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3
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Sep
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14
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6
1446
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p
p
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t
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VC
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o
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er
L
C
o
r
L
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L
f
il
ter
s
[
1
5
-
1
7
]
.
I
t
ca
n
b
e
s
ee
n
t
h
at
th
e
co
n
tr
o
l
m
et
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o
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t
h
e
DG
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n
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t
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al
i
m
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c
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th
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en
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o
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th
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tr
ic
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esis
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f
ee
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er
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t p
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s
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te
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r
e
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o
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ce
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
Fig
u
r
e
1
ill
u
s
tr
ates
th
e
co
n
f
i
g
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r
atio
n
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p
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ase
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G
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ar
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(
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co
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o
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ai
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C
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p
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y
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h
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s
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alo
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e
DG
u
n
it
s
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ab
l
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d
Fig
u
r
es
ar
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p
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ted
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ter
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as s
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o
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d
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d
L
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C
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Fig
u
r
e
1
.
Si
m
p
li
f
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o
n
e
-
li
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e
d
iag
r
a
m
o
f
a
s
in
g
le
p
h
a
s
e
m
ic
r
o
g
r
id
s
er
v
ice.
2
.
1
Dis
t
ribute
d P
a
ra
m
et
er
M
o
del in G
rid
-
T
ied O
pera
t
i
o
n
Fo
r
a
p
r
o
tr
ac
ted
f
ee
d
er
,
as
illu
s
tr
ated
in
F
ig
u
r
e
1
,
a
lu
m
p
ed
p
ar
am
eter
m
o
d
el
is
n
'
t
ab
le
to
d
escr
ib
e
its
r
eso
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an
ce
p
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p
ag
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n
ch
ar
ac
ter
is
tics
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A
lter
n
a
tiv
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th
e
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i
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u
ted
p
ar
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e
ter
m
o
d
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w
a
s
m
en
tio
n
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in
[
3
]
an
d
[
6
]
,
w
h
er
e
t
h
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v
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lta
g
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d
is
t
o
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k
t
h
P
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h
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f
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DG
Un
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th
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cu
r
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ased
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Fig
u
r
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2.
E
q
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k
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m
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(
x
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l
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N
o
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Fig
u
r
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3.
E
q
u
iv
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n
t c
ir
cu
it o
f
a
s
in
g
le
is
la
n
d
in
g
DG
u
n
i
t a
t th
e
k
t
h
h
ar
m
o
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ic
f
r
eq
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en
c
y
N
o
te
th
at
w
it
h
t
h
e
in
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g
r
al
co
n
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o
l
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late
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h
e
DG
u
n
it
v
o
ltag
e
m
ag
n
it
u
d
e
i
n
(
7
)
,
th
e
s
tead
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-
s
tate
r
ea
ctiv
e
p
o
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tr
o
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er
r
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r
in
th
e
g
r
id
tied
o
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er
atio
n
is
ze
r
o
.
On
ce
th
e
v
o
ltag
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m
a
g
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e
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en
ce
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h
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n
t
an
eo
u
s
v
o
lt
a
g
e
r
ef
er
en
ce
(
V
reff
)
ca
n
b
e
ea
s
il
y
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
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
14
4
5
–
14
5
6
1448
o
b
tain
ed
.
T
h
e
eq
u
iv
ale
n
t
i
m
p
ed
an
ce
o
f
VC
M
-
b
ased
DG
u
n
it
w
it
h
an
L
C
f
ilter
h
a
s
alr
ea
d
y
b
ee
n
tu
n
ed
to
b
e
r
esis
ti
v
e,
b
y
ad
d
in
g
a
DG
li
n
e
cu
r
r
en
t
(
I
DG
)
f
ee
d
-
f
o
r
w
ar
d
ter
m
t
o
th
e
v
o
lta
g
e
co
n
tr
o
l
r
ef
er
en
ce
.
A
lt
h
o
u
g
h
p
r
ev
io
u
s
V
C
M
-
b
ased
DG
eq
u
iv
ale
n
t
i
m
p
ed
an
ce
s
h
ap
i
n
g
te
ch
n
iq
u
es,
m
ai
n
l
y
f
o
cu
s
o
n
i
m
p
r
o
v
in
g
th
e
p
o
w
er
s
h
ar
i
n
g
p
er
f
o
r
m
an
ce
o
f
m
u
l
tip
le
DG
u
n
it
s
in
a
n
i
s
lan
d
i
n
g
m
i
cr
o
g
r
id
,
s
i
m
ilar
id
ea
ca
n
a
ls
o
b
e
u
s
ed
to
m
it
ig
ate
th
e
h
ar
m
o
n
ic
p
r
o
p
ag
atio
n
alo
n
g
th
e
f
ee
d
er
as
=
−
=
−
.
(
(
)
.
)
(
8
)
W
h
er
e
V
reff
is
t
h
e
f
u
n
d
a
m
e
n
ta
l
v
o
lta
g
e
r
ef
er
e
n
ce
d
er
iv
ed
f
r
o
m
d
r
o
o
p
co
n
tr
o
l
in
(
6
)
an
d
(
7
)
,
V
AD
i
s
th
e
h
ar
m
o
n
ic
v
o
lta
g
e
r
ef
er
en
c
e
f
o
r
DG
u
n
it
h
ar
m
o
n
ic
i
m
p
e
d
an
ce
s
h
ap
i
n
g
,
I
DG
i
s
th
e
m
ea
s
u
r
ed
DG
u
n
it
li
n
e
cu
r
r
en
t
as
s
h
o
w
n
in
Fi
g
u
r
e
1
,
H
D
(
s
)
is
th
e
tr
an
s
f
er
f
u
n
ct
io
n
o
f
a
h
ar
m
o
n
ic
d
etec
to
r
,
w
h
ic
h
ex
tr
ac
t
s
th
e
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
o
f
D
G
u
n
it
li
n
e
c
u
r
r
en
t,
an
d
R
V
i
s
th
e
v
ir
t
u
al
r
esis
tan
ce
co
m
m
an
d
.
Sin
ce
a
g
r
id
-
co
n
n
ec
ted
D
G
u
n
i
t
u
s
i
n
g
eit
h
er
C
C
M
o
r
VC
M
ca
n
b
e
m
o
d
eled
b
y
a
n
eq
u
i
v
ale
n
t
h
ar
m
o
n
ic
i
m
p
ed
an
ce
at
t
h
e
r
ec
eiv
in
g
e
n
d
o
f
th
e
f
ee
d
er
,
th
e
f
o
llo
w
in
g
b
o
u
n
d
ar
y
co
n
d
itio
n
s
ca
n
b
e
o
b
tain
ed
:
(
)
(
)
=
(
9
)
(
0
)
=
(
1
0
)
B
y
s
o
lv
i
n
g
(
1
)
,
(
2
)
,
(
9
)
,
an
d
(
1
0
)
,
th
e
h
ar
m
o
n
ic
v
o
lta
g
e
p
r
o
p
ag
atio
n
at
t
h
e
h
ar
m
o
n
ic
o
r
d
er
k
ca
n
b
e
ex
p
r
ess
ed
as
(
)
=
c
os
ℎ
(
(
−
)
)
+
s
in
ℎ
(
(
−
)
)
c
os
ℎ
(
)
+
s
in
ℎ
(
)
.
(
1
1
)
W
ith
th
e
o
b
tain
ed
eq
u
atio
n
i
n
(
1
1
)
,
th
e
im
p
ac
t
o
f
t
h
e
DG
ac
tiv
e
d
a
m
p
i
n
g
s
c
h
e
m
e
to
th
e
h
ar
m
o
n
ic
v
o
ltag
e
p
r
o
p
ag
atio
n
alo
n
g
t
h
e
f
ee
d
er
ca
n
b
e
ea
s
il
y
a
n
al
y
ze
d
.
No
te
th
at
w
h
e
n
th
e
m
icr
o
g
r
id
f
ee
d
er
is
p
u
r
el
y
R
L
i
m
p
ed
a
n
ce
,
t
h
e
DG
u
n
it
c
an
s
till
w
o
r
k
as
a
v
ir
tu
al
h
ar
m
o
n
ic
r
esi
s
to
r
at
t
h
e
e
n
d
o
f
t
h
e
f
ee
d
er
.
I
n
t
h
is
ca
s
e,
th
e
DG
u
n
it
h
a
s
t
h
e
ca
p
ab
ilit
y
o
f
ab
s
o
r
b
in
g
s
o
m
e
P
C
C
n
o
n
l
in
ea
r
lo
ad
cu
r
r
en
t
i
f
it
i
s
d
esi
g
n
ed
an
d
co
n
tr
o
lled
p
r
o
p
er
ly
2
.
2
.
Dis
t
ribute
d P
a
ra
m
et
er
M
o
del in Is
la
nd
ing
O
pera
t
io
n
T
h
e
p
r
ev
io
u
s
s
ec
tio
n
f
o
cu
s
es
o
n
t
h
e
an
al
y
s
is
o
f
g
r
id
-
tied
DG
u
n
i
ts
.
Fo
r
an
is
la
n
d
i
n
g
m
icr
o
g
r
id
s
y
s
te
m
,
t
h
e
V
C
M
o
p
er
atio
n
o
f
DG
u
n
it
s
i
s
n
ee
d
ed
f
o
r
d
i
r
ec
t
v
o
lta
g
e
s
u
p
p
o
r
t.
T
o
th
e
b
est
o
f
th
e
au
th
o
r
s
’
k
n
o
w
led
g
e,
th
e
q
u
a
n
titat
iv
e
a
n
al
y
s
i
s
o
f
is
la
n
d
in
g
m
icr
o
g
r
id
h
ar
m
o
n
ic
p
r
o
p
ag
atio
n
is
n
o
t
av
ailab
le.
W
h
e
n
o
n
l
y
a
s
in
g
le
DG
u
n
it
is
p
lac
ed
in
th
e
is
lan
d
i
n
g
s
y
s
te
m
,
co
n
s
ta
n
t
v
o
lta
g
e
m
a
g
n
it
u
d
e
an
d
co
n
s
ta
n
t
f
r
eq
u
e
n
c
y
(
C
VM
C
F)
co
n
tr
o
l
ca
n
b
e
u
s
e
d
.
M
u
ltip
le
D
G
u
n
i
ts
in
th
e
m
icr
o
g
r
id
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
,
th
e
d
r
o
o
p
co
n
tr
o
l
m
et
h
o
d
in
(
6
)
a
n
d
(
7
)
[
b
y
s
ett
in
g
KQ
=
0
in
(
7
)
]
s
h
all
b
e
e
m
p
lo
y
ed
to
r
ea
lize
p
r
o
p
er
p
o
w
er
s
h
ar
in
g
a
m
o
n
g
th
ese
DG
u
n
it
s
.
C
o
n
s
id
er
i
n
g
th
e
f
o
cu
s
o
f
t
h
i
s
s
ec
tio
n
is
to
in
v
es
tig
a
te
t
h
e
h
ar
m
o
n
ic
v
o
l
tag
e
d
a
m
p
in
g
in
a
s
tan
d
alo
n
e
is
la
n
d
in
g
s
y
s
te
m
,
a
s
in
g
le
DG
u
n
it
at
t
h
e
r
ec
ei
v
i
n
g
e
n
d
o
f
t
h
e
f
ee
d
er
is
co
n
s
id
er
ed
.
T
h
e
cir
cu
it
m
o
d
el
o
f
an
is
la
n
d
in
g
s
y
s
te
m
at
t
h
e
h
ar
m
o
n
ic
o
r
d
er
k
i
s
ill
u
s
tr
ated
in
Fi
g
u
r
e
3
,
W
it
h
t
h
e
k
n
o
w
led
g
e
o
f
b
o
u
n
d
ar
y
co
n
d
itio
n
s
at
b
o
th
s
e
n
d
in
g
an
d
r
ec
eiv
in
g
en
d
s
a
s
(
0
)
=
(
1
2
)
(
)
(
)
=
(
1
3
)
T
h
e
k
th
h
ar
m
o
n
ic
v
o
ltag
e
d
i
s
t
o
r
tio
n
alo
n
g
t
h
e
f
ee
d
er
ca
n
b
e
o
b
tain
ed
(
)
=
(
−
1
+
(
(
−
)
/
(
+
)
)
2
−
1
+
(
(
+
)
−
)
)
)
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
R
eso
n
a
n
ce
p
r
o
p
a
g
a
tio
n
a
n
d
E
limin
a
tio
n
in
I
n
te
g
r
a
ted
a
n
d
I
s
la
n
d
ed
Micr
o
g
r
id
s
(
K
.
V
.
S
iva
R
ed
d
y
)
1449
Fro
m
(
1
4
)
,
it
ca
n
b
e
n
o
ticed
th
at
t
h
e
v
o
lta
g
e
p
r
o
p
ag
atio
n
i
n
a
n
i
s
lan
d
i
n
g
s
y
s
te
m
h
ar
m
o
n
ic
i
s
al
s
o
r
elate
d
to
th
e
DG
-
u
n
it
eq
u
i
v
alen
t
h
ar
m
o
n
ic
i
m
p
ed
a
n
ce
.
I
n
o
r
d
er
to
m
ain
ta
in
s
ati
s
f
ied
v
o
ltag
e
q
u
ali
t
y
,
th
e
eq
u
iv
ale
n
t
h
ar
m
o
n
ic
i
m
p
ed
an
ce
o
f
is
lan
d
i
n
g
DG
u
n
it
s
s
h
all
also
b
e
p
r
o
p
er
ly
d
esi
g
n
ed
.
3.
RE
A
L
I
Z
AT
I
O
N
O
F
VIR
T
U
AL
DAM
P
I
NG
I
M
P
E
DANC
E
T
H
RO
U
G
H
D
G
VO
L
T
A
G
E
CO
NT
RO
L
I
t
h
as
b
ee
n
clar
i
f
ied
t
h
at
a
n
L
C
L
f
il
ter
g
r
id
-
s
id
e
in
d
u
ct
o
r
(
L
2
)
ca
n
af
f
ec
t
t
h
e
p
er
f
o
r
m
an
ce
o
f
d
is
tr
ib
u
tio
n
s
y
s
te
m
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
,
esp
ec
iall
y
i
n
th
e
ca
s
e
o
f
m
u
ltip
le
DG
u
n
its
.
I
n
o
r
d
er
to
co
m
p
en
s
ate
th
e
i
m
p
ac
t
o
f
L
C
L
f
ilter
g
r
id
-
s
id
e
in
d
u
cto
r
,
th
e
h
ar
m
o
n
ic
v
o
ltag
e
d
a
m
p
i
n
g
s
c
h
e
m
e
as
s
h
o
w
n
in
(
8
)
s
h
all
b
e
f
u
r
t
h
er
i
m
p
r
o
v
ed
.
3
.
1
.
Co
nv
ent
i
o
na
l V
o
lt
a
g
e
T
ra
ck
i
ng
First,
a
n
eg
a
tiv
e
v
ir
tu
a
l
in
d
u
cto
r
ca
n
b
e
p
r
o
d
u
ce
d
b
y
VC
M.
A
cc
o
r
d
in
g
l
y
,
t
h
e
m
o
d
if
ie
d
v
o
ltag
e
r
ef
er
en
ce
is
o
b
tain
ed
as
=
−
−
=
−
(
)
.
−
(
−
2
)
.
(
)
.
(
1
5
)
B
y
f
u
r
th
er
lo
o
k
i
n
g
in
to
(
1
5
)
,
o
n
e
ca
n
f
in
d
t
h
at
t
h
e
i
m
p
le
m
en
tatio
n
o
f
v
ir
t
u
al
i
n
d
u
cto
r
in
v
o
l
v
es
d
er
iv
ativ
e
o
p
er
atio
n
,
w
h
ic
h
m
a
y
ad
v
er
s
el
y
a
m
p
li
f
y
s
y
s
te
m
b
ac
k
g
r
o
u
n
d
n
o
i
s
es.
Fo
r
in
s
tan
ce
,
if
a
b
an
d
-
s
to
p
f
ilter
is
s
elec
ted
to
f
ilter
o
u
t t
h
e
f
u
n
d
a
m
e
n
tal
co
m
p
o
n
en
ts
as
(
)
=
1
−
2
2
+
2
+
2
(
1
6
)
W
h
er
e
ω
BP
is
th
e
cu
to
f
f
b
an
d
w
id
t
h
o
f
th
e
b
an
d
-
s
to
p
f
il
ter
,
th
e
v
o
lta
g
e
co
m
p
en
s
atio
n
ter
m
V
Co
m
p
i
n
(
1
5
)
ca
n
b
e
ex
p
r
ess
ed
as
=
(
−
2
)
.
(
)
=
(
−
2
+
2
2
2
2
+
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u
r
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I
SS
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2
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u
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.
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[
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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F
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4
.
3
.
M
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s
G
ri
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ied O
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t
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n
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er
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cir
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m
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n
it
s
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t
w
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g
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co
n
n
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ted
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u
n
it
s
at
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e
s
a
m
e
p
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w
er
r
at
in
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ar
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p
lace
d
at
t
h
e
r
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n
g
e
n
d
o
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th
e
f
ee
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er
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t
h
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m
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ee
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eiv
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d
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ilt
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le
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it 2
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as a
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LC
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u
r
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1
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.
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m
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allel
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n
its
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.
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h
e
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v
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h
ar
m
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n
ic
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t
o
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t
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Fi
g
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.
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ir
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k
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h
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w
n
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e
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ir
s
t
co
lu
m
n
o
f
Fig
u
r
e
10
.
I
n
th
i
s
ca
s
e,
t
h
er
e
ar
e
s
o
m
e
v
o
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g
e
d
is
to
r
tio
n
s
a
t
th
e
n
o
d
es
1
an
d
3
.
W
h
en
o
n
l
y
v
ir
t
u
al
r
es
is
to
r
r
eg
u
la
tio
n
u
s
in
g
(
8
)
is
ap
p
lied
t
o
b
o
th
DG
u
n
it
s
,
it
ca
n
b
e
s
e
en
f
r
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m
t
h
e
s
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o
n
d
co
lu
m
n
o
f
F
ig
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r
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1
4
t
h
at
h
ar
m
o
n
ic
v
o
lta
g
e
d
is
to
r
tio
n
ar
e
m
it
ig
ated
.
Evaluation Warning : The document was created with Spire.PDF for Python.