I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
w
er
E
ng
ineering
(
I
J
AP
E
)
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t
201
7
,
p
p
.
5
5
~6
2
I
SS
N:
2252
-
8
7
9
2
DOI
:
1
0
.
1
1
5
9
1
/i
j
ap
e.
v
6
.
i2
.
p
p
5
5
-
62
55
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
J
APE
Po
w
er S
y
ste
m
P
e
rfor
m
a
n
ce I
m
pro
v
e
m
en
t
by
O
pt
i
ma
l
Place
m
ent
and Si
z
ing
of
SV
C using
G
en
etic
Algo
rith
m
P
ra
s
a
nth
Dura
is
a
m
y
,
Arul
P
o
nn
us
a
m
y
De
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
E
n
g
in
e
e
rin
g
,
Ja
y
a
r
a
m
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
,
T
h
u
ra
i
y
u
r,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
n
2
,
2
0
1
7
R
ev
i
s
ed
J
u
l 8
,
2
0
1
7
A
cc
ep
ted
J
u
l 2
3
,
2
0
1
7
T
h
e
p
o
we
r
s
y
ste
m
lo
ss
m
in
i
m
iza
t
io
n
b
e
c
o
m
e
s
m
o
re
i
m
p
o
rtan
t
a
s
t
h
e
n
e
e
d
o
f
p
o
w
e
r
g
e
n
e
ra
ti
o
n
is
m
o
re
re
c
e
n
t
d
a
y
s.
T
h
e
lo
ss
m
in
i
m
iza
ti
o
n
imp
ro
v
e
s
th
e
v
o
l
tag
e
p
ro
f
il
e
w
h
ich
i
m
p
ro
v
e
s
t
h
e
lo
a
d
a
b
il
i
ty
o
f
th
e
s
y
ste
m
.
In
m
a
n
y
t
y
p
e
s
o
f
f
lex
ib
l
e
A
C
tran
s
m
issio
n
s
y
ste
m
(F
A
CT
S
)
d
e
v
ice
s
sta
ti
c
v
a
r
c
o
m
p
e
n
sa
to
rs
(S
V
C)
a
re
c
o
st
v
ise
it
is
a
f
f
o
rd
a
b
le
a
n
d
it
im
p
ro
v
e
s
th
e
sy
ste
m
p
e
rf
o
r
m
a
n
c
e
w
it
h
les
se
r
siz
e
.
He
r
e
S
V
C
is
o
p
ti
m
a
ll
y
p
lac
e
d
in
a
tes
t
s
y
ste
m
o
f
3
0
b
u
s
s
y
ste
m
.
G
e
n
e
ti
c
a
lg
o
rit
h
m
is
u
se
d
to
f
in
d
th
e
o
p
t
im
a
l
re
su
lt
s.
K
ey
w
o
r
d
:
F
A
C
T
S
Gen
etic
al
g
o
r
ith
m
L
o
s
s
m
i
n
i
m
izatio
n
Op
ti
m
al
p
lace
m
en
t
SVC
Co
p
y
rig
h
t
©
201
7
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
P
r
ash
an
t
h
Du
r
ai
s
a
m
y
,
Dep
ar
t
m
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
i
n
ee
r
in
g
,
J
ay
ar
a
m
co
lle
g
e
o
f
E
n
g
g
.
An
d
T
ec
h
,
T
h
u
r
r
ai
y
u
r
,
T
r
ich
y
,
ta
m
iln
ad
u
,
I
n
d
ia.
E
m
ail: p
r
as
h
an
t
h
d
2
2
2
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
As
th
e
g
r
o
w
t
h
o
f
co
m
p
le
x
elec
tr
ical
p
o
w
er
n
e
t
w
o
r
k
in
c
r
ea
s
es,
a
n
e
w
ap
p
r
o
ac
h
ca
lled
f
lex
ib
le
alter
n
ati
n
g
cu
r
r
en
t
tr
a
n
s
m
is
s
i
o
n
s
y
s
te
m
(
F
A
C
T
S)
h
a
s
b
ee
n
i
m
p
le
m
en
ted
to
in
cr
ea
s
e
t
h
e
ca
p
ab
ilit
y
o
f
t
h
e
ex
is
t
in
g
tr
a
n
s
m
is
s
io
n
s
y
s
te
m
s
.
T
h
r
o
u
g
h
t
h
is
ap
p
r
o
ac
h
,
n
e
w
p
o
w
er
elec
tr
o
n
ic
co
n
tr
o
lle
r
s
w
it
h
h
i
g
h
cu
r
r
en
t,
h
ig
h
v
o
lta
g
e
w
er
e
in
tr
o
d
u
ce
d
to
co
n
tr
o
l
v
o
lta
g
e
lev
el
an
d
p
o
w
er
f
lo
w
s
o
n
tr
a
n
s
m
is
s
i
o
n
s
y
s
te
m
w
it
h
o
u
t
d
ec
r
ea
s
in
g
t
h
e
s
y
s
te
m
s
tab
ilit
y
an
d
s
ec
u
r
it
y
[
1
-
3
]
.
Hin
g
o
r
an
i,
as
t
h
e
p
io
n
ee
r
h
as
p
u
t
f
o
r
w
ar
d
FAC
T
S,
an
d
aim
ed
to
tr
an
s
p
o
r
t
th
e
co
n
tr
o
l
t
ec
h
n
o
lo
g
y
b
ased
o
n
th
y
r
is
to
r
i
n
to
t
h
e
AC
s
y
s
te
m
.
F
AC
T
S
is
ad
o
p
ted
m
o
d
er
n
p
o
w
er
elec
tr
o
n
ic
s
ap
p
licatio
n
at
t
h
e
i
m
p
o
r
tan
t
lo
ca
tio
n
o
f
t
h
e
tr
a
n
s
m
i
s
s
io
n
s
y
s
te
m
in
o
r
d
er
to
co
n
tr
o
l
an
d
ad
j
u
s
t
o
n
e
o
r
m
o
r
e
o
f
th
e
m
ain
p
ar
am
eter
s
o
f
th
e
tr
a
n
s
m
i
s
s
io
n
s
y
s
te
m
,
to
en
h
a
n
ce
t
h
e
v
al
u
e
o
f
ac
tr
an
s
m
i
s
s
io
n
ass
et
s
.
T
h
ese
p
ar
am
eter
s
in
cl
u
d
e
v
o
lta
g
es,
i
m
p
ed
a
n
ce
,
p
h
ase
a
n
g
le,
c
u
r
r
en
t,
ac
t
iv
e
p
o
w
er
a
n
d
r
ea
ctiv
e
p
o
w
er
.
T
h
e
ap
p
licatio
n
o
f
F
A
C
T
S
p
r
o
v
ed
th
at
t
h
e
tec
h
n
o
lo
g
y
b
r
in
g
s
m
a
n
y
b
en
e
f
i
ts
to
t
h
e
w
o
r
ld
a
n
d
th
er
e
a
r
e
m
a
n
y
ar
ea
s
o
f
i
m
p
r
o
v
e
m
en
t.
I
n
t
h
e
m
ea
n
ti
m
e,
cu
r
r
en
t r
esear
ch
es a
r
e
f
o
cu
s
ed
to
in
cr
ea
s
e
its
ef
f
ec
ti
v
e
n
es
s
[
4
]
.
F
A
C
T
S
i
n
v
o
l
v
e
r
eliab
le
a
n
d
h
ig
h
-
s
p
ee
d
p
o
w
er
elec
tr
o
n
ic
s
w
itc
h
es
in
s
tead
o
f
m
e
ch
an
ica
ll
y
co
n
tr
o
lled
d
ev
ices.
FAC
T
S
is
also
s
u
p
p
o
r
ted
b
y
ad
v
an
ce
s
in
d
ig
ital
p
r
o
tectiv
e
r
ela
y
s
,
d
ig
ital
co
n
tr
o
ls
,
in
te
g
r
ated
co
m
m
u
n
icatio
n
s
a
n
d
ad
v
an
ce
d
co
n
tr
o
l
ce
n
ter
s
.
T
h
e
h
ea
r
t
o
f
F
AC
T
S
is
t
h
y
r
is
to
r
s
:
s
m
all,
h
i
g
h
v
o
ltag
e,
s
e
m
ico
n
d
u
cto
r
b
ased
d
ev
ices
th
a
t
ca
n
s
w
itc
h
elec
tr
icit
y
at
m
e
g
a
-
w
a
tt
lev
e
ls
w
it
h
in
m
illi
s
ec
o
n
d
s
[
5
-
7
]
.
Her
e
co
s
t
-
e
f
f
ec
t
iv
e
SVC
d
e
v
i
ce
s
w
h
ic
h
ar
e
u
s
ed
to
i
m
p
r
o
v
e
th
e
v
o
lta
g
e
s
tab
il
it
y
i
f
p
lace
d
o
p
tim
all
y
it r
ed
u
ce
s
th
e
lo
s
s
also
is
u
s
ed
as F
A
C
T
S d
ev
ice
f
o
r
i
m
p
r
o
v
i
n
g
v
o
ltag
e
p
r
o
f
ile
a
n
d
r
ed
u
cin
g
th
e
lo
s
s
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t 2
0
1
7
:
55
–
62
56
2.
P
RO
B
L
E
M
DE
F
I
NIT
I
O
N
2
.
1
.
SVC
m
o
deli
ng
Fig
u
r
e
1
s
h
o
w
s
eq
u
i
v
alen
t
ci
r
cu
it
o
f
an
SV
C
co
n
n
ec
ted
to
a
ter
m
i
n
al
.
T
h
e
S
VC
is
m
o
d
eled
b
y
a
s
h
u
n
t
v
ar
iab
le
ad
m
itta
n
ce
an
d
ca
n
b
e
p
lace
d
eith
er
at
th
e
ter
m
i
n
al
b
u
s
o
f
a
tr
an
s
m
is
s
io
n
li
n
e
o
r
in
th
e
m
id
d
le
o
f
a
lo
n
g
lin
e.
C
o
n
s
id
er
i
n
g
t
h
e
SVC
w
ith
o
u
t
lo
s
s
e
s
,
th
e
ad
m
itta
n
ce
o
n
l
y
h
as
it
s
i
m
a
g
i
n
a
r
y
co
m
p
o
n
en
t
a
n
d
it
ca
n
tak
e
v
a
lu
e
s
in
a
s
p
ec
i
f
ie
d
r
an
g
e
(
u
s
u
all
y
b
et
w
ee
n
0
an
d
th
e
m
a
x
i
m
u
m
SVC
ca
p
ac
it
y
s
t
u
d
ied
,
h
er
e
5
MV
A
r
)
.
T
h
is
is
d
en
o
ted
b
y
:
(
1
)
Fig
u
r
e
1
.
E
q
u
iv
ale
n
t c
ir
cu
it o
f
an
SVC
co
n
n
ec
ted
to
a
ter
m
i
n
al
I
n
th
i
s
ca
s
e,
o
n
l
y
o
n
e
ter
m
o
f
th
e
n
o
d
al
ad
m
itta
n
ce
s
m
atr
i
x
is
m
o
d
if
ied
,
co
r
r
esp
o
n
d
in
g
to
t
h
e
n
o
d
e
w
h
er
e
th
e
SVC
i
s
co
n
n
ec
ted
:
(
2
)
So
,
th
e
Yb
u
s
m
atr
i
x
m
atr
i
x
m
o
d
if
ied
as b
elo
w
[Y
bus
]
=
(
)
(
3
)
Her
e
y
ik
–
ad
m
itta
n
ce
v
alu
e
o
f
b
u
s
i t
o
k
y
i
k
0
-
co
m
p
en
s
ato
r
ad
m
itta
n
ce
y
s
v
c
–
SV
C
ad
m
itta
n
ce
v
al
ue
Y
ii
–
s
elf
ad
m
ita
n
ce
T
h
e
ab
o
v
e
y
b
u
s
m
atr
i
x
is
ta
k
e
n
in
p
o
w
er
f
lo
w
a
n
al
y
s
is
f
o
r
ca
lcu
latio
n
o
f
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
2
.
2
.
O
bje
ct
iv
e
f
un
ct
io
n
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
p
o
w
er
s
y
s
te
m
lo
s
s
m
i
n
i
m
izat
io
n
,
w
h
ic
h
is
g
iv
e
n
b
elo
w
Min
i
m
ize
T
o
tal
L
o
s
s
=
∑
(
4
)
=
∑
(
5
)
W
h
er
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Mo
d
elin
g
,
A
n
a
lysi
s
a
n
d
C
o
n
tr
o
l o
f D
iffer
en
t D
C
-
DC
C
o
n
ye
r
ter To
p
o
lo
g
ies…
(
Mo
h
a
mma
d
Ta
u
q
u
ir
I
q
b
a
l
)
57
n
-
n
u
m
b
er
o
f
b
r
an
c
h
es
l
-
li
n
e
n
u
m
b
er
Vi
–
s
en
d
i
n
g
e
n
d
v
o
lta
g
e
Vj
–
r
ec
eiv
in
g
e
n
d
v
o
ltag
e
δi
–
s
en
d
i
n
g
e
n
d
v
o
lta
g
e
an
g
le
δj
–
r
ec
eiv
in
g
e
n
d
v
o
ltag
e
a
n
g
le
Yij
–
s
en
d
in
g
e
n
d
to
r
ec
eiv
in
g
e
n
d
lin
e
ad
m
itta
n
ce
2
.
3
.
Co
ns
t
ra
ints
Y
sv
c
l
i
m
its
(
6
)
(
7
)
3.
G
E
NE
T
I
C
A
L
G
O
RI
T
H
M
A
g
e
n
etic
al
g
o
r
ith
m
is
a
p
r
o
b
ab
ilis
tic
s
ea
r
c
h
tec
h
n
iq
u
e
t
h
at
c
o
m
p
u
tatio
n
all
y
s
i
m
u
late
s
t
h
e
p
r
o
ce
s
s
o
f
b
io
lo
g
ical
ev
o
l
u
tio
n
.
I
t
m
i
m
ic
s
ev
o
l
u
tio
n
i
n
n
at
u
r
e
b
y
r
ep
ea
ted
l
y
alter
i
n
g
a
p
o
p
u
latio
n
o
f
ca
n
d
id
ate
s
o
l
u
tio
n
s
u
n
t
il a
n
o
p
ti
m
al
s
o
l
u
tio
n
i
s
f
o
u
n
d
.
T
h
e
GA
ev
o
lu
tio
n
ar
y
c
y
cle
s
tar
ts
w
ith
a
r
an
d
o
m
l
y
s
elec
te
d
in
itial
p
o
p
u
latio
n
.
T
h
e
ch
an
g
es
to
th
e
p
o
p
u
latio
n
o
cc
u
r
t
h
r
o
u
g
h
th
e
p
r
o
ce
s
s
es
o
f
s
elec
tio
n
b
ased
o
n
f
it
n
ess
,
an
d
alter
atio
n
u
s
in
g
cr
o
s
s
o
v
er
a
n
d
m
u
tatio
n
.
T
h
e
ap
p
licatio
n
o
f
s
elec
tio
n
a
n
d
alter
atio
n
lead
s
t
o
a
p
o
p
u
latio
n
w
i
th
a
h
i
g
h
er
p
r
o
p
o
r
tio
n
o
f
b
etter
s
o
lu
tio
n
s
.
T
h
e
ev
o
lu
tio
n
ar
y
c
y
cle
co
n
ti
n
u
e
s
u
n
til
an
ac
ce
p
t
ab
le
s
o
lu
tio
n
is
f
o
u
n
d
i
n
th
e
c
u
r
r
en
t
g
e
n
er
atio
n
o
f
p
o
p
u
latio
n
,
o
r
s
o
m
e
co
n
tr
o
l p
ar
a
m
eter
s
u
c
h
a
s
t
h
e
n
u
m
b
er
o
f
g
e
n
er
atio
n
s
i
s
e
x
ce
ed
ed
.
Fi
g
u
r
e
2
s
h
o
w
s
g
e
n
etic
alg
o
r
ith
m
e
v
o
lu
tio
n
ar
y
c
y
cle
.
Fig
u
r
e
2
.
Gen
etic
al
g
o
r
ith
m
e
v
o
lu
tio
n
ar
y
c
y
cle
T
h
e
s
m
a
lles
t
u
n
i
t
o
f
a
g
en
et
ic
alg
o
r
ith
m
i
s
ca
lled
a
g
en
e,
wh
ich
r
ep
r
esen
ts
a
u
n
it
o
f
in
f
o
r
m
atio
n
i
n
th
e
p
r
o
b
le
m
d
o
m
ai
n
.
A
s
er
ies
o
f
g
en
e
s
,
k
n
o
w
n
as
a
ch
r
o
m
o
s
o
m
e,
r
ep
r
ese
n
ts
o
n
e
p
o
s
s
ib
le
s
o
lu
tio
n
to
t
h
e
p
r
o
b
lem
.
E
ac
h
g
e
n
e
i
n
th
e
c
h
r
o
m
o
s
o
m
e
r
ep
r
esen
t
s
o
n
e
co
m
p
o
n
en
t o
f
t
h
e
s
o
lu
tio
n
p
atter
n
.
T
h
e
m
o
s
t c
o
m
m
o
n
f
o
r
m
o
f
r
e
p
r
esen
tin
g
a
s
o
l
u
tio
n
as a
ch
r
o
m
o
s
o
m
e
i
s
a
s
tr
i
n
g
o
f
b
in
ar
y
d
ig
it
s
.
E
ac
h
b
it
in
t
h
is
s
tr
in
g
i
s
a
g
e
n
e.
T
h
e
p
r
o
ce
s
s
o
f
co
n
v
er
ti
n
g
t
h
e
s
o
lu
tio
n
f
r
o
m
its
o
r
i
g
in
a
l
f
o
r
m
i
n
to
th
e
b
it
s
tr
i
n
g
i
s
k
n
o
w
n
a
s
co
d
in
g
.
T
h
e
s
p
ec
i
f
ic
co
d
in
g
s
c
h
e
m
e
u
s
ed
i
s
ap
p
licatio
n
d
ep
en
d
en
t.
T
h
e
s
o
l
u
tio
n
b
it
s
tr
in
g
s
ar
e
d
ec
o
d
ed
to
en
ab
le
th
eir
ev
alu
a
tio
n
u
s
in
g
a
f
itn
e
s
s
m
ea
s
u
r
e.
I
n
b
io
lo
g
ical
ev
o
l
u
tio
n
,
o
n
l
y
t
h
e
f
ittes
t
s
u
r
v
i
v
e
an
d
t
h
eir
g
e
n
e
p
o
o
l
co
n
tr
ib
u
tes
to
t
h
e
cr
ea
tio
n
o
f
t
h
e
n
ex
t
g
en
er
atio
n
.
Select
io
n
i
n
GA
is
also
b
ased
o
n
a
s
i
m
ilar
p
r
o
ce
s
s
.
I
n
a
co
m
m
o
n
f
o
r
m
o
f
s
elec
tio
n
,
k
n
o
w
n
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t 2
0
1
7
:
55
–
62
58
f
it
n
es
s
p
r
o
p
o
r
tio
n
al
s
elec
tio
n
,
ea
ch
ch
r
o
m
o
s
o
m
e
’
s
l
ik
el
ih
o
o
d
o
f
b
ein
g
s
elec
ted
as
a
g
o
o
d
o
n
e
is
p
r
o
p
o
r
tio
n
al
to
its
f
it
n
es
s
v
al
u
e.
T
h
e
alter
atio
n
s
tep
in
th
e
g
en
etic
alg
o
r
ith
m
r
ef
in
e
s
th
e
g
o
o
d
s
o
lu
tio
n
f
r
o
m
th
e
c
u
r
r
en
t
g
e
n
er
atio
n
to
p
r
o
d
u
ce
th
e
n
ex
t
g
e
n
er
atio
n
o
f
ca
n
d
id
ate
s
o
lu
tio
n
s
.
I
t is ca
r
r
ied
o
u
t b
y
p
er
f
o
r
m
in
g
cr
o
s
s
o
v
e
r
an
d
m
u
ta
tio
n
.
C
r
o
s
s
o
v
er
m
a
y
b
e
r
eg
ar
d
ed
a
s
ar
tif
icial
m
ati
n
g
i
n
w
h
ic
h
c
h
r
o
m
o
s
o
m
es
f
r
o
m
t
w
o
i
n
d
iv
i
d
u
als
ar
e
co
m
b
i
n
ed
to
cr
ea
te
t
h
e
c
h
r
o
m
o
s
o
m
e
f
o
r
t
h
e
n
ex
t
g
en
er
atio
n
.
T
h
is
i
s
d
o
n
e
b
y
s
p
lici
n
g
t
w
o
ch
r
o
m
o
s
o
m
e
s
f
r
o
m
t
w
o
d
i
f
f
er
en
t
s
o
lu
tio
n
s
at
a
cr
o
s
s
o
v
er
p
o
in
t
an
d
s
w
ap
p
in
g
t
h
e
s
p
liced
p
ar
ts
.
T
h
e
id
ea
is
t
h
at
s
o
m
e
g
e
n
es
w
it
h
g
o
o
d
ch
ar
ac
ter
is
tic
s
f
r
o
m
o
n
e
ch
r
o
m
o
s
o
m
e
m
a
y
as
a
r
es
u
lt
co
m
b
in
e
w
it
h
s
o
m
e
g
o
o
d
g
e
n
es
in
th
e
o
th
er
ch
r
o
m
o
s
o
m
e
to
cr
ea
te
a
b
etter
s
o
lu
tio
n
r
ep
r
ese
n
ted
b
y
th
e
n
e
w
c
h
r
o
m
o
s
o
m
e
.
Fig
u
r
e
3
s
h
o
ws
ch
r
o
m
o
s
o
m
e
r
ep
r
ese
n
t
atio
n
.
Fi
g
u
r
e
3
.
C
h
r
o
m
o
s
o
m
e
r
ep
r
esen
tatio
n
Mu
tatio
n
is
a
r
an
d
o
m
ad
j
u
s
t
m
en
t
in
t
h
e
g
en
e
tic
co
m
p
o
s
i
tio
n
.
I
t
is
u
s
e
f
u
l
f
o
r
in
tr
o
d
u
cin
g
n
e
w
ch
ar
ac
ter
is
tic
s
in
a
p
o
p
u
latio
n
–
s
o
m
et
h
i
n
g
n
o
t
ac
h
ie
v
ed
th
r
o
u
g
h
cr
o
s
s
o
v
er
alo
n
e.
C
r
o
s
s
o
v
er
o
n
l
y
r
ea
r
r
an
g
e
s
ex
i
s
t
in
g
ch
ar
ac
ter
is
tics
to
g
i
v
e
n
e
w
co
m
b
in
at
io
n
s
.
Fo
r
ex
a
m
p
le,
if
t
h
e
f
ir
s
t
b
it
in
ev
er
y
ch
r
o
m
o
s
o
m
e
o
f
a
g
en
er
atio
n
h
ap
p
en
s
to
b
e
a
1
,
an
y
n
e
w
c
h
r
o
m
o
s
o
m
e
cr
ea
ted
th
r
o
u
g
h
cr
o
s
s
o
v
er
w
ill also
h
a
v
e
1
as th
e
f
ir
s
t b
it.
T
h
e
m
u
tatio
n
o
p
er
ato
r
ch
an
g
es
t
h
e
cu
r
r
en
t
v
al
u
e
o
f
a
g
en
e
to
a
d
if
f
er
en
t
o
n
e.
Fo
r
b
it
s
tr
in
g
ch
r
o
m
o
s
o
m
e,
t
h
i
s
ch
a
n
g
e
a
m
o
u
n
t
s
to
f
lip
p
i
n
g
a
0
b
it to
a
1
o
r
v
ice
v
er
s
a.
A
lt
h
o
u
g
h
u
s
e
f
u
l
f
o
r
in
tr
o
d
u
ci
n
g
n
e
w
tr
aits
in
th
e
s
o
l
u
tio
n
p
o
o
l,
m
u
tat
io
n
s
ca
n
b
e
co
u
n
ter
p
r
o
d
u
ctiv
e,
an
d
ap
p
lied
o
n
ly
i
n
f
r
eq
u
e
n
tl
y
an
d
r
an
d
o
m
l
y
T
h
e
s
tep
s
in
th
e
t
y
p
ical
g
en
eti
c
alg
o
r
ith
m
f
o
r
f
in
d
i
n
g
a
s
o
lu
t
io
n
to
a
p
r
o
b
lem
ar
e
lis
ted
b
elo
w
:
a.
C
r
ea
te
an
i
n
itial so
l
u
tio
n
p
o
p
u
latio
n
o
f
a
ce
r
tain
s
ize
r
an
d
o
m
l
y
b.
E
v
alu
a
te
ea
ch
s
o
l
u
tio
n
i
n
t
h
e
c
u
r
r
en
t g
e
n
er
atio
n
an
d
ass
ig
n
it
a
f
itn
e
s
s
v
al
u
e.
c.
S
elec
t “
g
o
o
d
”
s
o
lu
tio
n
s
b
ased
o
n
f
it
n
es
s
v
al
u
e
a
n
d
d
is
ca
r
d
th
e
r
est.
d.
I
f
ac
ce
p
tab
le
s
o
lu
tio
n
(
s
)
f
o
u
n
d
in
t
h
e
cu
r
r
en
t
g
e
n
er
atio
n
o
r
m
a
x
i
m
u
m
n
u
m
b
er
o
f
g
e
n
er
atio
n
s
is
ex
ce
ed
ed
th
en
s
to
p
s
.
e.
A
lter
t
h
e
s
o
l
u
tio
n
p
o
p
u
latio
n
u
s
in
g
cr
o
s
s
o
v
er
a
n
d
m
u
tatio
n
to
cr
ea
te
a
n
e
w
g
en
er
atio
n
o
f
s
o
l
u
tio
n
s
.
f.
Go
to
s
tep
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Mo
d
elin
g
,
A
n
a
lysi
s
a
n
d
C
o
n
tr
o
l o
f D
iffer
en
t D
C
-
DC
C
o
n
ye
r
ter To
p
o
lo
g
ies…
(
Mo
h
a
mma
d
Ta
u
q
u
ir
I
q
b
a
l
)
59
4.
I
M
P
L
E
M
E
NT
AT
I
O
N
F
L
O
WCH
ART
Fig
u
r
e
4
s
h
o
w
s
f
lo
w
c
h
ar
t o
f
i
m
p
le
m
tatio
n
.
Fig
u
r
e
4
.
Flo
w
c
h
ar
t o
f
i
m
p
le
m
tatio
n
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
I
E
E
E
3
0
b
u
s
s
y
s
te
m
i
s
u
s
ed
to
test
th
e
o
p
ti
m
a
l
s
izi
n
g
an
d
p
lace
m
e
n
t
o
f
SV
C
co
n
ce
p
t.
T
h
e
s
y
s
te
m
h
a
s
2
8
3
.
4
MW
lo
a
d
o
f
r
ea
l
p
o
w
er
a
n
d
1
2
6
.
2
Mv
ar
o
f
r
ea
ctiv
e
p
o
w
er
w
it
h
1
0
0
MV
A
a
s
B
ase
p
o
w
er
.
W
ith
o
u
t S
VC
it p
r
o
d
u
ce
s
1
7
.
5
9
9
MW
r
ea
l
p
o
w
er
lo
s
s
e
s
.
Fig
u
r
e
5
s
h
o
w
s
th
e
b
ef
o
r
e
a
n
d
af
ter
p
lace
m
e
n
t
o
f
S
VC
.
T
h
e
g
en
e
tic
al
g
o
r
ith
m
is
r
u
n
f
o
r
5
0
0
iter
atio
n
s
a
n
d
5
0
p
o
p
u
latio
n
(
ch
r
o
m
o
s
o
m
es).
I
d
en
ti
f
ied
b
est b
u
s
is
6
t
h
b
u
s
a
n
d
th
e
p
o
w
er
S
VC
v
al
u
e
p
lace
d
i
s
1
.
3
7
7
9
p
.
u
o
f
ad
m
itta
n
ce
.
T
h
e
p
o
w
er
lo
s
s
r
ed
u
ce
d
to
6
.
2
2
9
9
MW
.
T
h
e
lo
s
s
p
er
ce
n
tag
e
i
m
p
r
o
v
ed
is
6
4
.
6
%.
S
t
a
r
t
I
n
i
t
i
a
l
i
z
e
B
u
s
d
a
t
a
,
L
i
n
e
d
a
t
a
a
n
d
g
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
p
a
r
a
me
t
e
r
s
(
p
o
p
u
l
a
t
i
o
n
si
z
e
,
i
t
e
r
a
t
i
o
n
c
o
u
n
t
,
mu
t
a
t
i
o
n
a
n
d
c
r
o
ss o
v
e
r
p
r
o
b
a
b
i
l
i
t
y
)
Ev
a
l
u
a
t
e
F
i
t
n
e
ss v
a
l
u
e
u
s
i
n
g
e
q
(
5
)
i
n
n
e
w
t
o
n
R
a
p
h
so
n
p
o
w
e
r
f
l
o
w
S
e
l
e
c
t
g
o
o
d
so
l
u
t
i
o
n
s (l
e
sse
r
l
o
ss)
C
r
e
a
t
e
P
o
p
u
l
a
t
i
o
n
s
a
s
c
h
r
o
mo
so
me
s (S
i
z
e
a
n
d
p
l
a
c
e
s)
C
r
o
ss o
v
e
r
t
h
e
w
o
r
st
so
l
u
t
i
o
n
s
mu
t
a
t
i
o
n
En
d
i
f
t
h
e
i
t
e
r
a
t
i
o
n
c
o
u
n
t
i
s l
a
st
I
n
c
r
e
me
n
t
I
t
e
r
a
t
i
o
n
c
o
u
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t 2
0
1
7
:
55
–
62
60
Fig
u
r
e
5
.
A
f
ter
an
d
b
ef
o
r
e
p
lace
m
en
t o
f
SV
C
T
h
e
v
o
ltag
e
i
m
p
r
o
v
e
m
en
t
i
n
d
icate
s
t
h
at
t
h
e
i
n
cr
ea
s
e
i
n
lo
ad
ab
ilit
y
o
f
t
h
e
s
y
s
te
m
.
Fig
u
r
e
6
s
h
o
w
s
th
e
v
o
ltag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
en
t
in
p
er
ce
n
ta
g
e
a
n
d
b
ar
ch
ar
t.
Fig
u
r
e
7
s
h
o
w
s
th
e
p
o
w
er
f
a
cto
r
i
m
p
r
o
v
e
m
e
n
t
p
er
ce
n
tag
e
i
n
b
ar
ch
ar
t.
Fig
u
r
e
6
.
Vo
ltag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
e
n
t i
n
%
Fig
u
r
e
7
.
P
er
ce
n
tag
e
o
f
p
o
w
er
f
ac
to
r
i
m
p
r
o
v
e
m
en
t i
n
ea
ch
b
u
s
0.95
1
1.05
1.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
I
EEE 30
b
u
s
s
y
s
t
em
V
o
lt
ag
e
p
r
o
fi
le
W
i
th
S
V
C
V
o
l
tag
e
in
pu
W
i
th
o
u
t
S
V
C
V
o
l
tag
e
in
p
u
0
1
2
3
4
Bus
n
u
mb
e
r
C
h
an
g
e i
n
v
ol
t
ag
e
in %
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
b
u
s
n
u
mb
e
r
% of
p
owe
r
f
ac
t
or
im
p
r
ov
m
en
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Mo
d
elin
g
,
A
n
a
lysi
s
a
n
d
C
o
n
tr
o
l o
f D
iffer
en
t D
C
-
DC
C
o
n
ye
r
ter To
p
o
lo
g
ies…
(
Mo
h
a
mma
d
Ta
u
q
u
ir
I
q
b
a
l
)
61
T
h
e
T
ab
le
1
s
h
o
w
s
t
h
e
w
i
th
a
n
d
w
it
h
o
u
t
SV
C
p
lace
m
e
n
t.
T
h
e
T
ab
le
1
r
ep
r
esen
ts
th
e
v
o
lt
ag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
en
t
in
ea
c
h
b
u
s
a
f
ter
an
d
b
ef
o
r
e
p
lacin
g
S
VC
.
T
h
e
5
th
an
d
6
t
h
co
lu
m
n
i
n
d
icate
s
t
h
e
p
o
w
er
i
n
j
ec
tio
n
at
ea
ch
b
u
s
-
v
e
s
y
m
b
o
l
in
d
ica
tes
lo
ad
an
d
+v
e
s
y
m
b
o
l
in
d
ic
ated
g
en
er
atio
n
.
T
h
e
r
ea
l
p
o
w
er
g
en
er
atio
n
f
r
o
m
s
lack
b
u
s
is
r
ed
u
ce
d
d
u
e
to
t
h
e
SV
C
p
lace
m
e
n
t
a
n
d
lo
s
s
es
g
o
t
r
ed
u
ce
d
.
T
h
e
7
th
an
d
8
th
co
lu
m
n
s
h
o
w
s
t
h
e
p
o
w
er
f
ac
to
r
i
m
p
r
o
v
e
m
e
n
t
a
f
t
er
an
d
b
ef
o
r
e
p
lace
m
en
t
o
f
S
VC
.
la
s
t
co
l
u
m
n
s
h
o
w
s
th
e
i
m
p
r
o
v
e
m
en
t
o
f
p
o
w
er
f
ac
to
r
af
ter
p
lacin
g
t
h
e
SV
C
.
A
t
3
0
th
b
u
s
t
h
e
p
o
w
er
f
ac
to
r
i
m
p
r
o
v
e
m
en
t
i
s
h
i
g
h
.
Fro
m
t
h
is
r
esu
lt
s
it
ca
n
b
e
co
n
clu
d
ed
t
h
at
a
s
i
n
g
le
S
VC
p
lace
m
en
t
at
6
t
h
b
u
s
i
n
cr
ea
s
e
s
t
h
e
lo
ad
ab
ilit
y
,
r
ed
u
ce
s
th
e
l
o
s
s
es
a
n
d
i
n
cr
ea
s
e
s
p
o
w
er
f
ac
to
r
an
d
v
o
ltag
e
p
r
o
f
ile.
An
d
it
ca
n
b
e
n
o
ted
t
h
at
p
lacin
g
at
6
th
b
u
s
n
o
t
o
n
l
y
e
f
f
e
ctin
g
o
n
6
t
h
b
u
s
i
t
i
m
p
r
o
v
es t
h
e
o
v
er
all
s
y
s
te
m
p
er
f
o
r
m
an
ce.
T
ab
le
1
.
W
ith
an
d
w
it
h
o
u
t S
V
C
P
lace
m
en
t V
o
ltag
e,
P
o
w
er
I
n
j
ec
tio
n
an
d
P
o
w
er
Facto
r
b
u
s
n
o
.
W
i
t
h
S
V
C
V
o
l
t
a
g
e
i
n
pu
W
i
t
h
o
u
t
S
V
C
V
o
l
t
a
g
e
i
n
pu
%
i
n
c
r
e
a
se
i
n
v
o
l
t
a
g
e
w
i
t
h
S
V
C
p
o
w
e
r
i
n
j
e
c
t
i
o
n
w
i
t
h
o
u
t
sv
c
p
o
w
e
r
i
n
j
e
c
t
i
o
n
w
i
t
h
S
V
C
p
o
w
e
r
F
a
c
t
o
r
w
i
t
h
o
u
t
S
V
C
p
o
w
e
r
F
a
c
t
o
r
%
i
mp
r
o
v
e
-
me
n
t
p
o
w
e
r
F
a
c
t
o
r
1
1
.
0
6
1
.
0
6
0
.
0
0
1
0
5
.
5
7
2
6
1
.
0
0
1
.
0
0
1
.
0
0
0
.
0
0
2
1
.
0
4
1
.
0
4
0
.
0
0
1
8
.
3
0
1
8
.
3
0
1
.
0
0
1
.
0
0
0
.
3
9
3
1
.
0
6
1
.
0
2
3
.
7
9
-
2
.
4
0
-
2
.
4
0
1
.
0
0
0
.
9
9
0
.
8
5
4
1
.
0
4
1
.
0
1
2
.
7
5
-
7
.
6
0
-
7
.
6
0
1
.
0
0
0
.
9
9
1
.
2
5
5
1
.
0
1
1
.
0
1
0
.
0
0
-
9
4
.
2
0
-
94.
20
0
.
9
9
0
.
9
7
2
.
0
1
6
1
.
0
3
1
.
0
1
2
.
1
5
0
.
0
0
0
.
0
0
1
.
0
0
0
.
9
8
1
.
8
1
7
1
.
0
2
1
.
0
0
1
.
2
8
-
2
2
.
8
0
-
2
2
.
8
0
0
.
9
9
0
.
9
7
2
.
0
8
8
1
.
0
2
1
.
0
1
1
.
0
0
-
3
0
.
0
0
-
3
0
.
0
0
1
.
0
0
0
.
9
8
2
.
0
0
9
1
.
0
6
1
.
0
5
1
.
2
8
0
.
0
0
0
.
0
0
0
.
9
9
0
.
9
7
2
.
5
0
10
1
.
0
6
1
.
0
4
1
.
4
9
-
5
.
8
0
-
5
.
8
0
0
.
9
9
0
.
9
6
2
.
8
4
11
1
.
0
8
1
.
0
8
0
.
0
0
0
.
0
0
0
.
0
0
0
.
9
9
0
.
9
7
2
.
5
0
12
1
.
0
7
1
.
0
6
1
.
0
7
-
1
1
.
2
0
-
1
1
.
2
0
0
.
9
9
0
.
9
6
2
.
5
2
13
1
.
0
7
1
.
0
7
0
.
0
0
0
.
0
0
0
.
0
0
0
.
9
9
0
.
9
6
2
.
5
2
14
1
.
0
5
1
.
0
4
1
.
1
2
-
6
.
2
0
-
6
.
2
0
0
.
9
9
0
.
9
6
2
.
7
3
15
1
.
0
5
1
.
0
4
1
.
2
3
-
8
.
2
0
-
8
.
2
0
0
.
9
9
0
.
9
6
2
.
7
7
16
1
.
0
6
1
.
0
4
1
.
2
8
-
3
.
5
0
-
3
.
5
0
0
.
9
9
0
.
9
6
2
.
7
1
17
1
.
0
5
1
.
0
4
1
.
4
4
-
9
.
0
0
-
9
.
0
0
0
.
9
9
0
.
9
6
2
.
8
5
18
1
.
0
4
1
.
0
3
1
.
3
4
-
3
.
2
0
-
3
.
2
0
0
.
9
9
0
.
9
6
2
.
9
5
19
1
.
0
4
1
.
0
3
1
.
4
0
-
9
.
5
0
-
9
.
5
0
0
.
9
9
0
.
9
6
3
.
0
2
20
1
.
0
4
1
.
0
3
1
.
4
3
-
2
.
2
0
-
2
.
2
0
0
.
9
9
0
.
9
6
2
.
9
9
21
1
.
0
5
1
.
0
3
1
.
5
1
-
1
7
.
5
0
-
1
7
.
5
0
0
.
9
9
0
.
9
6
2
.
9
4
22
1
.
0
5
1
.
0
3
1
.
5
1
0
.
0
0
0
.
0
0
0
.
9
9
0
.
9
6
2
.
9
4
23
1
.
0
4
1
.
0
3
1
.
3
6
-
3
.
2
0
-
3
.
2
0
0
.
9
9
0
.
9
6
2
.
9
1
24
1
.
0
4
1
.
0
2
1
.
5
3
-
8
.
7
0
-
8
.
7
0
0
.
9
9
0
.
9
6
3
.
0
1
25
1
.
0
4
1
.
0
2
1
.
7
8
0
.
0
0
0
.
0
0
0
.
9
9
0
.
9
6
2
.
9
7
26
1
.
0
2
1
.
0
0
1
.
8
1
-
3
.
5
0
-
3
.
5
0
0
.
9
9
0
.
9
6
3
.
0
7
27
1
.
0
4
1
.
0
3
1
.
9
1
0
.
0
0
0
.
0
0
0
.
9
9
0
.
9
6
2
.
8
8
28
1
.
0
3
1
.
0
1
1
.
8
8
0
.
0
0
0
.
0
0
1
.
0
0
0
.
9
8
1
.
9
7
29
1
.
0
3
1
.
0
1
1
.
9
5
-
2
.
4
0
-
2
.
4
0
0
.
9
9
0
.
9
6
3
.
1
7
6.
CO
NCLU
SI
O
N
Op
ti
m
al
s
iz
in
g
an
d
p
lacin
g
o
f
SVC
i
s
i
m
p
le
m
e
n
ted
w
ith
g
en
etic
al
g
o
r
ith
m
u
s
i
n
g
I
E
E
E
3
0
b
u
s
s
y
s
te
m
.
T
h
e
s
y
s
te
m
lo
s
s
es
i
m
p
r
o
v
ed
b
y
6
4
.
6
%
b
y
u
s
i
n
g
th
e
lo
s
s
f
u
n
ctio
n
a
s
o
b
j
ec
tiv
e
f
u
n
ctio
n
an
d
p
lace
an
d
s
ize
o
f
SVC
a
s
ch
r
o
m
o
s
o
m
es
.
b
y
u
s
in
g
5
0
0
iter
atio
n
s
an
d
r
u
n
t
h
e
alg
o
r
ith
m
f
o
r
m
u
l
tip
le
ti
m
es
w
e
g
o
t
b
est
r
esu
lt
s
as
6
th
b
u
s
a
n
d
1
.
3
7
7
9
p
.
u
as
SV
C
ad
m
itta
n
ce
v
al
u
e.
A
n
d
it
i
s
id
e
n
ti
f
ied
t
h
at
b
y
r
e
d
u
cin
g
r
ea
l
p
o
w
er
l
o
s
s
af
ter
p
lacin
g
SVC
in
cr
ea
s
es
th
e
o
v
er
all
v
o
lta
g
e
p
r
o
f
ile
o
f
th
e
s
y
s
te
m
an
d
p
o
w
er
f
ac
to
r
o
f
ea
ch
b
u
s
n
ea
r
l
y
0
.
9
9
.
Hen
ce
th
e
p
er
f
o
r
m
a
n
ce
o
f
I
E
E
E
3
0
b
u
s
s
y
s
te
m
i
s
i
m
p
r
o
v
ed
b
y
o
p
ti
m
all
y
p
laci
n
g
th
e
SV
C
w
it
h
o
p
tim
a
l size.
RE
F
E
R
E
NC
E
S
[1
]
Ed
ris,
"
F
A
CT
S
tec
h
n
o
lo
g
y
d
e
v
e
l
o
p
m
e
n
t:
a
n
u
p
d
a
te,"
in
IEE
E
P
o
we
r
En
g
i
n
e
e
rin
g
Rev
iew
,
v
o
l.
2
0
,
n
o
.
3
,
p
p
.
4
-
9
,
M
a
rc
h
2
0
0
0
.
[2
]
R.
M
Ín
g
u
e
z
,
F
.
M
il
a
n
o
,
R
.
ZÁ
ra
te
-
M
iÑa
n
o
a
n
d
A
.
J.
Co
n
e
jo
,
"
Op
ti
m
a
l
Ne
t
w
o
rk
P
lac
e
m
e
n
t
o
f
S
V
C
De
v
ice
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.
2
2
,
n
o
.
4
,
p
p
.
1
8
5
1
-
1
8
6
0
,
No
v
.
2
0
0
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t 2
0
1
7
:
55
–
62
62
[3
]
J.
G
.
S
in
g
h
,
S
.
N.
S
in
g
h
a
n
d
S
.
C.
S
riv
a
sta
v
a
,
"
A
n
A
p
p
ro
a
c
h
f
o
r
Op
ti
m
a
l
P
lac
e
m
e
n
t
o
f
S
tatic
V
Ar
Co
m
p
e
n
sa
to
rs
Ba
se
d
o
n
Re
a
c
ti
v
e
P
o
w
e
r
S
p
o
t
P
r
ice
,
"
in
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
Po
we
r S
y
ste
ms
,
v
o
l.
2
2
,
n
o
.
4
,
p
p
.
2
0
2
1
-
2
0
2
9
,
No
v
.
2
0
0
7
.
[4
]
L
.
J.
Ca
i,
I.
Erl
ich
a
n
d
G
.
S
ta
m
t
sis,
"
Op
ti
m
a
l
c
h
o
ice
a
n
d
a
ll
o
c
a
ti
o
n
o
f
F
A
C
T
S
d
e
v
ice
s
in
d
e
re
g
u
late
d
e
lec
tri
c
it
y
m
a
rk
e
t
u
sin
g
g
e
n
e
ti
c
a
lg
o
rit
h
m
s,
"
IEE
E
PE
S
Po
we
r
S
y
ste
ms
Co
n
fer
e
n
c
e
a
n
d
Exp
o
siti
o
n
,
2
0
0
4
.
,
Ne
w
Yo
rk
,
NY
,
2
0
0
4
,
p
p
.
2
0
1
-
2
0
7
v
o
l
.
1
.
[5
]
N.G
.
Hin
g
o
ra
n
i,
L
.
Gy
u
g
y
i,
a
n
d
Un
d
e
rsta
n
d
i
n
g
F
A
C
T
S
:
Co
n
c
e
p
t
s
a
n
d
T
e
c
h
n
o
lo
g
y
o
f
F
le
x
ib
le
AC
T
ra
n
s
m
is
sio
n
S
y
st
e
m
s.
IEE
E
Pre
ss
,
P
isc
a
ta
w
a
y
,
NJ
,
2
0
0
0
.
[6
]
Y.H.
S
o
n
g
,
A
.
Jo
h
n
s,
F
lex
ib
le A
C
tran
sm
issio
n
sy
ste
m
s
-
F
A
CT
S
.
IEE
Pre
ss
,
L
o
n
d
o
n
,
1
9
9
9
.
[7
]
M
.
K.
V
e
rm
a
,
S
.
C.
S
riv
a
sta
v
a
,
"
Op
ti
m
a
l
P
lac
e
m
e
n
t
o
f
S
V
C
f
o
r
S
tatic
a
n
d
D
y
n
a
m
ic
V
o
lt
a
g
e
S
e
c
u
rit
y
En
h
a
n
c
e
m
e
n
t,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
i
n
g
El
e
c
tric P
o
we
r
S
y
ste
ms
,
v
o
l.
2
,
n
o
.
2
,
A
rti
c
le 1
0
5
0
,
2
0
0
5
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
P
ra
sa
n
t
h
D
re
c
e
iv
e
d
th
e
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
f
ro
m
g
n
a
n
a
m
a
n
i
c
o
ll
e
g
e
o
f
e
n
g
in
e
e
rin
g
a
n
d
p
re
se
n
tl
y
,
h
e
is
p
u
rsu
i
n
g
th
e
M
.
T
e
c
h
d
e
g
re
e
in
p
o
w
e
r
s
y
st
e
m
f
ro
m
ja
y
a
ra
m
c
o
ll
e
g
e
o
f
e
n
g
in
e
e
rin
g
a
n
d
tec
h
n
o
l
o
g
y
a
t
th
u
ra
i
y
u
r,
in
d
ia.
His
re
sh
a
rc
h
in
tere
sts
in
c
lu
d
e
F
A
C
T
S
.
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
,
o
p
ti
m
a
l
p
lac
e
m
e
n
t
o
f
sv
c
,
o
p
ti
m
iza
ti
o
n
.
A
ru
l
P
o
n
n
u
sa
m
y
,
(c
e
ll
.
n
o
:
+
9
1
9
4
4
3
1
7
9
2
2
7
)
,
e
m
a
il
-
a
ru
l.
p
h
d
@g
m
a
il
.
c
o
m
,
w
o
rk
in
g
a
s
a
A
s
so
c
iate
P
ro
f
e
ss
o
r
in
t
h
e
d
e
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
t
ro
n
ics
E
n
g
in
e
e
rin
g
,
Ja
y
a
ra
m
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
T
a
m
il
n
a
d
u
,
In
d
ia.
He
re
c
e
i
v
e
d
h
is
B.
E.
d
e
g
re
e
in
El
e
c
tri
c
a
l
&
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
f
ro
m
th
e
G
o
v
e
rn
m
e
n
t
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Ba
rg
u
r,
In
d
ia
in
2
0
0
1
.
He
re
c
e
iv
e
d
M
.
E
(P
o
w
e
r
S
y
ste
m
En
g
in
e
e
rin
g
)
d
e
g
re
e
in
A
n
n
a
m
a
lai
Un
iv
e
rsit
y
,
Ch
id
a
m
b
a
ra
m
,
In
d
ia
in
th
e
y
e
a
r
2
0
0
4
.
He
is
a
re
s
e
a
rc
h
s
c
h
o
lar
o
f
A
n
n
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i.
He
h
a
s
p
u
b
li
s
h
e
d
1
5
p
a
p
e
rs
in
n
a
ti
o
n
a
l
a
n
d
in
tern
a
t
io
n
a
l
Co
n
f
e
re
n
c
e
s
a
n
d
jo
u
rn
a
ls.
His
a
re
a
o
f
in
tere
st
in
c
lu
d
e
s
P
o
w
e
r
S
y
ste
m
s,
F
A
C
T
S
,
Op
ti
m
iza
ti
o
n
a
n
d
S
o
f
t
Co
m
p
u
ti
n
g
T
e
c
h
n
iq
u
e
s.
He
is
th
e
m
e
m
b
e
r
o
f
IS
T
E.
Evaluation Warning : The document was created with Spire.PDF for Python.