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CC B
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C
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:
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m
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1.
I
NT
RO
D
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O
N
I
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co
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tem
p
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elec
tr
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tem
s
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p
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b
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k
s
f
o
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r
ea
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co
m
p
en
s
atio
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an
d
p
o
w
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f
ac
to
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co
r
r
ec
tio
n
h
as
led
to
th
e
em
er
g
en
ce
o
f
r
eso
n
a
n
ce
cu
r
r
en
ts
,
g
ar
n
er
in
g
s
ig
n
if
ican
t
atten
tio
n
[
1
]
,
[
2
]
.
T
h
ese
cu
r
r
en
ts
ca
n
h
av
e
d
etr
im
en
tal
ef
f
ec
ts
,
ca
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s
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h
ar
m
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c
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is
to
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tio
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p
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ality
d
eg
r
ad
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,
an
d
p
o
te
n
tial
eq
u
ip
m
en
t
d
am
ag
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[
3
]
,
[
4
]
.
Ad
d
r
ess
in
g
r
eso
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a
n
ce
cu
r
r
en
ts
h
as
b
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m
e
cr
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cial
to
en
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in
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m
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tem
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’
r
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le
an
d
ef
f
ic
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t o
p
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.
R
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ts
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in
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f
th
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p
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tem
[
5
]
.
W
h
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t
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ca
p
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in
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e
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tan
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ite
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s
ig
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d
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k
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o
wn
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o
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s
.
At
th
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h
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p
ar
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co
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in
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m
es
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al,
allo
win
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th
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a
m
p
lifi
ca
tio
n
o
f
h
ar
m
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cu
r
r
en
ts
[
6
]
.
T
h
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c
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r
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am
p
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f
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th
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tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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N:
2088
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8
6
9
4
E
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ith
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)
2471
T
h
ese
in
clu
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e
in
cr
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s
ed
th
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m
al
s
tr
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o
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p
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b
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f
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r
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in
ac
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ag
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ailu
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[
7
]
.
Ad
d
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ally
,
r
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u
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r
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n
ca
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s
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en
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e
n
t a
n
d
in
cr
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s
ed
lo
s
s
es in
th
e
s
y
s
tem
[
8
]
,
[
9
]
.
I
n
r
ec
en
t
y
ea
r
s
,
th
e
ad
v
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t
o
f
s
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n
t
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SAPF
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h
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em
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g
s
o
lu
tio
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f
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co
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p
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c
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r
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ca
p
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b
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k
s
[
1
0
]
-
[
1
5
]
.
SAPF
s
ar
e
p
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tr
o
n
ic
d
ev
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th
at
ac
tiv
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co
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p
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atin
g
c
u
r
r
en
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in
to
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co
m
p
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atin
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e
h
ar
m
o
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ic
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d
r
eso
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an
ce
cu
r
r
e
n
ts
[
1
6
]
.
Un
lik
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p
ass
iv
e
f
ilter
s
,
SAPF
s
o
f
f
er
d
y
n
am
ic
an
d
ad
a
p
tiv
e
ca
p
ab
ilit
ies,
en
ab
lin
g
th
em
t
o
r
e
s
p
o
n
d
e
f
f
e
ctiv
ely
to
v
ar
y
in
g
s
y
s
tem
co
n
d
itio
n
s
an
d
h
ar
m
o
n
ic
p
r
o
f
iles
[
1
7
]
.
T
h
e
e
f
f
icien
cy
a
n
d
ef
f
ec
tiv
e
n
ess
o
f
SAPF
s
h
ea
v
ily
r
ely
o
n
th
e
ex
tr
ac
tio
n
alg
o
r
ith
m
u
s
ed
to
d
etec
t a
n
d
an
aly
s
es
th
e
h
ar
m
o
n
ic
cu
r
r
en
ts
,
in
clu
d
in
g
r
e
s
o
n
an
ce
cu
r
r
en
ts
in
th
e
s
y
s
tem
.
T
h
e
m
o
s
t
co
m
m
o
n
e
x
tr
ac
tio
n
alg
o
r
ith
m
u
s
ed
in
ex
t
r
ac
tin
g
r
eso
n
an
ce
cu
r
r
en
ts
in
SAPF
o
p
er
atio
n
is
k
n
o
wn
as
th
e
r
ec
u
r
s
iv
e
d
is
cr
ete
Fo
u
r
ier
tr
an
s
f
o
r
m
(
R
DFT)
alg
o
r
ith
m
[
1
1
]
-
[
1
3
]
.
I
t
is
a
co
m
p
u
tatio
n
al
alg
o
r
ith
m
th
at
ef
f
icien
tly
ca
lcu
lates
th
e
d
is
cr
ete
Fo
u
r
ier
tr
a
n
s
f
o
r
m
(
D
FT)
o
f
a
s
eq
u
en
ce
o
f
d
ata
p
o
i
n
ts
[
1
8
]
,
m
ak
in
g
it
s
u
itab
le
f
o
r
an
aly
s
in
g
th
e
f
r
eq
u
en
cy
co
n
te
n
t
o
f
d
is
cr
ete
-
tim
e
s
ig
n
als
[
1
9
]
.
T
h
e
R
DFT
alg
o
r
ith
m
ex
tr
ac
ts
th
e
h
ar
m
o
n
ic
v
o
ltag
e
co
m
p
o
n
e
n
t
f
r
o
m
th
e
p
o
in
t
o
f
c
o
m
m
o
n
co
u
p
lin
g
(
PC
C
)
v
o
ltag
e
at
th
e
r
e
s
o
n
a
n
ce
f
r
eq
u
en
cy
.
Su
b
s
eq
u
en
tly
,
th
e
al
g
o
r
ith
m
u
tili
s
es
th
e
ex
tr
ac
ted
h
ar
m
o
n
i
c
v
o
ltag
e
co
m
p
o
n
e
n
t
to
g
e
n
e
r
ate
th
e
r
eso
n
an
ce
-
d
am
p
in
g
cu
r
r
en
t
r
ef
e
r
en
ce
f
o
r
th
e
SAPF
[
1
1
]
-
[
1
3
]
.
Fig
u
r
e
1
(
a
)
d
ep
icts
a
b
lo
ck
d
iag
r
am
o
f
a
clo
s
ed
-
lo
o
p
R
DFT
alg
o
r
ith
m
to
e
x
tr
ac
t
r
eso
n
a
n
ce
cu
r
r
en
t
u
tili
s
ed
in
a
SAPF
s
y
s
tem
.
Alth
o
u
g
h
th
e
R
DFT
alg
o
r
ith
m
s
o
f
f
e
r
co
m
p
u
tatio
n
al
ef
f
icien
c
y
in
Fo
u
r
ier
tr
an
s
f
o
r
m
ca
lcu
latio
n
s
,
th
ey
p
o
s
e
ch
allen
g
es
r
eg
ar
d
in
g
m
em
o
r
y
u
s
ag
e
d
u
e
to
th
eir
r
ec
u
r
s
iv
e
n
atu
r
e
an
d
t
h
e
n
ec
ess
ity
to
s
to
r
e
in
ter
m
e
d
iate
r
esu
lts
.
T
h
is
in
cr
ea
s
ed
m
em
o
r
y
u
s
ag
e
ca
n
b
e
ch
allen
g
in
g
,
esp
ec
ially
f
o
r
lar
g
e
d
atasets
o
r
en
v
ir
o
n
m
e
n
ts
with
lim
ited
m
em
o
r
y
r
eso
u
r
ce
s
[
2
0
]
.
T
o
ad
d
r
ess
th
e
lim
itatio
n
s
o
f
R
DFT
alg
o
r
ith
m
s
,
r
esear
ch
er
s
in
[
1
4
]
s
u
b
s
titu
ted
th
em
with
ad
ap
tiv
e
lin
ea
r
n
e
u
r
o
n
(
Ad
alin
e
)
alg
o
r
it
h
m
s
.
Ad
alin
e
is
an
ar
tific
ial
n
e
u
r
al
n
etwo
r
k
t
h
at
p
o
s
s
ess
es
th
e
ca
p
ab
ilit
y
to
lear
n
an
d
a
d
ap
t
to
n
o
n
lin
ea
r
d
ata
p
a
tter
n
s
,
allo
win
g
it
to
ef
f
ec
tiv
el
y
m
o
d
el
in
tr
icate
r
elatio
n
s
h
ip
s
b
etwe
en
i
n
p
u
t
an
d
o
u
tp
u
t
v
ar
iab
les
[
2
1
]
,
[
2
2
]
.
A
d
d
itio
n
ally
,
it
ca
n
b
e
tr
ain
e
d
t
o
b
e
r
o
b
u
s
t
to
n
o
is
e
an
d
d
is
tu
r
b
an
ce
s
in
th
e
i
n
p
u
t
d
ata,
m
ak
in
g
it
s
u
itab
le
f
o
r
ap
p
licatio
n
s
wh
er
e
th
e
d
ata
m
ay
b
e
co
r
r
u
p
ted
o
r
n
o
is
y
.
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
e
b
lo
ck
d
iag
r
am
o
f
th
e
A
d
alin
e
alg
o
r
ith
m
f
o
r
e
x
tr
ac
tin
g
th
e
r
eso
n
an
ce
cu
r
r
en
t.
T
h
e
au
th
o
r
s
r
etain
ed
th
e
en
tire
ar
ch
itectu
r
e
ex
ce
p
t f
o
r
th
e
ex
tr
ac
tio
n
alg
o
r
ith
m
s
.
(
a)
(
b
)
Fig
u
r
e
1
.
E
x
tr
ac
tio
n
r
eso
n
an
ce
cu
r
r
en
t
r
ef
er
en
ce
s
ig
n
al
u
s
in
g
(
a)
R
DFT
alg
o
r
ith
m
[
8
]
an
d
(
b
)
A
d
alin
e
al
g
o
r
ith
m
[
1
5
]
Acc
o
r
d
in
g
to
Fig
u
r
e
1
,
th
e
al
g
o
r
ith
m
d
er
iv
e
d
th
e
e
x
tr
ac
ted
r
eso
n
an
ce
cu
r
r
e
n
t
f
r
o
m
r
eg
u
latin
g
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
f
u
n
ctio
n
(
HDF)
u
s
in
g
a
p
r
o
p
o
r
tio
n
al
-
i
n
t
eg
r
al
(
PI)
co
n
tr
o
ller
.
I
n
wh
ich
th
e
HDF
wa
s
s
elec
ted
b
ased
o
n
I
E
E
E
5
1
9
-
1
9
9
2
.
Ho
wev
er
,
th
e
alg
o
r
ith
m
m
u
s
t
ex
tr
ac
t
th
e
f
u
n
d
am
en
tal
v
o
ltag
e
to
ac
h
iev
e
th
e
o
b
jectiv
e.
T
h
u
s
,
it
co
m
p
licate
s
th
e
alg
o
r
ith
m
d
u
e
to
t
h
e
in
v
o
lv
em
en
t
o
f
m
u
ltip
le
p
ar
am
et
er
s
.
Mo
r
eo
v
e
r
,
t
h
e
o
p
tim
al
p
er
f
o
r
m
an
ce
o
f
b
o
th
alg
o
r
ith
m
s
d
ep
en
d
s
o
n
p
r
ec
is
e
p
ar
am
eter
tu
n
in
g
in
th
eir
clo
s
ed
-
lo
o
p
c
o
n
tr
o
ller
s
.
As
a
r
esu
lt,
m
in
o
r
v
ar
iatio
n
s
o
r
in
ac
cu
r
ac
ies
in
s
y
s
tem
p
ar
am
eter
s
m
ay
r
esu
lt
in
s
u
b
o
p
tim
al
o
r
u
n
s
tab
le
b
eh
av
io
r
[
2
3
]
.
N
o
tab
ly
,
n
eith
er
ex
tr
ac
tio
n
s
tr
ateg
y
d
i
r
ec
tly
ex
t
r
ac
ts
th
e
r
eso
n
an
ce
cu
r
r
en
t
f
r
o
m
th
e
cu
r
r
en
t
its
elf
;
in
s
tead
,
th
e
alg
o
r
ith
m
m
u
s
t c
o
n
v
er
t th
e
e
x
tr
ac
ted
v
o
ltag
es to
r
eso
n
an
ce
c
u
r
r
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2470
-
2
4
7
9
2472
T
h
is
r
esear
ch
p
ap
er
aim
s
to
in
tr
o
d
u
ce
a
s
in
g
le
A
d
alin
e
alg
o
r
ith
m
f
o
r
ex
tr
ac
ti
n
g
th
e
r
eso
n
a
n
c
e
cu
r
r
en
t.
I
n
s
tead
o
f
ex
tr
ac
tin
g
th
e
r
eso
n
an
ce
cu
r
r
en
t
f
r
o
m
th
e
PC
C
v
o
ltag
e,
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
ex
tr
ac
ts
cu
r
r
e
n
t
d
ir
ec
tly
f
r
o
m
th
e
s
u
p
p
l
y
cu
r
r
e
n
t.
T
h
is
s
h
if
t
o
f
f
er
s
d
ir
ec
t
ex
tr
ac
tio
n
s
tr
ateg
ies
to
allev
iate
th
e
co
m
p
u
tatio
n
b
u
r
d
en
ass
o
ciate
d
with
tr
ad
itio
n
al
tech
n
iq
u
es.
Fu
r
th
e
r
m
o
r
e
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
d
o
es
n
o
t
jeo
p
ar
d
i
s
e
th
e
ef
f
icac
y
an
d
ef
f
ec
tiv
en
ess
o
f
th
e
ex
t
r
ac
tio
n
p
r
o
ce
s
s
.
Ad
d
itio
n
ally
,
th
e
p
ap
er
will
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
an
d
ef
f
ec
tiv
en
ess
o
f
SAPF
s
in
m
i
tig
atin
g
r
eso
n
a
n
ce
cu
r
r
en
ts
,
d
r
a
win
g
co
m
p
a
r
is
o
n
s
with
tr
ad
itio
n
al
tech
n
iq
u
es
,
an
d
h
ig
h
lig
h
tin
g
th
e
p
o
ten
tial b
en
e
f
its
an
d
ch
allen
g
es a
s
s
o
ciate
d
with
th
eir
d
ep
lo
y
m
en
t.
2.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
m
eth
o
d
o
lo
g
y
f
o
c
u
s
es
o
n
co
m
p
r
eh
e
n
s
iv
ely
an
aly
s
in
g
p
o
wer
s
y
s
tem
h
ar
m
o
n
ics
an
d
r
eso
n
an
ce
cu
r
r
en
ts
.
I
n
itially
,
th
e
m
ain
p
o
wer
s
y
s
tem
is
co
n
s
tr
u
cted
,
f
o
llo
wed
b
y
an
e
v
alu
atio
n
o
f
th
e
i
m
p
ac
t o
f
h
ar
m
o
n
ic
an
d
r
eso
n
a
n
ce
cu
r
r
en
ts
.
Fu
r
t
h
er
m
o
r
e
,
ad
v
a
n
ce
d
s
tr
ateg
ies
f
o
r
cu
r
r
en
t
e
x
tr
ac
tio
n
ar
e
d
ev
elo
p
e
d
th
r
o
u
g
h
wav
ef
o
r
m
an
aly
s
is
,
em
p
l
o
y
in
g
th
e
Ad
alin
e
al
g
o
r
ith
m
,
an
d
co
n
s
tr
u
ctin
g
a
SAPF
to
m
iti
g
ate
th
e
ef
f
ec
ts
o
f
h
ar
m
o
n
ic
c
u
r
r
e
n
ts
an
d
p
a
r
allel
r
eso
n
an
ce
.
2
.
1
.
Co
ns
t
ruct
ing
t
he
m
a
in po
wer
s
y
s
t
em
a
nd
a
s
s
ess
ing
ha
rm
o
nic a
nd
re
s
o
na
nce
curr
ent
s
im
pa
ct
s
I
n
itially
,
two
p
o
wer
s
y
s
tem
s
ar
e
co
n
s
tr
u
cted
.
Fig
u
r
e
2
(
a
)
d
ep
icts
a
cir
c
u
it
co
n
f
ig
u
r
atio
n
with
a
n
in
d
u
ctiv
e
n
o
n
lin
ea
r
lo
a
d
.
Me
an
wh
ile,
Fig
u
r
e
2
(
b
)
ex
h
ib
its
an
o
th
er
cir
c
u
it
co
n
f
i
g
u
r
atio
n
in
co
r
p
o
r
atin
g
a
n
in
d
u
ctiv
e
n
o
n
lin
ea
r
lo
a
d
a
n
d
a
ca
p
ac
ito
r
b
an
k
.
B
o
th
ci
r
cu
its
c
o
n
n
ec
t
t
o
a
2
3
0
V
alter
n
atin
g
c
u
r
r
en
t
(
AC
)
s
o
u
r
ce
with
a
s
m
all
lin
e
im
p
ed
an
ce
.
T
h
e
n
o
n
lin
ea
r
lo
ad
co
m
p
r
is
es
a
s
in
g
le
-
p
h
ase
u
n
co
n
tr
o
llab
le
r
ec
tifie
r
with
an
in
d
u
ctiv
e
elem
e
n
t,
d
e
n
o
ted
as
th
e
in
d
u
ctiv
e
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o
n
lin
ea
r
lo
ad
.
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h
e
wo
r
k
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esti
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ates
th
e
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f
e
c
ts
o
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th
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o
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ad
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ito
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o
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esh
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e
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ar
m
o
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ic
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tio
n
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T
HD)
an
d
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iv
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al
h
a
r
m
o
n
ic
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is
to
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tio
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r
d
is
to
r
tio
n
f
ac
to
r
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o
f
th
e
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s
tan
tan
e
o
u
s
s
u
p
p
ly
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r
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ef
o
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m
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h
e
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alu
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ar
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m
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ar
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e
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E
E
E
5
1
9
-
2
0
1
4
s
tan
d
ar
d
.
Su
b
s
eq
u
en
tly
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th
e
r
elatio
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s
h
ip
b
etwe
en
th
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y
s
tem
’
s
in
s
tan
tan
eo
u
s
cu
r
r
en
ts
is
s
tu
d
ied
to
ascer
tain
th
e
ap
p
r
o
p
r
iate
s
tr
ateg
y
to
ex
t
r
ac
t th
e
r
eso
n
an
ce
cu
r
r
e
n
t.
(
a)
(
b
)
Fig
u
r
e
2
.
C
ir
cu
it c
o
n
f
ig
u
r
atio
n
co
n
s
is
ts
o
f
(
a)
n
o
n
lin
ea
r
lo
a
d
o
n
ly
an
d
(
b
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n
o
n
lin
ea
r
lo
a
d
an
d
ca
p
ac
ito
r
b
an
k
2
.
2
.
Ass
es
s
ing
t
he
pro
pert
ies
o
f
curr
ent
wa
v
ef
o
rm
s
t
o
dev
elo
p
ef
f
ec
t
iv
e
s
t
ra
t
eg
ies
f
o
r
curr
e
nt
ex
t
ra
ct
io
n
Un
d
er
s
tan
d
in
g
t
h
e
p
r
o
p
er
ties
o
f
cu
r
r
en
t
wav
ef
o
r
m
s
b
ef
o
r
e
an
d
af
ter
th
e
SAPF
im
p
lem
en
tatio
n
is
cr
u
cial
f
o
r
d
ev
is
in
g
ef
f
ec
tiv
e
s
tr
ateg
ies in
th
e
r
eso
n
an
ce
c
u
r
r
en
t e
x
tr
ac
tio
n
tech
n
iq
u
e.
Fig
u
r
e
3
s
h
o
ws th
e
f
lo
w
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ci
n
g
p
o
w
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u
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lity:
A
n
A
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ith
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f
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r
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ts
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n
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ter
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Acc
o
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d
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g
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Fig
u
r
e
3
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a
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,
th
e
in
s
tan
tan
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s
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u
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p
l
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S
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eq
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i
L
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h
u
s
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as in
(
1
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(
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=
(
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(
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Ho
wev
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u
e
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th
e
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o
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ea
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ity
o
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th
e
lo
ad
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e
p
a
r
allel
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ce
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tem
m
in
g
f
r
o
m
th
e
ca
p
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ito
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b
an
k
C
PF
,
i
L
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t)
e
n
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m
p
ass
es
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u
n
d
am
en
tal,
r
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d
h
ar
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o
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ic
lo
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d
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en
t
c
o
m
p
o
n
e
n
ts
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I
t
ca
n
b
e
e
x
p
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ess
ed
as (
2
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a
n
d
(
3
)
.
W
h
er
e:
i
L1
(
t)
is
th
e
in
s
tan
tan
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u
s
f
u
n
d
am
en
tal
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ad
cu
r
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en
t w
ith
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n
a
m
p
litu
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e
o
f
I
L1
.
i
Lr
(
t)
is
th
e
in
s
tan
tan
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u
s
r
eso
n
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ce
lo
ad
cu
r
r
e
n
t w
ith
an
am
p
litu
d
e
o
f
I
Lr
.
i
Lh
(
t)
is
th
e
in
s
tan
tan
eo
u
s
h
ar
m
o
n
ic
lo
ad
cu
r
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e
n
t w
ith
an
am
p
litu
d
e
o
f
I
Lh
.
(
)
=
1
(
)
+
(
)
+
∑
ℎ
(
)
∞
ℎ
=
3
,
7
,
9
,
…
(
2
)
(
)
=
1
s
in
(
)
+
s
in
(
−
)
+
∑
ℎ
s
in
(
−
ℎ
)
∞
ℎ
=
3
,
7
,
9
,
…
(
3
)
B
y
r
ep
lacin
g
(
3
)
wi
t
h
(
1
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,
f
o
u
n
d
(
4
)
.
(
)
=
1
s
in
(
)
+
s
in
(
+
)
+
∑
ℎ
s
in
(
+
ℎ
)
∞
ℎ
=
3
,
7
,
9
,
…
(
4
)
Acc
o
r
d
in
g
t
o
Fig
u
r
e
3
(
b
)
,
(
4
)
b
ec
o
m
es
(
5
)
.
(
)
+
(
)
=
1
s
in
(
)
+
s
in
(
+
)
+
∑
ℎ
s
in
(
+
ℎ
)
∞
ℎ
=
3
,
7
,
9
,
…
(
5
)
W
h
er
e
i
F
(
t)
is
th
e
in
s
tan
tan
eo
u
s
co
m
p
en
s
atio
n
cu
r
r
en
t in
jecte
d
b
y
th
e
SAPF
.
W
h
en
th
e
SAPF
s
o
lely
p
er
f
o
r
m
s
h
ar
m
o
n
ic
co
m
p
en
s
atio
n
,
i
F
(
t)
p
r
o
p
er
ties
in
clu
d
e
r
eso
n
an
ce
an
d
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
.
I
t c
a
n
b
e
ex
p
r
ess
ed
as
(
6
)
.
(
)
=
s
in
(
+
)
+
∑
ℎ
s
in
(
+
ℎ
)
∞
ℎ
=
3
,
7
,
9
,
…
(
6
)
Nev
er
th
eless
,
as
o
u
tlin
ed
in
[
1
3
]
,
r
esid
u
al
h
ar
m
o
n
ic
cu
r
r
en
ts
ca
n
s
till
tr
ig
g
er
p
ar
allel
r
eso
n
an
ce
,
d
is
to
r
tin
g
th
e
s
u
p
p
ly
cu
r
r
en
t
ar
o
u
n
d
th
e
r
eso
n
an
ce
f
r
eq
u
e
n
cy
.
C
o
n
s
eq
u
en
tly
,
as
in
(
7
)
.
I
Sr
is
th
e
am
p
litu
d
e
o
f
th
e
r
eso
n
a
n
ce
cu
r
r
en
t
d
u
e
to
t
h
e
in
ter
ac
tio
n
b
etwe
en
th
e
r
esid
u
al
h
ar
m
o
n
ic
cu
r
r
en
ts
an
d
C
PF
.
(
)
=
1
s
in
(
)
+
s
in
(
+
)
(
7
)
T
h
u
s
,
SAPF
m
u
s
t
also
ex
tr
ac
t
th
e
r
esid
u
al
r
eso
n
a
n
ce
c
u
r
r
en
t
to
e
n
h
an
ce
r
eso
n
a
n
ce
d
am
p
i
n
g
.
Acc
o
r
d
in
g
to
(
7
)
,
it
is
f
ea
s
ib
le
to
e
x
tr
ac
t
t
h
e
r
esid
u
al
r
eso
n
a
n
ce
cu
r
r
en
t
f
r
o
m
t
h
e
i
S
(
t)
wav
ef
o
r
m
in
s
tead
o
f
t
h
e
i
L
(
t)
wav
ef
o
r
m
,
as
p
r
ac
tice
d
b
y
o
th
er
r
esear
ch
er
s
.
T
h
is
wo
r
k
ex
tr
ac
ts
th
e
r
esid
u
al
r
eso
n
a
n
ce
cu
r
r
e
n
t
u
s
in
g
a
s
in
g
le
ad
ap
tiv
e
lin
ea
r
n
eu
r
o
n
(
Ad
alin
e)
alg
o
r
ith
m
to
s
im
p
lify
th
e
ex
tr
ac
tio
n
p
r
o
ce
s
s
.
(
a)
(
b
)
Fig
u
r
e
3
.
C
u
r
r
e
n
t f
lo
ws
:
(
a)
b
e
f
o
r
e
an
d
(
b
)
af
ter
SAPF
im
p
lem
en
tatio
n
2
.
3
.
Ut
ili
s
ing
A
da
lin
e
a
lg
o
rit
hm
t
o
ex
t
r
a
ct
f
un
da
m
ent
a
l
l
o
a
d
curr
ent
a
nd
re
s
idu
a
l
re
s
o
na
nce
s
up
ply
curr
ent
co
m
po
nents
Fig
u
r
e
4
s
h
o
ws
th
e
co
n
f
ig
u
r
ati
o
n
o
f
th
e
Ad
alin
e
alg
o
r
ith
m
s
d
esig
n
ed
to
ex
tr
ac
t
t
h
e
I
L1
a
n
d
r
eso
n
an
ce
cu
r
r
en
t
I
Sr
c
o
m
p
o
n
en
ts
.
T
h
e
f
ig
u
r
e
s
h
o
ws
th
at
th
e
r
eso
n
an
ce
cu
r
r
en
t
ex
t
r
ac
tio
n
o
n
ly
r
eq
u
ir
e
s
a
s
in
g
le
alg
o
r
ith
m
f
o
r
t
h
e
ex
tr
ac
ti
o
n
p
r
o
ce
s
s
.
H
en
ce
,
s
im
p
lify
th
e
c
o
m
p
u
tatio
n
al
p
r
o
ce
s
s
o
f
ex
tr
ac
tin
g
th
e
co
m
p
o
n
en
t.
B
o
th
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2470
-
2
4
7
9
2474
alg
o
r
ith
m
s
u
s
e
th
e
s
am
e
o
p
er
atin
g
p
r
in
cip
le
to
d
er
iv
e
th
e
am
p
litu
d
e
o
f
b
o
th
co
m
p
o
n
en
ts
.
Deta
iled
in
s
ig
h
ts
in
to
th
e
ex
ec
u
tio
n
o
f
th
e
ex
tr
ac
tio
n
p
r
o
ce
s
s
b
y
th
e
Ad
alin
e
alg
o
r
ith
m
s
ar
e
p
r
o
v
id
ed
in
[
2
4
]
,
[
2
5
]
.
As
p
er
th
e
d
ep
ictio
n
in
Fig
u
r
e
4
,
th
e
i
Lh
(
t)
s
ig
n
al
is
g
en
er
ate
d
b
y
co
m
p
u
tin
g
th
e
d
if
f
er
e
n
ce
b
etwe
en
th
e
ex
tr
ac
ted
i
L1
(
t)
with
th
e
m
e
asu
r
e
i
L
(
t)
.
Su
b
s
eq
u
en
tly
,
th
e
c
o
m
b
in
atio
n
o
f
th
e
r
esu
ltan
t
i
Lh
(
t)
an
d
t
h
e
ex
tr
ac
te
d
i
Sr
(
t)
y
ield
s
th
e
in
s
tan
tan
eo
u
s
r
ef
er
en
ce
s
ig
n
al
i
ref
(
t)
u
tili
s
ed
f
o
r
th
e
SAPF
.
T
h
e
f
ilter
in
te
g
r
ates
a
h
y
s
ter
esis
co
n
tr
o
ller
to
r
e
g
u
late
i
F
(
t)
b
y
g
en
er
atin
g
a
p
u
ls
e
wid
th
m
o
d
u
l
atio
n
(
PW
M)
s
ig
n
al
f
o
r
t
h
e
f
ilt
er
’
s
o
p
er
atio
n
.
T
h
e
ex
tr
ac
ted
s
ig
n
als
ar
e
co
m
p
ar
e
d
with
th
e
s
am
e
p
a
r
am
eter
s
g
en
er
ated
b
y
t
h
e
MA
T
L
AB
f
ast
Fo
u
r
ier
t
r
an
s
f
o
r
m
(
FF
T
)
an
aly
s
is
to
v
er
if
y
th
e
Ad
alin
e
alg
o
r
ith
m
’
s
ef
f
icac
y
.
Fig
u
r
e
4
.
A
d
alin
e
co
n
f
ig
u
r
atio
n
f
o
r
e
x
tr
ac
tin
g
I
L1
an
d
I
Sr
s
ig
n
als
2
.
4
.
Co
ns
t
ruct
ing
SAPF
a
nd
ex
pl
o
ring
t
he
ef
f
ec
t
s
o
f
ha
rmo
nic c
urre
nts a
nd
pa
ra
llel r
eso
n
a
nce
Acc
o
r
d
in
g
t
o
Fig
u
r
e
3
(
b
)
u
n
til
Fig
u
r
e
4
,
th
e
wo
r
k
im
p
lem
e
n
t
s
a
s
in
g
le
-
p
h
ase
v
o
ltag
e
s
o
u
r
c
e
in
v
er
ter
(
VSI
)
as
a
SAPF
.
T
h
e
in
v
er
te
r
ex
h
i
b
its
a
co
n
v
en
tio
n
al
f
o
u
r
-
s
witch
co
n
f
ig
u
r
atio
n
with
a
d
ir
ec
t
cu
r
r
e
n
t
(
DC
)
-
lin
k
ca
p
ac
ito
r
,
C
DC
.
T
h
e
DC
-
li
n
k
v
o
ltag
e
is
s
et
at
6
5
0
V
to
e
n
s
u
r
e
th
e
SAPF
ca
n
in
ject
s
u
f
f
icien
t
i
F
(
t)
i
n
to
t
h
e
m
ain
p
o
we
r
s
y
s
tem
.
Su
b
s
eq
u
e
n
tly
,
in
v
esti
g
atin
g
th
e
ef
f
ec
ts
o
f
h
a
r
m
o
n
ic
cu
r
r
en
t
a
n
d
p
ar
all
el
r
eso
n
an
ce
o
n
th
e
q
u
ality
o
f
th
e
i
S
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t)
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ef
o
r
m
en
tails
o
b
s
er
v
atio
n
,
m
ea
s
u
r
em
en
t,
an
d
co
m
p
ar
is
o
n
.
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h
is
ex
am
in
atio
n
is
p
ar
ticu
lar
ly
cr
itical
wh
en
t
h
e
SAPF
p
er
f
o
r
m
s
two
d
is
tin
ct
f
u
n
ctio
n
s
: h
ar
m
o
n
ic
cu
r
r
e
n
t c
o
m
p
en
s
atio
n
o
n
l
y
o
r
a
co
m
b
in
atio
n
o
f
h
ar
m
o
n
ic
cu
r
r
en
t c
o
m
p
e
n
s
atio
n
an
d
r
eso
n
an
ce
cu
r
r
en
t
d
am
p
in
g
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Fig
u
r
e
5
illu
s
tr
ates
th
e
im
p
ac
t
o
f
p
a
r
allel
r
eso
n
an
ce
o
n
cu
r
r
en
t
wav
ef
o
r
m
s
in
a
p
o
we
r
s
y
s
tem
with
a
n
o
n
lin
ea
r
lo
a
d
.
I
n
Fig
u
r
e
5
(
a
)
,
d
is
to
r
tio
n
s
in
th
e
cu
r
r
e
n
t
wav
ef
o
r
m
ar
e
v
is
ib
le
d
u
e
to
h
ar
m
o
n
ic
cu
r
r
en
ts
g
en
er
ated
b
y
th
e
n
o
n
lin
ea
r
lo
a
d
,
with
a
T
HD
v
alu
e
o
f
1
1
.
8
9
%.
Ho
wev
er
,
Fig
u
r
e
5
(
b
)
d
em
o
n
s
tr
ates
a
n
o
tab
l
y
m
o
r
e
d
is
to
r
ted
cu
r
r
e
n
t
wav
ef
o
r
m
th
an
Fig
u
r
e
5
(
a
)
.
T
h
e
in
cr
e
ased
d
is
to
r
tio
n
is
attr
ib
u
ted
to
th
e
in
tr
o
d
u
ctio
n
o
f
r
eso
n
an
ce
cu
r
r
en
t
ca
u
s
ed
b
y
th
e
ca
p
ac
ito
r
b
a
n
k
.
T
h
e
T
HD
s
p
ik
es
s
ig
n
if
ican
tly
to
8
8
.
6
6
%.
T
h
e
g
r
ap
h
s
d
em
o
n
s
tr
ate
th
at
p
ar
allel
r
eso
n
an
ce
ca
n
g
r
ea
tly
i
n
ten
s
if
y
cu
r
r
en
t d
is
to
r
tio
n
i
n
a
p
o
wer
s
y
s
tem
with
a
n
o
n
lin
ea
r
lo
ad
.
Fu
r
th
e
r
m
o
r
e,
it a
ls
o
s
h
o
ws th
at
th
e
p
ar
allel
r
eso
n
an
ce
o
cc
u
r
s
in
th
e
1
1
th
h
a
r
m
o
n
ic
o
r
d
er
,
5
5
0
Hz.
(
a)
(
b
)
Fig
u
r
e
5
.
W
av
ef
o
r
m
s
o
f
i
S
(
t
)
: (
a)
with
o
u
t a
n
d
(
b
)
with
p
ar
alle
l
r
eso
n
an
ce
ef
f
ec
t
Fig
u
r
e
6
(
a)
p
r
esen
ts
th
e
im
p
ac
t
o
f
p
ar
allel
r
eso
n
an
ce
o
n
th
e
cu
r
r
en
t
wav
ef
o
r
m
’
s
T
H
Di
v
alu
es.
C
o
n
cu
r
r
en
tly
,
Fig
u
r
e
6
(
b
)
s
h
o
ws
a
tab
u
lated
b
r
ea
k
d
o
wn
o
f
i
n
d
iv
id
u
al
d
is
to
r
tio
n
lim
its
ac
c
o
r
d
in
g
to
th
e
I
E
E
E
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ci
n
g
p
o
w
er q
u
a
lity:
A
n
A
d
a
lin
e
a
lg
o
r
ith
m
fo
r
d
ir
ec
t res
o
n
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n
ce
…
(
N
o
r
F
a
r
a
h
a
id
a
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b
d
u
l R
a
h
ma
n
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2475
519
-
2
0
1
4
s
tan
d
ar
d
.
W
ith
o
u
t
p
ar
allel
r
eso
n
an
ce
,
T
HDi
v
alu
es
ac
r
o
s
s
v
ar
io
u
s
h
ar
m
o
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ic
o
r
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er
s
r
an
g
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f
r
o
m
1
.
2
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s
u
r
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ass
in
g
th
e
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er
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is
s
ib
le
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it
o
f
0
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T
h
ese
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er
ce
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es
in
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icate
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cu
r
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en
t w
av
ef
o
r
m
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er
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a
p
u
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e
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wav
e,
s
u
g
g
esti
n
g
m
o
d
e
r
ate
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i
s
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s
o
lely
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u
e
to
th
e
n
o
n
lin
ea
r
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ad
.
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wev
er
,
with
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ar
allel
r
eso
n
an
ce
,
T
HD
v
alu
es
d
r
am
a
tically
escalate
f
r
o
m
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.
2
8
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alar
m
in
g
8
7
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4
9
%.
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h
e
h
ig
h
T
HDi
p
er
ce
n
tag
es
in
d
icate
th
at
th
e
p
ar
allel
r
es
o
n
an
ce
am
p
lifie
s
d
is
to
r
tio
n
,
p
ar
ticu
lar
ly
ar
o
u
n
d
th
e
9
th
a
n
d
1
1
th
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
.
Ho
wev
er
,
Fig
u
r
e
6
(
a)
s
h
o
ws
th
at
th
e
ca
p
ac
ito
r
b
an
k
ca
n
m
itig
ate
T
HD
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alu
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at
h
ig
h
er
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ar
m
o
n
ic
o
r
d
er
s
th
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t
h
e
r
eso
n
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n
ce
f
r
e
q
u
en
cy
,
ap
p
r
o
ac
h
in
g
th
e
I
E
E
E
lim
its
.
Nev
er
th
eless
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th
e
ef
f
ec
t
is
o
v
er
s
h
ad
o
wed
b
y
th
e
d
o
m
i
n
an
ce
o
f
T
HDi
v
a
lu
es
n
ea
r
th
e
r
eso
n
an
ce
f
r
e
q
u
en
cy
.
I
n
s
u
m
m
a
r
y
,
Fig
u
r
e
6
(
a
)
d
em
o
n
s
tr
ates
th
at
p
ar
allel
r
eso
n
an
ce
s
ig
n
if
ican
tl
y
in
cr
ea
s
es
th
e
T
HDi
o
f
in
d
i
v
id
u
al
h
a
r
m
o
n
ic
co
m
p
o
n
en
ts
in
a
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o
wer
s
y
s
tem
,
p
o
ten
tially
b
r
ea
c
h
in
g
I
E
E
E
St
an
d
ar
d
5
1
9
-
2
0
1
4
.
Fig
u
r
e
7
s
h
o
ws
th
e
ex
tr
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tio
n
s
ig
n
als
o
f
i
L1
(
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a
n
d
i
S11
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t)
t
o
v
alid
ate
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e
ef
f
e
ctiv
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ess
o
f
t
h
e
Ad
alin
e
alg
o
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ith
m
.
As
m
e
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ed
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i
L1
(
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i
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ig
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als
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e
ex
tr
ac
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f
r
o
m
i
L
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t
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n
d
i
S
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e
f
o
r
m
s
,
r
esp
ec
tiv
ely
.
W
h
en
co
m
p
ar
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g
Fig
u
r
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7
(
a)
with
th
e
cu
r
r
en
t
am
p
litu
d
es
o
b
tain
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f
r
o
m
t
h
e
MA
T
L
AB
FF
T
an
aly
s
is
,
th
e
Ad
alin
e
alg
o
r
ith
m
ac
cu
r
ately
ex
tr
ac
ts
cu
r
r
en
t
a
m
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litu
d
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o
f
1
0
A
an
d
8
.
7
6
A
b
ef
o
r
e
im
p
lem
en
tin
g
SAPF
.
Ho
wev
er
,
with
th
e
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in
o
p
er
atio
n
,
t
h
e
Ad
alin
e
e
x
tr
ac
ts
a
lo
wer
i
S11
(
t)
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ig
n
al
f
r
o
m
th
e
co
m
p
en
s
ated
i
S
(
t)
wav
ef
o
r
m
,
as sh
o
wn
in
Fi
g
u
r
e
7
(
b
)
.
Acc
o
r
d
in
g
to
th
e
MA
T
L
AB
FF
T
an
aly
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is
,
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e
Ad
alin
e
s
h
o
u
ld
ex
tr
ac
t
a
s
ig
n
al
o
f
0
.
2
2
A
o
f
r
eso
n
an
c
e
cu
r
r
en
t.
Ho
we
v
er
,
Fig
u
r
e
7
(
b
)
ex
h
ib
its
a
lo
wer
am
p
litu
d
e
o
f
th
e
i
S11
(
t)
s
ig
n
al
ex
tr
ac
ted
b
y
t
h
e
Ad
alin
e
alg
o
r
ith
m
.
T
h
e
d
is
cr
ep
a
n
cy
m
a
y
r
esu
lt
f
r
o
m
th
e
Ad
alin
e
alg
o
r
ith
m
’
s
lim
itatio
n
in
ex
tr
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g
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am
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litu
d
e
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ig
n
als
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en
th
e
SAPF
o
p
er
atio
n
in
tr
o
d
u
ce
s
a
n
o
n
lin
ea
r
r
elati
o
n
s
h
ip
b
etwe
en
its
in
p
u
t
an
d
o
u
tp
u
t
s
ig
n
als
[
2
6
]
.
Nev
er
t
h
eless
,
in
tr
o
d
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cin
g
a
g
a
in
o
f
1
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4
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as
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f
ec
tiv
ely
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n
cr
e
ased
th
e
am
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litu
d
e
o
f
th
e
ex
tr
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ted
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S11
(
t)
s
ig
n
al.
B
esid
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th
at,
th
e
e
x
tr
ac
ted
i
S11
(
t)
s
ig
n
al
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n
s
is
ts
o
f
a
h
ig
h
r
ip
p
le
an
d
in
c
o
n
s
is
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.
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t m
ay
ca
u
s
e
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y
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e
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ar
allel
r
e
s
o
n
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ce
.
T
h
ese
f
in
d
i
n
g
s
u
n
d
e
r
s
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r
e
b
o
th
th
e
f
u
n
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n
ality
a
n
d
th
e
ch
allen
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es o
f
th
e
Ad
alin
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alg
o
r
ith
m
in
s
ig
n
a
l e
x
tr
ac
tio
n
p
r
o
ce
s
s
es.
(
a)
(
b
)
Fig
u
r
e
6
.
I
n
d
iv
id
u
al
T
HD
v
alu
e
o
f
(
a)
i
S
(
t)
wav
ef
o
r
m
with
o
u
t (
o
r
an
g
e)
an
d
with
(
b
l
u
e)
p
a
r
a
llel r
eso
n
an
ce
an
d
(
b
)
I
E
E
E
5
1
9
-
2
0
1
4
s
tan
d
a
r
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2470
-
2
4
7
9
2476
Fig
u
r
e
8
p
r
esen
ts
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ef
o
r
m
s
o
f
i
S
(
t)
,
i
F
(
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,
an
d
i
L
(
t)
u
n
d
er
two
co
n
d
itio
n
s
:
h
a
r
m
o
n
ic
co
m
p
en
s
atio
n
o
n
ly
,
s
h
o
w
in
Fig
u
r
e
8
(
a
)
a
n
d
h
ar
m
o
n
ic
co
m
p
e
n
s
atio
n
with
r
eso
n
an
ce
d
am
p
in
g
,
s
h
o
w
in
Fig
u
r
e
8
(
b
)
.
Me
an
wh
ile,
Fig
u
r
e
9
illu
s
tr
ates
T
HDi
v
alu
es
f
o
r
th
ese
s
ce
n
ar
io
s
.
T
h
e
wav
esh
ap
e
o
f
b
o
th
i
S
(
t)
wav
ef
o
r
m
s
r
ev
ea
ls
th
at
th
e
SAPF
ca
n
s
ep
ar
ately
o
r
co
n
cu
r
r
en
tly
p
er
f
o
r
m
h
ar
m
o
n
ic
co
m
p
en
s
atio
n
a
n
d
r
eso
n
a
n
ce
d
am
p
in
g
f
u
n
ctio
n
s
.
Ho
wev
er
,
Fig
u
r
e
8
(
a)
ex
h
ib
its
m
o
r
e
p
r
o
n
o
u
n
ce
d
d
is
to
r
tio
n
in
i
S
(
t)
wav
ef
o
r
m
th
an
Fig
u
r
e
8
(
b
)
.
I
t
i
s
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id
en
t
th
at
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[
1
]
A
.
L
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J.
W
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[
3
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.
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o
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La
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Pr
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[
4
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Ł.
M
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c
,
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.
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i
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s
k
i
,
T.
S
i
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s
k
i
,
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n
o
w
i
c
z
,
Ł.
Ja
si
ń
sk
i
,
a
n
d
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.
S
u
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sh
,
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mp
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.
[
5
]
J.
C
.
D
a
s,
P
o
w
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r
S
y
st
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m
H
a
rm
o
n
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.
[
6
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S
.
R
a
h
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,
K
.
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l
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a
d
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AUTH
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RS
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n
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M
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,
S
h
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m
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lan
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r
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n
g
.
(Ho
n
s.)
a
n
d
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.
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g
.
d
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g
re
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s
fro
m
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),
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n
d
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h
.
D
.
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n
P
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r
En
g
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n
e
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rin
g
fro
m
Un
i
v
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rsiti
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u
tr
a
M
a
lay
sia
(UPM
).
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r
re
se
a
rc
h
in
tere
sts
a
re
a
c
ti
v
e
fil
ters
,
p
o
we
r
q
u
a
li
ty
a
n
d
p
o
we
r
e
lec
tro
n
ics
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
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m
a
il
:
fa
ra
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it
m
.
e
d
u
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m
y
.
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h
a
m
m
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d
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m
m
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g
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tri
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l
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c
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fro
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tra
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sia
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in
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1
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th
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.
S
c
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tri
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l
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n
g
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rin
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m
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n
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rs
it
i
P
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tra
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a
lay
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,
i
n
2
0
1
3
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a
n
d
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n
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g
u
st
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rd
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d
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h
.
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.
d
e
g
re
e
fro
m
De
p
a
rtme
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t
o
f
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c
tri
c
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l
a
n
d
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lec
tro
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n
g
i
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rin
g
,
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a
c
u
lt
y
o
f
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g
in
e
e
ri
n
g
,
U
n
iv
e
rsiti
P
u
tra
M
a
lay
sia
.
He
is
a
m
e
m
b
e
r
o
f
IEE
E
a
n
d
a
re
g
istere
d
g
ra
d
u
a
t
e
e
n
g
in
e
e
rs
M
a
lay
sia
(B
EM
)
i
n
t
h
e
e
lec
tri
c
a
l
trac
k
.
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rre
n
tl
y
,
h
e
is
a
se
n
io
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lec
tu
re
r
a
t
De
p
a
rtme
n
t
o
f
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e
c
tri
c
a
l,
E
lec
tro
n
ic
a
n
d
S
y
ste
m
En
g
in
e
e
rin
g
,
Un
iv
e
rsiti
Ke
b
a
n
g
sa
a
n
M
a
lay
sia
(UK
M
).
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h
a
s
a
u
th
o
re
d
a
n
d
c
o
-
a
u
th
o
re
d
n
u
m
b
e
r
o
f
we
l
l
re
c
o
g
n
ise
d
j
o
u
r
n
a
ls
a
n
d
c
o
n
fe
re
n
c
e
p
a
p
e
rs.
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re
se
a
rc
h
i
n
tere
sts
a
re
in
p
o
we
r
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tro
n
ics
,
p
o
we
r
q
u
a
li
t
y
,
re
n
e
wa
b
l
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n
e
rg
y
s
y
ste
m
s
a
n
d
a
p
p
li
e
d
a
rti
fic
ial
in
telli
g
e
n
t
in
e
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tri
c
a
l
sy
ste
m
s.
He
is
a
n
a
c
ti
v
e
re
se
a
rc
h
m
e
m
b
e
r
a
t
UMP
EDAC
a
n
d
ALP
ER
(UP
M
).
H
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
m
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Evaluation Warning : The document was created with Spire.PDF for Python.
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Evaluation Warning : The document was created with Spire.PDF for Python.