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tr
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m
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tr
ib
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tio
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h
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s
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n
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p
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ss
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rticle
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th
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CC B
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SA
li
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e
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se
.
C
o
r
r
e
s
p
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A
uth
o
r
:
Mo
h
d
Hatta
J
o
p
r
i
,
Facu
lty
o
f
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lectr
ical
an
d
E
lectr
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n
ic
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n
g
in
ee
r
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g
T
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h
n
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lo
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y
,
Un
iv
er
s
iti T
ek
n
ik
al
Ma
lay
s
ia
Me
lak
a
(
UT
eM
)
,
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g
T
u
ah
J
ay
a
St.
,
7
6
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D
u
r
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g
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lay
s
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E
m
ail: h
atta@
u
tem
.
ed
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
As th
e
p
o
wer
q
u
ality
(
PQ
)
is
s
u
e
s
ca
u
s
ed
m
ain
ly
b
y
h
a
r
m
o
n
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cs d
ir
ec
tly
af
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th
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er
all
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n
tin
u
atio
n
o
f
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tr
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tr
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s
m
is
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d
is
tr
ib
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tio
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n
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k
,
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e
u
n
i
n
ter
r
u
p
te
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m
o
n
ito
r
in
g
o
f
elec
tr
ic
p
o
wer
s
y
s
tem
s
(
E
PS
s
)
h
as
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o
m
e
h
ig
h
ly
n
ec
ess
ar
y
f
o
r
th
e
u
tili
ty
in
d
u
s
tr
y
[
1
,
2
]
.
T
h
e
h
a
r
m
o
n
ic
d
is
to
r
tio
n
ca
u
s
es
s
ev
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al
ad
v
er
s
e
ef
f
ec
ts
s
u
ch
as
o
v
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atin
g
o
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tatio
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al
m
ac
h
in
es,
s
tatic
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ac
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in
es,
an
d
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r
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en
t‐
ca
r
r
y
in
g
co
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d
u
cto
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s
.
Fu
r
th
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m
o
r
e
,
it
ca
u
s
es
p
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tu
r
e
b
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ac
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n
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ar
m
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itu
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th
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to
m
er
s
'
E
PS
an
d
m
eter
in
g
im
p
r
ec
is
io
n
s
[
2
,
3
]
.
I
n
E
PS
,
m
u
ltip
le
h
ar
m
o
n
ic
s
o
u
r
ce
s
ca
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b
e
f
o
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n
d
at
th
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u
til
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s
id
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k
n
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wn
as
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p
s
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d
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h
ar
m
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n
ic
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s
lo
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cu
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to
m
er
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id
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with
r
esp
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a
m
ea
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r
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m
en
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t
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p
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n
t
o
f
c
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m
m
o
n
c
o
u
p
lin
g
(
PC
C
)
[
4
,
5
]
.
Pre
v
io
u
s
ly
,
n
u
m
er
o
u
s
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
id
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n
tific
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ca
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b
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f
o
u
n
d
in
m
an
y
k
in
d
s
o
f
liter
atu
r
e.
T
h
e
ea
r
lies
t
tech
n
iq
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e
t
o
lo
ca
lize
t
h
e
h
ar
m
o
n
ic
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o
u
r
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s
is
u
tili
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g
p
o
wer
d
ir
ec
tio
n
tech
n
iq
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e.
Ho
wev
e
r
,
th
is
m
eth
o
d
u
s
ed
l
im
ited
h
ar
m
o
n
ic
p
o
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-
b
ased
in
d
ices,
wh
er
ea
s
m
ath
em
atica
l
an
aly
s
is
h
as
s
h
o
wn
t
h
e
p
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ir
ec
tio
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m
eth
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d
is
n
o
t
s
u
itab
le
f
o
r
h
a
r
m
o
n
ic
s
o
u
r
ce
d
etec
tio
n
[
6
,
7
]
.
Fu
r
th
er
m
o
r
e
,
a
s
tate
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
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T
elec
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m
m
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n
C
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m
p
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t E
l Co
n
tr
o
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A
cc
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r
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te
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a
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mo
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ic
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o
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r
ce
id
e
n
tifi
ca
tio
n
u
s
in
g
S
-
tr
a
n
s
fo
r
m
(
Mo
h
d
Ha
tta
Jo
p
r
i
)
2709
esti
m
atio
n
m
eth
o
d
is
p
r
esen
te
d
with
th
e
ac
co
m
p
lis
h
m
en
t
o
f
least
s
q
u
ar
e
an
d
Ki
r
ch
h
o
f
f
c
u
r
r
en
t
law
[
8
]
.
Yet,
a
s
tu
d
y
f
r
o
m
[
9
]
,
e
x
p
lain
ed
t
h
at
th
e
s
tate
esti
m
at
io
n
tech
n
iq
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e
r
eq
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ir
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u
m
er
o
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s
m
ea
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r
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t
d
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d
u
n
r
ea
s
o
n
ab
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s
etu
p
co
s
t
f
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r
t
h
e
lar
g
e
p
o
wer
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y
s
tem
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T
h
u
s
,
to
o
v
er
c
o
m
e
th
e
p
r
ev
io
u
s
co
n
s
tr
ain
t,
th
e
cr
itical
im
p
ed
an
ce
m
eth
o
d
is
in
tr
o
d
u
c
ed
[
1
0
,
1
1
]
.
T
h
e
m
ain
d
is
ad
v
a
n
tag
e
o
f
th
is
m
eth
o
d
is
to
k
n
o
w
th
e
v
alu
e
o
f
s
o
u
r
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in
ter
n
al
im
p
ed
a
n
ce
s
o
f
c
u
s
to
m
er
an
d
u
tili
ty
,
wh
er
ea
s
it
is
d
if
f
icu
lt
to
o
b
tain
t
h
ese
p
ar
am
eter
s
with
o
u
t
s
witch
in
g
test
s
[
1
2
,
1
3
]
.
C
o
n
s
eq
u
en
tly
,
a
h
ar
m
o
n
ic
cu
r
r
e
n
t
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eth
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is
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tr
o
d
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ce
d
d
u
e
to
s
o
lv
in
g
th
e
p
r
ev
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s
m
eth
o
d
d
r
awb
ac
k
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Ho
wev
er
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th
e
m
ea
s
u
r
em
en
t
l
o
n
g
-
d
r
awn
-
o
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t
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d
h
ar
d
to
a
n
aly
ze
h
ar
m
o
n
ic
im
p
e
d
an
ce
s
at
th
e
cu
s
to
m
er
s
id
e
[
1
4
-
1
6
]
.
I
n
th
e
p
r
ev
i
o
u
s
s
tu
d
ies
[
1
7
-
2
0
]
,
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
esti
m
atio
n
is
d
is
cu
s
s
ed
b
y
ap
p
ly
in
g
th
e
B
ay
esian
esti
m
atio
n
an
d
h
ar
m
o
n
ic
s
tate
esti
m
atio
n
(
HSE)
.
Un
f
o
r
tu
n
a
tely
,
th
is
tech
n
iq
u
e
i
n
v
o
lv
es
h
ig
h
co
m
p
u
tatio
n
al
co
m
p
lex
ity
an
d
th
e
s
et
-
u
p
co
s
t
o
f
th
e
d
is
tr
ib
u
ted
m
ea
s
u
r
em
en
t
s
y
s
tem
s
tatio
n
is
v
er
y
ex
p
en
s
iv
e
[
5
,
21
,
2
2
]
.
I
n
r
ea
l
-
tim
e,
ac
cu
r
ac
y
,
f
ast
an
aly
s
is
an
d
lo
w
co
s
t
ar
e
ess
en
ti
al.
T
h
er
ef
o
r
e
,
th
e
lim
itatio
n
o
f
p
r
ev
io
u
s
an
aly
s
is
tech
n
iq
u
es
ca
n
b
e
s
o
lv
ed
b
y
u
s
in
g
s
ig
n
al
p
r
o
ce
s
s
in
g
tech
n
iq
u
es
s
u
ch
as
f
ast
f
o
u
r
ier
tr
an
s
f
o
r
m
(
FF
T
)
,
s
p
ec
tr
o
g
r
am
a
n
d
S
-
tr
an
s
f
o
r
m
[
2
]
.
A
h
ar
m
o
n
ic
s
o
u
r
ce
id
e
n
tific
ati
o
n
u
s
in
g
FF
T
is
in
tr
o
d
u
ce
d
to
p
r
o
v
id
e
f
ast
an
aly
s
is
in
d
eter
m
in
in
g
th
e
lo
ca
tio
n
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
s
in
t
h
e
E
PS
.
T
h
e
s
ig
n
if
ica
n
t
r
elatio
n
s
h
ip
o
f
s
p
ec
tr
al
im
p
ed
an
ce
,
w
h
ich
a
r
e
f
u
n
d
am
e
n
tal
an
d
h
ar
m
o
n
ic
i
m
p
ed
an
ce
ar
e
u
s
ed
d
u
e
to
id
e
n
tify
th
e
h
ar
m
o
n
ic
lo
ca
tio
n
o
f
th
e
h
ar
m
o
n
i
c
s
o
u
r
ce
[
2
3
,
2
4
]
.
Ho
wev
e
r
,
th
e
d
r
awb
ac
k
o
f
th
e
FF
T
tech
n
iq
u
e,
s
u
ch
as
th
e
s
ig
n
al
in
f
o
r
m
atio
n
,
f
o
r
in
s
tan
ce
,
am
p
litu
d
e
f
r
eq
u
en
cies
an
d
p
h
a
s
es,
ca
n
n
o
t
b
e
ac
q
u
ir
e
d
co
r
r
ec
t
ly
.
T
h
is
is
b
ec
au
s
e
o
f
th
e
lea
k
a
g
e,
aliasin
g
ef
f
ec
ts
,
an
d
p
ick
e
t f
e
n
ce
f
o
r
m
ed
b
y
th
e
FF
T
[
2
5
-
2
7
]
.
As a
r
esu
lt o
f
t
h
e
FF
T
lim
itatio
n
,
t
h
e
s
p
ec
tr
o
g
r
am
is
p
r
esen
ted
t
o
id
en
tify
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
l
o
ca
tio
n
[
2
8
]
.
C
o
n
v
er
s
ely
,
th
e
s
p
ec
tr
o
g
r
a
m
h
as
two
m
ain
d
is
ad
v
an
tag
es.
First,
it
s
tim
e
-
f
r
eq
u
e
n
cy
r
eso
lu
tio
n
is
li
m
ited
b
y
Hei
s
en
b
e
r
g
’
s
Un
ce
r
t
ain
ty
Prin
cip
le.
Seco
n
d
ly
,
b
o
t
h
its
en
er
g
y
lo
ca
tio
n
in
th
e
tim
e
-
f
r
e
q
u
en
c
y
r
ep
r
esen
tatio
n
an
d
its
r
eso
lu
tio
n
ca
n
v
a
r
y
with
th
e
win
d
o
w
s
elec
ted
[
2
9
-
3
2
]
.
T
h
e
S
-
tr
an
s
f
o
r
m
is
th
e
ad
v
a
n
ce
m
en
t
o
f
wav
elet
tr
a
n
s
f
o
r
m
(
W
T
)
an
d
s
h
o
r
t
-
tim
e
f
o
u
r
ier
tr
an
s
f
o
r
m
(
STFT
)
b
y
its
v
ar
iab
le
win
d
o
w
an
d
p
h
ase
co
r
r
ec
tio
n
,
r
esp
e
ctiv
ely
.
Similar
to
W
T
,
it
o
f
f
er
s
an
im
p
r
o
v
ed
tim
e
an
d
f
r
e
q
u
en
c
y
r
e
p
r
esen
tatio
n
o
f
a
s
ig
n
al.
Ad
d
itio
n
ally
,
t
h
e
s
ca
lab
le
an
d
m
o
v
ab
le
Ga
u
s
s
ian
win
d
o
w
p
r
o
p
er
ties
o
f
th
e
ST
ca
n
b
e
u
tili
ze
d
f
o
r
s
u
p
e
r
io
r
r
ec
o
g
n
itio
n
o
f
a
n
y
p
o
wer
q
u
ality
ev
en
ts
[
2
,
33
-
3
5
]
.
Du
e
to
th
e
ex
ce
llen
t
f
ea
tu
r
es o
f
t
h
e
S
-
tr
an
s
f
o
r
m
in
p
o
wer
q
u
ality
an
aly
s
is
,
it is
a
n
ec
ess
ity
to
p
er
f
o
r
m
an
an
aly
s
is
o
f
id
en
tify
in
g
th
e
lo
ca
tio
n
o
f
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
s
u
s
in
g
th
is
t
ec
h
n
iq
u
e.
I
n
t
h
is
p
a
p
e
r
,
t
h
e
S
-
t
r
a
n
s
f
o
r
m
is
p
r
o
p
o
s
e
d
t
o
i
d
e
n
t
i
f
y
t
h
e
l
o
c
a
t
i
o
n
o
f
t
h
e
h
a
r
m
o
n
i
c
s
o
u
r
ce
i
n
t
h
e
d
is
t
r
i
b
u
ti
o
n
s
y
s
t
e
m
wi
th
a
s
i
n
g
l
e
-
p
o
i
n
t
m
e
a
s
u
r
e
m
e
n
t
ap
p
r
o
a
c
h
a
t
t
h
e
p
o
i
n
t
o
f
c
o
m
m
o
n
c
o
u
p
l
i
n
g
(
PC
C
)
.
S
-
t
r
a
n
s
f
o
r
m
is
a
te
c
h
n
i
q
u
e
t
h
at
u
s
e
s
t
i
m
e
-
f
r
e
q
u
e
n
c
y
a
n
al
y
s
is
t
o
d
i
s
t
i
n
g
u
is
h
t
h
e
s
i
g
n
a
l
s
i
n
t
i
m
e
a
n
d
f
r
e
q
u
e
n
c
y
r
e
p
r
es
en
t
a
t
i
o
n
(
T
F
R
)
[
3
6
,
3
7
]
.
T
h
e
S
-
t
r
a
n
s
f
o
r
m
is
p
r
o
p
o
s
e
d
b
e
c
a
u
s
e
i
t
is
a
b
l
e
t
o
p
r
o
v
i
d
e
p
r
o
v
i
d
e
s
b
e
t
t
e
r
f
r
e
q
u
e
n
c
y
r
e
s
o
lu
t
i
o
n
f
o
r
l
o
w
-
f
r
e
q
u
e
n
c
y
c
o
m
p
o
n
e
n
t
s
a
n
d
a
ls
o
o
f
f
e
r
s
b
e
t
t
e
r
t
i
m
e
r
e
s
o
l
u
t
i
o
n
f
o
r
h
i
g
h
-
f
r
e
q
u
e
n
c
y
c
o
m
p
o
n
e
n
t
s
.
2.
P
RO
P
O
SE
D
M
E
T
H
O
D
Har
m
o
n
ic
cu
r
r
en
t
s
o
u
r
ce
ty
p
e
-
lo
ad
is
s
elec
ted
as
a
f
r
eq
u
en
t
an
d
wid
ely
u
s
e
o
f
h
ar
m
o
n
ic
p
r
o
d
u
cin
g
lo
ad
s
in
in
d
u
s
tr
ial
[
3
8
,
3
9
]
.
A
tim
e
-
f
r
eq
u
e
n
cy
an
aly
s
is
wh
ich
is
u
s
ed
in
th
is
r
esear
ch
i
s
th
e
S
-
tr
an
s
f
o
r
m
.
T
h
r
ee
s
tep
s
ar
e
p
r
o
p
o
s
ed
in
th
is
m
eth
o
d
.
Firstl
y
,
m
ea
s
u
r
em
en
t
o
f
v
o
ltag
e
an
d
cu
r
r
en
t
at
th
e
PC
C
.
Seco
n
d
ly
,
th
ese
s
ig
n
als
ar
e
an
aly
ze
d
u
s
in
g
S
-
t
r
an
s
f
o
r
m
d
u
e
to
o
b
tain
th
e
s
ig
n
al
p
ar
a
m
eter
s
in
tim
e
-
f
r
e
q
u
en
cy
r
ep
r
esen
tatio
n
(
T
FR
)
p
lan
e.
T
h
ir
d
ly
,
th
e
s
p
ec
tr
al
im
p
e
d
an
ce
c
o
m
p
o
n
en
ts
ar
e
ex
tr
ac
ted
f
r
o
m
th
e
T
FR
im
p
ed
an
ce
a
n
d
th
e
s
ig
n
if
ican
t r
elatio
n
s
h
ip
o
f
t
h
ese
co
m
p
o
n
en
ts
ar
e
u
s
ed
i
n
i
d
en
tify
in
g
th
e
h
a
r
m
o
n
ic
s
o
u
r
c
e
lo
ca
tio
n
.
2
.
1
.
S
-
t
r
a
ns
f
o
rm
S
-
tr
an
s
f
o
r
m
c
o
m
b
in
es
t
h
e
ele
m
en
t
o
f
wav
elet
tr
a
n
s
f
o
r
m
(
W
T
)
an
d
th
e
s
h
o
r
t
-
tim
e
f
o
u
r
i
er
tr
an
s
f
o
r
m
(
STFT
)
,
wh
ich
in
h
er
its
th
e
a
d
v
an
tag
e
o
f
W
T
an
d
STFT
i
n
s
ig
n
al
p
r
o
ce
s
s
in
g
.
I
n
p
a
r
ticu
lar
,
ST
em
p
lo
y
s
a
m
o
v
in
g
a
n
d
s
ca
lab
le
lo
ca
liz
in
g
Gau
s
s
ian
win
d
o
w
in
th
e
t
r
an
s
f
o
r
m
atio
n
p
r
o
ce
s
s
.
T
h
e
G
au
s
s
ian
win
d
o
w
is
as
sh
o
wn
in
(
2
)
.
Ma
th
em
atica
l
ly
ST
ca
n
b
e
d
ef
in
ed
as [
2
9
]
,
(
,
)
=
∫
(
)
|
|
√
2
−
(
−
)
2
2
2
−
2
∞
−
∞
(
1
)
(
)
=
1
√
2
−
2
2
2
(
2
)
(
)
=
1
|
|
(
3
)
wh
er
e
(
)
is
th
e
s
ig
n
al,
is
th
e
ti
m
e,
is
th
e
f
r
eq
u
en
cy
,
(
)
is
th
e
s
ca
la
b
le
Gau
s
s
ian
win
d
o
w,
an
d
(
)
i
s
a
p
ar
am
eter
th
at
c
o
n
tr
o
ls
th
e
p
o
s
itio
n
o
f
th
e
Ga
u
s
s
ian
win
d
o
w.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
7
0
8
-
2
717
2710
2
.
2
.
Sig
na
l pa
ra
m
et
er
s
T
h
e
p
ar
am
eter
s
o
f
p
o
we
r
q
u
a
lity
s
ig
n
als
ar
e
ex
tr
ac
ted
f
r
o
m
th
e
T
FR
to
p
r
o
v
id
e
th
e
in
f
o
r
m
atio
n
o
f
th
e
s
ig
n
al
in
tim
e.
2
.
2
.
1
.
I
ns
t
a
nt
a
neo
us
t
o
t
a
l no
n
-
ha
rm
o
nic dis
t
o
rt
io
n
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
T
HD,
is
u
s
ed
to
m
ea
s
u
r
e
o
f
h
o
w
m
u
ch
h
a
r
m
o
n
ic
co
n
ten
t
in
a
wav
ef
o
r
m
[
4
0
]
.
T
h
e
in
s
tan
ta
n
eo
u
s
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
o
f
a
wav
ef
o
r
m
is
d
ef
i
n
ed
m
a
th
em
atica
lly
as
(
4
)
,
(
)
=
√
∑
ℎ
,
(
)
2
ℎ
=
2
1
(
)
(
4
)
wh
er
e
V
h,
rms
(
t
)
is
R
MS
h
ar
m
o
n
ic
v
o
ltag
e
an
d
V
h
,
rms
(
t)
is
R
MS
f
u
n
d
a
m
en
tal
v
o
ltag
e.
T
h
e
in
s
tan
tan
eo
u
s
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
a
wav
e
f
o
r
m
is
d
ef
i
n
ed
m
ath
e
m
atica
lly
as
.
2
.
2
.
2
.
I
ns
t
a
nta
n
eo
us
t
o
t
a
l no
n
-
ha
rm
o
nic dis
t
o
rt
io
n
B
esid
es
h
ar
m
o
n
ic,
a
s
ig
n
al
als
o
co
n
tain
s
in
ter
h
a
r
m
o
n
ic
co
m
p
o
n
en
ts
th
at
ar
e
n
o
t
m
u
ltip
le
in
teg
er
s
o
f
th
e
p
o
wer
s
y
s
tem
f
r
e
q
u
en
c
y
[
2
7
]
.
R
ef
er
r
in
g
t
o
th
is
as
th
e
in
s
tan
tan
eo
u
s
to
tal
n
o
n
h
a
r
m
o
n
ic
d
is
to
r
tio
n
,
(
Tn
HD(
t)
)
,
th
e
n
f
o
r
t
h
is
p
ar
am
eter
is
wr
itten
as
(
5
)
.
(
)
=
√
(
)
2
−
∑
ℎ
,
(
)
2
ℎ
=
0
1
(
)
(
5
)
2
.
3
.
Sp
ec
t
ra
l i
m
peda
nce
T
h
e
s
p
e
c
t
r
a
l
i
m
p
e
d
a
n
c
e
(
Z
S
)
c
o
m
p
o
n
e
n
t
s
a
r
e
e
x
t
r
a
c
t
e
d
f
r
o
m
t
h
e
T
F
R
i
m
p
e
d
a
n
c
e
(
Z
T
F
R
)
.
T
h
e
Z
TFR
c
a
n
b
e
c
a
l
c
u
l
a
t
e
d
u
s
i
n
g
e
q
u
a
t
i
o
n
a
t
e
a
c
h
h
a
r
m
o
n
i
c
f
r
e
q
u
e
n
c
y
a
n
d
t
h
e
v
a
l
u
e
s
t
h
e
n
p
l
o
t
t
e
d
.
T
h
e
Z
T
F
R
i
s
e
x
p
r
e
s
s
e
d
a
s
(
6
)
[
1
3
]
.
=
(
,
)
(
,
)
(
6
)
w
h
er
e
S
V
(
t,f
)
is
th
e
T
F
R
o
f
v
o
ltag
e
an
d
S
I
(
t,f
)
is
th
e
T
F
R
o
f
cu
r
r
en
t.
T
h
e
s
p
ec
tr
al
im
p
ed
an
ce
co
n
s
is
t
s
o
f
a
f
u
n
d
am
en
tal
im
p
ed
a
n
ce
(
Z
1
)
,
wh
er
ea
s
t
h
e
h
a
r
m
o
n
ic
im
p
e
d
an
ce
(
Z
h
)
is
a
h
ar
m
o
n
ic
im
p
ed
an
ce
at
th
e
o
r
d
er
n
u
m
b
er
o
f
h
ar
m
o
n
ic.
2
.
4
.
I
m
ple
m
ent
a
t
io
n o
f
pro
po
s
ed
m
et
ho
d
I
n
m
o
s
t
r
ec
en
t
s
tu
d
ies,
s
u
g
g
est
t
h
e
ex
ec
u
tio
n
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
ca
n
b
e
r
ea
li
z
ed
as
d
ep
icts
in
Fig
u
r
e
1
(
a)
a
n
d
Fig
u
r
e
1
(
b
)
u
s
in
g
I
E
E
E
4
-
b
u
s
test
f
ee
d
e
r
s
,
wh
ile
t
h
e
h
ar
m
o
n
ic
s
o
u
r
c
e
is
m
o
d
eled
as
an
in
v
er
ter
-
b
ased
lo
a
d
,
wh
ich
is
k
n
o
wn
as
h
ar
m
o
n
ic
cu
r
r
en
t
s
o
u
r
ce
ty
p
e
-
lo
a
d
[
4
1
-
43
]
,
w
h
er
e
N
is
a
lin
ea
r
lo
ad
,
wh
ich
is
a
r
esis
to
r
wh
er
ea
s
H
i
s
a
h
ar
m
o
n
ic
s
o
u
r
ce
.
B
esid
es,
f
o
u
r
s
p
ec
if
ic
ca
s
es
ar
e
co
n
s
id
e
r
ed
in
th
is
r
esear
ch
,
s
u
ch
as
[
1
5
,
44
,
4
5
]
:
-
C
ase
1
:
No
h
ar
m
o
n
ic
s
o
u
r
ce
i
n
th
e
p
o
wer
n
etwo
r
k
s
y
s
tem
-
C
ase
2
: H
ar
m
o
n
ic
s
o
u
r
ce
at
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
-
C
ase
3
: H
ar
m
o
n
ic
s
o
u
r
ce
s
at
u
p
s
tr
ea
m
an
d
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
-
C
ase
4
: H
ar
m
o
n
ic
s
o
u
r
ce
at
u
p
s
tr
ea
m
o
f
th
e
PC
C
(
a)
(
b
)
Fig
u
r
e
1
.
(
a
)
Up
s
tr
ea
m
-
d
o
wn
s
tr
ea
m
f
o
r
c
ase
1
,
(
b
)
I
E
E
E
4
-
b
u
s
test
f
ee
d
er
s
f
o
r
ca
s
e
2
,
3
an
d
4
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
n
th
is
s
ec
tio
n
,
it
is
ex
p
lain
ed
th
e
r
esu
lts
o
f
th
e
r
ese
ar
ch
an
d
at
th
e
s
am
e
tim
e
is
g
iv
en
th
e
co
m
p
r
e
h
en
s
iv
e
d
is
cu
s
s
io
n
.
R
esu
lts
ca
n
b
e
p
r
esen
ted
in
f
i
g
u
r
es
an
d
ta
b
les
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
cc
u
r
a
te
h
a
r
mo
n
ic
s
o
u
r
ce
id
e
n
tifi
ca
tio
n
u
s
in
g
S
-
tr
a
n
s
fo
r
m
(
Mo
h
d
Ha
tta
Jo
p
r
i
)
2711
3
.
1
.
Ca
s
e
1
:
No
ha
r
m
o
nic so
urce
in t
he
po
wer
net
wo
rk
s
y
s
t
em
T
h
e
lin
ea
r
lo
ad
,
wh
ich
i
s
r
esis
t
iv
e
lo
ad
s
,
a
r
e
lo
ca
ted
u
p
s
tr
ea
m
an
d
d
o
w
n
s
tr
ea
m
o
f
th
e
PC
C
.
As
ca
n
b
e
s
ee
n
in
Fig
u
r
e
s
2
(
a)
an
d
(
b
)
s
h
o
w
th
e
m
ea
s
u
r
e
d
v
o
ltag
e
a
n
d
cu
r
r
en
t
s
ig
n
al
s
in
th
e
tim
e
d
o
m
ain
.
T
h
e
p
ea
k
v
o
ltag
e
is
3
2
6
.
5
V
.
I
n
co
n
tr
ast,
th
e
p
ea
k
cu
r
r
e
n
t
is
6
6
.
5
A
,
r
esp
ec
tiv
ely
.
B
esid
es
,
Fig
u
r
e
2
(
c
)
s
h
o
w
s
th
e
THD(
t
)
an
d
Tn
HD(
t)
o
f
v
o
ltag
e
a
n
d
b
o
th
p
a
r
am
eter
s
ar
e
ze
r
o
p
er
ce
n
t.
Me
an
wh
ile,
Fig
u
r
e
2
(
d
)
p
r
esen
ts
th
e
THD(
t)
an
d
Tn
HD(
t)
o
f
cu
r
r
en
t
an
d
b
o
th
p
ar
am
ete
r
s
ar
e
ze
r
o
p
er
ce
n
t
to
o
.
I
t
s
h
o
ws
th
at
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
s
ig
n
al
h
av
e
n
eith
er
h
a
r
m
o
n
ic
n
o
r
i
n
ter
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
.
Fig
u
r
e
2
(
e)
s
h
o
ws
th
e
Z
TFR
o
f
th
e
PC
C
,
wh
ile
Fig
u
r
e
2
(
f
)
p
r
esen
ts
th
e
Z
S
.
T
h
e
m
o
s
t
s
tr
ik
in
g
r
esu
lt
f
r
o
m
Z
S
,
it
is
s
h
o
wn
th
at
th
e
Z
1
at
5
0
Hz
is
o
f
4
.
8
o
h
m
an
d
n
o
h
a
r
m
o
n
ic
im
p
ed
a
n
ce
s
ex
is
t.
T
h
u
s
,
f
o
r
ca
s
e
1
,
th
e
s
ig
n
if
ica
n
t
r
elatio
n
s
h
ip
b
etw
ee
n
Z
1
a
n
d
Z
h
at
th
e
c
o
n
d
itio
n
o
f
n
o
h
ar
m
o
n
ic
s
o
u
r
ce
in
th
e
p
o
wer
s
y
s
tem
n
etwo
r
k
,
wh
er
e
f
o
r
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t,
h
is
an
y
p
o
s
itiv
e
in
teg
er
wh
er
ea
s
,
f
o
r
in
te
r
h
ar
m
o
n
ic,
h
is
an
y
p
o
s
itiv
e
n
o
n
-
in
teg
e
r
.
ca
n
b
e
wr
itten
as:
1
≠
0
ℎ
(
7
)
ℎ
≠
0
ℎ
(
8
)
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
2
.
C
ase
1
;
(
a)
v
o
ltag
e
s
ig
n
al
in
tim
e
d
o
m
ain
,
(
b
)
c
u
r
r
e
n
t sig
n
al
in
tim
e
d
o
m
ain
,
(
c)
THD(
t)
an
d
Tn
HD(
t)
o
f
v
o
ltag
e,
(
d
)
THD(
t)
an
d
Tn
HD(
t)
o
f
cu
r
r
en
t
,
(
e)
T
FR
o
f
im
p
ed
a
n
ce
(
Z
TFR
)
,
(
f
)
s
p
ec
tr
al
im
p
e
d
an
ce
co
m
p
o
n
en
t
3
.
2
.
Ca
s
e
2
:
H
a
r
m
o
nic so
ur
ce
a
t
do
wns
t
re
a
m
o
f
t
he
P
C
C
F
o
r
ca
s
e
2
,
t
h
e
h
ar
m
o
n
ic
s
o
u
r
c
e
is
lo
ca
ted
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
.
As
ca
n
b
e
s
ee
n
in
Fig
u
r
e
3
(
a)
an
d
Fig
u
r
e
3
(
b
)
s
h
o
w
t
h
e
m
ea
s
u
r
ed
v
o
ltag
e
a
n
d
c
u
r
r
en
t
s
ig
n
al
s
in
th
e
tim
e
d
o
m
ain
.
T
h
e
p
ea
k
v
o
ltag
e
is
3
2
6
.
5
V
.
I
n
co
n
t
r
ast,
th
e
p
ea
k
cu
r
r
e
n
t
i
s
6
6
.
5
A
,
r
esp
ec
tiv
el
y
.
I
n
ad
d
i
tio
n
,
Fig
u
r
e
3
(
c)
s
h
o
w
s
th
e
THD(
t)
an
d
Tn
HD(
t)
m
ea
n
o
f
v
o
ltag
e
ar
e
1
.
5
1
%
a
n
d
6
.
0
5
%,
r
esp
ec
tiv
ely
.
I
n
th
e
m
ea
n
tim
e,
Fig
u
r
e
3
(
d
)
p
r
esen
ts
th
e
THD(
t)
an
d
Tn
HD(
t)
m
ea
n
o
f
cu
r
r
en
t,
w
h
ich
ar
e
1
.
6
7
% a
n
d
6
.
6
8
%,
r
esp
ec
tiv
ely
.
T
h
e
v
alu
es
o
f
THD(
t)
an
d
Tn
HD(
t)
s
h
o
w
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
7
0
8
-
2
717
2712
th
at
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
s
ig
n
als
d
o
h
av
e
h
ar
m
o
n
ic
an
d
in
ter
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
.
Fig
u
r
e
3
(
e)
s
h
o
ws
th
e
Z
TFR
o
f
th
e
PC
C
a
n
d
th
e
Z
S
is
o
b
tain
ed
b
y
ex
tr
ac
tin
g
th
e
p
ar
am
eter
s
f
r
o
m
th
e
Z
TFR
.
Me
an
wh
ile,
Fig
u
r
e
3
(
f
)
p
r
esen
ts
th
e
Z
S
th
at
co
n
s
is
ts
o
f
th
e
Z
1
.
I
n
co
n
tr
ast
th
e
h
a
r
m
o
n
ic
im
p
ed
an
ce
co
n
s
is
ts
o
f
Z
275
,
Z
375
,
Z
600
,
Z
700
,
Z
825
an
d
Z
900
,
r
esp
ec
tiv
ely
.
I
t
is
cr
u
cial
to
o
b
s
er
v
e
th
e
r
elatio
n
s
h
ip
o
f
Z
S
co
m
p
o
n
en
ts
d
u
e
to
id
en
tify
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
lo
ca
tio
n
in
th
e
p
o
wer
s
y
s
tem
n
etwo
r
k
.
I
n
ter
esti
n
g
ly
,
a
s
s
h
o
wn
in
T
ab
le
1
,
th
e
Z
1
v
alu
e
at
5
0
Hz,
i
s
alwa
y
s
h
ig
h
er
th
an
a
n
y
Z
h
.
T
h
u
s
,
f
o
r
ca
s
e
2
,
th
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
Z
1
a
n
d
Z
h
at
th
e
co
n
d
itio
n
o
f
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
l
o
ca
ted
at
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
ca
n
b
e
co
n
clu
d
e
d
an
d
wr
itten
as:
1
≠
0
ℎ
(
9
)
ℎ
<
1
(
1
0
)
w
h
er
e
f
o
r
h
ar
m
o
n
ic
c
o
m
p
o
n
en
t,
h
is
an
y
p
o
s
itiv
e
in
teg
e
r
wh
er
ea
s
,
f
o
r
in
ter
h
ar
m
o
n
ic,
h
is
an
y
p
o
s
itiv
e
non
-
in
te
g
er
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
3
.
C
ase
2
;
(
a)
v
o
ltag
e
s
ig
n
al
in
tim
e
d
o
m
ain
,
(
b
)
c
u
r
r
e
n
t sig
n
al
in
tim
e
d
o
m
ain
,
(
c)
THD(
t)
an
d
Tn
HD(
t)
o
f
v
o
ltag
e,
(
d
)
THD(
t)
an
d
Tn
HD(
t)
o
f
cu
r
r
en
t,
(
e)
T
FR
o
f
im
p
ed
a
n
ce
(
Z
TFR
)
,
(
f
)
s
p
ec
tr
al
im
p
e
d
an
ce
co
m
p
o
n
en
t
3.
3
.
Ca
s
e
3
:
H
a
r
m
o
nic so
ur
ce
s
a
t
up
s
t
re
a
m
a
nd
do
wns
t
re
a
m
o
f
t
he
P
CC
Fo
r
ca
s
e
3
,
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
is
lo
ca
ted
u
p
s
tr
ea
m
a
n
d
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
.
As
ca
n
b
e
s
ee
n
in
Fig
u
r
e
s
4
(
a)
an
d
(
b
)
s
h
o
w
th
e
m
ea
s
u
r
ed
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
s
ig
n
al
s
in
th
e
tim
e
d
o
m
ain
.
T
h
e
p
ea
k
v
o
ltag
e
is
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
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KOM
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m
m
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tr
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p
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2713
32
4
.
7
V,
wh
ile
th
e
p
ea
k
cu
r
r
e
n
t
is
4
4
.
6
A
,
r
esp
ec
tiv
ely
.
B
esi
d
es
,
Fig
u
r
e
4
(
c)
s
h
o
w
s
th
e
THD(
t)
an
d
Tn
HD(
t)
m
ea
n
o
f
v
o
ltag
e
ar
e
1
.
4
7
%
a
n
d
6
.
0
4
%,
r
esp
ec
tiv
ely
.
I
n
th
e
m
ea
n
tim
e,
Fig
u
r
e
4
(
d
)
p
r
esen
ts
th
e
THD(
t)
an
d
Tn
HD(
t)
m
ea
n
o
f
cu
r
r
e
n
t,
wh
i
ch
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e
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.
9
1
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d
4
5
.
1
8
%,
r
esp
ec
tiv
ely
.
T
h
e
v
al
u
es
o
f
THD(
t)
an
d
Tn
HD(
t)
s
h
o
w
th
at
th
e
v
o
ltag
e
an
d
c
u
r
r
en
t
s
ig
n
als
d
o
h
av
e
h
ar
m
o
n
ic
an
d
in
ter
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
.
Fig
u
r
e
4
(
e)
s
h
o
ws
th
e
Z
TFR
o
f
th
e
PC
C
,
wh
ile
Fig
u
r
e
4
(
f
)
p
r
esen
ts
th
e
Z
S
th
at
b
ee
n
e
x
tr
ac
ted
f
r
o
m
t
h
e
Z
TFR
.
Fu
r
th
er
m
o
r
e
,
Fig
u
r
e
4
(
f
)
s
h
o
ws
th
at
th
e
Z
1
is
5
.
3
6
o
h
m
;
in
co
n
tr
ast
th
e
h
ar
m
o
n
ic
im
p
ed
a
n
ce
co
n
s
is
ts
o
f
Z
275
,
Z
375
,
Z
4
00
,
Z
6
00
,
Z
700
an
d
Z
900
,
r
esp
ec
tiv
ely
.
T
h
e
ch
ar
ac
ter
is
tic
o
f
th
e
s
p
ec
tr
al
i
m
p
ed
an
ce
,
Z
S
ar
e
s
u
m
m
ar
ized
in
T
ab
le
2
.
W
h
at
i
s
s
u
r
p
r
is
in
g
is
th
at
t
h
e
v
alu
e
o
f
Z
1
is
alwa
y
s
s
m
aller
th
a
n
an
y
h
ar
m
o
n
ic
im
p
e
d
a
n
ce
s
,
Z
h
.
I
t
is
ap
p
ar
e
n
t
f
r
o
m
th
e
r
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lt
th
at
th
e
Z
S
co
m
p
o
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en
ts
ca
n
b
e
ch
ar
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ter
ized
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u
e
to
id
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tify
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e
lo
ca
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o
f
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
.
As
a
r
esu
lt,
f
o
r
ca
s
e
3
,
th
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
Z
1
an
d
Z
h
at
th
e
co
n
d
itio
n
o
f
t
h
e
h
ar
m
o
n
ic
s
o
u
r
ce
lo
ca
ted
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
ca
n
b
e
wr
itten
as:
1
≠
0
ℎ
(
1
1
)
ℎ
>
1
(
1
2
)
w
h
er
e
f
o
r
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t,
h
is
an
y
p
o
s
itiv
e
in
teg
er
w
h
er
ea
s
,
f
o
r
i
n
ter
h
ar
m
o
n
ic,
h
is
an
y
p
o
s
itiv
e
non
-
in
te
g
er
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f
)
Fig
u
r
e
4
C
ase
3
;
(
a)
v
o
ltag
e
s
i
g
n
al
in
tim
e
d
o
m
ain
,
(
b
)
c
u
r
r
e
n
t sig
n
al
in
tim
e
d
o
m
ain
,
(
c)
THD(
t)
an
d
Tn
HD(
t)
o
f
v
o
ltag
e,
(
d
)
THD(
t)
an
d
Tn
HD(
t)
o
f
cu
r
r
en
t
,
(
e)
T
FR
o
f
im
p
ed
a
n
ce
(
Z
TFR
)
,
(
f
)
s
p
ec
tr
al
im
p
e
d
an
ce
co
m
p
o
n
en
t
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
1
6
9
3
-
6
9
3
0
T
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L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
7
0
8
-
2
717
2714
T
ab
le
1
.
Ma
g
n
itu
d
es o
f
th
e
s
p
e
ctr
al
im
p
ed
an
ce
f
o
r
ca
s
e
2
u
s
in
g
S
-
tr
an
s
f
o
r
m
tech
n
iq
u
e
S
p
e
c
t
r
a
l
I
mp
e
d
a
n
c
e
O
h
m
Z
1
5
.
3
6
Z
275
3
.
8
1
Z
375
3
.
6
8
Z
600
4
.
1
9
Z
700
4
.
3
4
Z
825
3
.
9
4
Z
900
3
.
6
8
T
ab
le
2
.
Ma
g
n
itu
d
es o
f
th
e
s
p
ec
tr
al
im
p
ed
an
ce
f
o
r
ca
s
e
3
u
s
in
g
S
-
tr
an
s
f
o
r
m
tech
n
iq
u
e
S
p
e
c
t
r
a
l
I
mp
e
d
a
n
ce
O
h
m
Z
1
6
.
5
Z
275
1
2
.
8
Z
375
1
1
.
8
Z
400
1
2
.
3
Z
600
1
2
.
2
Z
700
1
2
.
5
Z
900
1
2
.
9
3
.
4
.
Ca
s
e
4
:
H
a
r
m
o
nic so
ur
ce
a
t
up
s
t
re
a
m
o
f
t
he
P
CC
I
n
ca
s
e
4
,
th
e
h
ar
m
o
n
ic
s
o
u
r
c
e
is
lo
ca
ted
u
p
s
tr
ea
m
o
f
th
e
P
C
C
.
T
h
e
v
o
ltag
e
an
d
c
u
r
r
en
t
s
ig
n
als
in
th
e
tim
e
d
o
m
ain
a
r
e
m
ea
s
u
r
e
d
at
th
e
PC
C
ar
e
s
h
o
wn
in
Fig
u
r
e
s
5
(
a)
an
d
(
b
)
.
T
h
e
p
ea
k
v
o
ltag
e
is
3
2
4
.
3
V,
wh
er
ea
s
th
e
p
ea
k
cu
r
r
e
n
t
is
3
0
.
6
5
A
an
d
th
e
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
cy
is
5
0
Hz.
T
h
ese
s
ig
n
als
ar
e
u
s
ed
as
th
e
in
p
u
ts
f
o
r
an
aly
zin
g
h
ar
m
o
n
ic
s
o
u
r
ce
s
u
s
in
g
th
e
S
-
tr
a
n
s
f
o
r
m
te
ch
n
iq
u
e.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
th
e
wav
ef
o
r
m
s
th
at
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
w
av
ef
o
r
m
s
ar
e
d
is
to
r
ted
b
ec
au
s
e
o
f
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
p
r
es
en
t
s
in
th
e
n
etwo
r
k
s
y
s
tem
.
Fu
r
th
er
m
o
r
e,
Fig
u
r
e
5
(
c
)
s
h
o
ws
th
e
T
HD(
t)
an
d
T
n
HD(
t)
m
ea
n
o
f
v
o
ltag
e
,
wh
ich
ar
e
1
.
4
7
%
an
d
6
.
0
4
%,
r
esp
ec
tiv
ely
.
Mo
r
eo
v
er
,
Fig
u
r
e
5
(
d
)
s
h
o
w
s
th
e
THD(
t)
an
d
Tn
HD(
t)
m
ea
n
o
f
cu
r
r
en
t
ar
e
1
.
5
%
an
d
6
.
0
5
%,
r
esp
ec
tiv
ely
.
T
h
e
v
alu
es
o
f
THD(
t)
an
d
Tn
HD(
t)
s
h
o
w
th
at
th
e
v
o
ltag
e
an
d
c
u
r
r
en
t
s
ig
n
als
d
o
h
av
e
h
ar
m
o
n
ic
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d
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n
ter
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
.
T
h
e
Z
S
co
m
p
o
n
e
n
ts
ar
e
ex
t
r
ac
ted
f
r
o
m
t
h
e
Z
TFR
s
h
o
wn
in
Fig
u
r
e
5
(
e)
.
As
s
h
o
wn
in
Fig
u
r
e
5
(f)
, t
h
e
s
p
ec
tr
al
i
m
p
ed
a
n
c
e,
Z
S,
co
n
s
is
ts
o
f
f
u
n
d
am
en
tal
i
m
p
ed
an
ce
,
Z
1
at
5
0
Hz,
wh
er
ea
s
th
e
h
ar
m
o
n
ic
im
p
ed
an
ce
s
s
u
ch
as Z
275
,
Z
300
,
Z
375
,
Z
400
,
Z
600
,
Z
700
,
Z
900
,
r
esp
ec
tiv
ely
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
5
.
C
ase
4
,
(
a
)
Vo
ltag
e
s
ig
n
al
in
tim
e
d
o
m
ain
,
(
b
)
C
u
r
r
en
t sig
n
al
in
tim
e
d
o
m
ain
,
(
c)
THD(
t)
an
d
Tn
HD(
t)
o
f
v
o
ltag
e,
(
d
)
THD(
t)
an
d
Tn
HD(
t)
o
f
cu
r
r
en
t
,
(
e)
T
FR
o
f
im
p
ed
a
n
ce
(
Z
TFR
)
,
(
f
)
Sp
ec
tr
al
im
p
e
d
an
ce
c
o
m
p
o
n
en
t
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
cc
u
r
a
te
h
a
r
mo
n
ic
s
o
u
r
ce
id
e
n
tifi
ca
tio
n
u
s
in
g
S
-
tr
a
n
s
fo
r
m
(
Mo
h
d
Ha
tta
Jo
p
r
i
)
2715
T
h
e
Z
S
c
o
m
p
o
n
en
ts
r
elatio
n
s
h
ip
ar
e
t
h
e
cr
itical
d
r
iv
in
g
f
ac
t
o
r
o
f
h
a
r
m
o
n
ic
s
o
u
r
ce
id
en
tifi
ca
tio
n
an
d
th
e
v
alu
es
o
f
th
e
co
m
p
o
n
en
ts
ar
e
s
u
m
m
ar
ized
in
T
ab
le
3
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
Z
1
is
a
lwa
y
s
th
e
s
am
e
v
alu
e
as
all
h
ar
m
o
n
ic
im
p
ed
an
ce
s
,
Z
h
.
B
ased
o
n
th
e
r
esu
lts
,
it
ca
n
b
e
co
n
clu
d
ed
th
at
t
h
e
Z
S
c
o
m
p
o
n
en
ts
ca
n
b
e
u
s
ed
to
id
en
tify
th
e
lo
ca
tio
n
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
s
.
Hen
ce
,
f
o
r
ca
s
e
4
,
th
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
b
etwe
en
Z
1
an
d
Z
h
at
th
e
co
n
d
itio
n
o
f
t
h
e
h
ar
m
o
n
ic
s
o
u
r
ce
lo
ca
ted
at
d
o
wn
s
tr
ea
m
o
f
t
h
e
PC
C
ca
n
b
e
wr
itten
as:
1
≠
0
ℎ
(
1
3
)
ℎ
=
1
(
1
4
)
w
h
er
e
f
o
r
h
ar
m
o
n
ic
c
o
m
p
o
n
en
t,
h
is
an
y
p
o
s
itiv
e
in
teg
e
r
wh
er
ea
s
,
f
o
r
in
ter
h
ar
m
o
n
ic,
h
is
an
y
p
o
s
itiv
e
non
-
in
te
g
er
.
T
ab
le
3
.
Ma
g
n
itu
d
es o
f
th
e
s
p
ec
tr
al
im
p
ed
an
ce
f
o
r
ca
s
e
4
u
s
in
g
S
-
t
r
an
s
f
o
r
m
tech
n
iq
u
e
S
p
e
c
t
r
a
l
I
mp
e
d
a
n
c
e
O
h
m
Z
1
1
0
.
6
Z
275
1
0
.
6
Z
300
1
0
.
6
Z
375
1
0
.
6
Z
400
1
0
.
6
Z
600
1
0
.
6
Z
700
1
0
.
6
Z
900
1
0
.
6
3.
5
.
P
er
f
o
r
m
a
nce
o
f
t
he
pro
po
s
ed
m
et
ho
d
T
h
is
r
esear
ch
p
r
o
v
id
es
an
ex
citin
g
o
p
p
o
r
t
u
n
ity
to
ad
v
a
n
ce
th
e
u
n
d
er
s
tan
d
in
g
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
id
en
tific
atio
n
u
s
in
g
th
e
S
-
tr
a
n
s
f
o
r
m
tech
n
i
q
u
e.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
o
f
th
is
an
aly
s
is
is
th
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
o
f
th
e
s
p
ec
tr
al
i
m
p
ed
an
ce
co
m
p
o
n
en
ts
,
Z
S
s
u
ch
as
f
u
n
d
am
en
tal
im
p
ed
an
c
e,
Z
1
an
d
h
ar
m
o
n
ic
im
p
ed
an
ce
,
Z
h
in
id
en
tify
in
g
th
e
lo
ca
t
io
n
o
f
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
in
th
e
n
etwo
r
k
s
y
s
tem
.
T
h
e
s
p
ec
tr
al
im
p
ed
an
ce
ch
ar
ac
ter
is
tics
ar
e
u
s
ed
to
id
e
n
tify
th
e
lo
ca
tio
n
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
s
an
d
th
e
p
er
f
o
r
m
an
c
e
o
f
th
is
p
r
o
p
o
s
ed
m
eth
o
d
ar
e
s
u
m
m
ar
izes
in
T
a
b
le
4
.
T
ab
le
4
.
Per
f
o
r
m
an
ce
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
i
d
en
tific
atio
n
u
s
in
g
s
p
ec
tr
al
im
p
ed
a
n
ce
co
m
p
o
n
en
ts
ch
ar
ac
ter
is
tic
s
C
a
se
U
p
st
r
e
a
m s
i
d
e
D
o
w
n
s
t
r
e
a
m
si
d
e
S
p
e
c
t
r
a
l
i
mp
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d
a
n
c
e
,
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S
c
h
a
r
a
c
t
e
r
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c
%
C
o
r
r
e
c
t
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t
i
f
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c
a
t
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o
n
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N
Z
1
≠
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o
h
m
Z
h
=
0
o
h
m
1
0
0
2
N
H
Z
1
≠
0
o
h
m
Z
1
>
Z
h
1
0
0
3
H
H
Z
1
≠
0
o
h
m
Z
h
>
Z
1
1
0
0
4
N
H
Z
1
≠
0
o
h
m
Z
h
=
Z
1
1
0
0
4.
CO
NCLU
SI
O
N
T
h
e
m
ain
co
n
ce
r
n
o
f
th
is
r
es
ea
r
ch
is
to
id
en
tif
y
th
e
lo
ca
ti
o
n
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
th
at
c
o
n
n
ec
ted
to
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
u
tili
zin
g
th
e
S
-
tr
an
s
f
o
r
m
tech
n
i
q
u
e.
T
h
e
m
ain
c
o
n
tr
ib
u
tio
n
o
f
th
is
r
esear
ch
is
th
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
o
f
Z
S
co
m
p
o
n
en
ts
th
at
o
b
tain
ed
f
r
o
m
th
e
S
-
tr
an
s
f
o
r
m
an
a
ly
s
is
in
id
en
tify
in
g
th
e
lo
ca
tio
n
o
f
h
ar
m
o
n
ic
s
o
u
r
c
es
.
B
ased
o
n
T
ab
le
4
,
th
e
c
o
r
r
ec
tn
ess
of
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
1
0
0
%
f
o
r
ea
ch
ca
s
e
an
d
th
e
s
ig
n
if
ican
t
r
elatio
n
s
h
ip
o
f
Z
S
f
o
r
id
e
n
tific
atio
n
o
f
h
ar
m
o
n
ic
s
o
u
r
ce
lo
ca
ti
o
n
ar
e
s
u
m
m
ar
ized
as f
o
llo
w:
-
If
Z
1
≠
0
an
d
Z
h
=
0
,
th
e
r
e
is
n
o
s
o
u
r
ce
in
th
e
n
etwo
r
k
s
y
s
tem
.
-
If
Z
1
≠
0
an
d
Z
1
>
Z
h
,
th
er
e
is
a
h
ar
m
o
n
ic
s
o
u
r
ce
lo
ca
ted
at
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
.
-
If
Z
1
≠
0
an
d
Z
h
>
Z
1
,
th
er
e
a
r
e
a
h
ar
m
o
n
ic
s
o
u
r
ce
s
lo
c
ated
at
u
p
s
tr
ea
m
an
d
d
o
wn
s
tr
ea
m
o
f
th
e
PC
C
.
-
If
Z
1
≠
0
an
d
Z
1
=
Z
h
,
th
e
r
e
is
a
h
ar
m
o
n
ic
s
o
u
r
ce
lo
ca
ted
at
u
p
s
tr
ea
m
o
f
th
e
PC
C
.
C
o
n
s
eq
u
en
tly
,
co
n
s
id
er
in
g
t
h
e
r
esu
lts
,
th
is
m
eth
o
d
ca
n
b
e
u
s
ed
ac
cu
r
ately
in
d
is
tin
g
u
is
h
in
g
th
e
lo
ca
tio
n
o
f
th
e
h
ar
m
o
n
ic
s
o
u
r
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
1
6
9
3
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6
9
3
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No
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5
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Octo
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2
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717
2716
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Hig
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r
at
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lly
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k
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o
wled
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ed
.
RE
F
E
R
E
NC
E
S
[1
]
D.
D.
F
e
rre
ira
e
t
a
l
.
,
“
M
e
th
o
d
b
a
s
e
d
o
n
i
n
d
e
p
e
n
d
e
n
t
c
o
m
p
o
n
e
n
t
a
n
a
ly
sis
fo
r
h
a
rm
o
n
ic
e
x
trac
ti
o
n
fr
o
m
p
o
we
r
s
y
ste
m
sig
n
a
ls,”
El
e
c
tr.
P
o
we
r S
y
st.
Res
.
,
v
o
l
.
1
1
9
,
p
p
.
1
9
-
2
4
,
F
e
b
r
u
a
ry
2
0
1
5
.
[2
]
M
.
M
ish
ra
,
“
P
o
we
r
q
u
a
li
t
y
d
istu
rb
a
n
c
e
d
e
tec
ti
o
n
a
n
d
c
las
sifica
ti
o
n
u
si
n
g
sig
n
a
l
p
r
o
c
e
ss
in
g
a
n
d
so
ft
c
o
m
p
u
ti
n
g
tec
h
n
iq
u
e
s:
A
c
o
m
p
re
h
e
n
siv
e
re
v
iew
,
”
In
ter
n
a
t
io
n
a
l
T
r
a
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
En
e
rg
y
S
y
ste
ms
,
v
o
l.
2
9
,
n
o
.
2
,
M
a
rc
h
2
0
1
9
.
[3
]
M
.
F
a
rh
o
o
d
n
e
a
,
e
t
a
l.
,
“
An
imp
ro
v
e
d
m
e
th
o
d
f
o
r
d
e
term
in
in
g
c
o
n
tri
b
u
ti
o
n
o
f
u
ti
li
t
y
a
n
d
c
u
st
o
m
e
r
h
a
rm
o
n
ic
d
isto
rti
o
n
s
in
a
p
o
we
r
d
istri
b
u
ti
o
n
sy
ste
m
,
”
In
t.
J
.
El
e
c
tr.
En
g
.
I
n
f
o
rm
a
ti
c
s
,
v
o
l.
2
,
n
o
.
3
,
p
p
.
2
0
4
-
2
1
5
,
2
0
1
0
.
[4
]
M
.
F
a
rh
o
o
d
n
e
a
,
A.
M
o
h
a
m
e
d
,
a
n
d
H.
S
h
a
re
e
f,
“
A
sin
g
le
p
o
in
t
m
e
a
su
re
m
e
n
t
m
e
th
o
d
f
o
r
e
v
a
lu
a
ti
n
g
h
a
rm
o
n
i
c
c
o
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tri
b
u
ti
o
n
s
o
f
u
ti
li
t
y
a
n
d
c
u
st
o
m
e
r
in
p
o
we
r
d
istri
b
u
ti
o
n
sy
ste
m
s,”
J
o
u
rn
a
l
o
f
Ap
p
li
e
d
S
c
ien
c
e
s
,
v
o
l.
1
1
,
n
o
.
2
.
p
p
.
2
5
7
-
26
5
,
F
e
b
ru
a
ry
2
0
1
1
.
[5
]
A.
R.
A
b
d
u
ll
a
h
,
e
t
a
l.
,
“
L
o
c
a
li
z
a
ti
o
n
o
f
m
u
lt
i
p
le
h
a
rm
o
n
ic
so
u
r
c
e
s
fo
r
i
n
v
e
rter
l
o
a
d
s
u
ti
l
izin
g
p
e
rio
d
o
g
ra
m
,
”
J
.
T
e
k
n
o
l.
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
8
7
-
9
1
,
Ja
n
u
a
ry
2
0
1
6
.
[6
]
W.
Xu
,
“
P
o
we
r
d
irec
ti
o
n
m
e
th
o
d
c
a
n
n
o
t
b
e
u
se
d
fo
r
h
a
rm
o
n
ic
so
u
rc
e
d
e
tec
ti
o
n
,
”
2
0
0
0
P
o
we
r
En
g
i
n
e
e
rin
g
S
o
c
iety
S
u
mm
e
r M
e
e
ti
n
g
(Ca
t.
N
o
.
0
0
CH3
7
1
3
4
)
,
v
o
l.
2
,
p
p
.
8
7
3
-
8
7
6
,
Ju
ly
2
0
0
0
.
[7
]
F
.
Xu
,
e
t
a
l.
,
“
S
tu
d
y
o
n
c
o
n
stra
in
ts
fo
r
h
a
rm
o
n
ic
s
o
u
rc
e
d
e
term
in
a
ti
o
n
u
si
n
g
a
c
ti
v
e
p
o
we
r
d
irec
ti
o
n
,
”
IEE
E
T
r
a
n
s
.
Po
we
r De
li
v
.
,
v
o
l.
3
3
,
n
o
.
6
,
p
p
.
2
6
8
3
-
2
6
9
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c
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8
.
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]
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Li
u
,
e
t
a
l.
,
“
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rm
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so
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rc
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ti
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li
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d
,
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2
0
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-
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c
if
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c
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,
2
0
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9
,
p
p
.
1
-
5,
M
a
rc
h
2
0
0
9
.
[9
]
A.
R.
Ab
d
u
ll
a
h
,
G
.
Z.
P
e
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g
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n
d
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.
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G
h
a
n
i,
“
A
n
e
w
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ft
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th
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h
a
rm
o
n
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rc
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e
te
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ti
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n
a
t
p
o
in
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o
f
c
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m
m
o
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u
p
li
n
g
,
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c
.
2
0
1
4
I
EE
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t
h
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n
t.
Po
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r E
n
g
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ti
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f.
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0
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4
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1
1
0
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1
1
4
,
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a
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0
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4
.
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0
]
F
.
S
a
fa
rg
h
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li
,
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.
M
a
lek
ian
,
a
n
d
W.
S
c
h
u
fft,
“
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t
h
e
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o
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in
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n
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h
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d
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n
ti
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n
-
P
a
rt
II:
Ap
p
li
c
a
ti
o
n
a
n
d
i
n
terp
re
tatio
n
o
f
m
e
th
o
d
s
,
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I
EE
E
T
ra
n
s
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n
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r De
li
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p
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8
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1
2
8
7
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n
.
2
0
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8
.
[1
1
]
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.
S
a
fa
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h
o
li
,
K.
M
a
lek
ian
,
a
n
d
W.
S
c
h
u
ff
t,
“
On
t
h
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rc
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id
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n
-
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rt
I:
Re
v
iew
o
f
M
e
th
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d
s,”
IEE
E
T
ra
n
s.
P
o
we
r De
li
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,
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3
,
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3
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1
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6
8
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7
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n
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2
0
1
8
.
[1
2
]
A.
R.
A
b
d
u
ll
a
h
,
e
t
a
l.
,
“
L
o
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li
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ti
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m
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h
a
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ti
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g
p
e
rio
d
o
g
ra
m
,
”
J
.
T
e
lec
o
mm
u
n
.
El
e
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tro
n
.
Co
mp
u
t.
En
g
.
,
v
o
l.
8
,
n
o
.
2
,
2
0
1
6
.
[1
3
]
A.
Ab
d
u
l
lah
,
M
.
M
a
n
a
p
,
e
t
al
.
,
“
An
imp
ro
v
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d
sp
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tr
o
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ra
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ti
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lt
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s
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d
istri
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sy
ste
m
with
in
v
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s
,
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o
c
e
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in
g
s
o
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t
h
e
In
ter
n
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ti
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l
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lt
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fer
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o
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g
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n
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ter
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ien
ti
sts
.
,
v
o
l.
II,
p
p
.
0
-
5
,
M
a
rc
h
2
0
1
7
.
[1
4
]
N.
Ha
m
z
a
h
,
e
t
a
l.
,
“
Id
e
n
ti
fica
ti
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o
f
h
a
rm
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n
ic
so
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rc
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t
th
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c
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m
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p
li
n
g
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se
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o
n
v
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lt
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g
e
in
d
ice
s
,
”
J
.
T
e
k
n
o
l.
,
v
o
l.
4
3
,
n
o
.
1
,
p
p
.
1
1
-
3
2
,
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c
.
2
0
0
5
.
[1
5
]
A.
Ab
d
u
ll
a
h
,
a
n
d
M
.
M
a
n
a
p
,
“
An
imp
ro
v
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d
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c
tr
o
g
ra
m
to
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d
e
n
ti
f
y
m
u
lt
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le
h
a
rm
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ic
so
u
rc
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s
in
d
istr
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ti
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sy
ste
m
with
in
v
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rter
lo
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d
s
,
”
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c
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i
n
g
s
o
f
th
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ter
n
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ti
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a
l
M
u
lt
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o
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g
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n
d
Co
m
p
u
ter
S
c
ien
ti
sts
.
,
v
o
l.
7
,
n
o
.
4
,
p
p
.
1
1
5
9
1
,
2
0
1
7
.
[1
6
]
A.
Ba
n
sh
wa
r
a
n
d
A
.
K.
Ch
a
n
d
e
l,
“
Id
e
n
ti
fi
c
a
ti
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n
o
f
h
a
rm
o
n
ic
so
u
r
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e
s
u
sin
g
f
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z
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y
l
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ic,”
2
0
1
0
J
t
.
I
n
t.
C
o
n
f
.
Po
we
r
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e
c
tro
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ive
s E
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2
0
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Po
we
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n
d
i
a
,
p
p
.
1
–
7
,
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c
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b
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r
2
0
1
0
.
[1
7
]
C.
Ja
ip
ra
d
id
th
a
m
,
“
A
c
o
n
tr
o
l
o
f
re
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l
v
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lt
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g
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n
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h
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ic
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n
a
ly
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with
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d
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r
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r
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t
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re
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M
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rk
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th
o
d
,
”
2
0
1
6
IE
EE
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t
h
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n
t.
Co
n
f.
Po
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r
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st.
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CPS
2
0
1
6
,
n
o
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1
,
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a
rc
h
2
0
1
6
.
[1
8
]
T.
Zan
g
,
e
t
a
l.
,
“
Ha
rm
o
n
ic
so
u
rc
e
lo
c
a
li
z
a
ti
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a
p
p
ro
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c
h
b
a
se
d
o
n
fa
s
t
k
e
rn
e
l
e
n
tro
p
y
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p
ti
m
iza
ti
o
n
ICA
a
n
d
m
in
imu
m
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o
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i
t
io
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tr
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p
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,
”
E
n
tro
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,
v
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l.
1
8
,
n
o
.
6
,
p
p
.
2
1
4
,
Ju
n
e
2
0
1
6
.
[1
9
]
T.
P
fa
jfar,
B.
Blaž
ič,
a
n
d
I.
P
a
p
ič,
“
Ha
rm
o
n
ic
c
o
n
tri
b
u
t
io
n
s
e
v
a
lu
a
ti
o
n
wi
th
t
h
e
h
a
rm
o
n
ic
c
u
rre
n
t
v
e
c
to
r
m
e
th
o
d
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
w
e
r
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l
iv
e
ry
,
v
o
l.
2
3
,
n
o
.
1
,
p
p
.
4
2
5
-
4
3
3
,
Ja
n
u
a
ry
2
0
0
8
.
[2
0
]
A.
R.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
An
i
d
e
n
ti
fica
ti
o
n
o
f
m
u
lt
i
p
le
h
a
rm
o
n
ic
so
u
rc
e
s
in
a
d
istri
b
u
ti
o
n
sy
s
tem
b
y
u
sin
g
sp
e
c
tro
g
ra
m
,
”
Bu
l
l
e
ti
n
o
f
E
lec
tr
ica
l
.
E
n
g
i
n
e
e
rin
g
a
n
d
I
n
f
o
rm
a
ti
c
s
,
v
o
l.
7
,
n
o
.
2
,
p
p
.
2
4
4
-
2
5
6
,
Ju
n
e
2
0
1
8
.
[2
1
]
P
.
S
u
p
ri
y
a
a
n
d
T
.
N.
P
a
d
m
a
n
a
b
h
a
n
Na
m
b
iar,
“
Re
v
iew
o
f
h
a
rm
o
n
ic
so
u
rc
e
id
e
n
ti
fica
ti
o
n
tec
h
n
iq
u
e
s,”
In
t
e
rn
a
ti
o
n
a
l
.
Rev
iew
.
El
e
c
tr
ica
l
.
En
g
i
n
e
e
rin
g
.
,
v
o
l.
7
,
n
o
.
3
,
p
p
.
4
5
2
5
-
4
5
3
1
,
Ju
n
e
2
0
1
2
.
[2
2
]
G
.
D’A
n
to
n
a
,
e
t
a
l.
,
“
Ha
rm
o
n
ic
so
u
rc
e
e
stim
a
ti
o
n
i
n
d
istr
ib
u
ti
o
n
s
y
ste
m
s,”
Ap
p
l.
M
e
a
s.
P
o
we
r
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y
st.
(AM
PS
)
,
2
0
1
0
IEE
E
In
t.
W
o
rk
.
,
v
o
l
.
6
0
,
n
o
.
1
0
,
p
p
.
1
-
5,
S
e
p
tem
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r
2
0
1
0
.
[2
3
]
A.
R.
A
b
d
u
ll
a
h
,
e
t
a
l.
,
“
A
fa
st
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c
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z
a
ti
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n
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f
m
u
lt
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p
le
h
a
rm
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ic
so
u
r
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s
fo
r
re
c
ti
fier
l
o
a
d
s
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t
il
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p
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rio
d
o
g
ra
m
,
”
T
e
lko
mn
ika
(
T
e
lec
o
mm
u
n
ica
ti
o
n
Co
mp
u
t
er
.
El
e
c
tro
n
ics
.
a
n
d
C
o
n
tr
o
l.
,
v
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l.
1
5
,
n
o
.
1
,
M
a
rc
h
2
0
1
7
.
[2
4
]
A.
Ra
h
im Ab
d
u
l
la
h
,
e
t
a
l.
,
“
P
e
rfo
rm
a
n
c
e
e
v
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lu
a
ti
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o
f
re
a
l
p
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we
r
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a
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t
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d
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u
rb
a
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s a
n
a
ly
sis u
sin
g
S
-
tran
sfo
rm
,
”
Ap
p
l
.
M
e
c
h
.
M
a
ter
.
,
v
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l
.
7
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p
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1
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4
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0
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5
.
[2
5
]
A.
R.
Ab
d
u
l
lah
,
e
t
a
l.
,
“
S
h
o
r
t
-
c
ircu
it
sw
it
c
h
e
s
fa
u
lt
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n
a
ly
sis
o
f
v
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l
tag
e
so
u
rc
e
i
n
v
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rter
u
sin
g
sp
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c
tr
o
g
ra
m
,
”
El
e
c
tr.
M
a
c
h
.
S
y
st.
(IC
EM
S
),
2
0
1
3
I
n
t.
C
o
n
f
.
,
p
p
.
1
8
0
8
-
1
8
1
3
,
Oc
to
b
e
r
2
0
1
3
.
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2717
[2
6
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N.
A.
Ab
i
d
u
ll
a
h
,
e
t
a
l.
,
“
Re
a
l
-
ti
m
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p
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we
r
q
u
a
li
ty
sig
n
a
ls
m
o
n
it
o
rin
g
sy
ste
m
,
”
Pro
c
e
e
d
in
g
-
2
0
1
3
IEE
E
S
t
u
d
e
n
t
Co
n
fer
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n
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Res
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De
v
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p
me
n
t,
S
CORe
D 2
0
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3
,
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n
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r
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.
[2
7
]
A.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
A
u
ti
li
sa
ti
o
n
o
f
imp
r
o
v
e
d
g
a
b
o
r
tran
sf
o
rm
f
o
r
h
a
rm
o
n
i
c
sig
n
a
ls
d
e
tec
ti
o
n
a
n
d
c
las
sifica
ti
o
n
a
n
a
ly
sis
,
”
In
t
e
rn
a
ti
o
n
a
l
. J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
7
,
n
o
.
1
,
p
p
.
2
1
-
2
8
,
F
e
b
ru
a
ry
2
0
1
7
.
[2
8
]
A.
R.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
An
imp
r
o
v
e
d
o
f
m
u
lt
i
p
le
h
a
rm
o
n
ic
so
u
rc
e
s
id
e
n
ti
fica
ti
o
n
in
d
istri
b
u
ti
o
n
sy
ste
m
with
in
v
e
rter
lo
a
d
s b
y
u
sin
g
sp
e
c
tro
g
ra
m
,
”
Bu
ll
.
El
e
c
tr.
En
g
.
I
n
f
o
rm
a
ti
c
s
,
v
o
l.
7
,
n
o
.
2
,
p
p
.
2
4
4
-
2
5
6
,
De
c
e
m
b
e
r
2
0
1
8
.
[2
9
]
A.
R.
Ab
d
u
ll
a
h
,
e
t
a
l
.
,
“
An
a
c
c
u
ra
te
c
las
sifica
ti
o
n
m
e
th
o
d
o
f
h
a
rm
o
n
ic
sig
n
a
ls
in
p
o
we
r
d
istr
ib
u
ti
o
n
sy
ste
m
by
u
ti
li
si
n
g
S
-
t
ra
n
sf
o
rm
,
”
T
EL
K
OM
NIKA
T
e
lec
o
mm
u
n
ica
ti
o
n
,
C
o
mp
u
t
in
g
,
El
e
c
tro
n
ics
a
n
d
C
o
n
tro
l
,
v
o
l
.
1
5
,
n
o
.
1
,
p
p
.
1
2
-
2
0
,
M
a
rc
h
2
0
1
7
.
[3
0
]
A
.
R.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
P
o
we
r
q
u
a
li
ty
sig
n
a
ls
c
las
sifica
ti
o
n
sy
ste
m
u
sin
g
ti
m
e
-
fre
q
u
e
n
c
y
d
istri
b
u
ti
o
n
,
”
Ap
p
l.
M
e
c
h
.
M
a
te
r.
,
v
o
l.
4
9
4
-
4
9
5
,
p
p
.
1
8
8
9
-
1
8
9
4
,
2
0
1
4
.
[3
1
]
A.
R.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
P
e
rfo
rm
a
n
c
e
v
e
rifi
c
a
ti
o
n
o
f
p
o
we
r
q
u
a
li
t
y
sig
n
a
ls
c
las
sifica
ti
o
n
sy
ste
m
,
”
Ap
p
l
ied
.
M
e
c
h
a
n
ics
and
.
M
a
ter
ia
ls
.
,
v
o
l.
7
5
3
,
p
p
.
1
1
5
8
-
1
1
6
3
,
Ap
r
il
2
0
1
5
.
[3
2
]
A.
R.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
An
imp
r
o
v
e
d
d
e
tec
ti
o
n
a
n
d
c
las
sifica
ti
o
n
te
c
h
n
iq
u
e
o
f
h
a
rm
o
n
ic
sig
n
a
ls
in
p
o
we
r
d
istri
b
u
ti
o
n
b
y
u
ti
li
z
i
n
g
s
p
e
c
tro
g
ra
m
,
”
In
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
El
e
c
tr
ica
l
a
n
d
C
o
mp
u
t
er
E
n
g
i
n
e
e
rin
g
,
v
o
l.
7
,
n
o
.
1
,
p
p
.
1
2
-
2
0
,
2
0
1
7
.
[3
3
]
A.
G
.
M
iam
e
e
,
“
No
n
sta
ti
o
n
a
ry
sto
c
h
a
stic
p
r
o
c
e
ss
e
s
a
n
d
t
h
e
ir
a
p
p
li
c
a
ti
o
n
s
,
”
W
o
rk
sh
o
p
o
n
No
n
sta
t
io
n
a
ry
S
to
c
h
a
sti
c
Pro
c
e
ss
e
s a
n
d
T
h
e
ir A
p
p
li
c
a
ti
o
n
,
p
p
.
1
-
2
9
8
,
Au
g
u
st
1
9
9
1
.
[3
4
]
N.
H.
T.
Ah
m
a
d
,
A.
R.
A
b
d
u
ll
a
h
a
n
d
N.
A
.
A
b
i
d
u
l
lah
,
“
An
a
l
y
sis
o
f
p
o
we
r
q
u
a
li
t
y
d
is
tu
r
b
a
n
c
e
s
u
si
n
g
sp
e
c
tro
g
ra
m
a
n
d
S
-
t
ra
n
sfo
rm
,
”
In
t
e
rn
a
ti
o
n
a
l
R
e
v
iew o
f
El
e
c
tr
ica
l
E
n
g
i
n
e
e
rin
g
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
6
1
1
-
6
1
9
,
Ju
n
e
2
0
1
4
.
[3
5
]
A.
R.
Ab
d
u
ll
a
h
,
e
t
a
l.
,
“
A
c
rit
ica
l
re
v
iew
o
f
ti
m
e
-
fre
q
u
e
n
c
y
d
istri
b
u
ti
o
n
a
n
a
l
y
sis
f
o
r
d
e
tec
ti
o
n
a
n
d
c
las
sifica
ti
o
n
o
f
h
a
rm
o
n
ic sig
n
a
l
i
n
p
o
we
r
d
istri
b
u
ti
o
n
sy
ste
m
,
”
In
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
El
e
c
tr
ica
l
a
n
d
.
C
o
mp
u
t
er
En
g
i
n
e
e
rin
g
,
v
o
l.
8
,
n
o
.
6
,
p
p
.
4
6
0
3
-
4
6
1
8
,
De
c
e
m
b
e
r
2
0
1
8
.
[3
6
]
N.
A.
Ab
id
u
ll
a
h
,
e
t
a
l.
,
“
Re
a
l
-
ti
m
e
p
o
we
r
q
u
a
l
it
y
sig
n
a
ls
m
o
n
it
o
ri
n
g
sy
ste
m
,
”
Pro
c
e
e
d
in
g
-
2
0
1
3
IEE
E
S
t
u
d
e
n
t
Co
n
f.
Res
.
De
v
.
S
CORe
D 2
0
1
3
,
p
p
.
4
3
3
-
4
3
8
,
De
c
e
m
b
e
r
2
0
1
3
.
[3
7
]
N.
H.
T
.
Hu
d
a
,
A.
R.
A
b
d
u
ll
a
h
,
e
t
al
.
,
“
P
o
we
r
q
u
a
li
ty
sig
n
a
ls
d
e
tec
ti
o
n
u
sin
g
S
-
tran
sfo
rm
,
”
Pro
c
.
2
0
1
3
IEE
E
7
th
In
t
.
Po
we
r E
n
g
.
Op
ti
m.
C
o
n
f.
PE
OC
O 2
0
1
3
,
p
p
.
5
5
2
-
5
5
7
,
Ju
n
e
2
0
1
3
.
[3
8
]
C.
-
I.
Ch
e
n
a
n
d
Y.
C
h
e
n
,
“
A
n
e
u
ra
l
-
n
e
two
rk
-
b
a
se
d
d
a
ta
-
d
ri
v
e
n
n
o
n
li
n
e
a
r
m
o
d
e
l
o
n
ti
m
e
-
a
n
d
fre
q
u
e
n
c
y
-
d
o
m
a
in
v
o
lt
a
g
e
-
c
u
rre
n
t
c
h
a
ra
c
teriz
a
ti
o
n
f
o
r
p
o
we
r
-
q
u
a
li
ty
stu
d
y
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
on
P
o
we
r
De
li
v
e
ry
,
v
o
l.
3
0
,
n
o
.
3
,
p
p
.
1
5
7
7
-
1
5
8
4
,
Ju
n
.
2
0
1
5
.
[3
9
]
J.
Wu
,
e
t
a
l.
,
“
I
d
e
n
ti
fica
ti
o
n
o
f
m
u
lt
ip
le
h
a
rm
o
n
ic
so
u
rc
e
s
i
n
c
y
b
e
r
-
p
h
y
sic
a
l
e
n
e
rg
y
sy
ste
m
u
sin
g
s
u
p
e
rv
ise
d
in
d
e
p
e
n
d
e
n
t
c
o
m
p
o
n
e
n
t
a
n
a
l
y
si
s,”
2
0
1
4
IEE
E
I
n
ter
n
a
ti
o
n
a
l
I
n
stru
me
n
ta
ti
o
n
a
n
d
M
e
a
su
re
me
n
t
T
e
c
h
n
o
l
o
g
y
Co
n
fer
e
n
c
e
,
p
p
.
4
9
6
-
5
0
1
,
2
0
1
4
.
[4
0
]
M
.
M
a
n
a
p
,
e
t
a
l.
,
“
Co
m
p
a
riso
n
o
f
o
p
e
n
a
n
d
sh
o
rt
-
c
ircu
it
sw
it
c
h
e
s
fa
u
lt
s
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter
(VSI
)
a
n
a
ly
sis
u
si
n
g
ti
m
e
-
fre
q
u
e
n
c
y
d
istri
b
u
ti
o
n
s
,
”
A
p
p
l
ied
M
e
c
h
a
n
ics
a
n
d
M
a
ter
ia
ls
.
,
v
o
l.
7
5
2
–
7
5
3
,
p
p
.
1
1
6
4
-
1
1
6
9
,
Ap
ril
2
0
1
5.
[4
1
]
M
.
L.
Ba
u
g
h
m
a
n
a
n
d
R.
C.
Du
g
a
n
,
“
IEE
E
4
N
o
d
e
Tes
t
F
e
e
d
e
r,
”
I
n
st.
El
e
c
tr.
El
e
c
tro
n
.
E
n
g
.
In
c
,
p
p
.
1
-
9
,
2
0
0
9
.
[4
2
]
A.
K.
Bh
a
ra
ti
a
n
d
V.
Ajjara
p
u
,
“
In
v
e
stig
a
ti
o
n
o
f
re
lev
a
n
t
d
istri
b
u
t
io
n
s
y
ste
m
re
p
re
se
n
tatio
n
wi
th
D
G
fo
r
v
o
lt
a
g
e
sta
b
il
it
y
m
a
rg
in
a
ss
e
ss
m
e
n
t
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
o
n
Po
we
r S
y
st
em
,
v
o
l,
9
9
,
p
p
.
1
-
1
,
Oc
t.
2
0
1
9
.
[4
3
]
M
.
J
.
E
.
A
l
a
m
,
K
.
M
.
M
u
t
t
a
q
i
,
a
n
d
D
.
S
u
t
a
n
t
o
,
“
A
t
h
r
e
e
-
p
h
a
s
e
p
o
w
e
r
f
l
o
w
a
p
p
r
o
a
c
h
f
o
r
i
n
t
e
g
r
a
t
e
d
3
-
w
i
r
e
M
V
a
n
d
4
-
w
i
r
e
m
u
l
t
i
g
r
o
u
n
d
e
d
L
V
n
e
t
w
o
r
k
s
w
i
t
h
r
o
o
f
t
o
p
s
o
l
a
r
P
V
,
”
I
E
E
E
T
r
a
n
s
.
P
o
w
e
r
S
y
s
t
.
,
v
o
l
.
2
8
,
n
o
.
2
,
p
p
.
1
7
2
8
-
1737,
2013
.
[4
4
]
M
.
Na
rima
n
i,
S
.
H.
Ho
ss
e
in
ian
,
a
n
d
B.
Va
h
i
d
i,
“
A
m
e
th
o
d
fo
r
h
a
rm
o
n
ic
p
o
we
r
trac
in
g
b
y
u
sin
g
u
p
stre
a
m
a
n
d
d
o
wn
stre
a
m
d
istri
b
u
ti
o
n
m
a
tri
c
e
s
,
”
El
e
c
tr.
Po
we
r Co
mp
o
n
e
n
ts S
y
st.
,
v
o
l.
4
7
,
n
o
.
1
3
,
p
p
.
1
1
6
9
-
1
1
7
9
,
Au
g
.
2
0
1
9
.
[
45]
P
.
S
i
n
h
a
,
S
.
K.
G
o
sw
a
m
i,
a
n
d
S
.
De
b
n
a
th
,
“
Ha
rm
o
n
ic
so
u
rc
e
id
e
n
t
ifi
c
a
ti
o
n
in
d
istr
ib
u
ti
o
n
s
y
ste
m
u
s
in
g
n
o
n
-
a
c
ti
v
e
p
o
we
r
q
u
a
n
ti
t
ies
,
”
In
t.
J
.
Po
we
r E
n
e
rg
y
Co
n
v
e
rs
.
,
v
o
l
.
8
,
n
o
.
1
,
p
p
.
9
0
-
1
1
1
,
Ja
n
u
a
ry
2
0
1
7
.
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