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I
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4
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Dec
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201
7
:
2
7
7
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28
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es
th
e
i
n
f
o
r
m
atio
n
r
e
g
ar
d
in
g
th
e
m
ec
h
a
n
i
s
m
o
f
i
n
s
tab
ili
t
y
[
1
2
]
.
Am
o
n
g
t
h
e
s
h
u
n
t
co
n
n
ec
te
d
d
ev
ices,
a
n
al
y
s
i
s
o
f
S
VC
f
o
r
v
o
ltag
e
s
tab
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y
u
s
i
n
g
m
o
d
al
a
n
al
y
s
i
s
w
as
d
o
n
e
b
y
Y.
Ma
n
s
o
u
r
,
W
ils
u
n
X
u
,
F.Alv
ar
ad
o
an
d
C
.
R
i
n
zin
[
1
4
]
.
Vo
ltag
e
s
tab
il
it
y
m
ar
g
i
n
e
n
h
an
ce
m
e
n
t
b
y
S
VC
an
d
ST
A
T
C
OM
w
a
s
co
m
p
ar
e
d
in
[
1
5
]
u
s
in
g
C
o
n
t
in
u
atio
n
p
o
w
er
f
lo
w
m
et
h
o
d
.
Stu
d
y
o
f
ST
A
T
C
OM
an
d
UP
FC
C
o
n
tr
o
ller
s
f
o
r
Vo
ltag
e
S
tab
il
it
y
i
s
ca
r
r
ied
o
u
t
u
s
i
n
g
C
o
n
tin
u
atio
n
p
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w
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f
lo
w
b
ased
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n
Sad
d
le
-
No
d
e
B
if
u
r
ca
tio
n
A
n
a
l
y
s
is
[
3
]
,
[
1
6
]
a
n
d
[
1
8
]
.
A
r
th
it
s
o
d
e
-
Yo
m
e
[
3
]
an
d
R
.
Nate
s
an
,
G.
R
ad
m
a
n
[
1
6
]
u
tili
ze
d
t
h
e
U
W
P
Flo
w
,
a
r
esear
ch
to
o
l,
to
ca
lcu
late
t
h
e
lo
ad
ab
le
m
ar
g
i
n
s
u
s
i
n
g
P
W
M
b
ased
s
tea
d
y
s
tate
E
MT
P
m
o
d
els.
M.
A
.
P
er
ez
et
al
[
1
8
]
u
tili
ze
d
UP
FC
m
o
d
el
w
h
ic
h
is
a
m
o
d
if
icatio
n
o
f
v
o
lta
g
e
s
o
u
r
ce
m
o
d
el
an
d
d
id
n
‟
t c
o
n
s
i
d
er
th
e
o
p
er
atin
g
li
m
its
o
f
th
e
UP
FC
.
T
h
e
p
r
esen
t
w
o
r
k
u
s
e
s
v
o
lta
g
e
s
o
u
r
ce
m
o
d
el
o
f
UP
FC
,
[
1
9
]
to
ex
a
m
i
n
e
t
h
e
ab
ilit
y
o
f
UP
FC
i
n
en
h
a
n
ci
n
g
v
o
ltag
e
s
tab
ilit
y
,
at
its
v
ar
io
u
s
o
p
er
atin
g
m
o
d
es.
Mo
d
al
an
al
y
s
i
s
o
f
th
e
m
o
d
i
f
ie
d
J
ac
o
b
ian
m
atr
i
x
i
s
u
s
ed
to
id
en
t
if
y
cr
itica
l
b
u
s
p
r
o
n
e
to
v
o
ltag
e
in
s
tab
ilit
y
.
T
h
e
ad
v
an
ta
g
e
o
f
th
is
Mo
d
el
te
ch
n
iq
u
e
o
v
er
o
t
h
er
s
tatic
a
n
al
y
s
is
m
et
h
o
d
s
f
o
r
v
o
ltag
e
s
tab
ili
t
y
i
s
t
h
at
it
p
r
o
v
id
es
b
o
th
a
r
elativ
e
p
r
o
x
i
m
i
t
y
o
f
t
h
e
s
y
s
te
m
to
v
o
ltag
e
i
n
s
tab
ilit
y
,
a
s
w
ell
as t
h
e
m
ec
h
a
n
is
m
o
r
k
e
y
co
n
tr
ib
u
tin
g
f
ac
to
r
s
to
i
n
s
tab
ilit
y
.
2.
M
O
DAL ANA
L
YSI
S
T
h
e
Mo
d
al
A
n
al
y
s
i
s
T
ec
h
n
iq
u
e
[
1
2
]
co
m
p
u
te
s
th
e
e
ig
e
n
v
alu
es
a
n
d
th
e
a
s
s
o
ci
ated
eig
e
n
v
ec
to
r
s
o
f
th
e
r
ed
u
ce
d
p
o
w
er
s
y
s
te
m
s
te
ad
y
s
tate
J
ac
o
b
ian
m
atr
i
x
w
h
ich
r
etai
n
s
t
h
e
Q
-
V
r
elat
io
n
s
h
ip
in
t
h
e
n
et
w
o
r
k
.
T
h
e
p
ar
ticip
atio
n
f
ac
to
r
f
o
r
th
e
m
i
n
i
m
u
m
ei
g
en
v
alu
e
id
e
n
ti
f
ies
t
h
e
w
ea
k
es
t
b
u
s
es.
B
y
u
s
in
g
th
e
r
ed
u
ce
d
J
ac
o
b
ian
m
atr
i
x
,
th
e
r
ela
tio
n
s
h
ip
b
et
w
ee
n
t
h
e
i
n
cr
e
m
e
n
tal
c
h
an
g
e
s
in
b
u
s
r
ea
cti
v
e
p
o
w
er
ca
n
b
e
ex
a
m
in
ed
.
T
h
e
lin
ea
r
ized
s
tead
y
s
tate,
p
o
w
er
v
o
lta
g
e
eq
u
at
io
n
s
ar
e
ex
p
r
ess
ed
as
s
h
o
w
n
i
n
eq
u
atio
n
(
1
)
:
[
]
[
]
[
]
(
1
)
W
h
er
e:
∆P
=in
cr
e
m
en
tal
ch
a
n
g
e
in
b
u
s
r
ea
l p
o
w
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∆Q
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cr
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m
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h
a
n
g
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b
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s
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p
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T
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all
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,
∆P
=
0
ca
n
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ass
u
m
ed
,
th
i
s
y
ield
s
as
s
h
o
w
n
in
eq
u
atio
n
(
2
)
.
[
]
(
2
)
R
ea
r
r
an
g
e
m
e
n
t o
f
eq
u
a
tio
n
(
2
)
g
iv
e
s
eq
u
atio
n
(
3
)
(
3
)
W
h
er
e
eq
u
atio
n
(
4
)
[
]
(
4
)
is
th
e
r
ed
u
ce
d
J
ac
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b
ian
m
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x
o
f
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s
y
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m
,
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r
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p
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b
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ag
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I
t c
an
b
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r
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r
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t
ed
as
s
h
o
w
n
i
n
eq
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at
io
n
(
5
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.
(
5
)
W
h
er
e
:
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f
t e
i
g
en
v
ec
to
r
o
f
m
atr
ix
o
f
=
r
ig
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m
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E
q
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5
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an
d
(
3
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y
ield
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i
n
eq
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s
(
6
-
7)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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p
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S
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Mu
b
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279
(
6
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A
nd
(
7
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W
h
er
e
:
,
is
th
e
v
ec
to
r
o
f
m
o
d
al
v
o
ltag
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v
ar
iatio
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s
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,
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et
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eq
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3
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al.
E
q
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(
3
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r
ep
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u
n
c
o
u
p
led
f
ir
s
t
o
r
d
er
e
q
u
atio
n
s
[
1
2
]
.
T
h
u
s
f
o
r
th
e
i
th
m
o
d
e
lik
e
as
s
h
o
w
n
i
n
eq
u
atio
n
(
8
)
.
(
8
)
T
h
e
eig
e
n
v
alu
e
s
o
f
t
h
e
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ed
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m
atr
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e
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ti
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y
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if
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m
co
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ld
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ta
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T
h
e
m
ag
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d
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o
f
t
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p
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y
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T
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f
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m
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elate
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t
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e
m
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h
a
n
i
s
m
o
f
lo
s
s
o
f
v
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s
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I
f
>
0
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th
e
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th
m
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d
al
v
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d
t
h
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m
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d
al
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p
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alo
n
g
th
e
s
a
m
e
d
ir
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tio
n
,
in
d
icatin
g
th
at
th
e
s
y
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m
is
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I
f
<
0
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v
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m
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ea
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ar
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alo
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tio
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t
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y
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m
i
s
v
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u
n
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le.
I
n
t
h
is
s
e
n
s
e,
t
h
e
m
ag
n
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tu
d
e
o
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d
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m
i
n
es
t
h
e
d
eg
r
ee
o
f
s
tab
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y
o
f
t
h
e
it
h
m
o
d
al
v
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ltag
e.
T
h
e
s
m
al
ler
th
e
m
ag
n
it
u
d
e
o
f
p
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s
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tiv
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th
e
clo
s
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th
e
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th
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al
v
o
ltag
e
i
s
to
b
ein
g
u
n
s
tab
le.
F
r
o
m
eq
u
a
tio
n
(
6
)
,
th
e
s
tab
ili
t
y
o
f
a
m
o
d
e
i
w
i
th
r
esp
ec
t to
r
ea
ctiv
e
p
o
w
er
ch
a
n
g
e
is
d
ef
i
n
ed
b
y
t
h
e
m
o
d
al
eig
en
v
al
u
e
.
L
ar
g
e
v
al
u
es
o
f
s
u
g
g
est
s
m
a
l
l
ch
an
g
es
i
n
t
h
e
m
o
d
al
v
o
lta
g
e
f
o
r
r
ea
ctiv
e
p
o
w
er
ch
a
n
g
e
s
.
As
th
e
s
y
s
te
m
is
s
tr
es
s
ed
,
th
e
v
al
u
e
o
f
b
ec
o
m
e
s
s
m
al
ler
an
d
t
h
e
m
o
d
al
v
o
ltag
e
b
ec
o
m
e
s
w
ea
k
er
.
I
f
t
h
e
m
ag
n
it
u
d
e
o
f
is
eq
u
al
to
ze
r
o
,
th
e
co
r
r
e
s
p
o
n
d
in
g
m
o
d
al
v
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lta
g
e
co
llap
s
es
s
i
n
ce
it
u
n
d
er
g
o
es
in
f
i
n
ite
ch
a
n
g
es
f
o
r
r
ea
ctiv
e
p
o
w
er
ch
a
n
g
e
s
.
A
s
y
s
te
m
is
t
h
er
ef
o
r
e
d
ef
i
n
ed
as
v
o
ltag
e
s
t
ab
le
if
all
t
h
e
eig
en
v
al
u
e
s
o
f
ar
e
p
o
s
itiv
e.
T
h
e
b
if
u
r
ca
tio
n
o
r
v
o
ltag
e
s
tab
le
li
m
i
t
is
r
ea
c
h
ed
w
h
e
n
at
least
o
n
e
ei
g
en
v
al
u
e
r
ea
ch
es
ze
r
o
;
th
a
t
is
,
o
n
e
o
r
m
o
r
e
m
o
d
al
v
o
lta
g
e
c
o
llap
s
es.
I
f
an
y
o
f
t
h
e
ei
g
en
v
alu
es
ar
e
n
e
g
ati
v
e,
t
h
e
s
y
s
te
m
is
u
n
s
tab
le.
T
h
e
m
ag
n
it
u
d
e
o
f
th
e
ei
g
e
n
v
al
u
es
p
r
o
v
id
es
a
r
elativ
e
m
ea
s
u
r
e
o
f
th
e
p
r
o
x
i
m
i
t
y
o
f
t
h
e
s
y
s
te
m
to
i
n
s
tab
il
it
y
.
T
h
e
cr
itical
m
o
d
es
(
ass
o
ciate
d
w
ith
m
in
i
m
u
m
e
ig
e
n
v
alu
e
s
)
ar
e
o
f
m
aj
o
r
im
p
o
r
tan
ce
in
t
h
e
v
o
ltag
e
s
tab
ilit
y
an
al
y
s
is
.
T
h
e
le
f
t
a
n
d
r
i
g
h
t
eig
en
v
ec
to
r
s
co
r
r
esp
o
n
d
in
g
t
o
th
e
cr
itical
m
o
d
es
i
n
t
h
e
s
y
s
te
m
ca
n
p
r
o
v
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e
in
f
o
r
m
atio
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co
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ce
r
n
i
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g
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m
ec
h
a
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i
s
m
o
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i
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y
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en
ti
f
y
in
g
t
h
e
ele
m
e
n
ts
p
ar
ticip
atin
g
i
n
th
ese
m
o
d
es.
T
h
e
b
u
s
p
ar
ticip
atio
n
f
ac
to
r
m
ea
s
u
r
i
n
g
t
h
e
p
ar
ticip
atio
n
o
f
th
e
k
t
h
a
n
d
t
h
e
i
th
m
o
d
e
ca
n
b
e
g
i
v
e
n
as
s
h
o
w
n
i
n
eq
u
atio
n
(
9
)
.
(
9
)
B
u
s
p
ar
ticip
atio
n
f
ac
to
r
s
co
r
r
esp
o
n
d
in
g
to
th
e
cr
itical
m
o
d
es
ca
n
p
r
ed
ict
ar
ea
s
o
r
n
o
d
es
in
th
e
p
o
w
er
s
y
s
te
m
s
u
s
ce
p
tib
le
to
v
o
ltag
e
i
n
s
tab
ilit
y
.
B
u
s
es
w
i
th
l
ar
g
e
p
ar
ticip
atio
n
f
ac
to
r
s
to
th
e
cr
itical
m
o
d
e
co
r
r
esp
o
n
d
to
th
e
m
o
s
t c
r
it
ical
s
y
s
te
m
b
u
s
es
[
1
2
]
.
3.
O
P
E
RAT
I
N
G
P
RINC
I
P
L
E
O
F
UP
F
C
Un
i
f
ied
p
o
w
er
f
lo
w
co
n
tr
o
lle
r
is
a
co
m
b
in
a
tio
n
o
f
a
S
h
u
n
t
an
d
a
s
er
ies
co
n
n
ec
ted
F
AC
T
S
d
ev
ice
ca
p
ab
le
o
f
p
r
o
v
id
in
g
s
i
m
u
ltan
eo
u
s
co
n
tr
o
l
o
f
s
er
ies
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
,
b
et
w
ee
n
t
h
e
t
w
o
n
o
d
es.
I
t
ca
n
also
p
r
o
v
id
e
r
ea
ctiv
e
p
o
w
er
c
o
m
p
e
n
s
at
io
n
s
i
m
u
l
tan
eo
u
s
l
y
t
o
th
e
s
en
d
i
n
g
en
d
n
o
d
e
to
w
h
ich
it
is
attac
h
ed
.
I
t
h
as
n
u
m
er
o
u
s
o
p
er
atin
g
co
n
s
t
r
ain
ts
as
w
el
l
as
m
o
d
es
o
f
o
p
er
atio
n
.
Fig
u
r
e
1
s
h
o
w
s
t
h
e
s
c
h
e
m
atic
d
iag
r
a
m
o
f
UP
FC
co
n
n
ec
ted
b
et
w
ee
n
t
w
o
n
o
d
es.
T
h
e
s
h
u
n
t
co
n
n
ec
ted
co
n
v
er
te
r
s
u
p
p
lies
r
ea
l
p
o
w
er
to
t
h
e
d
c
lin
k
ca
p
ac
ito
r
(
to
m
ee
t
t
h
e
d
em
a
n
d
o
f
s
er
ies
co
n
n
ec
ted
co
n
v
er
ter
)
an
d
p
r
o
v
id
es
s
h
u
n
t
r
ea
cti
v
e
co
m
p
e
n
s
atio
n
f
o
r
th
e
tr
an
s
m
i
s
s
i
o
n
lin
e.
T
h
e
f
lo
w
o
f
r
ea
l
p
o
w
er
i
n
o
r
o
u
t
o
f
t
h
e
d
c
lin
k
ca
p
ac
ito
r
is
co
n
tr
o
lled
b
y
t
h
e
r
ea
l
p
o
w
er
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c
h
a
n
g
e
b
et
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th
e
s
h
u
n
t
co
n
v
er
ter
an
d
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h
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ac
p
o
w
er
s
y
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te
m
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h
is
r
ea
l
p
o
w
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ex
c
h
a
n
g
e
is
g
o
v
er
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ed
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y
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e
p
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ase
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g
le
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et
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t
h
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in
v
er
ter
a
n
d
t
h
e
ac
s
y
s
te
m
v
o
ltag
e
s
.
B
y
co
n
tr
ast,
th
e
r
ea
ctiv
e
p
o
w
er
e
x
ch
a
n
g
e,
r
es
u
ltin
g
f
r
o
m
th
e
li
n
e
co
m
p
e
n
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at
io
n
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eter
m
i
n
ed
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y
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h
e
a
m
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lit
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d
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e
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ce
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et
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n
th
e
i
n
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ter
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ac
s
y
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te
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v
o
lta
g
es,
I
f
th
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d
if
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er
e
n
ce
is
ze
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th
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n
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ter
v
o
ltag
e
h
as
th
e
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a
m
e
a
m
p
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t
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,
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r
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cti
v
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p
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w
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c
h
a
n
g
e
i
s
also
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o
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if
i
t
i
s
p
o
s
iti
v
e,
t
h
e
n
t
h
e
co
n
v
er
ter
g
en
er
ate
s
r
ea
cti
v
e
p
o
w
er
f
o
r
t
h
e
ac
s
y
s
te
m
,
an
d
if
it i
s
n
e
g
ati
v
e,
th
e
co
n
v
e
r
ter
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
w
er
f
r
o
m
th
e
ac
s
y
s
te
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
,
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
:
2
7
7
–
28
5
280
Ser
ies
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v
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lta
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j
ec
tio
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a
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d
ar
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o
t
d
ir
ec
tl
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o
llab
le;
th
e
r
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b
etw
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r
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d
r
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e
p
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w
er
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eter
m
i
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b
y
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h
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h
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j
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v
o
ltag
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a
n
d
th
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lin
e
cu
r
r
en
t.
[
2
0
]
T
h
e
UP
FC
ca
n
b
e
r
ep
r
esen
ted
as
t
w
o
id
ea
l
v
o
lta
g
e
s
o
u
r
ce
s
in
s
er
ie
s
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tr
a
n
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m
is
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d
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n
s
h
u
n
t
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
[
3
]
.
T
h
e
lo
s
s
es
o
f
t
h
e
co
u
p
li
n
g
t
r
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s
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ar
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m
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d
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m
p
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ce
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i
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w
it
h
t
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g
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o
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r
ce
s
.
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id
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l v
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ar
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t
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ath
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s
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eq
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(
1
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{
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(
1
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)
W
h
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e
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d
ar
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Fig
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1
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UP
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E
q
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r
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it
T
h
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FC
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ter
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eq
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(
1
1
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.
(
1
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T
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ac
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n
o
d
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r
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y
[
1
2
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,
[
1
3
]
as sh
o
w
n
in
eq
u
atio
n
s
(
1
2
-
13)
.
(
1
2
)
(
1
3
)
W
h
er
e
eq
u
atio
n
s
(
1
4
-
16)
(
1
4
)
(
1
5
)
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
A
p
p
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281
4.
DE
VI
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M
O
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L
I
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H
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NE
T
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RK
T
h
e
U
P
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p
o
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eq
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ar
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it
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as e
q
u
atio
n
(
1
7
-
20
)
.
|
|
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|
|
{
(
)
}
(
17
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|
|
∑
|
|
{
(
)
}
(
1
8
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|
|
∑
|
|
{
(
)
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(
1
9
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|
|
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|
|
{
(
)
}
(
2
0
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I
n
th
e
ab
o
v
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eq
u
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s
t
h
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s
u
m
m
atio
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ter
m
s
r
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r
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a
m
e
eq
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s
f
o
r
th
e
s
y
s
te
m
w
it
h
o
u
t th
e
UP
FC
.
T
h
e
e
q
u
atio
n
s
,
ar
e
th
e
p
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w
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f
lo
w
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ies co
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ter
f
lo
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g
f
r
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m
k
to
m
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f
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m
m
to
k
r
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el
y
.
T
h
ese
ca
n
b
e
r
ep
r
esen
ted
b
y
t
h
e
eq
u
atio
n
s
(
2
1
-
22
).
(
2
1
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(
22
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T
h
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p
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w
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f
lo
w
eq
u
at
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s
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th
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et
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a
m
e
a
s
o
f
th
e
s
y
s
te
m
w
it
h
o
u
t U
P
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h
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eq
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s
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e
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ea
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ized
w
i
th
r
esp
ec
t t
o
th
e
s
tate
v
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o
f
th
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et
w
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an
d
t
h
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UP
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h
e
lin
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r
ized
p
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w
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f
lo
w
eq
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s
ca
n
b
e
r
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r
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ted
as
[
F(X
)
]
=
[
J
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[
∆X
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e
[
F(X
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is
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w
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l
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w
m
is
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atio
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2
3
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,
[
J
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m
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q
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2
4
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[
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2
5
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[
1
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.
(2
3)
[
]
[
]
(
2
4
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[
]
(2
5
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T
h
e
in
tr
o
d
u
ctio
n
o
f
UP
F
C
in
Ne
w
to
n
R
ap
h
s
o
n
al
g
o
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it
h
m
ca
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s
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s
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m
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th
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d
al
p
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eq
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s
o
f
n
o
d
e
k
a
n
d
m
.
T
h
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last
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h
r
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m
n
an
d
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r
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p
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en
s
iti
v
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r
elati
o
n
s
[
1
8
]
.
T
h
e
o
p
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atin
g
li
m
its
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f
t
h
e
UP
FC
ar
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co
n
s
id
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ed
in
t
h
i
s
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ap
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.
T
h
is
m
o
d
el
allo
w
s
t
h
e
f
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g
m
o
d
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f
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f
t
h
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UP
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en
h
a
n
cin
g
th
e
v
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tab
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m
it.
a.
Ser
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A
cti
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P
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w
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Flo
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n
tr
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l:
I
n
th
is
c
o
n
tr
o
l
m
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ies
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ted
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ad
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.
is
at
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.
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b.
Ser
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R
ea
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v
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P
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tr
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l:
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n
t
h
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tr
o
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m
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th
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ted
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ad
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.
I
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th
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m
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e
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is
n
o
r
ea
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o
w
er
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n
tr
o
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
J
R
A
,
Vo
l.
6
,
No
.
4
,
Dec
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b
er
201
7
:
2
7
7
–
28
5
282
c.
Vo
ltag
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Ma
g
n
it
u
d
e
R
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g
u
latio
n
:
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n
t
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co
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tr
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ies
v
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ase
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v
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b
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to
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s
t
th
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u
s
.
d.
UP
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ca
n
o
p
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ate
as
a
co
m
b
in
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f
ab
o
v
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t
h
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ee
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t
w
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e
at
a
ti
m
e
f
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h
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p
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at
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j
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v
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n
lin
e.
e.
I
n
d
ep
en
d
en
t
Vo
ltag
e
C
o
n
tr
o
l
Mo
d
e:
I
n
th
is
co
n
tr
o
l
m
o
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th
e
s
h
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n
t
v
o
ltag
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in
j
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ted
to
t
h
e
n
o
d
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to
s
u
p
p
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t its
v
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lta
g
e.
5.
T
E
ST
CA
SE
AN
D
SI
M
UL
A
T
I
O
N
T
h
e
I
E
E
E
1
4
b
u
s
as
s
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n
in
Fi
g
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r
e
2
is
u
s
ed
f
o
r
v
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e
s
tab
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T
h
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s
y
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t
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h
a
s
5
g
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ati
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o
d
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s
tan
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d
P
V
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u
s
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T
h
e
lo
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b
u
s
es
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r
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r
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as
co
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ta
n
t
P
Q
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ated
w
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n
d
w
it
h
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t U
P
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.
Fig
u
r
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2
.
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E
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1
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u
s
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te
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s
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f
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a
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in
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in
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th
e
lo
ad
s
g
r
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u
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b
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a
f
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to
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.
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h
e
lo
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ca
n
th
e
n
b
e
d
ef
in
ed
as
s
h
o
w
n
i
n
eq
u
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s
(
2
6
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.
(
2
6
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(
2
7
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
A
I
SS
N:
2089
-
4856
A
p
p
lica
tio
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f U
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w
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a
min
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.
Mu
b
ee
n
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283
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h
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m
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h
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b
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UP
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d
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h
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UP
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o
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m
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ar
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k
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a)
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m
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Vo
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m
o
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el
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s
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p
o
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ated
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w
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e
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4
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9
.
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r
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ab
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3
.
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t
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e
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CO
NCLU
SI
O
N
Ser
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a
n
d
s
h
u
n
t
co
m
p
e
n
s
a
tio
n
d
ev
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s
b
ased
o
n
p
o
w
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ctr
o
n
ics,
s
u
p
p
o
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ts
th
e
p
o
w
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s
y
s
te
m
to
i
m
p
r
o
v
e
t
h
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v
o
lta
g
e
s
tab
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y
.
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FC
w
h
ic
h
i
s
a
co
m
b
i
n
a
tio
n
o
f
b
o
th
th
e
s
er
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s
a
s
w
el
l
as
s
h
u
n
t
d
ev
ice
is
ev
alu
a
ted
h
er
e.
Mo
d
al
an
al
y
s
is
tech
n
iq
u
e
h
a
s
b
ee
n
e
m
p
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ed
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t
h
e
ap
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p
r
i
at
e
lo
ca
tio
n
o
f
t
h
e
F
A
C
T
S d
ev
ice.
T
h
e
r
es
u
lts
o
b
tain
ed
s
h
o
w
s
t
h
at
UP
FC
ca
n
s
ig
n
if
ican
t
l
y
in
cr
ea
s
e
t
h
e
v
o
lta
g
e
m
a
g
n
i
tu
d
e
a
t t
h
e
cr
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m
o
d
e
f
o
r
b
o
th
,
th
e
b
a
s
e
ca
s
e
an
d
th
e
m
a
x
i
m
u
m
lo
a
d
in
g
ca
s
e.
T
h
e
UP
FC
also
h
as
th
e
m
u
lti
co
n
tr
o
l
ab
ilit
y
a
n
d
ca
n
b
e
w
o
r
k
ed
u
p
o
n
d
if
f
er
en
t
m
o
d
e
o
f
o
p
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n
s
p
r
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v
id
in
g
d
i
f
f
er
e
n
t
le
v
el
o
f
s
u
p
p
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r
t
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en
h
a
n
ce
th
e
v
o
lta
g
e
p
r
o
f
ile.
RE
F
E
R
E
NC
E
S
[1
]
P
.
Ku
n
d
u
r
,
e
t
a
l.
,
“
Pra
c
ti
c
a
l
c
o
n
s
id
e
ra
ti
o
n
i
n
v
o
lt
a
g
e
sta
b
il
it
y
Ass
e
s
sm
e
n
t
”
,
El
e
c
tri
c
a
l
P
o
w
e
r
&
En
e
rg
y
S
y
ste
m
,
v
o
l.
1
5
,
No
.
4
,
1
9
9
3
,
p
p
.
2
0
5
-
2
1
5
.
[2
]
A
.
E.
F
a
ra
g
,
e
t
a
l.
,
“
Vo
lt
a
g
e
S
t
a
b
il
it
y
Asse
ss
me
n
t
u
sin
g
M
o
d
a
l
A
n
a
lys
is
o
f
Po
we
r
S
y
ste
ms
in
c
lu
d
i
n
g
fl
e
x
ib
le
AC
T
ra
n
sm
issio
n
S
y
ste
m
(
FA
CT
S
)
”
Co
n
f
e
re
n
c
e
P
ro
c
e
e
d
in
g
s
o
f
L
a
rg
e
En
g
in
e
e
r
in
g
S
y
ste
m
s
Co
n
f
e
r
e
n
c
e
o
n
P
o
w
e
r
En
g
in
e
e
rin
g
,
L
ES
CO
P
E'
0
3
.
7
-
9
M
a
y
2
0
0
3
p
p
.
1
0
5
-
1
0
8
.
[3
]
A
.
S
o
d
e
-
Yo
m
e
,
e
t
a
l.
,
“
S
tatic
V
o
l
tag
e
S
tab
il
it
y
M
a
rg
in
En
h
a
n
c
e
m
e
n
t
u
sin
g
S
T
AT
COM,
T
CS
C,
a
n
d
S
S
S
C
.
IEE
E/
P
E
S
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
Co
n
f
e
re
n
c
e
&
Ex
h
ib
it
io
n
:
A
sia
&
P
a
c
if
i
c
Da
li
a
n
,
Ch
in
a
p
p
.
1
-
6.
[4
]
A
.
S
o
d
e
-
Yo
m
e
,
e
t
a
l.
,
“
Co
mp
a
ri
so
n
o
f
sh
u
n
t
c
a
p
a
c
it
o
r
,
S
VC
a
n
d
S
T
AT
COM
in
sta
ti
c
v
o
lt
a
g
e
sta
b
il
it
y
M
a
rg
in
En
h
a
n
c
e
me
n
t,
”
In
tern
a
t
io
n
a
l
Jo
u
r
n
a
l
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
E
d
u
c
a
ti
o
n
UMIS
T
v
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[5
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N.
F
lata
b
o
,
e
t
a
l.
,
"
Vo
lt
a
g
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S
ta
b
il
it
y
Co
n
d
it
i
o
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n
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Po
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lcu
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ted
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y
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e
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it
y
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e
th
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s
"
.
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
P
o
w
e
r
S
y
ste
m
s,
V
o
l.
5
.
No
.
4
,
1
9
9
0
p
p
.
1
2
8
6
-
1
2
9
3
.
[6
]
P
.
Ke
ss
e
l.
A
n
d
H.
G
lav
it
c
h
,
"
Es
ti
ma
ti
n
g
t
h
e
Vo
lt
a
g
e
S
t
a
b
il
it
y
o
f
a
Po
we
r
S
y
ste
m
"
,
IEE
E
T
ra
n
sa
c
t
io
n
o
n
P
o
w
e
r
De
li
v
e
r
y
,
v
o
l.
P
W
RD
-
1
,
No
.
3
.
1
9
8
6
p
p
.
3
4
6
-
3
5
4
.
[7
]
R.
J.
T
h
o
m
a
s
a
n
d
A
.
T
ir
a
n
u
c
h
it
.
''
V
o
lt
a
g
e
In
st
a
b
il
it
ies
in
El
e
c
tric
Po
we
r
Ne
two
rk
s
"
.
P
ro
c
.
Ei
g
h
tee
n
th
S
o
u
th
e
a
st
S
y
m
p
o
siu
m
o
n
S
y
ste
m
T
h
e
o
r
y
,
1
9
8
6
,
p
p
.
3
5
9
-
3
6
3
.
[8
]
Y.
T
a
m
u
ra
,
e
t
a
l.
,
"
Re
latio
n
sh
ip
b
e
tw
e
e
n
V
o
lt
a
g
e
In
sta
b
i
li
ty
a
n
d
M
u
lt
ip
le
L
o
a
d
F
l
o
w
S
o
lu
ti
o
n
s
i
n
E
l
e
c
tri
c
P
o
w
e
r
S
y
st
e
m
s
"
.
IEE
E
T
ra
n
s.
v
o
l.
P
A
S
-
1
0
2
.
No
.
5
,
p
p
.
1
1
1
5
-
1
1
2
5
.
M
a
y
1
9
8
3
.
[9
]
R.
A
.
S
c
h
lu
e
ter,
e
t
a
l.
,
“
Vo
lt
a
g
e
S
t
a
b
il
i
ty a
n
d
S
e
c
u
rity A
ss
e
ss
me
n
t
"
.
EP
RI
F
in
a
l
Re
p
o
r
t
El
-
5
9
6
7
o
n
P
r
o
jec
t
1
9
9
9
-
8
.
M
a
y
1
9
8
8
.
[1
0
]
P
.
Ku
n
d
u
r,
P
o
w
e
r
S
y
ste
m
S
tab
il
it
y
a
n
d
Co
n
tr
o
l,
S
e
ries
.
E
P
RI
P
o
w
e
r
S
y
st
e
m
En
g
in
e
e
rin
g
S
e
ries
Ne
w
Yo
rk
:
M
c
-
G
ra
w
-
Hill
,
1
9
9
4
.
[1
1
]
C.
S
h
a
rm
a
a
n
d
M
.
G
.
G
a
n
n
e
ss
,
“
D
e
ter
min
a
ti
o
n
o
f
t
h
e
Ap
p
li
c
a
b
il
i
ty
o
f
u
si
n
g
M
o
d
a
l
A
n
a
lys
is
fo
r
t
h
e
Pre
d
ictio
n
o
f
Vo
lt
a
g
e
S
t
a
b
il
it
y
’
‟.
T
ra
n
sm
issio
n
a
n
d
Distri
b
u
ti
o
n
Co
n
f
e
re
n
c
e
a
n
d
Ex
p
o
siti
o
n
,
2
0
0
8
.
T
&
D.
IEE
E/
P
ES
2
0
0
8
,
p
p
.
1
-
7.
[1
2
]
B.
G
a
o
,
e
t
a
l.
,
”
Vo
lt
a
g
e
st
a
b
il
it
y
A
n
a
lys
is
u
si
n
g
M
o
d
a
l
A
n
a
lys
is.
”
IE
EE
T
ra
n
s,
v
o
l.
7
N
o
.
4
,
1
9
9
2
,
p
p
.
1
5
2
9
-
1
5
4
2
.
[1
3
]
V
.
Ba
lam
o
u
ro
u
g
a
n
,
e
t
a
l.
,
“
T
e
c
h
n
i
q
u
e
f
o
r
o
u
tl
i
n
e
p
re
d
ictio
n
o
f
V
o
lt
a
g
e
C
o
ll
a
p
se
.
”
IE
EE
P
ro
c
e
e
d
in
g
s
G
e
n
e
ra
ti
o
n
,
T
ra
n
s
m
issio
n
a
n
d
Distri
b
u
ti
o
n
,
v
o
l.
1
5
1
,
No
.
4
,
2
0
0
4
,
p
p
4
5
3
-
4
6
0
.
[1
4
]
Y.M
a
n
so
u
r
,
e
t
a
l.
,
“
S
VC
Pl
a
c
e
me
n
t
u
sin
g
c
riti
c
a
l
mo
d
e
s
o
f
Vo
l
ta
g
e
In
sta
b
il
it
y
.
”
P
r
o
c
e
e
d
in
g
s
o
f
P
o
w
e
r
In
d
u
stry
Co
m
p
u
ter A
p
p
li
c
a
ti
o
n
C
o
n
f
e
re
n
c
e
,
4
-
7
,
1
9
9
3
p
p
.
1
3
1
-
1
3
7
.
[1
5
]
A
.
Ka
z
e
m
i,
e
t
a
l.
,
“
S
tu
d
y
o
f
S
T
A
T
COM
a
n
d
UP
FC
Co
n
tro
l
ler
s
fo
r
Vo
lt
a
g
e
S
ta
b
il
it
y
Eva
lu
a
ted
b
y
S
a
d
d
le
-
No
d
e
Bi
fu
rc
a
ti
o
n
A
n
a
lys
is,
”
F
irst
In
te
rn
a
ti
o
n
a
l
P
o
w
e
r
a
n
d
En
e
rg
y
C
o
n
f
e
re
n
c
e
P
ECo
n
/IE
EE
,
P
u
traja
y
a
,
M
a
la
y
sia
,
No
v
e
m
b
e
r
2
8
-
2
9
,
2
0
0
6
.
[1
6
]
R.
Na
tes
a
n
a
n
d
G
.
Ra
d
m
a
n
,
“
Ef
fec
ts
o
f
S
T
AT
COM
,
S
S
S
C
a
n
d
U
PF
C
o
n
Vo
lt
a
g
e
S
ta
b
il
it
y
,
”
P
r
o
c
e
e
d
in
g
s
o
f
th
e
s
y
ste
m
th
e
o
r
y
th
irt
y
-
S
ix
th
S
o
u
th
e
a
ste
rn
s
y
m
p
o
siu
m
,
2
0
0
4
,
p
p
.
5
4
6
-
5
5
0
.
[1
7
]
M
.
A
.
Ka
m
a
rp
o
sh
ti
a
n
d
M
.
A
li
n
e
z
h
a
d
“
Co
mp
a
riso
n
o
f
S
VC
a
n
d
S
T
AT
COM
i
n
S
t
a
t
ic
Vo
lt
a
g
e
S
t
a
b
il
it
y
M
a
r
g
in
En
h
a
n
c
e
me
n
t
”
W
o
rld
A
c
a
d
e
m
y
o
f
S
c
ien
c
e
,
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
5
0
2
0
0
9
,
p
p
.
8
6
0
-
8
6
5
.
[1
8
]
M
.
A
.
P
e
re
z
,
e
t
a
l.
,
“
Ap
p
li
c
a
ti
o
n
o
f
FA
CT
S
d
e
v
ice
s
to
imp
ro
v
e
S
tea
d
y
S
ta
te
Vo
l
ta
g
e
S
ta
b
il
it
y
”
IEE
E
P
o
w
e
r
En
g
in
e
e
rin
g
S
o
c
iety
S
u
m
m
e
r
M
e
e
ti
n
g
,
2
0
0
0
v
o
l
2
,
1
6
-
2
0
,
2
0
0
0
,
p
p
.
1
1
1
5
-
1
1
2
0
.
[1
9
]
C.
R.
F
u
e
rte
-
Esq
u
iv
e
l,
e
t
a
l.
,
„A
c
o
m
p
re
h
e
n
siv
e
Ne
w
to
n
-
Ra
p
h
so
n
U
P
F
C
m
o
d
e
l
f
o
r
th
e
q
u
a
d
ra
ti
c
p
o
w
e
r
f
lo
w
so
lu
ti
o
n
o
f
p
ra
c
ti
c
a
l
p
o
w
e
r
n
e
two
rk
s‟,
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
P
o
we
r
S
y
ste
m
s,
v
o
l.
1
5
,
No
.
1
,
F
e
b
.
2
0
0
0
,
p
p
.
1
0
2
-
1
0
9
.
[2
0
]
L
Gy
u
g
y
i
“
Un
if
ied
p
o
we
r
-
fl
o
w
Co
n
tro
l
Co
n
c
e
p
t
f
o
r
fl
e
x
ib
le
AC
T
ra
n
sm
issio
n
S
y
ste
ms
”
IE
E
P
ro
c
e
e
d
in
g
s
-
C,
v
o
l
1
3
9
,
No
.
4
,
Ju
ly
1
9
9
2
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Dr
.
S
a
m
in
a
.
E.
M
u
b
e
e
n
re
c
e
iv
e
d
h
e
r
B.
E
i
n
El
e
c
tri
c
a
l
E
n
g
in
e
e
rin
g
f
ro
m
Ra
v
ish
a
n
k
a
r
Un
iv
e
rsit
y
,
Ra
ip
u
r
in
th
e
y
e
a
r
1
9
9
1
a
n
d
M
.
T
e
c
h
d
e
g
re
e
f
ro
m
R
a
jee
v
Ga
n
d
h
i
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
Bh
o
p
a
l
in
th
e
y
e
a
r
2
0
0
2
re
sp
e
c
ti
v
e
l
y
.
Cu
rre
n
tl
y
sh
e
is
p
u
rsu
i
n
g
h
e
r
P
h
.
D
in
El
e
c
tr
ica
l
En
g
in
e
e
rin
g
De
p
a
rtme
n
t
a
t
M
a
u
lan
a
A
z
a
d
N
a
ti
o
n
a
l
In
stit
u
te
o
f
T
e
c
h
n
o
l
o
g
y
.
H
e
r
f
i
e
ld
o
f
w
o
rk
is
a
p
p
li
c
a
ti
o
n
o
f
F
A
C
T
S
d
e
v
ice
s
in
tran
sm
issio
n
n
e
tw
o
rk
.
In
teg
ra
ted
re
n
e
wa
b
le
e
n
e
rg
y
tec
h
n
o
lo
g
y
,
S
m
a
rt
G
rid
.
Dr
.
B
a
se
e
m
K
h
a
n
(M
‟1
6
)
re
c
e
iv
e
d
th
e
b
a
c
h
e
lo
r‟s
o
f
e
n
g
i
n
e
e
rin
g
d
e
g
re
e
in
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lec
tri
c
a
l
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g
in
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rin
g
f
ro
m
Ra
ji
v
Ga
n
d
h
i
T
e
c
h
n
o
lo
g
ica
l
Un
iv
e
rsit
y
in
2
0
0
8
,
M
a
ste
r'
s
o
f
Tec
h
n
o
lo
g
y
a
n
d
P
h
D
d
e
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re
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in
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tri
c
a
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in
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rin
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f
ro
m
th
e
M
a
u
lan
a
A
z
a
d
Na
t
io
n
a
l
I
n
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
,
In
d
ia,
in
2
0
1
0
a
n
d
2
0
1
4
,
re
sp
e
c
ti
v
e
l
y
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S
in
c
e
2
0
1
5
,
h
e
h
a
s
b
e
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n
A
ss
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t
P
ro
f
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o
r
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it
h
Ha
w
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a
Un
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rsit
y
In
stit
u
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o
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T
e
c
h
n
o
l
o
g
y
,
Ha
wa
ss
a
,
E
th
io
p
ia
.
His
re
se
a
rc
h
in
tere
st
in
c
lu
d
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s
p
o
w
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s
y
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re
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tu
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,
p
o
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sy
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sm
a
rt
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rid
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m
e
ta
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h
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risti
c
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p
t
im
iza
ti
o
n
tec
h
n
iq
u
e
s an
d
re
n
e
w
a
b
le en
e
rg
y
in
teg
ra
ti
o
n
Dr
.
R.
K
.
Ne
m
a
h
a
s rec
e
i
v
e
d
h
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P
h
D d
e
g
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e
in
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lec
tri
c
a
l
En
g
in
e
e
rin
g
f
ro
m
Ba
r
k
a
tu
ll
a
h
Un
iv
e
rsit
y
,
Bh
o
p
a
l,
In
d
ia
in
2
0
0
4
.
He
is
c
u
rre
n
tl
y
A
P
a
t
th
e
De
p
a
rtm
e
n
t
o
f
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e
c
tri
c
a
l
En
g
g
,
M
A
NI
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,
Bh
o
p
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