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s
e
d on
de
v
e
l
opm
e
nt
of
t
h
r
e
e
-
p
h
a
s
e
u
n
ba
l
a
n
c
e
d pow
e
r
f
l
o
w
us
i
ng
P
V
a
n
d
P
Q
m
ode
l
s
f
or
D
G
’
s
a
n
d s
t
u
d
y
of
t
h
e
i
m
pa
c
t
of
D
G
m
ode
l
s
.
K
h
us
h
a
l
a
n
i e
t a
l
.
[1
5
]
in
v
e
s
ti
g
a
te
d
th
e
d
i
f
f
e
r
e
n
tia
l i
m
p
a
c
t o
f
D
G
m
ode
l
s
on s
t
u
d
y
of
po
w
e
r
f
l
o
w
u
s
i
ng
v
a
r
y
i
ng
D
G
pe
n
e
t
r
a
t
i
on
r
e
l
a
t
e
d t
o t
h
e
i
n
c
r
e
a
s
e
i
n
l
oa
di
ng
.
S
y
s
t
e
m
l
o
s
s
es
an
d
v
o
l
t
a
g
e d
ev
i
a
t
i
o
n
s
ar
e co
m
p
ar
ed
.
S
i
m
i
l
ar
l
y
,
S
u
y
an
t
o
et
al
.
[
1
6
]
f
o
u
n
d
a t
h
r
e
e p
h
as
e
p
ow
e
r
f
l
ow
m
et
h
o
d
t
h
at
can
h
an
d
l
e p
as
s
i
v
e/
act
i
v
e a
n
d
r
ad
i
al
/
w
ea
k
l
y
m
e
s
h
ed
d
i
s
t
r
i
b
u
t
i
o
n
n
et
w
o
r
k
s
.
T
h
e M
o
d
i
f
i
ed
d
i
r
ect
-
Z
B
R
m
e
t
h
od i
s
de
v
e
l
ope
d a
nd c
o
m
bi
n
e
d
w
i
t
h P
a
r
t
i
c
l
e
S
w
a
r
m
O
pt
i
m
i
z
a
t
i
on
(
P
S
O
)
.
I
n S
hi
r
m
oh
a
m
m
a
di
e
t
a
l
.
[
1
7
]
,
t
h
ei
r
p
ap
er
d
es
cr
i
b
e a n
e
w
p
o
w
er
f
l
o
w
m
e
t
h
od
f
or
s
ol
vi
n
g
w
e
a
k
l
y
m
e
s
h
e
d di
s
t
r
i
b
u
t
i
o
n
a
n
d t
r
a
ns
m
i
s
s
i
on
ne
t
w
o
r
k
s
,
us
i
n
g a
m
ul
t
i
-
por
t
c
om
pe
n
s
a
t
i
on
t
e
c
h
n
i
q
u
e
a
n
d
ba
s
i
c
f
or
m
u
l
a
t
i
o
n
s
of
K
i
r
c
hh
of
f
'
s
l
a
w
s
.
T
h
u
s
fa
r
,
p
r
e
vi
o
us
s
t
ud
i
e
s
ha
ve
b
e
g
u
n t
o
e
xa
m
i
ne
t
he
us
e
o
f
p
o
w
e
r
f
l
o
w
i
n F
A
C
T
S
d
e
vi
c
e
s
s
uc
h
a
s
th
y
r
i
s
to
r
c
o
n
tr
o
lle
d
s
er
i
es
co
m
p
en
s
at
o
r
s
co
n
t
r
o
l
s
t
h
e p
o
w
er
f
l
o
w
i
n
t
h
e
ne
t
w
o
r
k,
b
y
T
a
di
k
on
da
e
t a
l.
[1
8
].
T
h
i
s
p
ap
er
d
et
ai
l
s
t
h
e d
ev
el
o
p
m
en
t
o
f
p
o
w
er
f
l
o
w
b
as
ed
o
n
A
M
o
d
i
f
i
ed
B
ack
w
ar
d
-
F
or
w
a
r
d m
e
t
h
od.
T
h
e M
o
d
i
f
i
ed
B
ack
w
ar
d
-
F
o
r
w
ar
d
i
s
o
n
e o
f
t
h
e
m
o
s
t
w
i
de
l
y
us
e
d
m
e
t
h
ods
of
de
v
e
l
op
m
e
n
t
of
po
w
e
r
f
l
o
w
a
n
d
h
as
b
een
ex
t
e
n
s
i
v
el
y
u
s
ed
f
o
r
v
o
l
t
ag
e p
r
o
f
i
l
e an
al
y
s
i
s
.
T
h
es
e
m
et
h
o
d
w
a
s
u
s
ed
t
o
cap
t
u
r
e
t
h
e co
m
p
l
e
x
i
t
i
e
s
o
f
unb
a
l
a
nc
e
d
t
hr
e
e
p
ha
s
e
r
a
d
i
a
l
d
i
s
t
r
i
b
ut
i
o
n s
ys
t
e
m
i
n t
he
2
0
kV
d
i
s
t
r
i
b
ut
i
o
n ne
t
w
o
r
k i
n S
ur
a
b
a
y
a ci
t
y
,
E
as
t
J
a
va
,
I
nd
o
ne
s
i
a
w
i
t
hi
n c
o
ns
i
d
e
r
i
ng i
nj
e
c
t
i
o
n o
f
d
i
s
t
r
i
b
ut
e
d
ge
ne
r
a
t
i
o
n
m
o
d
e
l
s
w
h
e
r
e
th
e
m
o
d
if
ie
d
th
e
m
odi
f
i
e
d 34 B
U
S
I
E
E
E
s
y
s
t
e
m
i
s
a
s
t
e
s
t
t
h
e
e
f
f
e
c
t
i
ve
n
e
s
s
of
t
h
e
pr
opos
e
d a
l
g
or
i
t
hm
.
A
c
t
u
a
lly
th
e
c
o
m
p
le
x
itie
s
o
f
t
h
e
m
a
r
e
f
ir
s
tl
y
t
h
e
lo
a
d
c
h
a
n
ge
c
a
u
s
e
s
t
he
vo
l
t
a
ge
va
l
ue
c
ha
nge
,
s
e
c
o
nd
l
y
vo
l
t
a
ge
s
o
ur
c
e
o
f
m
a
i
n
f
e
e
de
r
i
s
on
l
y
di
s
u
ppor
t
e
d by
m
a
i
n
g
r
i
d (
P
L
N
g
r
i
d)
da
n f
i
n
a
l
l
y
i
n
n
e
t
w
or
k
ope
r
a
t
i
on
,
i
t
i
s
n
ot
a
ppl
i
e
d f
or
D
G
i
n
j
ect
ed
t
o
m
ai
n
g
r
i
d
y
et
.
I
n
g
e
n
er
al
,
t
h
er
ef
o
r
e,
i
t
s
ee
m
s
t
h
a
t
d
ev
el
o
p
m
en
t
of
po
w
e
r
f
l
o
w
ba
s
e
d o
n
a
M
o
d
i
f
i
ed
B
ack
w
ar
d
-
F
o
r
w
a
r
d
m
e
t
h
o
d
w
ill
c
o
n
tr
ib
u
te
to
v
o
l
ta
g
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
e
n
t.
T
h
is
is
a
n
i
m
p
o
r
ta
n
t
i
s
s
ue
f
o
r
f
ut
ur
e
r
e
s
e
a
r
c
h i
n o
p
e
r
a
t
i
o
na
l
a
nd
m
a
na
ge
m
e
nt
o
f
a
d
i
s
t
r
i
b
ut
i
o
n
ne
t
w
o
r
k
.
2.
D
EV
ELO
P
M
EN
T O
F
P
O
W
ER
F
LO
W
IN
UNB
AL
ANC
E
D
T
H
RE
E
P
H
A
S
E
R
A
D
I
A
L
D
IS
TR
I
B
U
TI
O
N
S
Y
S
T
EM
I
n
a
s
t
u
d
y
w
hi
c
h
s
e
t
out
t
o de
t
e
r
m
i
n
e
po
w
e
r
f
l
o
w
,
S
h
i
r
m
o
h
a
m
m
a
di
e
t
a
l
.
[
17]
f
oun
d t
h
a
t
d
ev
el
o
p
m
en
t
o
f
p
o
w
er
f
l
o
w
s
o
l
u
t
i
o
n
al
g
o
r
i
t
h
m
h
ad
t
h
e
f
o
l
l
o
w
i
n
g
g
e
n
er
al
ch
ar
act
er
i
s
t
i
cs
.
T
h
ey
ar
e cap
ab
l
e o
f
s
o
l
vi
ng
r
a
d
i
a
l
a
nd
w
e
a
kl
y
m
e
s
he
d
d
i
s
t
r
i
b
ut
i
o
n ne
t
w
o
r
k
s
w
i
t
h up
t
o
s
e
ve
r
a
l
t
ho
us
a
nd
l
i
ne
s
e
c
t
i
o
ns
(
b
r
a
nc
he
s
)
&
n
ode
s
(
bu
s
e
s
)
,
r
obu
s
t
a
n
d
e
f
f
i
c
i
e
nt
.
T
o be
t
t
e
r
u
n
de
r
s
t
a
nd t
h
e
m
e
c
h
a
n
i
s
m
s
of
de
v
e
l
opm
e
nt
of
po
w
e
r
f
l
o
w
an
d
i
t
s
ef
f
ect
s
,
C
h
an
g
et
.
al
[
1
2
]
an
al
y
s
ed
t
h
e b
ack
-
w
a
r
d/
f
or
w
a
r
d (
B
W
/
B
F
)
s
w
e
e
p
m
e
t
h
od i
s
c
om
m
on
l
y
us
e
d
d
ue
t
o
t
he
c
o
m
p
ut
a
t
i
o
na
l
e
f
f
i
c
i
e
nc
y
a
nd
s
o
l
ut
i
o
n a
c
c
ur
a
c
y.
2.
1.
T
h
e B
a
ck
-
W
a
r
d
/
F
o
r
w
a
r
d
(B
W
/
B
F
) M
e
th
o
d
U
p t
o n
o
w
,
a
num
be
r
of
s
t
u
di
e
s
h
a
v
e
s
h
o
w
n t
h
a
t
t
h
e
a
u
t
h
or
s
pr
opos
e
t
h
e
ba
c
k
-
w
a
rd
/
f
o
r
w
a
rd
(
BW/
BF
)
m
e
t
h
o
d
f
o
r
u
n
b
al
an
ced
t
h
r
ee
-
p
h
a
s
e
r
a
d
ia
l d
is
tr
ib
u
tio
n
s
y
s
te
m
p
o
w
e
r
-
f
l
o
w
an
al
y
s
i
s
.
T
h
es
e m
et
h
o
d
i
n
cl
u
d
es
t
w
o
s
t
ag
e
s
:
t
h
e b
a
ck
w
ar
d
s
t
ag
e a
n
d
t
h
e d
eco
m
p
o
s
ed
f
o
r
w
ar
d
s
t
a
g
e.
I
n
t
h
e b
ack
w
ar
d
s
t
ag
e,
K
i
rc
h
o
ff’
s
C
u
rre
n
t
L
a
w
(K
C
L
)
a
n
d
K
i
rc
h
o
f
f’
s
V
o
l
t
a
g
e
L
a
w
(K
V
L
) a
re
a
p
p
l
i
e
d
to
f
in
d
th
e
c
a
lc
u
la
te
d
v
o
lta
g
e
f
o
r
each
u
p
s
t
r
ea
m
b
u
s
o
f
a
l
i
n
e.
I
n
t
h
e d
eco
m
p
o
s
ed
f
o
r
w
ar
d
s
t
a
g
e,
t
h
e
l
i
n
ear
p
r
o
p
o
r
t
i
o
n
al
p
r
i
n
ci
p
l
es
i
s
e
m
p
l
o
y
ed
t
o
u
p
d
at
e t
h
e v
o
l
t
a
g
e at
each
d
o
w
n
s
t
r
ea
m
b
u
s
.
2.
2.
T
he
M
o
di
f
i
e
d B
a
c
k
-
W
a
r
d
/
F
o
r
w
a
r
d
(B
W
/
B
F
) M
e
th
o
d
T
hi
s
d
e
ve
l
o
p
m
e
nt
o
f
po
w
e
r
f
l
o
w
s
h
e
ds
n
e
w
l
i
gh
t
on t
h
e
m
odi
f
i
e
d ba
c
k
-
w
a
rd
/
f
o
r
w
a
rd
(B
W
/
B
F
)
m
e
t
h
od.
T
h
e
m
odi
f
i
e
d ba
c
k
-
w
a
r
d/
f
or
w
a
r
d (
B
W
/
B
F
)
m
e
t
hod i
s
a
de
v
e
l
opm
e
n
t
of
t
h
e
ba
c
k
-
w
ar
d
/
f
o
r
w
ar
d
(
B
W
/
B
F
)
m
et
h
o
d
w
h
i
c
h
can
p
er
f
o
r
m
t
h
e
co
m
p
u
t
at
i
o
n
al
ef
f
i
ci
en
c
y
a
n
d
s
o
l
u
t
i
o
n
acc
u
r
ac
y
o
f
p
o
we
r
f
l
o
w
an
al
y
s
i
s
.
T
h
e b
ack
w
ar
d
-
f
or
w
a
r
d m
odi
f
i
e
d
m
e
t
h
od i
s
a
bl
e
t
o a
c
c
om
m
oda
t
e
t
h
e
un
ba
l
a
n
c
e
d t
h
r
e
e
-
p
h
as
e o
f
r
a
d
ia
l d
is
tr
ib
u
tio
n
s
y
s
te
m
b
y
u
s
i
n
g
o
f
m
a
t
h
e
m
a
tic
a
l c
a
lc
u
la
tio
n
s
a
n
d
m
o
d
e
li
n
g
s
y
s
te
m
s
.
T
h
e
m
o
d
if
ie
d
b
ack
w
ar
d
-
f
or
w
a
r
d
m
e
t
h
od i
s
a
r
e
l
a
t
i
on
s
hi
p be
t
w
e
e
n
n
ode
s
a
dj
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IJ
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P
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1)
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2
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[B
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
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IJ
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6
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20
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2008
F
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3)
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BC
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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−
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1
−
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0
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0
0
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0
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0
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0
0
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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1
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⎥
⎥
⎥
⎥
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⎥
⎥
⎥
⎤
(4
)
2.
2.
2.
B
C
B
V
M
a
tr
i
x
F
o
r
m
a
ti
o
n
T
he
B
C
B
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a
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a
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a
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on f
r
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e
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n
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c
t
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t
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o
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dopt
e
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A
c
c
or
di
ng
t
o E
qu
a
t
i
on
(
3)
,
B
C
B
V
m
a
t
r
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x
f
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a
t
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on
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s
s
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s
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l
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−
2
=
1
.
1
2
1
−
3
=
1
.
1
2
−
2
.
2
3
1
−
4
=
1
.
1
2
−
2
.
2
3
−
3
.
3
4
1
−
5
=
1
.
1
2
−
2
.
2
3
−
3
.
3
4
−
4
.
4
5
1
−
6
=
1
.
1
2
−
2
.
2
3
−
3
.
3
4
−
4
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4
5
−
5
.
2
6
(5
)
⎣
⎢
⎢
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1
−
2
1
−
3
1
−
4
1
−
5
1
−
6
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=
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1
2
0
0
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0
1
2
2
3
0
0
0
1
2
2
3
3
4
0
0
1
2
2
3
3
4
4
5
0
1
2
2
3
0
0
3
6
⎦
⎥
⎥
⎥
⎤
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⎢
⎢
⎢
⎡
1
2
3
4
5
⎦
⎥
⎥
⎥
⎤
(6
)
[
∆
V
]
=
[
BC
BV
]
[
B]
(7
)
B
C
B
V
m
a
t
r
i
x
c
a
n
be
de
r
i
v
e
d f
r
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m
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qu
a
t
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on
(
7)
a
n
d i
t
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s
j
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d t
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e
t
h
e
r
w
i
t
h B
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B
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m
a
t
r
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T
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r
e
f
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,
i
t
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s
ga
i
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d
a
vo
l
t
a
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d
r
o
p a
s
s
ho
w
n E
q
ua
t
i
o
n (
8
)
.
[
∆
V
]
=
[
B
C
B
V
]
[
B
I
B
C
]
[
I
]
(8
)
B
a
s
e
d
o
n t
hr
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p
ha
s
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a
na
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s
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c
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f
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ack
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b
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
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3.
1.
D
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M
od
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l
as
N
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gat
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P
Q
L
oad
F
o
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u
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a v
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a s
p
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f
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c v
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u
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2.
3.
2.
D
G
M
od
e
l
as
P
V
M
od
e
l
D
G
as
P
V
m
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d
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h
as
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l
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t
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v
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w
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n
l
i
m
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t
ed
r
an
g
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d
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t
can
co
n
t
r
o
l
v
o
l
t
ag
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o
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co
n
n
ec
t
ed
b
u
s
.
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i
t
h
i
n
D
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co
n
s
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a
s
n
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h
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act
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t
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3.
R
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A
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y
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t
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m
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cs
o
f
B
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B
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d
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B
C
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w
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4
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s
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f
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A
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F
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r
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
IJ
E
C
E
V
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l
.
6
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5
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20
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F
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.
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h
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Evaluation Warning : The document was created with Spire.PDF for Python.