I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
201
7
,
p
p
.
3
1
7
6
~
31
89
I
SS
N:
2
0
8
8
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/i
j
ec
e.
v
7
i6
.
p
p
3
1
7
6
-
3189
3176
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
JE
C
E
M
ulti
-
M
a
chine
St
a
bility Usin
g
Dyn
a
m
ic Inv
ersio
n
T
echnique
Abha
T
ripa
t
hi
1
,
K
.
U
m
a
Ra
o
2
,
L
.
Ven
k
a
t
esh
a
3
1
De
p
a
rte
m
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
P
ES
I
n
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
2
De
p
a
rte
m
e
n
t
o
f
El
e
c
tri
c
a
l
&
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
RV Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
3
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
&
El
e
c
tro
n
ics
E
n
g
in
e
e
rin
g
,
BM
S
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
20
,
2
0
1
6
R
ev
i
s
ed
Ma
y
1
2
,
2
0
1
7
A
cc
ep
ted
J
u
n
6
,
2
0
1
7
S
tab
il
it
y
stu
d
ies
o
f
m
u
lt
i
m
a
c
h
in
e
sy
ste
m
a
re
a
m
a
jo
r
c
o
n
c
e
rn
to
p
o
w
e
r
s
y
ste
m
e
n
g
in
e
e
rs
d
u
e
to
t
h
e
in
c
re
a
sin
g
c
o
m
p
lex
it
y
in
v
o
lv
e
d
.
T
h
is
p
a
p
e
r
d
e
a
ls
w
it
h
th
e
a
p
p
li
c
a
ti
o
n
o
f
a
n
o
n
li
n
e
a
r
tec
h
n
iq
u
e
c
a
ll
e
d
Dy
n
a
m
ic
In
v
e
rsio
n
,
t
o
T
CS
C
f
o
r
th
e
i
m
p
ro
v
e
m
e
n
t
o
f
sta
b
il
it
y
o
f
m
u
lt
i
-
m
a
c
h
in
e
s
y
s
tem
.
T
h
e
tran
sie
n
t
sta
b
il
it
y
stu
d
ies
f
o
r
v
a
rio
u
s
c
a
se
s:
w
it
h
o
u
t
a
n
y
c
o
n
tr
o
ll
e
r,
w
it
h
7
5
%
li
n
e
c
o
m
p
e
n
sa
ti
o
n
a
n
d
w
it
h
Dy
n
a
m
ic In
v
e
rsio
n
tec
h
n
i
q
u
e
,
a
re
c
o
m
p
a
re
d
.
T
h
e
c
rit
ica
l
c
lea
rin
g
ti
m
e
a
s
w
e
ll
a
s
th
e
m
a
x
i
m
u
m
lo
a
d
in
g
a
b
il
it
y
is
a
lso
d
isc
u
ss
e
d
.
T
h
e
re
su
lt
f
o
r
t
h
e
n
o
n
li
n
e
a
r
c
o
n
tro
ll
e
r
is
f
o
u
n
d
to
b
e
b
e
tt
e
r
th
a
n
a
ll
th
e
o
t
h
e
r
c
a
se
s
.
K
ey
w
o
r
d
:
D
y
n
a
m
ic
i
n
v
er
s
io
n
T
h
y
r
i
s
to
r
c
o
n
tr
o
lled
s
er
ies
C
o
m
p
en
s
atio
n
Mu
lti
-
Ma
c
h
i
n
e
Stab
ilit
y
No
n
-
l
in
ea
r
t
ec
h
n
iq
u
e
Co
p
y
rig
h
t
©
2
0
1
7
In
stit
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
:
A
b
h
a
T
r
ip
ath
i,
Dep
ar
te
m
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
i
n
ee
r
in
g
,
P
E
S I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
,
1
0
0
Feet
Ou
ter
R
in
g
R
o
ad
,
B
an
as
h
an
k
ar
i I
I
I
Stag
e,
B
an
g
alo
r
e,
5
6
0
0
8
5
,
I
n
d
ia
.
E
m
ail: a
b
h
atr
ip
at
h
i
@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
An
i
m
p
o
r
tan
t
is
s
u
e
in
m
u
lti
-
m
ac
h
in
e
s
y
s
te
m
s
is
t
h
e
ch
o
i
ce
o
f
lo
ca
tio
n
o
f
v
ar
io
u
s
d
e
v
ices.
I
t
is
k
n
o
w
n
t
h
at
m
u
l
ti
-
m
ac
h
i
n
e
s
y
s
te
m
s
,
n
o
r
m
all
y
,
s
p
lit
i
n
to
t
wo
g
r
o
u
p
s
in
i
tiall
y
,
w
h
e
n
e
v
er
t
h
e
s
y
s
te
m
b
ec
o
m
e
s
u
n
s
tab
le
[
1
]
,
[
2
]
.
C
o
n
s
eq
u
e
n
tl
y
th
er
e
is
a
cr
itical
c
u
t
-
s
et
wh
ich
s
ep
ar
ates
th
e
s
y
s
te
m
i
n
t
o
th
ese
t
w
o
g
r
o
u
p
s
.
L
o
ca
ti
n
g
s
er
ies
d
ev
ice
s
i
n
t
h
ese
li
n
es
w
ill
s
tr
e
n
g
t
h
e
n
t
h
e
m
a
n
d
t
h
u
s
aid
in
i
m
p
r
o
v
in
g
s
tab
ili
t
y
.
T
h
e
co
m
p
e
n
s
at
in
g
d
ev
ice
s
ca
n
t
h
er
ef
o
r
e
b
e
lo
ca
ted
in
li
n
e
s
w
h
ic
h
f
o
r
m
t
h
e
cr
itical
cu
t
-
s
et
f
o
r
cr
itical
co
n
tin
g
e
n
cies
[
3
]
.
An
o
t
h
er
k
e
y
is
s
u
e
in
m
u
lti
-
m
ac
h
in
e
s
y
s
te
m
s
i
s
t
h
e
ch
o
ice
o
f
co
n
tr
o
l
s
i
g
n
als.
I
t
i
s
es
s
en
t
ial
f
o
r
r
o
b
u
s
t
o
p
er
atio
n
an
d
co
n
tr
o
l,
th
at
ea
ch
d
ev
ice
ca
n
b
e
co
n
tr
o
lled
b
y
s
ig
n
als
t
h
at
ar
e
lo
ca
ll
y
m
ea
s
u
r
ab
le
an
d
r
eq
u
ir
e
m
in
i
m
u
m
tele
m
etr
y
f
r
o
m
o
t
h
er
ar
ea
s
.
T
r
a
j
ec
to
r
y
s
e
n
s
it
iv
i
t
y
an
al
y
s
is
(
T
SA
)
w
a
s
u
s
ed
to
m
ea
s
u
r
e
th
e
tr
an
s
ie
n
t
s
tab
ilit
y
co
n
d
iti
o
n
o
f
th
e
s
y
s
te
m
i
n
[
4
]
.
T
h
e
T
C
SC
w
a
s
m
o
d
elled
b
y
a
v
ar
iab
le
ca
p
a
cito
r
,
th
e
v
alu
e
o
f
w
h
ich
ch
a
n
g
e
s
w
ith
t
h
e
f
ir
i
n
g
an
g
le.
I
t
w
a
s
s
h
o
w
n
t
h
at
T
SA
co
u
ld
b
e
u
s
ed
in
t
h
e
d
esi
g
n
o
f
t
h
e
co
n
tr
o
ller
.
T
h
e
o
p
tim
al
lo
ca
tio
n
s
o
f
t
h
e
T
h
y
r
i
s
to
r
C
o
n
tr
o
lled
Ser
ies
C
o
m
p
e
n
s
at
io
n
(
T
C
SC
)
-
co
n
tr
o
ller
f
o
r
d
if
f
er
en
t
f
au
lt
co
n
d
i
tio
n
s
co
u
ld
also
b
e
id
en
ti
f
ied
w
ith
t
h
e
h
elp
o
f
T
SA
.
I
n
o
r
d
er
to
im
p
r
o
v
e
t
h
e
T
r
an
s
i
en
t
Stab
il
it
y
o
f
a
9
B
u
s
S
y
s
te
m
w
it
h
F
ix
ed
C
o
m
p
en
s
atio
n
o
n
Var
io
u
s
L
i
n
es
a
n
d
Op
ti
m
a
l
L
o
ca
tio
n
w
a
s
in
v
e
s
tig
a
ted
u
s
in
g
tr
aj
ec
to
r
y
s
en
s
iti
v
it
y
an
a
l
y
s
is
i
n
[
5
]
.
A
f
u
zz
y
co
n
tr
o
lled
T
C
SC
d
ev
ice
w
as
u
s
ed
a
n
d
th
e
r
e
s
u
l
ts
h
i
g
h
lig
h
ted
t
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
t
h
e
ap
p
licati
o
n
o
f
a
T
C
SC
i
n
i
m
p
r
o
v
i
n
g
t
h
e
tr
an
s
ien
t
s
tab
i
lit
y
o
f
a
m
u
lti
m
ac
h
i
n
e
p
o
w
er
s
y
s
te
m
.
I
n
[
6
]
,
th
e
ef
f
ec
t
o
f
ST
A
T
C
OM
f
o
r
i
m
p
r
o
v
i
n
g
t
h
e
s
tab
ili
t
y
o
f
t
h
e
m
u
l
ti
m
ac
h
i
n
e
p
o
w
er
s
y
s
te
m
w
as
i
n
v
esti
g
ated
.
T
h
e
ST
A
T
C
OM
w
as
u
s
ed
to
co
n
tr
o
l
p
o
w
er
f
lo
w
o
f
p
o
w
er
s
y
s
te
m
b
y
i
n
j
ec
tin
g
ap
p
r
o
p
r
iate
r
ea
ctiv
e
p
o
w
er
d
u
r
i
n
g
d
y
n
a
m
ic
s
tate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mu
lti Ma
ch
in
e
S
ta
b
ilit
y
Usi
n
g
Dyn
a
mic
I
n
ve
r
s
io
n
Tech
n
iq
u
e
(
A
b
h
a
Tr
ip
a
th
i)
3177
Si
m
u
latio
n
r
es
u
lts
s
h
o
w
ed
t
h
at
ST
A
T
C
OM
n
o
t
o
n
l
y
co
n
s
id
er
ab
l
y
i
m
p
r
o
v
ed
tr
an
s
ien
t
s
tab
ilit
y
b
u
t
al
s
o
co
m
p
e
n
s
ated
t
h
e
r
ea
ctiv
e
p
o
w
er
i
n
s
tead
y
s
tate.
T
h
is
w
a
s
i
m
p
le
m
en
ted
o
n
a
t
h
r
ee
m
ac
h
in
e
n
in
e
b
u
s
,
p
o
w
er
s
y
s
te
m
.
A
n
o
v
el
h
y
b
r
id
p
o
w
er
f
lo
w
co
n
tr
o
ller
(
HP
FC
)
to
p
o
lo
g
y
f
o
r
Fle
x
ib
le
AC
T
r
an
s
m
i
s
s
io
n
S
y
s
te
m
(
FAC
T
S)
w
a
s
p
r
o
p
o
s
ed
in
[
7
]
.
T
h
e
k
e
y
b
e
n
ef
i
t
o
f
t
h
e
n
e
w
to
p
o
lo
g
y
w
a
s
t
h
at
it
f
u
ll
y
u
tili
ze
d
e
x
i
s
ti
n
g
eq
u
ip
m
e
n
t.
T
h
e
M
A
T
L
A
B
/
SIM
UL
I
NK
m
o
d
els
o
f
t
h
r
ee
d
if
f
er
e
n
t
co
n
f
i
g
u
r
atio
n
s
o
f
HP
FC
h
ad
b
ee
n
in
v
e
s
ti
g
ated
f
o
r
th
e
ir
d
if
f
er
e
n
t
ch
ar
ac
ter
is
ti
c
s
,
b
y
in
co
r
p
o
r
atin
g
t
h
e
m
in
t
h
e
m
u
lti
m
ac
h
i
n
e
s
y
s
te
m
.
A
m
o
d
el
f
o
r
ass
es
s
m
en
t
o
f
tr
an
s
ie
n
t
s
tab
il
it
y
o
f
p
o
w
er
s
y
s
te
m
w
as
d
ev
elo
p
ed
in
[
8
]
.
T
h
is
w
a
s
test
ed
f
o
r
a
s
i
n
g
le
m
ac
h
i
n
e
i
n
f
i
n
ite
b
u
s
s
y
s
te
m
as
w
ell
a
s
m
u
l
ti
-
m
a
ch
in
e
s
y
s
te
m
.
An
U
n
i
f
ied
P
o
w
er
F
lo
w
C
o
n
tr
o
ller
(
UP
FC
)
w
as
d
e
m
o
n
s
tr
ated
i
n
[
9
]
to
i
m
p
r
o
v
e
t
h
e
d
a
m
p
i
n
g
o
f
o
s
cillatio
n
s
as
w
ell
a
s
i
n
cr
ea
s
e
th
e
cr
itical
clea
r
in
g
ti
m
e
f
o
r
m
u
lt
i
-
m
ac
h
i
n
e
s
y
s
te
m
.
I
n
th
i
s
p
ap
er
a
n
o
n
-
lin
ea
r
tec
h
n
iq
u
e
ca
lled
D
y
n
a
m
ic
I
n
v
er
s
io
n
h
as
b
ee
n
i
m
p
le
m
en
ted
t
h
r
o
u
g
h
T
C
S
C
to
i
m
p
r
o
v
e
th
e
v
ar
io
u
s
a
s
p
ec
ts
o
f
s
tab
ilit
y
is
s
u
e
s
in
m
u
lti
-
m
ac
h
in
e
s
y
s
te
m
,
s
u
c
h
as tr
an
s
ie
n
t stab
ili
t
y
,
cr
iti
ca
l c
lear
in
g
ti
m
e,
lo
ad
in
g
,
etc.
2.
DYNA
M
I
C
I
NVER
SI
O
N
T
E
CH
NI
Q
U
E
D
y
n
a
m
ic
I
n
v
er
s
io
n
is
a
tec
h
n
iq
u
e
to
tr
ac
k
th
e
d
esire
d
o
u
tp
u
t
b
y
f
o
r
ci
n
g
t
h
e
er
r
o
r
to
ze
r
o
[
1
0
]
.
L
et
th
e
s
tate
d
y
n
a
m
ic
s
b
e
d
ef
in
ed
as:
u
x
g
x
f
x
)]
(
[
)
(
(
1
)
w
h
er
e
x
is
th
e
s
tate
v
ec
to
r
,
)
(
x
f
is
t
h
e
d
y
n
a
m
ics
w
i
th
o
u
t
t
h
e
co
n
tr
o
l
an
d
)
(
x
g
is
t
h
e
s
tate
d
y
n
a
m
ics
w
it
h
th
e
co
n
tr
o
l
u
.
I
f
th
e
o
u
tp
u
t
v
ec
to
r
is
id
en
tical
to
t
h
e
s
ta
te
v
ec
to
r
,
th
e
n
eq
u
atio
n
(
1
)
m
a
y
b
e
w
r
i
tten
a
s
f
o
llo
w
s
:
u
x
g
x
f
y
)]
(
[
)
(
(
2
)
I
f
d
e
s
i
r
e
d
y
is
th
e
d
esire
d
o
u
tp
u
t a
n
d
th
e
ac
tu
al
o
u
tp
u
t is
y
,
er
r
o
r
ca
n
b
e
d
ef
in
ed
as
d
e
s
i
r
e
d
y
y
e
(
3
)
T
h
e
er
r
o
r
ca
n
b
e
f
o
r
ce
d
to
ap
p
r
o
ac
h
ze
r
o
b
y
u
s
in
g
t
h
e
b
elo
w
g
iv
e
n
eq
u
at
io
n
:
0
ke
e
,
(
4
)
w
h
er
e
k
>
0
an
d
e
is
th
e
d
er
iv
ati
v
e
o
f
er
r
o
r
an
d
is
g
i
v
en
b
y
d
e
s
i
r
e
d
y
y
e
(
5
)
T
h
e
s
o
lu
tio
n
o
f
eq
u
a
tio
n
(
5
)
is
0
e
e
e
kt
(
6
)
w
h
er
e
0
e
is
th
e
in
itial
er
r
o
r
.
Fro
m
eq
u
atio
n
(
6
)
,
w
e
ca
n
o
b
s
er
v
e
th
at
th
e
er
r
o
r
w
il
l
ten
d
to
ze
r
o
as
tim
e
t
ten
d
s
to
in
f
i
n
it
y
.
Usi
n
g
t
h
e
v
al
u
e
o
f
er
r
o
r
an
d
th
e
d
er
iv
at
iv
e
o
f
er
r
o
r
f
r
o
m
eq
u
a
tio
n
s
(
3
)
an
d
(
5
)
an
d
s
u
b
s
tit
u
ti
n
g
t
h
e
s
a
m
e
i
n
eq
u
atio
n
(
4
)
,
w
e
g
et
a
n
d
tak
i
n
g
0
de
s
i
r
e
d
y
as th
e
d
esire
d
o
u
tp
u
t is
f
i
x
ed
.
0
)
(
)]
(
[
)
(
d
e
s
i
r
e
d
y
y
k
u
x
g
x
f
(
7
)
Hen
ce
th
e
co
n
tr
o
ller
is
g
i
v
e
n
b
y
:
)
}
]
(
)
(
{
)]
(
[
1
x
f
y
y
k
x
g
u
d
e
s
i
r
e
d
(
8
)
T
h
e
ab
o
v
e
co
n
tr
o
ller
eq
u
atio
n
an
d
g
i
v
es
t
h
e
v
al
u
e
o
f
t
h
e
co
n
tr
o
llab
le
p
ar
a
m
eter
u
to
g
et
t
h
e
d
esire
d
o
u
tp
u
t.
u
is
co
m
p
u
ted
u
s
i
n
g
e
q
u
atio
n
(
8
)
i
n
r
ea
l
ti
m
e.
T
h
i
s
co
n
tr
o
l
la
w
ca
n
b
e
ap
p
lied
to
an
y
d
y
n
a
m
ic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
1
7
6
–
3
1
8
9
3178
s
y
s
te
m
a
n
d
r
ep
o
r
ted
in
[
1
0
]
,
[
1
1
]
an
d
h
as
s
u
cc
ess
f
u
ll
y
b
ee
n
i
m
p
le
m
e
n
ted
in
t
h
e
co
m
m
a
n
d
tr
ac
k
in
g
o
f
h
i
g
h
p
er
f
o
r
m
a
n
ce
air
cr
af
t.
D
y
n
a
m
i
c
I
n
v
er
s
io
n
tech
n
iq
u
e
h
a
s
b
ee
n
ap
p
lied
to
an
SMI
B
an
d
its
r
o
b
u
s
t
n
es
s
also
ch
ec
k
ed
i
n
[
1
2
]
-
[
1
4
]
.
3.
F
I
VE
B
US P
O
W
E
R
SYS
T
E
M
WI
T
H
T
WO
M
ACH
I
NE
S (
T
E
S
T
SY
ST
E
M
1
)
Fig
u
r
e
1
s
h
o
w
s
a
f
iv
e
b
u
s
n
et
w
o
r
k
co
n
tain
i
n
g
t
w
o
g
e
n
er
ato
r
s
an
d
s
ev
e
n
tr
an
s
m
is
s
io
n
li
n
e
s
[
1
5
]
.
T
h
e
lo
ad
s
ar
e
in
MW
an
d
MV
A
r
an
d
a
b
ase
o
f
1
0
0
MV
A
is
co
n
s
id
er
ed
.
A
ll
t
h
e
r
ea
ctan
ce
s
an
d
th
e
h
alf
l
in
e
ch
ar
g
i
n
g
ad
m
itta
n
ce
s
ar
e
m
e
n
t
io
n
ed
in
p
er
u
n
it.
T
h
e
lin
e
r
esi
s
tan
ce
s
an
d
m
ac
h
i
n
e
r
esis
ta
n
c
es
ar
e
n
eg
lecte
d
.
I
t
is
as
s
u
m
ed
t
h
at
t
h
er
e
is
a
th
r
ee
p
h
ase
f
au
lt
o
n
b
u
s
5
a
n
d
t
h
e
s
a
m
e
i
s
clea
r
ed
w
it
h
o
u
t
c
h
an
g
i
n
g
th
e
s
y
s
te
m
co
n
f
i
g
u
r
atio
n
.
Fig
u
r
e
1
.
Mu
lti
-
m
ac
h
i
n
e
T
est s
y
s
te
m
B
u
s
1
is
co
n
s
id
er
ed
as a
s
lack
o
r
s
w
i
n
g
b
u
s
,
b
u
s
2
is
a
g
en
er
ato
r
o
r
a
P
V
b
u
s
an
d
b
u
s
e
s
3
,
4
an
d
5
ar
e
lo
ad
o
r
P
Q
b
u
s
.
T
h
e
f
o
ll
o
w
i
n
g
p
ar
a
m
eter
s
ar
e
u
s
ed
:
I
n
er
tia
co
n
s
tan
t
o
f
t
h
e
t
w
o
m
ac
h
in
e
s
ar
e
M
V
A
MJ
H
/
50
1
an
d
M
V
A
MJ
H
/
1
2
;
Dir
ec
t
ax
i
s
tr
a
n
s
ie
n
t
r
e
ac
tan
ce
o
f
th
e
f
ir
s
t
m
ac
h
in
e
is
pu
x
d
1
'
1
an
d
f
o
r
th
e
s
ec
o
n
d
m
ac
h
in
e
i
s
pu
x
d
5
.
1
'
2
.
3
.
1
.
T
ra
ns
ie
nt
Sta
bil
it
y
Ana
ly
s
is
w
it
ho
ut
D
I
T
ec
hn
iq
ue
A
ll
lo
ad
s
ar
e
co
n
v
er
ted
to
p
er
u
n
it
o
n
a
co
m
m
o
n
b
ase
o
f
1
0
0
MV
A
.
L
o
ad
f
lo
w
a
n
al
y
s
i
s
u
s
in
g
Ne
w
to
n
R
ap
h
s
o
n
m
et
h
o
d
w
a
s
d
o
n
e
p
r
io
r
t
o
th
e
f
au
lt a
n
d
t
h
e
r
esu
lt
s
ar
e
as sh
o
w
n
i
n
T
ab
le
1
.
T
ab
le
1
.
L
o
ad
Flo
w
An
al
y
s
i
s
B
u
s
N
o
.
P
G
+
j
Q
G
(
M
W
+
j
M
V
A
r
)
P
L
+
j
Q
L
(
M
W
+
j
M
V
A
r
)
V
θ
(
i
n
p
u
)
1
7
0
+
j
1
0
.
8
4
0
1
.
0
6
0
0
2
2
0
+
j
3
0
.
1
5
0
1
.
0
4
5
-
7
.
2
6
0
3
0
2
0
+
j
1
0
1
.
0
3
5
-
6
.
5
9
0
4
0
3
0
+
j
2
0
1
.
0
2
3
-
8
.
6
6
0
5
0
4
0
+
j
3
0
1
.
0
1
7
-
9
.
4
6
0
T
h
e
lo
ad
s
ar
e
co
n
v
er
ted
to
ad
m
itta
n
ce
s
.
T
h
e
v
o
lta
g
es
a
t
th
e
v
ar
io
u
s
b
u
s
e
s
,
c
u
r
r
en
t
f
r
o
m
th
e
g
en
er
ato
r
s
a
n
d
h
e
n
ce
t
h
e
p
o
w
er
s
f
r
o
m
t
h
e
g
e
n
er
ato
r
s
ar
e
ca
lcu
lated
.
T
h
e
s
tate
d
y
n
a
m
ics
e
q
u
atio
n
s
ar
e
s
o
lv
e
d
u
s
i
n
g
R
u
n
g
e
-
K
u
tta
4
th
o
r
d
er
m
eth
o
d
.
T
h
e
f
o
u
r
s
tate
d
y
n
a
m
ic
eq
u
atio
n
s
f
o
r
th
e
t
w
o
g
e
n
er
ato
r
s
ar
e
as f
o
llo
w
s
:
s
dt
d
1
1
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mu
lti Ma
ch
in
e
S
ta
b
ilit
y
Usi
n
g
Dyn
a
mic
I
n
ve
r
s
io
n
Tech
n
iq
u
e
(
A
b
h
a
Tr
ip
a
th
i)
3179
1
1
1
1
2
e
m
s
P
P
H
dt
d
(
1
0
)
s
dt
d
2
2
(
1
1
)
2
2
2
2
2
e
m
s
P
P
H
dt
d
(
1
2
)
w
h
er
e
1
an
d
2
ar
e
th
e
r
o
to
r
a
n
g
le
s
,
1
an
d
2
ar
e
th
e
an
g
u
lar
f
r
eq
u
en
cie
s
o
f
m
ac
h
in
e
1
an
d
2
r
esp
ec
tiv
el
y
a
n
d
s
is
th
e
s
y
n
c
h
r
o
n
o
u
s
o
r
n
o
m
in
al
f
r
eq
u
e
n
c
y
o
f
th
e
s
y
s
te
m
.
3
.
2
.
T
ra
ns
ie
nt
Sta
bil
it
y
Ana
ly
s
is
w
it
h 7
5
%
L
ine C
o
m
pe
ns
a
t
io
n
I
n
th
i
s
ca
s
e
i
t
ass
u
m
ed
th
a
t
th
e
lin
e
w
h
er
e
T
C
SC
w
il
l
b
e
co
n
n
ec
ted
i
s
7
5
%
co
m
p
en
s
ated
b
y
a
s
er
ies
ca
p
ac
itan
ce
co
n
n
ec
ted
to
it.
T
h
e
lin
e
r
ea
cta
n
ce
n
o
w
b
ec
o
m
e
s
0
.
2
p
er
u
n
it in
s
tead
o
f
0
.
8
p
u
.
3
.
3
.
T
ra
n
s
ie
nt
Sta
bil
it
y
Ana
ly
s
is
w
it
h D
I
T
ec
hn
i
qu
e
As
d
ep
icted
in
F
i
g
u
r
e
2
,
t
h
e
T
C
SC
is
p
r
esen
t
in
th
e
li
n
e
c
o
n
n
ec
ti
n
g
b
u
s
es
1
a
n
d
2
.
T
h
e
lin
e
i
s
5
0
%
co
m
p
e
n
s
ated
b
y
f
i
x
ed
ca
p
ac
ito
r
an
d
th
e
T
C
S
C
r
ea
cta
n
ce
i
s
v
ar
ied
b
et
w
ee
n
0
–
2
5
%.
T
h
e
r
ea
ctan
ce
o
f
th
e
li
n
e
w
il
l
ch
a
n
g
e
d
y
n
a
m
icall
y
as
t
h
e
T
C
SC
r
ea
ctan
ce
i
s
v
ar
ied
.
T
h
e
T
C
SC
is
o
p
er
ated
o
n
ly
in
t
h
e
ca
p
ac
itiv
e
r
eg
io
n
.
Fig
u
r
e
2
.
P
ar
t o
f
th
e
n
et
w
o
r
k
w
h
er
e
T
C
SC
is
i
n
s
er
ted
L
et
U
b
e
th
e
T
C
SC
r
ea
ctan
ce
(
ca
p
ac
itiv
e)
.
T
h
e
ele
m
en
ts
o
f
Y
w
i
ll
ch
a
n
g
e
as
t
h
e
co
n
tr
o
l
v
ar
ies.
Sin
ce
T
C
SC
i
s
in
li
n
e
1
-
2
,
h
en
ce
f
o
u
r
ele
m
e
n
ts
o
f
Y
th
at
w
ill
ch
an
g
e,
w
ill
b
e
12
Y
,
21
Y
,
11
Y
,
22
Y
an
d
th
e
y
ar
e
as g
iv
e
n
u
n
d
er
n
ea
t
h
:
)
/(
1
12
21
12
jU
jx
Y
Y
(
1
3
)
13
12
13
12
11
/
1
)
/(
1
h
l
c
h
l
c
y
y
jx
jU
jx
Y
(
1
4
)
25
24
23
12
25
24
23
12
22
/
1
/
1
/
1
)
/(
1
h
l
c
h
l
c
h
l
c
h
l
c
y
y
y
y
jx
jx
jx
jU
jx
Y
(
1
5
)
w
h
er
e
25
24
23
13
12
,
,
,
,
x
x
x
x
x
ar
e
th
e
s
er
ies
r
ea
ctan
ce
s
25
24
23
13
12
,
,
,
,
h
l
c
h
l
c
h
l
c
h
l
c
h
l
c
y
y
y
y
y
ar
e
th
e
h
al
f
li
n
e
ch
ar
g
i
n
g
ad
m
it
tan
ce
s
o
f
li
n
es
b
et
w
ee
n
b
u
s
e
s
1
-
2
,
1
-
3
,
2
-
3
,
2
-
4
an
d
2
-
5
r
esp
ec
ti
v
el
y
.
As
t
h
e
Y
ele
m
en
t
s
ar
e
ch
an
g
i
n
g
,
t
h
e
v
o
lta
g
e
s
d
u
r
in
g
th
k
)
1
(
ti
m
e
iter
atio
n
at
v
ar
io
u
s
b
u
s
e
s
w
ill c
h
a
n
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
1
7
6
–
3
1
8
9
3180
1
11
16
3
11
13
2
11
12
1
1
E
Y
Y
V
Y
Y
V
Y
Y
V
k
k
k
(
1
6
)
2
22
27
5
22
25
4
22
24
3
22
23
1
1
22
21
1
2
E
Y
Y
V
Y
Y
V
Y
Y
V
Y
Y
V
Y
Y
V
k
k
k
k
k
(
1
7
)
k
k
k
k
V
Y
Y
V
Y
Y
V
Y
Y
V
4
33
34
1
2
33
32
1
1
33
31
1
3
(
1
8
)
k
k
k
k
V
Y
Y
V
Y
Y
V
Y
Y
V
5
44
45
1
3
44
43
1
2
44
41
1
4
(
1
9
)
1
4
55
54
1
2
55
52
1
5
k
k
k
V
Y
Y
V
Y
Y
V
(
2
0
)
E
lectr
ical
p
o
w
er
o
f
f
ir
s
t
m
ac
h
i
n
e,
d
u
r
in
g
t
h
e
th
k
)
1
(
is
g
i
v
e
n
b
y
)
)
(
R
e
(
1
1
1
1
1
1
1
1
k
k
k
k
e
I
E
P
(
2
1
)
)
)
/
)
((
R
e
(
1
1
1
1
1
1
1
1
1
1
1
1
1
d
k
k
k
k
k
k
e
jx
V
E
E
P
(
2
2
)
Usi
n
g
t
h
e
v
o
lta
g
e
ex
p
r
es
s
io
n
f
r
o
m
eq
u
a
tio
n
(
1
7
)
,
1
1
1
11
16
3
11
13
2
11
12
1
1
1
1
1
1
1
1
1
1
/
.
.
.
.
Re
d
k
k
k
k
k
k
k
k
e
jx
E
Y
Y
V
Y
Y
V
Y
Y
E
E
P
(
2
3
)
Fin
all
y
,
)
)
)
/(
1
)(
(
/(
)
s
i
n
(
)
)
)
/(
1
)(
(
/(
)
s
i
n
(
12
1
12
1
1
3
1
1
13
1
2
1
1
12
1
12
1
1
2
1
1
1
2
1
1
1
1
U
x
a
U
x
x
Y
V
E
U
x
a
U
x
x
V
E
P
d
k
k
k
k
d
k
k
k
k
k
e
(
2
4
)
w
h
er
e
13
1
13
12
1
/
1
/
1
x
x
y
y
a
d
h
l
c
h
l
c
an
d
1
2
k
,
1
3
k
ar
e
th
e
a
n
g
les
o
f
v
o
lta
g
es
1
2
k
V
an
d
1
3
k
V
r
esp
ec
tiv
el
y
a
t
th
e
th
k
)
1
(
ti
m
e
iter
ati
o
n
.
No
w
,
th
e
f
o
u
r
s
ta
tes
ar
e
2
2
1
1
,
,
an
d
h
en
ce
t
h
e
s
ta
te
eq
u
atio
n
s
ca
n
b
e
r
e
w
r
itte
n
as
f
o
llo
w
s
:
s
x
dt
dx
x
2
1
1
(
2
5
)
1
1
1
2
2
2
e
m
s
P
P
H
dt
dx
x
(
2
6
)
s
x
dt
dx
x
4
3
3
(
27)
2
2
2
4
4
2
e
m
s
P
P
H
dt
dx
x
(
2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mu
lti Ma
ch
in
e
S
ta
b
ilit
y
Usi
n
g
Dyn
a
mic
I
n
ve
r
s
io
n
Tech
n
iq
u
e
(
A
b
h
a
Tr
ip
a
th
i)
3181
T
h
e
d
esire
d
o
u
tp
u
t
d
x
2
is
to
m
ain
tai
n
th
e
s
p
ee
d
o
f
th
e
f
ir
s
t
m
ac
h
in
e,
s
ta
te
2
x
,
co
n
s
tan
t,
at
3
7
7
r
ad
/s
ec
(
o
r
n
o
m
i
n
al
f
r
eq
u
en
c
y
as 6
0
Hz)
.
T
h
e
er
r
o
r
e
is
d
ef
i
n
ed
as
d
x
x
e
2
2
(
2
9
)
T
h
e
d
er
iv
ativ
e
o
f
er
r
o
r
is
d
x
x
e
2
2
(
3
0
)
T
h
e
er
r
o
r
d
y
n
a
m
ic
s
is
en
f
o
r
ce
d
as f
o
llo
w
s
:
0
1
e
K
e
(
3
1
)
No
w
t
h
e
s
o
lu
tio
n
o
f
s
u
c
h
an
e
q
u
atio
n
is
g
i
v
en
a
s
f
o
llo
w
s
:
t
K
e
e
t
e
1
0
)
(
(
3
2
)
w
h
er
e
1
K
is
a
p
o
s
iti
v
e
co
n
s
ta
n
t
w
h
ic
h
e
n
s
u
r
es
t
h
at
t
h
e
er
r
o
r
t
en
d
s
to
ze
r
o
as
ti
m
e
te
n
d
s
to
in
f
i
n
it
y
.
A
s
th
e
d
esire
d
o
u
tp
u
t is f
ix
ed
,
its
d
er
i
v
ati
v
e
is
ze
r
o
.
Usi
n
g
eq
u
at
io
n
s
(
2
6
)
in
eq
u
atio
n
(
3
0
)
,
th
e
f
o
llo
w
i
n
g
is
o
b
tain
ed
:
0
2
1
1
1
e
m
s
P
P
H
e
(
3
3
)
B
y
e
n
f
o
r
cin
g
er
r
o
r
d
y
n
a
m
ics
f
r
o
m
eq
u
a
tio
n
(
3
3
)
,
th
e
f
o
llo
w
i
n
g
i
s
o
b
tain
ed
:
0
)
(
0
2
2
2
1
1
1
1
d
e
m
s
x
x
K
P
P
H
(
3
4
)
Usi
n
g
t
h
e
v
alu
e
o
f
t
h
e
elec
tr
i
ca
l
p
o
w
er
f
r
o
m
eq
u
atio
n
(
2
4
)
,
in
eq
u
atio
n
(
3
4
)
,
th
e
co
n
tr
o
l
v
ar
iab
le
w
h
ic
h
i
s
r
ea
ctan
ce
o
f
T
C
SC
,
is
o
b
tain
e
d
as f
o
llo
w
s
:
'
1
3
1
13
3
1
'
1
2
1
2
1
2
2
1
1
1
/
)
s
i
n
(
/(
)
/
)
s
i
n
(
/
)
(
2
(
d
d
s
d
m
x
Y
V
E
x
V
E
x
x
H
K
P
U
)
/
1
)(
/
)
(
2
(
13
12
13
2
2
1
1
1
h
l
c
h
l
c
s
d
m
y
y
x
x
x
H
K
P
(
3
5
)
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS F
O
R
1
st
T
E
S
T
SYS
T
E
M
T
h
er
e
ar
e
tw
o
ca
s
e
s
tu
d
ies
d
o
n
e
an
d
th
e
r
es
u
lt
s
f
o
r
all
t
h
e
ca
s
es
ar
e
e
x
p
lain
ed
i
n
d
etail
in
t
h
e
f
o
llo
w
in
g
s
u
b
–
s
ec
tio
n
s
.
4
.
1
.
Ca
s
e
1
:
When f
a
ult
clea
ring
t
i
m
e
i
s
0
.
3
6
s
ec
o
nd
I
t
is
ass
u
m
ed
th
a
t
t
h
er
e
is
a
3
s
y
m
m
etr
ical
f
au
l
t
at
b
u
s
5
an
d
t
h
e
s
a
m
e
i
s
clea
r
ed
af
ter
0
.
3
2
s
ec
o
n
d
s
w
it
h
o
u
t
d
is
t
u
r
b
in
g
th
e
s
y
s
te
m
co
n
f
ig
u
r
atio
n
.
T
h
e
o
s
cillatio
n
s
o
f
t
h
e
r
o
to
r
a
n
g
le
an
d
s
p
ee
d
o
f
m
ac
h
i
n
e
2
ar
e
o
b
s
er
v
ed
.
T
h
e
s
y
s
te
m
i
s
s
i
m
u
lated
an
d
s
tab
ilit
y
w
i
th
a
n
d
with
o
u
t
DI
tech
n
iq
u
e
is
o
b
s
er
v
ed
.
T
h
e
r
esu
lt
s
ar
e
g
iv
e
n
u
n
d
er
n
ea
th
:
4
.
1
.
1
.
Wit
ho
ut
DI T
ec
hn
iq
ue
Fig
u
r
e
3
s
h
o
w
s
t
h
e
v
ar
iatio
n
o
f
t
h
e
d
elta
o
f
s
ec
o
n
d
m
ac
h
in
e
an
d
it
is
clea
r
t
h
at
th
e
s
y
s
te
m
i
s
b
ec
o
m
i
n
g
u
n
s
tab
le.
T
h
e
v
ar
ia
tio
n
o
f
s
p
ee
d
o
f
t
h
e
s
ec
o
n
d
m
ac
h
in
e
is
d
ep
i
cted
i
n
F
ig
u
r
e
4
.
T
h
e
s
y
s
te
m
is
u
n
s
tab
le
as it i
s
ev
id
e
n
t f
r
o
m
t
h
is
p
lo
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
1
7
6
–
3
1
8
9
3182
Fig
u
r
e
3
.
Delt
a
Var
iatio
n
w
it
h
o
u
t D
I
T
ec
h
n
iq
u
e
Fig
u
r
e
4
.
Sli
p
v
ar
iatio
n
w
it
h
o
u
t D
I
4
.
1
.
2
.
Wit
h 7
5
%
L
ine C
o
m
pe
ns
a
t
i
o
n
T
h
e
d
elta
v
ar
iatio
n
is
s
h
o
w
n
i
n
F
i
g
u
r
e
5
.
T
h
e
s
y
s
te
m
s
tab
ilit
y
is
lo
s
t.
T
h
e
r
o
to
r
a
n
g
le
k
ee
p
s
in
cr
ea
s
i
n
g
.
T
h
e
s
lip
v
ar
ia
tio
n
w
it
h
7
5
%
l
in
e
co
m
p
en
s
atio
n
i
s
s
h
o
w
n
in
F
i
g
u
r
e
6
.
T
h
e
s
lip
in
cr
ea
s
es
w
it
h
ti
m
e
an
d
th
e
s
y
s
te
m
b
ec
o
m
e
s
u
n
s
ta
b
le.
Fig
u
r
e
5
.
Delta
Var
iatio
n
w
it
h
7
5
% L
in
e
C
o
m
p
en
s
atio
n
Fig
u
r
e
6
.
Sli
p
Var
iatio
n
w
it
h
7
5
% L
i
n
e
C
o
m
p
e
n
s
at
io
n
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
-200
0
-150
0
-100
0
-500
0
500
1000
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
D
e
l
t
a
(
i
n
D
e
g
r
e
e
s
)
M
/
C
2
R
elat
iv
e
D
elt
a
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
-0.
06
-0.
04
-0.
02
0
0.
02
0.
04
0.
06
0.
08
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
S
L
I
P
(
i
n
p
e
r
u
n
i
t
)
M
/
C
2
SLI
P
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
-100
0
0
1000
2000
3000
4000
5000
6000
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
D
e
l
t
a
(
i
n
D
e
g
r
e
e
s
)
M
/
C
2
R
elat
iv
e
D
elt
a
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
S
L
I
P
(
i
n
p
e
r
u
n
i
t
)
M
/
C
2
SLI
P
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mu
lti Ma
ch
in
e
S
ta
b
ilit
y
Usi
n
g
Dyn
a
mic
I
n
ve
r
s
io
n
Tech
n
iq
u
e
(
A
b
h
a
Tr
ip
a
th
i)
3183
4
.
1
.
3
.
Wit
h DI Tec
hn
i
qu
e
T
h
e
d
elta
o
f
t
h
e
s
ec
o
n
d
m
ac
h
i
n
e
i
s
d
ep
icted
in
F
i
g
u
r
e
7
.
W
ith
DI
tec
h
n
iq
u
e
th
e
d
a
m
p
i
n
g
o
f
t
h
e
d
el
t
a
i
m
p
r
o
v
es
a
n
d
t
h
e
s
y
s
te
m
te
n
d
s
to
w
ar
d
s
s
tab
ilit
y
.
T
h
e
s
p
ee
d
o
f
m
ac
h
i
n
e
2
is
p
lo
tted
i
n
F
ig
u
r
e
8
.
Fro
m
t
h
e
g
r
ap
h
it
is
v
er
y
clea
r
th
a
t
th
e
d
am
p
i
n
g
h
as
i
m
p
r
o
v
ed
.
T
h
e
r
ea
ctan
ce
o
f
th
e
T
C
SC
is
c
h
an
g
in
g
to
k
ee
p
u
p
w
i
th
d
esire
d
r
esu
lts
a
n
d
th
e
p
lo
t o
f
th
e
s
a
m
e
is
s
h
o
w
n
in
F
ig
u
r
e
9
.
Fig
u
r
e
7
.
Delta
Var
iatio
n
w
it
h
DI
tech
n
iq
u
e
Fig
u
r
e
8
.
Sp
ee
d
Var
iatio
n
w
it
h
DI
T
ec
h
n
iq
u
e
Fig
u
r
e
9
.
T
C
SC
R
ea
ctan
ce
Va
r
iatio
n
4
.
2
.
Ca
s
e
2
:
Crit
ica
l C
lea
ring
T
im
e
a
n
d M
a
x
i
m
u
m
lo
a
din
g
a
t
bu
s
es
W
ith
t
h
e
lo
ad
f
i
x
ed
at
t
h
e
i
n
i
tial
v
al
u
es
(
p
r
io
r
to
th
e
f
a
u
lt)
,
a
3
s
y
m
m
etr
ical
f
a
u
lt
at
b
u
s
5
w
as
ass
u
m
ed
.
T
h
e
f
a
u
lt
clea
r
i
n
g
ti
m
e
w
as
i
n
cr
ea
s
ed
to
o
b
tain
th
e
cr
itical
clea
r
in
g
ti
m
e.
Nex
t,
f
o
r
th
e
s
a
m
e
n
atu
r
e
o
f
f
au
lt
at
b
u
s
5
an
d
f
au
l
t
clea
r
in
g
ti
m
e
f
ix
ed
at
0
.
3
s
ec
,
th
e
lo
ad
in
g
w
as
i
n
cr
ea
s
ed
at
v
ar
io
u
s
b
u
s
es.
T
h
is
w
a
y
th
e
m
a
x
i
m
u
m
lo
ad
in
g
p
o
s
s
ib
l
e
at
all
lo
ad
b
u
s
es,
w
it
h
o
u
t
DI
tech
n
iq
u
e,
w
it
h
7
5
%
lin
e
co
m
p
e
n
s
atio
n
an
d
w
it
h
DI
tech
n
iq
u
e,
w
as tab
u
la
te
d
.
T
h
e
s
a
m
e
is
g
iv
e
n
i
n
T
ab
le
2
.
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
-200
-150
-100
-50
0
50
100
150
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
D
e
l
t
a
(
i
n
D
e
g
r
e
e
s
)
M
/
C
2
D
elt
a
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
-0.
06
-0.
04
-0.
02
0
0.
02
0.
04
0.
06
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
S
L
I
P
(
i
n
p
e
r
u
n
i
t
)
M
/
C
2
SLI
P
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
0
0.
05
0.
1
0.
15
0.
2
T
i
m
e
(
i
n
s
e
c
o
n
d
s
)
X
t
c
s
c
(
i
n
p
e
r
u
n
i
t
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
1
7
6
–
3
1
8
9
3184
T
ab
le
2
.
C
C
T
an
d
Ma
x
i
m
u
m
L
o
ad
in
g
A
t
t
r
i
b
u
t
e
W
i
t
h
o
u
t
T
C
S
C
W
i
t
h
7
5
%
C
o
mp
e
n
s
a
t
i
o
n
W
i
t
h
T
C
S
C
C
r
i
t
i
c
a
l
C
l
e
a
r
i
n
g
t
i
me
(
i
n
se
c
)
0
.
3
1
5
se
c
0
.
3
3
8
se
c
0
.
3
6
se
c
M
a
x
i
m
u
m
L
o
a
d
i
n
g
a
t
b
u
s
3
4
0
M
W
7
5
M
W
8
4
M
W
M
a
x
i
m
u
m
L
o
a
d
i
n
g
a
t
b
u
s
4
4
0
M
W
8
2
M
W
9
5
M
W
M
a
x
i
m
u
m
l
o
a
d
i
n
g
a
t
b
u
s
5
5
5
M
W
8
5
M
W
9
6
M
W
5.
SE
CO
ND
T
E
ST
S
YS
T
E
M
:
T
H
RE
E
M
ACH
I
NE
5
B
US P
O
WE
R
SY
ST
E
M
T
h
e
s
a
m
e
p
o
w
er
s
y
s
te
m
as
d
ep
icted
in
f
i
g
u
r
e
1
is
co
n
s
id
er
ed
.
T
h
e
o
n
l
y
d
if
f
er
en
ce
i
s
th
at
a
th
ir
d
m
ac
h
in
e
i
s
co
n
s
id
er
ed
at
b
u
s
3
an
d
th
at
t
h
at
b
u
s
i
s
co
n
s
id
er
ed
to
b
e
a
P
V
b
u
s
.
T
h
e
ac
tiv
e
p
o
w
er
b
ei
n
g
f
i
x
ed
at
0
.
1
p
u
an
d
th
e
m
a
g
n
it
u
d
e
o
f
t
h
e
v
o
lta
g
e
at
1
.
0
2
p
u
.
T
h
e
r
esis
ta
n
ce
o
f
t
h
e
li
n
es
is
n
e
g
le
cted
.
As
m
en
tio
n
ed
ea
r
lier
,
th
e
v
alu
e
s
o
f
t
h
e
r
ea
ct
an
ce
s
ar
e
i
n
p
er
u
n
it.
A
p
ar
t
f
r
o
m
t
h
e
f
o
u
r
s
tate
eq
u
atio
n
s
m
e
n
tio
n
ed
b
e
f
o
r
e
f
o
r
2
m
ac
h
in
e
s
s
y
s
te
m
,
t
h
er
e
ar
e
t
w
o
m
o
r
e
s
tate
eq
u
a
tio
n
s
f
o
r
th
e
th
ir
d
m
ac
h
i
n
e
w
h
ic
h
ar
e
as f
o
l
lo
w
s
:
0
3
3
dt
d
(
3
6
)
3
3
3
3
2
e
m
s
P
P
H
dt
d
(
3
7
)
5
.
1
.
Wit
ho
ut
DI
T
ec
hn
iq
ue
T
h
e
lo
ad
f
lo
w
a
n
al
y
s
i
s
is
d
o
n
e
an
d
th
e
v
ar
io
u
s
r
es
u
lts
ar
e
ta
b
u
lated
in
T
ab
le
3
.
T
h
e
f
au
lt
i
s
ass
u
m
ed
to
b
e
at
b
u
s
5
an
d
th
e
s
a
m
e
i
s
r
ec
tif
ied
w
it
h
o
u
t a
f
f
ec
tin
g
s
y
s
t
e
m
co
n
f
i
g
u
r
atio
n
.
T
ab
le
3
.
L
o
ad
Flo
w
An
al
y
s
i
s
R
es
u
lts
B
u
s
N
o
.
P
G
(
i
n
M
W
)
Q
G
(
i
n
M
V
A
r
)
P
L
(
i
n
M
W
)
Q
L
(
i
n
M
V
A
r
)
V
θ
(
i
n
p
u
)
1
40
1
4
.
8
5
0
0
1
.
0
6
0
0
2
20
44
0
0
1
.
0
4
5
-
4
.
7
1
0
3
10
-
3
1
.
9
8
0
0
1
.
0
2
-
3
.
6
5
0
4
0
0
30
20
1
.
0
1
5
-
5
.
9
4
0
5
0
0
40
30
1
.
0
1
4
-
6
.
8
6
0
5
.
2
.
Ana
ly
s
is
w
it
h 7
5
%
L
ine C
o
m
p
en
s
a
t
io
n
T
h
e
lin
e
co
n
n
ec
ted
b
et
w
ee
n
b
u
s
e
s
2
an
d
4
is
7
5
%
co
m
p
en
s
ated
an
d
h
en
ce
th
e
n
e
w
r
ea
cta
n
ce
o
f
th
e
lin
e
b
ec
o
m
es
h
al
f
o
f
0
.
2
3
p
er
u
n
i
t.
5
.
3
.
Ana
ly
s
is
w
it
h DI Tec
hn
iq
ue
DI
tech
n
iq
u
e
is
r
ea
lized
th
r
o
u
g
h
t
h
e
T
C
SC
w
h
ic
h
is
p
lace
d
as d
ep
icted
in
F
ig
u
r
e
1
0
.
Fig
u
r
e
10.
P
ar
t
o
f
th
e
n
et
w
o
r
k
w
h
er
e
T
C
SC
is
p
r
esen
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mu
lti Ma
ch
in
e
S
ta
b
ilit
y
Usi
n
g
Dyn
a
mic
I
n
ve
r
s
io
n
Tech
n
iq
u
e
(
A
b
h
a
Tr
ip
a
th
i)
3185
T
C
SC
is
ass
u
m
ed
to
b
e
p
r
ese
n
t
in
li
n
e
co
n
n
ec
tin
g
b
u
s
es
2
an
d
4
.
T
h
er
ef
o
r
e
th
e
r
ea
ctan
ce
o
f
th
e
lin
e
w
il
l c
h
a
n
g
e
d
y
n
a
m
icall
y
a
s
t
h
e
T
C
SC
r
ea
ctan
ce
is
v
ar
ied
.
U
is
th
e
T
C
SC
r
ea
cta
n
ce
(
ca
p
ac
it
iv
e)
an
d
s
o
m
e
o
f
th
e
ele
m
e
n
t
s
o
f
Y
w
ill
c
h
an
g
e
ac
co
r
d
in
g
l
y
.
Sin
ce
T
C
SC
i
s
in
lin
e
2
-
4
,
h
en
ce
f
o
u
r
ele
m
e
n
ts
o
f
Y
th
at
w
il
l
ch
an
g
e
w
ill b
e
24
Y
,
42
Y
,
44
Y
an
d
22
Y
an
d
th
e
y
ar
e
as g
iv
e
n
u
n
d
er
n
ea
t
h
:
)
/(
1
24
24
42
jU
jx
Y
Y
(
3
8
)
45
43
24
45
43
24
44
/
1
/
1
)
/(
1
h
l
c
h
l
c
h
l
c
y
y
y
jx
jx
jU
jx
Y
(
3
9
)
25
24
23
21
25
23
21
'
2
24
22
/
1
....
/
1
/
1
/
1
)
/(
1
h
l
c
h
l
c
h
l
c
h
l
c
d
y
y
y
y
jx
jx
jx
jx
jU
jx
Y
(
4
0
)
w
h
er
e
25
24
23
21
,
,
,
x
x
x
x
ar
e
th
e
s
er
ies
r
ea
ctan
ce
s
25
24
23
21
,
,
,
h
l
c
h
l
c
h
l
c
h
l
c
y
y
y
y
ar
e
t
h
e
h
al
f
li
n
e
c
h
ar
g
i
n
g
ad
m
itta
n
ce
s
o
f
li
n
es
b
et
w
ee
n
b
u
s
es
2
-
1
,
2
-
3
,
2
-
4
a
n
d
2
-
5
r
esp
ec
tiv
el
y
.
T
h
e
d
esire
d
o
u
tp
u
t
d
x
4
is
to
m
ai
n
tai
n
th
e
s
p
ee
d
o
f
th
e
s
ec
o
n
d
m
ac
h
in
e,
s
tate
4
x
,
co
n
s
tan
t,
at
3
7
7
r
a
d
/s
ec
(
o
r
n
o
m
i
n
al
f
r
eq
u
en
c
y
a
s
6
0
Hz)
.
E
lectr
ical
p
o
w
er
o
f
s
ec
o
n
d
m
a
ch
in
e,
d
u
r
i
n
g
th
e
th
k
)
1
(
is
g
i
v
e
n
b
y
)
(
1
2
2
1
2
2
k
k
e
I
E
P
(
4
1
)
)
/
)
((
2
1
2
2
1
2
2
1
2
2
d
k
k
k
e
jx
V
E
E
P
(
4
2
)
Usi
n
g
t
h
e
v
o
lta
g
e
ex
p
r
es
s
io
n
f
r
o
m
eq
u
a
tio
n
(
1
7
)
,
2
1
2
22
27
5
22
25
4
22
24
3
22
23
1
1
22
21
2
1
2
2
1
2
2
/
j
x
d
E
Y
Y
V
Y
Y
V
Y
Y
V
Y
Y
V
Y
Y
E
E
P
k
k
k
k
k
k
k
e
(
4
3
)
Fin
all
y
,
)
)
)
/(
1
(
(
)
s
i
n
(
)
)
)
/(
1
)(
(
(
)
s
i
n
(
)
)
)
/(
1
(
(
)
s
i
n
(
)
)
)
/(
1
(
(
)
s
i
n
(
24
2
2
5
2
25
1
5
1
2
24
2
24
2
4
2
24
1
4
1
2
24
2
2
3
2
23
1
3
1
2
24
2
2
1
2
12
1
1
1
2
2
U
x
a
x
Y
V
E
U
x
a
U
x
x
Y
V
E
U
x
a
x
Y
V
E
U
x
a
x
Y
V
E
P
d
k
k
d
k
k
d
k
k
d
k
k
e
(
4
4
)
w
h
er
e
25
23
21
2
15
24
23
21
2
/
1
/
1
/
1
.
.
.
.
.
/
1
x
x
x
x
y
y
y
y
a
d
h
l
c
h
l
c
h
l
c
h
l
c
an
d
3
1
,
,
5
4
,
ar
e
th
e
an
g
les
o
f
v
o
ltag
es
1
2
k
V
,
1
3
k
V
,
1
4
k
V
an
d
1
5
k
V
r
esp
ec
tiv
el
y
.
T
h
e
er
r
o
r
e
is
d
ef
in
ed
as
d
x
x
e
4
4
(
4
5
)
T
h
e
d
er
iv
ativ
e
o
f
er
r
o
r
is
d
x
x
e
4
4
(
4
6
)
As th
e
d
esire
d
o
u
tp
u
t is
f
ix
ed
,
th
en
i
ts
d
er
iv
ati
v
e
i
s
ze
r
o
.
Usi
n
g
t
h
i
s
co
n
ce
p
t a
n
d
th
e
eq
u
ati
o
n
(
4
5
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.