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t
io
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l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
14
,
No
.
6
,
Dec
em
b
er
20
24
,
p
p
.
6
0
5
7
~
6
0
6
5
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
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.
1
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5
9
1
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v
14
i
6
.
pp
6
0
5
7
-
6
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6
5
6057
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Cha
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r
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c
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fi
lt
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r
(S
HA
P
F
)
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k
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wn
a
s
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ry
e
ffe
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ti
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e
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rm
o
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ic
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teri
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m
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e
l
in
p
o
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sy
ste
m
s.
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p
ica
ll
y
,
S
HA
P
F
is
c
o
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tro
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e
d
b
y
a
c
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tr
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m
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se
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su
p
p
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y
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a
rm
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ic
c
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t.
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we
v
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t
h
e
a
b
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ts
a
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e
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c
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l
m
e
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r
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.
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in
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d
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tr
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m
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th
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larg
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f
u
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p
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it
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ti
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m
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ls
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n
d
sim
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latio
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lt
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stra
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t
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ffe
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ss
o
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th
e
p
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p
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se
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m
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d
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re
d
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d
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o
f
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p
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t,
v
o
lt
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imiz
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c
o
m
p
e
n
sa
ti
o
n
e
rro
r
a
t
ste
a
d
y
sta
te.
K
ey
w
o
r
d
s
:
Activ
e
p
o
wer
f
ilter
C
o
m
b
in
ed
co
n
tr
o
l m
eth
o
d
Hy
b
r
id
ac
tiv
e
p
o
wer
f
ilter
Pas
s
iv
e
p
o
wer
f
ilter
Pro
p
o
r
tio
n
al
in
teg
r
al
co
n
tr
o
lle
r
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
C
h
au
Min
h
T
h
u
y
en
Facu
lty
o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
T
ec
h
n
o
lo
g
y
,
I
n
d
u
s
tr
ial
Un
iv
er
s
ity
o
f
Ho
C
h
i M
in
h
C
ity
1
2
Ng
u
y
en
Van
B
ao
R
o
ad
,
Go
Vap
Dis
tr
ict,
Ho
C
h
i M
in
h
C
ity
7
0
0
0
0
0
,
Vietn
am
E
m
ail:
ch
au
m
in
h
t
h
u
y
e
n
@
iu
h
.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
T
o
d
ay
,
d
u
e
to
th
e
ch
a
r
ac
ter
is
tics
o
f
m
an
u
f
ac
tu
r
in
g
in
d
u
s
tr
ies,
elec
tr
ical
eq
u
ip
m
en
t
is
r
eq
u
ir
ed
to
o
p
er
ate
i
n
m
a
n
y
d
if
f
e
r
en
t
m
o
d
es,
with
m
o
s
t
lo
ad
s
b
ein
g
co
n
tr
o
lled
b
y
p
o
wer
elec
tr
o
n
ic
d
ev
ices.
As
a
r
esu
lt,
th
e
lo
ad
s
g
e
n
er
ate
c
u
r
r
en
t
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
,
wh
ic
h
d
is
to
r
t
an
d
s
h
if
t
p
h
ase
c
o
m
p
ar
ed
to
th
e
s
o
u
r
ce
v
o
ltag
e.
Fr
o
m
th
er
e,
a
s
h
u
n
t
a
ctiv
e
p
o
wer
f
ilter
(
Sh
u
n
t
APF)
was
b
o
r
n
t
o
f
ilter
cu
r
r
en
t
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
[
1
]
.
H
o
wev
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,
h
ar
m
o
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m
p
o
n
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n
ts
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ly
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b
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o
ad
s
,
th
ey
ar
e
also
g
en
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ated
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s
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T
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e
h
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r
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ate
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o
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o
n
th
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lo
a
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,
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t
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tiv
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p
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f
ilter
(
s
er
ies
APF)
was
b
o
r
n
as
a
n
ec
ess
ity
[
2
]
–
[
4
]
.
Ho
wev
e
r
,
th
e
s
er
ies
APF
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s
o
n
ly
ca
p
ab
le
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f
f
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ic
co
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p
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n
ts
f
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o
m
th
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o
u
r
ce
,
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u
t
it
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n
o
t
ca
p
a
b
le
o
f
f
ilter
in
g
h
a
r
m
o
n
ic
co
m
p
o
n
e
n
ts
g
en
er
ate
d
f
r
o
m
th
e
lo
ad
.
Fo
r
th
is
r
ea
s
o
n
,
s
er
ies
h
y
b
r
i
d
ac
tiv
e
p
o
wer
f
ilter
(
SHAPF
)
was
b
o
r
n
.
I
t
is
a
co
m
b
in
atio
n
o
f
th
e
s
er
ies
AP
F
an
d
p
ass
iv
e
p
o
wer
f
ilter
s
(
PP
Fs
)
[
5
]
,
[
6
]
.
PP
Fs
h
av
e
th
e
f
u
n
ctio
n
o
f
f
ilter
in
g
lo
ad
cu
r
r
e
n
t
h
ar
m
o
n
i
cs
wh
ile
th
e
s
er
ie
s
AP
F
f
ilter
s
v
o
ltag
e
h
ar
m
o
n
ics
em
itted
f
r
o
m
th
e
s
o
u
r
ce
.
T
h
er
ef
o
r
e,
r
esear
ch
o
n
SHAPF
h
as
p
r
ac
tical
s
ig
n
if
ican
ce
,
it
c
o
n
tr
ib
u
tes
to
im
p
r
o
v
e
th
e
p
o
wer
q
u
ality
o
f
th
e
p
o
we
r
s
y
s
tem
.
Pu
b
lis
h
ed
r
esear
ch
o
n
SHAPF
f
o
cu
s
in
g
o
n
th
e
d
esig
n
o
f
PP
Fs
f
o
r
SHAPF
is
ca
r
r
ied
o
u
t
in
[
7
]
–
[
9
]
.
R
esear
ch
o
n
co
n
tr
o
l stra
teg
ies f
o
r
SHAPF
b
ased
o
n
th
e
lo
ad
h
ar
m
o
n
ic
v
o
ltag
e
an
d
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t is
cited
in
[
1
0
]
–
[
1
3
]
.
Ma
n
y
s
tu
d
i
es
o
n
co
n
tr
o
l
f
o
r
SHAPF
h
av
e
also
b
ee
n
ca
r
r
ied
o
u
t
s
u
ch
a
s
d
ea
d
-
b
ea
t
co
n
t
r
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
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8
8
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8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
0
5
7
-
6
0
6
5
6058
[
1
4
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m
o
n
ic
v
o
ltag
e
o
n
th
e
lo
ad
.
I
n
s
u
m
m
ar
y
,
p
r
e
v
io
u
s
s
tu
d
ies
o
n
SH
APF
o
n
ly
u
s
e
d
co
n
tr
o
l
m
eth
o
d
s
b
ased
o
n
t
h
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t
o
r
h
a
r
m
o
n
ic
v
o
ltag
e
o
n
th
e
lo
ad
.
W
ith
th
e
co
n
tr
o
l
m
eth
o
d
b
ased
o
n
t
h
e
s
u
p
p
l
y
h
ar
m
o
n
ic
cu
r
r
en
t,
t
h
e
co
n
tr
o
l
co
ef
f
icien
t
m
u
s
t
b
e
lar
g
e
en
o
u
g
h
,
an
d
th
e
v
o
ltag
e
ap
p
lied
to
th
e
lo
ad
co
n
t
ain
s
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
t
o
f
th
e
s
o
u
r
ce
v
o
lt
ag
e.
W
ith
th
e
co
n
tr
o
l
m
eth
o
d
b
ased
o
n
th
e
h
ar
m
o
n
ic
v
o
lta
g
e
o
n
th
e
lo
ad
,
th
e
co
n
tr
o
l
c
o
ef
f
icien
t
m
u
s
t
b
e
lar
g
e
en
o
u
g
h
to
elim
in
ate
th
e
h
a
r
m
o
n
ic
c
o
m
p
o
n
en
t
o
f
th
e
v
o
lt
ag
e
o
n
th
e
lo
ad
b
u
t
ca
n
n
o
t
elim
in
ate
th
e
h
ar
m
o
n
i
c
co
m
p
o
n
en
t
in
t
h
e
s
u
p
p
ly
c
u
r
r
en
t.
T
h
u
s
,
th
e
d
is
ad
v
an
tag
e
o
f
th
e
a
b
o
v
e
two
m
eth
o
d
s
is
th
at
th
e
co
n
tr
o
l c
o
e
f
f
icien
t m
u
s
t b
e
lar
g
e
en
o
u
g
h
,
wh
ich
ca
n
ea
s
ily
ca
u
s
e
s
y
s
tem
in
s
tab
ilit
y
.
Fro
m
th
e
ab
o
v
e
an
aly
s
is
,
th
is
ar
ticle
p
r
o
p
o
s
es
a
n
ew
co
n
tr
o
l
m
eth
o
d
f
o
r
SHAPF
.
I
t
i
s
a
co
n
tr
o
l
m
eth
o
d
b
ased
o
n
th
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t a
n
d
th
e
s
o
u
r
c
e
h
ar
m
o
n
ic
v
o
ltag
e.
T
h
e
ad
v
a
n
tag
e
o
f
th
is
m
eth
o
d
is
th
at
it
ca
n
r
ed
u
ce
th
e
h
ar
m
o
n
ic
co
n
ten
t
i
n
th
e
s
u
p
p
ly
cu
r
r
en
t
an
d
th
e
h
ar
m
o
n
ic
v
o
ltag
e
ap
p
lied
to
th
e
l
o
ad
with
a
co
n
tr
o
l
c
o
ef
f
icien
t
n
o
t
to
o
lar
g
e.
T
h
e
h
ar
m
o
n
ic
v
o
lta
g
e
ap
p
lied
t
o
th
e
lo
a
d
will
n
o
t
b
e
af
f
ec
ted
b
y
th
e
h
ar
m
o
n
ic
c
o
m
p
o
n
en
t
o
f
th
e
s
o
u
r
ce
v
o
ltag
e.
T
h
is
ca
n
in
cr
e
ase
th
e
s
tab
ilit
y
o
f
th
e
s
y
s
te
m
an
d
im
p
r
o
v
e
th
e
h
ar
m
o
n
ic
f
ilter
in
g
ef
f
icien
cy
o
f
SHAPF
.
Ho
wev
er
,
th
e
ac
t
u
al
lo
ad
will
v
a
r
y
.
T
h
er
e
f
o
r
e,
to
r
esp
o
n
d
well
t
o
lo
ad
ch
an
g
es,
a
f
u
zz
y
-
p
r
o
p
o
r
t
io
n
al
in
teg
r
al
(
Fu
zz
y
-
PI)
co
n
t
r
o
ller
is
d
esig
n
ed
f
o
r
SHAPF
with
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l m
eth
o
d
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
ar
ticle
in
c
lu
d
es
f
iv
e
s
ec
tio
n
s
.
An
o
v
er
v
i
ew
o
f
SHAPF
i
s
p
r
esen
ted
in
s
ec
tio
n
1
.
Stru
ctu
r
e
an
d
c
o
n
tr
o
l
o
f
SHAPF
ar
e
in
tr
o
d
u
ce
d
in
s
ec
tio
n
2
.
Fu
zz
y
-
PI
co
n
t
r
o
ller
d
esig
n
is
g
iv
en
in
s
ec
tio
n
3
.
Simu
latio
n
r
esu
lts
an
d
d
is
cu
s
s
io
n
ar
e
p
er
f
o
r
m
ed
in
s
ec
tio
n
4
.
Fin
ally
,
th
e
r
esear
c
h
r
esu
lts
ar
e
s
u
m
m
ar
ized
in
s
ec
tio
n
5.
2.
ST
RUC
T
UR
E
AND
CO
N
T
RO
L
O
F
SH
AP
F
T
h
e
s
tr
u
ctu
r
e
o
f
a
SHAPF
is
s
h
o
wn
in
Fig
u
r
e
1
.
SHAPF
co
n
s
is
ts
o
f
two
m
ain
p
ar
ts
:
PP
Fs
an
d
th
e
ac
tiv
e
p
ar
t
(
in
v
er
te
r
,
o
u
tp
u
t
f
il
ter
an
d
tr
an
s
f
o
r
m
er
)
.
PP
Fs
ar
e
d
esig
n
ed
to
f
ilter
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
em
itted
b
y
th
e
lo
ad
,
wh
ile
th
e
ac
tiv
e
p
ar
t
is
d
esig
n
ed
to
co
m
p
e
n
s
ate
f
o
r
th
e
r
e
m
ain
d
er
.
T
h
e
ac
tiv
e
p
ar
t
ca
n
b
e
v
iewe
d
as
an
im
p
e
d
an
ce
.
I
t
h
as
a
v
al
u
e
o
f
ze
r
o
at
th
e
f
u
n
d
am
en
tal
f
r
eq
u
en
cy
an
d
e
q
u
al
to
in
f
i
n
ity
at
th
e
h
ar
m
o
n
ic
f
r
eq
u
e
n
cy
.
I
t
p
r
ev
e
n
ts
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
f
r
o
m
th
e
s
o
u
r
c
e
in
to
th
e
lo
a
d
.
s
U
s
Z
dc
U
0
L
0
C
0
C
0
C
PPFs
s
I
L
I
R
Ca
U
Cb
U
Cc
U
I
nv
e
rt
e
r
L
L
U
+
-
L
R
C
Fig
u
r
e
1
.
T
h
e
s
tr
u
ctu
r
e
o
f
a
S
HAPF
I
n
wh
ich
:
an
d
ar
e
th
e
v
o
ltag
e
an
d
im
p
ed
an
ce
o
f
th
e
s
o
u
r
ce
.
T
h
e
n
o
n
lin
ea
r
lo
ad
is
m
o
d
ell
ed
b
y
two
th
r
ee
-
p
h
ase
u
n
co
n
tr
o
lled
b
r
id
g
e
r
ec
tifie
r
s
with
lo
ad
s
R
,
L
,
C
,
an
d
R
L
.
PP
Fs
ar
e
p
ass
iv
e
p
o
wer
f
ilter
s
d
esig
n
ed
to
s
u
p
p
r
ess
th
e
h
ig
h
h
ar
m
o
n
ics
o
f
th
e
n
o
n
lin
ea
r
lo
ad
.
,
,
an
d
ar
e
th
e
co
m
p
en
s
atio
n
v
o
ltag
es
f
r
o
m
th
e
in
v
er
te
r
.
0
0
is
o
u
tp
u
t
f
ilter
o
f
th
e
i
n
v
er
ter
an
d
is
p
o
wer
s
u
p
p
l
y
v
o
ltag
e
f
o
r
th
e
in
v
er
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
co
mb
in
ed
co
n
tr
o
l m
eth
o
d
o
f su
p
p
ly
h
a
r
mo
n
ic
c
u
r
r
en
t a
n
d
s
o
u
r
ce
h
a
r
mo
n
ic
…
(
C
h
a
u
Min
h
Th
u
ye
n
)
6059
SHAPF
co
n
s
is
t
s
o
f
two
m
ain
p
ar
ts
:
PP
Fs
an
d
th
e
ac
tiv
e
p
ar
t
(
in
v
er
ter
,
o
u
t
p
u
t
f
ilter
an
d
tr
a
n
s
f
o
r
m
er
)
.
PP
Fs
ar
e
d
esig
n
ed
t
o
f
ilter
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
e
m
itted
b
y
th
e
lo
a
d
,
wh
ile
th
e
ac
tiv
e
p
ar
t
is
d
esig
n
e
d
t
o
co
m
p
en
s
ate
f
o
r
th
e
r
em
ain
d
er
.
T
h
e
ac
tiv
e
p
ar
t
ca
n
b
e
v
iew
ed
as
an
im
p
ed
an
ce
.
I
t
h
as
a
v
alu
e
o
f
ze
r
o
at
th
e
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
an
d
e
q
u
al
to
in
f
in
ity
at
th
e
h
ar
m
o
n
ic
f
r
eq
u
en
c
y
.
I
t
p
r
ev
e
n
ts
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
f
r
o
m
th
e
s
o
u
r
ce
in
to
th
e
lo
a
d
.
T
h
e
s
in
g
le
-
p
h
ase
eq
u
i
v
ale
n
t
cir
cu
it
in
th
e
h
ar
m
o
n
ic
d
o
m
ain
o
f
SHAPF
i
s
s
h
o
wn
in
Fig
u
r
e
2
.
T
o
r
e
d
u
ce
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
f
r
o
m
t
h
e
n
o
n
lin
ea
r
l
o
ad
an
d
s
o
u
r
ce
,
th
e
co
m
p
en
s
atio
n
v
o
ltag
e
f
r
o
m
th
e
ac
tiv
e
p
ar
t
o
f
APF
ca
n
b
e
b
ased
o
n
th
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t
o
r
th
e
lo
ad
h
ar
m
o
n
ic
v
o
ltag
e.
T
h
er
ef
o
r
e,
ca
n
b
e
co
n
s
id
er
ed
as
a
d
e
p
en
d
e
n
t
v
o
ltag
e
s
o
u
r
ce
.
Fro
m
F
ig
u
r
e
2
,
co
n
tr
o
l
m
eth
o
d
s
f
o
r
SHAPF
ca
n
b
e
lis
ted
as f
o
llo
ws:
+
-
Lh
I
sh
I
sh
Z
C
U
sh
U
Fh
I
PPF
Lh
U
Fig
u
r
e
2
.
T
h
e
s
in
g
le
-
p
h
ase
eq
u
iv
alen
t c
ir
cu
it in
t
h
e
h
ar
m
o
n
i
c
d
o
m
ain
o
f
SHAPF
a.
C
o
n
tr
o
l m
eth
o
d
=
ℎ
[
1
1
]
Fro
m
Fig
u
r
e
2
,
ℎ
an
d
ℎ
ca
n
b
e
ca
lcu
lated
as
(
1
)
an
d
(
2
)
.
ℎ
=
ℎ
+
ℎ
ℎ
ℎ
+
+
ℎ
(
1
)
ℎ
=
ℎ
−
(
+
ℎ
)
ℎ
(
2
)
Fro
m
(
1
)
a
n
d
(
2
)
we
ca
n
s
ee
th
at:
if
is
lar
g
e
en
o
u
g
h
,
th
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t
ℎ
will
d
ec
r
ea
s
e
to
ze
r
o
.
Ho
wev
er
,
t
h
e
v
o
ltag
e
ap
p
lied
to
t
h
e
l
o
ad
will
h
av
e
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
o
f
s
o
u
r
ce
s
ℎ
an
d
ℎ
−
(
+
ℎ
)
ℎ
will
n
o
t
d
ec
r
ea
s
e
b
u
t
i
n
cr
ea
s
e.
On
th
e
o
th
er
h
an
d
,
if
is
to
o
lar
g
e,
it
ca
n
ea
s
ily
ca
u
s
e
s
y
s
tem
in
s
tab
ilit
y
.
b.
C
o
n
tr
o
l
m
eth
o
d
=
ℎ
[
1
1
]
Fro
m
Fig
u
r
e
2
,
ℎ
an
d
ℎ
ca
n
b
e
ca
lcu
lated
as
(
3
)
an
d
(
4
)
.
ℎ
=
ℎ
+
(
1
+
)
ℎ
ℎ
ℎ
+
(
1
+
)
ℎ
(
3
)
ℎ
=
ℎ
−
ℎ
ℎ
1
+
(
4
)
Fro
m
(
3
)
an
d
(
4
)
we
ca
n
s
ee
th
at:
if
is
lar
g
e
en
o
u
g
h
,
ℎ
will
d
ec
r
ea
s
e
to
ze
r
o
an
d
p
r
ev
en
t
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
in
to
lo
a
d
f
r
o
m
t
h
e
s
o
u
r
ce
.
H
o
wev
er
,
t
h
is
m
eth
o
d
ca
n
n
o
t
r
ed
u
ce
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
in
th
e
s
u
p
p
ly
cu
r
r
en
t.
I
n
s
h
o
r
t,
th
is
m
eth
o
d
is
o
n
ly
u
s
ed
to
r
ed
u
ce
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
o
f
th
e
s
o
u
r
ce
v
o
ltag
e
ap
p
lied
to
th
e
lo
ad
b
u
t is n
o
t c
ap
ab
le
o
f
r
ed
u
ci
n
g
th
e
h
ar
m
o
n
ic
co
n
ten
t o
f
th
e
s
u
p
p
ly
cu
r
r
en
t.
c.
Pro
p
o
s
ed
co
n
tr
o
l m
eth
o
d
Fro
m
th
e
ab
o
v
e
two
m
eth
o
d
s
,
th
is
p
ap
er
p
r
o
p
o
s
es
a
n
ew
co
n
tr
o
l
m
eth
o
d
.
I
t
is
a
co
m
b
i
n
atio
n
o
f
th
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t
an
d
t
h
e
s
o
u
r
ce
h
ar
m
o
n
ic
v
o
ltag
e
=
1
ℎ
+
2
ℎ
.
Fro
m
Fig
u
r
e
2
,
ℎ
an
d
ℎ
ca
n
b
e
ca
lcu
lated
as
(
5
)
a
n
d
(
6
)
:
ℎ
=
(
1
−
2
)
ℎ
+
ℎ
ℎ
ℎ
+
1
+
ℎ
(
5
)
ℎ
=
(
1
−
2
)
ℎ
−
(
1
+
ℎ
)
ℎ
(
6
)
Fro
m
(
5
)
an
d
(
6
)
we
ca
n
s
ee
th
at:
if
we
c
o
n
tr
o
l
th
em
s
o
th
at
2
=
1
an
d
1
ar
e
n
o
t
to
o
lar
g
e
(
th
e
y
d
o
n
o
t
n
ee
d
to
b
e
to
o
lar
g
e
as
in
m
eth
o
d
=
ℎ
)
,
we
ca
n
r
ed
u
ce
ℎ
an
d
ℎ
.
I
n
p
ar
ticu
lar
,
th
is
m
eth
o
d
h
as
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
0
5
7
-
6
0
6
5
6060
ab
ilit
y
to
elim
in
ate
th
e
in
f
l
u
e
n
ce
o
f
s
o
u
r
ce
h
a
r
m
o
n
ic
v
o
lta
g
e
ℎ
on
ℎ
an
d
ℎ
,
an
d
it
ca
n
a
v
o
id
in
s
tab
ilit
y
d
u
e
to
to
o
lar
g
e
K
co
n
tr
o
l c
o
e
f
f
icien
t a
s
in
m
eth
o
d
=
ℎ
.
K
,
K
1
an
d
K
2
ar
e
co
n
tr
o
llab
le
co
ef
f
icie
n
ts
.
T
h
e
r
ef
er
e
n
ce
s
ig
n
als
ℎ
,
ℎ
an
d
ℎ
ar
e
d
eter
m
in
e
d
f
r
o
m
,
an
d
u
s
in
g
th
e
i
p
-
i
q
m
eth
o
d
[
7
]
as
s
h
o
wn
in
F
ig
u
r
e
3
.
T
h
e
co
m
p
o
n
e
n
ts
,
,
ar
e
co
n
v
er
ted
f
r
o
m
th
e
abc
r
o
tatio
n
co
o
r
d
in
ate
s
y
s
tem
to
th
e
s
tatio
n
ar
y
co
o
r
d
in
ate
s
y
s
t
em
d
q
0
,
th
en
p
ass
th
r
o
u
g
h
a
lo
w
-
p
ass
f
ilter
to
b
lo
ck
th
e
h
i
g
h
-
o
r
d
er
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
an
d
p
ass
th
e
f
u
n
d
am
en
tal
co
m
p
o
n
e
n
ts
.
Fi
n
al
ly
,
th
e
d
q
0
→a
b
c
in
v
er
s
e
t
r
a
n
s
f
o
r
m
is
u
s
e
d
to
o
b
t
ai
n
th
e
f
u
n
d
a
m
e
n
t
al
f
r
e
q
u
e
n
cy
c
o
m
p
o
n
e
n
ts
,
,
an
d
.
T
h
e
r
e
f
e
r
e
n
c
e
h
a
r
m
o
n
i
c
co
m
p
o
n
en
ts
ar
e
o
b
tai
n
e
d
:
{
ℎ
=
−
ℎ
=
−
ℎ
=
−
(
7
)
T
h
e
tr
an
s
f
o
r
m
atio
n
b
etwe
en
c
o
o
r
d
in
ates is sh
o
wn
th
r
o
u
g
h
f
o
r
m
u
las (
8
)
an
d
(
9
)
.
[
0
]
=
2
3
[
(
−
2
/
3
)
(
+
2
/
3
)
(
−
2
/
3
)
(
+
2
/
3
)
1
/
2
1
/
2
1
/
2
]
[
]
(
8
)
[
]
=
2
3
[
1
(
−
2
/
3
)
(
−
2
/
3
)
1
(
+
2
/
3
)
(
+
2
/
3
)
1
]
[
0
]
(
9
)
θ
(
r
ad
)
is
th
e
a
n
g
le
b
etwe
en
th
e
a
an
d
q
ax
es
o
r
th
e
an
g
le
b
et
wee
n
th
e
a
an
d
d
ax
es.
C
o
m
p
o
n
en
ts
ℎ
an
d
ℎ
ar
e
also
d
eter
m
in
ed
s
im
ilar
ly
.
d
q
0
a
b
c
a
b
c
d
q
0
sa
I
sb
I
sc
I
sha
I
shb
I
shc
I
sfa
I
sfb
I
sfc
I
Fig
u
r
e
3
.
Dete
r
m
i
n
atio
n
o
f
r
ef
er
en
ce
h
ar
m
o
n
ic
s
ig
n
al
u
s
in
g
t
h
e
i
p
-
i
q
m
eth
o
d
3.
DE
S
I
G
N
O
F
F
UZ
Z
Y
-
P
I
CO
NT
RO
L
L
E
R
F
O
R
SH
AP
F
B
ec
au
s
e
th
e
lo
ad
ch
an
g
es
d
u
r
in
g
co
n
tr
o
l,
th
e
an
d
p
ar
am
eter
s
o
f
th
e
PI
co
n
tr
o
ller
n
ee
d
to
b
e
co
n
tin
u
o
u
s
ly
ad
ju
s
ted
ac
co
r
d
in
g
to
th
e
lo
ad
ch
a
n
g
e.
T
h
is
p
ap
er
d
esig
n
s
a
f
u
zz
y
r
eg
u
lato
r
to
ad
ju
s
t
th
e
p
ar
am
eter
s
an
d
o
f
t
h
e
PI
co
n
tr
o
ller
.
T
h
e
c
o
n
tr
o
l
d
iag
r
am
f
o
r
SHAPF
u
s
in
g
t
h
e
Fu
zz
y
-
PI
co
n
t
r
o
ller
i
s
s
h
o
wn
in
Fig
u
r
e
4
.
C
re
fe
re
nc
e
U
−
P
K
I
K
1
s
I
n
v
e
r
t
e
r
O
u
t
p
u
t
f
i
l
t
e
r
de
dt
F
u
z
z
y
r
e
g
u
l
a
t
o
r
C
U
e
rror
-
+
P
K
I
K
+
+
+
+
Fig
u
r
e
4
.
C
o
n
tr
o
l d
iag
r
am
o
f
SHAPF
u
s
in
g
Fu
zz
y
-
PI
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
co
mb
in
ed
co
n
tr
o
l m
eth
o
d
o
f su
p
p
ly
h
a
r
mo
n
ic
c
u
r
r
en
t a
n
d
s
o
u
r
ce
h
a
r
mo
n
ic
…
(
C
h
a
u
Min
h
Th
u
ye
n
)
6061
T
h
e
in
itial
an
d
p
ar
am
eter
s
ar
e
d
eter
m
in
ed
ac
co
r
d
in
g
to
th
e
Z
ieg
ler
-
Nich
o
ls
m
eth
o
d
.
T
h
e
o
u
tp
u
ts
o
f
th
e
f
u
zz
y
r
eg
u
lato
r
ar
e
an
d
.
T
h
ey
ar
e
a
d
ju
s
ted
b
ased
o
n
th
e
er
r
o
r
b
etwe
en
th
e
r
ef
er
en
ce
s
ig
n
al
an
d
th
e
r
ea
l sig
n
al
an
d
t
h
e
ch
an
g
e
o
f
t
h
is
er
r
o
r
.
{
=
+
=
+
(
1
0
)
T
h
e
in
p
u
ts
an
d
o
u
tp
u
ts
o
f
th
e
f
u
zz
y
r
e
g
u
lato
r
ar
e
r
ep
r
esen
t
ed
as
s
ev
en
m
em
b
er
s
h
ip
f
u
n
c
tio
n
s
:
n
eg
ativ
e
b
i
g
(
NB
)
,
n
eg
ativ
e
m
ed
iu
m
(
NM
)
,
n
eg
ativ
e
s
m
all
(
NS)
,
ze
r
o
(
Z
0
)
,
p
o
s
itiv
e
s
m
all
(
PS
)
,
p
o
s
itiv
e
m
ed
iu
m
(
PM)
an
d
p
o
s
itiv
e
b
i
g
(
PB
)
as sh
o
wn
in
Fig
u
r
es 5
(
a)
an
d
5
(
b
)
.
Z
0
P
S
P
M
P
B
N
S
N
M
N
B
-
1
0
1
0
0
3
6
-
3
-
6
,
e
de
Z
0
P
S
P
M
P
B
N
S
N
M
N
B
-
5
5
0
1
3
-
1
-
3
,
PI
KK
(
a)
(
b
)
Fig
u
r
e
5
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
o
f
th
e
f
u
zz
y
v
ar
iab
le:
(
a)
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
o
f
th
e
e
,
de
an
d
(
b
)
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
o
f
t
h
e
an
d
Fu
zz
y
r
u
les ar
e
th
e
c
o
r
e
o
f
th
e
f
u
zz
y
a
d
ju
s
to
r
an
d
it is
b
u
ilt b
ased
o
n
th
e
f
o
llo
win
g
p
r
in
cip
l
es:
−
If
|
|
is
lar
g
e,
a
lar
g
e
v
alu
e
is
n
e
ed
ed
; I
f
|
|
is
s
m
all,
a
s
m
all
v
alu
e
is
n
ee
d
ed
−
If
|
|
is
ap
p
r
o
x
im
ately
ze
r
o
th
en
th
e
cu
r
r
e
n
t
v
alu
e
is
ap
p
r
o
p
r
iate
−
If
.
>
0
th
en
a
lar
g
e
v
alu
e
is
n
ee
d
e
d
; I
f
.
<
0
th
en
a
s
m
all
v
alu
e
is
n
ee
d
ed
−
If
|
|
an
d
|
|
ar
e
lar
g
e,
a
lar
g
e
v
alu
e
o
f
an
d
=
0
is
n
ee
d
ed
T
h
e
f
u
zz
y
r
u
les
ar
e
s
h
o
wn
i
n
T
ab
le
1
.
T
h
e
i
n
f
er
en
ce
m
e
th
o
d
u
s
es
th
e
MA
X
-
MI
N
m
e
th
o
d
.
T
h
e
ce
n
tr
o
id
m
eth
o
d
is
u
s
ed
f
o
r
d
e
f
u
zz
if
ica
tio
n
.
T
ab
le
1
.
Fu
zz
y
r
u
les o
f
an
d
/
NB
NM
NS
ZO
PS
PM
PB
NB
P
B
/
ZO
P
B
/
ZO
P
M
/
N
B
P
M
/
N
M
P
S
/
N
M
P
S
/
ZO
ZO
/
ZO
NM
P
M
/
ZO
P
M
/
ZO
P
M
/
N
M
P
S
/
N
M
P
S
/
N
S
ZO
/
ZO
ZO
/
ZO
NS
P
M
/
ZO
P
M
/
ZO
P
S
/
N
S
P
S
/
N
S
ZO
/
ZO
N
S
/
ZO
N
M
/
ZO
ZO
P
M
/
ZO
P
S
/
ZO
ZO
/
N
S
ZO
/
N
M
N
S
/
P
S
N
M
/
ZO
N
M
/
ZO
PS
P
S
/
ZO
P
S
/
ZO
ZO
/
ZO
N
S
/
P
S
N
S
/
P
S
N
M
/
ZO
N
B
/
ZO
PM
ZO
/
ZO
ZO
/
ZO
N
S
/
P
S
N
M
/
P
M
N
M
/
P
M
N
B
/
ZO
N
B
/
ZO
PB
ZO
/
ZO
N
S
/
ZO
N
B
/
N
S
N
M
/
P
M
N
M
/
P
B
N
B
/
ZO
N
B
/
ZO
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
T
o
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
.
T
h
e
s
im
u
latio
n
r
esu
lts
ar
e
p
er
f
o
r
m
ed
o
n
a
SHAPF
s
y
s
t
em
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
p
ar
am
eter
s
o
f
a
SHAPF
s
y
s
tem
ar
e
g
iv
en
i
n
T
ab
le
2
.
T
ab
le
2
.
Par
am
eter
s
o
f
a
SHAPF
s
y
s
tem
P
a
r
a
me
t
e
r
s
V
a
l
u
e
S
o
u
r
c
e
(
U
s
-
rms
=
2
2
0
V;
f
=
5
0
H
z
)
+
(
U
pe
ak
=
2
5
V;
f
=
1
0
0
0
H
z
)
S
o
u
r
c
e
i
mp
e
d
a
n
c
e
Rs
=
0
.
1
;
L
s
=
0
.
2
mH
Lo
a
d
R
=
2
0
;
L
=
3
0
mH
;
C
=
5
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;
R
L
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5
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Tr
a
n
sf
o
r
mer r
a
t
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1
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P
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l
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L
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I
n
v
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
7
0
8
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n
t J E
lec
&
C
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m
p
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n
g
,
Vo
l.
14
,
No
.
6
,
Dec
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e
r
20
24
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6
0
5
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5
6062
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h
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wav
ef
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r
m
s
th
at
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e
co
n
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clu
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s
o
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r
c
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v
o
ltag
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,
lo
ad
cu
r
r
e
n
t
,
s
u
p
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ly
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r
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en
t
,
v
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p
lie
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to
lo
ad
an
d
co
m
p
en
s
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n
er
r
o
r
o
f
p
h
ase
a
.
At
t
=0
.
3
s
t
h
e
lo
ad
c
h
an
g
es
in
th
e
d
ir
ec
tio
n
o
f
in
cr
ea
s
in
g
t
o
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
−
W
ith
co
n
tr
o
l
m
et
h
o
d
=
ℎ
u
s
in
g
a
PI
co
n
tr
o
ller
.
C
o
n
tr
o
l
co
ef
f
icien
t
K
=5
0
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
wav
ef
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
ℎ
ar
e
s
h
o
wn
in
Fig
u
r
e
6
.
−
W
ith
co
n
tr
o
l
m
eth
o
d
=
ℎ
,
PI
co
n
tr
o
ller
is
u
s
ed
.
C
o
n
tr
o
l
co
ef
f
i
cien
t
K
=5
0
.
T
h
e
s
im
u
latio
n
r
e
s
u
lts
o
f
th
e
wav
e
f
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
ℎ
ar
e
s
h
o
wn
i
n
Fig
u
r
e
7
.
−
W
ith
co
n
tr
o
l
m
eth
o
d
=
1
ℎ
+
2
ℎ
u
s
in
g
a
PI
co
n
tr
o
ller
.
C
o
n
tr
o
l
co
ef
f
icien
t
K
=2
0
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
wav
ef
o
r
m
s
with
co
n
tr
o
l
m
et
h
o
d
=
1
ℎ
+
2
ℎ
u
s
in
g
a
PI
co
n
tr
o
ller
ar
e
s
h
o
wn
in
Fig
u
r
e
8
.
−
W
ith
co
n
tr
o
l
m
eth
o
d
=
1
ℎ
+
2
ℎ
u
s
in
g
Fu
zz
y
-
PI
co
n
tr
o
ller
.
C
o
n
t
r
o
l
co
ef
f
icien
t
K
=2
0
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
wav
e
f
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
1
ℎ
+
2
ℎ
u
s
in
g
a
Fu
zz
y
-
PI
c
o
n
tr
o
ller
ar
e
s
h
o
wn
in
Fig
u
r
e
9
.
sa
U
La
I
sa
I
La
U
e
r
r
or
0
.
6
0
.
1
0
.
1
0
.
1
0
.
1
0
.
2
0
.
2
0
.
2
0
.
2
0
.
3
0
.
3
0
.
3
0
.
3
0
.
4
0
.
4
0
.
4
0
.
4
0
.
5
0
.
5
0
.
5
0
.
5
0
.
6
0
.
6
0
.
6
T
i
m
e
(
s
)
T
i
m
e
(
s
)
T
i
m
e
(
s
)
T
i
m
e
(
s
)
Fig
u
r
e
6
.
Simu
latio
n
r
esu
lts
o
f
th
e
wav
ef
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
ℎ
sa
U
La
I
sa
I
La
U
e
r
r
o
r
0
.
6
0
.
1
0
.
1
0
.
1
0
.
1
0
.
2
0
.
2
0
.
2
0
.
2
0
.
3
0
.
3
0
.
3
0
.
3
0
.
4
0
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4
0
.
4
0
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4
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.
5
0
.
5
0
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5
0
.
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0
.
6
0
.
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6
T
i
m
e
(
s
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T
i
m
e
(
s
)
T
i
m
e
(
s
)
T
i
m
e
(
s
)
Fig
u
r
e
7
.
Simu
latio
n
r
esu
lts
o
f
th
e
wav
ef
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
ℎ
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
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co
mb
in
ed
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n
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l m
eth
o
d
o
f su
p
p
ly
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6063
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T
i
m
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(
s
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i
m
e
(
s
)
T
i
m
e
(
s
)
T
i
m
e
(
s
)
Fig
u
r
e
8
.
Simu
latio
n
r
esu
lts
o
f
th
e
wav
ef
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
1
ℎ
+
2
ℎ
u
s
in
g
a
PI
co
n
tr
o
ller
sa
U
La
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sa
I
La
U
e
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r
0
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0
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1
0
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1
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1
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0
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2
0
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2
0
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2
0
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3
0
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3
0
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3
0
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3
0
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4
0
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4
0
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0
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T
i
m
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s
)
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i
m
e
(
s
)
T
i
m
e
(
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)
Fig
u
r
e
9
.
Simu
latio
n
r
esu
lts
o
f
th
e
wav
ef
o
r
m
s
with
co
n
tr
o
l
m
eth
o
d
=
1
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+
2
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u
s
in
g
a
Fu
zz
y
-
PI
co
n
tr
o
ller
T
h
e
s
u
m
m
ar
y
tab
le
o
f
s
im
u
latio
n
r
esu
lts
with
co
n
tr
o
l
m
eth
o
d
s
is
s
h
o
wn
in
T
ab
le
3
.
Fro
m
th
e
r
esu
lts
in
T
ab
le
3
,
we
ca
n
s
ee
th
at
th
e
co
n
tr
o
l
m
eth
o
d
=
ℎ
with
K
=5
0
is
ca
p
ab
le
o
f
r
ed
u
cin
g
T
H
D
o
f
th
e
s
u
p
p
ly
cu
r
r
en
t
an
d
v
o
ltag
e
ap
p
lied
to
lo
ad
.
Ho
we
v
er
,
it
is
o
n
ly
ef
f
ec
tiv
e
w
h
en
th
e
co
n
tr
o
l
co
ef
f
icien
t
K
is
lar
g
e
en
o
u
g
h
.
C
o
n
tr
o
l
m
eth
o
d
=
ℎ
with
K
=5
0
is
o
n
ly
ca
p
ab
le
o
f
r
ed
u
cin
g
T
HD
o
f
th
e
v
o
ltag
e
ap
p
lied
to
th
e
lo
ad
.
Ho
wev
er
,
it
is
o
n
ly
ef
f
ec
tiv
e
wh
en
th
e
co
n
tr
o
l
co
ef
f
icien
t
K
is
lar
g
e
en
o
u
g
h
.
C
o
n
tr
o
l
m
et
h
o
d
=
1
ℎ
+
2
ℎ
u
s
in
g
a
PI
co
n
tr
o
ller
is
ca
p
ab
le
o
f
r
ed
u
cin
g
T
HD
o
f
th
e
s
u
p
p
ly
cu
r
r
en
t
an
d
th
e
v
o
ltag
e
ap
p
lied
to
th
e
lo
ad
with
a
co
n
tr
o
l
co
ef
f
icien
t
K
is
n
o
t
to
o
lar
g
e
(
K
=2
0
)
,
an
d
esp
ec
ially
it
h
as
th
e
ab
ilit
y
to
elim
in
ate
th
e
in
f
lu
en
ce
o
f
t
h
e
s
o
u
r
ce
v
o
ltag
e
h
ar
m
o
n
ic
o
n
th
e
v
o
ltag
e
ap
p
lied
to
t
h
e
lo
ad
.
T
o
f
u
r
t
h
er
im
p
r
o
v
e
th
e
ef
f
icien
cy
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
wh
e
n
th
e
lo
a
d
ch
an
g
es
s
u
d
d
e
n
ly
,
a
f
u
zz
y
r
eg
u
lato
r
is
u
s
ed
to
ad
ju
s
t
th
e
K
P
,
K
I
p
ar
am
eter
s
o
f
th
e
PI
c
o
n
tr
o
ller
.
T
h
e
s
im
u
latio
n
r
esu
lts
in
T
ab
le
3
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
et
h
o
d
u
s
in
g
a
Fu
zz
y
-
PI
co
n
tr
o
ller
is
m
o
r
e
e
f
f
ec
tiv
e
th
an
u
s
in
g
a
PI
c
o
n
tr
o
ller
i
n
r
ed
u
cin
g
T
HD
an
d
co
m
p
en
s
atio
n
e
r
r
o
r
at
s
tead
y
s
tate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
0
5
7
-
6
0
6
5
6064
T
ab
le
3
.
Su
m
m
a
r
y
o
f
s
im
u
latio
n
r
esu
lts
with
co
n
tr
o
l
m
eth
o
d
s
C
o
n
t
r
o
l
me
t
h
o
d
s
TH
D
%
e
rro
r
TH
D
%
e
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r
0
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0
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0
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3
s
0
.
3
s÷
0
.
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=
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.
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5
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2
2
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3
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1
5
8
.
0
5
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3
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=
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5
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.
1
9
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e
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y
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a
r
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.
4
4
.
9
v
e
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y
l
a
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=
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+
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s
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n
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a
P
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c
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l
l
e
r
8
.
0
5
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0
4
2
.
4
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±
1
0
8
.
0
5
38
3
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2
4
4
.
2
±
1
0
=
1
ℎ
+
2
ℎ
u
s
i
n
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a
F
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y
-
P
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c
o
n
t
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l
l
e
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.
0
5
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1
.
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1
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8
.
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±5
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
p
er
f
o
r
m
ed
a
co
n
tr
o
l
a
n
aly
s
is
f
o
r
SHAPF
an
d
p
r
o
p
o
s
ed
a
n
ew
c
o
n
tr
o
l
m
eth
o
d
f
o
r
SHAPF
,
wh
ich
is
a
co
m
b
in
atio
n
o
f
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
e
n
t
an
d
s
o
u
r
ce
h
a
r
m
o
n
ic
v
o
lta
g
e.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
is
ca
p
ab
le
o
f
r
e
d
u
cin
g
th
e
h
ar
m
o
n
ic
c
o
n
ten
ts
o
f
th
e
s
u
p
p
ly
c
u
r
r
e
n
t
an
d
t
h
e
h
ar
m
o
n
ic
v
o
lta
g
e
a
p
p
lied
to
th
e
lo
ad
with
a
c
o
n
tr
o
l
c
o
ef
f
icien
t
is
n
o
t
to
o
lar
g
e.
T
h
is
co
n
tr
ib
u
tes
to
im
p
r
o
v
in
g
th
e
s
tab
ilit
y
o
f
th
e
s
y
s
tem
.
A
Fu
zz
y
-
PI
co
n
tr
o
ller
is
d
esig
n
ed
t
o
im
p
r
o
v
e
th
e
ef
f
icien
cy
o
f
th
e
tr
a
d
itio
n
al
PI
co
n
tr
o
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.
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tr
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RE
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E
R
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NC
E
S
[
1
]
R
.
K
u
m
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r
,
H
.
O
.
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[
2
]
K
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K
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[
3
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b
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[
4
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[
5
]
L.
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,
D
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S
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.
[
6
]
T.
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g
,
D
.
L
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J
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,
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2
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[
7
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C
.
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.
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,
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8
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,
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[
9
]
C
.
M
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,
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.
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.
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[
1
1
]
J.
G
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n
g
,
J.
L
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o
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L
.
H
e
,
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.
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2
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.
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.
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