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ca
p
ac
ito
r
s
an
d
in
d
u
cto
r
s
.
Sev
er
al
m
et
h
o
d
s
o
f
p
ass
i
v
e
d
am
p
i
n
g
[
1
1
]
-
[
1
2
]
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
s
tiff
g
r
id
o
p
er
atio
n
.
On
t
h
e
o
th
er
h
a
n
d
,
th
e
ac
ti
v
e
d
a
m
p
i
n
g
m
et
h
o
d
is
u
s
ed
w
i
th
co
s
tl
y
s
e
n
s
o
r
s
a
n
d
p
o
w
er
elec
tr
o
n
ic
s
f
o
r
w
ea
k
g
r
id
an
d
d
y
n
a
m
ic
g
r
id
v
ar
iatio
n
s
.
T
h
is
p
ap
er
m
ai
n
l
y
f
o
cu
s
e
s
o
n
co
n
tr
o
l
s
tr
u
ct
u
r
e
o
f
s
in
g
le
p
h
a
s
e
g
r
id
co
n
n
ec
ted
P
V
in
v
er
ter
w
it
h
f
ilter
d
esig
n
a
n
al
y
s
i
s
.
Sectio
n
I
I
i
llu
s
tr
ates
th
e
co
n
s
tr
ain
t
s
o
f
t
h
e
L
C
L
f
ilter
d
es
ig
n
a
n
d
i
m
p
o
r
tan
ce
o
f
Q
-
f
ac
to
r
w
i
t
h
s
en
s
iti
v
it
y
an
al
y
s
is
.
An
i
m
p
r
o
v
ed
L
L
C
L
f
il
ter
is
i
n
tr
o
d
u
c
ed
,
in
o
r
d
er
to
r
e
d
u
ce
th
e
to
t
al
in
d
u
cta
n
ce
o
f
th
e
co
n
v
e
n
tio
n
al
f
ilter
.
T
h
e
m
o
d
i
f
ied
L
L
C
L
f
il
ter
is
d
esig
n
ed
w
ith
o
u
t
a
n
y
ch
a
n
g
e
i
n
t
h
e
f
r
eq
u
en
c
y
r
e
s
p
o
n
s
e
ch
ar
ac
ter
is
tic
o
f
L
C
L
f
ilter
.
Mo
r
e
ad
v
an
ta
g
e
i
n
s
u
p
p
r
ess
i
n
g
t
h
e
r
eso
n
an
ce
p
ea
k
w
ith
i
m
p
r
o
v
ed
s
tab
ilit
y
an
d
d
y
n
a
m
ic
r
esp
o
n
s
e.
T
h
r
ee
ca
s
es
o
f
p
ar
a
m
eter
d
esi
g
n
h
a
v
e
b
ee
n
d
if
f
er
en
tiated
an
d
a
n
al
y
ze
d
w
it
h
s
i
m
u
lated
r
esu
lt
s
i
n
s
ec
tio
n
I
I
I
.
I
m
p
r
o
v
ed
cu
r
r
en
t
co
n
tr
o
l
s
tr
u
ct
u
r
e
i
s
s
ee
n
i
n
s
ec
t
io
n
I
V
b
y
i
m
p
l
e
m
en
tin
g
f
ee
d
b
ac
k
lin
ea
r
izatio
n
f
o
r
f
ast
D
C
v
o
lt
ag
e
co
n
tr
o
l
ap
p
lied
to
PW
M
in
v
er
ter
.
A
n
d
it
is
v
er
i
f
ied
b
y
m
o
d
eli
n
g
a
s
i
n
g
le
p
h
ase
g
r
id
co
n
n
ec
ted
P
V
in
v
er
ter
w
it
h
s
i
m
u
lated
an
d
ex
p
er
i
m
en
tal
r
esu
lts
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
A
ND
CH
ARAC
T
E
R
I
S
T
I
C
S
2
.
1
.
Cla
s
s
ica
l
M
et
ho
ds
a
nd
Co
ns
t
ra
ints o
n L
C
L
F
ilte
r
D
esig
n
I
n
g
r
id
p
o
w
er
co
n
v
er
ter
s
,
s
w
it
ch
in
g
f
r
eq
u
en
cie
s
at
in
ter
v
al
s
3
-
2
0
k
Hz
ca
u
s
es
g
r
ea
ter
h
ar
m
o
n
ics
an
d
d
is
tu
r
b
s
t
h
e
elec
tr
ic
g
r
id
.
I
t
is
th
er
ef
o
r
e
ess
e
n
tial
to
atte
n
u
a
t
e
th
e
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
h
ar
m
o
n
ic
s
an
d
r
ed
u
ce
th
e
c
u
r
r
en
t r
ip
p
les to
f
u
lf
ill t
h
e
s
tan
d
ar
d
s
o
f
t
h
e
I
E
E
E
1
5
4
7
.
2
.
Hig
h
f
r
eq
u
e
n
c
y
co
m
p
o
n
e
n
t
cu
r
r
en
ts
w
o
u
ld
lead
to
elec
tr
o
m
ag
n
etic
in
ter
f
er
en
c
e
n
o
is
e
m
ai
n
l
y
d
u
e
to
th
e
p
ar
asit
ic
ca
p
ac
ita
n
ce
d
is
t
u
r
b
in
g
t
h
e
b
eh
a
v
io
r
o
f
h
i
g
h
f
r
eq
u
en
c
ies.
T
h
e
m
et
h
o
d
o
f
d
esig
n
i
n
g
L
C
L
f
ilter
s
d
ep
en
d
s
o
n
r
ati
n
g
o
f
p
o
w
er
co
n
v
er
ter
s
,
f
u
n
d
a
m
e
n
tal
a
n
d
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
a
s
in
p
u
t
s
w
i
th
an
i
n
te
g
r
ated
co
n
tr
o
l
d
esig
n
o
f
f
ilter
s
as
ex
p
lain
ed
in
[
1
3
]
.
Fro
m
th
e
Fig
u
r
e
2
(
a)
.
th
e
i
n
v
er
ter
o
u
tp
u
t
i
n
d
u
cto
r
L
1
,
t
h
e
f
ilter
ca
p
a
cito
r
C
f
,
a
n
d
th
e
g
r
id
-
s
id
e
i
n
d
u
cto
r
L
2
co
n
s
t
itu
te
th
e
L
C
L
f
ilter
o
f
th
e
in
v
er
ter
.
C
o
m
p
ar
ed
to
L
f
ilter
,
L
C
L
f
il
t
er
is
p
r
o
v
ed
to
h
a
v
e
a
b
etter
h
ar
m
o
n
ic
at
ten
u
atio
n
f
o
r
th
e
r
ed
u
ctio
n
o
f
f
ilter
in
d
u
ctan
ce
v
o
lu
m
e
[
1
4
]
w
h
ic
h
b
y
p
a
s
s
t
h
e
h
i
g
h
f
r
eq
u
e
n
c
y
h
ar
m
o
n
ic
s
th
r
o
u
g
h
th
e
ca
p
ac
itan
ce
b
r
an
ch
.
T
h
e
s
co
p
e
is
to
lo
w
er
th
e
h
i
g
h
er
o
r
d
er
h
ar
m
o
n
ics
o
n
th
e
g
r
id
s
id
e
an
d
to
r
ed
u
ce
th
e
o
s
cillatio
n
e
f
f
ec
t
s
.
T
h
er
ef
o
r
e,
in
L
C
L
f
ilter
d
esi
g
n
,
i
n
d
u
cto
r
s
s
h
o
u
ld
b
e
p
r
o
p
er
ly
d
esig
n
e
d
in
o
b
s
er
v
in
g
t
h
e
cu
r
r
en
t
r
ip
p
le,
f
il
ter
ca
p
ac
itan
ce
an
d
d
a
m
p
in
g
o
f
r
eso
n
a
n
ce
i
n
f
ilter
s
.
T
h
e
r
eso
n
a
n
t
f
r
eq
u
e
n
c
y
s
h
o
u
ld
b
e
i
n
th
e
r
an
g
e
10ω
0
≤
ω
r
es
≤
ω
sw
2
[
1
5
]
.
Fig
u
r
e
2
(
b
)
,
(
c)
d
ep
icts
th
e
p
ass
iv
e
d
a
m
p
ed
to
p
o
l
o
g
y
o
f
L
C
L
f
i
lter
.
Fre
q
u
en
c
y
r
esp
o
n
s
e
a
n
al
y
s
i
s
o
f
p
ass
i
v
e
d
a
m
p
ed
L
C
L
f
il
ter
s
w
it
h
d
a
m
p
in
g
r
es
is
to
r
s
in
s
e
r
ies
to
atte
n
u
a
te
t
h
e
r
eso
n
an
ce
w
it
h
th
e
tr
an
s
f
er
f
u
n
ct
io
n
as
in
(
1
)
an
d
im
p
r
o
v
ed
m
et
h
o
d
s
w
i
th
p
ass
iv
e
ele
m
en
ts
as
in
(
2
)
ar
e
s
h
o
w
n
in
F
ig
u
r
e
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
114
–
1
2
5
116
Fig
u
r
e
2
.
a)
.
L
C
L
f
il
ter
,
b
)
p
as
s
iv
e
d
a
m
p
ed
L
C
L
f
ilter
w
it
h
R
d
,
c)
p
ass
iv
e
d
a
m
p
ed
L
C
L
f
ilt
er
w
it
h
R
d
-
C
d
T
r
an
s
f
er
f
u
n
ctio
n
o
f
L
C
L
f
ilte
r
:
G
v
i
→
i
g
(
s
)
=
i
g
(
s
)
v
i
(
s
)
=
1
L
2
(
S
2
+
R
d
C
f
Z
2
LC
S
+
Z
2
LC
)
(
S
2
+
R
d
C
f
ω
r
e
s
2
S
+
ω
r
e
s
2
)
(
1
)
I
f
R
d
is
ze
r
o
th
e
n
,
G
v
i
→
i
g
(
s
)
=
i
g
(
s
)
v
i
(
s
)
=
1
L
2
(
S
2
+
Z
2
LC
)
(
S
2
+
ω
r
es
2
)
W
h
er
e,
Z
2
LC
=
[
L
1
C
f
]
−
1
ω
2
r
es
=
L
2
Z
LC
2
L
Fo
r
i
m
p
r
o
v
ed
p
ass
iv
e
d
a
m
p
i
n
g
,
G
v
i
→
i
g
(
s
)
=
i
g
(
s
)
v
i
(
s
)
=
(
R
d
C
d
S
+
1
)
S
(
L
1
L
2
R
d
C
d
C
f
S
3
+
L
1
L
2
(
C
d
+
C
f
)
S
2
+
R
d
C
d
(
L
1
+
L
2
)
S
+
L
1
L
2
)
(
2
)
Fro
m
Fi
g
u
r
e
3
it
i
s
clea
r
t
h
at
th
e
m
a
g
n
i
tu
d
e
o
f
L
C
L
f
il
ter
i
s
h
i
g
h
w
i
th
a
r
eso
n
a
n
t
p
ea
k
g
ain
o
f
2
5
0
d
B
at
4
.
6
k
Hz.
Ho
w
ev
er
,
i
n
p
ass
i
v
e
d
a
m
p
i
n
g
a
n
d
i
m
p
r
o
v
ed
p
ass
iv
e
d
a
m
p
in
g
,
t
h
e
atte
n
u
ati
o
n
is
r
ed
u
ce
d
to
1
0
d
B
o
r
less
th
a
n
th
at
at
2
.
5
k
Hz
w
it
h
s
o
m
e
p
o
w
er
lo
s
s
d
u
e
to
th
e
r
esis
to
r
.
Fig
u
r
e
3
.
Fre
q
u
en
c
y
r
e
s
p
o
n
s
e
o
f
L
C
L
f
i
lter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
Desig
n
o
f O
p
tima
l LLC
L F
ilte
r
w
ith
a
n
I
mp
r
o
ve
d
C
o
n
tr
o
l S
t
r
a
teg
y
fo
r
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in
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P
h
a
s
e
Gri
d
…
(
K
.
A
r
u
lku
ma
r
)
117
2
.
2
.
Select
io
n o
f
F
ilte
r
Ca
pa
c
it
a
nce
(
C
f
)
T
h
e
s
elec
tio
n
o
f
ca
p
ac
ito
r
[
1
6
]
is
d
eter
m
i
n
ed
b
et
w
ee
n
r
ea
ctiv
e
p
o
w
er
i
n
C
f
an
d
L
1
.
I
f
t
h
e
ca
p
ac
itan
ce
is
h
ig
h
,
t
h
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
in
g
i
n
to
it
is
m
o
r
e
w
h
ic
h
lead
s
to
cu
r
r
en
t
d
em
an
d
s
in
L
1
.
I
n
t
h
e
d
esig
n
co
n
s
id
er
atio
n
lar
g
e
i
n
d
u
ctan
ce
(
L
1
)
an
d
s
m
aller
ca
p
ac
itan
ce
(
C
f
)
lead
to
th
e
v
o
ltag
e
d
r
o
p
ac
r
o
s
s
th
e
in
d
u
cto
r
L
1
.
So
,
r
ea
ctiv
e
p
o
wer
is
ch
o
s
e
n
1
5
%
o
f
r
ated
p
o
w
er
as
in
(
3
)
an
d
f
r
o
m
th
at
th
e
ca
p
ac
itan
ce
v
a
lu
e
ca
n
b
e
ch
o
s
en
a
s
:
C
=
15%
P
r
at
ed
3
∗
2π
f
l
ine
V
r
at
ed
2
(
3
)
W
h
er
e,
P
rated
is
r
ated
p
o
w
er
an
d
V
rated
is
g
r
id
R
MS
v
o
ltag
e.
2
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m
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t
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e
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h
e
v
al
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e
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Q
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f
ac
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r
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ce
s
i
n
p
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m
p
i
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a
d
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m
in
a
n
t r
eso
n
an
t
f
r
eq
u
e
n
c
y
[
1
7
]
.
T
h
e
q
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a
lit
y
f
ac
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o
f
L
f
-
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f
ca
n
b
e
ex
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f
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L
f
C
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4
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r
r
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a
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3
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DE
SI
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DIFIE
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ased
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ted
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r
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ip
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L
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[
1
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ig
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atic
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c
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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0
8
8
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8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
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Ma
r
ch
2
0
1
8
:
114
–
1
2
5
118
3
.
1
.
P
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s
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Da
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L
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CL
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r
Mo
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if
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L
L
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L
f
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to
p
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lo
g
y
[
1
9
]
is
u
s
ed
to
r
ed
u
ce
th
e
d
a
m
p
in
g
p
o
w
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d
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ig
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m
o
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s
h
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w
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Fi
g
u
r
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5
(
a)
,
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b
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.
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ies
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it
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th
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ig
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5
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g
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c
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n
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s
a
m
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s
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h
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u
r
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L
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Fig
u
r
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6
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ased
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n
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r
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6
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6
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d
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
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I
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N:
2
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8
8
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694
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