I
nte
rna
t
io
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l J
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l o
f
E
lect
rica
l a
nd
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m
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I
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Vo
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15
,
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.
2
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A
p
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il
20
25
,
p
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1
3
6
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8
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0
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,
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: 1
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1
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1
/ijece.
v
15
i
2
.
pp
1
3
6
1
-
1
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7
1
1361
J
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ttp
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Three
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B
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Hy
b
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a
c
ti
v
e
p
o
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r
fil
ter
(HA
P
F
)
is
c
o
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d
a
n
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ffe
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ti
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e
s
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ti
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n
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terin
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a
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n
ics
a
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d
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p
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n
sa
ti
n
g
re
a
c
ti
v
e
p
o
we
r
in
p
o
we
r
sy
ste
m
s.
It
is
a
c
o
m
b
in
a
ti
o
n
o
f
p
a
ss
iv
e
p
o
we
r
fil
ters
a
n
d
a
n
a
c
ti
v
e
p
o
we
r
fil
t
e
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to
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o
rm
m
a
n
y
d
i
ffe
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n
t
str
u
c
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re
s
d
e
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ste
m
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o
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n
d
l
o
a
d
c
h
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ra
c
teristics
.
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is
p
a
p
e
r
a
ims
to
i
n
tro
d
u
c
e
a
n
o
v
e
ra
ll
p
ict
u
re
o
f
th
e
re
su
lt
s
o
f
re
se
a
rc
h
o
n
th
re
e
-
p
h
a
se
HA
P
F
sy
ste
m
s,
su
c
h
a
s:
HA
P
F
m
o
d
e
ls,
a
d
v
a
n
tag
e
s,
d
isa
d
v
a
n
tag
e
s,
a
n
d
sc
o
p
e
o
f
a
p
p
li
c
a
ti
o
n
o
f
e
a
c
h
m
o
d
e
l;
m
e
th
o
d
s
fo
r
d
e
term
in
in
g
p
a
ra
m
e
ters
o
f
p
a
s
siv
e
p
o
we
r
fil
ters
;
str
u
c
tu
re
,
re
sp
o
n
se
ti
m
e
,
re
so
n
a
n
c
e
,
p
o
we
r
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ss
a
n
d
c
o
st
o
f
ty
p
e
s
o
f
o
u
t
p
u
t
fil
ters
;
in
v
e
rter
stru
c
tu
re
a
n
d
c
o
m
m
o
n
l
y
u
se
d
p
u
lse
wid
t
h
m
o
d
u
latio
n
m
e
th
o
d
s
in
HA
P
F
;
c
o
n
tr
o
l
stra
teg
ies
a
n
d
u
se
d
c
o
n
tr
o
ll
e
rs
a
re
a
lso
li
ste
d
a
n
d
c
o
m
p
a
re
d
;
t
h
e
D
C
L
i
n
k
v
o
l
t
a
g
e
st
a
b
i
l
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z
a
t
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o
n
is
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lso
su
m
m
a
rize
d
a
n
d
a
n
a
ly
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e
d
.
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i
n
a
ll
y
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t
h
e
e
x
isti
n
g
p
ro
b
lem
s a
n
d
t
h
e
d
e
v
e
l
o
p
m
e
n
t
tren
d
s
o
f
HA
P
F
.
K
ey
w
o
r
d
s
:
Activ
e
p
o
wer
f
ilter
DC
lin
k
Har
m
o
n
ic
f
ilter
Hy
b
r
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ilter
Pas
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ilter
T
h
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CC B
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C
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A
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r
:
C
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au
Min
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T
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Facu
lty
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f
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d
u
s
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ial
Un
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s
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o
f
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ity
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en
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C
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ail: c
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u
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v
n
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I
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RO
D
UCT
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O
N
C
u
r
r
en
tly
,
t
h
e
m
ajo
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ity
o
f
in
d
u
s
tr
ial
lo
ad
s
ar
e
elec
tr
ic
m
o
to
r
s
.
T
h
e
s
p
ee
d
o
f
th
o
s
e
elec
tr
ic
m
o
to
r
s
is
co
n
tr
o
lled
b
y
p
o
wer
elec
tr
o
n
i
cs.
T
o
en
s
u
r
e
th
e
d
esire
d
s
p
ee
d
,
p
o
wer
elec
tr
o
n
ic
d
ev
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ar
e
r
eq
u
ir
ed
to
tu
r
n
ON
an
d
OFF
at
v
er
y
h
ig
h
f
r
e
q
u
en
cies,
r
esu
ltin
g
in
th
e
g
e
n
er
atio
n
o
f
h
a
r
m
o
n
ics
in
th
e
el
ec
tr
ical
s
y
s
tem
.
T
h
e
ex
is
ten
ce
o
f
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
in
th
e
elec
tr
ical
s
y
s
tem
will
ca
u
s
e
v
er
y
s
er
io
u
s
co
n
s
eq
u
en
ce
s
,
s
u
ch
as:
r
ed
u
cin
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th
e
life
o
f
elec
tr
ical
eq
u
ip
m
e
n
t,
ca
u
s
in
g
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p
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te
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s
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s
tem
to
o
p
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ate
in
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ec
tly
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o
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h
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tin
g
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eq
u
ip
m
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t,
a
n
d
ca
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s
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g
in
ter
f
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ce
in
th
e
i
n
f
o
r
m
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s
y
s
tem
s
.
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o
r
e,
th
e
is
s
u
e
o
f
h
an
d
li
n
g
h
ar
m
o
n
ics
in
th
e
p
o
wer
s
y
s
tem
is
o
f
u
r
g
en
t
s
ig
n
if
ican
ce
,
c
o
n
tr
ib
u
tin
g
to
im
p
r
o
v
in
g
th
e
p
o
wer
q
u
ality
in
th
e
p
o
wer
s
y
s
tem
.
T
o
elim
in
ate
h
ar
m
o
n
ics
g
en
er
ated
f
r
o
m
lo
ad
s
,
h
y
b
r
id
ac
tiv
e
p
o
wer
f
ilter
(
HAPF)
i
s
o
n
e
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
s
o
lu
tio
n
s
.
HAPF
is
co
n
s
tr
u
cted
f
r
o
m
a
h
y
b
r
i
d
o
f
p
a
s
s
iv
e
p
o
wer
f
ilter
s
(
PP
Fs
)
an
d
ac
tiv
e
p
o
wer
f
ilter
(
APF)
[
1
]
–
[
3
0]
.
T
h
er
ef
o
r
e,
it
h
as
all
th
e
ad
v
an
tag
es
o
f
b
o
th
PP
F
an
d
APF.
HAP
F
h
as
two
f
o
r
m
s
:
p
ar
allel
[
1
]
–
[
1
3
]
an
d
s
er
ies
[
1
4
]
–
[
1
6
]
.
PP
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ar
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ty
p
ically
d
esig
n
e
d
to
s
u
p
p
r
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th
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h
ig
h
h
a
r
m
o
n
i
cs
o
f
th
e
lo
ad
an
d
co
m
p
en
s
ate
f
o
r
r
ea
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er
,
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ile
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is
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ig
n
ed
to
s
u
p
p
r
ess
th
e
r
em
ain
in
g
l
o
w
h
ar
m
o
n
ics.
T
h
e
ad
v
an
tag
e
o
f
PP
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is
th
at
it
h
as
a
s
im
p
le
s
tr
u
ctu
r
e
an
d
is
ea
s
y
to
u
s
e.
Ho
wev
e
r
,
it
also
h
as
d
is
ad
v
an
tag
es,
s
u
ch
as:
b
ein
g
s
en
s
itiv
e
to
th
e
en
v
i
r
o
n
m
en
t,
s
u
s
ce
p
tib
le
to
r
eso
n
a
n
ce
with
th
e
s
y
s
tem
im
p
e
d
an
c
e,
an
d
less
f
lex
ib
le
wh
en
th
e
lo
ad
ch
an
g
es.
T
o
o
v
er
co
m
e
th
e
d
is
ad
v
a
n
tag
es
o
f
PP
Fs
,
th
e
APF
is
ad
d
ed
.
T
h
e
s
tr
u
ctu
r
e
o
f
APF
is
a
p
o
wer
elec
tr
o
n
ic
s
y
s
tem
.
T
h
e
wo
r
k
in
g
p
r
i
n
cip
le
o
f
APF
is
th
at
it
co
m
p
en
s
ates
in
to
th
e
g
r
id
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
with
a
h
ar
m
o
n
ic
c
u
r
r
en
t
eq
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al
to
t
h
e
lo
a
d
h
ar
m
o
n
ic
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r
r
e
n
t,
r
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ltin
g
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n
th
e
s
u
p
p
ly
cu
r
r
en
t
h
av
in
g
n
o
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
o
f
th
e
lo
ad
.
B
ec
au
s
e
PP
F
s
ar
e
d
esig
n
ed
to
s
u
p
p
r
ess
h
ig
h
o
r
d
er
h
a
r
m
o
n
ics.
T
h
er
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o
r
e,
th
e
APF
o
n
ly
h
as
to
co
m
p
en
s
ate
f
o
r
th
e
l
o
wer
h
ar
m
o
n
ics.
T
h
is
m
ea
n
s
r
e
d
u
cin
g
th
e
s
witch
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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8
8
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8
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8
I
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t J E
lec
&
C
o
m
p
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g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
3
6
1
-
1
3
7
1
1362
f
r
eq
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e
n
cy
o
f
th
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in
v
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ter
b
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a
u
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e
it
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ly
h
as
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witch
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lo
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HAPF
h
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o
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th
e
f
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llo
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co
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ten
t
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h
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m
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etec
tio
n
m
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o
d
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p
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p
o
wer
f
ilter
d
esig
n
,
i
n
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er
ter
s
t
r
u
ctu
r
e,
o
u
tp
u
t f
ilter
,
p
u
ls
e
wid
th
m
o
d
u
latio
n
m
eth
o
d
,
APF co
n
tr
o
l a
n
d
DC
lin
k
v
o
ltag
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s
tab
ilizatio
n
.
Ho
wev
e
r
,
b
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au
s
e
HAPF
h
as
m
an
y
d
if
f
er
en
t
s
tr
u
ctu
r
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th
e
ab
o
v
e
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n
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ts
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e
also
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if
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er
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t.
Pas
s
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p
o
wer
f
ilter
s
ar
e
s
o
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etim
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d
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ed
with
r
eso
n
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o
m
p
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ts
o
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o
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d
er
1
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1
3
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5
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T
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ter
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ally
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NPC
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o
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t
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t
f
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L
,
L
-
C
,
L
-
C
-
L
an
d
L
-
C
-
L
-
C
.
Pu
ls
e
wid
th
m
o
d
u
latio
n
m
et
h
o
d
s
in
cl
u
d
e
s
in
u
s
o
id
al
p
u
ls
e
wid
t
h
m
o
d
u
latio
n
,
s
p
ac
e
v
ec
to
r
,
h
y
s
ter
esis
.
C
o
n
tr
o
l
f
o
r
HAPF
is
v
er
y
r
ich
a
n
d
d
i
v
er
s
e
f
r
o
m
th
e
m
eth
o
d
to
th
e
co
n
tr
o
ller
u
s
ed
.
Fin
ally
,
th
e
DC
lin
k
v
o
ltag
e
s
tab
ilizatio
n
.
Dep
e
n
d
in
g
o
n
ea
ch
m
o
d
el,
th
e
DC
lin
k
s
tab
ilizatio
n
m
eth
o
d
is
also
d
if
f
er
en
t
s
u
ch
as
th
e
m
eth
o
d
with
an
d
with
o
u
t
p
o
wer
s
u
p
p
ly
f
r
o
m
th
e
s
y
s
tem
th
r
o
u
g
h
a
th
r
ee
-
p
h
ase
b
r
id
g
e
r
ec
tifie
r
co
n
n
ec
ted
to
th
e
DC
lin
k
.
T
h
er
ef
o
r
e,
to
p
r
o
v
i
d
e
r
ea
d
er
s
with
a
n
o
v
er
v
iew
o
f
HAPF,
th
is
p
ap
er
p
r
esen
ts
a
co
m
p
r
eh
e
n
s
iv
e
an
aly
s
is
o
f
th
e
s
tr
u
ctu
r
e,
d
esig
n
,
an
d
c
o
n
tr
o
l
o
f
HAPF in
th
r
ee
-
p
h
ase
th
r
ee
-
wi
r
e
s
y
s
tem
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
p
ap
er
in
clu
d
es
f
iv
e
s
ec
tio
n
s
:
s
ec
tio
n
1
p
r
esen
ts
th
e
u
r
g
en
cy
o
f
h
ar
m
o
n
ic
f
ilter
in
g
,
th
e
i
n
ev
itab
ilit
y
o
f
t
h
e
b
ir
th
o
f
HAPF
an
d
r
esear
c
h
es
o
n
HAPF.
Mo
d
els
o
f
HAPF
ar
e
p
r
esen
ted
in
s
ec
tio
n
2
.
T
h
e
d
esig
n
an
d
co
n
tr
o
l
o
f
HAPF
ar
e
g
iv
en
in
s
ec
tio
n
3
.
R
esu
lts
an
d
d
is
cu
s
s
io
n
ar
e
in
tr
o
d
u
ce
d
in
s
ec
tio
n
4
an
d
s
ec
tio
n
5
is
th
e
c
o
n
clu
s
io
n
.
2.
H
AP
F
M
O
DE
L
S
B
ec
au
s
e
HA
PF
i
s
a
h
y
b
r
id
b
etwe
en
APF
an
d
PP
Fs
a
s
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
er
e
f
o
r
e,
it
h
as
th
e
f
o
llo
win
g
ty
p
ical
m
o
d
el
ty
p
es
,
th
e
f
ir
s
t
m
o
d
el
is
s
h
o
wn
i
n
Fig
u
r
e
1
(
a
)
.
T
h
e
s
tr
u
ctu
r
e
o
f
t
h
is
m
o
d
el
in
clu
d
es
PP
Fs
an
d
an
APF
co
n
n
ec
ted
in
p
ar
allel
with
th
e
lo
ad
,
s
o
th
i
s
m
o
d
el
is
also
ca
lled
a
s
h
u
n
t h
y
b
r
id
ac
tiv
e
p
o
wer
f
ilter
[
1
]
–
[
3
]
.
PP
Fs
ar
e
d
es
ig
n
ed
to
s
u
p
p
r
ess
h
ig
h
-
o
r
d
e
r
h
ar
m
o
n
ics
g
en
er
ated
f
r
o
m
n
o
n
lin
ea
r
lo
a
d
s
.
Me
an
wh
ile,
APF
is
u
s
ed
to
eli
m
in
ate
th
e
r
em
ain
in
g
lo
w
-
o
r
d
er
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
,
s
u
ch
as
th
e
3
rd
,
5
th
,
a
n
d
7
th
.
T
h
e
a
d
v
an
tag
e
o
f
t
h
is
m
o
d
el
is
th
at
it
o
v
er
co
m
es
th
e
r
e
s
o
n
an
ce
p
h
e
n
o
m
e
n
o
n
b
etwe
e
n
th
e
im
p
e
d
an
ce
o
f
th
e
PP
F
an
d
th
e
s
y
s
tem
im
p
e
d
an
ce
,
r
ed
u
cin
g
s
witch
in
g
lo
s
s
es
b
ec
au
s
e
th
e
in
v
er
ter
ci
r
cu
it
o
n
ly
o
p
er
ates
t
o
co
m
p
en
s
ate
f
o
r
l
o
w
-
o
r
d
er
h
ar
m
o
n
ics.
Ho
wev
er
,
it a
ls
o
h
as th
e
d
is
ad
v
an
tag
e
th
at
th
e
s
y
s
te
m
v
o
ltag
e
is
ap
p
lied
d
ir
ec
tly
to
th
e
APF in
v
er
ter
,
lead
in
g
to
a
n
in
cr
ea
s
e
in
in
itial i
n
v
estme
n
t c
o
s
ts
.
I
t is o
n
ly
ca
p
ab
le
o
f
elim
in
atin
g
cu
r
r
en
t
h
ar
m
o
n
ics
g
en
er
ated
b
y
th
e
lo
a
d
.
Fro
m
th
e
ab
o
v
e
ch
ar
ac
ter
is
tics
,
th
is
m
o
d
el
ca
n
o
n
ly
b
e
ap
p
lied
t
o
f
ilter
cu
r
r
en
t
h
ar
m
o
n
ics f
o
r
n
o
n
lin
ea
r
lo
ad
s
in
l
o
w
v
o
ltag
e
g
r
id
s
an
d
th
e
s
o
u
r
ce
is
id
ea
l.
T
h
e
s
ec
o
n
d
m
o
d
el
h
as
th
e
s
tr
u
ctu
r
e
s
h
o
w
n
in
Fig
u
r
e
1
(
b
)
.
I
n
wh
ich
th
e
APF
is
co
n
n
e
cted
in
s
er
ies
with
th
e
PP
F
an
d
all
ar
e
co
n
n
ec
ted
in
p
ar
allel
with
th
e
lo
a
d
[
4
]
,
[
5
]
.
PP
Fs
ar
e
d
esig
n
e
d
to
elim
in
ate
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
th
at
ac
co
u
n
t
f
o
r
a
lar
g
e
p
r
o
p
o
r
tio
n
(
5
th
,
7
th
)
o
f
th
e
lo
ad
.
Me
an
wh
ile,
APF
o
n
ly
p
lay
s
th
e
r
o
le
o
f
im
p
r
o
v
in
g
th
e
e
f
f
icien
cy
o
f
PP
F
an
d
o
v
er
co
m
in
g
th
e
r
es
o
n
an
ce
p
r
o
b
lem
b
etwe
en
t
h
e
im
p
ed
an
ce
o
f
t
h
e
s
o
u
r
ce
an
d
th
e
im
p
ed
a
n
ce
o
f
t
h
e
PP
F.
T
h
e
ad
v
an
tag
e
o
f
th
is
m
o
d
el
is
th
at
it r
ed
u
ce
s
th
e
v
o
ltag
e
ap
p
lied
to
th
e
in
v
er
ter
,
th
e
APF'
s
ca
p
ac
ity
c
an
b
e
r
ed
u
ce
d
m
an
y
tim
es
co
m
p
ar
ed
to
t
h
e
ca
p
a
city
o
f
lo
a
d
.
Fro
m
th
er
e
,
th
is
m
o
d
el
ca
n
b
e
u
s
ed
f
o
r
h
ig
h
p
o
wer
lo
a
d
s
.
T
h
e
d
is
ad
v
an
ta
g
e
is
th
at
it
ca
n
o
n
ly
elim
i
n
ate
a
f
ew
s
elec
ted
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
o
f
th
e
l
o
ad
,
an
d
it is
u
n
ab
le
to
elim
in
ate
h
ar
m
o
n
ics g
e
n
er
ated
f
r
o
m
th
e
s
o
u
r
ce
.
T
h
e
th
ir
d
m
o
d
el
is
s
tr
u
ctu
r
ed
as
s
h
o
wn
in
Fig
u
r
e
1
(
c)
.
T
h
is
m
o
d
el
u
s
es
a
f
u
n
d
am
en
tal
f
r
eq
u
e
n
c
y
r
eso
n
an
t
cir
c
u
it.
1
an
d
1
r
eso
n
at
e
at
th
e
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
c
y
an
d
c
o
u
p
le
to
.
T
h
e
APF
is
co
n
n
ec
ted
in
p
ar
allel
with
th
e
r
eso
n
an
t
cir
c
u
it
1
-
1
an
d
is
co
n
n
ec
te
d
d
ir
ec
tly
to
th
e
tr
an
s
f
o
r
m
e
r
.
is
d
ir
ec
tl
y
co
n
n
ec
te
d
to
g
r
id
v
o
ltag
e
an
d
h
as
t
h
e
a
b
ilit
y
to
co
m
p
en
s
ate
f
o
r
r
ea
ct
iv
e
p
o
wer
[
6
]
–
[
8
]
.
Me
a
n
wh
il
e,
th
e
f
u
n
d
am
en
tal
f
r
eq
u
e
n
cy
r
eso
n
an
t
cir
c
u
it
o
n
ly
s
tan
d
s
f
o
r
h
ar
m
o
n
ic
v
o
ltag
e.
T
h
is
s
ig
n
if
ican
tly
r
ed
u
ce
s
t
h
e
ca
p
ac
ity
o
f
t
h
e
APF
an
d
m
in
im
izes
th
e
r
ated
v
o
ltag
e
ap
p
lied
to
th
e
p
o
wer
elec
tr
o
n
ic
s
witch
es
o
f
th
e
in
v
er
ter
.
T
h
er
ef
o
r
e,
th
is
m
o
d
el
ca
n
b
e
u
s
ed
ef
f
ec
tiv
el
y
in
m
e
d
iu
m
v
o
ltag
e
p
o
wer
g
r
id
s
o
f
6
k
V,
1
5
k
V,
a
n
d
3
5
k
V.
Har
m
o
n
ics
g
en
er
ated
f
r
o
m
t
h
e
s
o
u
r
ce
ca
n
n
o
t b
e
h
an
d
led
.
T
h
e
f
o
u
r
t
h
m
o
d
el
h
as
th
e
s
tr
u
ctu
r
e
s
h
o
wn
in
Fig
u
r
e
1
(
d
)
.
Si
m
ilar
to
th
e
m
o
d
el
in
Fig
u
r
e
1
(
c)
.
PP
Fs
ar
e
d
esig
n
ed
to
s
u
p
p
r
ess
h
ig
h
er
h
ar
m
o
n
ics
(
1
1
th
,
13
th
)
[
9
]
–
[
1
3
]
.
T
h
is
m
o
d
el
also
ca
n
n
o
t
h
an
d
le
v
o
ltag
e
h
ar
m
o
n
ics
f
r
o
m
th
e
s
o
u
r
ce
.
B
ec
au
s
e
it
u
s
es
a
f
u
n
d
am
en
tal
f
r
eq
u
en
c
y
r
eso
n
a
n
t
cir
cu
it,
it
r
e
ce
iv
es
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
p
o
wer
f
r
o
m
th
e
g
r
i
d
.
T
h
e
r
ef
o
r
e
,
th
e
m
o
d
els
in
Fig
u
r
es
1
(
c
)
an
d
1
(
d
)
a
r
e
d
if
f
ic
u
lt
to
s
tab
ilize
th
e
DC
lin
k
v
o
lta
g
e,
wh
e
n
ev
er
th
e
s
o
u
r
ce
v
o
ltag
e
s
ag
s
o
r
d
is
to
r
ts
,
th
e
DC
lin
k
v
o
ltag
e
will
i
n
cr
ea
s
e
o
r
d
ec
r
ea
s
e
s
u
d
d
en
ly
.
T
h
er
ef
o
r
e,
th
is
m
o
d
el
at
th
e
DC
lin
k
is
u
s
u
ally
s
u
p
p
lied
b
y
a
th
r
ee
-
p
h
ase
u
n
co
n
tr
o
lled
b
r
id
g
e
r
ec
tifie
r
.
T
h
e
f
if
th
m
o
d
el
h
as
th
e
s
tr
u
ctu
r
e
s
h
o
wn
in
Fig
u
r
e
1
(
e
)
.
T
h
is
m
o
d
el
in
clu
d
es
PP
Fs
co
n
n
ec
ted
in
p
ar
allel
with
th
e
lo
ad
.
T
h
e
APF
is
co
n
n
ec
ted
in
s
er
ies
with
th
e
l
o
ad
t
h
r
o
u
g
h
a
tr
a
n
s
f
o
r
m
er
[
1
4
]
–
[
1
6
]
.
T
h
e
PP
Fs
ar
e
d
esig
n
ed
to
r
eso
n
ate
at
cu
r
r
en
t
h
ar
m
o
n
ic
f
r
eq
u
en
c
ies.
APF
h
as
th
e
f
u
n
ctio
n
o
f
e
lim
in
atin
g
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Th
r
ee
-
p
h
a
s
e
h
yb
r
id
a
ctive
p
o
w
er filte
r
:
a
n
o
ve
r
view
(
Le
Qu
a
n
g
B
in
h
)
1363
h
ar
m
o
n
ics
f
r
o
m
th
e
s
o
u
r
ce
,
it
ac
ts
lik
e
a
lar
g
e
im
p
ed
an
ce
to
b
lo
ck
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
f
r
o
m
th
e
s
o
u
r
ce
b
u
t
p
ass
th
r
o
u
g
h
th
e
f
u
n
d
am
en
tal
co
m
p
o
n
en
ts
.
As
a
r
esu
lt,
th
e
v
o
ltag
e
ap
p
lied
to
th
e
lo
ad
is
an
id
ea
l
s
in
u
s
o
id
al.
T
h
u
s
,
th
is
m
o
d
el
is
ca
p
a
b
le
o
f
h
a
n
d
lin
g
cu
r
r
en
t
h
ar
m
o
n
ics
f
r
o
m
n
o
n
lin
ea
r
lo
a
d
s
an
d
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
e
d
is
ad
v
an
tag
e
o
f
th
is
m
o
d
el
i
s
th
e
ir
o
n
lo
s
s
d
u
e
to
th
e
u
s
e
o
f
a
tr
an
s
f
o
r
m
er
.
W
h
en
th
e
s
o
u
r
ce
h
as
m
an
y
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
,
th
e
in
v
er
ter
m
u
s
t
s
witch
at
h
ig
h
f
r
e
q
u
en
cy
,
lead
in
g
to
s
witch
in
g
lo
s
s
es.
T
h
er
ef
o
r
e,
th
is
cir
cu
it is
r
ar
ely
u
s
ed
in
p
r
ac
tice.
T
h
e
s
ix
th
m
o
d
el
h
as
th
e
s
tr
u
ctu
r
e
s
h
o
wn
in
Fig
u
r
e
1
(
f
)
.
T
h
is
m
o
d
el
is
a
co
m
b
in
atio
n
o
f
th
e
f
ir
s
t
m
o
d
el
a
n
d
th
e
f
if
th
m
o
d
el.
T
h
is
m
o
d
el
u
s
es
two
v
o
ltag
e
s
o
u
r
ce
in
v
er
te
r
s
s
h
ar
in
g
t
h
e
s
am
e
DC
lin
k
.
T
h
er
ef
o
r
e,
it
is
ca
p
a
b
le
o
f
e
lim
in
atin
g
th
e
c
u
r
r
e
n
t
h
ar
m
o
n
ics
g
en
er
ated
f
r
o
m
th
e
lo
a
d
an
d
th
e
v
o
ltag
e
h
ar
m
o
n
ics
g
en
er
ated
f
r
o
m
th
e
s
o
u
r
ce
.
I
n
a
d
d
itio
n
,
it
also
h
a
s
all
th
e
ad
v
a
n
tag
es
an
d
d
is
ad
v
an
tag
es
o
f
th
e
f
i
r
s
t
m
o
d
el
an
d
th
e
f
if
t
h
m
o
d
el.
N
o
n
l
i
n
e
a
r
l
o
a
d
S
o
u
r
c
e
D
C
l
i
n
k
P
P
F
s
I
n
v
e
r
t
e
r
L
R
s
Z
0
L
O
u
t
p
u
t
f
i
l
t
e
r
P
C
C
N
o
n
l
i
n
e
a
r
l
o
a
d
S
o
u
r
c
e
P
P
F
s
L
R
s
Z
0
L
D
C
l
i
n
k
0
C
5
C
7
C
5
L
7
L
O
u
t
p
u
t
f
i
l
t
e
r
(
a)
(
b
)
N
o
n
l
i
n
e
a
r
l
o
a
d
S
o
u
r
c
e
I
n
j
e
c
t
i
o
n
c
a
p
a
c
i
t
o
r
L
R
s
Z
0
L
D
C
l
i
n
k
0
C
1
L
1
C
F
C
F
u
n
d
a
m
e
n
t
a
l
r
e
s
o
n
a
n
c
e
c
i
r
c
u
i
t
O
u
t
p
u
t
f
i
l
t
e
r
N
o
n
l
i
n
e
a
r
l
o
a
d
S
o
u
r
c
e
P
P
F
s
L
R
s
Z
0
L
D
C
l
i
n
k
0
C
1
L
1
C
F
C
O
u
t
p
u
t
f
i
l
t
e
r
(
c)
(
d
)
N
o
n
l
i
n
e
a
r
l
o
a
d
S
o
u
r
c
e
P
P
F
s
L
R
s
Z
0
L
0
C
Ca
U
Cb
U
Cc
U
D
C
l
i
n
k
O
u
t
p
u
t
f
i
l
t
e
r
N
o
n
l
i
n
e
a
r
l
o
a
d
S
o
u
r
c
e
P
P
F
s
L
R
s
Z
0
C
C
a
U
C
b
U
C
c
U
D
C
l
i
n
k
(
e)
(f)
Fig
u
r
e
1
.
HAPF m
o
d
els
:
(
a)
P
PF
s
an
d
an
APF co
n
n
ec
ted
in
p
ar
allel
with
th
e
lo
ad
(
b
)
APF
is
co
n
n
ec
ted
in
s
er
ies with
th
e
PP
F a
n
d
all
ar
e
co
n
n
ec
ted
in
p
ar
allel
with
th
e
lo
ad
(
c)
APF is
co
n
n
ec
ted
in
p
ar
allel
with
th
e
r
eso
n
an
t c
ir
cu
it
1
-
1
(
d
)
APF is
c
o
n
n
ec
ted
i
n
p
ar
allel
with
th
e
r
eso
n
an
t c
ir
cu
it a
n
d
PP
Fs
(
e)
PP
Fs
ar
e
co
n
n
ec
ted
i
n
p
ar
allel
with
th
e
lo
ad
,
APF is
co
n
n
ec
ted
in
s
er
i
es with
th
e
lo
ad
an
d
(
f
)
PP
Fs
a
r
e
co
n
n
ec
te
d
in
p
ar
allel
with
lo
ad
a
n
d
APF to
co
m
p
e
n
s
ate
b
o
th
v
o
ltag
e
an
d
cu
r
r
e
n
t h
ar
m
o
n
ics
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
3
6
1
-
1
3
7
1
1364
3.
DE
S
I
G
N
AND
CO
N
T
RO
L
F
O
R
H
AP
F
3
.
1
.
Ca
lcula
t
e
t
he
pa
ra
m
et
er
s
o
f
P
P
F
PP
Fs
ar
e
d
esig
n
ed
to
ca
n
ce
l
h
ig
h
-
o
r
d
er
h
ar
m
o
n
ics
g
en
e
r
ate
d
b
y
n
o
n
lin
ea
r
lo
ad
s
a
n
d
to
c
o
m
p
en
s
ate
f
o
r
r
ea
ctiv
e
p
o
wer
.
T
h
e
ty
p
es
o
f
PP
Fs
ar
e
li
s
ted
in
Fig
u
r
e
2
.
Am
o
n
g
th
em
,
t
h
e
PP
F
in
Fig
u
r
e
2
(
a)
is
th
e
m
o
s
t
u
s
ed
[
9
]
–
[
1
3
]
b
ec
au
s
e
o
f
its
s
im
p
licity
.
T
y
p
es
o
f
p
ass
iv
e
f
ilter
cir
cu
its
in
Fig
u
r
e
s
2
(
b
)
to
2
(
f
)
ar
e
r
ar
ely
u
s
ed
.
T
h
er
e
ar
e
two
way
s
to
ca
lcu
l
ate
PP
Fs
p
ar
am
eter
s
:
b
ased
o
n
lo
ad
c
h
ar
ac
ter
is
tics
an
d
u
s
in
g
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
.
1
C
1
C
C
1
C
1
L
1
R
C
L
R
R
C
L
R
L
2
C
R
L
2
C
R
2
C
2
R
3
R
2
L
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
2
.
T
y
p
es o
f
p
ass
iv
e
f
ilter
cir
cu
its
:
(
a)
s
in
g
le
-
tu
n
e
d
f
ilt
er
(
b
)
d
o
u
b
le
-
tu
n
e
d
f
ilter
(
c
)
1
s
t o
r
d
er
h
ig
h
-
p
ass
f
ilter
(
d
)
2
n
d
o
r
d
e
r
h
ig
h
-
p
ass
f
ilter
(
e)
3
r
d
o
r
d
er
h
i
g
h
-
p
ass
f
il
ter
an
d
(
f
)
ty
p
e
C
f
ilter
a.
B
ased
o
n
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
lo
ad
:
First
th
e
v
alu
e
o
f
C
n
is
ca
lcu
lated
b
ased
o
n
th
e
r
ea
ctiv
e
p
o
w
er
r
eq
u
ir
e
m
en
t
o
f
th
e
lo
a
d
=
2
(
1
)
I
n
wh
ic
h
is
th
e
p
h
ase
v
o
ltag
e
ap
p
lied
to
ca
p
ac
ito
r
C
n
a
n
d
is
th
e
f
u
n
d
am
en
tal
an
g
u
lar
f
r
eq
u
en
cy
o
f
th
e
s
o
u
r
ce
.
T
o
elim
in
ate
th
e
n
th
h
ar
m
o
n
ic
co
m
p
o
n
en
t,
L
n
an
d
C
n
m
u
s
t r
eso
n
ate
at
th
e
n
th
f
r
e
q
u
en
cy
.
=
1
2
2
(
2
)
T
h
e
s
er
ies r
esis
tan
ce
f
o
r
th
e
in
d
u
cto
r
o
f
th
e
n
th
o
r
d
er
is
=
(
3
)
wh
er
e
is
th
e
q
u
ality
f
ac
to
r
o
f
th
e
in
d
u
cto
r
,
wh
ich
is
n
o
r
m
all
y
co
n
s
id
er
e
d
as
10
<
<
100
b.
Usi
n
g
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
:
th
e
p
ar
a
m
eter
s
o
f
th
e
PP
F
ar
e
also
d
ete
r
m
in
ed
b
y
a
p
p
ly
in
g
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
a
lg
o
r
ith
m
s
s
u
ch
as
g
en
etic
alg
o
r
ith
m
[
1
7
]
–
[
1
9
]
,
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
[
2
0
]
–
[
2
2
]
,
C
u
ck
o
o
s
ea
r
c
h
alg
o
r
ith
m
[
2
3
]
,
Fo
r
tr
a
n
f
ea
s
ib
le
s
eq
u
en
tial
q
u
ad
r
atic
p
r
o
g
r
am
m
in
g
[
1
9
]
.
T
h
e
r
e
ar
e
also
a
f
ew
s
tu
d
ies
u
s
in
g
m
u
lti
-
o
b
jectiv
e
o
p
tim
iz
atio
n
alg
o
r
ith
m
s
to
f
in
d
all
th
e
p
ar
am
eter
s
o
f
PP
F,
APF
an
d
co
n
tr
o
l
cir
cu
it
[
2
5
]
–
[
2
8
]
.
PS
O
with
s
y
s
tem
s
tab
ilit
y
co
n
s
tr
ain
ts
[
2
5
]
,
So
c
ial
Sp
id
er
alg
o
r
ith
m
[
2
6
]
,
Vo
r
tex
alg
o
r
ith
m
[
2
7
]
,
J
ay
a
[
2
8
]
with
co
n
s
tr
ai
n
ts
:
,
,
an
d
an
o
b
jectiv
e
f
u
n
ctio
n
s
u
ch
as
m
in
im
izin
g
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
o
f
th
e
v
o
ltag
e
ap
p
lied
t
o
th
e
lo
ad
(
)
o
r
m
in
im
ize
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
th
e
s
u
p
p
ly
cu
r
r
en
t (
).
3
.
2
.
Desig
n t
he
o
utput
f
ilte
r
T
h
e
o
u
t
p
u
t
f
ilter
(
OF)
is
d
esig
n
ed
to
f
ilter
u
n
wan
ted
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
at
t
h
e
in
v
e
r
te
r
o
u
tp
u
t.
I
t
af
f
ec
ts
th
e
co
m
p
e
n
s
atio
n
ef
f
e
ct
o
f
HAPF.
T
h
e
r
eq
u
ir
em
en
t
s
wh
en
d
esig
n
in
g
th
e
OF
f
o
r
HAPF
ar
e:
s
im
p
le
s
tr
u
ctu
r
e,
f
ast
r
esp
o
n
s
e
tim
e
,
av
o
id
in
g
r
eso
n
a
n
ce
p
r
o
b
lem
s
,
r
ed
u
cin
g
DC
lin
k
v
o
ltag
e,
att
en
u
atio
n
with
h
i
g
h
o
r
d
er
h
ar
m
o
n
ics,
lo
w
in
itial
in
v
estme
n
t
co
s
ts
an
d
p
o
wer
lo
s
s
.
T
h
e
ty
p
es
o
f
OF
c
o
m
m
o
n
ly
u
s
ed
in
HAPF
ar
e
s
h
o
wn
in
Fig
u
r
e
3
.
Fig
u
r
e
3
(
a
)
[
1
5
]
,
[
3
1
]
,
an
d
F
ig
u
r
e
3
(
b
)
[
4
]
,
[
6
]
,
[
7
]
,
[
9
]
–
[
1
3
]
,
[
2
6
]
–
[
2
8
]
h
av
e
a
s
im
p
le
s
tr
u
ctu
r
e.
Ho
wev
er
,
with
th
is
s
tr
u
ctu
r
e,
th
e
ca
p
ac
ity
r
eq
u
ir
e
m
en
t
o
f
th
e
APF
m
u
s
t
b
e
lar
g
e,
lead
in
g
to
in
cr
ea
s
ed
in
itial
in
v
estme
n
t
co
s
ts
an
d
lar
g
e
lo
s
s
es,
m
ak
in
g
it
d
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Fig
u
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3
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Fig
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3
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y
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tp
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t f
ilter
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a)
L
t
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b
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C
ty
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e
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ty
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e
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ty
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e
3
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3
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T
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ee
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ase
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o
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g
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o
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r
ce
in
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ter
s
[
4
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,
[
6
]
,
[
7
]
,
[
9
]
–
[
1
3
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,
[
3
3
]
,
[
3
4
]
an
d
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s
e
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ly
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ter
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ican
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r
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ir
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h
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r
m
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ce
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h
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e
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h
e
m
o
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co
m
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o
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h
er
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is
t
o
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s
e
a
th
r
ee
-
lev
el
NPC
in
v
er
ter
[
3
5
]
–
[
3
8
]
an
d
a
n
in
e
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lev
el
v
o
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e
s
o
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to
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eth
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d
[
3
9
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3
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4
.
Co
ntr
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ra
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eg
ies a
nd
m
et
h
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T
h
e
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en
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al
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n
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o
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b
lo
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g
r
am
o
f
HAPF
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s
h
o
wn
in
Fi
g
u
r
e
4
.
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h
e
r
ef
e
r
en
ce
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r
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er
e
ca
n
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e
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e
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u
p
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ly
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ar
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r
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t
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r
th
e
lo
ad
h
ar
m
o
n
ic
cu
r
r
en
t
[
4
0
]
–
[
4
2
]
.
I
t
d
ep
e
n
d
s
o
n
th
e
s
tr
u
ctu
r
e
o
f
th
e
HAPF
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d
th
e
ch
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en
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o
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tr
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l
s
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T
h
e
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er
e
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ce
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r
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ally
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eter
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s
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eth
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as
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Fig
u
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5
.
W
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La
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Fig
u
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4
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C
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HAPF
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Fig
u
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e
5
.
Har
m
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eth
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d
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s
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n
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h
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e
T
h
e
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ar
m
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ic
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etec
tio
n
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eth
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s
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g
th
e
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n
ch
r
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o
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s
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f
r
am
e
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as
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ad
v
a
n
tag
e
o
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im
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wev
er
,
it
h
as
th
e
d
is
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an
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e
o
f
d
e
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en
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n
g
o
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h
ig
h
-
p
ass
f
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(
HPF)
o
r
l
o
w
-
p
ass
f
ilter
(
L
PF
)
.
W
h
en
th
e
L
PF
h
as
a
h
ig
h
cu
t
-
o
f
f
f
r
e
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en
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y
,
its
d
y
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ic
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es
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e
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ast,
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u
t
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e
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.
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th
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o
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ar
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,
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e
c
u
t
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o
f
f
f
r
eq
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t
h
e
d
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n
s
e
tim
e
will
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e,
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u
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s
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e
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ar
m
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ic
c
o
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t
in
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e
f
u
n
d
a
m
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r
r
en
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e
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er
y
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w.
Fu
r
th
e
r
m
o
r
e,
wh
en
u
s
in
g
L
PF
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e
o
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er
s
h
o
o
t
d
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r
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g
th
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tr
an
s
itio
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will
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lar
g
e.
T
o
r
ed
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ce
th
e
d
e
p
en
d
en
ce
o
n
L
PF
.
Stu
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ies
h
av
e
u
s
ed
n
eu
r
al
n
etwo
r
k
to
d
eter
m
in
e
th
e
h
ar
m
o
n
ic
cu
r
r
en
t
[
3
1
]
,
[
4
4
]
.
T
h
e
lo
ad
c
u
r
r
en
t
wi
ll
b
e
an
aly
ze
d
in
to
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ep
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ate
co
m
p
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d
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h
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m
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en
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ig
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ed
a
weig
h
t.
Du
r
in
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k
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e
n
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p
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ate
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ad
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s
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e
weig
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ts
s
o
th
at
t
h
e
e
r
r
o
r
is
ze
r
o
.
T
h
is
m
eth
o
d
h
a
s
th
e
ad
v
an
tag
e
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
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lec
&
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Vo
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15
,
No
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2
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Ap
r
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20
25
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1
3
6
1
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1
3
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1
1366
d
eter
m
in
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e
ex
ac
t
h
ar
m
o
n
ic
co
m
p
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n
en
ts
at
s
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Ho
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also
h
as
th
e
d
is
a
d
v
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tag
e
o
f
a
s
lo
w
d
y
n
am
ic
r
esp
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n
s
e
tim
e.
A
f
e
w
s
tu
d
ies
h
av
e
im
p
r
o
v
e
d
th
e
p
-
q
h
a
r
m
o
n
ic
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etec
tio
n
m
eth
o
d
,
s
u
ch
as
ch
an
g
i
n
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th
e
cu
t
o
f
f
f
r
e
q
u
en
c
y
u
s
in
g
1
st
,
2
nd
,
3
rd
lo
w
-
p
ass
o
r
h
ig
h
-
p
a
s
s
f
ilter
s
[
4
3
]
,
[
4
5
]
–
[
4
7
]
u
s
e
a
r
eg
u
lato
r
f
u
zz
y
to
im
p
r
o
v
e
th
e
L
PF
in
t
h
e
p
-
q
h
ar
m
o
n
ic
d
eter
m
in
atio
n
m
et
h
o
d
to
r
ed
u
ce
d
y
n
am
ic
r
esp
o
n
s
e
tim
e.
R
ef
er
en
ce
s
[
4
8
]
an
d
[
4
9
]
u
s
e
a
n
im
p
r
o
v
e
d
least
m
ea
n
s
q
u
ar
e
(
L
MS)
a
lg
o
r
ith
m
th
at
m
a
k
es
th
e
d
y
n
a
m
ic
r
esp
o
n
s
e
tim
e
f
aster
an
d
in
d
ep
en
d
en
t
o
f
L
PF
.
Mo
r
ad
i
an
d
Pich
an
[
5
0
]
u
s
ed
th
e
wav
elet
tr
an
s
f
o
r
m
to
id
en
tify
h
ar
m
o
n
ics.
T
h
is
m
eth
o
d
d
o
es
n
o
t
u
s
e
L
PF
,
b
u
t
co
llectin
g
s
am
p
le
d
ata
is
co
m
p
licated
,
esp
ec
ially
wh
en
th
e
lo
ad
ch
an
g
es.
B
o
u
s
s
aid
et
a
l.
[
5
1
]
u
s
ed
m
u
lt
iv
ar
iab
le
f
ilter
s
(
MV
F)
to
in
cr
ea
s
e
th
e
h
ar
m
o
n
ic
f
ilter
in
g
e
f
f
icien
cy
an
d
r
e
d
u
ce
th
e
h
ar
m
o
n
ic
co
n
ten
t
i
n
th
e
f
u
n
d
am
en
tal
h
a
r
m
o
n
ic
c
u
r
r
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n
t.
T
ao
et
a
l.
[
5
2
]
d
ete
r
m
in
es
h
ar
m
o
n
ics
b
ased
o
n
a
n
im
p
r
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e
d
Gr
ay
W
o
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alg
o
r
ith
m
with
o
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ized
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iatio
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m
o
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e
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itio
n
.
T
h
e
r
ef
er
en
ce
cu
r
r
e
n
t
s
ig
n
al
ca
n
b
e
b
ased
o
n
th
e
s
u
p
p
ly
h
a
r
m
o
n
ic
c
u
r
r
e
n
t
o
r
th
e
lo
ad
h
ar
m
o
n
ic
c
u
r
r
en
t,
d
e
p
en
d
in
g
o
n
t
h
e
ch
o
s
en
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
er
r
o
r
b
etwe
en
t
h
e
r
ef
er
e
n
ce
s
ig
n
al
an
d
th
e
c
o
m
p
en
s
atio
n
s
ig
n
al
will
b
e
p
ass
ed
th
r
o
u
g
h
th
e
co
n
tr
o
ller
,
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
,
in
v
er
ter
,
o
u
tp
u
t
f
ilter
an
d
ap
p
lied
to
th
e
g
r
id
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
.
Mo
s
t
r
esear
ch
f
o
cu
s
es
o
n
co
n
tr
o
ller
s
th
at
m
in
im
ize
er
r
o
r
s
an
d
r
esp
o
n
d
to
lo
ad
ch
an
g
es.
T
h
e
s
im
p
lest
is
to
u
s
e
s
in
g
le
co
n
tr
o
ller
s
s
u
ch
as:
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
PI)
[
5
3
]
–
[
5
7
]
,
d
ea
d
b
ea
t
[
5
8
]
,
f
u
zz
y
[
5
9
]
,
n
eu
r
al
[
6
0
]
.
T
h
e
ab
o
v
e
s
in
g
le
co
n
tr
o
ller
s
h
av
e
th
e
d
is
ad
v
an
tag
e
o
f
s
lo
w
r
esp
o
n
s
e
an
d
co
n
s
tan
t
p
ar
am
eter
s
d
u
r
in
g
co
n
tr
o
l,
s
o
th
ey
ar
e
n
o
t
s
u
itab
le
f
o
r
ch
a
n
g
in
g
lo
a
d
s
y
s
tem
s
an
d
h
av
e
lar
g
e
er
r
o
r
s
.
Sin
ce
th
en
,
h
y
b
r
i
d
co
n
tr
o
ller
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
,
s
u
c
h
as:
PI
-
f
u
zz
y
[
6
1
]
,
PI
-
n
eu
r
al
[
6
2
]
,
[
6
3
]
an
d
f
u
zz
y
-
n
eu
r
a
l
[
6
4
]
–
[
6
7
]
.
Sev
er
al
r
ec
en
t
s
tu
d
ies
u
s
ed
p
r
o
p
o
r
tio
n
al
r
eso
n
an
t
(
PR
)
co
n
tr
o
ller
[
6
8
]
,
[
6
9
]
.
T
h
e
ad
v
an
tag
e
o
f
PR
co
n
tr
o
ller
is
th
at
it
g
i
v
es
er
r
o
r
at
s
tead
y
s
tate
eq
u
al
t
o
ze
r
o
.
Ho
wev
e
r
,
it
o
f
te
n
h
as
a
l
o
n
g
tr
a
n
s
ien
t
tim
e.
T
h
er
ef
o
r
e,
PR
co
n
tr
o
ller
is
o
f
ten
co
m
b
i
n
ed
with
f
u
zz
y
co
n
tr
o
ller
s
[
7
0
]
to
r
ed
u
ce
tr
an
s
i
en
t
tim
e.
T
h
er
e
ar
e
also
a
f
ew
s
tu
d
ies
u
s
in
g
s
elf
-
ad
ap
tiv
e
co
n
tr
o
l
[
7
1
]
,
p
r
e
d
ic
tiv
e
co
n
tr
o
l
[
7
2
]
,
[
7
3
]
an
d
s
lid
in
g
c
o
n
tr
o
l
[
7
4
]
.
T
h
ese
co
n
tr
o
ls
ar
e
m
o
d
er
n
an
d
h
ig
h
l
y
ef
f
icien
t a
n
d
ar
e
s
u
ita
b
le
f
o
r
v
ar
iab
le
lo
a
d
s
itu
atio
n
s
.
3
.
5
.
DC
L
ink
v
o
lt
a
g
e
s
t
a
bil
iza
t
io
n
Stab
ilizin
g
th
e
DC
lin
k
v
o
lta
g
e
o
f
th
e
in
v
er
ter
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
ta
n
t
jo
b
s
in
t
h
e
HAPF
s
y
s
tem
.
Dep
en
d
in
g
o
n
th
e
s
tr
u
ctu
r
e
o
f
ea
ch
s
y
s
tem
,
th
e
m
eth
o
d
o
f
s
tab
ilizin
g
th
e
DC
lin
k
v
o
ltag
e
is
also
d
if
f
er
en
t.
No
r
m
ally
,
th
e
DC
l
in
k
v
o
ltag
e
is
ad
ju
s
ted
as
in
Fig
u
r
e
6
.
T
h
e
ac
tu
al
v
o
ltag
e
o
n
th
e
DC
lin
k
i
s
co
m
p
ar
ed
with
t
h
e
r
ef
er
en
ce
DC
v
o
ltag
e
v
al
u
e,
will b
e
p
ass
ed
th
r
o
u
g
h
th
e
PI
co
n
tr
o
ller
,
a
n
d
th
e
r
esu
lt
will
b
e
ad
d
ed
to
th
e
r
ea
ctiv
e
cu
r
r
en
t c
o
m
p
o
n
en
t in
th
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
a
m
e
[
7
5
]
,
[
7
6
]
.
Ho
wev
er
,
th
is
m
eth
o
d
is
o
f
ten
s
u
itab
le
f
o
r
s
y
s
tem
s
w
ith
s
m
all
DC
lin
k
v
o
ltag
e
f
lu
ct
u
atio
n
s
.
L
u
o
et
a
l.
[
7
7
]
p
r
o
p
o
s
ed
two
m
eth
o
d
s
to
s
tab
ilize
th
e
DC
lin
k
v
o
ltag
e
f
o
r
t
h
e
f
o
u
r
th
m
o
d
el:
th
e
f
ir
s
t
m
eth
o
d
is
to
u
s
e
a
cir
cu
it
to
d
is
ch
ar
g
e
en
er
g
y
th
r
o
u
g
h
a
r
esis
to
r
,
wh
er
eb
y
wh
en
th
e
v
o
ltag
e
o
n
th
e
DC
lin
k
in
cr
ea
s
es,
it
w
ill
b
e
d
i
s
ch
ar
g
ed
th
r
o
u
g
h
a
r
esis
to
r
b
y
an
in
s
u
lated
-
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
GB
T
)
k
ey
.
T
h
e
s
ec
o
n
d
m
eth
o
d
is
to
u
s
e
a
co
n
tr
o
lled
r
ec
tifie
r
co
n
n
ec
ted
t
o
th
e
i
n
v
er
ter
v
ia
t
h
e
DC
lin
k
,
wh
er
e
b
y
wh
e
n
th
e
DC
lin
k
v
o
ltag
e
i
n
cr
ea
s
es,
it
will
b
e
d
is
ch
ar
g
e
d
in
to
th
e
g
r
id
an
d
v
ice
v
er
s
a.
L
am
et
a
l.
[
7
8
]
p
r
o
p
o
s
es
an
ad
ap
tiv
e
DC
lin
k
v
o
ltag
e
co
n
t
r
o
l
m
eth
o
d
ac
co
r
d
in
g
to
lo
ad
ch
an
g
es.
T
h
is
s
tu
d
y
is
d
if
f
er
e
n
t
f
r
o
m
p
r
e
v
io
u
s
s
tu
d
i
es
in
th
at
it
allo
ws
t
h
e
DC
lin
k
v
o
lta
g
e
to
ch
an
g
e
ac
co
r
d
in
g
to
th
e
lo
a
d
,
ea
ch
l
o
ad
will
co
r
r
esp
o
n
d
to
an
o
p
ti
m
al
DC
v
o
ltag
e
v
alu
e.
I
n
th
e
ca
s
e
o
f
a
f
ix
ed
DC
lin
k
v
o
ltag
e,
th
e
s
witch
in
g
lo
s
s
will
b
e
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
th
e
DC
lin
k
v
o
ltag
e,
th
e
s
y
s
tem
will
o
b
tain
a
lar
g
e
lo
s
s
if
t
h
e
DC
lin
k
v
al
u
e
is
lar
g
e,
an
d
v
ice
v
er
s
a.
T
h
er
ef
o
r
e,
if
th
e
DC
lin
k
v
o
ltag
e
is
ad
ap
tiv
ely
ad
ju
s
ted
ac
co
r
d
in
g
t
o
th
e
d
if
f
er
en
t
p
o
wer
s
itu
atio
n
s
o
f
th
e
lo
ad
,
t
h
e
s
y
s
tem
ca
n
ac
h
ie
v
e
b
etter
a
n
d
m
o
r
e
f
lex
ib
le
r
esu
lts
.
B
ao
an
d
T
h
u
y
en
[
7
9
]
p
r
o
p
o
s
ed
a
m
eth
o
d
to
s
tab
ilize
th
e
DC
lin
k
v
o
ltag
e
u
s
in
g
a
n
u
n
co
n
tr
o
lled
b
r
id
g
e
r
ec
tifie
r
co
m
b
in
ed
with
a
B
o
o
s
t
DC
/DC
co
n
v
er
ter
.
Go
n
g
et
a
l.
[
8
0
]
u
s
ed
a
n
o
n
lin
ea
r
PID
co
n
tr
o
ller
b
ased
o
n
r
o
b
u
s
t e
x
a
ct
d
if
f
er
en
tiatio
n
to
im
p
r
o
v
e
t
h
e
d
y
n
am
ic
r
esp
o
n
s
e
tim
e
o
n
t
h
e
DC
lin
k
v
o
ltag
e.
s
u
La
i
Lb
i
Lc
i
d
i
q
i
d
i
q
i
-
D
C
re
f
U
L
ah
i
L
bh
i
L
c
h
i
si
n
c
os
−
P
L
L
L
P
F
L
P
F
/0
ab
c
dq
Lb
i
La
i
Lc
i
+
+
+
−
−
−
DC
U
Contr
ol
l
e
r
+
+
+
−
0/
dq
ab
c
Fig
u
r
e
6
.
DC
lin
k
v
o
ltag
e
s
tab
ilizatio
n
d
iag
r
am
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
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m
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I
SS
N:
2088
-
8
7
0
8
Th
r
ee
-
p
h
a
s
e
h
yb
r
id
a
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p
o
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er filte
r
:
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view
(
Le
Qu
a
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in
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1367
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Fro
m
th
e
ab
o
v
e
an
aly
s
is
r
esu
lts
,
we
ca
n
s
ee
th
at
w
h
ich
m
o
d
el
to
u
s
e
d
ep
e
n
d
s
o
n
t
h
e
p
u
r
p
o
s
e
a
n
d
f
u
n
ctio
n
o
f
ea
ch
m
o
d
el,
th
e
f
u
n
ctio
n
o
f
ea
ch
m
o
d
el
ca
n
b
e
s
u
m
m
ar
ized
as
in
T
ab
le
1
.
T
h
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
s
tr
u
ctu
r
e
o
f
PP
F
is
th
e
f
o
r
m
in
Fig
u
r
e
2
(
a
)
.
C
alcu
late
th
e
p
ar
am
eter
s
o
f
PP
Fs
in
Fig
u
r
e
2
(
a)
ca
n
b
e
b
ased
o
n
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
l
o
ad
to
f
in
d
th
e
v
al
u
es
o
f
L
a
n
d
C
s
o
th
at
it
r
eso
n
ates
at
a
ce
r
tain
h
a
r
m
o
n
ic
f
r
eq
u
e
n
cy
o
r
u
s
e
m
u
lti
-
o
b
j
ec
tiv
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
.
So
m
e
s
tu
d
ies
h
av
e
u
s
ed
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
to
d
et
er
m
in
e
th
e
p
ar
am
eter
s
f
o
r
b
o
t
h
PP
F
an
d
co
n
tr
o
l.
I
n
th
e
ca
s
e
o
f
ch
an
g
in
g
lo
ad
,
d
eter
m
in
in
g
th
e
c
o
n
tr
o
l
cir
c
u
it
p
ar
am
eter
s
is
n
o
t
n
ec
es
s
ar
y
.
Mo
r
e
o
v
er
,
in
o
n
lin
e
c
o
n
tr
o
l,
t
h
e
co
n
tr
o
l
p
ar
am
eter
s
m
u
s
t b
e
c
o
n
tin
u
o
u
s
ly
u
p
d
ated
.
Desig
n
in
g
th
e
OF
p
lay
s
a
d
ec
is
iv
e
r
o
le
in
th
e
ac
cu
r
ac
y
o
f
th
e
co
m
p
en
s
atio
n
s
ig
n
al
t
o
th
e
g
r
id
.
Ou
tp
u
t
f
ilter
s
also
co
m
e
in
m
an
y
f
o
r
m
s
.
T
h
e
r
ef
o
r
e
,
wh
en
d
ec
id
in
g
wh
ic
h
ty
p
e
t
o
u
s
e,
we
s
h
o
u
ld
co
n
s
id
er
f
ac
to
r
s
s
u
ch
as
s
tr
u
ctu
r
e
,
r
esp
o
n
s
e
tim
e,
r
eso
n
a
n
ce
,
DC
lin
k
v
o
ltag
e
v
alu
e,
h
ig
h
h
ar
m
o
n
ic
atten
u
atio
n
,
p
o
wer
lo
s
s
an
d
in
v
estme
n
t
co
s
t.
B
elo
w
is
a
co
m
p
ar
is
o
n
o
f
th
e
c
h
ar
ac
ter
is
tics
o
f
th
e
o
u
tp
u
t
f
ilter
s
s
u
m
m
ar
ized
in
T
ab
le
2
.
T
ab
le
1
.
Fu
n
ctio
n
al
co
m
p
ar
is
o
n
o
f
HAPF m
o
d
els
C
o
m
p
e
n
s
a
t
i
o
n
f
o
r
sp
e
c
i
f
i
c
a
p
p
l
i
c
a
t
i
o
n
H
y
b
r
i
d
a
c
t
i
v
e
p
o
w
e
r
f
i
l
t
e
r
s
m
o
d
e
l
s
1
st
m
o
d
e
l
2
nd
m
o
d
e
l
3
rd
m
o
d
e
l
4
th
mo
d
e
l
5
th
mo
d
e
l
6
th
mo
d
e
l
C
u
r
r
e
n
t
h
a
r
mo
n
i
c
s
*
*
*
*
*
V
o
l
t
a
g
e
h
a
r
m
o
n
i
c
s
**
*
R
e
a
c
t
i
v
e
p
o
w
e
r
*
**
**
**
*
*
V
o
l
t
a
g
e
i
m
b
a
l
a
n
c
e
a
n
d
d
i
st
o
r
t
i
o
n
**
*
V
o
l
t
a
g
e
r
e
g
u
l
a
t
i
o
n
**
*
H
i
g
h
e
r
n
u
mb
e
r
o
f
‘
*
’
i
s m
o
r
e
p
r
e
f
e
r
r
e
d
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
o
f
ch
ar
a
cter
is
tics
o
f
o
u
tp
u
t
f
ilter
s
O
u
t
p
u
t
f
i
l
t
e
r
s
S
t
r
u
c
t
u
r
e
R
e
s
p
o
n
se
t
i
me
R
e
s
o
n
a
n
c
e
V
o
l
t
a
g
e
D
C
-
l
i
n
k
H
i
g
h
-
o
r
d
e
r
h
a
r
m
o
n
i
c
s
a
t
t
e
n
u
a
t
i
o
n
P
o
w
e
r
l
o
ss
C
o
s
t
L
[
1
5
]
,
[
3
1
]
S
i
mp
l
e
F
a
st
No
H
i
g
h
La
r
g
e
La
r
g
e
M
e
d
i
u
m
L
C
[
9
]
–
[
1
3
]
S
i
mp
l
e
F
a
st
No
H
i
g
h
La
r
g
e
M
e
d
i
u
m
M
e
d
i
u
m
L
C
L
[
2
9
]
,
[
3
0
]
C
o
m
p
l
e
x
M
e
d
i
u
m
No
H
i
g
h
S
mal
l
La
r
g
e
H
i
g
h
L
C
L
C
[
3
2
]
C
o
m
p
l
e
x
M
e
d
i
u
m
No
Lo
w
S
mal
l
S
mal
l
M
e
d
i
u
m
I
n
v
er
ter
s
tr
u
ctu
r
e
an
d
p
u
ls
e
w
id
th
m
o
d
u
latio
n
m
eth
o
d
:
I
n
th
e
HAPF
s
tr
u
ctu
r
es,
it
is
o
n
ly
n
ec
ess
ar
y
to
u
s
e
th
r
ee
-
p
h
ase
two
-
lev
el
v
o
ltag
e
s
o
u
r
ce
in
v
e
r
ter
(
VSI
)
with
o
u
t
u
s
in
g
m
u
lti
-
lev
el
in
v
er
ter
s
.
T
h
e
m
o
s
t
p
o
p
u
lar
m
o
d
u
latio
n
m
eth
o
d
h
er
e
is
th
e
s
in
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
m
eth
o
d
b
ec
au
s
e
o
f
its
s
im
p
licity
an
d
ea
s
e
o
f
ex
p
e
r
im
en
tal
im
p
lem
en
tati
o
n
,
b
u
t
th
e
o
u
t
p
u
t
p
o
wer
o
f
t
h
e
in
v
er
ter
is
n
o
t
lar
g
e.
T
h
e
H
y
s
ter
esis
m
eth
o
d
h
as
th
e
ad
v
a
n
tag
e
o
f
f
ast
r
esp
o
n
s
e,
b
u
t
t
h
e
d
is
ad
v
a
n
tag
e
is
th
a
t
th
e
s
tead
y
-
s
tate
er
r
o
r
is
p
o
o
r
.
T
h
e
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
m
eth
o
d
ca
n
g
iv
e
an
o
u
tp
u
t
p
o
wer
o
f
t
h
e
i
n
v
er
ter
lar
g
er
t
h
an
th
e
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
m
eth
o
d
,
b
u
t
it
is
co
m
p
licated
.
T
h
is
m
eth
o
d
is
o
f
ten
u
s
ed
f
o
r
m
o
d
el
1
,
ac
co
m
p
an
ied
b
y
th
e
u
s
e
o
f
a
th
r
ee
-
lev
el
NPC
in
v
er
ter
.
C
o
n
tr
o
l stra
teg
ies an
d
m
eth
o
d
s
: T
h
e
ch
o
ice
o
f
co
n
tr
o
l stra
teg
y
b
ased
o
n
th
e
l
o
ad
h
ar
m
o
n
ic
cu
r
r
en
t o
r
th
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t
(
m
o
d
els
1
to
4
)
o
r
b
ased
o
n
th
e
lo
ad
h
ar
m
o
n
ic
v
o
ltag
e
o
r
th
e
s
u
p
p
ly
h
ar
m
o
n
ic
cu
r
r
en
t
(
m
o
d
els
5
a
n
d
6
)
is
d
ep
en
d
s
o
n
s
y
s
tem
ch
ar
ac
ter
is
tics
.
Nex
t
is
th
e
s
elec
tio
n
o
f
t
h
e
co
n
tr
o
ller
.
T
h
e
s
elec
ted
co
n
tr
o
ller
m
u
s
t
en
s
u
r
e
ac
cu
r
ac
y
,
f
ast
r
esp
o
n
s
e,
s
m
a
ll
er
r
o
r
an
d
h
as
th
e
ab
ilit
y
t
o
u
p
d
ate
o
n
lin
e
with
ch
an
g
es
in
lo
ad
an
d
ea
s
y
to
im
p
lem
en
t
in
p
r
ac
tice.
Sin
g
le
co
n
tr
o
ller
s
ar
e
s
im
p
le
an
d
ea
s
y
to
im
p
lem
en
t
in
p
r
ac
tice
alth
o
u
g
h
th
e
y
h
av
e
t
h
e
d
is
ad
v
an
tag
e
o
f
p
o
o
r
s
tead
y
-
s
tate
p
er
f
o
r
m
a
n
ce
.
T
h
er
e
f
o
r
e,
th
ey
ar
e
o
f
ten
co
m
b
in
ed
with
f
u
zz
y
,
n
eu
r
al,
ad
ap
tiv
e
co
n
tr
o
ller
s
.
Ho
wev
er
,
th
e
ab
o
v
e
co
m
b
in
e
d
co
n
tr
o
ller
s
ar
e
co
m
p
lex
an
d
d
if
f
icu
lt
to
m
in
im
ize
th
e
s
tead
y
-
s
tate
er
r
o
r
.
T
h
e
r
ef
o
r
e,
a
n
ew
tr
en
d
is
to
u
s
e
PR
co
n
tr
o
l
ler
co
m
b
in
e
d
with
f
u
zz
y
a
n
d
n
eu
r
al
co
n
tr
o
ller
s
t
o
co
n
t
r
o
l
o
n
lin
e
with
l
o
ad
c
h
an
g
es
an
d
ca
n
r
ed
u
ce
th
e
co
m
p
en
s
atio
n
er
r
o
r
to
ze
r
o
at
s
tead
y
-
s
tate.
DC
lin
k
v
o
ltag
e
s
tab
ilizatio
n
:
Fro
m
th
e
ab
o
v
e
s
u
m
m
ar
ies,
we
ca
n
s
ee
th
at
t
h
er
e
a
r
e
two
m
ain
m
eth
o
d
s
o
f
DC
lin
k
v
o
ltag
e
s
tab
ilizatio
n
as
f
o
llo
ws
:
f
o
r
m
o
d
els
with
o
u
t
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
r
eso
n
an
ce
cir
cu
it
(
m
o
d
els
1
,
2
,
5
,
6
)
,
we
ca
n
u
s
e
th
e
m
et
h
o
d
in
Fi
g
u
r
e
6
.
Fo
r
m
o
d
els
3
,
4
,
th
e
r
e
is
a
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
cy
r
eso
n
a
n
ce
cir
cu
it,
s
o
th
e
v
o
ltag
e
ap
p
lied
to
th
e
in
v
er
ter
is
m
ain
ly
h
ar
m
o
n
ic,
s
o
o
n
ce
th
e
v
o
lta
g
e
at
th
e
co
m
m
o
n
co
n
n
ec
tio
n
p
o
in
t
is
s
ag
g
ed
o
r
d
is
to
r
ted
,
th
e
v
o
lt
ag
e
o
n
th
e
DC
lin
k
will f
lu
ctu
ate
g
r
ea
tly
,
ca
u
s
in
g
d
an
g
er
to
th
e
s
y
s
tem
.
T
h
e
r
ef
o
r
e,
DC
lin
k
v
o
ltag
e
s
tab
ilizatio
n
o
f
th
ese
m
o
d
els
m
u
s
t
b
e
p
o
wer
ed
f
r
o
m
a
th
r
ee
-
p
h
ase
s
o
u
r
ce
th
r
o
u
g
h
a
t
h
r
ee
-
p
h
ase
PW
M
o
r
u
n
co
n
tr
o
lled
r
ec
tifie
r
[
7
7
]
as
in
Fig
u
r
e
7
.
T
h
e
ex
is
tin
g
p
r
o
b
lem
s
an
d
th
e
f
u
tu
r
e
d
ev
elo
p
m
en
t d
i
r
ec
tio
n
s
:
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.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
3
6
1
-
1
3
7
1
1368
a.
T
h
e
cir
cu
it
t
h
at
d
eter
m
in
es
th
e
r
ef
er
e
n
ce
h
a
r
m
o
n
ic
cu
r
r
en
t
d
ep
en
d
s
o
n
p
h
ase
-
lo
c
k
ed
lo
o
p
(
PLL
)
a
n
d
L
PF
.
T
h
er
ef
o
r
e,
d
u
r
in
g
th
e
tr
an
s
ien
t
p
er
io
d
,
th
e
r
ef
e
r
en
ce
cu
r
r
en
t
s
ig
n
al
g
en
er
ated
is
n
o
t
ac
cu
r
ate
an
d
th
e
tr
an
s
ien
t
tim
e
is
lo
n
g
.
As
a
r
esu
lt,
th
e
s
u
p
p
ly
cu
r
r
e
n
t
d
u
r
in
g
t
h
e
tr
an
s
ien
t
p
er
io
d
o
r
wh
en
th
e
lo
ad
c
h
an
g
es
s
u
d
d
en
ly
will b
e
v
er
y
lar
g
e,
w
h
ich
ca
n
ea
s
ily
ca
u
s
e
s
y
s
tem
in
s
tab
ilit
y
.
T
h
er
ef
o
r
e
,
it is
n
ec
ess
ar
y
to
s
tu
d
y
a
m
eth
o
d
to
d
eter
m
in
e
h
ar
m
o
n
i
c
cu
r
r
en
ts
with
o
u
t
u
s
in
g
PLL
an
d
L
PF
.
b.
HAPF
s
h
av
e
a
r
ath
er
lar
g
e
D
C
-
lin
k
v
o
ltag
e
an
d
h
ig
h
s
witch
in
g
f
r
e
q
u
en
c
y
.
T
h
is
r
esu
lts
in
a
lar
g
e
v
o
ltag
e
ap
p
lied
to
th
e
I
GB
T
an
d
la
r
g
e
s
witch
in
g
lo
s
s
.
T
h
er
e
f
o
r
e,
r
esear
ch
to
im
p
r
o
v
e
th
e
s
tr
u
ctu
r
e
o
f
t
h
e
tr
ad
itio
n
al
two
-
lev
el
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
is
n
ec
ess
ar
y
.
c.
I
n
p
r
ac
tical
ap
p
licatio
n
s
,
th
e
I
GB
T
s
in
th
e
in
v
er
ter
m
ay
h
av
e
a
co
n
d
u
ct
to
g
et
h
er
p
h
e
n
o
m
e
n
o
n
th
at
ca
u
s
es
s
h
o
r
t
cir
cu
its
an
d
o
p
en
cir
cu
it
s
in
th
e
in
v
er
ter
.
T
h
is
is
v
er
y
d
an
g
er
o
u
s
.
T
h
er
ef
o
r
e,
r
esear
c
h
to
im
p
r
o
v
e
th
e
VSI
s
tr
u
ctu
r
e
an
d
co
n
tr
o
l
m
et
h
o
d
s
o
th
at
it
ca
n
o
v
er
co
m
e
t
h
e
co
n
d
u
ct
to
g
eth
er
,
s
h
o
r
t
cir
cu
it,
o
p
en
cir
cu
it
p
h
en
o
m
en
a
in
t
h
e
in
v
er
te
r
.
I
t c
o
n
tr
ib
u
tes to
im
p
r
o
v
i
n
g
th
e
s
a
f
ety
d
u
r
in
g
th
e
o
p
er
atio
n
o
f
H
APF.
d.
B
ec
au
s
e
th
e
s
tr
u
ctu
r
e
o
f
HA
PF
in
clu
d
es
m
an
y
R
,
L
,
C
elem
en
ts
co
n
n
ec
ted
to
g
et
h
er
.
T
h
er
ef
o
r
e,
th
e
co
m
p
en
s
atio
n
s
ig
n
al
to
th
e
g
r
id
at
th
e
PC
C
will
b
e
p
h
ase
s
h
if
ted
co
m
p
ar
ed
to
th
e
r
ef
er
e
n
ce
s
ig
n
al.
As
a
r
esu
lt,
th
er
e
is
alwa
y
s
a
d
ev
iat
io
n
b
etwe
en
th
e
r
e
f
er
en
ce
s
ig
n
al
an
d
th
e
co
m
p
en
s
atio
n
s
ig
n
al.
So
,
it
is
v
er
y
im
p
o
r
tan
t
to
s
tu
d
y
a
co
n
tr
o
l
m
eth
o
d
h
as
f
ast
r
esp
o
n
s
e,
s
m
all
er
r
o
r
an
d
p
h
ase
s
h
if
t
co
m
p
en
s
atio
n
ca
p
ab
ilit
y
.
e.
I
n
ap
p
licatio
n
s
th
at
r
eq
u
ir
e
d
y
n
am
ic
co
m
p
en
s
atio
n
o
f
a
lar
g
e
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
,
HAPF
i
s
o
f
ten
n
o
t
s
atis
f
y
.
T
h
er
ef
o
r
e,
r
esear
c
h
o
n
HAPF
m
o
d
els
with
co
n
n
ec
tio
n
s
b
etwe
en
s
tatic
v
ar
c
o
m
p
en
s
ato
r
an
d
ac
tiv
e
p
o
wer
f
ilter
is
n
ec
ess
ar
y
.
f.
Har
m
o
n
ic
f
ilter
in
g
f
o
r
s
m
ar
t
g
r
id
s
.
Sm
ar
t
g
r
id
s
a
r
e
lar
g
e
s
y
s
tem
s
with
m
an
y
in
ter
co
n
n
e
ctio
n
s
an
d
m
an
y
h
ar
m
o
n
ic
g
en
e
r
atin
g
d
ev
ices
s
u
ch
as
in
v
er
ter
s
a
n
d
c
o
n
v
e
r
ter
s
co
n
n
ec
ted
to
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
.
T
h
er
ef
o
r
e,
r
esear
ch
o
n
h
ar
m
o
n
ic
f
ilter
in
g
f
o
r
s
m
ar
t g
r
id
s
also
n
ee
d
s
to
b
e
in
ter
ested
.
S
o
u
r
c
e
3
8
0
V
D
C
l
i
n
k
I
n
v
e
r
t
e
r
0
L
P
W
M
o
r
u
n
c
o
n
t
r
o
l
l
e
d
r
e
c
t
i
f
i
e
r
Fig
u
r
e
7
.
DC
lin
k
v
o
ltag
e
s
tab
ilit
y
with
th
e
th
ir
d
m
o
d
el
an
d
f
o
u
r
th
m
o
d
el
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
g
iv
en
a
n
o
v
e
r
v
iew
o
f
th
e
th
r
ee
-
p
h
ase
th
r
ee
-
w
ir
e
HAPF
s
y
s
tem
s
,
in
clu
d
in
g
:
s
tr
u
ctu
r
es
o
f
HAPF,
ca
lcu
latio
n
o
f
p
ass
iv
e
p
o
wer
f
ilter
s
,
o
u
tp
u
t
f
ilter
d
esig
n
,
in
v
er
ter
s
tr
u
ctu
r
e
an
d
p
u
ls
e
wid
th
m
o
d
u
latio
n
m
eth
o
d
s
,
co
n
tr
o
l
s
tr
ateg
ies,
an
d
DC
lin
k
v
o
lta
g
e
s
tab
ilizatio
n
an
d
c
o
n
tr
o
l
m
eth
o
d
s
.
T
h
is
s
tu
d
y
also
s
er
v
es
as
a
b
asis
f
o
r
r
ese
ar
ch
er
s
to
r
esear
ch
,
a
p
p
ly
,
a
n
d
d
ev
elo
p
HAPF
in
p
r
ac
tice.
Stu
d
ies
h
av
e
p
r
o
v
en
th
at:
HAPF
h
as
m
an
y
ad
v
an
t
ag
es
in
h
ar
m
o
n
ic
f
ilter
in
g
an
d
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
.
Ho
wev
er
,
it
also
h
as
m
an
y
s
h
o
r
tco
m
in
g
s
th
at
n
ee
d
t
o
b
e
ad
d
r
ess
ed
in
th
e
f
u
tu
r
e
,
s
u
ch
as:
a
d
ap
tiv
e
c
o
n
tr
o
l
ac
c
o
r
d
in
g
to
ch
an
g
es
in
lo
ad
,
s
tab
ilizin
g
t
h
e
DC
lin
k
v
o
ltag
e
in
ca
s
e
th
e
lo
ad
h
as
lar
g
e
h
a
r
m
o
n
ic
c
ap
ac
ity
an
d
s
u
d
d
en
ch
an
g
es,
la
r
g
e
r
ea
ctiv
e
p
o
w
er
to
b
e
co
m
p
en
s
ated
,
lar
g
e
in
v
estme
n
t
co
s
ts
as
well
a
s
lo
s
s
e
s
d
u
r
in
g
th
e
s
witch
in
g
p
r
o
ce
s
s
,
s
h
o
r
t c
ir
cu
i
t o
r
o
p
e
n
cir
cu
it
o
f
th
e
s
em
ico
n
d
u
cto
r
s
witch
es o
f
th
e
in
v
e
r
ter
.
RE
F
E
R
E
NC
E
S
[
1
]
B
.
S
i
n
g
h
,
V
.
V
e
r
m
a
,
A
.
C
h
a
n
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a
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d
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f
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me
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Pro
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9
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p
-
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0
0
4
5
0
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7
.
[
2
]
S
.
D
a
s
B
i
sw
a
s,
S
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C
h
o
w
d
h
u
r
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C
.
N
a
n
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i
,
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n
d
B
.
D
a
s,
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P
o
w
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me
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p
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f
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l
t
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r
,
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n
2
0
2
3
I
EEE
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n
t
e
r
n
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t
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o
n
a
l
C
o
n
f
e
re
n
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n
P
o
w
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r
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e
c
t
ro
n
i
c
s,
S
m
a
rt
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r
i
d
,
a
n
d
R
e
n
e
w
a
b
l
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En
e
rg
y
:
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o
w
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r
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c
t
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m
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rt
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3
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0
4
1
2
6
.
[
3
]
I
.
A
l
h
a
mr
o
u
n
i
,
F
.
N
.
H
a
n
a
f
i
,
M
.
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a
l
e
m,
N
.
H
.
A
.
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ma
n
,
A
.
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so
h
,
a
n
d
T.
S
u
t
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k
n
o
,
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n
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sh
u
n
t
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y
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r
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d
a
c
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p
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l
t
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o
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p
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sa
t
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g
h
a
r
m
o
n
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c
c
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t
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e
l
k
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m
n
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k
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(
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c
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t
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n
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o
m
p
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El
e
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r
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n
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4
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1
5
1
5
6
.
[
4
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W
.
Z
h
a
o
,
R
.
C
h
e
n
,
a
n
d
A
.
Lu
o
,
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R
e
c
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si
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g
r
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En
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7
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.
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5
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W
.
K
.
S
o
u
e
t
a
l
.
,
“
A
d
e
a
d
b
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t
c
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o
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Em
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W
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Zh
a
o
,
A
.
Lu
o
,
Z.
J
.
S
h
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n
,
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,
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c
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r
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p
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1369
[
7
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C
.
W
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.
L
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o
,
Z.
L
v
,
Z.
S
h
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