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I
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A
m
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s
m
is
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tem
,
s
o
m
etim
es
r
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ed
to
as
a
“g
r
id
”
[
1
]
-
[
3
]
.
B
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s
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en
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ated
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m
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a
f
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r
m
o
f
d
is
tr
ib
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g
en
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atio
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[
4
]
.
W
h
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th
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m
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p
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ates
in
s
tan
d
alo
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m
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p
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m
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s
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m
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[
5
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.
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also
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th
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c
h
ar
ac
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is
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f
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n
e
v
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tio
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[
6
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.
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tem
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tab
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;
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eq
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T
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ty
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v
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[8
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R
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[
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tech
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iq
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es [
10
].
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to
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d
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to
p
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[
1
1
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[
1
2
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.
T
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p
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wid
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witch
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en
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f
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[
1
1
]
,
[
1
2
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.
An
o
th
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way
to
ac
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iev
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AC
/AC
co
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v
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s
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is
to
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AC
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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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Dr
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,
Vo
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1
6
,
No
.
1
,
Ma
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c
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20
2
5
:
389
-
406
390
DC
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C
th
r
o
u
g
h
an
in
ter
m
e
d
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te
DC
lin
k
an
d
im
p
r
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en
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wab
le
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g
y
s
o
u
r
ce
s
'
en
er
g
y
ef
f
icien
cy
[
8
]
,
[
1
3
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.
W
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at
u
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p
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to
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p
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r
tr
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s
f
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ed
f
r
o
m
th
e
DC
g
r
id
to
th
e
AC
g
r
id
[
1
4
]
.
C
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v
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AC
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co
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m
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n
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s
y
s
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s
.
T
h
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co
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v
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ter
s
ar
e
h
ig
h
ly
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f
icien
t
in
co
n
tr
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g
AC
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MS
v
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ltag
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an
d
f
r
e
q
u
en
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in
v
ar
io
u
s
a
p
p
licatio
n
s
[
1
5
]
,
[
1
6
]
.
Po
wer
f
ac
to
r
co
r
r
ec
tio
n
(
PF
C
)
is
an
o
th
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m
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u
s
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o
f
AC
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co
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v
er
ter
s
in
p
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wer
d
is
tr
ib
u
tio
n
s
y
s
tem
s
,
esp
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lar
g
e
in
d
u
s
tr
ial
an
d
co
m
m
er
cial
ap
p
licatio
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s
[
1
7
]
,
[
1
8
]
,
wh
er
e
p
o
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r
p
o
wer
f
ac
to
r
lead
s
to
in
cr
ea
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d
p
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r
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g
y
lo
s
s
,
m
ain
tain
a
p
o
wer
f
ac
to
r
clo
s
e
to
1
,
an
d
im
p
r
o
v
e
o
v
er
all
p
o
wer
q
u
ality
[
1
9
]
,
[
2
0
]
.
Un
in
ter
r
u
p
tib
le
p
o
wer
s
u
p
p
ly
(
UPS)
co
n
v
er
ter
s
en
s
u
r
e
th
e
ef
f
icien
t
o
p
er
atio
n
o
f
s
en
s
itiv
e
elec
tr
o
n
ic
d
ev
ices,
s
u
ch
as
co
m
p
u
ter
s
,
s
er
v
er
s
,
an
d
m
ed
ical
eq
u
ip
m
en
t,
in
th
e
e
v
en
t
o
f
p
o
wer
q
u
ality
p
r
o
b
lem
s
,
b
y
r
eg
u
latin
g
th
e
R
MS
o
u
tp
u
t v
o
ltag
e
a
n
d
f
r
eq
u
en
cy
[
2
1
]
.
B
lo
ck
d
iag
r
am
o
f
th
e
s
y
s
te
m
co
n
n
ec
tin
g
AC
m
icr
o
g
r
i
d
s
u
s
in
g
DC
/DC
,
D
C
/A
C
,
an
d
AC
/A
C
co
n
v
er
ter
s
to
f
lex
ib
l
y
d
is
tr
ib
u
t
e
th
e
g
r
id
an
d
o
p
tim
ize
th
e
ef
f
icien
cy
o
f
d
is
tr
ib
u
ted
en
e
r
g
y
s
o
u
r
ce
s
as sh
o
wn
in
Fig
u
r
e
1
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
f
lex
ib
le
AC
/A
C
co
n
v
er
ter
with
a
s
im
p
le
s
tr
u
ctu
r
e
an
d
d
i
r
ec
t
p
o
wer
tr
an
s
f
er
co
n
n
ec
tin
g
two
AC
m
icr
o
g
r
id
s
.
T
h
is
co
n
v
er
ter
p
er
f
o
r
m
s
e
n
er
g
y
tr
a
n
s
m
is
s
io
n
p
r
o
ce
s
s
es
b
etwe
en
two
g
r
id
s
to
en
s
u
r
e
v
o
ltag
e
q
u
ality
o
n
th
e
t
wo
g
r
id
s
,
o
p
tim
ize
o
p
er
atio
n
,
an
d
im
p
r
o
v
e
th
e
in
p
u
t
ef
f
icien
cy
o
f
th
e
co
n
v
er
ter
an
d
th
e
ef
f
icien
cy
o
f
en
er
g
y
u
s
e
f
r
o
m
d
is
tr
ib
u
te
d
s
o
u
r
ce
s
t
h
r
o
u
g
h
p
r
io
r
ity
lo
a
d
s
ac
co
r
d
i
n
g
to
th
e
c
o
n
d
itio
n
s
an
d
r
eg
u
latio
n
s
o
f
Vietn
am
a
n
d
th
e
wo
r
l
d
[
2
2
]
.
T
h
e
p
ap
er
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
i)
Sectio
n
2
d
escr
ib
es
i
n
d
etail
th
e
wo
r
k
in
g
p
r
i
n
cip
le
o
f
th
e
p
r
o
p
o
s
ed
s
tr
u
ctu
r
e
; ii)
Sectio
n
3
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
with
th
eo
r
y
to
ev
alu
ate
th
e
co
n
v
er
ter
p
er
f
o
r
m
an
ce
;
iii)
Sectio
n
4
p
r
esen
ts
th
e
ex
p
er
im
e
n
tal
r
esu
lts
to
ev
alu
ate
th
e
co
n
v
e
r
ter
p
er
f
o
r
m
an
ce
an
d
th
e
th
e
o
r
etic
al
asp
ec
ts
,
s
im
u
latio
n
,
an
d
ty
p
ical
r
ef
er
en
ce
s
;
an
d
iv
)
Secti
o
n
5
c
o
n
clu
d
es
an
d
s
u
m
m
ar
izes th
e
im
p
o
r
ta
n
t a
ch
iev
em
en
ts
o
f
th
e
w
o
r
k
in
th
e
p
ap
er
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
th
e
AC
m
icr
o
g
r
id
co
n
n
ec
tio
n
s
y
s
tem
2.
F
L
E
X
I
B
L
E
A
C/AC
CO
NV
E
RT
E
R
Fig
u
r
e
2
s
h
o
ws
th
e
p
r
in
cip
le
o
f
a
p
r
o
p
o
s
ed
b
i
d
ir
ec
tio
n
al
AC
/AC
co
n
v
er
ter
cir
cu
it
b
ased
o
n
B
o
o
s
t
an
d
B
u
ck
.
I
t
co
n
s
is
ts
o
f
th
r
ee
p
o
wer
s
witch
es
co
n
n
ec
ted
to
a
d
io
d
e
b
r
id
g
e
to
r
ed
u
ce
v
o
ltag
e
s
tr
ess
,
two
co
il
s
L
1
an
d
L2
,
an
d
two
L
C
f
ilter
s
o
n
b
o
th
s
id
es c
o
n
n
ec
ted
to
two
g
r
id
s
AC
1
an
d
AC
2
.
T
h
e
p
o
wer
cir
c
u
it o
f
th
e
c
o
n
v
er
te
r
r
ep
r
esen
ts
th
e
m
ain
s
witch
es
in
th
e
cir
cu
it
th
at
p
er
f
o
r
m
th
e
p
o
wer
co
n
v
er
s
io
n
,
th
e
r
ec
o
v
er
y
cir
cu
it
c
o
m
p
o
n
en
ts
an
d
th
e
co
n
n
ec
tio
n
t
o
th
e
s
to
r
ag
e
s
y
s
tem
ar
e
a
n
aly
ze
d
in
m
o
r
e
d
etail
in
s
ec
tio
n
2
.
2
o
f
t
h
is
s
ec
tio
n
.
Fig
u
r
e
3
s
h
o
ws
th
e
m
ain
wav
e
f
o
r
m
s
o
f
t
h
e
AC
/AC
co
n
v
er
ter
o
p
er
atio
n
.
A
p
o
wer
s
witch
is
ac
tiv
ated
b
y
a
h
ig
h
-
f
r
eq
u
e
n
cy
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
la
tio
n
(
SP
W
M)
d
u
r
in
g
ea
c
h
h
alf
cy
cle
o
f
t
h
e
in
p
u
t
v
o
ltag
e
.
E
a
ch
s
witch
in
g
cy
cle
h
as
two
s
tates,
as
s
h
o
wn
in
Fig
u
r
e
3
.
I
n
th
e
m
ain
wav
ef
o
r
m
g
r
ap
h
s
h
o
ws
th
e
f
u
ll
c
y
cle
o
f
t
h
e
alter
n
atin
g
cu
r
r
en
t
(
2
p
i
cy
cle)
.
C
o
n
tr
o
l f
r
eq
u
e
n
cy
f
o
r
th
e
elec
tr
o
n
ic
s
witch
es M
1
-
M3
.
2
.
1
.
O
pera
t
ing
princip
le
o
f
t
he
co
nv
er
t
er
I
n
th
is
p
r
o
p
o
s
ed
co
n
v
er
ter
two
b
id
ir
ec
tio
n
al
s
witch
es
ar
e
u
s
ed
wh
ich
ar
e
co
n
n
ec
ted
in
B
o
o
s
t
an
d
B
u
ck
f
o
r
m
.
T
h
r
o
u
g
h
th
e
f
ilter
cir
cu
its
,
h
ar
m
o
n
ic
f
ilter
in
g
o
f
o
r
d
er
s
3
,
5
,
an
d
7
is
p
er
f
o
r
m
ed
.
T
h
is
co
n
v
er
ter
co
n
v
er
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
B
id
ir
ec
tio
n
a
l A
C
/AC c
o
n
ve
r
ter lin
kin
g
tw
o
micro
g
r
id
s
in
a
flexib
le
micro
g
r
id
(
N
g
u
ye
n
Th
e
V
in
h
)
391
en
er
g
y
d
ir
ec
tly
f
r
o
m
two
AC
p
o
wer
g
r
id
s
,
s
o
th
e
g
eo
g
r
a
p
h
i
ca
l
co
n
d
itio
n
s
o
f
th
e
two
g
r
id
s
m
u
s
t
al
s
o
b
e
clo
s
e
to
ea
ch
o
th
er
(
d
is
tan
ce
1
0
-
1
0
0
0
m
)
[
2
3
]
,
[
2
4
]
.
T
h
e
s
witch
es
a
r
e
s
elec
ted
to
s
u
it
th
e
p
o
wer
r
a
n
g
e
in
th
e
co
n
v
er
ter
.
T
h
e
co
n
d
itio
n
s
d
u
r
i
n
g
th
e
e
n
er
g
y
tr
an
s
f
er
b
etwe
en
two
m
icr
o
g
r
id
AC
s
ar
e
as f
o
llo
ws:
−
L
o
ad
co
n
d
itio
n
s
ar
e
p
r
ef
er
en
t
ial
f
o
r
cu
s
to
m
er
s
f
r
o
m
ty
p
e
1
to
ty
p
e
3
ac
co
r
d
in
g
to
Vietn
am
'
s
r
eg
u
latio
n
s
[
2
5
]
.
I
n
th
e
AC
m
icr
o
g
r
id
,
th
e
r
e
ar
e
p
r
ac
tical
civ
il a
n
d
d
o
m
e
s
tic
lo
ad
s
.
−
T
h
e
o
p
tim
al
g
r
i
d
-
in
d
e
p
en
d
e
n
t
o
p
er
atin
g
co
n
d
itio
n
s
u
s
in
g
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
: in
two
AC
g
r
id
s
th
er
e
is
a
co
m
b
in
atio
n
o
f
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
an
d
s
to
r
ag
e
s
y
s
tem
s
.
−
L
ev
el
1
p
r
io
r
ity
is
th
e
lo
a
d
s
in
th
e
2
m
icr
o
g
r
id
s
wh
e
n
th
e
A
C
/A
C
u
n
it p
r
o
p
o
s
es to
co
n
n
ec
t.
−
Gr
id
-
co
n
n
e
cted
co
n
d
itio
n
,
u
s
in
g
b
o
th
lo
a
d
p
r
io
r
ity
a
n
d
AC
m
icr
o
g
r
id
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
wo
r
k
in
g
in
d
ep
en
d
en
tly
.
Fo
r
ex
am
p
le,
if
tr
an
s
m
itted
f
r
o
m
AC
1
to
AC
2
g
r
id
.
2
>
2
+
2
+
−
2
(
1
)
W
h
er
e
2
is
P
V
p
o
wer
ca
p
ac
ity
in
th
e
AC
2
g
r
id
;
2
is
W
in
p
o
wer
ca
p
ac
ity
in
AC
2
g
r
id
;
−
2
is
a
p
o
wer
s
o
u
r
ce
in
th
e
AC
2
g
r
id
.
Fig
u
r
e
2
.
C
ir
cu
it d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
p
r
in
cip
le
Fig
u
r
e
3
.
B
asic o
p
er
atin
g
d
iag
r
am
o
f
t
h
e
p
r
o
p
o
s
ed
AC
/AC
co
n
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
389
-
406
392
I
n
p
r
ac
tice
th
e
Pp
v
an
d
Pwin
s
o
u
r
ce
s
f
lu
ctu
ate
in
s
tan
tan
e
o
u
s
ly
in
a
v
alu
e
th
at
r
e
q
u
ir
es
co
m
p
en
s
atio
n
an
d
en
er
g
y
c
o
n
s
u
m
p
tio
n
.
2
>
2
+
−
2
(
2
)
Pp
v
s
to
p
s
g
en
er
atin
g
elec
tr
icity
d
u
r
i
n
g
o
f
f
-
p
ea
k
h
o
u
r
s
,
o
r
wh
en
th
e
b
am
b
o
o
is
o
b
s
cu
r
ed
b
y
clo
u
d
s
.
2
>
−
2
(
3
)
Pp
v
an
d
Pwin
s
o
u
r
ce
s
d
o
n
o
t
g
en
er
ate
en
e
r
g
y
.
2.
1
.
1
.
Scena
rio
o
ne
T
h
e
p
o
wer
t
r
an
s
m
itted
f
r
o
m
g
r
id
AC
1
to
AC
2
in
th
is
s
ce
n
ar
io
h
as th
e
f
o
ll
o
win
g
m
o
d
es
:
a)
Mo
d
e
1
P
o
s
itiv
e
h
alf
cy
cle
(
0
-
p
i)
,
s
wit
ch
es
M1
-
M3
ar
e
co
n
tr
o
lled
s
e
q
u
en
tially
as
ca
s
es
:
i)
S
witch
es
M1
an
d
M2
ar
e
co
n
tr
o
lled
t
o
g
eth
er
in
a
ce
r
tain
p
er
io
d
o
f
tim
e
ac
co
r
d
in
g
t
o
th
e
s
witch
in
g
c
y
cle
as
s
h
o
wn
in
Fig
u
r
e
4
;
ii)
I
n
t
h
e
tim
e
p
er
io
d
t1
-
t
2
in
th
e
s
witch
in
g
cy
cle
M1
is
tu
r
n
ed
o
n
,
M2
a
n
d
M3
ar
e
tu
r
n
ed
o
f
f
as
s
h
o
w
n
in
Fig
u
r
e
5
;
an
d
iv
)
I
n
th
e
tim
e
p
er
io
d
t2
-
t3
in
th
e
s
witch
in
g
cy
cle
M2
is
tu
r
n
ed
o
n
M1
an
d
M3
ar
e
tu
r
n
ed
o
f
f
as
s
h
o
wn
in
Fig
u
r
e
6
.
I
n
Fig
u
r
e
4
,
in
th
is
h
alf
cy
cle,
th
e
co
n
v
er
ter
p
o
wer
cir
cu
it
p
er
f
o
r
m
s
th
e
e
n
er
g
y
tr
an
s
f
er
p
r
o
ce
s
s
with
th
e
b
asic
B
o
o
s
t
cir
cu
it
w
o
r
k
i
n
g
p
r
in
cip
le.
T
h
e
p
o
wer
s
witch
es
M1
an
d
M2
ar
e
co
n
tr
o
lled
at
th
e
s
am
e
tim
e.
T
h
e
en
er
g
y
is
m
ain
ly
tr
an
s
m
itted
to
th
e
AC
2
g
r
id
s
id
e,
an
d
a
p
ar
t
is
d
is
p
er
s
ed
to
s
o
m
e
co
m
p
o
n
en
ts
in
th
e
p
o
wer
cir
cu
it
s
u
ch
as
th
e
co
il
s
id
e
L
1
an
d
f
o
r
C
ac
2
.
T
h
e
lo
s
t
en
er
g
y
is
d
iv
id
ed
a
m
o
n
g
th
e
s
witch
in
g
m
o
lec
u
les
M1
,
M2
,
D2
,
D4
,
D5
,
an
d
D7
.
T
h
e
o
u
t
p
u
t
v
o
ltag
e
ex
p
r
ess
io
n
at
g
r
id
AC
2
is
:
B
ased
o
n
Kir
ch
h
o
f
f
'
s
v
o
ltag
e
a
n
d
c
u
r
r
en
t
laws
(
KVL
an
d
KC
L
)
,
th
e
i
n
s
tan
tan
eo
u
s
v
o
ltag
e
an
d
cu
r
r
e
n
t
o
f
th
e
in
d
u
c
to
r
an
d
ca
p
ac
ito
r
ar
e
d
ete
r
m
in
ed
b
y
(
4
)
f
o
r
th
e
o
n
s
tate
o
f
M1
an
d
M
2
.
2
=
1
1
−
1
√
2
.
1
(V)
(
4
)
Fig
u
r
e
4
.
Statu
s
d
iag
r
a
m
o
f
th
e
co
n
v
er
te
r
o
p
e
r
atio
n
wh
e
n
s
witch
es M
1
an
d
M2
a
r
e
o
n
at
th
e
s
am
e
tim
e
Fig
u
r
e
5
s
h
o
ws
th
e
o
p
er
atio
n
o
f
th
e
co
n
v
er
ter
cir
cu
it
wh
en
o
n
ly
M1
is
o
n
.
M1
h
as
a
co
n
tr
o
l
p
u
ls
e
to
o
p
en
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
AC
2
is
eq
u
al
to
th
e
v
o
ltag
e
o
n
ca
p
a
cito
r
C
ac
2
an
d
is
s
u
p
p
lied
with
en
er
g
y
f
r
o
m
C
ca
2
.
E
x
p
r
ess
io
n
f
o
r
th
e
s
tate:
2
=
2
Fig
u
r
e
6
d
escr
ib
es
th
e
o
p
er
atio
n
o
f
th
e
AC
/AC
p
o
wer
cir
cu
it
wh
en
M2
is
o
n
,
th
e
en
er
g
y
o
f
th
e
AC
2
g
r
id
is
s
u
p
p
lied
f
r
o
m
th
e
AC
1
g
r
id
th
r
o
u
g
h
m
o
lecu
les D5
,
M
2
,
an
d
D7
th
e
v
o
ltag
e
ex
p
r
ess
io
n
o
f
t
h
e
AC
2
g
r
id
.
2
=
2
√
2
.
1
(V)
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
B
id
ir
ec
tio
n
a
l A
C
/AC c
o
n
ve
r
ter lin
kin
g
tw
o
micro
g
r
id
s
in
a
flexib
le
micro
g
r
id
(
N
g
u
ye
n
Th
e
V
in
h
)
393
Fig
u
r
e
5
.
State
d
iag
r
am
o
f
co
n
v
er
ter
o
p
er
atio
n
wh
e
n
M1
is
on
Fig
u
r
e
6
.
State
d
iag
r
am
o
f
co
n
v
er
ter
o
p
er
atio
n
wh
e
n
M2
is
on
b)
Mo
d
e
2
N
e
g
a
t
i
v
e
h
a
l
f
c
y
c
l
e
(
-
2
)
,
t
h
e
s
w
i
t
c
h
es
M
1
-
M
3
a
r
e
c
o
n
t
r
o
l
l
ed
s
e
q
u
e
n
t
i
a
l
l
y
a
s
i
n
t
h
e
c
a
s
e
s
:
i
)
M
2
a
n
d
M
3
a
r
e
b
o
t
h
c
o
n
t
r
o
l
l
e
d
f
o
r
a
c
e
r
t
a
i
n
p
e
r
i
o
d
o
f
ti
m
e
a
c
c
o
r
d
in
g
t
o
t
h
e
s
wi
t
c
h
i
n
g
c
y
cl
e
as
s
h
o
w
n
i
n
Fi
g
u
r
e
7
;
i
i
)
d
u
r
i
n
g
t
h
e
t
i
m
e
p
e
r
i
o
d
t
1
-
t2
i
n
t
h
e
s
w
i
t
c
h
i
n
g
c
y
c
l
e
M
3
is
t
u
r
n
e
d
o
n
i
n
F
i
g
u
r
e
8
,
M
1
an
d
M
2
a
r
e
o
f
f
;
a
n
d
i
i
i
)
d
u
r
i
n
g
t
h
e
t
i
m
e
p
e
r
i
o
d
t
2
-
t
3
i
n
t
h
e
s
wi
t
c
h
i
n
g
c
y
cl
e
M
2
is
t
u
r
n
e
d
o
n
M
1
a
n
d
M
3
a
r
e
o
f
f
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
9
.
Fig
u
r
e
7
d
escr
ib
es in
th
is
h
alf
cy
cle;
th
e
c
o
n
v
e
r
ter
p
o
wer
cir
cu
it p
er
f
o
r
m
s
th
e
en
er
g
y
tr
an
s
f
er
p
r
o
ce
s
s
with
th
e
b
asic
B
o
o
s
t
cir
cu
it
wo
r
k
in
g
p
r
in
cip
le.
T
h
e
p
o
wer
s
witch
es
M2
an
d
M
3
ar
e
c
o
n
tr
o
lle
d
at
th
e
s
am
e
tim
e.
T
h
e
en
er
g
y
is
m
ain
ly
tr
an
s
m
itted
to
th
e
AC
2
g
r
id
s
id
e,
an
d
a
p
ar
t
is
d
is
p
er
s
ed
to
s
o
m
e
co
m
p
o
n
en
ts
in
th
e
p
o
wer
cir
cu
it
s
u
ch
as
th
e
co
il
s
id
e
L
2
.
T
h
e
lo
s
t
en
er
g
y
is
d
iv
id
ed
am
o
n
g
th
e
s
witch
in
g
m
o
lecu
l
es
M2
,
M3
,
D6
,
D8
,
D9
,
an
d
D1
1
.
T
h
e
o
u
t
p
u
t
v
o
ltag
e
ex
p
r
ess
io
n
at
g
r
id
AC
2
is
:
B
ased
o
n
Kir
ch
h
o
f
f
'
s
v
o
ltag
e
a
n
d
c
u
r
r
en
t
laws
(
KVL
an
d
KC
L
)
,
th
e
i
n
s
tan
tan
eo
u
s
v
o
ltag
e
an
d
cu
r
r
e
n
t
o
f
th
e
in
d
u
c
to
r
an
d
ca
p
ac
ito
r
ar
e
d
ete
r
m
in
ed
b
y
(
6
)
f
o
r
th
e
o
n
s
tate
o
f
M1
an
d
M
2
.
2
=
1
1
−
1
√
2
.
1
(V)
(
6
)
Fig
u
r
e
8
d
escr
ib
es
th
e
o
p
er
atio
n
o
f
th
e
AC
/AC
p
o
wer
cir
cu
it
wh
en
M2
is
o
n
,
th
e
en
er
g
y
o
f
th
e
AC
2
g
r
id
is
s
u
p
p
lied
f
r
o
m
th
e
AC
1
g
r
id
th
r
o
u
g
h
m
o
lecu
les D6
,
M
2
,
an
d
D8
th
e
v
o
ltag
e
ex
p
r
ess
io
n
o
f
t
h
e
AC
2
g
r
id
.
2
=
2
√
2
.
1
(V)
(
7
)
Fig
u
r
e
9
s
h
o
ws
th
e
o
p
er
atio
n
o
f
th
e
co
n
v
er
ter
cir
cu
it
wh
en
o
n
ly
M3
is
o
n
,
M3
h
as
a
co
n
tr
o
l
p
u
ls
e
to
o
p
en
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
AC
2
is
eq
u
al
to
th
e
v
o
ltag
e
o
n
L
2
an
d
o
n
th
e
M3
.
E
n
e
r
g
y
is
also
ch
ar
g
ed
to
ca
p
ac
ito
r
C
ac
2
.
I
n
th
is
s
ce
n
ar
io
o
f
tr
an
s
m
itti
n
g
en
er
g
y
f
r
o
m
g
r
i
d
AC
1
to
g
r
id
AC
2
,
th
e
c
o
n
v
e
r
ter
ca
n
ad
ju
s
t
th
e
v
o
ltag
e
u
p
o
r
d
o
wn
to
en
s
u
r
e
th
at
th
e
o
u
tp
u
t
o
f
th
e
g
r
id
r
ec
ei
v
es e
n
e
r
g
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
389
-
406
394
Fig
u
r
e
7
.
Statu
s
d
iag
r
a
m
o
f
th
e
co
n
v
er
te
r
o
p
e
r
atio
n
wh
e
n
s
witch
es M
2
an
d
M3
a
r
e
o
n
at
th
e
s
am
e
tim
e
Fig
u
r
e
8
.
State
d
iag
r
am
o
f
co
n
v
er
ter
o
p
er
atio
n
wh
e
n
M2
s
wi
tch
es a
r
e
o
n
(
-
2
)
Fig
u
r
e
9
.
State
d
iag
r
am
o
f
co
n
v
er
ter
o
p
er
atio
n
wh
e
n
M3
a
r
e
o
n
2.
1
.
2
.
Scena
rio
t
wo
L
ik
e
s
ce
n
ar
io
1
AC
2
-
AC
1
g
r
id
en
er
g
y
,
in
th
is
s
ce
n
ar
io
,
th
er
e
ar
e
s
im
ilar
m
o
d
es
an
d
co
n
v
er
te
r
o
p
er
atio
n
s
as
AC
1
to
AC
2
g
r
i
d
en
er
g
y
s
ce
n
ar
io
with
b
asic
co
n
d
itio
n
s
.
G
r
id
-
co
n
n
ec
ted
co
n
d
itio
n
,
u
s
in
g
b
o
th
lo
ad
p
r
io
r
ity
an
d
AC
m
icr
o
g
r
i
d
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
wo
r
k
in
g
in
d
ep
en
d
en
tly
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
B
id
ir
ec
tio
n
a
l A
C
/AC c
o
n
ve
r
ter lin
kin
g
tw
o
micro
g
r
id
s
in
a
flexib
le
micro
g
r
id
(
N
g
u
ye
n
Th
e
V
in
h
)
395
1
>
1
+
1
+
−
1
(
8
)
I
n
p
r
ac
tice
,
th
e
Pp
v
an
d
Pwin
s
o
u
r
ce
s
f
lu
ctu
ate
in
s
tan
tan
eo
u
s
ly
in
a
v
alu
e
th
at
r
e
q
u
ir
es c
o
m
p
en
s
atio
n
an
d
en
er
g
y
c
o
n
s
u
m
p
tio
n
.
1
>
1
+
−
1
(
9
)
Pp
v
s
to
p
s
g
en
er
atin
g
elec
tr
icity
d
u
r
i
n
g
o
f
f
-
p
ea
k
h
o
u
r
s
,
o
r
wh
en
th
e
b
am
b
o
o
is
o
b
s
cu
r
ed
b
y
clo
u
d
s
.
1
>
−
1
(
1
0
)
Pp
v
an
d
Pwin
s
o
u
r
ce
s
d
o
n
o
t
g
en
er
ate
en
e
r
g
y
.
2
.
2
.
Ca
s
es wher
e
inte
g
ra
t
io
n into
t
he
pro
po
s
ed
AC/AC
co
nv
er
t
er
is
po
s
s
ibl
e
2
.
2
.
1
.
Scena
rio
t
hree
Scen
ar
io
3
is
two
g
r
id
s
s
u
p
p
ly
en
er
g
y
to
th
e
s
to
r
ag
e
s
y
s
tem
wh
en
th
e
lo
a
d
o
f
g
r
id
AC
1
an
d
g
r
id
AC
2
d
ec
r
ea
s
es
o
r
th
e
p
o
wer
s
o
u
r
ce
o
f
th
e
two
g
r
id
s
in
cr
ea
s
es,
lea
d
in
g
to
ex
ce
s
s
en
er
g
y
f
r
o
m
th
e
two
g
r
id
s
.
At
th
is
tim
e,
th
e
s
to
r
a
g
e
s
y
s
tem
is
s
u
p
p
lied
(
c
h
ar
g
e
d
)
with
en
er
g
y
th
r
o
u
g
h
AC
/DC
o
r
AC
/AC
to
AC
/DC
co
n
v
er
ter
s
co
n
n
ec
ted
at
t
h
e
n
o
d
e
o
f
p
in
s
D
o
f
s
witch
es M
1
an
d
M3
i
n
t
h
e
p
o
wer
ci
r
cu
it
co
n
v
er
ter
as
s
h
o
wn
in
Fig
u
r
e
2
.
2
.
2
.
2
.
Scena
rio
f
o
ur
Scen
ar
io
4
is
two
m
icr
o
g
r
id
s
AC
1
an
d
AC
2
p
r
o
v
id
e
en
o
u
g
h
p
o
wer
f
o
r
th
e
lo
ad
,
th
e
AC
/AC
co
n
v
er
ter
d
o
es
n
o
t
o
p
er
ate,
an
d
th
e
two
g
r
id
s
wo
r
k
in
d
e
p
en
d
e
n
tly
.
I
n
th
e
p
o
wer
cir
cu
it,
th
er
e
m
u
s
t
b
e
t
wo
en
er
g
y
r
ec
o
v
er
y
cir
cu
its
Dp
h
1
an
d
C
p
h
1
t
o
lim
it
th
e
v
o
ltag
e
s
tr
ess
o
n
M1
an
d
M3
.
T
h
is
cir
cu
it
is
co
n
n
e
cted
to
th
e
D
p
o
le
o
f
M1
an
d
M3
as
s
h
o
wn
in
Fig
u
r
e
1
0
.
W
h
en
th
e
en
er
g
y
ac
cu
m
u
lated
f
r
o
m
th
e
co
ils
L
1
an
d
C
p
h
1
d
u
r
i
n
g
th
e
p
e
r
io
d
t1
-
t2
o
p
e
r
ates
in
th
e
p
o
s
itiv
e
h
alf
cy
cle,
th
e
o
p
en
in
g
tim
e
o
f
M1
en
d
s
at
t2
,
t
h
e
en
er
g
y
is
tr
an
s
f
er
r
ed
alo
n
g
th
e
p
ath
L
1
-
D3
-
Dp
h
1
-
AC
2
g
r
id
a
n
d
C
p
h
1
-
AC
2
g
r
i
d
.
L
i
k
e
r
ec
o
v
er
y
ci
r
cu
it
2
(
Dp
h
2
an
d
C
p
h
2
)
wh
e
n
o
p
er
atin
g
in
th
e
n
eg
ativ
e
h
alf
c
y
cle.
Fig
u
r
e
1
1
s
h
o
ws
a
r
ec
o
v
er
y
cir
cu
it
s
o
lu
tio
n
to
r
ed
u
ce
t
h
e
v
o
ltag
e
s
tr
ess
o
n
s
wi
tch
es
M1
an
d
M3
in
th
e
co
n
v
e
r
ter
.
T
h
is
is
a
s
u
itab
le
s
o
lu
tio
n
f
o
r
th
e
p
o
wer
cir
cu
it wh
en
th
e
v
o
ltag
e
s
tr
ess
s
ig
n
al
o
n
M1
is
ab
s
en
t a
n
d
th
er
e
is
a
r
ec
o
v
er
y
ci
r
cu
it so
lu
tio
n
.
2
.
3
.
P
r
o
po
s
ed
co
ntr
o
l m
ec
h
a
nis
m
f
o
r
AC/AC
co
nv
er
t
er
T
h
e
co
n
tr
o
l
m
eth
o
d
in
th
is
co
n
v
er
ter
is
as
f
o
llo
ws:
Ad
ju
s
t
th
e
v
o
ltag
e
p
ar
am
eter
s
.
B
y
ad
j
u
s
tin
g
th
e
p
u
ls
e
wid
th
ac
co
r
d
in
g
to
th
e
PW
M
[
2
6
]
m
o
d
u
latio
n
m
eth
o
d
as
s
h
o
wn
i
n
Fig
u
r
e
1
2
.
T
h
e
m
ea
s
u
r
ed
f
ee
d
b
ac
k
s
ig
n
al
is
th
e
v
o
ltag
e,
f
r
eq
u
e
n
c
y
an
d
p
h
ase
an
g
le
p
ar
am
eter
s
at
th
e
AC
2
m
icr
o
g
r
i
d
co
m
p
ar
e
d
to
th
e
in
p
u
t
s
ig
n
al
f
r
o
m
th
e
AC
1
g
r
i
d
,
th
er
e
b
y
p
r
o
v
id
in
g
c
o
n
tr
o
l
s
ig
n
als
f
o
r
th
e
s
witch
es
M1
,
M2
,
an
d
M3
with
th
e
DC
s
witch
in
g
tech
n
o
lo
g
y
in
th
e
p
o
wer
ci
r
cu
it
in
Fig
u
r
e
2
.
A
d
ju
s
t
th
e
o
p
er
atin
g
m
o
d
e
ac
co
r
d
in
g
to
t
h
e
p
o
wer
cir
cu
it
d
esig
n
o
f
th
e
AC
/AC
u
n
it
as
s
h
o
wn
in
Fig
u
r
e
1
2
.
Acc
o
r
d
i
n
g
to
th
e
f
o
u
r
m
ain
o
p
er
atin
g
s
ce
n
ar
i
o
s
o
f
t
h
e
co
n
v
er
ter
,
th
er
e
ar
e
s
ix
s
p
ec
if
ic
m
o
d
es a
s
an
aly
ze
d
a
b
o
v
e
f
o
r
s
ce
n
a
r
io
1
.
Fig
u
r
e
1
0
.
Vo
ltag
e
s
tr
ess
r
ed
u
ce
s
th
e
r
ec
o
v
er
y
cir
cu
it o
n
M1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
389
-
406
396
(
a)
(
b
)
Fig
u
r
e
1
1
.
C
ir
cu
it d
iag
r
am
c
o
m
p
ar
in
g
v
o
ltag
e
v
alu
es o
n
M
1
an
d
M3
w
h
en
th
er
e
is
a
r
ec
o
v
er
y
cir
cu
it
:
(
a)
v
o
ltag
e
o
n
M
1
with
o
u
t
r
ec
o
v
er
y
ci
r
cu
it Dp
h
1
&
C
p
h
1
an
d
(
b
)
v
o
ltag
e
o
n
M1
wh
en
th
e
r
e
is
r
ec
o
v
er
y
cir
cu
it Dp
h
1
&
C
p
h
1
Fig
u
r
e
1
2
.
B
lo
ck
d
iag
r
a
m
o
f
th
e
o
v
er
all
c
o
n
tr
o
l sectio
n
o
f
th
e
AC
/A
C
co
n
v
er
ter
o
p
er
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
B
id
ir
ec
tio
n
a
l A
C
/AC c
o
n
ve
r
ter lin
kin
g
tw
o
micro
g
r
id
s
in
a
flexib
le
micro
g
r
id
(
N
g
u
ye
n
Th
e
V
in
h
)
397
3.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
w
a
v
e
f
o
r
m
c
o
n
v
e
r
s
i
o
n
w
i
ll
b
e
a
f
f
e
c
t
e
d
b
y
p
a
r
a
m
e
t
e
r
s
s
u
c
h
a
s
p
a
r
a
s
i
ti
c
c
o
m
p
o
n
e
n
t
s
i
n
e
l
e
c
t
r
o
n
i
c
e
l
e
m
e
n
ts
;
p
u
ls
e
w
i
d
t
h
;
v
a
l
u
es
o
f
p
a
s
s
i
v
e
e
le
m
e
n
t
s
i
n
t
h
e
p
o
we
r
c
i
r
c
u
i
t;
s
w
it
c
h
i
n
g
k
e
y
,
a
n
d
s
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
.
T
h
e
s
i
m
u
l
a
t
i
o
n
p
a
r
t
wi
t
h
d
i
f
f
e
r
e
n
t
p
a
r
a
m
e
t
e
r
s
:
c
o
n
t
r
o
l
f
r
e
q
u
e
n
c
y
;
p
u
l
s
e
wi
d
t
h
M
1
,
M
3
,
M
2
;
an
d
l
o
a
d
p
o
w
e
r
v
a
l
u
e.
Fig
u
r
e
s
1
3
an
d
1
4
s
h
o
w
th
e
in
p
u
t
cu
r
r
en
t
an
d
v
o
ltag
e
s
ig
n
als
(
AC
1
g
r
id
-
co
r
r
esp
o
n
d
in
g
t
o
th
e
I
(
AC
m
g
1
)
a
n
d
V(
Acm
g
1
)
p
r
o
b
es)
a
n
d
th
e
o
u
tp
u
t
(
AC
2
g
r
i
d
-
co
r
r
esp
o
n
d
in
g
to
t
h
e
I
(
R
lo
ad
)
an
d
V(
R
lo
ad
)
p
r
o
b
es).
T
h
e
av
er
ag
e
p
o
wer
m
ea
s
u
r
e
d
at
th
e
in
p
u
t a
n
d
o
u
tp
u
t o
f
th
e
AC
/AC
co
n
v
er
ter
is
clo
s
e
to
th
e
v
alu
e
o
f
3
-
3
.
5
k
W
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
am
p
litu
d
e
v
alu
e
d
ec
r
ea
s
es
b
y
8
.
7
V
(
T
HD
=
3
.
9
)
,
w
h
en
in
cr
ea
s
in
g
th
e
d
u
ty
v
alu
e
o
f
M1
a
n
d
M2
t
o
7
5
%,
th
e
o
u
t
p
u
t
v
o
ltag
e
am
p
litu
d
e
d
ec
r
ea
s
es
with
in
th
e
v
alu
e
o
f
2
.
5
V
(
T
HD)
as
s
h
o
wn
in
Fig
u
r
e
1
3
.
T
h
u
s
,
th
e
T
HD
p
ar
am
eter
is
with
in
th
e
allo
w
ab
le
r
an
g
e
an
d
th
e
p
u
ls
e
wid
th
ca
n
b
e
ad
j
u
s
ted
ac
co
r
d
in
g
l
y
b
ec
au
s
e
if
th
e
p
u
ls
e
wid
th
o
f
M1
o
r
M2
o
r
b
o
th
M1
an
d
M2
is
in
cr
ea
s
ed
,
it
will
af
f
ec
t
th
e
ef
f
icien
c
y
o
f
th
e
c
o
n
v
er
te
r
(
it w
ill r
ed
u
c
e
th
e
ef
f
icien
c
y
)
an
d
th
e
life
o
f
th
e
s
witch
.
T
h
e
cu
r
r
en
t I
E
C
s
t
an
d
ar
d
is
is
s
u
ed
b
y
th
e
I
n
ter
n
atio
n
al
T
ec
h
n
ical
C
o
m
m
ittee
I
n
ter
n
atio
n
al
E
lectr
o
t
ec
h
n
ical
C
o
m
m
is
s
io
n
p
u
b
lis
h
e
d
.
Fig
u
r
e
1
3
.
T
h
e
3
.
5
k
W
,
d
u
ty
M1
an
d
M3
=
10%
,
d
u
ty
M
2
=
6
0
%
,
f
r
e
q
u
en
c
y
f
o
r
s
witch
=
30
k
Hz
Fig
u
r
e
1
4
.
T
h
e
3
k
W
,
d
u
ty
M1
an
d
M3
=
10%
,
d
u
ty
M2
=
6
0
%
,
f
r
eq
u
en
c
y
f
o
r
s
witch
=
30
k
Hz
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
389
-
406
398
Fig
u
r
e
1
5
s
h
o
ws
th
e
in
p
u
t
an
d
o
u
tp
u
t
v
o
ltag
e
cu
r
r
en
t
s
ig
n
als
o
f
th
e
co
n
v
er
ter
,
th
e
av
er
ag
e
p
o
wer
v
alu
e
with
th
e
in
p
u
t
p
ar
a
m
eter
s
o
f
t
h
e
AC
/AC
co
n
v
er
ter
with
a
c
ap
ac
ity
o
f
2
.
5
k
W
.
W
ith
th
is
i
n
p
u
t
p
ar
am
eter
,
th
e
co
n
v
er
ter
o
p
e
r
ates
well
with
a
s
witch
in
g
co
n
tr
o
l
f
r
eq
u
en
cy
o
f
6
0
k
Hz.
T
h
e
o
u
tp
u
t
v
o
ltag
e
am
p
litu
d
e
v
alu
e
o
f
AC
g
r
id
2
is
r
e
d
u
ce
d
co
m
p
a
r
e
d
to
AC
g
r
id
1
b
y
6
V.
Fro
m
h
er
e,
we
ca
n
a
d
ju
s
t
th
e
f
r
e
q
u
en
cy
v
al
u
e,
an
d
th
e
p
u
ls
e
wid
th
o
f
th
e
M1
a
n
d
M
2
s
witch
es
to
en
s
u
r
e
th
at
th
e
v
o
ltag
e
am
p
litu
d
e
r
ea
ch
es
th
e
s
am
e
v
alu
e
as
th
e
s
in
g
le
-
p
h
ase
AC
g
r
id
.
Fig
u
r
e
1
6
s
h
o
ws
th
e
in
p
u
t
an
d
o
u
tp
u
t
v
o
ltag
e
cu
r
r
en
t
s
ig
n
als
o
f
th
e
co
n
v
er
ter
,
th
e
av
er
ag
e
p
o
wer
v
alu
e
with
th
e
in
p
u
t
p
ar
am
eter
s
o
f
t
h
e
AC
/AC
co
n
v
er
ter
with
a
ca
p
ac
ity
o
f
2
k
W
.
W
ith
th
is
in
p
u
t
p
ar
am
eter
,
t
h
e
co
n
v
er
ter
o
p
er
ates
well
with
a
s
witch
in
g
co
n
tr
o
l
f
r
eq
u
en
cy
o
f
3
0
k
Hz,
th
e
p
u
ls
e
wid
th
o
f
th
e
s
witch
es
v
ar
ies
with
th
e
v
alu
es
M1
an
d
M3
=
1
0
%,
M2
=
4
0
%.
T
h
e
o
u
tp
u
t
v
o
ltag
e
am
p
litu
d
e
v
al
u
e
o
f
A
C
g
r
id
2
is
r
ed
u
ce
d
co
m
p
ar
ed
to
AC
g
r
id
1
b
y
4
V.
Fro
m
h
er
e
,
we
ca
n
a
d
ju
s
t th
e
f
r
eq
u
en
cy
v
alu
e,
an
d
t
h
e
p
u
ls
e
wid
th
o
f
th
e
M1
an
d
M2
s
witch
es
to
en
s
u
r
e
th
at
th
e
v
o
ltag
e
a
m
p
litu
d
e
r
ea
c
h
es
th
e
s
am
e
v
alu
e
as
th
e
s
in
g
le
-
p
h
ase
AC
g
r
id
.
Fig
u
r
e
1
7
is
lik
e
th
e
ca
s
e
o
f
th
e
co
n
v
er
ter
d
escr
ib
ed
in
Fig
u
r
e
1
6
.
T
h
e
in
p
u
t
p
ar
am
eter
a
d
j
u
s
ts
th
e
p
o
wer
with
a
v
alu
e
o
f
1
.
5
k
W
.
T
h
e
b
asic o
u
tp
u
t v
o
ltag
e
a
n
d
cu
r
r
en
t f
o
r
m
d
o
n
o
t c
h
an
g
e
in
t
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
wh
en
s
witch
in
g
f
r
eq
u
e
n
cy
an
d
co
n
tr
o
l p
u
ls
e
wid
th
M1
a
n
d
M2
as sh
o
wn
in
Fig
u
r
e
1
6
.
Fig
u
r
e
1
5
.
C
ir
cu
it p
o
wer
2
.
5
k
W
,
d
u
ty
M1
an
d
M3
=
10%
,
d
u
ty
M2
=
6
0
%
,
f
r
e
q
u
en
c
y
f
o
r
s
witch
=
30
k
Hz
Fig
u
r
e
1
6
.
Po
wer
2
k
W
,
d
u
ty
M1
an
d
M3
=
10%
,
d
u
ty
M
2
=
4
0
%
,
f
r
e
q
u
en
c
y
f
o
r
s
witch
=
30
k
Hz
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