I
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l J
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f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
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s
(
I
J
P
E
DS
)
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
,
p
p
.
22
73
~
22
83
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
1
2
.
i
4
.
pp
2
273
-
22
83
2273
J
o
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l ho
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ep
a
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e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Simplified
cas
ca
de multip
ha
se DC
-
DC buc
k power
c
o
nv
erte
r
for lo
w vo
ltag
e larg
e curr
en
t
a
ppli
ca
tions
:
pa
rt
II
--
-
o
utpu
t
current
contro
lle
r
Nung
k
y
P
ra
m
eswa
ri,
Ana
nd
B
a
nn
et
G
a
nes
en,
F
a
la
h K
ha
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Nura
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J
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urqa
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Arw
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Arg
o
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ho
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Tec
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Ba
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Ba
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Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
y
27
,
2
0
2
1
R
ev
is
ed
Sep
2
2
,
2
0
2
1
Acc
ep
ted
Sep
2
9
,
2
0
2
1
Th
is
p
a
p
e
r
p
r
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p
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se
s
a
c
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p
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fied
c
a
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c
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t
-
d
irec
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n
t
(
DC
-
DC
)
b
u
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k
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To
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rter,
a
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l
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teg
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(
P
I)
c
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tr
o
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se
d
to
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g
u
late
th
e
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t
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e
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sc
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e
m
e
a
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ly
sis is
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t
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y
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e
sm
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ll
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ly
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m
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a
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o
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b
tain
t
h
e
c
o
n
t
ro
l
p
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ra
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e
ters
(Kp
,
Ki,
a
n
d
Ti
)
.
S
im
u
latio
n
a
n
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e
x
p
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t
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su
lt
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o
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it
y
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p
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se
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o
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e
p
t.
K
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w
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d
s
:
B
u
ck
C
ascad
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C
ath
o
d
ic
p
r
o
tectio
n
C
o
n
tr
o
l
Mu
ltip
h
ase
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
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r
:
Nu
n
g
k
y
Pra
m
eswar
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Dep
ar
tm
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f
E
lectr
ical
E
n
g
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Sch
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n
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titu
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T
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lo
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B
an
d
u
n
g
Gan
esh
a
St.
N
o
.
1
0
,
B
an
d
u
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g
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0
1
3
2
,
I
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d
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m
ail: n
u
n
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k
y
p
r
am
eswar
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4
@
g
m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
C
o
r
r
o
s
io
n
is
o
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e
o
f
t
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d
estr
u
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p
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en
o
m
en
a
o
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d
eter
i
o
r
atio
n
o
f
th
e
q
u
ality
o
n
b
o
th
m
etallic
o
r
non
-
m
etallic
m
ater
ials
d
u
e
to
th
e
in
ter
ac
tio
n
b
etwe
en
t
h
e
m
ater
ials
with
th
e
s
u
r
r
o
u
n
d
i
n
g
en
v
ir
o
n
m
en
t
[
1
]
.
T
h
is
co
r
r
o
s
io
n
p
r
o
ce
s
s
u
s
u
all
y
o
cc
u
r
s
to
m
ater
ials
th
at
b
u
r
ied
in
th
e
g
r
o
u
n
d
,
s
u
ch
as
p
ip
e
lin
e
f
o
r
o
il
an
d
g
as
in
d
u
s
tr
y
.
T
h
e
r
e
ar
e
m
an
y
way
s
to
o
v
er
co
m
e
th
e
c
o
r
r
o
s
io
n
o
f
m
etal,
ca
th
o
d
ic
p
r
o
tecti
o
n
is
o
n
e
o
f
th
em
.
C
ath
o
d
ic
p
r
o
tectio
n
is
d
iv
id
ed
in
to
two
m
eth
o
d
s
,
s
ac
r
if
icial
an
o
d
e
m
et
h
o
d
a
n
d
im
p
r
ess
ed
cu
r
r
en
t m
et
h
o
d
[
2
]
.
T
h
is
s
tu
d
y
,
th
e
d
is
cu
s
s
io
n
is
f
o
cu
s
o
n
th
e
im
p
r
ess
ed
cu
r
r
en
t
m
eth
o
d
.
T
h
is
m
eth
o
d
in
j
ec
ts
d
ir
ec
t
cu
r
r
en
t
wh
ich
is
d
er
i
v
ed
f
r
o
m
a
s
in
g
le
-
p
h
ase
alter
n
atin
g
cu
r
r
en
t
(
AC
)
s
o
u
r
ce
th
r
o
u
g
h
a
f
u
ll
b
r
id
g
e
d
io
d
e
r
ec
tifie
r
an
d
a
s
tep
-
d
o
wn
D
C
-
DC
co
n
v
er
ter
.
T
h
e
n
eg
ati
v
e
o
u
tp
u
t
p
o
le
o
f
th
e
DC
-
D
C
co
n
v
er
ter
will
b
e
co
n
n
ec
ted
to
th
e
m
etal
u
n
d
er
g
r
o
u
n
d
,
wh
ich
f
u
n
ctio
n
s
as
a
ca
th
o
d
e,
a
n
d
t
h
e
p
o
s
itiv
e
p
o
le
w
ill
b
e
co
n
n
ec
ted
t
o
a
m
etal
co
n
s
is
tin
g
o
f
a
ce
r
tain
m
ater
ial
th
at
will b
e
f
u
n
ctio
n
ed
as a
n
an
o
d
e.
L
ater
,
th
e
an
o
d
e
m
etal
will
s
u
p
p
ly
th
e
im
p
r
ess
ed
c
u
r
r
e
n
t
f
r
o
m
th
e
DC
p
o
wer
s
u
p
p
ly
to
th
e
ca
th
o
d
e
[
3
]
.
T
h
e
s
tep
-
d
o
wn
DC
-
D
C
co
n
v
er
ter
f
o
r
t
h
is
p
u
r
p
o
s
e
m
u
s
t
h
av
e
a
v
e
r
y
lo
w
v
o
ltag
e
-
r
atio
n
a
n
d
lar
g
e
cu
r
r
e
n
t
with
v
er
y
lo
w
o
u
tp
u
t
cu
r
r
e
n
t
r
ip
p
le
[
4
]
,
[
5
]
.
I
n
o
r
d
er
to
m
ee
t
th
o
s
e
r
e
q
u
ir
em
en
ts
,
a
n
ew
s
im
p
lifie
d
ca
s
ca
d
ed
m
u
ltip
h
ase
t
o
p
o
lo
g
y
w
h
ich
h
as
h
ig
h
v
o
ltag
e
r
ed
u
ctio
n
r
atio
an
d
lar
g
e
o
u
tp
u
t
cu
r
r
en
ts
with
lo
w
r
ip
p
le
is
p
r
o
p
o
s
ed
in
Par
t
I
[
6
]
.
I
t
s
h
o
u
l
d
b
e
n
o
ted
th
at
t
h
is
co
n
v
er
ter
is
th
e
d
u
al
o
f
th
e
c
o
n
v
er
ter
th
at
h
as b
ee
n
p
r
o
p
o
s
ed
in
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
22
73
–
22
83
2274
Ap
ar
t f
r
o
m
s
p
ec
if
icatio
n
s
,
th
e
im
p
o
r
tan
t p
a
r
t in
DC
-
DC
co
n
v
er
ter
s
is
h
o
w
to
d
esig
n
th
e
co
n
tr
o
ller
b
y
d
ef
in
in
g
a
d
y
n
am
ic
m
o
d
el
o
f
th
e
s
y
s
tem
[
8
]
.
T
h
er
e
a
r
e
m
an
y
d
if
f
e
r
en
t
m
o
d
eli
n
g
tech
n
i
q
u
es
n
am
ely
s
m
all
s
ig
n
al
an
d
lar
g
e
s
ig
n
al
m
o
d
e
lin
g
tech
n
iq
u
es
th
at
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
to
d
escr
ib
e
th
e
d
y
n
am
ics
o
f
a
b
u
c
k
co
n
v
er
ter
.
Fro
m
th
is
tec
h
n
iq
u
e,
th
e
s
tate
-
s
p
ac
e
av
er
a
g
e
is
t
h
e
m
o
s
t
ac
ce
p
tab
le
way
t
o
o
b
tain
th
e
s
m
all
s
ig
n
al
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
DC
-
DC
co
n
v
er
ter
s
[
8
]
-
[
1
3
]
.
Fo
r
p
h
y
s
ical
im
p
lem
en
tatio
n
,
a
s
u
itab
le
co
n
tr
o
ller
m
u
s
t
b
e
u
s
ed
to
o
b
tain
s
tab
le
-
co
n
tr
o
ll
ed
DC
-
DC
p
o
wer
co
n
v
er
te
r
s
to
s
u
p
p
ly
th
e
cu
r
r
e
n
t
n
ee
d
ed
f
o
r
th
e
lo
a
d
with
lo
w
s
en
s
itiv
ity
ag
ain
s
t
v
ar
io
u
s
d
is
tu
r
b
a
n
ce
s
.
T
h
is
is
also
wh
at
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
r
e
q
u
ir
es,
n
am
el
y
a
s
im
p
le
an
d
r
eliab
le
co
n
tr
o
ller
ev
en
th
o
u
g
h
t
h
e
s
y
s
tem
is
n
o
n
-
lin
ea
r
.
T
h
er
e
ar
e
s
ev
er
al
n
o
n
-
lin
ea
r
a
n
d
lin
ea
r
co
n
tr
o
l
tec
h
n
iq
u
es
th
at
h
av
e
b
ee
n
d
is
cu
s
s
ed
in
th
e
liter
atu
r
e
t
o
en
s
u
r
e
th
at
th
e
b
u
c
k
co
n
v
er
ter
s
ca
n
wo
r
k
p
r
o
p
er
ly
wh
en
v
ar
io
u
s
d
is
tu
r
b
a
n
ce
s
ar
e
g
iv
e
n
[
1
4
]
-
[
1
7
]
.
T
h
e
n
o
n
lin
ea
r
c
o
n
tr
o
l
te
ch
n
iq
u
es
s
u
ch
as
H
-
∞
an
d
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
ar
e
s
u
cc
ess
f
u
l
in
co
n
tr
o
llin
g
th
e
b
u
ck
co
n
v
er
ter
,
b
u
t
elec
tr
o
m
a
g
n
etic
in
ter
f
er
en
ce
(
E
M
I
)
an
d
m
at
h
em
atica
l
co
m
p
lex
ities
ar
e
b
ec
o
m
e
th
e
o
th
er
is
s
u
es
o
f
th
o
s
e
tech
n
iq
u
es
[
1
8
]
.
Oth
er
n
o
n
lin
ea
r
c
o
n
tr
o
l
tec
h
n
iq
u
es
s
u
ch
as
f
u
zz
y
a
n
d
o
n
e
-
cy
cle
co
n
tr
o
l
also
h
av
e
lim
itatio
n
s
,
n
am
ely
th
e
f
u
zz
y
m
et
h
o
d
is
co
n
s
id
er
e
d
u
n
ab
le
to
p
r
o
v
id
e
b
etter
s
m
all
s
ig
n
al
r
esp
o
n
s
e
th
an
s
tan
d
ar
d
r
eg
u
lato
r
s
an
d
o
n
e
c
y
cle
co
n
tr
o
l
is
co
n
s
id
er
ed
ca
p
ab
le
o
f
ca
u
s
in
g
lar
g
e
h
ar
m
o
n
ic
cu
r
r
en
t
d
is
to
r
tio
n
[
1
9
]
-
[
2
1
]
.
I
n
t
h
e
o
t
h
e
r
h
a
n
d
,
l
i
n
e
a
r
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
s
s
u
c
h
a
s
P
I
/
p
r
o
p
o
r
t
i
o
n
a
l
-
i
n
t
e
g
r
al
-
d
e
r
i
v
a
t
i
v
e
(
P
I
D
)
a
r
e
c
o
n
t
r
o
l
l
e
r
s
t
h
a
t
a
r
e
c
o
n
s
i
d
e
r
e
d
q
u
i
t
e
s
i
m
p
l
e
,
e
as
y
t
o
i
m
p
l
e
m
en
t
,
a
n
d
s
u
i
t
a
b
l
e
f
o
r
a
c
h
i
e
v
i
n
g
s
y
s
t
e
m
p
e
r
f
o
r
m
a
n
c
e
a
n
d
s
t
a
b
i
li
t
y
.
T
h
is
is
e
v
i
d
e
n
c
e
d
b
y
t
h
e
m
a
n
y
a
p
p
l
i
c
a
t
i
o
n
s
i
n
t
h
e
i
n
d
u
s
t
r
y
t
h
a
t
u
s
e
t
h
is
c
o
n
t
r
o
l
le
r
[
2
2
]
-
[
2
4
]
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
co
n
tr
o
l
m
eth
o
d
f
o
r
a
n
ew
s
im
p
lifie
d
ca
s
ca
d
e
m
u
ltip
h
ase
DC
-
DC
b
u
c
k
co
n
v
er
ter
t
h
at
d
esig
n
ed
f
o
r
l
o
w
v
o
ltag
e
lar
g
e
c
u
r
r
e
n
t
ap
p
licatio
n
s
u
ch
as
ca
th
o
d
ic
p
r
o
tectio
n
,
wh
ich
u
s
es
s
in
g
le
lo
o
p
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI)
to
c
o
n
tr
o
l
th
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
c
o
n
v
e
r
ter
.
T
h
e
co
n
tr
o
l
s
ch
em
e
an
a
ly
s
is
is
ca
r
r
ied
o
u
t
b
y
lin
ea
r
izin
g
th
e
s
m
all
-
s
ig
n
al
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
to
f
o
r
m
t
h
e
o
u
t
p
u
t
cu
r
r
en
t
tr
an
s
f
er
f
u
n
ctio
n
s
.
Simu
latio
n
an
d
ex
p
e
r
im
en
t
r
esu
lts
ar
e
in
clu
d
ed
to
p
r
o
v
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
co
n
tr
o
l sy
s
tem
ag
ain
s
t th
e
v
ar
i
o
u
s
d
is
tu
r
b
an
c
es th
at
ar
e
g
iv
e
n
.
T
h
e
p
a
p
er
is
o
r
g
a
n
ized
is
b
ei
n
g
as
.
I
n
s
ec
tio
n
2
,
t
h
e
d
y
n
a
m
ic
m
o
d
elin
g
o
f
a
n
ew
s
im
p
le
ca
s
ca
d
e
m
u
ltip
h
ase
DC
-
DC
b
u
ck
p
o
w
er
co
n
v
e
r
ter
is
d
er
iv
e
d
.
Sectio
n
3
will
d
is
cu
s
s
cu
r
r
en
t
c
o
n
tr
o
ller
d
esig
n
f
o
r
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
.
T
h
en
,
s
ec
tio
n
4
an
d
s
ec
tio
n
5
,
r
esp
ec
tiv
ely
p
r
esen
t
th
e
s
im
u
latio
n
an
d
ex
p
er
im
e
n
tal
r
esu
lts
to
v
alid
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
lle
r
.
Fin
ally
,
co
n
cl
u
s
io
n
s
ar
e
o
f
f
e
r
ed
in
s
ec
tio
n
6
.
2.
DYNA
M
I
C
M
O
D
E
L
I
NG
O
F
NE
W
SI
M
P
L
I
F
I
E
D
C
ASCAD
E
M
U
L
T
I
P
H
AS
E
DC
-
DC
B
UCK
P
O
WE
R
CO
NV
E
RT
E
R
Acc
o
r
d
in
g
to
th
e
o
p
tim
izatio
n
th
at
h
as
b
ee
n
d
o
n
e
in
Par
t
I
,
it
ca
n
b
e
s
h
o
wn
th
at
th
e
to
p
o
lo
g
y
as
s
h
o
wn
in
Fig
u
r
e
1
is
th
e
o
p
tim
al
o
n
e.
T
h
is
is
a
s
im
p
lifie
d
two
-
s
tag
e
f
o
u
r
-
p
h
ase
DC
-
DC
b
u
ck
c
o
n
v
er
te
r
.
T
h
e
b
asic p
r
in
cip
le
o
f
th
is
co
n
v
e
r
ter
ca
n
b
e
e
x
p
lai
n
ed
as th
e
f
o
ll
o
win
g
.
I
f
o
n
e
o
f
th
e
s
witch
es
is
ON
(
f
o
r
ex
a
m
p
le
is
S
1
)
,
th
e
o
th
er
s
witch
es
ar
e
in
t
h
e
OFF
s
tate
an
d
th
e
D
ON
d
io
d
e
a
n
d
all
s
ec
o
n
d
ar
y
d
io
d
es
ex
ce
p
t
D
SEC1
will
b
e
f
o
r
wa
r
d
b
iased
,
wh
ile
t
h
e
o
th
er
d
io
d
es
will
b
e
r
ev
er
s
e
b
iased
.
Fro
m
t
h
is
m
ec
h
an
is
m
,
cu
r
r
e
n
t
will
f
lo
w
in
two
d
ir
ec
tio
n
s
:
f
r
o
m
DC
s
o
u
r
ce
E
d
to
t
h
e
p
r
im
a
r
y
in
d
u
cto
r
L
P
an
d
f
r
o
m
d
io
d
e
D
ON
to
c
ap
ac
ito
r
C
.
T
h
e
n
,
b
o
th
c
u
r
r
e
n
ts
will
ad
d
u
p
an
d
ch
ar
g
e
i
n
d
u
cto
r
L
S1
,
b
e
f
o
r
e
r
ea
ch
in
g
th
e
l
o
ad
an
d
th
e
o
th
er
s
ec
o
n
d
a
r
y
in
d
u
ct
o
r
s
will
d
is
ch
ar
g
e
its
cu
r
r
en
t
t
o
th
e
lo
a
d
.
An
d
th
e
s
ec
o
n
d
m
ec
h
an
is
m
is
wh
en
all
o
f
th
e
s
witch
es
ar
e
O
FF
,
wh
er
e
all
d
io
d
es
D
OFF
an
d
s
ec
o
n
d
ar
y
d
io
d
es
will
b
e
f
o
r
war
d
b
iased
an
d
d
io
d
es
D
ON
wil
l
b
e
r
ev
er
s
e
b
iased
.
Fro
m
th
is
m
ec
h
an
is
m
,
th
e
lo
ad
will
o
n
ly
r
ec
eiv
e
d
is
ch
ar
g
ed
cu
r
r
en
ts
f
r
o
m
th
e
s
ec
o
n
d
ar
y
i
n
d
u
cto
r
s
.
T
h
o
s
e
two
m
ec
h
an
i
s
m
s
also
ap
p
ly
alter
n
ately
t
o
o
th
er
s
witch
es.
As
th
e
o
u
tp
u
t
s
id
e
is
a
f
o
u
r
-
p
h
as
e
b
u
ck
co
n
v
er
ter
,
th
e
o
u
tp
u
t
cu
r
r
en
t
ca
p
a
b
ilit
y
is
lar
g
e
an
d
th
e
r
ip
p
le
c
o
n
ten
t
will
b
e
v
er
y
lo
w.
Un
d
er
co
n
ti
n
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e,
th
e
a
v
er
ag
e
o
u
t
p
u
t
v
o
ltag
e
r
atio
is
s
h
o
wn
in
(
1
)
,
wh
er
e
V
o
an
d
E
d
ar
e
th
e
o
u
tp
u
t a
n
d
i
n
p
u
t v
o
ltag
es o
f
th
e
co
n
v
er
ter
,
r
esp
ec
tiv
ely
.
=
4
2
(
1
)
with
=
(
2
)
is
th
e
d
u
ty
cy
cle
o
f
s
witch
in
g
d
ev
ices
with
a
m
ax
im
u
m
v
al
u
e
o
f
0
.
2
5
,
T
ON
is
th
e
ON
-
tim
e
o
f
tr
an
s
is
to
r
s
an
d
T
S
is
th
e
s
witch
in
g
p
er
io
d
o
f
t
h
e
tr
an
s
is
to
r
.
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:
2
0
8
8
-
8
694
S
imp
lifi
ed
ca
s
ca
d
e
mu
ltip
h
a
s
e
DC
-
DC
b
u
ck
p
o
w
er c
o
n
ve
r
ter fo
r
lo
w
vo
lta
g
e
la
r
g
e
…
(
N
u
n
g
ky
P
r
a
mesw
a
r
i
)
2275
In
(
1
)
s
h
o
ws
th
at
a
v
er
y
lo
w
o
u
tp
u
t
v
o
ltag
e
ca
n
b
e
o
b
tain
e
d
with
o
u
t
u
s
in
g
a
v
er
y
lo
w
d
u
ty
cy
cle.
Fo
r
two
-
s
tag
e
co
n
v
e
r
ter
,
it
ca
n
b
e
s
ee
n
th
at
th
e
o
u
tp
u
t
v
o
ltag
e
is
p
r
o
p
o
r
tio
n
al
to
th
e
s
q
u
ar
e
o
f
d
u
ty
c
y
cle.
T
h
e
o
u
tp
u
t c
u
r
r
en
t is co
n
tr
o
lled
b
y
u
s
in
g
a
cu
r
r
en
t
co
n
tr
o
ller
as s
h
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
New
s
im
p
lifie
d
two
-
s
tag
es f
o
u
r
-
p
h
ase
co
n
v
e
r
ter
with
cu
r
r
e
n
t c
o
n
tr
o
ller
T
o
d
esig
n
th
e
clo
s
ed
lo
o
p
s
y
s
tem
,
we
s
h
o
u
ld
m
o
d
el
th
e
s
y
s
tem
in
Fig
u
r
e
1
in
to
th
e
s
m
all
-
s
ig
n
al
m
o
d
el.
T
h
e
f
i
r
s
t
s
tep
is
s
tate
s
p
ac
e
av
er
ag
in
g
p
r
o
ce
s
s
.
Un
d
er
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
,
we
ca
n
d
eter
m
in
e
th
e
s
tate
-
s
p
ac
e
eq
u
atio
n
o
f
c
o
n
v
er
ter
wh
en
a
tr
a
n
s
is
to
r
in
f
o
u
r
-
p
h
ase
b
u
ck
c
o
n
v
e
r
ter
r
ec
eiv
es
an
ON
s
ig
n
al
an
d
s
tate
-
s
p
ac
e
eq
u
atio
n
wh
en
all
tr
an
s
is
to
r
s
r
ec
eiv
e
O
FF
s
ig
n
als.
T
h
e
s
tate
s
p
ac
e
eq
u
atio
n
f
o
r
th
o
s
e
two
co
n
d
itio
n
s
is
wr
itten
in
(
3
)
an
d
(
4
)
.
•
=
+
(
3
)
•
=
+
(
4
)
W
h
er
e
X
=
s
tate
s
p
ac
e
v
ar
iab
les (
p
r
i
m
ar
y
in
d
u
cto
r
c
u
r
r
e
n
t (
I
LP
)
,
o
u
tp
u
t c
u
r
r
e
n
t (
I
o
)
an
d
ca
p
ac
ito
r
v
o
ltag
e
(
V
c
),
Y
=
in
p
u
t v
a
r
iab
le
(
in
p
u
t v
o
ltag
e
(
E
d
)),
A
on
an
d
B
on
=
s
tate
s
p
ac
e
m
atr
ix
wh
ile
s
witch
es a
r
e
ON,
an
d
A
off
an
d
B
off
=
s
tate
s
p
ac
e
m
atr
ix
wh
ile
s
witch
es a
r
e
OFF.
B
ased
o
n
(
3
)
a
n
d
(
4
)
,
we
ca
n
d
eter
m
in
e
th
e
av
e
r
ag
e
s
tate
-
s
p
a
ce
in
o
n
e
s
witch
in
g
p
er
io
d
.
B
ased
o
n
th
e
co
n
v
e
r
ter
in
Fig
u
r
e
1
,
w
h
e
r
e
R
r
ep
r
esen
ts
th
e
lo
ad
o
f
th
e
co
n
v
er
ter
.
I
t c
an
b
e
s
h
o
wn
th
a
t th
e
f
o
llo
win
g
s
tate
-
s
p
ac
e
eq
u
atio
n
ca
n
b
e
o
b
tain
ed
.
[
_
_
_
]
=
[
0
0
−
1
0
−
(
1
1
+
1
2
+
1
3
+
1
4
)
(
1
1
+
1
2
+
1
3
+
1
4
)
1
−
0
]
[
_
_
_
]
+
[
4
0
0
]
(
5
)
As
a
f
u
n
ctio
n
o
f
d
u
ty
cy
cle
α
th
e
ab
o
v
e
s
tate
s
p
ac
e
eq
u
a
tio
n
is
n
o
n
lin
ea
r
.
T
o
lin
ea
r
iz
e
th
e
s
y
s
tem
,
it
is
ass
u
m
ed
th
at
th
e
d
u
t
y
cy
cle
o
f
tr
an
s
is
to
r
ca
n
b
e
wr
itten
as
.
=
̄
+
̃
(
6
)
C
om
pa
r
a
t
or
s
D
O
F
F
L
oa
d
+
V
O
_
L
P
E
d
D
S
E
C
1
L
S
1
S
1
D
ON
D
S
E
C
2
D
S
E
C
3
L
S
2
S
2
L
S
3
S
3
L
S
4
S
4
D
S
E
C
4
C
u
r
r
e
n
t
C
o
n
t
r
o
l
l
e
r
4 P
ha
s
e
C
a
r
r
i
e
r
S
i
gn
a
l
s
S
1
S
2
S
3
S
4
+
-
e
o
i
i
o
_
re
f
i
o
_
act
i
L
P
i
c
-
C
Vc
i
L
S
4
i
LS
3
i
LS
2
i
LS
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
22
73
–
22
83
2276
wh
er
e
b
ar
an
d
tild
e
o
v
er
th
e
v
ar
iab
les
r
ep
r
esen
t
th
e
av
er
a
g
e
an
d
th
e
s
m
all
-
s
ig
n
al
q
u
an
titi
es.
Su
b
s
titu
tin
g
(
6
)
in
to
(
5
)
an
d
ta
k
es th
e
s
m
all
-
s
ig
n
al
p
ar
ts
th
en
th
e
f
o
llo
win
g
s
m
all
-
s
ig
n
al
eq
u
atio
n
ca
n
b
e
o
b
t
ain
ed
:
[
~
~
~
]
=
[
0
0
−
1
0
−
_
1
−
_
0
]
[
~
~
~
]
+
[
4
−
]
~
(
7
)
wh
er
e
1
=
1
1
+
1
2
+
1
3
+
1
4
(
8
)
B
ased
o
n
(
7
)
,
th
e
o
p
en
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
o
f
o
u
tp
u
t
cu
r
r
en
t
as
a
f
u
n
ctio
n
o
f
d
u
ty
cy
cle
ca
n
b
e
o
b
tain
ed
as
s
h
o
wn
in
.
~
(
)
~
(
)
=
2
−
_
+
4
_
+
3
+
2
+
(
+
_
2
)
+
1
(
9
)
I
f
we
p
lo
t
(
9
)
with
th
e
ce
r
ta
in
v
alu
es
to
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
cu
r
v
e,
we
will
o
b
tain
th
e
p
h
as
e
m
ar
g
in
(
PM)
an
d
c
o
f
th
e
s
y
s
tem
with
o
u
t c
o
n
t
r
o
ller
.
T
h
ese
v
al
u
es will b
e
u
s
ed
to
ca
lcu
late
th
e
c
o
n
tr
o
l
p
ar
am
eter
s
.
3.
CURR
E
NT
CO
N
T
RO
L
L
E
R
DE
S
I
G
N
I
n
th
is
r
esear
ch
,
a
co
n
v
en
tio
n
al
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI)
c
o
n
tr
o
ller
is
u
s
ed
to
r
e
g
u
late
t
h
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
c
o
n
v
er
te
r
.
T
h
e
b
lo
ck
d
iag
r
am
o
f
th
e
s
y
s
tem
u
n
d
er
PI
cu
r
r
en
t
c
o
n
tr
o
lle
r
is
r
ep
r
esen
te
d
in
Fig
u
r
e
2
.
T
h
e
s
en
s
o
r
g
ain
,
H(
s
)
is
eq
u
al
to
u
n
ity
if
th
e
s
en
s
o
r
is
id
ea
l.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
PI
co
n
tr
o
ller
is
d
ef
i
n
ed
b
y
(
1
0
)
,
wh
er
e
p
an
d
ar
e
th
e
p
r
o
p
o
r
tio
n
al
an
d
i
n
teg
r
ato
r
g
ain
s
,
r
e
s
p
ec
tiv
ely
.
+
=
(
+
)
(
10
)
T
h
er
ef
o
r
e,
th
e
r
elatio
n
b
etwe
en
o
u
tp
u
t
cu
r
r
e
n
t
to
th
e
r
ef
er
en
ce
o
u
tp
u
t
cu
r
r
e
n
t
u
s
in
g
a
P
I
co
n
tr
o
ller
ca
n
b
e
r
ep
r
esen
ted
b
y
(
1
1
)
.
~
~
−
=
(
(
+
)
(
2
−
_
+
4
_
+
)
(
3
+
2
+
(
+
_
2
)
+
1
)
)
1
+
(
(
+
)
(
2
−
_
+
4
_
+
)
(
3
+
2
+
(
+
_
2
)
+
1
)
)
(
1
1
)
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
th
e
s
y
s
tem
I
o
_
r
ef
(s
)
-
+
⍺
(s)
I
o
(s)
P
l
a
n
t
P
I
C
ont
r
ol
l
e
r
S
e
n
s
o
r
G
a
i
n
H
(
s
)
~
~
~
~
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:
2
0
8
8
-
8
694
S
imp
lifi
ed
ca
s
ca
d
e
mu
ltip
h
a
s
e
DC
-
DC
b
u
ck
p
o
w
er c
o
n
ve
r
ter fo
r
lo
w
vo
lta
g
e
la
r
g
e
…
(
N
u
n
g
ky
P
r
a
mesw
a
r
i
)
2277
Fo
r
d
eter
m
in
in
g
th
e
cu
r
r
en
t
co
n
tr
o
l
p
ar
am
eter
s
,
K
p
an
d
K
i
,
we
ca
n
u
s
e
a
co
m
m
o
n
ly
p
r
o
ce
d
u
r
e
b
y
u
s
in
g
a
f
r
e
q
u
en
c
y
r
esp
o
n
s
e
cu
r
v
e
an
al
y
s
is
to
d
eter
m
in
e
th
e
cr
o
s
s
o
v
er
f
r
eq
u
e
n
cy
o
f
th
e
s
y
s
tem
wh
ich
is
ab
le
to
in
cr
ea
s
e
th
e
g
ai
n
at
lo
w
f
r
eq
u
en
cies
wh
ile
m
ain
tain
i
n
g
a
p
o
s
itiv
e
PM
[
2
5
]
-
[
2
8
]
.
I
n
th
is
s
tu
d
y
,
s
y
s
tem
p
ar
am
eter
s
as
s
h
o
wn
in
T
a
b
le
1
ar
e
u
s
ed
,
w
h
er
e
th
e
v
alu
es
o
f
co
m
p
o
n
e
n
ts
s
u
ch
as
in
d
u
ct
o
r
s
an
d
ca
p
ac
ito
r
s
ar
e
o
b
tain
e
d
b
ased
o
n
ca
lc
u
latio
n
s
to
ac
h
iev
e
co
n
tin
u
o
u
s
c
o
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
.
T
h
ese
p
ar
am
eter
s
ar
e
th
e
o
n
es
u
s
ed
in
Par
t
I
o
f
th
is
p
a
p
er
.
B
y
s
u
b
s
titu
tin
g
(
1
1
)
with
th
e
p
a
r
am
eter
s
in
T
ab
le
1
an
d
ad
ju
s
tin
g
it
to
th
e
g
ain
an
d
p
h
ase
m
ar
g
in
r
eq
u
ir
e
m
en
ts
,
th
e
f
o
l
lo
win
g
s
PI
p
ar
a
m
eter
s
ar
e
o
b
tain
ed
as
s
h
o
wn
in
T
ab
le
2
.
T
h
en
,
if
we
s
u
b
s
titu
te
(
1
2
)
with
th
e
p
a
r
am
eter
s
in
T
ab
le
s
1
an
d
2
,
w
e
will
g
et
th
e
th
e
b
o
d
e
p
l
o
t
d
i
ag
r
am
o
f
th
e
cu
r
r
e
n
t
co
n
tr
o
ller
u
s
in
g
PI
as
s
h
o
wn
i
n
Fig
u
r
e
3
.
I
t
is
s
h
o
wn
th
at
u
p
to
2
0
0
Hz,
th
e
g
ain
o
f
th
e
a
ctu
al
o
u
tp
u
t
c
u
r
r
e
n
t
ag
ain
s
t
th
e
r
ef
er
e
n
ce
cu
r
r
en
t
i
s
s
till
u
n
ity
.
Alth
o
u
g
h
at
2
0
0
Hz,
th
er
e
is
a
s
lig
h
t
p
h
ase
s
h
i
f
tin
g
b
etwe
en
th
e
ac
tu
al
cu
r
r
en
t a
n
d
th
e
r
ef
er
e
n
c
e
cu
r
r
en
t
(
-
1
.
7
9
o
).
T
ab
le
1
.
C
o
n
v
er
ter
d
esig
n
p
ar
am
eter
s
P
a
r
a
me
t
e
r
V
a
l
u
e
I
n
p
u
t
V
o
l
t
a
g
e
(
E
d
)
1
0
0
V
o
l
t
I
n
d
u
c
t
o
r
(
L
s1
)
1
.
0
3
mH
I
n
d
u
c
t
o
r
(
L
s2
)
1
.
0
3
mH
I
n
d
u
c
t
o
r
(
L
s3
)
1
.
0
3
mH
I
n
d
u
c
t
o
r
(
L
s4
)
1
.
0
3
mH
I
n
d
u
c
t
o
r
(
L
P
)
2
.
6
mH
C
a
p
a
c
i
t
o
r
(
C
)
4
7
0
F
N
o
mi
n
a
l
L
o
a
d
R
e
s
i
st
a
n
c
e
(
R
)
0
.
2
o
h
m
D
u
t
y
C
y
c
l
e
(
⍺
̅
)
0
.
0
9
5
T
ab
le
2
.
C
u
r
r
e
n
t c
o
n
tr
o
l p
ar
a
m
eter
s
P
a
r
a
me
t
e
r
V
a
l
u
e
K
p
0
.
0
8
4
3
K
i
6
3
1
.
8
3
T
i
1
.
3
3
4
.
1
0
-
4
Fig
u
r
e
3
.
B
o
d
e
p
lo
t d
ia
g
r
am
o
f
ac
tu
al
o
u
tp
u
t c
u
r
r
en
t a
g
ai
n
s
t a
r
ef
er
en
ce
o
u
tp
u
t c
u
r
r
e
n
t
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
A
n
ew
s
im
p
lifie
d
two
-
s
tag
es
f
o
u
r
-
p
h
ase
DC
-
DC
B
u
ck
co
n
v
er
ter
with
p
a
r
am
eter
s
as
s
h
o
w
n
in
T
a
b
le
1
was sim
u
lated
.
T
h
e
p
r
ev
io
u
s
PI
co
n
tr
o
ller
p
ar
am
eter
s
wer
e
u
s
ed
.
4
.
1
.
Ca
s
e
I
:
curr
ent
re
f
er
en
ce
v
a
ria
t
io
n
I
n
t
h
i
s
c
a
s
e
,
t
h
e
e
f
f
e
c
t
o
f
t
h
e
c
u
r
r
e
n
t
r
e
f
e
r
e
n
c
e
v
a
r
i
a
t
i
o
n
i
s
s
i
m
u
l
a
t
e
d
w
i
t
h
t
h
e
r
e
s
u
l
t
s
s
h
o
w
n
i
n
F
i
g
u
r
e
s
4
(
a
)
a
n
d
(
b
)
.
F
i
g
u
r
e
4
(
a
)
s
h
o
w
s
t
h
e
s
i
m
u
l
a
t
i
o
n
r
e
s
u
l
t
o
f
t
h
e
a
c
t
u
a
l
o
u
t
p
u
t
c
u
r
r
e
n
t
(
I
o
_
A
c
t
u
a
l
)
w
h
e
n
r
e
f
e
r
e
n
c
e
o
u
t
p
u
t
c
u
r
r
e
n
t
(
I
o
_
R
e
f
e
r
e
n
c
e
)
i
s
c
h
a
n
g
e
d
f
r
o
m
2
2
A
t
o
1
6
A
a
t
t
=
0
.
1
6
6
s
a
n
d
b
a
c
k
a
g
a
i
n
t
o
2
2
A
a
t
t
=
0
.
3
3
3
s
.
I
t
c
a
n
b
e
s
e
e
n
t
h
a
t
t
h
e
c
o
n
t
r
o
l
l
e
r
c
a
n
m
a
i
n
t
a
i
n
t
h
e
a
c
t
u
a
l
o
u
t
p
u
t
c
u
r
r
e
n
t
w
h
e
n
t
h
e
r
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f
e
r
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n
c
e
o
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t
p
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t
c
u
r
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t
c
h
a
n
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i
n
s
t
e
p
v
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t
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12
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4
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
22
73
–
22
83
2280
Fig
u
r
e
7
.
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s
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ch
.
RE
F
E
R
E
NC
E
S
[1
]
M
.
G
.
F
o
n
tan
a
,
Co
rr
o
sio
n
En
g
i
n
e
e
rin
g
,
M
c
G
ra
w
-
Hill
In
tern
a
ti
o
n
a
l
Ed
it
i
o
n
,
T
h
ird
Ed
i
ti
o
n
,
p
p
1
-
4
,
1
9
8
7
.
[2
]
NA
CE
In
tern
a
ti
o
n
a
l,
“
Co
n
tr
o
l
o
f
Ex
tern
a
l
C
o
rro
si
o
n
o
n
Un
d
e
rg
ro
u
n
d
o
r
S
u
b
m
e
rg
e
d
M
e
talli
c
P
ip
in
g
S
y
ste
m
s
,
En
g
i
n
e
e
rin
g
3
6
0
,
p
p
.
1
-
3
3
,
1
9
9
7
.
[3
]
NA
CE
In
tern
a
ti
o
n
a
l,
“
S
tan
d
a
r
d
re
c
o
m
m
e
n
d
e
d
p
ra
c
ti
c
e
:
d
e
si
g
n
,
in
sta
ll
a
ti
o
n
,
o
p
e
ra
ti
o
n
,
a
n
d
m
a
in
ten
a
n
c
e
o
f
imp
re
ss
e
d
c
u
rre
n
t
d
e
e
p
g
r
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u
n
d
b
e
d
s
,
”
En
g
in
e
e
rin
g
3
6
0
,
pp
.
1
-
1
9
,
2
0
0
1
.
[4
]
S.
A
.
H.
M
o
h
a
m
m
e
d
a
n
d
I
.
M
.
Ab
d
u
lb
a
q
i,
“
Nu
m
e
rica
l
S
t
u
d
y
a
n
d
De
sig
n
o
f
a
n
Im
p
re
ss
e
d
C
u
rre
n
t
Ca
th
o
d
ic
P
ro
tec
ti
o
n
S
y
ste
m
fo
r
Bu
ried
M
e
talli
c
P
ip
e
s,
”
2
0
1
8
T
h
ird
S
c
ien
ti
fi
c
Co
n
fer
e
n
c
e
o
f
El
e
c
trica
l
E
n
g
in
e
e
rin
g
(S
CEE
)
,
2
0
1
8
,
p
p
.
9
5
-
1
0
0
,
d
o
i:
1
0
.
1
1
0
9
/S
CEE
.
2
0
1
8
.
8
6
8
4
0
7
6
.
[5
]
S
.
S
.
Va
r
g
h
e
se
a
n
d
S
.
G
e
o
rg
e
,
“
An
a
ly
sis
o
f
AC
-
DC
C
o
n
v
e
rter
B
a
se
d
o
n
P
o
we
r
F
a
c
to
r
a
n
d
THD,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
Eme
rg
i
n
g
T
e
c
h
n
o
lo
g
y
a
n
d
Ad
v
a
n
c
e
En
g
i
n
e
e
rin
g
,
v
o
l.
3
,
n
o
.
2
,
p
p
.
3
5
0
-
3
5
6
,
F
e
b
r
u
a
ry
2
0
1
3
.
[6
]
A.
B.
G
a
n
e
se
n
,
N.
P
ra
m
e
sw
a
ri,
F
.
K.
Nu
ra
z
iz,
A.
Rizq
iaw
a
n
,
a
n
d
P
.
A.
Da
h
o
n
o
,
“
S
imp
li
fied
Ca
s
c
a
d
e
M
u
lt
ip
h
a
se
DC
-
DC
P
o
we
r
Co
n
v
e
rter
f
o
r
Lo
w
Vo
lt
a
g
e
Larg
e
Cu
rre
n
t
A
p
p
li
c
a
ti
o
n
s:
p
a
rt
---
ste
a
d
y
-
sta
te
a
n
a
ly
si
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
s
(IJ
PE
D
S
)
,
v
o
l.
1
2
,
n
o
.
3
,
p
p
.
1
7
0
8
-
1
7
1
9
,
S
e
p
te
m
b
e
r
2
0
2
1
,
d
o
i
:
1
0
.
1
1
5
9
1
/i
j
p
e
d
s.v
1
2
.
i3
.
p
p
1
7
0
8
-
1
7
1
9
.
[7
]
P
.
A.
Da
h
o
n
o
,
“
S
imp
li
fied
c
a
sc
a
d
e
m
u
lt
i
p
h
a
se
DC
-
DC b
o
o
st p
o
we
r
c
o
n
v
e
rters
f
o
r
h
ig
h
v
o
lt
a
g
e
-
g
a
i
n
a
n
d
lo
w
-
ri
p
p
l
e
a
p
p
li
c
a
ti
o
n
s,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
i
v
e
S
y
ste
ms
(IJ
PE
DS
)
,
v
o
l.
1
2
,
n
o
.
1
,
p
p
.
2
7
3
-
2
8
5
,
M
a
r
ch
2
0
2
1
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s
.
v
1
2
.
i
1
.
p
p
2
7
3
-
2
8
5
.
[8
]
V.
Vo
rp
e
rian
,
“
S
im
p
li
fied
a
n
a
ly
si
s
o
f
P
WM
c
o
n
v
e
rters
u
si
n
g
m
o
d
e
l
o
f
P
WM
sw
it
c
h
.
II.
Disc
o
n
ti
n
u
o
u
s
c
o
n
d
u
c
t
io
n
m
o
d
e
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Aer
o
sp
a
c
e
a
n
d
El
e
c
tro
n
ic
S
y
ste
ms
,
v
o
l
.
2
6
,
n
o
.
3
,
p
p
.
4
9
7
-
5
0
5
,
M
a
y
1
9
9
0
,
d
o
i:
1
0
.
1
1
0
9
/
7
.
1
0
6
1
2
7
.
[9
]
J.
M
a
h
d
a
v
i,
A.
Ema
a
d
i,
M
.
D.
Be
ll
a
r
,
a
n
d
M
.
E
h
sa
n
i,
“
An
a
l
y
sis
o
f
p
o
we
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ro
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h
,
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i
n
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
it
s a
n
d
S
y
ste
ms
I:
Fu
n
d
a
me
n
ta
l
T
h
e
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n
d
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p
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c
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6
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5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
22
73
–
22
83
2282
[1
0
]
K.
Na
tara
jan
a
n
d
M
.
Ye
k
taii,
“
M
o
d
e
li
n
g
o
f
DC
–
DC
Bu
c
k
Co
n
v
e
rters
fo
r
Larg
e
-
S
ig
n
a
l
F
re
q
u
e
n
c
y
Re
sp
o
n
se
a
n
d
Li
m
it
Cy
c
les
,
”
i
n
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Circ
u
i
ts
a
n
d
S
y
ste
ms
II:
Exp
re
ss
Briefs
,
v
o
l.
5
3
,
n
o
.
8
,
p
p
.
7
1
2
-
7
1
6
,
Au
g
u
st
2
0
0
6
,
d
o
i:
1
0
.
1
1
0
9
/T
CS
II
.
2
0
0
6
.
8
7
6
3
8
0
.
[1
1
]
R.
D.
M
id
d
leb
r
o
o
k
,
“
S
m
a
ll
-
sig
n
a
l
m
o
d
e
l
in
g
o
f
p
u
lse
-
wid
t
h
m
o
d
u
late
d
sw
it
c
h
e
d
-
m
o
d
e
p
o
we
r
c
o
n
v
e
rters
,
”
i
n
Pro
c
e
e
d
in
g
s
o
f
t
h
e
IEE
E
,
v
o
l.
7
6
,
n
o
.
4
,
p
p
.
3
4
3
-
3
5
4
,
Ap
ril
1
9
8
8
,
d
o
i:
1
0
.
1
1
0
9
/
5
.
4
4
2
1
.
[1
2
]
X.
Li
,
X.
R
u
a
n
,
Q.
Jin
,
M
.
S
h
a
,
a
n
d
C.
K.
Tse
,
“
S
m
a
ll
-
S
ig
n
a
l
M
o
d
e
ls
with
Ex
ten
d
e
d
F
re
q
u
e
n
c
y
Ra
n
g
e
fo
r
DC
-
DC
Co
n
v
e
rters
wi
th
Larg
e
M
o
d
u
lati
o
n
Ri
p
p
le
Am
p
li
t
u
d
e
,
”
i
n
I
EE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
3
3
,
n
o
.
9
,
p
p
.
8
1
5
1
-
8
1
6
3
,
S
e
p
t.
2
0
1
8
,
d
o
i:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
1
7
.
2
7
7
3
6
4
1
.
[1
3
]
R.
D.
M
i
d
d
le
b
ro
o
k
,
a
n
d
S
.
Cu
k
,
“
A
g
e
n
e
ra
l
u
n
ifi
e
d
a
p
p
ro
a
c
h
to
m
o
d
e
ll
in
g
sw
it
c
h
in
g
-
c
o
n
v
e
rter p
o
we
r
sta
g
e
s,
”
1
9
7
6
IEE
E
P
o
we
r E
lec
tro
n
ics
S
p
e
c
ia
li
sts Co
n
fer
e
n
c
e
,
1
9
7
6
,
p
p
.
1
8
-
3
4
,
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o
i:
1
0
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1
1
0
9
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E
S
C.
1
9
7
6
.
7
0
7
2
8
9
5
.
[1
4
]
Q
.
He
,
a
n
d
Y
.
Z
h
a
o
,
“
Th
e
d
e
sig
n
o
f
c
o
n
tro
l
ler
o
f
b
u
c
k
c
o
n
v
e
rter
,
”
2
0
1
0
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
Co
mp
u
ter
Ap
p
li
c
a
ti
o
n
a
n
d
S
y
ste
m
M
o
d
e
li
n
g
(ICC
AS
M
2
0
1
0
)
,
2
0
1
0
,
p
p
.
V1
5
-
2
5
1
-
V1
5
-
2
5
5
,
d
o
i:
1
0
.
1
1
0
9
/ICCAS
M
.
2
0
1
0
.
5
6
2
2
6
0
9
.
[1
5
]
H.
S
ira
-
Ra
m
írez
,
A.
Lu
v
ian
o
-
Ju
á
re
z
,
a
n
d
J.
Co
rtés
-
Ro
m
e
ro
,
“
Ro
b
u
st
in
p
u
t
-
o
u
t
p
u
t
sli
d
in
g
m
o
d
e
c
o
n
tro
l
o
f
t
h
e
b
u
c
k
c
o
n
v
e
rter,
”
Co
n
tro
l
E
n
g
in
e
e
rin
g
Pra
c
ti
c
e
,
v
o
l.
2
1
,
n
o
.
5
,
p
p
.
6
7
1
-
6
7
8
,
M
a
y
2
0
1
3
,
d
o
i:
1
0
.
1
0
1
6
/
j.
c
o
n
e
n
g
p
ra
c
.
2
0
1
2
.
0
3
.
0
0
8
.
[1
6
]
A.
Ku
g
i
,
a
n
d
K.
S
c
h
lac
h
e
r,
“
No
n
li
n
e
a
r
H/s
u
b
/sp
l
i
n
fi
n
//
c
o
n
tr
o
ll
e
r
d
e
sig
n
f
o
r
a
DC
-
to
-
DC
p
o
we
r
c
o
n
v
e
rter,
”
i
n
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
C
o
n
tro
l
S
y
ste
ms
T
e
c
h
n
o
lo
g
y
,
v
o
l
.
7
,
n
o
.
2
,
p
p
.
2
3
0
-
2
3
7
,
M
a
rc
h
1
9
9
9
,
d
o
i
:
1
0
.
1
1
0
9
/
8
7
.
7
4
8
1
4
9
.
[1
7
]
T.
S
a
to
,
T
.
Na
b
e
sh
ima
,
K.
Nish
ij
ima
,
a
n
d
T
.
Na
k
a
n
o
,
“
DC
-
D
C
Co
n
v
e
rters
with
a
No
v
e
l
Hy
ste
re
ti
c
P
WM
Co
n
tr
o
ll
e
r,
”
IECON
2
0
0
6
-
3
2
n
d
An
n
u
a
l
C
o
n
fer
e
n
c
e
o
n
IEE
E
In
d
u
stria
l
El
e
c
tro
n
ics
,
2
0
0
6
,
p
p
.
2
7
2
9
-
2
7
3
3
,
d
o
i
:
1
0
.
1
1
0
9
/I
ECON.2
0
0
6
.
3
4
8
0
6
1
.
[1
8
]
S
.
M
a
it
y
,
a
n
d
Y.
S
u
ra
j,
“
An
a
ly
sis
a
n
d
M
o
d
e
li
n
g
o
f
a
n
F
F
HC
-
Co
n
tr
o
ll
e
d
DC
–
DC Bu
c
k
Co
n
v
e
rter S
u
it
a
b
le fo
r
Wi
d
e
Ra
n
g
e
o
f
O
p
e
ra
ti
n
g
Co
n
d
it
io
n
s,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
7
,
n
o
.
1
2
,
p
p
.
4
9
1
4
-
4
9
2
4
,
De
c
.
2
0
1
2
,
d
o
i:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
1
2
.
2
1
9
3
6
2
0
.
[1
9
]
K.
S
wa
th
y
,
S
.
Ja
n
tre,
Y.
Ja
d
h
a
v
,
S
.
M
.
La
b
d
e
,
a
n
d
P
.
Ka
d
a
m
,
“
De
sig
n
a
n
d
Ha
rd
wa
re
Im
p
lem
e
n
t
a
ti
o
n
o
f
Clo
se
d
Lo
o
p
B
u
c
k
C
o
n
v
e
rter
Us
in
g
F
u
z
z
y
Lo
g
ic
Co
n
tr
o
ll
e
r,
”
2
0
1
8
S
e
c
o
n
d
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
El
e
c
tro
n
ics
,
Co
mm
u
n
ica
ti
o
n
a
n
d
Aer
o
sp
a
c
e
T
e
c
h
n
o
l
o
g
y
(ICECA
)
,
2
0
1
8
,
p
p
.
1
7
5
-
1
8
0
,
d
o
i:
1
0
.
1
1
0
9
/IC
ECA.
2
0
1
8
.
8
4
7
4
5
7
0
.
[2
0
]
K.
M
.
S
m
e
d
ley
,
a
n
d
S
.
C
u
k
,
“
On
e
-
c
y
c
le
c
o
n
tr
o
l
o
f
sw
it
c
h
in
g
c
o
n
v
e
rters
,
”
in
IEE
E
T
r
a
n
sa
c
t
io
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
1
0
,
n
o
.
6
,
p
p
.
6
2
5
-
6
3
3
,
No
v
.
1
9
9
5
,
d
o
i
:
1
0
.
1
1
0
9
/
6
3
.
4
7
1
2
8
1
.
[2
1
]
D.
M
a
k
sim
o
v
ic,
Y
.
Ja
n
g
,
a
n
d
R.
W.
Er
ick
so
n
,
“
No
n
li
n
e
a
r
-
c
a
rrier
c
o
n
tro
l
f
o
r
h
i
g
h
-
p
o
we
r
-
fa
c
to
r
b
o
o
st
re
c
ti
fiers
,
”
i
n
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
le
c
tro
n
ics
,
v
o
l.
1
1
,
n
o
.
4
,
p
p
.
5
7
8
-
5
8
4
,
J
u
ly
1
9
9
6
,
d
o
i
:
1
0
.
1
1
0
9
/
6
3
.
5
0
6
1
2
3
.
[2
2
]
P
.
Co
m
i
n
o
s
,
a
n
d
N.
M
u
n
ro
,
“
P
ID
c
o
n
tr
o
ll
e
rs:
Re
c
e
n
t
t
u
n
in
g
m
e
th
o
d
s
a
n
d
d
e
sig
n
t
o
sp
e
c
ifi
c
a
ti
o
n
,
”
IE
E
Pro
c
e
e
d
in
g
s:
Co
n
tro
l
T
h
e
o
ry
a
n
d
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
1
4
9
,
n
o
.
1
,
p
p
.
4
6
-
5
3
,
Ja
n
u
a
ry
2
0
0
2
,
d
o
i:
1
0
.
1
0
4
9
/i
p
-
c
ta:2
0
0
2
0
1
0
3
.
[2
3
]
R.
M
a
tu
su
,
“
Ca
lcu
latio
n
o
f
a
ll
sta
b
il
izin
g
P
I
a
n
d
P
ID
c
o
n
tr
o
ll
e
rs,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
M
a
th
e
ma
t
ics
a
n
d
Co
mp
u
ter
s i
n
S
imu
l
a
ti
o
n
v
o
l
.
5
,
n
o
.
3
,
pp
.
2
2
4
-
2
3
1
,
2
0
1
1
.
[2
4
]
R.
Ku
ro
k
a
wa
,
T.
S
a
t
o
,
R.
Vilan
o
v
a
,
a
n
d
Y.
Ko
n
is
h
i,
“
Clo
se
d
-
l
o
o
p
Da
ta
-
d
riv
e
n
Trad
e
-
o
ff
P
ID
C
o
n
tr
o
l
De
sig
n
,
”
IFA
C
-
Pa
p
e
rs
On
L
in
e
,
v
o
l.
5
1
,
n
o
.
4
,
p
p
.
2
4
4
-
2
4
9
,
Ja
n
u
a
ry
2
0
1
8
,
d
o
i:
1
0
.
1
0
1
6
/j
.
ifac
o
l.
2
0
1
8
.
0
6
.
0
7
3
.
[2
5
]
U.
R.
P
ra
sa
n
n
a
,
a
n
d
A.
K.
Ra
th
o
re
,
“
Two
lo
o
p
a
v
e
ra
g
e
c
u
rre
n
t
c
o
n
tr
o
l
imp
lem
e
n
tatio
n
u
si
n
g
c
y
p
re
ss
P
S
o
C
with
c
lo
se
d
l
o
o
p
e
x
p
e
rime
n
tal
re
su
lt
s,
”
2
0
1
3
IEE
E
E
n
e
rg
y
C
o
n
v
e
rs
io
n
Co
n
g
re
ss
a
n
d
Exp
o
siti
o
n
,
2
0
1
3
,
p
p
.
4
1
9
9
-
4
2
0
6
,
d
o
i:
1
0
.
1
1
0
9
/E
CCE
.
2
0
1
3
.
6
6
4
7
2
6
0
.
[2
6
]
K.
Og
a
ta,
“
M
o
d
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