II
GrY
–
D
Y
I
Y
III
Y
IV
-
Y
II
D
–
GrY
Y
II
Y
III
Y
IV
-
Y
I
Y
–
Y
Y
II
-
Y
II
Y
II
-
Y
II
D
–
Y
Y
II
Y
III
Y
IV
-
Y
II
GrY
–
Y
Y
II
-
Y
II
Y
II
-
Y
II
Y
–
GrY
Y
II
-
Y
II
Y
II
-
Y
II
N
o
t
e
:
G
r
s
t
a
n
d
s fo
r
g
r
o
u
n
d
e
d
2
.
2
.
T
ra
ns
f
o
rm
er
mo
del in pha
s
e
co
m
po
nents
T
h
r
ee
-
p
h
ase
lo
ad
f
lo
w
f
o
r
m
u
latio
n
p
r
o
p
o
s
ed
in
t
h
e
p
r
esen
t
wo
r
k
is
in
p
h
ase
c
o
m
p
o
n
en
ts
.
T
h
er
ef
o
r
e,
th
e
tr
an
s
f
o
r
m
er
m
o
d
el
d
escr
ib
ed
in
Sectio
n
2
.
1
n
ee
d
s
to
b
e
co
n
v
e
r
ted
in
to
its
eq
u
iv
alen
t
p
h
ase
co
m
p
o
n
en
ts
m
o
d
el.
T
h
e
f
ir
s
t step
in
th
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
is
t
o
r
ewr
ite
(
1
)
in
t
h
e
f
o
r
m
s
o
f
two
e
q
u
atio
n
s
as
(
6
)
an
d
(
7
)
.
0
1
2
S
0
1
2
PS
0
1
2
P
0
1
2
PP
0
1
2
P
V
Y
V
Y
I
+
=
(
6
)
0
1
2
S
0
1
2
SS
0
1
2
P
0
1
2
SP
0
1
2
S
V
Y
V
Y
I
+
=
(
7
)
T
h
e
n
,
b
a
s
e
d
o
n
s
y
m
m
e
t
r
i
ca
l
c
o
m
p
o
n
e
n
t
t
h
e
o
r
y
,
(
6
)
a
n
d
(
7
)
c
a
n
b
e
r
e
w
r
i
t
t
e
n
i
n
p
h
as
e
c
o
m
p
o
n
e
n
t
s
as
(
8
)
a
n
d
(
9
)
.
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
A
n
ew me
th
o
d
to
i
n
co
r
p
o
r
a
te
t
h
r
ee
-
p
h
a
s
e
p
o
w
er tr
a
n
s
fo
r
me
r
mo
d
el
in
to
d
is
tr
ib
u
tio
n
…
(
R
u
d
y
Gia
n
to
)
265
a
b
c
S
a
b
c
PS
a
b
c
P
a
b
c
PP
a
b
c
P
V
Y
V
Y
I
+
=
(
8
)
a
b
c
S
a
b
c
SS
a
b
c
P
a
b
c
SP
a
b
c
S
V
Y
V
Y
I
+
=
(
9
)
wh
er
e:
abc
S
abc
P
I
I
an
d
: tr
an
s
f
o
r
m
er
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
p
h
ase
cu
r
r
en
ts
a
b
c
S
a
b
c
P
V
V
an
d
: tr
an
s
f
o
r
m
er
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
p
h
ase
v
o
ltag
es
a
b
c
SS
a
b
c
SP
a
b
c
PS
a
b
c
PP
,
,
,
Y
Y
Y
Y
an
d
: tr
an
s
f
o
r
m
er
s
u
b
-
m
atr
ice
s
in
t
er
m
s
o
f
p
h
ase
co
m
p
o
n
en
ts
T
h
e
tr
an
s
f
o
r
m
er
s
u
b
-
m
atr
ices
abc
SS
abc
SP
abc
PS
abc
PP
,
,
,
Y
Y
Y
Y
an
d
in
(
8
)
an
d
(
9
)
ar
e
ca
lcu
lated
u
s
in
g
(
1
0
)
,
(
1
1
)
,
(
1
2
)
,
a
n
d
(
1
3
)
.
1
012
PP
abc
PP
−
=
A
AY
Y
(
10
)
1
012
PS
abc
PS
−
=
A
AY
Y
(
11
)
1
012
SP
abc
SP
−
=
A
AY
Y
(
12
)
1
012
SS
abc
SS
−
=
A
AY
Y
(
13
)
wh
er
e:
=
o
o
o
o
240
1
120
1
1
120
1
240
1
1
1
1
1
A
(
14
)
=
−
o
o
o
o
1
1
2
0
1
2
4
0
1
1
2
4
0
1
1
2
0
1
1
1
1
1
A
(
15
)
I
t
is
to
b
e
n
o
ted
th
at
th
e
s
e
q
u
en
ce
c
o
m
p
o
n
en
ts
tr
an
s
f
o
r
m
er
s
u
b
-
m
atr
ices
in
(
1
4
)
an
d
(
1
5
)
ar
e
ca
lcu
lated
b
ased
o
n
th
e
f
o
r
m
u
las
g
iv
en
in
T
ab
le
1
.
E
q
u
atio
n
s
(
8
)
an
d
(
9
)
ar
e
th
e
p
r
o
p
o
s
ed
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
m
ath
em
atica
l
m
o
d
el
to
b
e
in
teg
r
ated
in
to
DSLF
an
aly
s
is
.
Mo
r
e
d
etail
ex
p
lan
atio
n
o
f
th
e
m
o
d
el
in
teg
r
atio
n
will b
e
d
is
cu
s
s
ed
i
n
th
e
n
e
x
t sectio
n
.
3.
D
SL
F
ANA
L
Y
SI
S
3
.
1
.
DSL
F
f
o
r
m
ula
t
io
n
T
o
en
ab
le
in
co
r
p
o
r
atin
g
th
r
e
e
-
p
h
ase
tr
an
s
f
o
r
m
er
m
o
d
el
d
escr
ib
ed
in
s
ec
tio
n
2
in
t
o
th
e
DSLF
an
aly
s
is
,
a
n
ew
f
o
r
m
u
latio
n
o
f
DSLF
p
r
o
b
lem
is
also
p
r
o
p
o
s
ed
in
th
e
p
r
esen
t
wo
r
k
.
T
h
e
n
ew
DSLF
f
o
r
m
u
latio
n
is
e
x
p
r
ess
ed
in
t
er
m
s
o
f
b
r
a
n
ch
cu
r
r
en
ts
an
d
n
o
d
al
v
o
ltag
e
s
.
Fig
u
r
e
2
s
h
o
ws
a
s
ec
tio
n
o
f
a
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
As d
is
tr
ib
u
tio
n
lin
es d
o
n
o
t
u
s
u
ally
h
a
v
e
s
h
u
n
t a
d
m
ittan
ce
s
,
it h
as b
e
en
ass
u
m
ed
th
at
th
e
lin
e
s
ec
tio
n
h
as
o
n
ly
s
er
ies
a
d
m
ittan
ce
.
Ho
wev
e
r
,
if
n
ee
d
e
d
,
th
e
s
h
u
n
t
ad
m
ittan
ce
s
ca
n
b
e
in
clu
d
ed
i
n
th
e
f
o
r
m
u
latio
n
in
a
s
tr
aig
h
tf
o
r
wa
r
d
m
an
n
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
2
6
2
–
270
266
Fig
u
r
e
2
.
L
i
n
e
s
ec
tio
n
o
f
d
is
tr
ib
u
tio
n
n
etwo
r
k
B
ased
o
n
Fig
u
r
e
2
,
it
ca
n
b
e
o
b
tain
ed
(
1
6
)
.
(
)
a
b
c
RE
a
b
c
SE
a
b
c
B
a
b
c
B
V
V
Y
I
−
=
(
16
)
wh
er
e:
T
c
B
b
B
a
B
abc
B
I
I
I
=
I
: b
r
an
ch
(
lin
e)
cu
r
r
en
t
T
c
SE
b
SE
a
SE
a
b
c
SE
V
V
V
=
V
: lin
e
s
en
d
in
g
-
e
n
d
v
o
ltag
e
T
c
SE
b
SE
a
SE
a
b
c
SE
V
V
V
=
V
: lin
e
r
ec
eiv
in
g
-
e
n
d
v
o
ltag
e
abc
B
Y
: th
r
ee
-
p
h
ase
ad
m
ittan
ce
m
atr
i
x
I
t
is
to
b
e
n
o
ted
th
at
th
e
th
r
ee
-
p
h
ase
ad
m
ittan
ce
m
atr
i
x
in
(
16
)
is
th
e
a
d
m
ittan
ce
m
atr
ix
o
f
th
e
lin
e
s
ec
tio
n
in
Fig
u
r
e
2
.
T
h
is
ad
m
it
tan
ce
m
atr
ix
h
as th
e
f
o
r
m
as (
1
7
)
.
=
cc
cb
ca
bc
bb
ba
ac
ab
aa
a
bc
B
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
(
17
)
wh
er
e
Y
aa
,
Y
bb
an
d
Y
cc
ar
e
s
elf
ad
m
ittan
ce
s
o
f
th
e
lin
e
p
h
ases
;
Y
ab
,
Y
ac
,
Y
bc
,
Y
ba
,
Y
ca
an
d
Y
bc
ar
e
m
u
tu
al
ad
m
ittan
ce
s
b
etwe
en
lin
e
p
h
ases
.
I
n
a
d
d
itio
n
to
(
16
)
,
two
o
t
h
er
s
ets
o
f
eq
u
atio
n
s
ar
e
n
ee
d
ed
to
co
m
p
lete
th
e
p
r
o
p
o
s
ed
DSLF
f
o
r
m
u
latio
n
.
T
h
ese
two
s
ets
o
f
eq
u
atio
n
s
ca
n
b
e
d
er
i
v
e
d
b
y
ex
a
m
in
in
g
th
e
co
n
d
itio
n
o
f
n
o
d
es
o
f
t
h
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
as d
ep
ict
ed
in
Fig
u
r
e
3
.
(
a)
(
b
)
Fig
u
r
e
3
.
C
o
n
d
itio
n
s
at:
(
a)
Su
b
s
tatio
n
n
o
d
e
,
(
b
)
L
o
ad
n
o
d
e
B
ased
o
n
Fig
u
r
e
3
,
th
e
two
s
ets o
f
(
1
8
)
an
d
(
1
9
)
ar
e
o
b
tain
ed
.
(
)
(
)
=
−
a
b
c
o
u
t
,
B
a
b
c
SS
a
b
c
LS
a
b
c
G
d
i
a
g
I
V
S
S
(
18
)
(
)
(
)
−
=
a
b
c
o
u
t
,
B
a
b
c
in
,
B
a
b
c
L
a
b
c
LL
d
i
a
g
I
I
V
S
(
19
)
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
A
n
ew me
th
o
d
to
i
n
co
r
p
o
r
a
te
t
h
r
ee
-
p
h
a
s
e
p
o
w
er tr
a
n
s
fo
r
me
r
mo
d
el
in
to
d
is
tr
ib
u
tio
n
…
(
R
u
d
y
Gia
n
to
)
267
wh
er
e:
T
c
G
b
G
a
G
abc
G
S
S
S
=
S
: p
o
wer
s
u
p
p
lied
f
r
o
m
s
u
b
s
tatio
n
n
o
d
e
T
c
LS
b
LS
a
LS
a
b
c
LS
S
S
S
=
S
: p
o
wer
d
em
a
n
d
at
s
u
b
s
tatio
n
n
o
d
e
T
c
LL
b
LL
a
LL
a
b
c
LL
S
S
S
=
S
: p
o
wer
d
em
a
n
d
at
lo
a
d
n
o
d
e
T
c
SS
b
SS
a
SS
abc
SS
V
V
V
=
V
: su
b
s
tatio
n
n
o
d
e
v
o
ltag
e
T
c
L
b
L
a
L
a
b
c
L
V
V
V
=
V
: lo
ad
n
o
d
e
v
o
ltag
e
T
c
in
,
B
b
in
,
B
a
in
,
B
a
b
c
in
,
B
I
I
I
=
I
: b
r
an
ch
c
u
r
r
e
n
t e
n
ter
in
g
th
e
n
o
d
e
T
c
out
,
B
b
out
,
B
a
out
,
B
abc
out
,
B
I
I
I
=
I
: b
r
an
ch
c
u
r
r
e
n
t le
av
in
g
t
h
e
n
o
d
e
3
.
2
.
Su
mm
a
ry
o
f
equa
t
io
ns
a
nd
qu
a
ntit
ies
T
h
is
s
ec
tio
n
s
u
m
m
ar
izes a
ll o
f
th
e
s
ets o
f
n
o
n
lin
ea
r
e
q
u
atio
n
s
r
eq
u
ir
ed
to
s
o
lv
e
l
o
ad
f
l
o
w
p
r
o
b
lem
o
f
d
is
tr
ib
u
tio
n
s
y
s
tem
in
s
talled
with
th
r
ee
-
p
h
ase
p
o
wer
tr
a
n
s
f
o
r
m
er
s
s
ee
in
T
ab
le
2
.
All
o
f
th
e
elec
tr
ical
q
u
an
titi
es (
k
n
o
w
n
an
d
u
n
k
n
o
wn
)
ar
e
also
s
u
m
m
ar
ize
d
in
th
is
s
ec
tio
n
s
ee
in
T
ab
le
3
.
T
ab
le
2
.
Su
m
m
a
r
y
o
f
eq
u
atio
n
s
S
e
t
S
e
t
o
f
e
q
u
a
t
i
o
n
s
N
u
mb
e
r
o
f
e
q
u
a
t
i
o
n
s
1
a
n
d
2
0
V
Y
V
Y
I
0
V
Y
V
Y
I
=
−
−
=
−
−
a
b
c
S
a
b
c
SS
a
b
c
P
a
b
c
SP
a
b
c
S
a
b
c
S
a
b
c
PS
a
b
c
P
a
b
c
PP
a
b
c
P
6
×
n
T
(n
T
:
n
u
m
b
e
r
o
f
t
r
a
n
sf
o
r
mers
)
3
(
)
0
V
V
Y
I
=
−
−
a
b
c
RE
a
b
c
SE
a
b
c
B
a
b
c
B
3
×
n
L
(n
L
:
n
u
m
b
e
r
o
f
l
i
n
e
s)
4
(
)
(
)
0
I
V
S
S
=
−
−
a
b
c
o
u
t
,
B
a
b
c
SS
a
b
c
LS
a
b
c
G
d
i
a
g
3
5
(
)
(
)
0
I
I
V
S
=
−
−
a
b
c
o
u
t
,
B
a
b
c
in
,
B
a
b
c
L
a
b
c
LL
d
i
a
g
3
×
(
n
-
1)
(
n
:
t
o
t
a
l
n
u
mb
e
r
o
f
n
o
d
e
s)
T
ab
le
3
.
Su
m
m
a
r
y
o
f
q
u
an
titi
es
S
e
t
S
e
t
o
f
k
n
o
w
n
q
u
a
n
t
i
t
i
e
s
(
sy
s
t
e
m
d
a
t
a
o
r
s
p
e
c
i
f
i
e
d
)
S
e
t
o
f
u
n
k
n
o
w
n
q
u
a
n
t
i
t
i
e
s
(
t
o
b
e
c
a
l
c
u
l
a
t
e
d
)
1
a
n
d
2
abc
SS
abc
SP
abc
PS
abc
PP
,
,
,
Y
Y
Y
Y
abc
P
abc
P
I
I
an
d
3
abc
B
Y
a
b
c
o
u
t
,
B
a
b
c
in
,
B
a
b
c
B
a
b
c
,
,
:
I
I
I
I
4
T
o
o
o
abc
SS
120
1
120
1
0
1
−
=
V
abc
G
S
5
a
b
c
LL
a
b
c
LS
a
b
c
L
,
:
S
S
S
a
b
c
L
a
b
c
RE
a
b
c
SE
a
b
c
S
a
b
c
P
a
b
c
,
,
,
,
:
V
V
V
V
V
V
4.
VE
RIF
I
CA
T
I
O
N
O
F
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
4
.
1
.
T
est
s
y
s
t
em
a
nd
s
o
f
t
wa
re
co
nd
it
io
ns
T
h
is
s
ec
tio
n
d
is
cu
s
s
es
v
er
if
ica
tio
n
an
d
v
alid
atio
n
o
f
th
e
m
eth
o
d
p
r
o
p
o
s
ed
in
Secti
o
n
3
.
I
E
E
E
4
-
n
o
d
e
test
s
y
s
tem
[
3
0
]
is
u
s
ed
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th
e
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er
if
icatio
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s
s
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I
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al
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ith
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ec
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MA
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ilt
-
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o
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e
q
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atio
n
s
in
T
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le
2
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o
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th
e
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n
k
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wn
v
ar
iab
les d
e
s
cr
ib
ed
in
T
ab
le
3
.
4
.
2
.
Resul
t
s
a
nd
dis
cu
s
s
io
n
R
esu
lts
o
f
th
e
lo
a
d
f
l
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al
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s
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ter
m
s
o
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y
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tem
v
o
lta
g
e
p
r
o
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iles
ar
e
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iv
e
n
in
T
ab
le
s
4
-
12
.
Fo
r
th
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p
u
r
p
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o
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c
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p
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n
,
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esu
l
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f
DSLF
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aly
s
is
f
r
o
m
r
ef
.
[
3
0
]
a
r
e
also
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r
esen
ted
in
th
e
tab
les.
Fo
r
Y
co
n
n
ec
tio
n
s
,
V
x
,
V
y
an
d
V
z
a
r
e
u
s
ed
to
in
d
icate
V
a
,
V
b
a
n
d
V
c
,
r
esp
ec
tiv
ely
.
On
th
e
o
t
h
er
h
an
d
,
f
o
r
D
co
n
n
ec
tio
n
s
,
V
x
,
V
y
an
d
V
z
ar
e
u
s
ed
to
in
d
icate
V
ab
,
V
bc
an
d
V
ca
,
r
esp
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
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2
I
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t J
Ap
p
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er
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268
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.
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6
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.
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6
T
ab
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8
.
Vo
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p
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–
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co
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tio
n
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o
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f
.
[
3
0
]
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x
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9
T
ab
le
9
.
Vo
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.
[
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0
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T
ab
le
10.
V
o
ltag
e
p
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ile
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o
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–
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tio
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.
[
3
0
]
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V
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5
-
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T
ab
le
1
1
.
V
o
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p
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Y
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n
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tio
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N
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[
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0
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1
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7
-
-
-
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
A
n
ew me
th
o
d
to
i
n
co
r
p
o
r
a
te
t
h
r
ee
-
p
h
a
s
e
p
o
w
er tr
a
n
s
fo
r
me
r
mo
d
el
in
to
d
is
tr
ib
u
tio
n
…
(
R
u
d
y
Gia
n
to
)
269
T
ab
le
1
2
.
V
o
ltag
e
p
r
o
f
ile
f
o
r
Y
–
Gr
Y
co
n
n
ec
tio
n
N
o
d
e
P
r
o
p
o
se
d
m
e
t
h
o
d
R
e
f
.
[
3
0
]
V
x
V
y
V
z
V
x
V
y
V
z
1
7
1
9
9
.
6
/
0
7
1
9
9
.
6
/
-
1
2
0
7
1
9
9
.
6
/
1
2
0
-
-
-
2
7
1
1
5
.
2
/
-
0
.
3
7
1
2
5
.
9
/
-
1
2
0
.
4
7
1
2
6
.
4
/
1
1
9
.
6
-
-
-
3
2
3
2
3
.
2
/
-
1
.
1
2
1
3
2
.
2
/
-
1
2
3
.
9
2
3
2
1
.
8
/
1
1
4
.
2
-
-
-
4
2
0
1
7
.
5
/
-
5
.
5
1
8
8
1
.
2
/
-
1
2
9
.
5
2
0
6
8
.
4
/
1
0
8
.
7
-
-
-
T
ab
les
4
-
12
s
h
o
w
th
at
th
e
r
esu
lts
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
a
r
e
in
clo
s
e
ag
r
ee
m
en
t
with
th
o
s
e
g
iv
en
in
[
3
0
]
.
H
o
wev
er
,
th
e
m
eth
o
d
u
s
ed
in
[
3
0
]
r
e
q
u
ir
es
d
if
f
e
r
en
t
s
et
o
f
n
o
n
lin
ea
r
eq
u
atio
n
s
f
o
r
d
i
f
f
er
en
t
tr
an
s
f
o
r
m
er
co
n
n
ec
tio
n
s
wh
ich
is
n
o
t
co
n
v
en
ien
t
f
o
r
ef
f
icien
t
im
p
lem
e
n
tatio
n
an
d
in
co
r
p
o
r
atio
n
o
f
v
ar
io
u
s
tr
an
s
f
o
r
m
er
co
n
n
ec
tio
n
ty
p
es.
T
h
e
m
eth
o
d
p
r
o
p
o
s
ed
in
t
h
e
p
r
esen
t
p
ap
e
r
d
o
es
n
o
t
r
eq
u
i
r
e
an
y
s
p
ec
ial
eq
u
atio
n
to
h
a
n
d
le
th
e
tr
an
s
f
o
r
m
e
r
with
D
o
r
u
n
g
r
o
u
n
d
ed
Y
win
d
i
n
g
s
.
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
a
s
im
p
le
tech
n
iq
u
e
o
r
p
r
o
ce
d
u
r
e
f
o
r
in
clu
d
in
g
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
e
r
m
o
d
el
in
d
is
tr
ib
u
tio
n
s
y
s
tem
lo
ad
f
lo
w
(
DSLF
)
an
aly
s
is
h
as
b
ee
n
p
r
o
p
o
s
ed
.
First,
a
tr
an
s
f
o
r
m
er
m
o
d
el
b
ased
o
n
n
o
d
al
ad
m
ittan
ce
m
atr
ix
was
d
e
v
elo
p
ed
.
T
h
e
n,
th
e
m
o
d
el
is
in
c
o
r
p
o
r
ated
in
t
o
lo
ad
f
lo
w
an
al
y
s
is
.
I
n
th
e
p
a
p
er
,
t
h
e
lo
ad
f
lo
w
f
o
r
m
u
latio
n
in
te
r
m
s
o
f
b
r
an
c
h
cu
r
r
en
ts
a
n
d
n
o
d
al
v
o
ltag
es
h
as
also
b
ee
n
p
r
o
p
o
s
ed
to
en
ab
le
in
co
r
p
o
r
atin
g
th
e
m
o
d
el
in
to
th
e
an
aly
s
is
.
I
n
th
e
f
o
r
m
u
latio
n
,
s
ets
o
f
n
o
n
lin
ea
r
eq
u
atio
n
s
ar
e
d
er
iv
ed
at
ev
er
y
n
o
d
e
a
n
d
b
r
an
c
h
o
f
th
e
d
i
s
tr
ib
u
tio
n
s
y
s
tem
b
y
ex
am
i
n
in
g
th
e
co
n
d
itio
n
s
(
i
.
e.
el
ec
tr
ical
q
u
an
titi
es
r
elatio
n
s
h
ip
s
)
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
ca
n
s
o
lv
e
t
h
e
s
in
g
u
lar
ity
p
r
o
b
lem
,
a
n
d
m
a
k
es
th
e
ca
lcu
latio
n
s
in
f
o
r
war
d
/b
ac
k
war
d
s
wee
p
(
FB
S)
alg
o
r
ith
m
is
ea
s
y
to
b
e
ca
r
r
ied
o
u
t
.
T
h
e
r
esu
lts
in
d
icate
th
at
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
v
alid
a
n
d
ac
cu
r
ate
.
RE
F
E
R
E
NC
E
S
[1
]
B.
S
e
re
e
ter,
K.
Vu
i
k
a
n
d
C
.
W
i
tt
e
v
e
e
n
,
“
Ne
wto
n
p
o
we
r
fl
o
w
m
e
th
o
d
s
fo
r
u
n
b
a
lan
c
e
d
t
h
re
e
-
p
h
a
se
d
istri
b
u
ti
o
n
n
e
two
rk
s,
”
E
n
e
rg
ies
,
v
o
l
.
1
0
,
n
o
.
1
0
,
p
p
.
1
-
2
0
,
2
0
1
7
,
d
o
i:
1
0
.
3
3
9
0
/e
n
1
0
1
0
1
6
5
8
.
[2
]
A.
G
.
F
o
n
se
c
a
,
O.
L.
To
rtell
i
a
n
d
E
.
M
.
L
o
u
re
n
ç
o
,
“
Ex
ten
d
e
d
fa
st
d
e
c
o
u
p
led
p
o
we
r
fl
o
w
fo
r
r
e
c
o
n
fig
u
ra
ti
o
n
n
e
two
rk
s
in
d
istri
b
u
ti
o
n
s
y
ste
m
s,
”
IET
Ge
n
e
ra
ti
o
n
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l.
1
2
,
n
o
.
2
2
,
p
p
.
6
0
3
3
-
6
0
4
0
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
4
9
/
iet
-
g
t
d
.
2
0
1
8
.
5
8
8
6
.
[3
]
O.
L.
To
rtell
i,
E.
M
.
Lo
u
re
n
ç
o
,
A.
V.
G
a
rc
ia
a
n
d
B.
C.
P
a
l,
"
F
a
s
t
d
e
c
o
u
p
led
p
o
we
r
fl
o
w
t
o
e
m
e
rg
in
g
d
istr
ib
u
ti
o
n
sy
ste
m
s
v
ia
c
o
m
p
lex
p
u
n
o
rm
a
li
z
a
ti
o
n
,
"
i
n
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
v
o
l.
3
0
,
n
o
.
3
,
p
p
.
1
3
5
1
-
1
3
5
8
,
M
a
y
2
0
1
5
,
d
o
i
:
1
0
.
1
1
0
9
/T
P
WRS
.
2
0
1
4
.
2
3
4
3
1
9
3
.
[4
]
S
.
Bo
l
o
g
n
a
n
i
a
n
d
S
.
Zam
p
ieri,
"
On
th
e
e
x
iste
n
c
e
a
n
d
li
n
e
a
r
a
p
p
r
o
x
ima
ti
o
n
o
f
th
e
p
o
we
r
fl
o
w
so
l
u
ti
o
n
i
n
p
o
we
r
d
istri
b
u
ti
o
n
n
e
two
r
k
s,"
i
n
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
m
s
,
v
o
l.
3
1
,
n
o
.
1
,
p
p
.
1
6
3
-
1
7
2
,
Ja
n
.
2
0
1
6
,
d
o
i:
1
0
.
1
1
0
9
/
TP
WRS
.
2
0
1
5
.
2
3
9
5
4
5
2
.
[5
]
H.
Li
,
H.
Zh
o
u
,
T.
Li
u
a
n
d
Q
.
Ch
e
n
,
"
A
l
o
o
p
-
a
n
a
ly
sis
th
e
o
ry
b
a
se
d
li
n
e
a
r
p
o
we
r
fl
o
w
m
e
th
o
d
fo
r
t
h
re
e
-
p
h
a
se
d
istri
b
u
ti
o
n
p
o
we
r
sy
ste
m
,
"
in
IEE
E
Acc
e
ss
,
v
o
l.
7
,
p
p
.
1
5
7
3
8
9
-
1
5
7
4
0
0
,
Oc
t
.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
1
9
.
2
9
4
9
3
7
2
.
[6
]
H.
Li
,
X.
Ya
n
,
J.
Ya
n
,
A.
Z
h
a
n
g
a
n
d
F
.
Zh
a
n
g
,
"
A
t
h
re
e
-
p
h
a
se
u
n
b
a
lan
c
e
d
li
n
e
a
r
p
o
we
r
flo
w
so
lu
ti
o
n
wit
h
P
V
Bu
s
a
n
d
ZIP
lo
a
d
,
"
in
I
EE
E
Acc
e
ss
,
v
o
l.
7
,
p
p
.
1
3
8
8
7
9
-
1
3
8
8
8
9
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
1
9
.
2
9
4
0
2
2
9
.
[7
]
H.
Ah
m
a
d
i,
J.
R.
M
a
rtı
´
a
n
d
A.
v
o
n
M
e
ier,
"
A
li
n
e
a
r
p
o
we
r
fl
o
w
f
o
rm
u
latio
n
f
o
r
t
h
re
e
-
p
h
a
se
d
istri
b
u
ti
o
n
sy
ste
m
s,"
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
3
1
,
n
o
.
6
,
p
p
.
5
0
1
2
-
5
0
2
1
,
N
o
v
.
2
0
1
6
,
d
o
i
:
1
0
.
1
1
0
9
/
TP
WRS
.
2
0
1
6
.
2
5
3
3
5
4
0
.
[8
]
A.
G
a
r
c
e
s,
"
A
li
n
e
a
r
th
re
e
-
p
h
a
se
lo
a
d
flo
w
fo
r
p
o
we
r
d
istri
b
u
ti
o
n
sy
ste
m
s,"
i
n
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
3
1
,
n
o
.
1
,
p
p
.
8
2
7
-
8
2
8
,
Ja
n
.
2
0
1
6
,
d
o
i:
1
0
.
1
1
0
9
/
TP
W
RS
.
2
0
1
5
.
2
3
9
4
2
9
6
.
[9
]
K.
M
a
h
m
o
u
d
a
n
d
N.
Yo
ri
n
o
,
“
Ro
b
u
st
q
u
a
d
ra
ti
c
-
b
a
se
d
BF
S
p
o
we
r
flo
w
m
e
th
o
d
fo
r
m
u
lt
i
-
p
h
a
se
d
istri
b
u
ti
o
n
s
y
ste
m
s,
”
IET
Ge
n
e
ra
ti
o
n
T
r
a
n
s
miss
io
n
a
n
d
Distri
b
u
ti
o
n
,
v
o
l.
1
0
,
n
o
.
9
,
p
p
.
2
2
4
0
-
2
2
5
0
,
2
0
1
6
,
d
o
i:
1
0
.
1
0
4
9
/i
e
t
-
g
td
.
2
0
1
5
.
1
5
1
8
.
[1
0
]
S
.
P
e
tri
d
is,
O.
B
lan
a
s,
D.
Ra
k
o
p
o
u
l
o
s,
F
.
S
terg
i
o
p
o
u
l
o
s,
N.
Nik
o
l
o
p
o
u
l
o
s
a
n
d
S
.
Vo
u
teta
k
is
,
“
An
e
fficie
n
t
b
a
c
k
wa
rd
/fo
rwa
rd
sw
e
e
p
a
lg
o
rit
h
m
fo
r
p
o
we
r
flo
w
a
n
a
ly
sis
t
h
r
o
u
g
h
a
n
o
v
e
l
tree
-
li
k
e
stru
c
t
u
re
fo
r
u
n
b
a
lan
c
e
d
d
istri
b
u
ti
o
n
n
e
two
r
k
s,
”
En
e
rg
ies
,
v
o
l.
1
4
,
p
p
.
1
-
2
0
,
2
0
2
1
,
d
o
i:
1
0
.
3
3
9
0
/en
1
4
0
4
0
8
9
7
.
[1
1
]
Y.
Ju
,
W.
W
u
,
B.
Zh
a
n
g
a
n
d
H.
S
u
n
,
"
An
e
x
te
n
sio
n
o
f
F
BS
th
re
e
-
p
h
a
se
p
o
we
r
flo
w fo
r
h
a
n
d
li
n
g
P
V
n
o
d
e
s i
n
a
c
ti
v
e
d
istri
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L.
Wa
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m
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m
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I
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3
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U.
G
h
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n
d
V.
M
u
k
h
e
rjee
,
A
n
imp
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r
m
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d
e
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n
d
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o
n
s
y
ste
m
,
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e
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T.
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5
]
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.
S
.
M
o
o
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th
y
a
n
d
D.
H
o
a
d
le
y
,
"
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n
e
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a
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sfo
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u
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a
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a
ly
sis,"
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n
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E
T
ra
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6
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.
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Irv
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g
a
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d
A.
K.
Al
-
Ot
h
m
a
n
,
"
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it
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7
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.
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g
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F
.
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h
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a
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J
.
Li
,
"
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p
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e
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sf
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d
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l
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d
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lan
c
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ra
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ial
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n
sy
st
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m
s,"
in
IEE
E
T
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n
sa
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ti
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s
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Po
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[1
8
]
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.
Xia
o
,
D.
C.
Yu
a
n
d
W
.
Ya
n
,
"
A u
n
ifi
e
d
th
re
e
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p
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se
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l
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d
istri
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ti
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l
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d
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o
w
c
a
lcu
latio
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s,"
in
IEE
E
Tran
sa
c
ti
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s o
n
P
o
we
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y
st
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m
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[1
9
]
R.
Ve
rm
a
a
n
d
V.
S
a
rk
a
r
,
“
Ac
ti
v
e
d
istri
b
u
ti
o
n
n
e
two
rk
lo
a
d
flo
w
a
n
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ly
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ro
u
g
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re
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BS
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ra
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s wit
h
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teg
ra
ted
DG
a
n
d
tra
n
sfo
rm
e
r
m
o
d
e
li
n
g
,
”
IET
Ge
n
e
ra
ti
o
n
T
ra
n
sm
issio
n
a
n
d
Distri
b
u
t
io
n
,
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1
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4
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p
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.
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t
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td
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8
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5
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8
.
[2
0
]
U.
G
h
a
tak
a
n
d
V.
M
u
k
h
e
rjee
,
“
A
fa
st
a
n
d
e
fficie
n
t
l
o
a
d
fl
o
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t
e
c
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n
iq
u
e
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u
n
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a
lan
c
e
d
d
istr
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u
ti
o
n
sy
ste
m
,
”
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e
c
trica
l
Po
we
r a
n
d
En
e
rg
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ij
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.
[2
1
]
M
.
Ba
z
ra
fsh
a
n
a
n
d
N.
G
a
tsis,
"
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m
p
re
h
e
n
si
v
e
m
o
d
e
li
n
g
o
f
t
h
re
e
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p
h
a
se
d
istri
b
u
ti
o
n
sy
ste
m
s
v
ia
th
e
b
u
s
a
d
m
it
tan
c
e
m
a
tri
x
,
"
in
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
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l.
3
3
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o
.
2
,
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p
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9
,
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.
2
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.
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7
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1
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.
[2
2
]
M
.
Dilek
,
F
.
d
e
Le
o
n
,
R
.
Bro
a
d
wa
ter
a
n
d
S
.
Lee
,
"
A
ro
b
u
st
m
u
lt
ip
h
a
se
p
o
we
r
flo
w
f
o
r
g
e
n
e
ra
l
d
istr
ib
u
ti
o
n
n
e
two
rk
s,
"
i
n
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
S
y
ste
ms
,
v
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l.
2
5
,
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o
.
2
,
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p
.
7
6
0
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7
6
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M
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y
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:
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1
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9
/
TP
WRS
.
2
0
0
9
.
2
0
3
6
7
9
1
.
[2
3
]
A.
Ca
rre
n
o
,
M
.
P
e
re
z
,
C.
Ba
ier,
A.
Hu
a
n
g
,
S
.
Ra
jen
d
ra
n
a
n
d
M
.
M
a
li
n
o
ws
k
i
,
“
C
o
n
fi
g
u
ra
ti
o
n
s,
p
o
we
r
to
p
o
lo
g
ies
a
n
d
a
p
p
li
c
a
ti
o
n
s o
f
h
y
b
ri
d
d
istri
b
u
ti
o
n
tran
sf
o
rm
e
rs,”
En
e
rg
ies
,
v
o
l
.
1
4
,
p
p
.
1
–
3
5
,
2
0
2
1
,
d
o
i:
1
0
.
3
3
9
0
/en
1
4
0
5
1
2
1
5
.
[2
4
]
S
.
Clae
y
s,
G
.
De
c
o
n
in
c
k
a
n
d
F
.
G
e
th
,
“
De
c
o
m
p
o
siti
o
n
o
f
n
-
wi
n
d
in
g
tra
n
sfo
rm
e
r
fo
r
u
n
b
a
lan
c
e
d
o
p
ti
m
a
l
p
o
we
r
flo
w
,
”
IET
Ge
n
e
r
a
ti
o
n
T
r
a
n
sm
iss
io
n
a
n
d
Distri
b
u
ti
o
n
, v
o
l.
1
4
,
n
o
.
2
4
,
p
p
.
5
9
6
1
-
5
9
6
9
,
2
0
2
0
.
[2
5
]
U.
Emin
o
g
lu
a
n
d
M
.
H.
Ho
c
a
o
g
l
u
,
"
T
h
re
e
-
p
h
a
se
tran
sfo
rm
e
r
m
o
d
e
li
n
g
fo
r
f
o
rwa
rd
/
b
a
c
k
wa
rd
sw
e
e
p
-
b
a
se
d
d
istri
b
u
ti
o
n
s
y
ste
m
s
p
o
we
r
fl
o
w
a
lg
o
rit
h
m
s,"
2
0
0
7
4
2
n
d
I
n
ter
n
a
t
io
n
a
l
U
n
ive
rs
it
ies
Po
we
r
E
n
g
i
n
e
e
rin
g
C
o
n
fe
re
n
c
e
,
2
0
0
7
,
p
p
.
1
1
5
-
1
2
0
,
d
o
i:
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0
9
/
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C.
2
0
0
7
.
4
4
6
8
9
3
0
.
[2
6
]
U.
Emin
o
g
l
u
a
n
d
M
.
H.
Ho
c
a
o
g
l
u
,
"
Th
re
e
-
p
h
a
se
tran
sfo
rm
e
r
a
n
d
v
o
lt
a
g
e
re
g
u
lato
r
m
o
d
e
li
n
g
fo
r
b
a
c
k
wa
rd
/fo
rwa
rd
sw
e
e
p
-
b
a
se
d
d
istri
b
u
ti
o
n
s
y
ste
m
p
o
we
r
flo
w
a
l
g
o
ri
th
m
s,
"
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tric
a
l
E
n
g
i
n
e
e
rin
g
Ed
u
c
a
ti
o
n
,
v
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l
.
4
6
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o
.
1
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p
.
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4
6
,
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9
,
d
o
i:
1
0
.
7
2
2
7
/IJEE
E
.
4
6
.
1
.
3
.
[2
7
]
M.
Ab
d
e
l
-
Ak
h
e
r,
a
n
d
K.
M
a
h
m
o
u
d
,
“
Im
p
lem
e
n
tatio
n
o
f
t
h
re
e
-
p
h
a
se
tran
sfo
rm
e
r
m
o
d
e
l
i
n
r
a
d
ial
lo
a
d
-
fl
o
w
a
n
a
ly
sis,”
Ai
n
S
h
a
ms
E
n
g
i
n
e
e
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[2
8
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I.
Dž
a
fić,
R.
A.
Ja
b
r
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n
d
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Ne
isiu
s,
"
Tran
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two
r
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n
a
ly
sis,"
i
n
IEE
E
T
ra
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sa
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ti
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Po
we
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v
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P
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.
2
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3
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1
2
.
[2
9
]
W.
H.
Ke
rstin
g
,
Distri
b
u
t
io
n
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y
ste
m
mo
d
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li
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a
n
d
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n
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lys
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4
th
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d
.
,
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ss
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1
0
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2
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/
9
7
8
1
3
1
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1
2
0
7
8
2
.
[3
0
]
IEE
E
P
ES
Distrib
u
ti
o
n
S
y
ste
m
An
a
ly
sis
S
u
b
c
o
m
m
it
tee
,
I
EE
E
4
No
d
e
T
e
st
Fee
d
e
r
:
T
h
e
In
stit
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te
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
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ic E
n
g
i
n
e
e
rs In
c
.
,
2
0
0
6
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Rud
y
G
ia
n
t
o
re
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e
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e
d
BE,
M
E
a
n
d
P
h
D
d
e
g
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e
s
fro
m
Un
iv
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rsitas
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ju
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g
p
u
ra
in
1
9
9
1
,
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sti
tu
t
Tek
n
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lo
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i
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n
d
u
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g
in
1
9
9
5
,
a
n
d
Th
e
Un
i
v
e
rsity
o
f
Wes
tern
Au
stra
li
a
in
2
0
0
9
re
sp
e
c
ti
v
e
ly
.
Cu
rre
n
tl
y
,
h
e
is
a
n
As
so
c
iate
P
r
o
fe
ss
o
r
a
t
Un
iv
e
rsitas
Tan
j
u
n
g
p
u
ra
,
In
d
o
n
e
sia
.
He
h
a
s
p
u
b
li
s
h
e
d
se
v
e
ra
l
in
tern
a
ti
o
n
a
l
j
o
u
r
n
a
l
a
n
d
c
o
n
fe
re
n
c
e
p
a
p
e
rs.
His
re
se
a
rc
h
i
n
tere
sts
in
c
l
u
d
e
p
o
we
r
sy
ste
m
a
n
a
ly
sis,
sim
u
lati
o
n
o
f
p
o
we
r
sy
st
e
m
d
y
n
a
m
ics
,
a
n
d
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
.
Pu
r
wo
h
a
r
j
o
n
o
re
c
e
iv
e
d
BE
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M
E
a
n
d
Do
c
t
o
r
d
e
g
re
e
s
fro
m
Un
i
v
e
rsitas
Tan
ju
n
g
p
u
ra
in
1
9
9
7
,
In
stit
u
t
Tek
n
o
lo
g
i
S
e
p
u
l
u
h
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v
e
m
b
e
r
in
2
0
0
1
,
a
n
d
2
0
1
4
re
sp
e
c
ti
v
e
ly
.
C
u
rr
e
n
tl
y
,
h
e
is
a
n
As
so
c
iate
P
ro
fe
ss
o
r
a
t
Un
i
v
e
rsitas
Tan
ju
n
g
p
u
ra
,
I
n
d
o
n
e
sia
.
He
h
a
s
p
u
b
li
sh
e
d
se
v
e
ra
l
in
tern
a
ti
o
n
a
l
jo
u
rn
a
l
a
n
d
c
o
n
fe
re
n
c
e
p
a
p
e
rs.
His
re
se
a
rc
h
i
n
tere
sts
in
c
l
u
d
e
p
o
we
r
flo
w
a
n
a
l
y
sis,
a
n
d
sy
ste
m
o
p
ti
m
iza
ti
o
n
.
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