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.
11
,
No
.
2
,
A
p
r
il
2
0
2
1
,
p
p
.
9
2
9
~
9
4
4
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
1
1
i
2
.
p
p
9
2
9
-
944
929
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
A
m
ho
t
y
pe
phas
e
co
m
pa
ra
tor
rela
y
guidelin
e using
pha
se
co
m
pa
riso
n t
echn
ique f
o
r a
po
w
er s
y
ste
m
J
o
s
é
Ant
o
nio
G
o
nzá
lez
-
Cuet
o
Cruz
1
,
Z
a
i
d G
a
rc
ía
Sá
nche
z
2
,
G
us
t
a
v
o
Cre
s
po
Sá
nchez
3
,
H
er
ná
n H
er
ná
nd
ez
H
er
re
ra
4
,
J
o
rg
e
I
v
á
n Silv
a
-
O
rt
eg
a
5
,
Vice
nte
L
eo
nel M
a
rt
íne
z
Día
z
6
1,
2,
3
Ce
n
ter
o
f
En
e
rg
y
a
n
d
En
v
ir
o
n
m
e
n
tal
S
tu
d
ies
De
p
a
rtm
e
n
t,
Un
iv
e
rsid
a
d
d
e
Cien
f
u
e
g
o
s,
Cu
b
a
4,
6
Un
iv
e
rsid
a
d
S
im
ó
n
Bo
lí
v
a
r,
F
a
c
u
lt
a
d
d
e
I
n
g
e
n
iería
s,
Ba
rra
n
q
u
il
l
a
,
Co
lo
m
b
ia
5
De
p
a
rta
m
e
n
to
d
e
E
n
e
rg
ía,
Un
iv
e
rsid
a
d
d
e
la Co
sta
,
Ba
rra
n
q
u
il
la,
Co
lo
m
b
ia
Ar
t
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
6
,
2
0
1
9
R
ev
i
s
ed
A
u
g
1
7
,
2
0
2
0
A
cc
ep
ted
Sep
24
,
2
0
20
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
m
h
o
d
istan
c
e
re
la
y
si
m
u
latio
n
b
a
se
d
o
n
th
e
p
h
a
se
c
o
m
p
a
riso
n
tec
h
n
i
q
u
e
u
sin
g
a
ty
p
ica
l
e
lec
tri
c
a
l
p
o
w
e
r
s
y
ste
m
s
a
n
a
ly
sis
so
f
t
w
a
re
f
o
r
t
w
o
c
a
se
s:
w
h
e
n
th
e
o
p
e
ra
ti
o
n
sta
te
is
c
lo
se
to
th
e
sta
ti
c
v
o
lt
a
g
e
li
m
it
a
n
d
d
u
rin
g
a
d
y
n
a
m
ic
p
e
rtu
rb
a
ti
o
n
in
th
e
sy
ste
m
.
T
h
e
p
a
p
e
r
e
v
a
lu
a
tes
th
e
im
p
e
d
a
n
c
e
v
a
riatio
n
s
c
a
u
se
d
b
y
c
o
m
p
lex
v
o
lt
a
g
e
v
a
lu
e
s,
th
e
m
h
o
p
o
lariz
a
ti
o
n
,
a
n
d
t
h
e
c
o
m
p
a
ra
to
r
o
p
e
ra
ti
n
g
re
g
io
n
in
t
o
t
h
e
c
o
m
p
lex
p
lan
e
.
In
a
d
d
it
i
o
n
,
th
e
p
a
p
e
r
f
o
u
n
d
th
e
i
n
f
o
rm
a
ti
o
n
f
o
r
th
e
d
y
n
a
m
ic
p
e
rtu
rb
a
ti
o
n
s
f
ro
m
th
e
o
u
t
p
u
ts
c
o
n
si
d
e
rin
g
a
m
id
-
term
sta
b
il
it
y
p
ro
g
ra
m
.
T
h
e
si
m
u
latio
n
o
f
th
e
m
h
o
-
p
h
a
se
c
o
m
p
a
ra
to
r
in
th
e
sta
ti
c
v
o
lt
a
g
e
p
ro
x
i
m
it
y
li
m
it
d
e
tec
ts
u
n
it
d
istan
c
e
e
le
m
e
n
ts
w
it
h
i
m
p
e
d
a
n
c
e
m
e
a
su
re
d
c
lo
se
to
re
a
c
h
th
e
th
re
sh
o
ld
i
n
th
e
ste
a
d
y
-
sta
te.
D
y
n
a
m
i
c
m
h
o
sim
u
latio
n
s
in
th
e
c
o
m
p
lex
p
lan
e
a
re
su
c
c
e
ss
f
u
ll
y
tes
ted
b
y
p
lo
tt
in
g
ti
m
e
p
h
a
se
d
iff
e
re
n
c
e
c
u
rv
e
s
o
n
t
h
e
c
o
m
p
a
ra
to
r
in
p
u
t
sig
n
a
ls.
Re
la
y
p
ro
g
ra
m
m
e
rs
c
a
n
u
se
th
e
se
c
u
rv
e
s
to
a
n
a
ly
z
e
o
th
e
r
p
h
a
se
c
o
m
p
a
ra
to
rs
a
p
p
li
c
a
ti
o
n
s
a
n
d
t
h
e
c
o
rre
sp
o
n
d
i
n
g
m
o
d
e
ls
in
t
h
e
c
o
m
p
lex
p
lan
e
.
K
ey
w
o
r
d
s
:
Dis
ta
n
ce
r
ela
y
s
E
lectr
ic
p
o
w
er
n
et
w
o
r
k
a
n
al
y
s
is
Mid
-
ter
m
s
tab
ilit
y
Mh
o
p
h
ase
co
m
p
ar
ato
r
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Her
n
án
Her
n
án
d
ez
Her
r
er
a
Facu
ltad
d
e
I
n
g
e
n
ier
ía
Un
i
v
er
s
id
ad
Si
m
ó
n
B
o
lív
ar
B
ar
r
an
q
u
illa,
C
o
lo
m
b
ia
E
m
ail:
h
er
n
a
n
.
h
er
n
an
d
ez
@
u
n
i
s
i
m
o
n
b
o
liv
ar
.
ed
u
.
co
,
h
er
n
a
n
h
h
8
1
3
@
g
m
ail.
co
m
NO
M
E
NCLAT
UR
E
1
S
,
2
S
Ph
ase
co
m
p
ar
ato
r
co
m
p
le
x
in
p
u
t
v
o
ltag
e
s
ig
n
als.
1
,
2
An
g
u
lar
T
h
r
esh
o
ld
v
alu
es
i
n
a
p
h
ase
co
m
p
ar
ato
r
s
etu
p
.
1
k
,
2
k
,
3
k
,
4
k
P
h
a
s
e
c
o
m
p
a
r
a
t
o
r
c
o
m
p
l
e
x
c
o
n
s
t
a
n
t
s
w
h
i
c
h
d
e
f
i
n
e
t
h
e
t
h
r
e
s
h
o
l
d
t
o
o
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
s
.
Z
Ph
ase
co
m
p
ar
ato
r
in
p
u
t
co
m
p
le
x
im
p
ed
an
ce
m
easu
r
ed
.
p
k
C
o
m
p
lex
co
n
s
tan
t
t
o
ad
ju
s
t.
A
,
B
P
h
a
s
e
c
o
m
p
a
r
a
t
o
r
c
o
m
p
l
e
x
c
o
n
s
t
a
n
t
i
m
p
e
d
a
n
c
e
s
.
2
S
Valu
e in
a m
h
o
p
h
ase
c
o
m
p
ar
ato
r
.
r
Z
C
o
m
p
lex
r
ep
lica
im
p
ed
an
ce
o
f
m
h
o
p
h
ase
c
o
m
p
ar
ato
r
,
eq
u
al
to
th
e
r
eac
h
ed
b
y
th
e
r
ela
y
.
V
P
h
a
s
e
c
o
m
p
a
r
a
t
o
r
i
n
p
u
t
c
o
m
p
l
e
x
v
o
l
t
a
g
e
.
p
V
C
o
m
p
lex
s
ig
n
al
v
o
ltag
e
o
f
m
h
o
p
h
as
e
co
m
p
ar
ato
r
u
s
ed
f
o
r
i
n
cr
ease
r
eliab
ilit
y
p
o
lar
izatio
n
v
o
ltag
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
2
9
-
944
930
I
P
h
a
s
e
c
o
m
p
a
r
a
t
o
r
i
n
p
u
t
c
o
m
p
l
e
x
c
u
r
r
e
n
t
.
p
Z
C
o
m
p
lex
im
p
ed
an
ce re
lated
to
p
V
.
An
g
u
lar
d
if
f
er
en
ce
b
etween
1
S
,
2
S
.
p
A
C
o
m
p
lex
v
ar
iab
le
im
p
ed
an
ce
o
f
m
h
o
p
h
as
e
co
m
p
ar
ato
r
r
elated
to
p
Z
.
A
n
g
u
l
a
r
d
i
f
f
e
r
e
n
c
e
b
e
t
w
e
e
n
t
h
e
c
o
m
p
l
e
x
c
o
n
s
t
a
n
t
s
.
V
No
d
e v
o
ltag
e m
o
d
u
le o
f
p
o
s
itiv
e s
eq
u
en
ce.
P
Activ
e p
o
wer
lo
ad
.
Q
R
eactiv
e p
o
wer
lo
ad
.
pv
Activ
e p
o
wer
lo
ad
v
o
ltag
e ex
p
o
n
en
t.
qv
R
eactiv
e p
o
wer
lo
ad
v
o
ltag
e ex
p
o
n
e
n
t.
R
J
R
ed
u
ced
J
aco
b
ia
n
m
atr
ix
o
f
n
o
d
e
r
eactiv
e
p
o
wer
in
j
ecti
o
n
s
with
r
esp
ect
n
o
d
e
v
o
ltag
e
m
o
d
u
les.
QV
J
J
aco
b
ian
s
u
b
-
m
atr
ix
o
f
n
o
d
e
r
eactiv
e
p
o
wer
in
j
ecti
o
n
s
p
ar
tial
d
er
iv
ativ
es
with
r
esp
ect
n
o
d
e v
o
ltag
e m
o
d
u
les.
Q
J
J
aco
b
ian
s
u
b
-
m
atr
ix
o
f
n
o
d
e
r
eactiv
e
p
o
wer
in
j
ectio
n
s
p
ar
tial
d
er
iv
ativ
es
wi
th
r
esp
ect n
o
d
e v
o
ltag
e an
g
les.
1
P
J
I
n
v
er
s
e
J
aco
b
ian
s
u
b
-
m
atr
i
x
o
f
n
o
d
e
activ
e
p
o
wer
in
j
ectio
n
s
,
p
ar
tial
d
er
iv
ativ
es
with
r
esp
ect n
o
d
e v
o
ltag
e an
g
les.
PV
J
J
aco
b
ian
s
u
b
-
m
atr
ix
o
f
n
o
d
e
a
ctiv
e
p
o
wer
in
j
ecti
o
n
s
,
p
ar
tial
d
er
iv
ati
v
es
with
r
esp
ect
n
o
d
e v
o
ltag
e m
o
d
u
les.
Q
I
n
cr
em
en
tal
v
ar
iatio
n
s
v
ecto
r
o
f
n
o
d
e
r
eactiv
e p
o
wer
in
j
ecti
o
n
s
.
V
I
n
c
r
e
m
e
n
t
a
l
v
a
r
i
a
t
i
o
n
s
v
e
c
t
o
r
o
f
c
o
m
p
l
e
x
p
o
s
i
t
i
v
e
s
e
q
u
e
n
c
e
n
o
d
e
v
o
l
t
a
g
e
s
.
Ma
x
P
M
a
x
i
m
u
m
a
c
t
i
v
e
p
o
w
e
r
r
e
c
e
i
v
e
d
o
f
a
l
i
n
e
a
t
s
t
e
a
d
y
s
t
a
t
e
o
p
e
r
a
t
i
o
n
f
o
r
k
n
o
w
n
e
n
d
v
o
l
t
a
g
e
s
.
SR
Y
Po
s
itiv
e
s
eq
u
en
ce
m
u
tu
al
ad
m
is
s
io
n
m
o
d
u
le
f
r
o
m
th
e
s
en
d
in
g
e
n
d
t
o
th
e
r
eceiv
in
g
en
d
o
n
o
n
e li
n
e.
S
V
Po
s
itiv
e
s
eq
u
en
ce
v
o
ltag
e
m
o
d
u
le
o
f
a
li
n
e
s
en
d
in
g
en
d
.
R
V
Po
s
itiv
e
s
eq
u
en
ce
v
o
ltag
e
m
o
d
u
le
o
n
a
r
eceiv
in
g
en
d
lin
e.
RR
G
Po
s
itiv
e
s
eq
u
en
ce
s
elf
co
n
d
u
ctan
ce
o
f
a
lin
e
r
eceiv
in
g
en
d
.
S
I
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
en
ce
cu
r
r
en
t
in
lin
e
s
en
d
in
g
en
d
.
R
I
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
en
ce
cu
r
r
en
t
in
lin
e
r
eceiv
in
g
en
d
.
SR
Y
C
o
m
p
lex
m
u
tu
al
ad
m
ittan
ce
o
f
p
o
s
itiv
e
s
eq
u
en
ce
f
r
o
m
s
en
d
in
g
en
d
t
o
r
eceiv
in
g
en
d
in
a tran
s
m
is
s
io
n
lin
e.
RS
Y
C
o
m
p
lex
m
u
tu
al
ad
m
ittan
ce
o
f
p
o
s
itiv
e
s
eq
u
en
ce
f
r
o
m
r
eceiv
in
g
en
d
to
s
en
d
in
g
en
d
o
f
a li
n
e.
SS
Y
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
en
ce
s
elf
-
ad
m
ittan
ce
in
a li
n
e s
e
n
d
in
g
en
d
lin
e.
RR
Y
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
en
ce
s
el
f
-
ad
m
ittan
ce
o
f
a li
n
e rec
eiv
in
g
en
d
.
S
V
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
e
n
ce
v
o
l
tag
e
in
lin
e
s
en
d
in
g
en
d
.
R
V
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
e
n
ce
v
o
ltag
e
in
lin
e
r
eceiv
in
g
en
d
.
SM
Z
C
o
m
p
lex
im
p
ed
an
ce
m
easu
r
ed
in
lin
e
s
en
d
in
g
en
d
at b
alan
ce
d
co
n
d
iti
o
n
s
.
RM
Z
C
o
m
p
lex
im
p
ed
an
ce
m
easu
r
ed
in
li
n
e
r
eceiv
in
g
en
d
at b
alan
ced
co
n
d
i
tio
n
s
.
SH
Y
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
e
n
ce
s
h
u
n
t
ad
m
ittan
ce o
f
a li
n
e.
S
E
R
Y
C
o
m
p
lex
p
o
s
itiv
e
s
eq
u
en
ce
s
er
ies
ad
m
ittan
ce o
f
a li
n
e.
C
M
h
o
c
i
r
c
l
e
c
e
n
t
e
r
p
o
i
n
t
i
n
t
h
e
c
o
m
p
l
e
x
p
l
a
n
e
.
R
R
ad
iu
s
o
f
a m
h
o
cir
cle.
)
(
k
Z
ij
C
o
m
p
l
e
x
l
i
n
e
t
o
l
i
n
e
i
m
p
e
d
a
n
c
e
m
e
a
s
u
r
e
d
i
n
n
e
t
w
o
r
k
l
i
n
e
e
n
d
a
t
i
n
s
t
a
n
t
k.
)
(
k
Z
ph
C
o
m
p
lex
p
h
ase
im
p
ed
an
ce
m
ea
s
u
r
ed
in
lin
e
en
d
at i
n
s
tan
t
k.
)
(
k
V
ij
Po
s
itiv
e
s
eq
u
en
ce
co
m
p
lex
li
n
e
to
lin
e
v
o
ltag
e
ij
f
o
r
a
n
etwo
r
k
lin
e
en
d
at
in
s
tan
t
k.
)
(
k
I
i
C
o
m
p
lex
lin
e
cu
r
r
en
t
i
o
f
p
o
s
iti
v
e
s
eq
u
en
ce
in
a n
etwo
r
k
lin
e en
d
at i
n
s
tan
t
k.
)
(
k
V
i
C
o
m
p
l
e
x
p
h
a
s
e
v
o
l
t
a
g
e
i
o
f
p
o
s
i
t
i
v
e
s
e
q
u
e
n
c
e
i
n
a
n
e
t
w
o
r
k
l
i
n
e
e
n
d
a
t
i
n
s
t
a
n
t
k.
abc
i
V
C
o
m
p
lex
p
h
ase
v
o
ltag
e
v
ecto
r
o
f
n
o
d
e
i
i
n
-
p
h
ase
co
m
p
o
n
en
ts
.
012
i
V
C
o
m
p
lex
p
h
ase
v
o
lta
g
e
v
ecto
r
o
f
n
o
d
e
i
in
s
eq
u
en
ce co
m
p
o
n
en
ts
.
S
T
T
r
an
s
f
o
r
m
atio
n
m
atr
ix
o
f
s
eq
u
en
ce
co
m
p
o
n
en
ts
to
p
h
ase
co
m
p
o
n
en
ts
.
012
B
U
S
V
C
o
m
p
lex
b
u
s
v
o
ltag
e
v
ecto
r
f
o
r
a
n
etwo
r
k
in
s
eq
u
e
n
ce co
m
p
o
n
en
ts
.
012
B
U
S
Z
C
o
m
p
lex
b
u
s
im
p
ed
an
ce
m
atr
ix
f
o
r
a
n
etwo
r
k
in
s
eq
u
e
n
ce co
m
p
o
n
e
n
t
s
.
0
1
2
B
U
S
I
C
o
m
p
lex
b
u
s
cu
r
r
en
t
v
ecto
r
f
o
r
a
n
etwo
r
k
in
s
eq
u
e
n
ce co
m
p
o
n
en
ts
.
012
SS
Y
C
o
m
p
lex
s
elf
ad
m
ittan
ce
s
u
b
-
m
atr
i
x
o
f
a
lin
e s
en
d
i
n
g
en
d
i
n
s
eq
u
en
ce co
m
p
o
n
en
ts
.
0
1
2
SR
Y
C
o
m
p
lex
m
u
tu
al
ad
m
ittan
ce
s
u
b
-
m
atr
i
x
o
f
a
lin
e
f
r
o
m
s
en
d
in
g
en
d
t
o
r
eceiv
in
g
en
d
in
s
eq
u
en
ce co
m
p
o
n
en
ts
.
0
1
2
RS
Y
C
o
m
p
lex
m
u
tu
al ad
m
ittan
ce
s
u
b
-
m
atr
i
x
o
f
a
lin
e
f
r
o
m
r
eceiv
in
g
en
d
to
s
en
d
in
g
en
d
i
n
s
eq
u
en
ce co
m
p
o
n
en
ts
.
0
1
2
RR
Y
C
o
m
p
lex
s
elf
ad
m
ittan
ce,
s
u
b
-
m
atr
i
x
o
f
a
lin
e rec
eiv
in
g
en
d
in
s
eq
u
en
ce c
o
m
p
o
n
en
t
s
.
abc
S
I
C
o
m
p
lex
p
h
ase
c
u
r
r
en
t
v
ecto
r
o
f
a
lin
e
s
en
d
in
g
en
d
in
-
p
h
ase
co
m
p
o
n
en
ts
.
a
b
c
R
I
C
o
m
p
lex
p
h
ase
cu
r
r
en
t
v
ecto
r
o
f
a
lin
e
r
eceiv
in
g
en
d
in
-
p
h
ase
co
m
p
o
n
en
ts
.
0
1
2
S
V
C
o
m
p
lex
p
h
ase
v
o
ltag
e
v
e
cto
r
o
f
a
lin
e
s
en
d
in
g
an
e
n
d
i
n
s
eq
u
en
ce co
m
p
o
n
e
n
ts
.
012
R
V
C
o
m
p
lex
p
h
ase
v
o
ltag
e v
ecto
r
o
f
a li
n
e
r
eceiv
in
g
en
d
in
s
e
q
u
en
ce c
o
m
p
o
n
en
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
mh
o
typ
e
p
h
a
s
e
co
mp
a
r
a
to
r
r
ela
y
g
u
id
elin
e
u
s
in
g
…
(
Jo
s
é
A
n
to
n
io
G
o
n
z
á
lez
-
C
u
eto
C
r
u
z
)
931
1.
I
NT
R
O
D
UCT
I
O
N
Utilit
ie
s
an
d
m
an
u
f
ac
t
u
r
er
s
r
ec
o
g
n
ize
p
r
o
tectio
n
s
ch
e
m
e
m
o
d
eli
n
g
f
o
r
p
o
w
er
s
y
s
te
m
s
as
a
u
s
ef
u
l
to
o
l
to
an
al
y
ze
t
h
eir
o
p
er
atio
n
an
d
p
ar
a
m
eter
s
[
1
,
2
]
.
R
ese
ar
ch
er
s
d
ev
elo
p
ed
th
e
p
h
ase
-
co
m
p
ar
is
o
n
m
eth
o
d
m
an
y
y
ea
r
s
a
g
o
f
o
r
tr
an
s
m
i
s
s
i
o
n
-
li
n
es
s
c
h
e
m
e
p
r
o
tectio
n
s
[
3
,
4
]
.
Ho
w
e
v
er
,
o
p
ti
m
al
allo
c
atio
n
a
n
d
d
y
n
a
m
ic
d
esig
n
r
eq
u
ir
e
f
ea
t
u
r
e
to
i
m
p
r
o
v
e
[
2
,
5
]
.
R
ela
y
s
i
m
u
latio
n
in
P
o
w
er
S
y
s
te
m
s
is
a
n
ac
ti
v
it
y
r
ec
o
g
n
ized
b
y
tech
n
ical
liter
at
u
r
e
th
ir
t
y
y
ea
r
s
ag
o
as
a
n
o
p
tio
n
to
an
al
y
ze
its
o
p
er
atio
n
a
n
d
ad
j
u
s
ti
n
g
p
a
r
a
m
eter
s
[
6
]
,
tr
an
s
ie
n
t
a
n
al
y
s
is
[
7
]
,
an
d
m
o
d
elin
g
u
s
i
n
g
co
m
p
u
ter
s
c
ie
n
ce
s
f
o
r
d
is
tan
ce
r
ela
y
s
[
8
]
.
Sin
ce
t
h
en
,
r
ela
y
s
m
o
d
eli
n
g
i
s
a
co
m
p
le
m
en
tar
y
to
o
l
to
p
r
o
v
e
a
n
d
ad
j
u
s
t
o
p
e
r
atio
n
s
c
h
e
m
es
[
9
,
1
0
]
.
T
h
e
m
h
o
t
y
p
e
d
is
ta
n
ce
r
ela
y
d
ev
elo
p
m
en
t
an
d
a
n
al
y
s
i
s
co
n
s
id
er
s
e
v
er
al
p
o
lar
i
za
tio
n
m
et
h
o
d
s
f
o
r
tr
an
s
m
i
s
s
io
n
-
li
n
es
s
c
h
e
m
e
p
r
o
tectio
n
s
[
1
0
-
1
3
]
.
T
h
er
e
ar
e
p
r
ec
ed
en
ts
in
d
ig
ita
l
s
o
f
t
w
ar
e
d
ev
elo
p
m
e
n
t
to
an
a
l
y
ze
t
h
e
p
r
o
tectio
n
r
esp
o
n
s
e
in
th
e
co
m
p
le
x
p
lan
e
d
u
r
i
n
g
a
s
h
o
r
t
-
cir
c
u
it
ev
e
n
t
[
1
4
-
1
6
]
.
A
n
d
o
th
er
to
p
ics
r
elate
d
w
i
th
s
u
p
er
v
is
io
n
an
d
m
o
d
eli
n
g
s
u
ch
a
s
th
o
s
e
r
e
f
er
r
ed
to
in
[
1
7
,
1
8
].
B
ased
o
n
th
e
f
u
n
d
a
m
e
n
tal
s
o
f
th
e
p
h
a
s
e
co
m
p
ar
ato
r
s
,
t
h
is
p
ap
er
p
r
esen
ts
a
n
e
w
te
ch
n
iq
u
e
to
d
eter
m
in
ate
t
h
e
d
is
p
lace
m
e
n
t
o
p
er
atin
g
zo
n
e
i
n
a
m
h
o
r
ela
y
co
m
p
le
x
p
lan
e
i
s
a
n
o
v
el
asp
e
ct,
co
n
s
id
er
in
g
th
a
t
th
e
o
p
er
atin
g
th
r
e
s
h
o
ld
o
f
t
h
e
m
h
o
in
a
co
m
p
le
x
p
la
n
e
is
t
h
e
p
o
lar
ch
ar
ac
ter
is
tic
o
n
a
c
ir
cle.
T
h
e
r
esear
ch
in
tr
o
d
u
ce
s
r
elev
a
n
t
p
r
in
cip
les
an
d
tech
n
iq
u
es
u
s
ed
in
t
h
e
s
o
f
t
w
ar
e
d
esi
g
n
.
T
h
e
p
ap
er
also
d
escr
ib
es
th
e
m
ai
n
eq
u
atio
n
s
u
s
ed
b
y
t
h
e
s
o
f
t
w
ar
e
an
d
th
e
o
u
tp
u
t
r
esu
lts
u
s
ed
t
o
g
et
th
e
p
r
o
tectio
n
zo
n
es
c
h
a
r
ac
ter
is
tics
an
d
t
h
e
i
m
p
e
d
a
n
c
e
m
e
a
s
u
r
e
d
b
y
t
h
e
p
h
a
s
e
c
o
m
p
a
r
a
t
o
r
.
T
h
e
p
a
p
e
r
i
n
c
l
u
d
e
s
tw
o
s
t
u
d
y
c
a
s
e
s
t
o
a
s
s
e
s
s
t
h
e
s
i
m
u
latio
n
o
f
t
h
e
p
r
o
tectio
n
p
lo
ttin
g
t
h
e
t
i
m
e
p
h
ase
d
if
f
er
en
ce
cu
r
v
es
f
o
r
a
c
o
m
p
ar
ato
r
i
n
p
u
t
s
i
g
n
als.
T
h
es
e
cu
r
v
es
m
u
s
t
h
av
e
p
h
ase
d
if
f
er
en
ce
v
al
u
es
f
o
r
o
p
er
atin
g
co
n
d
itio
n
s
,
t
h
ese
v
al
u
es
h
av
e
a
r
an
g
e
b
et
w
ee
n
-
9
0
an
d
9
0
d
eg
r
ee
s
,
in
th
e
m
o
m
e
n
t
w
h
en
t
h
e
co
r
r
es
p
o
n
d
in
g
m
ea
s
u
r
ed
i
m
p
ed
an
ce
s
ar
e
ab
o
v
e
o
r
w
ith
in
t
h
e
o
p
er
atio
n
cir
cle
in
t
h
e
co
m
p
le
x
p
la
n
e.
T
h
e
p
r
esen
c
e
o
f
s
y
m
m
etr
ic
a
n
d
as
y
m
m
etr
ic
d
is
tu
r
b
an
ce
s
s
u
c
h
a
s
s
h
o
r
t
cir
cu
it
s
,
o
p
e
n
co
n
d
u
cto
r
s
i
n
a
tr
a
n
s
m
i
s
s
io
n
-
li
n
es
a
n
d
p
o
w
er
o
s
cillatio
n
s
co
n
s
id
er
s
t
h
e
e
f
f
ec
ts
o
f
p
o
l
ar
izatio
n
t
y
p
e
a
n
d
m
e
m
o
r
y
u
s
ag
e.
T
r
an
s
m
is
s
io
n
lin
es
ar
e
th
e
ca
s
e
s
t
u
d
y
u
s
ed
,
b
u
t
its
ap
p
licatio
n
s
a
s
p
h
ase
c
o
m
p
ar
is
o
n
also
ca
n
b
e
ab
le
to
in
cl
u
d
e
ca
s
es
co
n
s
id
er
in
g
p
r
o
tectio
n
s
w
it
h
F
AC
T
S
d
ev
ices
[
19
,
2
0
]
,
s
h
u
n
t
co
m
p
en
s
atio
n
li
n
e
p
r
o
tectio
n
s
[
2
1
]
,
s
er
ies co
m
p
en
s
atio
n
[
2
2
]
an
d
p
r
o
tectio
n
s
in
n
et
w
o
r
k
s
w
i
th
w
i
n
d
g
e
n
er
ato
r
s
[
2
3
].
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
T
w
o
-
inp
ut
ph
a
s
e
co
m
pa
ra
t
o
r
T
h
e
f
o
l
l
o
w
i
n
g
e
q
u
a
t
i
o
n
s
a
r
e
t
h
e
i
n
p
u
t
s
i
g
n
a
l
s
i
n
a
p
h
a
s
e
c
o
m
p
a
r
a
t
o
r
i
n
t
h
e
m
o
s
t
g
e
n
e
r
a
l
c
a
s
e
[
3
,
5
,
1
5
]:
I
k
V
k
S
2
1
1
(
1
)
I
k
V
k
S
4
3
2
(
2
)
P
h
ase
co
m
p
ar
ato
r
r
ea
ch
es
t
h
e
o
p
er
atin
g
co
n
d
itio
n
w
h
e
n
b
o
th
p
h
ase
d
i
f
f
er
e
n
ce
s
i
g
n
als
ar
e
in
th
e
f
o
llo
w
in
g
i
n
ter
v
al
:
2
2
1
1
)
/
a
r
g
(
S
S
(
3
)
w
h
er
e,
is
th
e
p
h
a
s
e
d
if
f
er
en
ce
o
f
S
1
a
n
d
S
2
.
1
an
d
2
ar
e
co
n
s
tan
t
m
ag
n
it
u
d
es.
R
ep
lacin
g
(
1
)
an
d
(
2
)
in
to
(
3
)
g
iv
e
s
an
eq
u
iv
a
len
t e
x
p
r
ess
io
n
s
h
o
w
ed
as f
o
llo
w
s
:
2
4
3
2
1
2
1
1
a
r
g
a
r
g
I
k
V
k
I
k
V
k
S
S
(
4
)
I
f
(
4
)
is
d
iv
id
ed
b
y
I
,
w
h
e
n
its
v
alu
e
i
s
d
if
f
er
i
n
g
f
r
o
m
ze
r
o
,
th
e
eq
u
atio
n
is
:
2
4
3
2
1
1
a
r
g
a
r
g
A
Z
B
Z
k
V
k
k
Z
k
(
5
)
w
h
er
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
2
9
-
944
932
3
4
k
k
A
,
1
2
k
k
B
,
3
1
a
r
g
k
k
(
6
)
W
e
ca
n
w
r
ite
(
5
)
as:
2
2
1
1
a
r
g
a
r
g
S
S
Z
Z
A
Z
B
Z
(
7
)
w
h
er
e,
B
Z
Z
S
1
an
d
A
Z
Z
S
2
T
h
e
f
o
r
m
a
n
d
d
im
e
n
s
io
n
s
o
f
a
p
h
ase
co
m
p
ar
ato
r
ch
ar
ac
ter
is
tics
in
t
h
e
co
m
p
lex
Z
-
p
la
n
e
ar
e
g
iv
e
n
b
y
th
e
th
r
es
h
o
ld
o
p
er
at
in
g
co
n
d
i
tio
n
s
,
u
s
in
g
co
n
d
itio
n
s
i
n
(
7
)
to
d
eter
m
in
e
t
h
e
eq
u
alit
y
.
k
,
an
d
v
al
u
e
s
d
ef
in
e
s
th
e
eq
u
a
lit
y
co
n
d
itio
n
s
.
C
o
n
s
ta
n
t
s
A
an
d
B
ar
e
th
e
i
m
p
ed
an
ce
v
al
u
es
w
h
ic
h
d
eter
m
i
n
ate
t
h
e
ch
ar
ac
ter
is
tic
i
n
t
h
e
co
m
p
lex
p
lan
e,
2
S
Z
Z
A
an
d
1
S
Z
Z
B
.
T
h
u
s
,
th
e
alter
n
at
in
g
c
u
r
r
en
t
s
an
d
v
o
ltag
e
s
a
m
p
lit
u
d
e
an
d
p
h
ase
v
ar
iatio
n
s
d
o
n
o
t a
f
f
ec
t t
h
e
co
m
p
ar
ato
r
o
p
er
atin
g
zo
n
e
i
n
t
h
e
co
m
p
le
x
p
lan
e,
w
h
i
le
u
s
in
g
co
m
p
u
tatio
n
al
to
o
ls
th
e
co
m
p
ar
ato
r
ca
n
m
ea
s
u
r
e
cu
r
r
en
t a
n
d
v
o
ltag
e.
2
.
2
.
M
ho
ph
a
s
e
co
m
pa
ra
t
o
r
T
h
e
f
o
llo
w
i
n
g
i
n
p
u
t si
g
n
a
ls
to
th
e
p
h
ase
co
m
p
ar
ato
r
allo
w
t
o
o
b
tain
a
m
h
o
t
y
p
e
r
ela
y
.
I
Z
V
S
r
1
(
8
)
V
S
2
(
9
)
w
h
er
e,
1
1
k
,
r
Z
k
2
,
1
3
k
an
d
0
4
k
T
h
e
r
ep
lica
im
p
ed
an
ce
Z
r
is
i
d
en
tical
to
th
e
d
esire
d
r
elay
r
an
g
e.
I
n
t
h
is
g
en
er
al
ca
s
e
t
h
e
m
h
o
t
y
p
e
r
ela
y
is
s
el
f
-
p
o
lar
ized
an
d
its
ch
ar
ac
ter
is
tic
i
n
t
h
e
co
m
p
le
x
p
lan
e
is
a
cir
cle
w
h
ic
h
p
ass
th
r
o
u
g
h
t
h
e
o
r
ig
i
n
w
h
e
n
th
e
li
m
it
s
an
d
co
n
s
tan
ts
ar
e:
1
−
=
9
0
°
,
2
−
=
−
9
0
°
,
0
A
,
r
Z
B
a
n
d
,
1
=
−
9
0
°
,
2
=
9
0
°
,
=
−
18
0
°
Hen
ce
,
Z
S1
an
d
S
1
h
a
v
e
a
p
h
as
e
d
if
f
er
e
n
ce
o
f
1
8
0
0
.
T
h
is
p
r
o
tectio
n
r
eq
u
ir
es p
o
lar
izatio
n
s
i
g
n
al
S
2
i
n
o
r
d
er
to
p
r
o
v
id
e
a
r
eliab
le
r
ef
er
e
n
ce
a
n
g
le
.
T
h
e
s
elf
-
p
o
lar
izatio
n
d
o
es
n
o
t
s
u
it
w
h
en
a
b
o
lted
f
a
u
lt
is
to
o
clo
s
e
to
th
e
s
i
g
n
a
l,
t
h
er
ef
o
r
e
ad
ap
ti
v
e
p
o
lar
izatio
n
is
a
b
etter
o
p
tio
n
.
I
t
ca
n
b
e
cr
o
s
s
,
co
m
b
i
n
ed
o
r
m
e
m
o
r
y
p
o
lar
ize
d
[
1
5
,
2
4
]
.
T
h
e
f
ir
s
t
t
w
o
f
a
il
o
n
b
o
ld
th
r
ee
-
p
h
ase
s
h
o
r
t
cir
cu
its
,
o
n
l
y
m
e
m
o
r
y
p
o
lar
izatio
n
s
o
lv
e
s
t
h
e
p
r
o
b
le
m
.
W
it
h
a
m
h
o
r
ela
y
w
i
th
co
m
b
in
ed
o
r
d
u
al
p
o
lar
izatio
n
,
th
e
S2
s
ig
n
al
d
es
cr
ib
es th
e
f
o
llo
w
i
n
g
m
at
h
r
elat
io
n
.
p
p
V
k
V
S
2
(
1
0
)
W
h
ile
f
o
r
th
e
cr
o
s
s
o
r
s
i
m
p
le
p
o
lar
izatio
n
,
th
e
S2
s
ig
n
al
is
p
p
V
k
S
2
(
1
1
)
T
h
e
m
h
o
th
r
es
h
o
ld
o
p
er
atin
g
c
o
n
d
itio
n
s
i
n
t
h
e
co
m
p
lex
p
la
n
e
ar
e:
2
2
1
a
r
g
a
r
g
p
S
r
A
Z
B
Z
Z
Z
Z
(1
2
)
I
n
t
h
e
m
h
o
A
p
a
n
d
B
a
r
e
a
l
s
o
i
m
p
e
d
a
n
c
e
v
a
l
u
e
s
w
h
i
c
h
d
e
t
e
r
m
i
n
e
t
h
e
c
i
r
c
l
e
d
i
a
m
e
t
e
r
i
n
t
h
e
c
o
m
p
l
e
x
p
l
a
n
e
.
1
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
mh
o
typ
e
p
h
a
s
e
co
mp
a
r
a
to
r
r
ela
y
g
u
id
elin
e
u
s
in
g
…
(
Jo
s
é
A
n
to
n
io
G
o
n
z
á
lez
-
C
u
eto
C
r
u
z
)
933
r
Z
B
(
13)
I
n
co
m
b
in
ed
p
o
lar
izatio
n
p
Z
Z
I
V
k
V
Z
p
p
S
/
)
(
2
(
1
4
)
an
d
th
e
v
ar
iab
le
i
m
p
ed
an
ce
in
th
e
co
m
p
lex
p
la
n
e
is
p
Z
Z
Z
A
S
p
2
(
1
5
)
I
n
s
i
m
p
le
p
o
lar
izatio
n
p
p
p
S
Z
I
V
k
Z
/
2
(
1
6
)
p
S
p
Z
Z
Z
Z
A
2
(
1
7
)
T
h
e
co
m
m
o
n
d
u
al
a
n
d
s
i
m
p
l
e
p
o
lar
izatio
n
s
i
g
n
al
s
ar
e
s
h
o
w
n
i
n
[
1
5
]
.
Usi
n
g
p
o
s
iti
v
e
s
eq
u
en
ce
,
p
o
lar
izatio
n
w
it
h
m
e
m
o
r
y
i
s
ex
p
lain
ed
in
[
2
4
]
.
T
h
u
s
,
t
h
e
ch
ar
ac
ter
is
tic
o
f
s
el
f
-
p
o
lar
ized
m
h
o
r
ela
y
w
ill
al
w
a
y
s
b
e
s
tatic
i
n
th
e
co
m
p
le
x
p
l
an
e
a
n
d
eq
u
al
f
o
r
all
p
h
a
s
e
an
d
lin
e
r
ela
y
s
w
i
th
t
h
e
s
a
m
e
r
an
g
e.
W
h
ile
f
o
r
th
e
co
m
b
i
n
ed
p
o
lar
izatio
n
,
t
h
e
ch
ar
ac
ter
is
tic
s
d
is
p
lace
s
f
r
o
m
t
h
e
o
r
ig
i
n
ac
co
r
d
in
g
w
i
th
t
h
e
v
alu
e
o
f
Z
p
.
Fo
r
u
n
b
ala
n
ce
d
co
n
d
itio
n
s
p
h
ase
to
g
r
o
u
n
d
a
n
d
lin
e
to
li
n
e
c
h
ar
ac
ter
is
tic
p
r
o
tectio
n
s
ar
e
d
if
f
er
en
t.
T
h
e
s
i
m
p
le
p
o
lar
izatio
n
b
eh
av
io
r
i
n
b
ala
n
ce
d
o
p
er
atio
n
an
d
w
i
th
o
u
t
m
e
m
o
r
y
ac
tio
n
i
s
id
en
t
ical
t
o
s
elf
-
p
o
lar
ized
.
I
n
u
n
b
ala
n
ce
d
co
n
d
itio
n
s
o
r
v
o
l
tag
e
v
ar
iatio
n
s
u
n
d
er
m
e
m
o
r
y
e
f
f
ec
t,
th
e
s
i
m
p
le
p
o
lar
izat
io
n
ch
ar
ac
ter
is
tic
s
d
is
p
lace
f
r
o
m
th
e
o
r
ig
i
n
.
I
n
u
n
b
ala
n
ce
d
o
p
er
atio
n
all
p
h
ases
an
d
lin
e
c
h
ar
ac
ter
is
tic
p
r
o
tectio
n
s
ar
e
also
d
if
f
er
e
n
t i
n
th
e
s
i
m
p
le
p
o
lar
izatio
n
.
T
h
e
f
o
llo
w
i
n
g
ex
a
m
p
le
d
escr
ib
e
th
ese
is
s
u
e
s
.
Fig
u
r
e
1
(
a)
s
h
o
w
s
th
e
co
m
p
lex
p
lan
e
co
n
s
id
er
in
g
t
h
r
ee
m
h
o
t
y
p
ical
c
h
ar
ac
ter
is
tic
s
,
M1
s
el
f
-
p
o
lar
ized
,
M2
an
d
M3
w
it
h
a
co
m
b
i
n
ed
p
o
lar
izatio
n
an
d
a
0
.
1
5
|
k
p
|
v
al
u
e.
T
h
e
last
o
n
e
h
as
a
r
ev
er
s
e
r
ea
ch
f
o
r
M1
,
M2
.
M3
h
a
v
e
an
8
0
%
m
o
d
u
lar
r
ea
ch
i
n
t
h
e
Z
l.
F
o
r
a
th
r
ee
-
p
h
ase
f
au
l
t
i
n
F,
m
i
d
d
le
o
f
t
h
e
l
i
n
e,
M1
an
d
M2
cu
r
r
en
ts
ar
e
I
=2
V/
Z
l
an
d
M3
cu
r
r
en
t
i
s
I
=
-
2
V/
Z
l.
T
h
e
p
o
in
ts
A
p
2
a
n
d
A
p
3
ar
e
m
atch
i
n
g
b
ec
a
u
s
e
t
h
e
M3
ch
ar
ac
ter
is
tic
in
Fi
g
u
r
e
1
(
a)
d
r
aw
a
1
8
0
-
p
h
ase
s
h
i
f
t
i
n
t
h
e
c
o
m
p
lex
p
lan
e
f
o
r
its
r
ev
er
s
e
r
ea
ch
.
W
h
en
M1
an
d
M2
o
p
er
ates,
M3
is
in
ac
tiv
e.
T
ab
le
1
s
h
o
w
s
th
e
m
o
s
t
i
m
p
o
r
tan
t
u
n
i
t
i
m
p
ed
an
ce
s
w
h
ile
Fig
u
r
e
1
(
b
)
s
h
o
w
s
th
e
i
n
p
u
t
s
i
g
n
al
v
al
u
es
a
n
d
it
s
p
h
ase
s
h
i
f
t
an
d
T
ab
le
1
d
escr
ib
es
ea
ch
u
n
it.
T
h
e
c
u
r
r
en
t
a
n
g
le
m
ea
s
u
r
ed
b
y
t
h
e
co
m
p
ar
ato
r
s
ca
u
s
e
t
h
e
p
h
ase
s
h
i
f
t
b
et
w
ee
n
Z
p
an
d
Z
r
an
d
s
u
b
s
eq
u
en
t
v
ar
iatio
n
i
n
t
h
e
M2
an
d
M3
d
iam
e
ter
s
,
r
esu
lti
n
g
a
s
h
if
t o
f
th
e
c
h
ar
ac
t
er
is
tics
.
(
a
)
(
b
)
Fig
u
r
e
1
.
I
n
p
u
t si
g
n
a
ls
v
alu
e
s
an
d
its
p
h
a
s
e
s
h
if
t o
f
M1
,
M2
an
d
M3
u
n
it
s
,
(
a)
co
m
p
le
x
p
lan
e,
(
b
)
ar
g
u
m
e
n
ts
(
S
1
/
S
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
2
9
-
944
934
T
ab
le
1
.
Valu
es o
f
th
e
i
n
p
u
t
s
i
g
n
al
s
an
d
i
m
p
o
r
tan
t i
m
p
ed
a
n
c
es o
f
M1
,
M2
an
d
M3
u
n
its
U
n
i
t
S
1
S
2
A
r
g
(
S
1
/
S
2
)
Z
r
Z
p
A
P
B
M1
0
.
6
V
V
0
0
0
.
8
Z
l
0
0
0
.
8
Z
l
M2
0
.
6
V
V
0
0
0
.
8
Z
l
0
.
1
5
Z
l
-
0
.
1
5
Z
l
0
.
8
Z
l
M3
-
1
.
6
V
V
1
8
0
0
0
.
8
Z
l
-
0
.
1
5
Z
l
-
0
.
1
5
Z
l
-
0
.
8
Z
l
3.
SYST
E
M
AN
AL
YS
I
S US
I
N
G
CO
M
P
UT
AT
I
O
N
AL
T
O
O
L
S
3
.
1
.
Sta
t
ic
v
o
lt
a
g
e
s
t
a
bil
it
y
Utilit
ie
s
a
n
d
R
ela
y
p
r
o
g
r
a
m
m
er
s
ca
n
f
i
n
d
t
h
e
n
et
w
o
r
k
o
p
er
atio
n
li
m
it
i
n
a
s
tead
y
s
tate,
i
n
cr
ea
s
i
n
g
th
e
lo
ad
i
n
d
i
f
f
er
e
n
t
s
elec
ti
v
e
f
o
r
m
s
.
T
h
e
s
o
f
t
w
ar
e
i
m
p
le
m
en
ts
th
r
ee
a
lg
o
r
it
h
m
s
:
i)
F
as
t
u
n
co
u
p
led
n
e
w
to
n
-
r
ap
h
s
o
n
al
g
o
r
ith
m
(
NR
)
[
2
5
]
;
ii)
Fo
r
m
a
l
NR
al
g
o
r
ith
m
[
2
6
,
2
7
]
an
d
;
iii)
C
o
n
tin
u
o
u
s
p
o
w
er
f
lo
w
a
lg
o
r
it
h
m
b
ased
o
n
N
R
[
2
8
]
.
Als
o
,
t
h
e
s
o
f
t
w
ar
e
p
lo
ts
th
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
v
s
v
o
lta
g
e
a
n
d
lo
ad
an
g
le
f
r
o
m
t
h
e
alg
o
r
ith
m
s
o
u
tp
u
t.
R
es
u
lts
s
h
o
w
s
th
e
p
o
w
er
lo
ad
f
lo
w
s
f
o
r
th
e
cr
itical
p
o
in
t.
T
h
e
v
o
ltag
e
co
llap
s
e
p
o
in
t
i
s
t
h
e
m
a
x
i
m
u
m
lo
ad
p
o
in
t
tr
an
s
f
er
r
ed
in
to
th
e
s
y
s
te
m
f
o
r
co
n
s
t
an
t
p
o
w
e
r
lo
ad
s
v
s
.
v
o
lta
g
e.
T
h
e
al
g
o
r
it
h
m
s
co
n
ti
n
u
e
in
cr
ea
s
in
g
th
e
b
u
r
d
en
w
h
ile
th
e
f
i
n
al
p
o
w
er
f
o
r
ea
c
h
iter
atio
n
ex
ce
ed
s
th
e
p
r
ev
io
u
s
iter
atio
n
.
T
h
e
cr
itical
p
o
in
t
is
in
v
ici
n
i
t
y
w
it
h
n
o
n
co
n
v
er
g
e
n
ce
p
o
w
er
f
lo
w
p
o
in
t.
T
h
e
v
o
ltag
e
v
s
t
h
e
co
n
s
tan
t
ac
ti
v
e
p
o
w
er
c
h
ar
ac
ter
is
tic
i
s
a
p
er
p
en
d
icu
lar
s
tr
ai
g
h
t
l
in
e
to
t
h
e
p
o
w
er
ax
is
.
T
h
e
m
ax
i
m
u
m
lo
ad
an
d
th
e
s
tatic
b
if
u
r
ca
tio
n
p
o
in
t
r
eq
u
ir
e
an
o
t
h
er
p
r
o
o
f
w
h
en
co
n
s
id
er
in
g
lo
ad
s
v
ar
y
i
n
g
w
it
h
t
h
e
v
o
ltag
e.
E
q
u
atio
n
s
s
h
o
w
ed
in
(
1
8
)
r
ep
r
esen
ts
lo
ad
s
b
elo
w
w
it
h
e
x
p
o
n
en
t
s
pv
an
d
qv
v
alu
es
d
if
f
er
e
n
t
f
r
o
m
ze
r
o
[
29
, 3
0
]
.
T
h
e
s
u
b
-
i
n
d
ex
0
id
en
tifie
s
t
h
e
in
i
tial state
o
f
th
e
alg
o
r
ith
m
.
pv
V
V
P
P
0
0
,
qv
V
V
Q
Q
0
0
(
1
8
)
Sear
ch
i
n
g
f
o
r
th
e
cr
itical
p
o
in
t
s
o
l
u
tio
n
s
,
it
ca
n
b
e
f
o
u
n
d
a
p
o
in
t
w
it
h
g
r
ea
ter
lo
ad
p
o
w
er
th
an
t
h
e
p
r
ev
io
u
s
o
n
e
u
n
d
er
u
n
s
tab
le
w
it
h
v
o
lta
g
e
d
ep
en
d
en
t
lo
ad
s
.
Fig
u
r
e
2
s
h
o
w
s
th
is
s
it
u
atio
n
n
ea
r
th
e
cr
itical
p
o
in
t.
P
o
in
t
A
is
n
o
t
t
h
e
m
a
x
i
m
u
m
p
o
i
n
t
an
d
f
o
r
an
i
n
cr
e
m
e
n
t
i
n
t
h
e
lo
ad
th
e
s
o
f
t
w
ar
e
ca
n
co
n
v
er
g
e
li
k
e
in
a
B
p
o
in
t,
w
h
ich
co
u
ld
b
e
an
u
n
s
tab
le
p
o
in
t.
W
e
ca
n
f
in
d
o
th
er
s
o
lu
tio
n
s
w
h
e
n
th
e
m
a
x
i
m
u
m
lo
ad
an
d
t
h
e
b
if
u
r
ca
tio
n
p
o
in
t a
r
e
d
if
f
er
en
t.
A
s
e
n
s
iti
v
it
y
te
s
t is a
g
o
o
d
s
o
lu
tio
n
i
n
t
h
ese
ca
s
e
s
.
[
2
7
,
29
, 3
1
].
Fi
g
u
r
e
2
.
C
r
itical
p
o
in
t v
icin
i
t
y
T
h
e
s
o
lu
tio
n
p
o
in
t
is
u
n
s
tab
l
e
in
th
e
s
e
n
s
iti
v
it
y
test
o
f
o
n
e
ter
m
o
n
t
h
e
m
ain
d
ia
g
o
n
al
if
J
R
-
1
is
n
eg
at
iv
e.
T
h
ese
ter
m
s
ar
e
t
h
e
to
tal
d
er
iv
ati
v
es
o
f
t
h
e
v
o
ltag
e
s
r
eg
ar
d
in
g
to
t
h
e
r
ea
cti
v
e
p
o
w
er
v
ar
iatio
n
s
.
T
h
e
m
atr
i
x
J
R
i
s
a
r
ed
u
ce
d
m
a
tr
ix
f
o
u
n
d
b
y
th
e
f
o
llo
w
in
g
m
atr
i
x
eq
u
atio
n
s
,
w
h
er
e
J
Pθ,
J
PV,
J
Qθ
a
n
d
J
QV
ar
e
n
e
t
w
o
r
k
j
ac
o
b
ian
s
u
b
-
m
a
tr
ices.
PV
P
Q
QV
R
J
J
J
J
J
1
(
1
9
)
V
J
Q
R
(
2
0
)
Q
J
V
R
1
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
mh
o
typ
e
p
h
a
s
e
co
mp
a
r
a
to
r
r
ela
y
g
u
id
elin
e
u
s
in
g
…
(
Jo
s
é
A
n
to
n
io
G
o
n
z
á
lez
-
C
u
eto
C
r
u
z
)
935
T
h
e
s
o
f
t
w
ar
e
ca
n
m
a
k
e
a
m
o
d
al
an
al
y
s
is
an
d
f
in
d
th
e
ei
g
e
n
v
al
u
e
s
u
s
i
n
g
a
r
ed
u
ce
d
m
a
tr
ix
J
R
w
i
th
a
cr
itical
s
tate
v
ar
iab
le
v
al
u
e.
T
h
e
p
ar
ticip
atio
n
f
ac
to
r
s
o
f
n
o
d
es,
b
r
an
ch
es
an
d
g
e
n
er
ato
r
s
ca
n
b
e
f
o
u
n
d
f
o
r
th
e
s
m
al
ler
eig
en
v
al
u
es
a
n
d
th
e
n
et
w
o
r
k
cr
itical
ele
m
e
n
ts
.
T
h
is
an
al
y
s
is
i
s
a
m
ea
s
u
r
e
o
f
th
e
v
i
cin
it
y
to
th
e
cr
itical
p
o
in
t
an
d
th
e
b
r
an
ch
e
s
w
i
th
h
ig
h
p
ar
ticip
atio
n
s
ar
e
w
ea
k
l
i
n
k
s
o
r
ar
e
h
ea
v
il
y
lo
ad
ed
[2
7
]
.
T
h
e
lin
e
w
i
t
h
t
h
e
h
i
g
h
e
s
t
a
c
t
i
v
e
p
o
w
e
r
p
e
r
c
e
n
t
t
r
a
n
s
f
e
r
r
e
d
i
s
d
e
t
e
r
m
i
n
e
d
b
y
(
2
2
)
.
T
h
e
s
e
e
l
e
m
e
n
t
s
a
r
e
u
s
e
f
u
l
f
o
r
c
o
n
t
i
n
g
e
n
c
y
s
e
l
e
c
t
i
o
n
a
n
d
i
t
a
l
l
o
w
t
o
i
d
e
n
t
i
f
y
t
h
e
p
r
o
t
e
c
t
i
o
n
s
c
l
o
s
e
r
t
o
t
h
e
i
r
r
e
a
c
h
t
h
r
e
s
h
o
l
d
v
a
l
u
e
s
i
n
t
h
e
cr
itical
s
tate.
2
R
RR
R
S
SR
M
a
x
V
G
V
V
Y
P
(
2
2
)
T
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
allo
w
to
f
in
d
t
h
e
b
r
an
c
h
e
s
cu
r
r
en
t
s
:
R
S
RR
RS
SR
SS
R
S
V
V
Y
Y
Y
Y
I
I
(
2
3
)
T
h
e
r
esu
lts
i
n
th
is
co
m
p
u
tati
o
n
al
to
o
l
co
n
s
id
er
s
b
alan
ce
d
p
h
ases
,
a
n
d
v
o
ltag
e
s
o
n
ea
c
h
en
d
o
f
th
e
lin
e
allo
w
i
n
g
to
f
i
n
d
th
e
i
m
p
e
d
an
ce
v
al
u
es.
)]
(
/[
R
S
S
E
R
S
SH
S
SM
V
V
Y
V
Y
V
Z
(
2
4
)
)]
(
/[
S
R
S
E
R
R
SH
R
RM
V
V
Y
V
Y
V
Z
(
2
5
)
Hen
ce
,
th
e
i
m
p
ed
an
ce
v
alu
e
s
ab
o
v
e
f
o
r
ea
ch
s
tab
le
s
ta
g
e
s
o
lu
tio
n
p
r
o
ce
d
u
r
e
f
r
o
m
th
e
in
itia
l
co
n
d
itio
n
to
th
e
cr
itical
p
o
i
n
t
p
lo
t
a
c
u
r
v
e
in
th
e
co
m
p
le
x
p
lan
e.
A
s
s
h
o
w
n
i
n
(
1
3
)
d
escr
ib
e
th
e
m
h
o
p
h
a
s
e
co
m
p
ar
ato
r
s
ch
ar
ac
ter
is
tics
i
n
th
e
co
m
p
lex
p
la
n
e
at
p
o
in
t
B
an
d
at
p
o
in
t
A
p
b
y
(
1
4
)
t
o
(
1
7
)
.
Dep
en
d
in
g
o
n
t
h
e
p
o
lar
izatio
n
ty
p
e,
B
an
d
A
p
ca
n
also
b
e
f
o
u
n
d
b
y
th
e
v
o
lt
ag
es
o
f
b
o
th
en
d
s
o
f
ea
ch
li
n
e
f
o
r
th
e
b
alan
ce
d
co
n
d
itio
n
s
i
n
t
h
e
cr
itical
s
tate.
T
h
ese
ch
ar
ac
ter
is
tics
ar
e
cir
cl
es
w
ith
ce
n
ter
in
(
2
6
)
an
d
r
ad
io
in
(
2
7
)
.
2
/
)
(
p
A
B
C
(
2
6
)
2
/
)
(
p
A
B
R
(
2
7
)
T
h
e
s
o
f
t
w
ar
e
s
h
o
w
s
t
h
e
i
m
p
ed
an
ce
m
ea
s
u
r
ed
c
u
r
v
es
a
n
d
all
t
h
e
zo
n
e
c
h
ar
ac
ter
is
t
ics
o
f
m
h
o
p
h
ase
co
m
p
ar
ato
r
s
i
n
th
e
co
m
p
le
x
p
l
an
e.
T
h
is
ca
n
also
b
e
d
o
n
e
f
o
r
all
s
elec
ted
lin
e
s
en
d
s
.
3
.
2
.
M
id
-
t
er
m
s
y
nc
hro
no
us
s
t
a
bi
lity
T
h
e
n
u
m
er
ical
m
et
h
o
d
u
s
ed
i
n
t
h
e
m
id
-
ter
m
s
tab
ilit
y
p
r
o
g
r
a
m
f
o
r
th
e
d
if
f
er
e
n
tial
eq
u
atio
n
s
o
l
u
tio
n
s
is
t
h
e
i
m
p
licit
tr
ap
ez
o
id
al
in
t
eg
r
atio
n
m
et
h
o
d
w
it
h
a
Z
Bus
l
o
ad
f
lo
w
f
o
r
t
h
e
n
et
w
o
r
k
s
o
lu
tio
n
[
2
6
,
3
2
]
.
T
h
e
m
ai
n
s
y
s
te
m
ele
m
en
ts
a
n
d
it
s
i
n
ter
r
elatio
n
s
h
ip
s
ar
e
s
h
o
w
n
i
n
Fig
u
r
e
3
.
Fig
u
r
e
3
.
E
le
m
en
t i
n
ter
r
elatio
n
s
h
ip
s
i
n
m
id
-
ter
m
s
tab
ilit
y
p
r
o
g
r
a
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
2
9
-
944
936
Fig
u
r
e
3
s
h
o
w
s
t
h
e
i
n
ter
ch
a
n
g
e
b
et
w
ee
n
t
h
e
n
et
w
o
r
k
s
w
ith
:
Gen
er
ato
r
s
an
d
its
co
n
tr
o
ls
.
T
h
e
n
et
w
o
r
k
a
n
d
g
en
er
ato
r
s
in
ter
ac
tio
n
s
ar
e
d
q
-
r
i
v
a
r
iab
le
t
r
an
s
f
o
r
m
atio
n
s
,
T
d
q
-
T
r
i;
an
d
r
ef
er
en
ce
an
d
f
ee
d
b
ac
k
s
i
g
n
a
ls
,
R
S,
FS
,
f
o
r
th
e
co
n
tr
o
ls
.
T
h
e
s
y
n
c
h
r
o
n
o
u
s
g
e
n
er
ato
r
s
r
ep
r
esen
t
th
e
s
i
m
p
lest
f
lu
x
m
o
d
el,
co
n
s
tan
t
e
m
f
,
to
d
an
d
q
s
u
b
-
tr
an
s
ien
t
e
f
f
ec
ts
w
it
h
s
atu
r
atio
n
.
T
h
e
p
r
im
e
m
o
to
r
s
m
a
y
b
e
s
tea
m
,
g
as
a
n
d
h
y
d
r
au
lics
t
u
r
b
in
es
a
n
d
in
ter
n
al
co
m
b
u
s
tio
n
m
o
to
r
s
.
A
l
s
o
,
it
ca
n
s
i
m
u
late
E
o
lic
t
u
r
b
in
es
w
i
th
i
n
d
u
ctio
n
g
e
n
er
ato
r
s
an
d
p
h
o
to
v
o
ltaic
g
en
er
atio
n
.
A
cti
v
e
p
r
o
tectio
n
s
,
w
i
th
i
n
p
u
t
s
i
g
n
al
s
a
n
d
tr
ip
p
in
g
s
i
g
n
als,
I
S
a
n
d
T
S.
T
h
ese
p
r
o
t
ec
tio
n
s
d
u
r
in
g
s
i
m
u
lat
io
n
ca
n
m
ea
s
u
r
e
f
r
eq
u
en
c
y
,
f
r
eq
u
e
n
c
y
v
ar
iatio
n
,
v
o
l
tag
e,
ac
ti
v
e
a
n
d
r
ea
cti
v
e
p
o
w
er
,
i
m
p
ed
an
ce
s
an
d
in
v
er
s
io
n
o
f
ac
tiv
e
p
o
w
er
.
B
r
e
a
k
e
r
o
p
e
r
a
t
i
o
n
s
a
n
d
s
i
m
u
l
a
t
e
d
f
a
u
l
t
s
,
w
i
t
h
m
a
t
r
i
x
m
o
d
i
f
i
c
a
t
i
o
n
a
n
d
-
o
r
l
o
a
d
v
a
r
i
a
t
i
o
n
,
M
t
x
M
o
d
a
n
d
L
V
.
L
o
ad
s
,
w
ith
i
ts
c
u
r
r
en
t
i
n
j
ec
t
io
n
s
I
i
u
n
d
er
v
o
ltag
e
v
ar
iatio
n
s
|
V
|
,
f
r
eq
u
e
n
c
y
a
n
d
lo
ad
s
h
ed
d
in
g
o
r
lo
ad
r
ec
lo
s
in
g
b
y
th
e
i
n
p
u
t
s
i
g
n
al
s
,
L
V.
Sh
u
n
t SVC
s
,
w
it
h
th
e
ir
in
p
u
t c
o
n
tr
o
l sig
n
als I
S a
n
d
o
u
tp
u
t r
e
ac
tiv
e
p
o
w
er
i
n
j
ec
tio
n
s
Qi.
T
h
e
3
x
3
s
eq
u
en
ce
co
m
p
o
n
en
t
ele
m
e
n
tar
y
s
u
b
-
m
atr
i
x
f
o
r
ea
ch
s
el
f
o
r
m
u
t
u
al
ad
m
i
ttan
ce
s
o
f
th
e
n
et
w
o
r
k
f
o
r
m
t
h
e
Y
Bus
m
atr
i
x
ter
m
s
.
T
h
u
s
,
a
s
h
u
n
t
f
a
u
lt is
r
e
p
r
esen
ted
b
y
a
f
ictitio
u
s
ad
m
it
tan
ce
lo
ad
i
n
s
e
r
t
i
o
n
i
n
t
h
e
m
a
t
r
i
x
c
o
r
r
e
s
p
o
n
d
i
n
g
n
o
d
e
,
l
i
k
e
i
n
F
i
g
u
r
e
4
.
T
h
e
f
a
u
l
t
i
s
d
e
t
e
r
m
i
n
e
d
b
y
t
h
e
f
o
u
r
a
d
m
i
t
t
a
n
c
e
s
v
a
l
u
e
s
a
n
d
t
h
e
3
x
3
p
h
a
s
e
c
o
m
p
o
n
e
n
t
s
u
b
m
a
t
r
i
x
i
s
o
b
t
a
i
n
e
d
b
y
K
r
o
n
e
l
i
m
i
n
a
t
i
o
n
o
n
t
h
e
n
e
u
t
r
a
l
n
o
d
e
.
T
h
e
n
t
h
e
r
esu
lti
n
g
3
x
3
f
au
lt
s
eq
u
en
ce
co
m
p
o
n
en
ts
s
u
b
-
m
at
r
ix
is
f
o
u
n
d
b
y
t
h
e
tr
an
s
f
o
r
m
at
io
n
:
S
abc
f
S
f
T
Y
T
Y
1
012
(
2
8
)
w
h
er
e,
[
T
S
]
: is th
e
tr
a
n
s
f
o
r
m
atio
n
m
a
tr
ix
f
o
r
s
eq
u
en
ce
co
m
p
o
n
e
n
ts
to
p
h
ase
co
m
p
o
n
en
ts
.
[
Y
f
]
abc
: is th
e
f
au
lt s
u
b
m
atr
i
x
i
n
-
p
h
as
e
co
m
p
o
n
e
n
t
s
.
[
Y
f
]
012
: is th
e
f
au
lt s
u
b
m
atr
i
x
i
n
s
eq
u
en
ce
co
m
p
o
n
e
n
ts
.
T
h
r
ee
s
er
ies ad
m
i
ttan
ce
s
r
ep
r
esen
t
s
er
ies f
a
u
lt
s
.
T
h
is
m
et
h
o
d
is
ea
s
ier
th
a
n
o
th
er
s
to
s
i
m
u
la
te:
S
i
m
u
l
t
a
n
e
o
u
s
s
y
m
m
e
t
r
i
c
a
l
o
r
a
s
y
m
m
e
t
r
i
c
a
l
f
a
u
l
t
s
i
n
v
a
r
i
o
u
s
n
e
t
w
o
r
k
p
o
i
n
t
s
.
S
h
u
n
t
f
a
u
l
t
s
i
n
i
n
t
e
r
n
a
l
p
o
i
n
t
s
o
f
t
h
e
l
i
n
e
.
B
r
e
a
k
e
r
s
w
i
t
c
h
i
n
g
.
A
cti
v
e
p
r
o
tectio
n
s
o
r
a
p
r
o
g
r
a
m
m
ed
s
w
i
tch
i
n
g
m
a
y
tr
ip
b
r
e
ak
er
s
b
y
a
s
elec
tio
n
f
o
r
m
a
s
i
s
s
h
o
w
n
i
n
Fig
u
r
e
5
.
T
h
e
m
u
t
u
al
i
n
d
u
c
tan
ce
e
f
f
ec
t
o
f
ze
r
o
s
eq
u
e
n
ce
in
tr
an
s
m
i
s
s
io
n
l
in
e
s
ca
n
b
e
s
i
m
u
lated
in
as
y
m
m
etr
ical
f
a
u
lts
ca
s
e
s
r
ela
ted
w
ith
g
r
o
u
n
d
.
T
h
e
r
es
u
lt
s
i
n
t
h
e
s
o
f
t
w
ar
e
ar
e
g
i
v
e
n
i
n
g
r
ap
h
ical
a
n
d
tab
u
lar
f
o
r
m
w
it
h
o
p
tio
n
al
co
n
f
i
g
u
r
ati
o
n
s
.
On
e
g
r
ap
h
ic
s
h
o
w
s
t
h
e
i
m
p
ed
a
n
ce
v
ar
iatio
n
cu
r
v
e
s
m
e
asu
r
ed
m
o
d
u
le
s
an
d
th
e
a
n
g
le
m
ea
s
u
r
ed
f
r
o
m
th
e
a
p
p
ar
en
t p
o
w
er
p
h
aso
r
s
v
er
s
u
s
ti
m
e,
i
n
b
o
th
li
n
e
e
n
d
s
.
T
h
e
ai
m
i
s
to
d
etec
t t
h
o
s
e
p
r
o
tectio
n
s
,
w
h
ich
ca
n
m
ea
s
u
r
e
i
m
p
ed
an
ce
s
o
r
o
s
cillato
r
y
v
alu
es
n
ea
r
t
h
eir
r
ea
ch
.
T
h
ese
v
alu
es
j
u
d
g
e
ag
ai
n
s
t
th
e
v
al
u
e
o
f
th
e
li
n
e
i
m
p
ed
an
ce
in
ea
ch
s
i
m
u
lat
io
n
in
s
tan
t.
T
h
e
p
h
ase
d
if
f
er
en
ce
b
et
w
ee
n
th
e
p
o
w
er
s
v
ec
to
r
s
ar
e
v
er
if
ied
all
in
s
ta
n
ts
.
F
ig
u
r
e
4
.
Sh
u
n
t
f
a
u
lt si
m
u
latio
n
Fig
u
r
e
5
.
B
r
ea
k
er
s
w
itc
h
i
n
g
c
o
n
f
i
g
u
r
atio
n
T
h
e
im
p
ed
an
ce
m
ea
s
u
r
ed
b
y
th
e
p
h
ase
c
o
m
p
ar
ato
r
ar
e
o
b
t
ain
ed
f
r
o
m
v
o
lta
g
es
o
b
tain
ed
f
r
o
m
th
e
s
en
d
i
n
g
a
n
d
r
ec
eiv
i
n
g
en
d
o
f
t
h
e
li
n
e
s
elec
ted
,
an
d
t
h
e
co
m
p
le
x
c
u
r
r
en
ts
r
e
g
is
ter
ed
o
n
it.
E
ac
h
p
o
in
t
co
r
r
esp
o
n
d
s
to
ea
ch
ti
m
e
s
te
p
k
o
n
t
h
e
s
i
m
u
latio
n
.
T
h
e
ex
p
r
ess
io
n
s
u
s
ed
f
o
r
th
e
li
n
e
to
lin
e
i
m
p
ed
a
n
c
e
m
ea
s
u
r
ed
ar
e:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
mh
o
typ
e
p
h
a
s
e
co
mp
a
r
a
to
r
r
ela
y
g
u
id
elin
e
u
s
in
g
…
(
Jo
s
é
A
n
to
n
io
G
o
n
z
á
lez
-
C
u
eto
C
r
u
z
)
937
)
(
)
(
)
(
)
(
k
I
k
I
k
V
k
Z
j
i
ij
ij
(
2
9
)
an
d
f
o
r
th
e
p
h
a
s
e
to
g
r
o
u
n
d
,
im
p
ed
a
n
ce
m
ea
s
u
r
ed
.
)
(
)
(
)
(
)
(
0
0
k
I
k
k
I
k
V
k
Z
i
i
ph
(
3
0
)
w
h
er
e,
L
L
L
Z
Z
Z
k
1
1
0
0
(
3
1
)
T
h
e
v
o
ltag
es
f
o
r
ea
ch
n
o
d
e
i a
n
d
s
tag
e
k
ar
e
o
b
tain
ed
f
r
o
m
t
h
e
v
o
lta
g
e
s
u
b
-
v
ec
to
r
.
012
i
S
a
b
c
i
V
T
V
(
3
2
)
Fro
m
th
e
n
et
w
o
r
k
v
o
ltag
e
v
ec
t
o
r
,
th
e
k
th
s
ta
g
e
s
o
lu
tio
n
is
:
012
012
012
B
U
S
B
U
S
B
U
S
I
Z
V
(
3
3
)
a
n
d
th
e
cu
r
r
e
n
ts
f
o
r
a
lin
e
S
R
b
y
t
h
e
m
atr
ix
r
elatio
n
.
012
012
012
012
012
012
R
S
RR
SR
RS
SS
s
abc
R
abc
S
V
V
Y
Y
Y
Y
T
I
I
(
3
4
)
T
h
e
ch
ar
ac
ter
is
tics
o
f
t
h
e
m
h
o
elem
e
n
t
s
in
t
h
e
co
m
p
le
x
p
lan
e
d
ef
i
n
e
th
e
d
is
ta
n
ce
ele
m
e
n
t
s
elec
ted
,
th
e
r
ea
c
h
a
n
d
t
h
e
p
o
lar
izatio
n
.
Fi
g
u
r
e
6
s
h
o
w
s
th
e
o
p
tio
n
al
s
elec
tio
n
s
,
th
i
s
ca
n
b
e
an
y
co
m
b
in
atio
n
,
in
cl
u
d
i
n
g
o
n
l
y
o
n
e
o
r
all
o
f
t
h
e
m
.
Fig
u
r
e
6
.
Op
tio
n
al
d
is
tan
ce
el
e
m
en
ts
T
ab
le
2
s
h
o
w
s
t
h
e
s
ix
p
o
s
s
ib
le
p
o
lar
i
za
tio
n
s
i
m
p
le
m
e
n
ted
o
n
t
h
is
p
r
o
g
r
a
m
v
er
s
io
n
.
T
h
ey
ar
e:
t
h
e
s
elf
-
p
o
lar
ized
,
t
w
o
co
m
b
in
ed
p
o
lar
izatio
n
s
an
d
th
r
ee
s
i
m
p
le
p
o
lar
izatio
n
s
.
T
h
e
last
o
n
e
u
s
es
t
h
e
p
o
s
itiv
e
s
eq
u
en
ce
v
o
lta
g
es,
a
n
d
th
e
o
t
h
er
s
co
n
s
id
er
s
a
li
n
e
o
r
p
h
ase
v
o
ltag
e
s
.
I
t
s
h
o
w
s
o
n
l
y
t
w
o
o
f
th
e
s
i
x
d
is
ta
n
ce
u
n
i
ts
f
o
r
ea
ch
ca
s
e.
T
ab
le
2
.
P
o
lar
izatio
n
s
i
m
p
le
m
en
ted
U
n
i
t
S
2
S
e
l
f
S
2
C
o
mb
i
n
e
d
S
2
C
o
mb
i
n
e
d
S
2
S
i
m
p
l
e
S
2
S
i
m
p
l
e
S
2
S
e
c
p
o
s
AB
ab
V
0
90
c
p
ab
V
k
V
0
1
2
0
ca
p
ab
V
k
V
p
k
0
1
2
0
bc
V
p
k
0
90
c
V
1
ab
V
A
a
V
0
90
bc
p
a
V
k
V
0
120
c
p
a
V
k
V
p
k
0
120
b
V
p
k
0
90
bc
V
1
a
V
T
h
e
s
o
f
t
w
ar
e
s
i
m
u
late
s
a
m
e
m
o
r
y
p
o
lar
izatio
n
w
ith
p
o
s
iti
v
e
s
eq
u
e
n
ce
v
o
lta
g
e
[
2
5
]
.
A
s
Sh
o
w
n
i
n
(3
5
)
d
eter
m
i
n
es t
h
e
p
o
lar
izatio
n
v
o
ltag
e
f
o
r
ea
ch
ti
m
e
s
tep
.
]
1
[
1
]
[
1
]
[
1
)
1
(
k
M
E
M
k
k
M
E
M
V
V
V
(3
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
2
9
-
944
938
w
h
er
e,
]
[
1
k
M
E
M
V
i
s
t
h
e
p
r
e
s
e
n
t
m
e
m
o
r
i
z
e
d
p
o
s
i
t
i
v
e
s
e
q
u
e
n
c
e
v
o
l
t
a
g
e
,
w
h
i
c
h
m
u
s
t
b
e
u
s
e
d
i
n
t
h
e
s
t
e
p
k
a
s
p
o
l
a
r
i
z
a
t
i
o
n
v
o
l
t
a
g
e
.
]
[
1
k
V
is
th
e
ac
t
u
al
p
o
s
iti
v
e
s
eq
u
e
n
c
e
v
o
ltag
e
v
alu
e.
]
1
[
1
k
M
E
M
V
is
th
e
p
r
ev
io
u
s
m
e
m
o
r
ized
p
o
s
itiv
e
s
eq
u
en
ce
v
o
lta
g
e
v
al
u
e.
is
th
e
m
e
m
o
r
y
ti
m
e
co
n
s
tan
t.
T
h
en
f
o
r
ea
ch
lin
e
s
elec
ted
,
with
a
m
h
o
p
h
ase
co
m
p
ar
ato
r
,
t
h
e
S
1
,
S
2
,
A
p
an
d
B
v
alu
es
ar
e
ca
lcu
lated
f
o
r
ea
ch
d
is
ta
n
ce
u
n
it
p
r
o
tectio
n
s
elec
ted
,
f
o
r
th
e
r
ea
ch
g
i
v
en
to
ea
ch
zo
n
e,
th
e
p
o
lar
izat
io
n
o
f
th
e
u
n
it
an
d
v
o
ltag
e
a
n
d
c
u
r
r
en
t o
u
tp
u
t
v
al
u
es
g
i
v
en
to
th
e
p
r
o
g
r
a
m
u
s
e
t
h
e
r
elatio
n
s
(
3
2
)
to
(
3
4
)
.
T
h
e
c
o
m
p
le
x
i
m
p
ed
an
c
e
cu
r
v
e
s
m
ea
s
u
r
ed
,
an
d
th
e
ch
a
r
ac
ter
is
tics
zo
n
e
s
i
n
a
m
h
o
p
h
ase
co
m
p
ar
ato
r
ar
e
in
a
co
m
p
lex
p
la
n
e.
Fi
g
u
r
e
7
s
h
o
w
s
t
h
e
i
m
p
ed
a
n
ce
m
ea
s
u
r
e
d
m
o
d
u
le
s
cu
r
v
es,
r
esi
s
tan
ce
o
r
r
ea
cta
n
ce
v
er
s
u
s
t
i
m
e
a
n
d
θ
an
g
le
s
v
er
s
u
s
t
i
m
e
u
s
i
n
g
an
a
lter
n
ati
v
e
f
o
r
m
.
Al
l
th
e
s
e
cu
r
v
es
ca
n
b
e
s
h
o
w
n
f
r
o
m
t
h
e
b
eg
in
n
i
n
g
o
f
t
h
e
s
i
m
u
latio
n
u
p
to
an
elec
ted
ti
m
e,
w
h
ile
t
h
e
ch
ar
a
cter
is
tics
o
f
t
h
e
m
h
o
u
n
i
ts
,
d
r
a
w
i
n
g
th
e
v
ar
iab
le
v
al
u
es
o
f
th
e
s
elec
ted
in
s
tan
t
ti
m
e.
E
v
er
y
p
o
in
t
o
f
t
h
e
c
u
r
v
es
an
d
g
r
ap
h
ics
in
th
e
co
m
p
le
x
p
lan
e
r
elate
s
t
h
e
co
r
r
esp
o
n
d
in
g
in
s
ta
n
t
ti
m
e
o
f
th
e
s
i
m
u
lat
io
n
.
T
h
e
co
m
p
le
x
m
o
d
el
ac
cu
r
ac
y
c
h
ar
ac
ter
is
tic
s
o
f
th
e
m
h
o
u
n
its
m
a
y
b
e
te
s
ted
w
it
h
r
eg
ar
d
i
n
g
th
e
θ
v
s
ti
m
e
c
u
r
v
e
s
,
b
ased
s
tr
aig
h
tf
o
r
w
ar
d
in
th
e
o
p
er
atin
g
p
r
in
cip
le
o
f
p
h
a
s
e
co
m
p
ar
i
s
o
n
co
n
s
id
er
in
g
t
h
e
in
p
u
t
s
ig
n
als
o
f
th
ese
u
n
its
.
A
ll
p
o
in
t
s
o
f
th
e
m
h
o
ch
ar
ac
ter
is
tics
an
d
i
m
p
ed
a
n
ce
m
ea
s
u
r
ed
cu
r
v
e
s
ar
e
s
u
b
tr
ac
ted
f
r
o
m
t
h
e
li
n
e
i
m
p
e
d
an
ce
Z
l
f
o
r
p
r
o
tectio
n
s
ar
e
o
n
th
e
r
ec
ei
v
i
n
g
en
d
o
f
a
l
in
e.
T
h
u
s
t
h
e
g
r
ap
h
ics
f
o
r
th
ese
p
r
o
tectio
n
s
ta
k
e
a
s
o
r
ig
i
n
o
f
t
h
e
co
m
p
le
x
p
la
n
et
h
e
v
a
lu
e
o
f
t
h
e
i
m
p
ed
an
ce
o
f
t
h
e
l
i
n
e
a
n
d
ar
e
r
o
tated
1
8
0
d
eg
r
ee
s
.
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
C
o
m
p
lex
p
l
a
n
e
an
d
r
elate
d
r
ea
ctan
ce
cu
r
v
e,
(
a)
i
m
p
ed
an
ce
m
ea
s
u
r
ed
cu
r
v
es a
n
d
m
h
o
c
h
ar
ac
ter
is
tc
s
,
(
b
)
r
ea
ctan
ce
v
er
s
u
s
ti
m
e,
(
c)
ar
g
.
(
S
1
/
S
2
)
v
er
s
u
s
ti
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.