I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
,
p
p
.
2
1
7
~
2
2
9
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
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.
1
1
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9
1
/ijap
e.
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.
p
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2
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-
229
217
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
p
e.
ia
esco
r
e.
co
m
Pros
pects of
rege
nera
tive cur
rent
brea
king
in
D
C ci
rcuit
brea
ker t
o
po
lo
g
y
S.
M
.
Sa
nza
d L
um
en,
Ra
m
a
ni K
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a
n,
No
r
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a
iha
r
Ya
ha
y
a
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
E
n
g
i
n
e
e
rin
g
,
Un
iv
e
rsiti
T
e
k
n
o
l
o
g
i
P
ET
RON
AS,
S
e
ri
Isk
a
n
d
a
r,
Ip
o
h
,
M
a
lay
sia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
17
,
2
0
20
R
ev
is
ed
Feb
5
,
2
0
21
Acc
ep
ted
Ap
r
4
,
2
0
21
Du
e
to
th
e
st
u
n
n
in
g
a
d
v
a
n
c
e
m
e
n
t
o
f
p
o
we
r
e
lec
tro
n
ics
,
DC
p
o
we
r
sy
ste
m
is
g
e
tt
in
g
imm
e
n
se
a
tt
e
n
ti
o
n
in
th
e
field
o
f
re
se
a
rc
h
.
P
r
o
tec
ti
o
n
a
n
d
h
e
re
a
fter
th
e
p
ro
tec
ti
v
e
d
e
v
ice
s
fo
r
th
e
DC
p
o
we
r
sy
ste
m
a
p
p
li
c
a
ti
o
n
a
re
two
v
it
a
l
a
re
a
s
th
a
t
n
e
e
d
to
b
e
e
x
p
l
o
re
d
a
n
d
d
e
v
e
l
o
p
e
d
fu
rt
h
e
r.
De
sig
n
in
g
a
p
ro
tec
ti
v
e
d
e
v
ice
su
c
h
a
s
DC
c
ircu
it
b
re
a
k
e
r
p
o
ss
e
ss
e
s
a
l
o
t
o
f
c
h
a
ll
e
n
g
e
s.
Th
e
m
a
in
c
h
a
ll
e
n
g
e
is
to
in
terru
p
t
a
c
u
r
re
n
t
wh
ich
d
o
e
s n
o
t
h
a
v
e
a
n
a
tu
ra
l
z
e
r
o
c
ro
ss
i
n
g
li
k
e
AC
c
u
rre
n
t
h
a
s.
I
n
a
d
d
it
i
o
n
,
e
n
e
rg
y
is
sto
re
d
i
n
t
h
e
n
e
two
rk
i
n
d
u
c
ta
n
c
e
s
d
u
ri
n
g
n
o
rm
a
l
o
p
e
ra
ti
o
n
.
I
n
sta
n
t
a
n
e
o
u
s
c
u
rre
n
t
b
re
a
k
i
n
g
is
o
p
p
o
se
d
b
y
t
h
is
sto
re
d
e
n
e
rg
y
d
u
rin
g
c
ircu
it
b
r
e
a
k
e
r
tri
p
p
i
n
g
,
h
e
n
c
e
,
a
ll
th
e
DC
c
ircu
it
b
re
a
k
e
r
to
p
o
lo
g
ies
p
ro
p
o
se
d
i
n
li
tera
tu
re
u
se
sn
u
b
b
e
r
n
e
two
r
k
,
n
o
n
l
in
e
a
r
re
sisto
r
t
o
d
issip
a
te
t
h
is
sto
re
d
e
n
e
rg
y
a
s
h
e
a
t
d
u
rin
g
th
e
c
u
rre
n
t
b
re
a
k
i
n
g
o
p
e
ra
ti
o
n
.
Ho
we
v
e
r,
it
is
p
o
ss
ib
le
to
st
o
re
th
is
e
n
e
rg
y
m
o
m
e
n
taril
y
a
n
d
re
u
se
it
late
r
b
y
d
e
v
e
l
o
p
i
n
g
a
n
imp
r
o
v
i
se
d
to
p
o
l
o
g
y
.
I
n
th
is
p
a
p
e
r,
th
e
p
ro
sp
e
c
ts
o
f
e
n
e
rg
y
re
c
o
v
e
ry
a
n
d
re
u
se
i
n
a
DC
c
ircu
it
b
re
a
k
e
r
wa
s
stu
d
ied
a
n
d
a
n
e
w
to
p
o
lo
g
y
wi
th
re
g
e
n
e
ra
ti
v
e
c
u
rre
n
t
b
re
a
k
i
n
g
c
a
p
a
b
il
it
y
h
a
d
b
e
e
n
p
ro
p
o
se
d
.
Th
is
n
e
w
to
p
o
l
o
g
y
c
a
n
fe
e
d
t
h
e
sto
re
d
e
n
e
r
g
y
o
f
th
e
n
e
two
r
k
b
a
c
k
in
t
o
th
e
sa
m
e
n
e
two
rk
a
fter
b
re
a
k
in
g
th
e
c
u
rre
n
t
a
n
d
th
u
s
c
a
n
imp
ro
v
e
th
e
o
v
e
ra
ll
sy
ste
m
e
fficie
n
c
y
.
K
ey
w
o
r
d
s
:
C
u
r
r
en
t b
r
ea
k
in
g
DC
cir
cu
it b
r
ea
k
er
Fau
lt c
u
r
r
en
t
Pro
tectio
n
R
eg
en
er
atio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
S.
M.
San
za
d
L
u
m
e
n
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
Un
iv
er
s
iti T
ek
n
o
lo
g
i PE
T
R
O
NAS
Ser
i I
s
k
an
d
ar
,
I
p
o
h
,
Ma
lay
s
ia
E
m
ail: s_
1
8
0
0
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3
0
9
@
u
tp
.
ed
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
Mic
r
o
g
r
id
c
o
n
ce
p
t
h
as
em
er
g
ed
as
th
e
n
ew
n
o
r
m
s
f
o
r
elec
t
r
icity
d
is
tr
ib
u
tio
n
r
ec
en
tly
.
As
s
tated
in
liter
atu
r
e
th
at
“M
icr
o
g
r
id
s
ar
e
lo
ca
l
en
er
g
y
n
etwo
r
k
s
th
at
in
v
o
lv
e
r
en
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
”.
DC
m
icr
o
g
r
id
is
a
c
o
n
v
en
ie
n
t
m
ec
h
a
n
is
m
f
o
r
in
te
g
r
atin
g
d
is
tr
ib
u
ted
en
e
r
g
y
r
es
o
u
r
ce
s
(
DE
R
s
)
an
d
lo
ca
l
lo
ad
s
in
to
a
f
u
lly
in
te
g
r
a
ted
s
y
s
tem
.
Dif
f
er
en
t
ty
p
es
o
f
v
o
ltag
e
s
o
u
r
ce
c
o
n
v
e
r
ter
(
VSC
)
lik
e
AC
to
D
C
,
DC
to
DC
ar
e
u
s
ed
as
b
u
ild
in
g
b
lo
c
k
s
f
o
r
t
h
e
m
icr
o
g
r
i
d
n
etwo
r
k
.
DC
m
icr
o
g
r
id
s
h
av
e
d
em
o
n
s
tr
ate
d
s
u
p
er
io
r
ity
o
v
er
AC
m
icr
o
g
r
id
s
in
te
r
m
s
o
f
r
eliab
ilit
y
,
ef
f
icien
cy
,
co
n
tr
o
l
s
im
p
lici
ty
,
in
teg
r
atio
n
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
an
d
co
n
n
ec
tio
n
o
f
DC
lo
ad
s
.
Nev
er
th
eless
,
DC
p
o
wer
s
y
s
t
em
is
also
g
ettin
g
im
m
en
s
e
atten
tio
n
in
th
e
f
ield
o
f
HVDC
tr
an
s
m
is
s
io
n
,
elec
tr
ic
v
eh
icle,
elec
tr
ic
tr
ac
tio
n
l
o
ad
.
Desp
ite
th
ese
m
an
y
a
d
v
an
tag
es,
t
h
er
e
ar
e
s
ig
n
if
ican
t
ch
alle
n
g
es
to
d
esig
n
an
ap
p
r
o
p
r
iate
p
r
o
tectio
n
s
ch
em
e
f
o
r
DC
p
o
wer
s
y
s
tem
as
well.
B
asically
,
th
e
ch
allen
g
e
s
tem
s
f
r
o
m
th
e
n
atu
r
e
o
f
DC
f
au
lt
c
u
r
r
e
n
t,
wh
ich
c
an
r
a
p
id
ly
in
cr
ea
s
e
to
m
o
r
e
th
a
n
a
h
u
n
d
r
ed
tim
es
o
f
th
e
n
o
m
in
al
c
u
r
r
en
t
d
u
r
i
n
g
s
u
d
d
en
f
au
lt
in
ce
p
tio
n
an
d
h
as
n
o
n
atu
r
ally
o
cc
u
r
r
in
g
ze
r
o
cr
o
s
s
in
g
p
o
in
t
lik
e
AC
h
as.
Pr
o
p
er
g
r
o
u
n
d
i
n
g
ar
ch
itectu
r
e,
f
ast
an
d
ef
f
icien
t
f
a
u
lt
d
etec
tio
n
s
tr
ateg
y
,
f
au
lt
c
u
r
r
e
n
t
lim
itin
g
m
eth
o
d
a
n
d
a
n
ap
p
r
o
p
r
iate
DC
cir
cu
it
b
r
ea
k
er
(
D
C
C
B
)
ar
e
r
eq
u
ir
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
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8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
2
1
7
–
229
218
to
ad
d
r
ess
th
e
ch
allen
g
es
o
f
DC
s
y
s
tem
p
r
o
tectio
n
[
1
]
-
[
3
]
.
DC
C
B
u
s
ed
f
o
r
cu
r
r
en
t
i
n
ter
r
u
p
tio
n
in
a
DC
n
etwo
r
k
is
an
in
teg
r
al
p
ar
t
o
f
th
e
s
y
s
tem
.
I
n
th
is
p
ap
er
,
d
if
f
er
en
t
ty
p
es
o
f
DC
C
B
to
p
o
lo
g
ies
h
ad
b
ee
n
d
is
cu
s
s
ed
to
ex
p
lo
it
th
eir
lim
it
atio
n
s
an
d
a
n
ew
t
o
p
o
lo
g
y
wit
h
u
n
iq
u
e
cu
r
r
en
t
b
r
ea
k
in
g
f
ea
t
u
r
e
was
p
r
esen
ted
an
d
e
v
alu
ated
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
p
ap
er
is
as
f
o
llo
ws:
S
ec
tio
n
1
g
iv
es
t
h
e
b
r
ief
b
ac
k
g
r
o
u
n
d
o
f
th
e
to
p
ic
alo
n
g
with
lit
er
atu
r
e
r
ev
iews,
r
elate
d
wo
r
k
s
,
an
d
p
r
o
b
lem
s
tatem
en
t.
Sectio
n
2
in
tr
o
d
u
ce
s
an
d
d
is
cu
s
s
es
th
e
n
ew
DC
C
B
to
p
o
lo
g
y
.
Sectio
n
3
d
escr
ib
es
th
e
r
esear
ch
m
eth
o
d
o
lo
g
y
in
d
etail
with
a
m
eth
o
d
o
lo
g
y
f
lo
w
ch
a
r
t
an
d
later
d
is
cu
s
s
es
th
e
m
ath
e
m
atica
l
m
o
d
ellin
g
a
n
d
wo
r
k
in
g
p
r
in
ci
p
le
o
f
t
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
th
o
r
o
u
g
h
ly
.
Sectio
n
4
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
,
co
m
p
ar
e
th
e
p
e
r
f
o
r
m
a
n
ce
with
co
n
v
e
n
tio
n
al
to
p
o
lo
g
y
an
d
t
h
u
s
v
alid
ates th
e
p
r
o
p
o
s
ed
co
n
ce
p
t.
I
n
o
r
d
er
to
b
r
ea
k
th
e
cu
r
r
en
t
in
an
y
n
etwo
r
k
,
cir
cu
it
b
r
ea
k
er
s
ar
e
u
s
ed
.
C
ir
cu
it
b
r
ea
k
e
r
s
u
s
u
ally
m
ak
e
a
b
r
ea
k
i
n
th
e
cu
r
r
e
n
t
p
ath
b
y
s
ep
ar
atin
g
m
ec
h
an
ica
l
co
n
tacts
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r
b
y
s
o
lid
s
tate
tu
r
n
o
f
f
p
r
o
ce
s
s
.
I
n
m
ec
h
an
ical
tu
r
n
o
f
f
p
r
o
ce
s
s
,
a
s
th
e
co
n
tacts
s
ep
ar
ate,
ar
c
is
in
itiated
in
b
etwe
en
th
em
,
a
n
d
th
is
ar
c
n
ee
d
s
to
b
e
ex
tin
g
u
is
h
e
d
q
u
ick
ly
to
b
r
ea
k
th
e
cu
r
r
en
t
e
f
f
icien
tly
as
well
as
to
k
ee
p
th
e
c
o
n
tacts
u
n
d
am
a
g
ed
.
I
n
AC
n
etwo
r
k
d
u
e
to
th
e
s
in
u
s
o
id
al
n
atu
r
e
o
f
th
e
cu
r
r
e
n
t,
n
at
u
r
al
c
u
r
r
en
t
ze
r
o
s
itu
atio
n
ar
is
es
twice
in
a
f
u
ll
cy
cle.
Usi
n
g
d
if
f
er
en
t
ar
c
ex
tin
g
u
is
h
in
g
tech
n
iq
u
es,
cir
c
u
it
b
r
ea
k
e
r
u
s
u
ally
b
r
ea
k
s
th
e
cu
r
r
en
t
at
th
ese
cu
r
r
en
t
ze
r
o
in
s
tan
ce
s
.
T
h
is
p
r
o
ce
s
s
o
f
cu
r
r
en
t
b
r
ea
k
in
g
is
q
u
ite
s
tr
aig
h
t
f
o
r
war
d
in
AC
n
etwo
r
k
b
u
t
in
DC
n
etwo
r
k
,
it
is
n
o
t
th
at
s
im
p
le.
Natu
r
al
c
u
r
r
en
t
ze
r
o
is
n
o
t
av
ailab
le
in
DC
n
etwo
r
k
an
d
th
at
m
ak
es
th
e
b
r
ea
k
in
g
o
f
DC
cu
r
r
en
t
u
s
in
g
co
n
v
en
tio
n
al
ci
r
cu
it
b
r
ea
k
e
r
v
er
y
ch
allen
g
in
g
[
4
]
,
[
5
]
.
Fu
r
th
er
m
o
r
e,
wh
e
n
cu
r
r
en
t
f
l
o
ws
in
a
DC
n
etwo
r
k
,
e
n
er
g
y
is
s
to
r
ed
in
th
e
in
d
u
ctan
ce
o
f
t
h
e
lin
e
as
well
as
in
th
e
f
ilter
elem
e
n
ts
o
f
th
e
DC
/DC
co
n
v
er
ter
s
.
As
a
r
esu
lt,
cu
r
r
e
n
t
in
th
is
n
etwo
r
k
ca
n
n
o
t
b
e
b
r
o
k
e
n
in
s
tan
tan
eo
u
s
ly
,
o
th
er
wis
e
it
will
cr
ea
te
h
ig
h
p
o
ten
tial
s
tr
ess
o
n
th
e
b
r
ea
k
er
co
n
tacts,
cr
ea
te
a
n
d
m
a
in
tain
ar
c
f
o
r
lo
n
g
er
p
e
r
io
d
o
f
tim
e
an
d
d
a
m
ag
e
th
e
co
n
tacts
in
th
e
p
r
o
ce
s
s
.
Similar
ly
,
in
ca
s
e
o
f
s
o
lid
s
tate
tu
r
n
o
f
f
p
r
o
ce
s
s
,
s
u
d
d
en
ce
asi
n
g
o
f
cu
r
r
en
t
f
lo
w
in
an
in
d
u
ctiv
e
DC
n
etwo
r
k
will
d
ev
elo
p
a
h
ig
h
p
o
te
n
tial
s
tr
ess
ac
r
o
s
s
th
e
d
ev
ice
an
d
m
ay
d
a
m
ag
e
it.
Fo
r
s
af
e
an
d
ef
f
icien
t
b
r
ea
k
in
g
o
f
DC
cu
r
r
e
n
t,
it
m
u
s
t
b
e
r
ed
u
c
ed
to
ze
r
o
an
d
th
e
s
to
r
ed
en
er
g
y
o
f
t
h
e
n
etwo
r
k
m
u
s
t
b
e
d
is
s
ip
ated
d
u
r
in
g
th
e
p
r
o
ce
s
s
.
Sn
u
b
b
er
n
etwo
r
k
o
r
im
p
e
d
an
ce
n
etwo
r
k
o
r
n
o
n
lin
ea
r
r
esis
to
r
o
r
a
co
m
b
in
atio
n
o
f
th
em
ar
e
u
s
ed
in
th
e
DC
C
B
to
ab
s
o
r
b
an
d
d
is
s
ip
ate
th
e
n
etwo
r
k
e
n
er
g
y
as
h
ea
t
an
d
to
ass
is
t
in
th
e
cu
r
r
en
t
r
ed
u
ctio
n
f
o
llo
wed
b
y
b
r
ea
k
in
g
.
As
p
er
liter
atu
r
e,
DC
cir
cu
it
b
r
ea
k
er
s
ar
e
m
ain
ly
d
iv
id
ed
in
to
th
r
ee
ca
teg
o
r
ies:
1
)
Me
ch
an
ic
al
cir
cu
it
b
r
ea
k
er
s
wh
ic
h
ar
e
s
im
ilar
to
th
e
tr
ad
itio
n
al
m
ec
h
an
ical
s
witch
es;
2
)
So
lid
-
s
tate
cir
cu
it
b
r
ea
k
er
s
th
at
p
er
f
o
r
m
in
ter
r
u
p
tio
n
b
y
p
o
wer
elec
tr
o
n
ic
d
e
v
ices
an
d
3
)
Hy
b
r
id
cir
c
u
it
b
r
ea
k
er
s
th
at
co
m
b
in
e
b
o
th
m
ec
h
an
ical
an
d
s
o
lid
-
s
tate
tech
n
o
lo
g
ies
to
g
eth
er
.
B
esid
es,
with
th
e
d
ev
elo
p
m
en
t
o
f
p
o
wer
elec
tr
o
n
ics,
DC
s
o
lid
-
s
tate
cir
cu
it
b
r
ea
k
er
s
h
av
e
also
b
ee
n
g
r
ea
tly
im
p
r
o
v
e
d
an
d
an
u
p
g
r
ad
ed
v
er
s
io
n
ca
lled
Z
-
s
o
u
r
ce
s
o
lid
-
s
tate
cir
cu
it b
r
ea
k
er
h
as b
ee
n
p
r
o
p
o
s
ed
[
6
]
-
[
8
]
.
T
h
e
b
asic
m
ec
h
an
ical
cir
cu
it
b
r
ea
k
er
(
MCB
)
is
co
m
p
o
s
ed
o
f
a
m
ec
h
an
ical
s
witch
,
a
co
m
m
u
tatio
n
cir
cu
it,
an
d
an
en
er
g
y
a
b
s
o
r
b
er
cir
cu
it.
T
h
e
s
ch
em
e
o
f
MCB
u
s
in
g
p
ass
iv
e
an
d
ac
tiv
e
c
o
m
m
u
tatio
n
cir
c
u
its
ar
e
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
.
U
n
d
er
n
o
r
m
al
o
p
er
atin
g
co
n
d
i
tio
n
,
th
e
m
ec
h
an
ical
s
witch
co
n
d
u
cts
t
h
e
lo
a
d
cu
r
r
en
t.
On
ce
th
e
b
r
ea
k
er
r
ec
e
iv
es
a
tr
ip
s
ig
n
al,
th
e
m
ec
h
an
ical
s
witch
o
p
en
s
,
an
d
an
ar
c
is
in
itiated
.
T
h
e
ar
c
v
o
ltag
e
f
o
r
ce
s
th
e
cu
r
r
e
n
t
to
s
h
if
t
f
r
o
m
t
h
e
lo
ad
c
u
r
r
en
t p
ath
to
th
e
co
m
m
u
tatio
n
p
ath
.
T
h
e
n
th
e
co
m
m
u
tatio
n
cir
cu
it
co
n
s
is
tin
g
o
f
a
ca
p
ac
i
to
r
an
d
in
d
u
cto
r
in
s
er
ies
g
e
n
er
ates
a
g
r
o
win
g
cu
r
r
e
n
t
o
s
cillatio
n
.
W
h
ile
th
e
am
p
litu
d
e
o
f
t
h
e
o
s
cillatin
g
c
o
m
m
u
tatio
n
c
u
r
r
en
t
(
I
c
)
b
ec
o
m
es
s
u
f
f
icien
tly
lar
g
e,
ze
r
o
-
c
r
o
s
s
in
g
p
o
in
ts
ar
e
cr
ea
ted
in
th
e
m
ec
h
an
ical
s
witch
cu
r
r
e
n
t
(
I
n
)
a
n
d
t
h
e
m
ec
h
an
ical
s
witch
ex
tin
g
u
is
h
es
th
e
ar
c
a
n
d
in
te
r
r
u
p
ts
th
e
cu
r
r
en
t
at
th
e
f
ir
s
t
ze
r
o
cr
o
s
s
in
g
p
o
in
t.
A
m
etal
o
x
id
e
v
ar
is
to
r
s
(
MO
V)
i
s
u
s
ed
to
lim
i
t
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
s
witch
.
T
h
e
m
ain
ad
v
an
t
ag
es
o
f
MCB
s
ar
e
lo
w
p
o
wer
lo
s
s
an
d
r
elativ
ely
lo
w
co
s
t;
h
o
wev
er
,
s
lo
w
r
esp
o
n
s
e
tim
e
an
d
lim
ited
cu
r
r
en
t in
ter
r
u
p
tio
n
ca
p
a
b
ilit
y
ar
e
th
e
m
ain
d
is
ad
v
a
n
tag
es [
9
]
,
[
1
0
]
.
Sem
ico
n
d
u
cto
r
b
ased
s
witch
es
ar
e
u
s
ed
as
th
e
cu
r
r
en
t
in
ter
r
u
p
tin
g
elem
en
t
in
DC
cir
cu
it
b
r
ea
k
er
to
ad
d
r
ess
th
e
p
r
o
b
lem
o
f
s
lo
w
tim
e
r
esp
o
n
s
e.
A
t
y
p
ical
s
o
lid
-
s
tate
cir
cu
it
b
r
ea
k
er
(
SS
C
B
)
is
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
.
Am
o
n
g
th
e
d
if
f
er
en
t
ty
p
e
o
f
s
em
ico
n
d
u
cto
r
s
witch
in
g
d
ev
ices,
th
y
r
is
to
r
,
GT
O
,
I
GC
T
an
d
I
GB
T
ar
e
m
o
s
tly
u
s
ed
as
SS
C
B
.
T
h
e
o
p
er
atio
n
p
r
o
ce
d
u
r
e
is
v
er
y
s
im
p
le
in
SS
C
B
.
E
x
ce
p
t
th
y
r
is
to
r
,
all
th
e
r
em
ain
in
g
s
witch
es
ar
e
f
u
lly
c
o
n
tr
o
llab
le
m
ea
n
in
g
t
h
at
th
ey
ca
n
b
e
tu
r
n
ed
o
n
o
r
tu
r
n
ed
o
f
f
ea
s
ily
b
y
co
n
tr
o
l
s
ig
n
al.
B
u
t
th
y
r
is
to
r
r
eq
u
ir
es
ex
tr
a
co
m
m
u
tatio
n
cir
c
u
it
f
o
r
tu
r
n
o
f
f
p
r
o
ce
s
s
an
d
it
tak
es
ti
m
e
an
d
th
is
d
elay
lead
s
to
h
ig
h
f
a
u
lt
cu
r
r
e
n
t.
Ho
wev
er
,
th
y
r
is
to
r
s
h
av
e
th
e
lo
west
co
n
d
u
ctio
n
lo
s
s
es
an
d
s
u
ch
a
lo
w
o
n
-
s
tate
lo
s
s
r
esu
lts
in
r
ed
u
ctio
n
o
f
o
v
er
all
co
s
ts
o
f
th
e
SS
C
B
.
A
MO
V
is
u
s
ed
p
ar
allel
to
th
e
s
witch
in
g
d
ev
ice
to
lim
it
th
e
v
o
ltag
e
s
u
r
g
e
d
u
r
in
g
cu
r
r
en
t
in
te
r
r
u
p
tio
n
.
T
h
o
u
g
h
SS
C
B
p
r
o
v
id
es
f
aster
o
p
er
atio
n
b
u
t
h
i
g
h
er
co
n
d
u
ctio
n
lo
s
s
an
d
b
u
lk
y
co
o
lin
g
s
y
s
tem
s
ar
e
two
o
f
its
lim
itatio
n
s
[
1
1
]
-
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
r
o
s
p
ec
ts
o
f reg
en
era
tive
cu
r
r
en
t b
r
ea
kin
g
in
DC
circu
it b
r
ea
ke
r
to
p
o
lo
g
y
(
S
.
M.
S
a
n
z
a
d
Lu
men
)
219
(
a)
(
b
)
Fig
u
r
e
1
.
T
y
p
ical
DC
C
B
to
p
o
lo
g
y
;
(
a
)
MCB
with
:
(
1
)
Pas
s
iv
e
co
m
m
u
tatio
n
cir
cu
it,
(
2
)
Activ
e
co
m
m
u
tatio
n
ci
r
cu
i
t
;
(
b
)
SS
C
B
b
ased
o
n
:
(
1
)
I
GB
T
,
(
2
)
T
h
y
r
is
to
r
Hy
b
r
id
cir
cu
it
b
r
ea
k
er
(
HC
B
)
is
a
n
ew
class
o
f
DC
C
B
th
at
co
m
b
in
es
b
o
t
h
th
e
MCB
an
d
th
e
SS
C
B
to
tak
e
ad
v
an
tag
es
o
f
b
o
th
.
A
s
a
r
esu
lt,
H
C
B
s
h
av
e
ad
v
an
tag
es
s
u
ch
as
f
ast
r
e
s
p
o
n
s
e,
lo
w
p
o
wer
lo
s
s
an
d
n
eg
lig
ib
le
ar
cin
g
ac
r
o
s
s
th
e
m
ec
h
an
ical
co
n
tacts.
As
s
h
o
wn
in
Fig
u
r
e
2
(
a)
,
a
co
n
v
e
n
ti
o
n
al
HC
B
h
as
th
r
ee
m
ain
p
ar
ts
in
clu
d
in
g
a
f
ast
-
m
ec
h
an
ical
s
witch
(
FMS)
,
a
h
ig
h
-
v
o
ltag
e
s
o
lid
s
tate
(
SS
)
s
witch
as
th
e
m
ain
b
r
ea
k
er
(
MB),
an
d
a
MO
V.
D
u
r
in
g
n
o
r
m
al
o
p
e
r
atio
n
,
t
h
e
cu
r
r
en
t
p
ass
es
th
r
o
u
g
h
FMS.
W
h
en
a
tr
i
p
s
ig
n
al
is
r
ec
eiv
ed
,
th
e
FMS
s
tar
ts
o
p
en
in
g
an
d
s
en
d
s
a
tu
r
n
-
o
n
s
ig
n
al
to
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e
MB.
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e
to
th
e
ar
c
v
o
l
tag
e,
cu
r
r
e
n
t
s
h
if
ts
n
atu
r
ally
f
r
o
m
th
e
FMS
to
th
e
MB.
On
ce
th
e
FMS
g
ai
n
s
s
u
f
f
icien
t
b
r
ea
k
d
o
wn
s
tr
en
g
th
,
th
e
MB
is
tu
r
n
ed
o
f
f
an
d
th
e
v
o
ltag
e
in
cr
ea
s
es
r
a
p
id
ly
b
ec
a
u
s
e
o
f
cir
cu
it
in
d
u
ctan
ce
s
.
W
h
ile
th
e
v
o
ltag
e
r
ea
ch
es
b
r
ea
k
d
o
wn
v
o
ltag
e,
th
e
MO
V
tu
r
n
s
o
n
t
o
clam
p
v
o
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an
d
th
e
f
au
lt
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u
r
r
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t
n
o
w
c
o
m
m
u
tes
th
r
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g
h
MO
V
an
d
d
ec
ay
s
to
ze
r
o
.
Fin
ally
,
wh
en
th
e
c
u
r
r
en
t
b
ec
o
m
es
ze
r
o
,
th
e
r
es
id
u
al
cu
r
r
en
t
b
r
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k
er
(
R
C
B
)
o
p
en
s
to
p
r
o
v
id
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co
m
p
lete
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alv
a
n
ic
is
o
latio
n
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Desp
ite
h
av
in
g
m
a
n
y
a
d
v
an
ta
g
es,
HC
B
h
as
f
ew
ch
allen
g
es
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well.
Dif
f
er
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ce
s
in
r
ea
ctio
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tim
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d
cu
r
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en
t
r
atin
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f
th
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FMS
b
r
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ch
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d
MB
b
r
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ch
,
d
ep
en
d
en
cy
o
f
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h
an
ical
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n
tacts
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ep
ar
atio
n
o
n
th
e
f
au
lt m
a
g
n
it
u
d
e,
r
e
q
u
ir
em
e
n
t f
o
r
a
h
ig
h
er
ar
c
v
o
ltag
e
a
r
e
f
ew
o
f
th
e
ch
al
len
g
es [
1
5
]
-
[
1
7
]
.
Z
-
So
u
r
ce
cir
c
u
it
b
r
ea
k
er
(
Z
SC
B
)
is
a
d
ev
elo
p
ed
f
o
r
m
o
f
th
e
SS
C
B
.
T
h
e
s
ch
em
e
o
f
t
h
e
o
r
ig
in
al
Z
SC
B
i
s
s
h
o
wn
in
Fig
u
r
e
2
(
b
)
.
W
h
ile
in
o
p
er
atio
n
,
o
n
ce
th
e
f
au
lt
o
cc
u
r
s
,
th
e
f
a
u
lt
cu
r
r
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n
t
f
lo
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th
r
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g
h
th
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ca
p
ac
ito
r
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a
s
th
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cu
r
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en
t
th
r
o
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g
h
th
e
in
d
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cto
r
ca
n
n
o
t
c
h
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g
e
in
s
tan
tan
eo
u
s
ly
.
At
th
is
p
o
in
t,
ea
ch
o
f
th
e
ca
p
ac
ito
r
cu
r
r
en
t
i
n
cr
ea
s
es
to
r
ea
ch
t
h
e
p
r
ef
au
lt
in
d
u
cto
r
cu
r
r
en
t.
W
h
en
th
e
ca
p
ac
ito
r
cu
r
r
en
t
e
q
u
als
th
e
in
d
u
cto
r
c
u
r
r
e
n
t,
th
e
SC
R
cu
r
r
en
t
b
ec
o
m
es
ze
r
o
an
d
ca
u
s
es
th
e
SC
R
to
tu
r
n
o
f
f
.
I
n
th
e
n
ex
t
s
tag
e,
th
e
two
s
er
ies
(
L
-
C
)
b
r
an
ch
es
co
n
n
e
cted
to
th
e
f
a
u
lt
an
d
lo
a
d
f
o
r
m
r
eso
n
a
n
ce
an
d
h
en
ce
cu
r
r
en
t
o
s
cillatio
n
is
d
ev
elo
p
e
d
.
Du
r
i
n
g
t
h
is
o
s
cillatio
n
,
th
e
d
io
d
es
tu
r
n
o
n
t
o
b
y
p
ass
th
e
cu
r
r
en
t
f
r
o
m
t
h
e
ca
p
ac
ito
r
.
T
h
e
ca
p
a
cito
r
s
d
is
ch
ar
g
e
th
r
o
u
g
h
th
e
r
esis
to
r
an
d
th
e
in
d
u
cto
r
cu
r
r
en
t
also
cir
cu
lates
in
th
e
in
d
u
cto
r
/r
esis
to
r
/d
io
d
e
lo
o
p
u
n
til
it
d
ec
ay
s
to
ze
r
o
.
Alth
o
u
g
h
Z
SC
B
h
a
s
s
o
m
e
b
en
ef
its
o
v
er
MCB
an
d
S
SC
B
,
it
ca
n
n
o
t
o
p
e
r
ate
f
o
r
less
s
ev
er
e
an
d
lo
wer
d
y
n
am
ic
f
au
lt.
I
n
a
d
d
itio
n
to
t
h
at,
Z
SC
B
also
f
ac
es
lim
itatio
n
s
lik
e
n
o
t
h
av
in
g
co
m
m
o
n
g
r
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u
n
d
b
etwe
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s
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d
lo
a
d
,
u
n
d
esira
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le
f
r
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q
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en
c
y
r
esp
o
n
s
e,
h
ig
h
s
p
ik
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cu
r
r
en
t
d
u
r
in
g
th
e
r
ec
o
n
n
ec
tio
n
[
1
8
]
,
[
1
9
]
.
(
a)
(
b
)
Fig
u
r
e
2
.
T
y
p
ical
DC
C
B
to
p
o
lo
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y
:
(
a
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Hy
b
r
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d
cir
cu
it b
r
ea
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,
(
b
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Z
-
s
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r
ce
cir
c
u
it b
r
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k
er
Ap
ar
t
f
r
o
m
th
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c
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e
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tio
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al
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o
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o
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p
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ated
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io
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ar
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also
p
r
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p
o
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p
r
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tiv
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h
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it b
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y
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with
C
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MU
T
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O
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ter
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p
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ch
ar
g
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t
u
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(
GDT
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b
ased
cir
cu
it b
r
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k
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[
2
0
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,
[
2
1
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.
T
ab
l
e
1
s
u
m
m
ar
izes th
e
ad
v
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tag
e
s
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d
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ta
g
es o
f
th
e
d
if
f
er
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t to
p
o
l
o
g
ies
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
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E
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Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
2
1
7
–
229
220
T
ab
l
e
1
.
An
o
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v
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o
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d
if
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b
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A
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R
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w
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2
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r
l
o
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3
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t
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l
y
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w
c
o
s
t
1
.
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l
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w
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e
d
2
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m
i
t
e
d
c
u
r
r
e
n
t
i
n
t
e
r
r
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p
t
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a
p
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b
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l
i
t
y
3
.
Lo
w
l
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f
e
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me
[9
-
1
0
]
2
S
o
l
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d
-
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t
a
t
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r
c
u
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t
B
r
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r
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.
U
l
t
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f
a
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p
e
r
a
t
i
o
n
2
.
V
e
r
y
l
o
n
g
l
i
f
e
t
i
m
e
1
.
H
i
g
h
o
n
-
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a
t
e
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o
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2
.
R
e
l
a
t
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c
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3
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[
1
1
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-
[
1
4
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3
C
o
n
v
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t
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n
a
l
H
y
b
r
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C
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a
k
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r
1
.
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w
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r
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2
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N
o
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n
g
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me
c
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c
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s
3
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R
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a
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n
a
b
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o
p
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n
s
p
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d
1
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o
mp
l
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x
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c
h
n
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y
2
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C
u
r
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[
1
5
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[
1
7
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4
Z
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r
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t
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a
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t
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2
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S
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3
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b
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d
1
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Fa
u
lt m
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2
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d
p
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c
t
i
o
n
3
.
N
o
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m
mo
n
g
r
o
u
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d
[
1
8
]
,
[
1
9
]
M
o
d
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f
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e
d
M
e
c
h
a
n
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c
a
l
C
i
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t
B
r
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a
k
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r
To
p
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l
o
g
y
1
.
1
G
a
s
d
i
sc
h
a
r
g
e
tu
b
e
(
G
D
T)
b
a
se
d
c
i
r
c
u
i
t
b
r
e
a
k
e
r
1
.
F
a
st
o
p
e
r
a
t
i
o
n
2
.
R
e
a
so
n
a
b
l
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e
f
f
i
c
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e
n
c
y
1
.
Li
f
e
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m
e
n
o
t
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v
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y
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t
2
.
C
o
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t
i
n
u
o
u
s
p
o
w
e
r
r
e
q
u
i
r
e
m
e
n
t
3
.
Ex
p
e
n
s
i
v
e
[
1
9
]
M
o
d
i
f
i
e
d
S
o
l
i
d
S
t
a
t
e
T
o
p
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y
2
.
1
S
S
C
B
To
p
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l
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t
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A
d
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t
Li
mi
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r
1
.
A
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m
a
t
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t
r
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p
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f
o
r
se
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f
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t
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l
2
.
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i
d
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p
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b
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l
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t
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3
.
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t
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m
a
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f
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n
t
l
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c
a
p
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b
i
l
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t
y
1
.
H
i
g
h
o
n
-
st
a
t
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l
o
sses
2
.
C
o
mp
l
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x
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c
h
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c
t
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r
e
3
.
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3
Bi
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M
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2
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[
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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P
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221
Dif
f
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ty
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DC
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h
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t t
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RO
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R
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w
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o
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Fig
u
r
e
3
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
DC
C
B
to
p
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lo
g
y
wh
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is
co
n
s
is
ted
o
f
m
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h
an
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s
witch
es,
th
y
r
is
to
r
s
,
d
io
d
es,
I
GB
T
,
ca
p
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cito
r
an
d
in
d
u
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r
.
As
p
er
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e
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h
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o
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is
d
i
v
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ted
f
r
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m
th
e
m
ain
b
r
a
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ch
to
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p
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ce
n
etwo
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k
(
L
-
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n
etwo
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)
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n
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it
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o
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n
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
2
1
7
–
229
222
Fig
u
r
e
3
.
Pro
p
o
s
ed
DC
C
B
to
p
o
lo
g
y
3.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
escr
ib
es
t
h
e
r
es
ea
r
ch
m
et
h
o
d
o
lo
g
y
,
p
r
esen
ts
th
e
m
eth
o
d
o
lo
g
y
f
lo
w
ch
ar
t,
a
n
d
f
i
n
ally
d
is
cu
s
s
es th
e
m
ath
em
atica
l m
o
d
ellin
g
an
d
wo
r
k
in
g
p
r
in
cip
l
e
o
f
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
th
o
r
o
u
g
h
ly
.
3
.
1
.
M
et
ho
do
lo
g
y
A
d
etail
g
r
ap
h
ical
r
ep
r
esen
ta
t
io
n
o
f
th
e
r
esear
ch
m
eth
o
d
o
lo
g
y
is
s
tated
in
Fig
u
r
e
4
th
at
s
h
o
ws
d
if
f
er
en
t
p
h
ases
o
f
th
e
r
esear
c
h
.
T
h
e
r
esear
ch
wo
r
k
was
co
n
d
u
cted
th
r
o
u
g
h
s
im
u
latio
n
a
n
d
an
aly
s
is
to
m
ee
t
th
e
f
o
llo
win
g
two
o
b
jectiv
es:
a.
T
o
d
esig
n
a
n
d
m
o
d
el
a
n
ew
D
C
C
B
to
p
o
lo
g
y
with
r
e
g
en
er
ati
v
e
cu
r
r
e
n
t b
r
ea
k
in
g
ca
p
ab
ilit
y
.
b.
T
o
s
im
u
late
an
d
e
v
alu
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el.
P
ha
s
e
-
1
:
L
it
er
a
t
ure
re
v
iew
a
nd
s
im
ula
t
io
n o
f
t
he
ex
is
t
ing
DCCB
m
o
dels
T
h
e
f
ir
s
t
s
tep
o
f
th
is
r
esea
r
ch
was
to
ex
ten
s
iv
ely
g
o
th
r
o
u
g
h
liter
atu
r
e
o
n
d
if
f
er
e
n
t
DC
C
B
to
p
o
lo
g
ies,
to
u
n
d
er
s
tan
d
th
eir
wo
r
k
in
g
p
r
in
ci
p
le
an
d
to
f
in
d
o
u
t
th
eir
lim
itatio
n
s
.
Sp
ec
ial
f
o
cu
s
was
g
iv
en
to
th
eir
cu
r
r
e
n
t b
r
ea
k
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g
m
ec
h
an
is
m
s
to
ex
p
lo
it th
e
d
r
awb
ac
k
s
an
d
to
g
en
er
ate
n
ew
i
d
ea
s
f
o
r
f
ea
s
ib
le
s
o
lu
tio
n
.
P
ha
s
e
-
2
:
M
o
delin
g
o
f
t
he
pro
po
s
ed
re
g
ener
a
t
iv
e
curr
ent
brea
k
ing
t
ec
hn
iqu
e
T
h
e
m
ath
em
atica
l
m
o
d
el
o
f
b
o
th
cu
r
r
en
t
b
r
ea
k
in
g
an
d
r
eg
e
n
er
atio
n
o
p
e
r
atio
n
was
d
ev
elo
p
ed
in
th
is
p
h
ase.
L
ater
,
a
n
ew
to
p
o
lo
g
y
was
d
ev
is
ed
to
b
e
b
est
f
it
ted
with
th
e
m
ath
em
atica
l
m
o
d
el
f
o
llo
we
d
b
y
d
ev
elo
p
in
g
a
co
n
tr
o
l a
lg
o
r
ith
m
f
o
r
g
en
er
atin
g
co
o
r
d
in
ated
s
witch
in
g
s
ig
n
als f
o
r
th
e
to
p
o
l
o
g
y
.
P
ha
s
e
-
3
:
Sim
ula
t
io
n a
nd
a
na
ly
s
is
I
n
th
e
f
in
al
p
h
ase,
th
e
p
r
o
p
o
s
e
d
DC
C
B
was
s
im
u
lated
in
PS
I
M
s
o
f
twar
e.
A
r
ad
ial
DC
n
etwo
r
k
with
s
o
u
r
ce
r
esis
tan
ce
an
d
in
d
u
cta
n
ce
was
u
s
ed
f
o
r
s
im
u
latio
n
.
T
h
e
p
r
o
p
o
s
ed
DC
C
B
m
o
d
el
was
ap
p
lied
in
th
is
n
etwo
r
k
to
b
r
ea
k
th
e
cu
r
r
en
t
an
d
to
r
eg
en
er
ate
cu
r
r
en
t
af
t
er
war
d
s
.
I
n
ad
d
itio
n
to
th
at,
p
r
o
p
er
ties
s
u
ch
as
cu
r
r
en
t
b
r
ea
k
i
n
g
tim
e,
v
o
ltag
e
s
tr
ess
o
n
th
e
b
r
ea
k
er
,
v
o
ltag
e
d
is
tu
r
b
a
n
ce
in
th
e
n
etw
o
r
k
.
wer
e
t
h
o
r
o
u
g
h
l
y
in
v
esti
g
ated
an
d
e
v
alu
ated
.
Fig
u
r
e
4
.
Me
th
o
d
o
lo
g
y
f
lo
w
c
h
ar
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
r
o
s
p
ec
ts
o
f reg
en
era
tive
cu
r
r
en
t b
r
ea
kin
g
in
DC
circu
it b
r
ea
ke
r
to
p
o
lo
g
y
(
S
.
M.
S
a
n
z
a
d
Lu
men
)
223
3
.
2
.
M
o
delin
g
Ma
th
em
atica
l
m
o
d
ellin
g
o
f
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
is
ex
p
lain
ed
in
th
is
s
u
b
s
ec
tio
n
.
Nec
ess
ar
y
d
if
f
er
en
tial
eq
u
atio
n
s
b
ased
o
n
s
im
p
le
cir
cu
ital
an
aly
s
is
ar
e
d
ev
elo
p
e
d
an
d
th
e
n
s
o
lv
ed
to
f
in
d
th
e
tim
e
d
o
m
ain
r
esp
o
n
s
es wh
ich
ju
s
tifie
s
th
e
wo
r
k
in
g
p
r
in
cip
le.
3
.
2
.
1
.
Ma
t
hem
a
t
ica
l
mo
del f
o
r
curr
ent
bre
a
k
ing
T
h
e
p
r
o
p
o
s
ed
r
eg
e
n
er
ativ
e
c
u
r
r
en
t
b
r
ea
k
in
g
tech
n
i
q
u
e
was
f
o
r
m
u
lated
b
ased
o
n
th
e
c
o
n
ce
p
t
th
at
in
d
u
cto
r
an
d
ca
p
ac
ito
r
f
o
r
m
r
eso
n
an
t
cir
cu
it
wh
ich
c
r
ea
tes
cu
r
r
en
t
o
s
cillatio
n
wh
en
co
n
n
ec
ted
to
a
v
o
ltag
e
s
o
u
r
ce
an
d
t
h
ey
s
to
r
e
e
n
er
g
y
cy
clica
lly
in
ter
m
s
o
f
c
u
r
r
en
t
(
I
)
an
d
v
o
ltag
e
(
V
)
r
esp
ec
tiv
ely
.
E
n
er
g
y
s
to
r
ed
in
an
in
d
u
cto
r
a
n
d
ca
p
ac
ito
r
is
ca
lcu
lated
as
1
2
2
an
d
1
2
2
r
esp
ec
tiv
ely
wh
er
e,
L
s
tan
d
s
f
o
r
in
d
u
ctan
ce
an
d
C
f
o
r
ca
p
ac
itan
ce
.
As s
h
o
wn
in
Fig
u
r
e
5
(
a)
,
wh
en
cu
r
r
en
t f
lo
ws in
a
DC
n
etwo
r
k
,
en
er
g
y
is
s
to
r
ed
in
th
e
s
o
u
r
ce
in
d
u
ctan
ce
L
s
.
As
s
o
o
n
as
th
e
b
r
ea
k
er
r
ec
eiv
es
a
tr
ip
s
ig
n
al,
th
e
f
ast
-
o
p
er
atin
g
m
ec
h
a
n
ical
s
witch
(
S2
)
o
p
en
s
,
an
d
an
ar
c
v
o
ltag
e
is
in
itiated
.
At
th
e
s
am
e
tim
e,
g
ate
p
u
ls
es
ar
e
s
en
t
to
th
e
th
y
r
is
to
r
s
(
T
1
&
T
2
)
.
Du
e
to
th
is
co
m
b
in
ed
ef
f
ec
t,
t
h
e
lo
ad
c
u
r
r
en
t
is
co
m
m
u
tated
f
r
o
m
th
e
m
ain
b
r
an
ch
i
n
to
th
e
s
ec
o
n
d
ar
y
b
r
an
c
h
(
im
p
ed
an
ce
n
etwo
r
k
)
as
s
h
o
w
n
in
Fig
u
r
e
5
(
b
)
.
T
h
is
im
p
ed
a
n
ce
n
etwo
r
k
co
n
s
is
tin
g
o
f
L
a
n
d
C
g
en
er
ates
a
cu
r
r
en
t
o
s
cillatio
n
at
its
n
atu
r
al
r
eso
n
an
t
f
r
eq
u
en
cy
.
T
h
is
cu
r
r
en
t
o
s
cillatio
n
d
iv
e
r
ts
th
e
m
ain
b
r
an
c
h
cu
r
r
en
t
co
m
p
letely
an
d
th
u
s
th
e
a
r
c
v
o
ltag
e
ca
n
n
o
t
g
o
v
er
y
h
ig
h
an
d
th
e
a
r
c
is
ex
tin
g
u
is
h
e
d
v
er
y
q
u
ick
ly
.
T
h
e
cu
r
r
en
t
o
s
cillatio
n
is
g
o
v
er
n
ed
b
y
(
1
)
.
I
t
is
to
b
e
n
o
ted
th
at
th
e
s
o
u
r
ce
cu
r
r
e
n
t
an
d
lo
ad
cu
r
r
e
n
t
ar
e
s
y
n
o
n
y
m
o
u
s
h
er
e
.
(
a)
(
b
)
Fig
u
r
e
5
.
C
u
r
r
e
n
t b
r
ea
k
in
g
o
p
er
atio
n
in
th
e
p
r
o
p
o
s
ed
cir
c
u
it b
r
ea
k
er
:
(
a
)
So
u
r
ce
cu
r
r
e
n
t p
at
h
b
ef
o
r
e
tr
ip
p
i
n
g
in
itiated
,
(
b
)
So
u
r
ce
cu
r
r
en
t p
a
th
af
ter
tr
ip
p
i
n
g
in
itiated
(
+
)
(
)
+
(
+
)
(
)
+
1
∫
(
)
=
,
(
=
0
)
=
0
(
1
)
wh
er
e,
V
=
DC
s
o
u
r
ce
v
o
ltag
e
,
L
s
=
s
o
u
r
ce
in
d
u
cta
n
ce
,
R
s
=
s
o
u
r
ce
r
esis
tan
ce
,
R
L
=
lo
ad
r
esis
tan
ce
,
i(
t)
=
s
o
u
r
ce
cu
r
r
en
t,
I
o
=
in
itial
v
alu
e
o
f
s
o
u
r
ce
cu
r
r
en
t,
L
=
b
r
ea
k
er
in
d
u
ct
an
ce
,
C
=
b
r
ea
k
er
ca
p
ac
itan
ce
.
T
h
e
s
o
lu
tio
n
o
f
(
1
)
is
g
iv
en
b
y
(
2
)
wh
e
r
e,
=
(
+
)
2
(
+
)
is
th
e
d
am
p
i
n
g
f
ac
to
r
,
=
1
√
(
+
)
is
th
e
r
eso
n
an
ce
f
r
eq
u
en
cy
,
=
√
2
−
2
,
=
0
an
d
=
+
0
(
−
)
.
(
)
=
−
(
+
)
(
2
)
In
(
2
)
is
a
d
am
p
ed
o
s
cillatio
n
wh
ich
d
ec
ay
s
to
ze
r
o
u
ltima
tely
as
s
h
o
wn
in
Fig
u
r
e
6
(
a)
.
Ho
wev
er
,
d
u
r
in
g
th
e
f
ir
s
t
ze
r
o
-
cr
o
s
s
in
g
p
o
in
t
o
f
th
is
o
s
cillatin
g
cu
r
r
en
t,
th
e
t
h
y
r
is
to
r
s
(
T
1
an
d
T
2
)
ar
e
t
u
r
n
e
d
o
f
f
b
y
n
atu
r
al
co
m
m
u
tatio
n
an
d
th
e
ca
p
ac
ito
r
C
r
em
ain
s
ch
ar
g
ed
as
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
.
As
th
e
th
y
r
is
to
r
s
ar
e
n
o
w
tu
r
n
ed
o
f
f
,
th
e
lo
a
d
b
ec
o
m
es
t
o
tally
d
is
co
n
n
ec
ted
f
r
o
m
th
e
s
o
u
r
ce
c
o
m
p
letin
g
th
e
cu
r
r
en
t
b
r
ea
k
in
g
o
p
e
r
atio
n
s
u
cc
ess
f
u
lly
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
2
1
7
–
229
224
(
a)
(
b
)
Fig
u
r
e
6
.
Dy
n
am
ic
r
esp
o
n
s
es d
u
r
in
g
cu
r
r
e
n
t b
r
ea
k
in
g
o
p
er
at
io
n
:
(
a)
C
u
r
r
e
n
t a
n
d
v
o
ltag
e
o
s
cillatio
n
as p
er
(
2
)
,
(
b
)
C
u
r
r
e
n
t b
r
ea
k
in
g
a
n
d
ca
p
a
cito
r
ch
ar
g
i
n
g
3
.
2
.
2
.
M
a
t
hem
a
t
ica
l
mo
del f
o
r
re
g
ener
a
t
io
n
O
n
ce
th
e
t
h
y
r
is
to
r
s
ar
e
tu
r
n
e
d
o
f
f
,
t
h
e
I
GB
T
tu
r
n
s
o
n
a
n
d
th
e
ca
p
ac
ito
r
C
d
is
ch
ar
g
es
th
r
o
u
g
h
th
e
in
d
u
cto
r
L
,
a
n
d
th
u
s
s
to
r
ed
e
n
er
g
y
o
f
th
e
ca
p
ac
ito
r
is
tr
an
s
f
er
r
ed
to
th
e
i
n
d
u
cto
r
as
s
h
o
wn
in
Fig
u
r
e
7
(
a
)
.
T
h
e
cu
r
r
en
t
r
esp
o
n
s
e
is
g
o
v
er
n
ed
b
y
(
3
)
wh
o
s
e
s
o
lu
t
io
n
is
(
4
)
wh
e
r
e,
V
co
=
in
itial
ca
p
ac
ito
r
v
o
ltag
e,
i
r
(
t)
=r
eg
en
er
ated
cu
r
r
e
n
t a
n
d
′
=
1
√
is
th
e
r
eso
n
an
ce
f
r
eq
u
e
n
cy
.
(
a)
(
b
)
Fig
u
r
e
7
.
R
eg
en
e
r
atio
n
o
p
er
ati
o
n
in
th
e
p
r
o
p
o
s
ed
cir
c
u
it b
r
ea
k
er
:
(
a)
C
ap
ac
ito
r
t
r
an
s
f
er
s
en
er
g
y
to
t
h
e
in
d
u
cto
r
,
(
b
)
I
n
d
u
cto
r
r
elea
s
es e
n
er
g
y
in
to
th
e
s
o
u
r
ce
s
id
e
n
etwo
r
k
(
)
+
1
∫
(
)
=
0
,
(
=
0
)
=
0
,
(
=
0
)
=
(
3
)
(
)
=
√
′
)
(
4
)
I
n
(
4
)
is
a
s
im
p
le
s
in
u
s
o
id
al
r
esp
o
n
s
e
wh
ich
c
y
clica
lly
tr
an
s
f
er
s
en
er
g
y
b
ac
k
an
d
f
o
r
th
in
b
etwe
en
L
an
d
C
as
ca
n
b
e
s
ee
n
i
n
Fig
u
r
e
8
(
a)
.
B
u
t
a
s
s
o
o
n
as
th
e
ca
p
ac
ito
r
is
co
m
p
letely
d
is
ch
ar
g
e
d
in
th
is
o
s
cillatio
n
,
th
e
co
n
tr
o
l sy
s
tem
tu
r
n
s
o
f
f
th
e
I
GB
T
f
o
r
cin
g
th
e
in
d
u
cto
r
c
u
r
r
en
t to
f
l
o
w
th
r
o
u
g
h
d
io
d
es
(
D1
&
D2
)
an
d
th
u
s
en
er
g
y
f
r
o
m
i
n
d
u
cto
r
is
r
elea
s
ed
in
to
t
h
e
s
o
u
r
ce
s
id
e
n
etwo
r
k
.
T
h
is
p
h
en
o
m
en
o
n
o
f
r
el
ea
s
in
g
en
er
g
y
b
ac
k
in
to
th
e
s
o
u
r
ce
s
id
e
n
etwo
r
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I
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8
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u
r
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ated
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RE
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ates
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eled
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im
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lated
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o
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ula
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im
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licity
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s
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le
r
ad
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etwo
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k
as sh
o
wn
in
Fig
u
r
e
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was sim
u
lated
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th
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f
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g
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im
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latio
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ar
am
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s
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L
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im
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u
r
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1
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1
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u
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im
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r
ec
o
r
d
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d
as 5
1
.
6
m
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
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8
7
9
2
I
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Ap
p
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3
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tem
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er
2
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1
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226
(
a)
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u
r
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.
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u
r
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u
r
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cu
it
b
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r
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o
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n
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t
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ce
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1
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2
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ener
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th
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r
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r
r
en
t
r
e
d
u
ce
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ze
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o
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e
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C
B
b
ec
o
m
es
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ea
d
y
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o
r
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r
atio
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s
eq
u
en
ce
.
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h
e
I
GB
T
tu
r
n
s
o
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at
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7
s
an
d
th
e
ch
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p
ac
it
o
r
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ts
d
is
ch
ar
g
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th
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n
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n
e
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g
y
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s
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er
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ed
f
r
o
m
th
e
ca
p
ac
ito
r
to
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e
in
d
u
ct
o
r
.
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s
o
o
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th
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ito
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m
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l
etely
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ito
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e
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cto
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g
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i
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u
cto
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e
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er
g
y
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n
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th
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o
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ce
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id
e
n
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lace
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d
u
cto
r
c
u
r
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t
wh
ich
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ec
o
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eg
e
n
er
a
ted
cu
r
r
en
t
is
s
h
o
wn
in
Fig
u
r
e
1
0
(
b
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.
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s
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ith
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ates
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ate
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ig
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als
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n
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g
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ig
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e
s
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u
r
e
1
1
(
a)
.
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h
e
m
ec
h
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ical
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r
n
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h
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n
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ated
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r
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r
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e
s
h
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Fig
u
r
e
1
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.
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o
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1
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