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o
n
l
y
i
n
o
n
e
DG
s
y
s
te
m
.
I
n
o
r
d
er
to
o
v
er
co
m
e
t
h
e
af
o
r
em
e
n
tio
n
ed
p
r
o
b
lem
,
in
te
n
s
iv
e
r
esear
c
h
es
ha
ve
b
ee
n
co
n
d
u
cted
to
d
ev
elo
p
a
m
eth
o
d
w
it
h
o
u
t
r
eq
u
ir
in
g
a
n
y
i
n
ter
co
n
n
ec
tio
n
b
etw
ee
n
p
ar
allel
-
co
n
n
ec
ted
in
v
er
ter
s
.
Am
o
n
g
t
h
es
e
m
et
h
o
d
s
,
a
d
r
o
o
p
co
n
tr
o
l
s
ch
e
m
e
h
as
b
ee
n
p
r
o
v
en
as
th
e
m
o
s
t
s
i
m
p
le
an
d
ef
f
ec
ti
v
e
o
n
e
[
5
]
.
Gen
er
all
y
,
th
e
d
r
o
o
p
m
et
h
o
d
is
s
i
m
p
le
to
i
m
p
le
m
en
t
a
n
d
it
d
o
es
n
o
t
r
eq
u
ir
e
an
y
co
m
m
u
n
icatio
n
b
et
w
ee
n
m
o
d
u
le
s
.
B
esid
es,
th
e
d
r
o
o
p
c
o
n
tr
o
l
h
as
th
e
p
lu
g
-
a
n
d
-
p
la
y
f
ea
tu
r
e
,
w
h
ic
h
en
a
b
les
th
e
s
y
s
te
m
ex
p
a
n
s
io
n
to
b
e
ea
s
y
a
n
d
allo
w
s
r
ep
lacin
g
DG
u
n
it
w
it
h
i
n
t
h
e
s
y
s
te
m
w
it
h
o
u
t
m
a
k
i
n
g
th
e
en
t
ir
e
s
y
s
te
m
s
h
u
td
o
w
n
.
T
h
er
ef
o
r
e,
th
is
co
n
f
i
g
u
r
atio
n
o
f
m
icr
o
g
r
id
is
q
u
ite
s
u
itab
le
f
o
r
ap
p
licatio
n
s
in
w
h
ich
D
G
s
y
s
te
m
s
s
p
r
ea
d
in
a
w
id
e
ar
ea
.
T
h
e
d
r
o
o
p
co
n
tr
o
l
s
ch
e
m
e
w
a
s
in
itial
l
y
d
ev
elo
p
ed
f
o
r
th
e
p
r
ed
o
m
i
n
a
n
tl
y
i
n
d
u
ct
iv
e
t
r
an
s
m
i
s
s
io
n
li
n
e.
W
h
en
t
h
e
d
r
o
o
p
co
n
tr
o
l
is
i
m
p
le
m
en
ted
i
n
a
n
in
d
u
cti
v
e
m
i
cr
o
g
r
id
,
its
ef
f
ec
ti
v
en
e
s
s
i
n
te
r
m
s
o
f
d
i
s
tr
ib
u
ti
n
g
to
tal
lo
ad
d
e
m
an
d
a
m
o
n
g
al
l
th
e
DG
s
y
s
te
m
s
w
it
h
i
n
m
icr
o
g
r
id
h
a
s
b
ee
n
p
r
o
v
e
n
i
n
[
6
]
.
Ho
w
e
v
er
,
th
e
lo
ad
s
h
ar
i
n
g
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
c
o
n
v
e
n
tio
n
al
d
r
o
o
p
co
n
tr
o
l
s
c
h
e
m
e
i
s
de
g
r
ad
ed
w
h
en
t
h
e
t
r
an
s
m
is
s
io
n
li
n
e
i
s
p
r
ed
o
m
in
a
n
tl
y
r
e
s
is
t
iv
e.
T
o
s
o
lv
e
s
u
ch
a
p
r
o
b
le
m
,
a
v
a
r
iatio
n
o
f
t
h
e
d
r
o
o
p
co
n
tr
o
l
s
c
h
e
m
e
h
as
b
ee
n
in
tr
o
d
u
ce
d
f
o
r
th
e
r
esis
t
iv
e
li
n
e
ca
s
e
in
[
7
]
as
th
e
p
u
r
p
o
s
e
o
f
p
r
o
v
id
in
g
a
g
o
o
d
l
o
ad
s
h
ar
in
g
p
er
f
o
r
m
a
n
ce
u
n
d
er
all
co
n
d
itio
n
.
Ho
w
e
v
er
,
th
e
se
d
r
o
o
p
co
n
tr
o
l
s
ch
e
m
e
s
s
till
ha
v
e
o
n
e
s
ig
n
i
f
ica
n
t
d
r
a
w
b
ac
k
,
w
h
ich
is
t
h
e
p
o
w
er
s
h
ar
in
g
p
er
f
o
r
m
a
n
ce
i
s
h
ig
h
l
y
s
e
n
s
iti
v
e
to
li
n
e
i
m
p
ed
an
ce
d
i
f
f
er
e
n
ce
b
et
w
ee
n
i
n
v
er
ter
s
.
E
s
p
ec
iall
y
,
t
h
e
r
ea
ctiv
e
p
o
w
er
s
ar
e
n
o
t p
r
o
p
er
l
y
s
h
ar
ed
b
et
w
ee
n
i
n
v
er
ter
s
wh
en
t
h
e
li
n
e
i
m
p
ed
an
ce
b
et
w
e
en
t
h
e
i
n
v
er
ter
s
a
n
d
th
e
p
o
in
t o
f
co
m
m
o
n
co
u
p
li
n
g
(
P
C
C
)
is
d
if
f
er
e
n
t.
T
h
is
p
r
o
b
lem
h
a
s
b
ee
n
s
o
lv
e
d
in
[
8
]
b
y
i
n
tr
o
d
u
ci
n
g
a
r
o
b
u
s
t
v
ir
t
u
al
i
m
p
ed
an
ce
lo
o
p
w
h
ic
h
ca
n
ch
an
g
e
th
e
i
n
v
er
ter
o
u
tp
u
t
i
m
p
ed
a
n
ce
a
s
w
el
l
as
m
iti
g
at
e
v
o
lta
g
e
d
is
to
r
tio
n
p
r
o
b
le
m
ca
u
s
ed
b
y
h
ar
m
o
n
ic
lo
ad
s
.
T
h
is
r
o
b
u
s
t
i
m
p
ed
an
ce
m
et
h
o
d
also
i
m
p
r
o
v
es
th
e
p
o
w
er
s
h
ar
in
g
p
er
f
o
r
m
a
n
ce
d
u
r
i
n
g
tr
a
n
s
ie
n
t
an
d
g
r
id
f
au
lt.
T
h
is
v
ir
tu
al
i
m
p
ed
a
n
ce
m
et
h
o
d
is
p
r
o
v
en
e
f
f
ec
ti
v
e
to
en
h
a
n
ce
t
h
e
p
o
w
er
s
h
ar
i
n
g
s
tab
ilit
y
a
n
d
to
eli
m
i
n
at
e
c
ir
cu
lati
n
g
c
u
r
r
en
t
s
b
et
w
ee
n
in
v
er
ter
s
.
I
n
[
9
]
-
[
1
1
]
,
v
ir
tu
al
i
m
p
ed
an
ce
h
a
s
b
e
en
i
m
p
le
m
en
ted
in
o
r
d
er
to
ac
h
iev
e
ac
cu
r
ate
r
ea
ctiv
e
p
o
w
er
s
h
ar
in
g
w
h
e
n
t
h
e
lin
e
i
m
p
ed
an
ce
b
et
w
ee
n
in
v
er
ter
s
is
d
if
f
er
en
t.
Ho
w
e
v
er
,
n
o
n
e
o
f
t
h
e
a
f
o
r
e
m
e
n
tio
n
ed
v
ar
iatio
n
s
o
f
v
ir
t
u
al
i
m
p
ed
a
n
ce
h
as
co
n
s
id
er
ed
th
e
ca
s
e
o
f
v
ar
y
i
n
g
li
n
e
i
m
p
ed
an
ce
d
u
r
i
n
g
o
p
er
atio
n
s
.
I
n
s
o
m
e
E
u
r
o
p
ea
n
co
u
n
tr
ies
,
an
es
ti
m
atio
n
o
f
g
r
id
i
m
p
ed
an
ce
is
a
m
a
n
d
ato
r
y
f
u
n
c
tio
n
f
or
a
p
h
o
to
v
o
ltaic
(
P
V)
s
y
s
te
m
co
n
n
ec
ted
to
t
h
e
u
ti
lit
y
g
r
id
f
o
r
is
lan
d
in
g
d
etec
tio
n
[
1
2
]
.
T
h
is
r
eq
u
ir
e
m
e
n
t
d
r
e
w
t
h
e
ac
ad
em
i
c
atte
n
tio
n
to
w
ar
d
g
r
i
d
i
m
p
ed
an
ce
id
e
n
ti
f
icatio
n
.
I
n
ad
d
itio
n
,
t
h
e
i
n
f
o
r
m
atio
n
o
n
li
n
e
i
m
p
ed
an
ce
is
u
s
e
f
u
l
f
o
r
f
a
u
lt
d
etec
tio
n
,
g
r
i
d
u
n
b
alan
ce
d
etec
tio
n
,
an
d
co
n
tr
o
l
p
u
r
p
o
s
es.
I
n
[
1
2
]
,
th
e
au
th
o
r
s
p
r
ese
n
t
ed
a
m
et
h
o
d
to
esti
m
ate
lin
e
i
m
p
ed
an
ce
u
s
i
n
g
t
h
e
v
ar
iatio
n
o
f
ac
t
iv
e
an
d
r
ea
cti
v
e
p
o
w
er
s
d
i
s
p
at
ch
ed
b
y
in
v
er
ter
s
.
T
h
is
m
eth
o
d
r
eq
u
ir
es
in
d
u
cin
g
th
e
v
ar
iat
io
n
o
f
b
o
th
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
s
m
a
n
u
a
ll
y
an
d
f
r
eq
u
e
n
tl
y
,
w
h
ic
h
is
u
n
d
es
ir
ab
le
in
a
d
r
o
o
p
co
n
tr
o
l
s
y
s
te
m
.
An
au
to
m
ated
i
m
p
ed
an
ce
e
s
ti
m
atio
n
m
et
h
o
d
h
as
b
ee
n
in
tr
o
d
u
ce
d
in
[
1
3
]
by
u
s
in
g
an
o
p
ti
m
izatio
n
a
lg
o
r
it
h
m
.
D
esp
ite
its
g
o
o
d
p
er
f
o
r
m
a
n
ce
in
li
n
e
i
m
p
ed
an
ce
esti
m
atio
n
,
t
h
is
m
e
th
o
d
s
u
f
f
er
s
f
r
o
m
h
i
g
h
co
m
p
u
tatio
n
a
l
b
u
r
d
en
,
an
d
th
u
s
,
it
ca
n
n
o
t
b
e
o
p
er
ate
d
in
r
ea
l
ti
m
e.
An
o
th
er
i
m
p
ed
a
n
ce
es
ti
m
atio
n
m
et
h
o
d
u
s
i
n
g
m
o
d
al
a
n
al
y
s
is
t
h
eo
r
y
h
a
s
b
ee
n
p
r
o
p
o
s
ed
to
ca
lcu
late
t
h
e
li
n
e
i
m
p
ed
an
ce
i
n
r
ea
l
ti
m
e
[
1
4
]
.
Ho
w
e
v
er
,
th
is
m
et
h
o
d
is
to
o
co
m
p
lica
ted
an
d
r
eq
u
ir
e
s
a
lo
t
o
f
ap
p
r
o
x
i
m
atio
n
an
d
s
i
m
p
li
f
icatio
n
d
u
r
in
g
ca
lc
u
latio
n
p
r
o
ce
s
s
,
w
h
ic
h
r
es
u
lt
s
in
lar
g
e
er
r
o
r
s
i
n
i
n
d
u
cta
n
ce
c
alcu
latio
n
.
I
n
[
1
5
]
,
a
co
m
b
i
n
atio
n
o
f
th
e
n
o
n
i
n
tr
u
s
iv
e
p
as
s
iv
e
m
et
h
o
d
s
an
d
th
e
ac
tiv
e
m
eth
o
d
s
h
as
b
ee
n
e
m
p
l
o
y
ed
to
esti
m
ate
t
h
e
lin
e
i
m
p
ed
a
n
ce
in
m
icr
o
g
r
id
.
E
v
en
th
o
u
g
h
t
h
e
co
m
m
u
n
i
ca
tio
n
b
et
w
ee
n
i
n
v
er
ter
s
i
s
n
o
t
d
esira
b
le,
it
is
n
ec
es
s
ar
y
to
i
m
p
le
m
en
t
a
co
m
m
u
n
icatio
n
s
y
s
te
m
b
et
w
ee
n
ea
c
h
i
n
v
er
ter
a
n
d
th
e
P
C
C
[
1
6
]
.
T
h
is
co
m
m
u
n
icatio
n
s
y
s
te
m
i
s
b
en
ef
icial
f
o
r
th
e
i
m
p
le
m
en
t
atio
n
o
f
m
u
ltil
e
v
el
co
n
tr
o
l
alg
o
r
ith
m
.
I
n
ad
d
itio
n
,
th
e
i
n
f
o
r
m
atio
n
o
n
t
h
e
P
C
C
v
o
ltag
e
ca
n
b
e
o
b
tain
ed
u
s
i
n
g
t
h
is
co
m
m
u
n
icatio
n
ch
a
n
n
e
l.
T
h
is
allo
w
s
t
h
e
co
n
tr
o
l
s
y
s
te
m
to
ca
lc
u
late
t
h
e
lin
e
i
m
p
ed
an
ce
i
n
r
ea
l
tim
e
w
it
h
s
m
all
co
m
p
u
tatio
n
a
l
r
eso
u
r
ce
an
d
h
ig
h
ac
cu
r
ac
y
.
T
h
is
p
ap
er
p
r
esen
ts
an
ad
ap
tiv
e
v
ir
tu
al
i
m
p
ed
an
ce
b
ased
d
r
o
o
p
co
n
tr
o
l
s
ch
e
m
e
f
o
r
p
ar
allel
in
v
er
ter
o
p
er
atio
n
in
lo
w
v
o
ltag
e
m
icr
o
g
r
id
to
en
s
u
r
e
th
e
p
o
w
er
s
h
ar
in
g
p
er
f
o
r
m
a
n
ce
e
v
e
n
w
h
e
n
t
h
e
lin
e
i
m
p
ed
an
ce
i
s
s
u
b
j
ec
t
to
ch
an
g
e
.
I
n
t
h
e
p
r
o
p
o
s
ed
m
e
th
o
d
,
th
e
li
n
e
i
m
p
ed
a
n
ce
is
f
ir
s
t
est
i
m
a
t
ed
in
r
ea
l
ti
me
an
d
t
h
e
v
ir
t
u
al
i
m
p
ed
an
ce
is
ad
j
u
s
ted
ac
co
r
d
in
g
l
y
to
r
ef
lect
t
h
e
c
h
an
g
e
i
n
li
n
e
i
m
p
ed
an
ce
b
y
th
e
e
s
ti
m
ate
d
v
alu
e.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
l
lo
w
s
.
Sectio
n
2
d
is
c
u
s
s
es
th
e
s
tan
d
ar
d
s
tr
u
c
tu
r
e
o
f
m
icr
o
g
r
i
d
an
d
th
e
co
n
v
e
n
tio
n
al
v
ir
t
u
al
i
m
p
ed
an
c
e
b
ased
d
r
o
o
p
co
n
tr
o
l
s
ch
e
m
e.
Sectio
n
3
ex
p
lai
n
s
t
h
e
p
r
o
p
o
s
ed
ad
ap
tiv
e
v
ir
tu
al
i
m
p
ed
an
ce
m
et
h
o
d
as
w
ell
a
s
th
e
esti
m
atio
n
s
ch
e
m
e
o
f
l
in
e
i
m
p
ed
an
ce
.
I
n
s
ec
tio
n
4
,
t
h
e
s
i
m
u
latio
n
r
es
u
lts
co
n
d
u
cted
in
Ma
tlab
/
Si
m
u
li
n
k
s
en
v
ir
o
n
m
en
t
s
is
p
r
ese
n
ted
.
F
in
all
y
,
th
i
s
p
ap
er
co
n
c
lu
d
es i
n
Sectio
n
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
n
A
d
a
p
tive
V
ir
tu
a
l I
mp
ed
a
n
c
e
B
a
s
ed
Dro
o
p
C
o
n
tr
o
l S
c
h
em
e
fo
r
P
a
r
a
llel I
n
ve
r
ter
…
(
N
g
u
ye
n
Tien
Ha
i
)
1311
2.
M
I
CRO
G
RID
ST
R
UCTU
RE
AN
D
CO
NV
E
N
T
I
O
N
AL
V
I
RT
UAL
I
M
P
E
DA
NCE
B
AS
E
D
DRO
O
P
CO
NT
RO
L
A
t
y
p
ical
s
tr
u
c
tu
r
e
o
f
a
m
icr
o
g
r
id
is
s
h
o
w
n
i
n
Fig
u
r
e
1
.
Mic
r
o
g
r
id
co
n
s
is
t
s
o
f
DG
s
y
s
te
m
s
an
d
lo
ad
s
ca
p
ab
le
o
f
o
p
er
atin
g
w
i
th
,
o
r
i
n
d
ep
en
d
en
tl
y
f
r
o
m
,
t
h
e
m
ai
n
p
o
w
er
g
r
id
.
M
icr
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g
r
id
is
co
n
n
ec
ted
to
th
e
p
o
w
er
g
r
id
at
t
h
e
P
C
C
.
Ho
w
e
v
er
,
wh
en
th
e
f
au
l
t
o
cc
u
r
s
i
n
t
h
e
u
til
it
y
g
r
id
,
m
icr
o
g
r
id
is
d
is
co
n
n
e
cted
f
r
o
m
th
e
m
a
in
p
o
w
er
g
r
id
a
n
d
is
tr
an
s
f
er
r
ed
to
is
lan
d
ed
m
o
d
e.
I
n
t
h
is
m
o
d
e,
m
icr
o
g
r
id
s
u
p
p
lies
e
n
tire
lo
ad
d
em
a
n
d
i
n
lo
ca
l
ar
ea
b
y
d
is
tr
ib
u
ti
n
g
t
h
e
to
tal
d
e
m
an
d
in
to
ea
ch
DG
s
y
s
te
m
a
cc
o
r
d
in
g
to
i
ts
r
ated
p
o
w
er
.
I
n
ad
d
itio
n
,
t
h
e
lea
s
t
i
m
p
o
r
tan
t
lo
ad
ca
n
b
e
s
h
u
td
o
w
n
if
m
icr
o
g
r
id
is
in
ad
eq
u
at
e
to
s
u
p
p
ly
t
h
e
en
tire
lo
ad
d
e
m
an
d
i
n
o
r
d
er
t
o
m
ai
n
tai
n
th
e
s
u
p
p
l
y
f
o
r
cr
itical
o
n
es
.
Fig
u
r
e
1
.
Sch
e
m
atic
d
iag
r
a
m
o
f
a
m
icr
o
g
r
id
Dr
o
o
p
co
n
tr
o
l
h
as
b
ee
n
a
p
o
p
u
lar
m
e
th
o
d
ad
o
p
ted
f
o
r
m
icr
o
g
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s
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ce
it
d
o
es
n
o
t
r
eq
u
ir
e
an
y
h
i
g
h
b
an
d
w
id
t
h
co
m
m
u
n
icatio
n
c
h
an
n
el
f
o
r
co
n
tr
o
l p
u
r
p
o
s
es
.
T
h
is
i
s
a
v
er
y
p
r
ef
er
r
ed
f
ea
t
u
r
e
i
n
m
icr
o
g
r
id
b
ec
a
u
s
e
th
e
DG
s
y
s
te
m
s
ar
e
o
f
te
n
d
i
s
t
r
ib
u
ted
in
w
id
e
ar
ea
.
T
h
e
m
ai
n
id
ea
o
f
th
e
d
r
o
o
p
co
n
tr
o
l
co
m
es
f
r
o
m
t
h
e
s
el
f
-
r
eg
u
lat
io
n
f
ea
tu
r
e
o
f
t
h
e
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
ato
r
.
Fig
u
r
e
2
d
e
m
o
n
s
tr
ates
a
s
i
m
p
lif
ied
m
o
d
el
r
ep
r
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tin
g
th
e
co
n
n
ec
tio
n
o
f
p
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w
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n
v
er
te
r
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u
ti
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it
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id
th
r
o
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g
h
tr
a
n
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m
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s
io
n
li
n
e
w
it
h
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n
i
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p
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a
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ce
.
I
n
Fi
g
u
r
e
2
(
a)
,
th
e
g
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id
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co
n
n
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in
v
er
ter
is
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ep
icted
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g
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o
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r
ce
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A
c
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d
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g
to
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p
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f
ied
d
iag
r
a
m
,
th
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d
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p
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tr
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th
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y
a
g
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n
v
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ter
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b
e
w
r
itte
n
as
f
o
llo
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:
1
2
1
2
22
c
o
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(
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i
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(
)
A
A
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2
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(
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v
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r
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i
Z
R
j
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is
th
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li
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e
i
m
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ce
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d
φ
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s
t
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cu
r
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n
t
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s
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le.
T
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e
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et
w
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n
A
V
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is
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icted
in
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h
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d
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ai
n
as
s
h
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w
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in
Fig
u
r
e
2
(
b
)
.
Fro
m
(
1
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d
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2
)
,
th
e
p
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ase
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e
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elate
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tiv
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p
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s
12
s
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(
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AA
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Q
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(
3
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12
c
o
s
(
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AA
AB
A
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P
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Q
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V
(
4
)
I
n
p
r
ac
tice,
th
e
m
o
s
t
co
m
m
o
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ca
s
e
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th
at
t
h
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m
p
ed
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o
f
m
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is
p
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el
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i
n
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ctiv
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n
th
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ca
s
e,
it
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s
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s
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n
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le
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o
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u
m
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t
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at
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h
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s
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v
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ar
t
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th
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li
n
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m
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ce
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n
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lecte
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Fu
r
t
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e,
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n
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ce
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et
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n
v
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ter
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t
v
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C
v
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12
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is
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m
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ca
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al
s
o
ass
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m
e
1
2
1
2
s
i
n
(
)
an
d
12
c
o
s
(
)
1
.
Fro
m
t
h
ese
a
s
s
u
m
p
tio
n
s
,
(
3
)
an
d
(
4
)
ar
e
r
e
w
r
i
tte
n
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
D
ec
em
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er
2
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1
6
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3
0
9
–
1
3
1
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1312
12
A
AB
XP
VV
(
5
)
A
AB
A
XQ
VV
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(
6
)
(
a)
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q
u
iv
ale
n
t c
ir
cu
it
(
b
)
P
h
aso
r
d
iag
r
a
m
Fig
u
r
e
2
.
Si
m
p
li
f
ied
m
o
d
el
r
ep
r
esen
tin
g
t
h
e
co
n
n
ec
t
io
n
o
f
p
o
w
er
co
n
v
er
ter
to
u
t
ilit
y
g
r
id
As
ca
n
b
e
s
ee
n
in
(
5
)
an
d
(
6
)
,
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
ar
e
d
e
p
en
d
en
t
o
n
th
e
v
o
lta
g
e
d
if
f
er
e
n
ce
an
d
p
o
w
er
an
g
le
12
()
.
T
h
e
a
ctiv
e
p
o
w
er
ca
n
b
e
co
n
tr
o
ll
ed
b
y
a
d
j
u
s
t
in
g
th
e
p
o
w
er
an
g
le.
T
h
e
r
ea
ctiv
e
p
o
w
er
ca
n
b
e
also
co
n
tr
o
lled
b
y
t
h
e
i
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e.
Fro
m
th
e
s
e
r
elatio
n
s
,
i
t
is
po
s
s
ib
le
to
r
eg
u
late
t
h
e
ac
tiv
e
a
n
d
r
ea
cti
v
e
p
o
w
er
s
in
j
ec
ted
to
th
e
g
r
id
b
y
co
n
tr
o
lli
n
g
t
h
e
m
a
g
n
i
tu
d
e
a
n
d
f
r
eq
u
e
n
c
y
o
f
th
e
i
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e.
T
h
is
s
c
h
e
m
e
p
er
m
its
t
h
e
co
o
r
d
in
atio
n
b
et
w
e
en
p
ar
allel
-
co
n
n
ec
ted
i
n
v
er
ter
s
in
m
icr
o
g
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id
s
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n
ce
it
is
p
o
s
s
ib
le
to
co
n
tr
o
l
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
s
o
f
e
ac
h
in
d
iv
id
u
al
in
v
er
ter
au
to
n
o
m
o
u
s
l
y
.
T
h
e
d
r
o
o
p
co
n
tr
o
l la
w
s
f
o
r
in
d
u
cti
v
e
lin
e
i
m
p
ed
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ce
ca
n
b
e
ex
p
r
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ed
as f
o
llo
w
s
:
*
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n
P
r
e
f
A
f
f
k
P
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(
7
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e
f
n
Q
r
e
f
A
v
V
k
Q
Q
(
8
)
w
h
er
e
*
f
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th
e
r
e
f
er
e
n
ce
f
r
eq
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en
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y
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n
f
is
t
h
e
r
ated
f
r
eq
u
e
n
c
y
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f
m
icr
o
g
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id
,
P
k
is
th
e
f
r
eq
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e
n
c
y
d
r
o
o
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co
ef
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e
f
P
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h
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ig
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ates
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t
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th
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f
ir
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e
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ti
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e
a
n
d
r
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i
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atch
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y
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ter
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lc
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lat
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t
h
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ea
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u
r
ed
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u
tp
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g
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an
d
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r
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en
ts
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h
e
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f
o
r
m
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o
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th
e
ac
tiv
e
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d
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ea
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e
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o
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er
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is
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ed
to
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e
d
r
o
o
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co
n
tr
o
ller
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r
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ce
th
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o
ltag
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d
f
r
eq
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en
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er
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n
ce
s
.
T
h
e
v
o
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a
n
d
f
r
eq
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en
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y
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f
er
en
ce
s
f
r
o
m
t
h
e
d
r
o
o
p
co
n
tr
o
l
s
ch
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m
e
ar
e
u
s
ed
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th
e
v
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h
o
s
e
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h
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r
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t
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f
o
r
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h
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cu
r
r
e
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r
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u
lato
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n
th
e
id
ea
l
co
n
d
itio
n
,
t
h
e
co
n
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e
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tio
n
al
d
r
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o
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co
n
tr
o
l
in
Fig
u
r
e
3
p
r
o
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id
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o
o
d
p
o
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er
s
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ar
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g
p
er
f
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a
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ce
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et
w
ee
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in
v
er
ter
s
.
Ho
w
ev
er
,
i
n
p
r
ac
tic
e,
th
e
li
n
e
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m
p
ed
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ce
s
b
et
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ee
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ter
s
an
d
t
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e
P
C
C
ar
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if
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er
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T
h
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atc
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r
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e
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alan
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ed
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p
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ical
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m
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ed
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ter
to
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alan
ce
t
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e
m
is
m
atc
h
.
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w
e
v
er
,
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I
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1313
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ical
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Fig
u
r
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3
.
B
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Vir
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m
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ll
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n
tr
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u
ctu
r
e.
I
n
t
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eth
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e
w
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er
e
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ce
v
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lu
e
f
or
th
e
v
o
ltag
e
r
eg
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o
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s
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g
t
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t o
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n
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co
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tr
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l
s
ch
e
m
e
a
s
f
o
llo
w
s
:
*
.
r
e
f
r
e
f
v
i
o
v
v
Z
i
(
9
)
w
h
er
e
r
e
f
v
is
n
e
w
r
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er
e
n
ce
v
al
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ed
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n
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Z
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h
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ck
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l
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m
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ed
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ased
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r
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co
n
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is
s
h
o
w
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in
Fi
g
u
r
e
4
.
W
h
en
t
h
e
ef
f
ec
t
o
f
v
ir
t
u
al
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m
p
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ce
is
in
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u
d
ed
in
t
h
e
co
n
tr
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l
s
tr
u
ct
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r
e,
th
e
eq
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ale
n
t
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m
p
ed
a
n
ce
o
f
in
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ter
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ca
n
b
e
o
b
tain
ed
as f
o
llo
w
s
:
e
q
v
i
i
Z
Z
Z
(
10
)
w
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er
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i
Z
is
t
h
e
p
h
y
s
ical
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n
e
i
m
p
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ce
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d
eq
Z
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th
e
eq
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iv
a
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.
Fig
u
r
e
4
.
B
lo
ck
d
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r
a
m
o
f
t
h
e
v
ir
tu
al
i
m
p
ed
an
ce
s
c
h
e
m
e
3.
ADAP
T
I
VE
V
I
RT
UAL
I
M
P
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DANC
E
M
E
T
H
O
D
USI
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eq
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ir
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y
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e
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o
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A
s
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o
in
te
d
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t
in
[
1
6
]
,
th
e
co
m
m
u
n
icatio
n
ch
a
n
n
el
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et
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allel
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ter
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e
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cial
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n
f
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r
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n
f
o
r
ca
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latio
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o
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li
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ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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IJ
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Vo
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er
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6
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–
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3
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9
1314
On
e
-
p
h
ase
p
h
ase
-
lo
ck
ed
lo
o
p
(
P
L
L
)
is
i
m
p
le
m
en
ted
at
th
e
P
C
C
to
d
eter
m
in
e
th
e
m
a
g
n
it
u
d
e
an
d
f
r
eq
u
en
c
y
o
f
t
h
e
P
C
C
v
o
ltag
e.
T
h
e
o
b
tai
n
ed
o
u
tp
u
ts
o
f
t
h
e
P
L
L
ar
e
tr
a
n
s
m
itted
to
t
h
e
co
n
tr
o
ller
of
t
h
e
in
d
iv
id
u
al
in
v
er
ter
.
T
h
e
co
s
t
o
f
i
m
p
le
m
e
n
ti
n
g
o
ne
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p
h
a
s
e
P
L
L
i
s
n
o
t
h
i
g
h
s
in
ce
it
r
eq
u
ir
es
o
n
l
y
o
n
e
v
o
lta
g
e
s
en
s
o
r
at
th
e
P
C
C
.
I
n
ad
d
itio
n
,
it
ca
n
b
e
r
ea
lized
w
i
th
s
m
all
co
m
p
u
tatio
n
al
e
f
f
o
r
t
an
d
r
ea
s
o
n
ab
le
ac
cu
r
ac
y
[
1
7
]
.
Fig
u
r
e
5
illu
s
tr
ate
s
th
e
d
etec
ti
o
n
s
ch
e
m
e
o
f
t
h
e
P
C
C
v
o
ltag
e
an
d
p
h
ase
a
n
g
le
u
s
i
n
g
o
n
e
-
p
h
ase
P
L
L
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y
m
ea
s
u
r
in
g
o
n
e
-
p
h
a
s
e
v
o
lta
g
e
.
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h
e
o
u
tp
u
ts
o
f
t
h
e
P
L
L
a
lg
o
r
ith
m
ar
e
th
e
p
h
ase
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g
le
2
an
d
th
e
m
ag
n
it
u
d
e
o
f
v
o
ltag
e
q
V
at
th
e
P
C
C
w
h
ic
h
ar
e
u
s
ed
in
th
e
est
i
m
a
tio
n
s
c
h
e
m
e
f
o
r
th
e
li
n
e
i
m
p
ed
a
n
ce
.
Usi
n
g
th
e
o
b
tain
ed
in
f
o
r
m
atio
n
o
n
th
e
P
C
C
,
t
h
e
li
n
e
i
m
p
ed
an
ce
b
et
w
ee
n
t
h
e
in
v
er
ter
an
d
th
e
P
C
C
ca
n
b
e
ca
lc
u
lated
as f
o
llo
w
s
:
12
3
AB
VV
Z
I
(
11
)
w
h
er
e
1
A
V
is
p
h
aso
r
e
x
p
r
ess
io
n
f
o
r
th
e
in
v
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ter
o
u
tp
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t
v
o
ltag
e,
2
B
V
is
p
h
a
s
o
r
ex
p
r
ess
io
n
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o
r
th
e
P
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v
o
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e
w
it
h
Bq
VV
,
3
I
is
p
h
aso
r
ex
p
r
ess
io
n
f
o
r
th
e
cu
r
r
en
t
in
tr
a
n
s
m
is
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n
li
n
e,
an
d
Z
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th
e
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e
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m
p
ed
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ce
.
S
in
ce
all
t
h
e
v
ar
i
ab
les
ar
e
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ai
lab
le
at
i
n
d
i
v
id
u
al
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n
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er
ter
co
n
tr
o
ller
,
t
h
e
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m
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ed
an
ce
esti
m
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n
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ch
e
m
e
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n
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y
e
x
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ted
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e
w
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m
p
u
t
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f
o
r
ts
.
Fig
u
r
e
5
.
D
etec
tio
n
o
f
P
C
C
v
o
ltag
e
an
d
p
h
a
s
e
an
g
le
u
s
i
n
g
o
n
e
-
p
h
a
s
e
P
L
L
m
et
h
o
d
Ma
in
d
is
ad
v
an
tag
e
o
f
t
h
e
co
n
v
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t
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n
al
v
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t
u
al
i
m
p
ed
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ce
b
ased
d
r
o
o
p
co
n
tr
o
l
is
th
at
it
ca
n
n
o
t
s
h
ar
e
th
e
r
ea
ctiv
e
p
o
w
er
p
r
o
p
er
ly
w
h
e
n
th
e
li
n
e
i
m
p
ed
a
n
ce
s
ar
e
ch
an
g
ed
d
u
r
in
g
o
p
er
atio
n
.
T
h
is
g
i
v
es
r
is
e
to
t
h
e
n
ee
d
o
f
a
co
n
tr
o
l
s
c
h
e
m
e
t
h
a
t
ca
n
ac
h
iev
e
ac
c
u
r
ate
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s
h
ar
in
g
ca
u
s
ed
b
y
t
h
e
d
if
f
er
en
ce
in
l
in
e
i
m
p
ed
a
n
c
e.
I
n
ad
d
itio
n
,
it
ad
ap
ts
to
t
h
e
c
h
an
g
e
o
f
li
n
e
i
m
p
ed
an
ce
i
n
r
ea
l
-
ti
m
e
,
w
h
ic
h
y
iel
d
s
a
p
r
ef
er
r
ed
f
ea
tu
r
e
o
f
DG
s
y
s
te
m
s
b
ec
au
s
e
it
d
o
es
n
o
t
n
ee
d
h
u
m
a
n
in
ter
v
e
n
tio
n
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
is
s
t
u
d
y
w
as
s
u
p
p
o
r
ted
b
y
th
e
R
e
s
ea
r
ch
P
r
o
g
r
a
m
f
u
n
d
e
d
b
y
t
h
e
Seo
u
l
Natio
n
a
l
U
n
i
v
er
s
it
y
o
f
Scien
ce
a
n
d
T
ec
h
n
o
lo
g
y
.
RE
F
E
R
E
NC
E
S
[1
]
J.
D
e
M
a
to
s,
F
.
S
il
v
a
,
a
n
d
L
.
Ri
b
e
iro
.
P
o
w
e
r
Co
n
tr
o
l
in
A
C
Iso
late
d
M
icro
g
rid
s
w
it
h
Re
n
e
w
a
b
le
En
e
rg
y
S
o
u
rc
e
s
a
n
d
E
n
e
rg
y
S
to
ra
g
e
S
y
ste
m
s.
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
.
2
0
1
4
;
6
2
(6
):
3
4
9
0
–
3
4
9
7
.
[2
]
J.
Ro
c
a
b
e
rt,
A
.
L
u
n
a
,
F
.
Blaa
b
j
e
rg
,
a
n
d
P
.
R
o
d
ríg
u
e
z
.
C
o
n
tr
o
l
o
f
P
o
w
e
r
Co
n
v
e
rters
in
A
C
M
i
c
ro
g
rid
s.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
i
c
s.
2
0
1
2
;
2
7
(
1
1
)
:
4
7
3
4
–
4
7
4
9
.
[3
]
H.
Ha
n
,
X.
Ho
u
,
J.
Ya
n
g
,
J.
W
u
,
M
.
S
u
,
a
n
d
J.
M
.
G
u
e
rre
ro
.
Re
v
ie
w
o
f
P
o
w
e
r
S
h
a
rin
g
Co
n
tr
o
l
S
trate
g
ies
f
o
r
Isla
n
d
in
g
Op
e
ra
ti
o
n
o
f
A
C
M
icro
g
rid
s.
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
S
ma
rt Grid
.
2
0
1
5
;
7
(1
)
:
2
0
0
–
2
1
5
.
[4
]
V
.
Na
sirian
,
Q.
S
h
a
f
iee
,
J.M
.
G
u
e
rre
ro
,
F
.
L
.
L
e
w
is
,
a
n
d
A
.
Da
v
o
u
d
i.
Dro
o
p
-
f
re
e
Distrib
u
ted
Co
n
tro
l
f
o
r
A
C
M
icro
g
rid
s.
IE
EE
T
r
a
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
.
2
0
1
6
;
3
1
(
2
):
1
6
0
0
–
1
6
1
7
.
[5
]
J.W
.
Ki
m
,
H.S
.
Ch
o
i
,
a
n
d
B
.
H.
C
h
o
.
A
No
v
e
l
Dro
o
p
M
e
th
o
d
f
o
r
Co
n
v
e
rter
P
a
ra
ll
e
l
Op
e
ra
ti
o
n
.
I
E
EE
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r E
lec
tro
n
ics
.
2
0
0
2
;
1
7
(1
):
2
5
–
3
2
.
[6
]
Q.C.
Zh
o
n
g
.
R
o
b
u
st
Dro
o
p
C
o
n
tro
ll
e
r
f
o
r
A
c
c
u
ra
te
P
r
o
p
o
rti
o
n
a
l
L
o
a
d
S
h
a
rin
g
a
m
o
n
g
In
v
e
rters
Op
e
ra
ted
in
P
a
ra
ll
e
l.
I
EE
E
T
ra
n
s
a
c
ti
o
n
s o
n
In
d
u
stria
l
E
lec
tro
n
ics
.
2
0
1
3
;
6
0
(
4
):
1
2
8
1
–
1
2
9
0
.
[7
]
J.
L
u
,
Y.
Zh
a
n
g
,
X
.
Qia
n
,
J.
L
o
n
g
,
a
n
d
Z.
Zh
a
o
,
A
No
v
e
l
V
irt
u
a
l
Im
p
e
d
a
n
c
e
M
e
th
o
d
f
o
r
Dro
o
p
Co
n
tro
ll
e
d
P
a
ra
ll
e
l
UP
S
I
n
v
e
rters
w
it
h
W
irele
ss
C
o
n
tr
o
l.
IE
EE
T
ra
n
sp
o
rtati
o
n
E
lec
tri
f
ica
ti
o
n
Co
n
f
e
re
n
c
e
a
n
d
Ex
p
o
,
IT
EC
A
sia
-
P
a
c
if
ic.
2
0
1
4
;
1
–
5.
[8
]
Y.W
.
L
i
a
n
d
C.
N.
Ka
o
.
A
n
A
c
c
u
ra
te
P
o
w
e
r
Co
n
tr
o
l
S
trate
g
y
f
o
r
P
o
w
e
r
-
e
lec
tro
n
ics
-
in
terf
a
c
e
d
Distrib
u
te
d
G
e
n
e
r
a
ti
o
n
Un
it
s
Op
e
ra
ti
n
g
in
a
L
o
w
-
v
o
lt
a
g
e
M
u
lt
ib
u
s
M
icro
g
rid
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
.
2
0
0
9
;
2
4
(
1
2
):
2
9
7
7
–
2
9
8
8
.
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