I
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t
e
r
n
at
ion
al
Jou
r
n
al
of
P
owe
r
E
lec
t
r
on
ics
an
d
Dr
ive
S
ys
t
e
m
s
(
I
JP
E
DS)
Vol.
13
,
No.
1
,
M
a
r
c
h
20
2
2
,
pp.
460
~
469
I
S
S
N:
2088
-
8694,
DO
I
:
10
.
11591/i
jpeds
.
v
13
.i
1
.
pp
460
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469
460
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D
C
t
o
D
C
co
n
v
ert
er.
K
e
y
w
o
r
d
s
:
DC
dis
tr
ibut
e
d
powe
r
s
upply
P
owe
r
ba
lanc
e
c
ontr
ol
T
e
c
hnique
a
ve
r
a
ge
s
mall
-
s
ignal
method
M
AT
L
AB
/
S
im
uli
nk
s
im
ulation
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
Uthe
n
Ka
mnar
n
De
pa
r
tm
e
nt
of
E
lec
tr
ica
l
E
nginee
r
ing,
R
a
jama
nga
la
Unive
r
s
it
y
of
T
e
c
hnology
L
a
nna
128
Hua
y
Ka
e
w
R
oa
d,
T
a
mbon
C
ha
ng
P
hue
a
k,
M
ua
ng,
C
hiang
M
a
i
50300,
T
ha
il
a
nd
E
mail:
Uthe
n@r
mu
tl
.
a
c
.
th
1.
I
NT
RODU
C
T
I
ON
F
r
om
the
1960s
,
s
e
mi
c
onduc
tor
tec
hnology
de
v
e
lopm
e
nt
s
tar
ted
a
nd
led
to
the
de
ve
lopm
e
nt
of
powe
r
e
lec
tr
onics
c
onve
r
ter
s
(
P
E
C
s
)
,
whic
h
i
mpr
ove
d
the
e
f
f
icie
nc
y
of
DC
powe
r
s
ys
tems
.
As
ne
w
tec
hnologi
e
s
c
onti
nue
to
e
mer
ge
,
powe
r
e
lec
tr
oni
c
c
onve
r
ter
s
ha
ve
be
e
n
c
onti
nuo
us
ly
im
pr
ove
d
in
ter
ms
of
e
f
f
icie
nc
y,
r
e
li
a
bil
it
y
,
c
os
t
,
a
nd
s
ize
,
to
the
poin
t
whe
r
e
DC
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tr
ibut
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s
ys
tems
now
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mons
tr
a
te
be
tt
e
r
e
f
f
icie
nc
y
than
AC
dis
tr
ibut
ion
s
ys
tems
[
1]
.
F
o
r
thi
s
r
e
a
s
on,
many
f
a
c
il
it
ies
nowa
da
ys
a
r
e
de
s
igned
to
be
mor
e
a
de
qua
te
f
or
DC
dis
tr
ibut
ion
s
ys
tems
,
whe
r
e
many
or
ga
niza
ti
ons
a
c
c
e
pted
dis
tr
ibut
e
d
bus
volt
a
ge
r
a
ti
ng
is
380
Vdc
a
tt
r
ibut
a
ble
to
high
e
f
f
icie
nc
y,
r
e
a
s
ona
ble
c
os
t,
a
nd
high
r
e
li
a
bil
it
y
[
2]
.
Nume
r
ous
indus
tr
y
s
tanda
r
ds
s
uc
h
a
s
e
M
e
r
ge
Alli
a
nc
e
,
the
I
nter
na
ti
ona
l
E
lec
tr
o
tec
hnica
l
C
omm
is
s
ion
(
I
E
C
)
,
the
S
o
c
iety
of
C
a
ble
T
e
lec
omm
unica
ti
ons
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nginee
r
s
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S
C
T
E
)
,
t
he
Alli
a
nc
e
f
or
T
e
lec
omm
unica
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ons
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ndus
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olut
ions
(
AT
I
S
)
,
Unde
r
wr
i
ter
s
L
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bor
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tor
ies
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UL
)
,
th
e
f
or
mation
of
the
I
nter
na
ti
ona
l
T
e
legr
a
ph
Union
-
T
e
lec
omm
unica
ti
on
S
tand
a
r
diza
ti
on
S
e
c
tor
(
I
T
U
-
T
)
,
E
u
r
ope
a
n
T
e
lec
omm
unica
ti
ons
S
tanda
r
ds
I
ns
ti
tut
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
De
s
ign
and
s
imulat
ion
of
DC
dis
tr
ibut
e
d
pow
e
r
s
upply
w
it
h
…
(
Uthe
n
K
amnar
n
)
461
(
E
T
S
I
)
,
the
Na
ti
ona
l
E
lec
tr
ica
l
M
a
nuf
a
c
tur
e
r
s
As
s
oc
iation
(
NE
M
A
)
,
a
nd
the
Na
ti
ona
l
E
lec
tr
ica
l
C
ode
(
NE
C
)
ha
ve
be
e
n
wor
king
on
s
tanda
r
ds
r
e
late
d
to
380
Vd
c
a
nd
a
f
e
w
indus
tr
y
s
tanda
r
ds
a
r
e
unde
r
de
ve
lop
ment
a
nd
s
ome
ha
ve
a
lr
e
a
dy
be
e
n
e
s
tablis
he
d
.
C
ompanie
s
s
uc
h
a
s
AB
B
L
td.
,
E
me
r
s
on
E
lec
tr
ic
C
o.
,
He
wle
tt
-
P
a
c
ka
r
d
De
ve
lopm
e
nt
C
ompany
(
HP
)
,
S
tar
li
ne
I
nc
.
,
S
c
h
ne
ider
E
lec
tr
ic
C
ompany
,
a
nd
GV
A
L
ight
ing
I
n
c
.
,
ha
ve
s
tar
ted
manuf
a
c
tur
ing
a
ppli
a
nc
e
s
that
a
r
e
c
ompati
ble
with
DC
dis
tr
ibut
ion
s
ys
tems
with
380
Vdc
di
s
tr
ibut
e
d
powe
r
bus
a
nd
ga
ini
ng
popular
it
y
a
mong
tele
c
om
a
nd
da
ta
c
e
nter
s
,
a
nd
c
ould
a
ls
o
be
us
e
d
f
or
c
omm
e
r
c
ial
or
r
e
s
idential
buil
dings
on
a
lar
ge
r
s
c
a
le
in
the
f
ut
ur
e
[
3]
.
I
n
s
uc
h
s
ys
tems
,
the
c
ontr
ol
method
of
the
c
onve
r
ter
c
ir
c
uit
is
c
r
uc
ial
in
e
ns
ur
ing
s
tabili
ty
,
pe
r
f
or
manc
e
,
r
e
li
a
bil
i
ty,
a
nd
good
r
e
s
pons
e
.
R
e
c
e
nt
wor
ks
s
ugge
s
ted
that
e
f
f
e
c
ti
ve
c
ontr
ol
de
s
ign
c
a
n
be
a
c
hieve
d
us
ing
c
ur
r
e
nt
mode
c
ontr
ol
a
nd
volt
a
ge
mode
c
ontr
ol
.
H
owe
ve
r
,
s
uc
h
c
ontr
ols
ha
ve
downs
ide
s
in
ter
ms
of
s
tabili
ty,
pe
r
f
o
r
manc
e
,
de
s
ign
c
ompl
e
xit
y,
including
li
mi
tations
c
a
us
e
d
by
the
non
-
mi
nim
um
pha
s
e
is
s
ue
[
4]
−
[
7]
.
T
o
ove
r
c
ome
thes
e
l
im
it
a
ti
ons
,
va
r
ious
c
ontr
ol
te
c
hniques
ha
ve
be
e
n
r
e
s
e
a
r
c
he
d
a
nd
de
ve
loped
[
8]
−
[
20]
ho
we
ve
r
,
thes
e
c
ontr
ol
tec
hniques
a
r
e
c
ompl
ica
ted
i
n
de
s
ign
a
nd
im
pleme
ntation.
T
o
s
olve
the
pr
oblems
,
the
p
owe
r
ba
lanc
e
c
ontr
ol
tec
hnique
a
nd
e
ne
r
gy
ba
lanc
e
c
ontr
ol
tec
hnique,
whic
h
pr
oduc
e
s
im
pler
c
ontr
o
l
de
s
ign
a
nd
be
tt
e
r
pe
r
f
or
ma
nc
e
c
ompar
e
d
to
the
r
e
gular
vol
tage
a
nd
c
ur
r
e
nt
mode
c
ont
r
ol,
ha
ve
be
e
n
de
ve
loped
[
21
]
−
[
25]
.
T
his
pa
pe
r
a
im
s
to
de
s
ign,
a
na
lyze
a
nd
s
im
ul
a
te
the
DC
dis
tr
ibut
ion
s
ys
tem
in
a
ll
pos
s
ibl
e
c
onne
c
ti
on
s
tr
uc
tur
e
s
(
i.
e
.
,
pa
r
a
ll
e
l,
c
a
s
c
a
de
,
s
our
c
e
s
pli
tt
ing,
load
s
pli
tt
ing
,
a
nd
s
tac
k)
us
ing
po
we
r
a
nd
e
ne
r
gy
ba
lanc
e
c
ontr
o
l
tec
hniques
to
im
pr
ove
th
e
pe
r
f
o
r
manc
e
of
s
ys
tems
that
a
r
e
c
onne
c
ted
in
va
r
ious
volt
a
ge
bus
s
tr
uc
tur
e
s
in
DC
dis
tr
ibut
ion
s
ys
tems
.
T
he
pr
opos
e
d
s
ys
tem
ha
s
a
tot
a
l
powe
r
r
a
ti
ng
o
f
1
kW
a
nd
c
ontains
6
volt
a
ge
bus
e
s
with
volt
a
ge
r
a
ti
ngs
of
3
80,
100,
60,
48,
24
,
a
nd
12
V
.
T
he
s
im
ulation
is
d
one
with
M
AT
L
AB
/
S
im
uli
nk.
2.
M
E
T
HO
D
T
he
pr
opos
e
d
DC
dis
tr
ibut
e
d
s
ys
tem
s
hown
in
F
igur
e
1
c
ons
is
ts
of
3
main
pa
r
ts
:
f
lybac
k
#1
-
5,
buc
k
#1
-
4,
a
nd
a
bidi
r
e
c
ti
ona
l
c
onve
r
ter
.
T
he
powe
r
ba
l
a
nc
e
e
qua
ti
on
of
the
s
ys
tem
is
:
(
)
(
)
(
)
1
,
2
1
2
3
3
1
4
,
5
4
4
5
5
4
,
5
4
5
2
3
1
=
=
=
+
+
−
=
+
=
+
−
N
N
N
N
in
L
B
o
o
o
o
o
lo
a
d
in
L
B
L
B
o
o
o
lo
a
d
i
V
I
k
I
V
V
V
I
P
V
I
k
I
k
V
I
I
P
(
)
(
)
(
)
(
)
6
,7
,
8
6
6
7
7
8
8
6
6
6
7
7
7
8
8
8
=
+
+
=
−
+
−
+
−
i
n
L
B
L
B
L
B
o
o
l
o
a
d
o
o
l
o
a
d
o
o
l
o
a
d
V
I
k
I
k
I
k
V
I
P
V
I
P
V
I
P
(
1)
F
igur
e
1.
T
he
pr
opos
e
d
1
kW
dis
tr
ibut
ion
s
ys
tem
2
.
1.
De
s
ign
c
on
s
id
e
r
at
ion
T
he
s
ys
tem
s
with
powe
r
ba
lanc
e
c
ontr
ol
tec
hni
que
a
r
e
s
hown
in
F
igur
e
s
2
(
a
)
-
(
c
)
s
hows
the
bidi
r
e
c
ti
ona
l
c
onve
r
ter
de
s
igned
to
wor
k
in
c
onti
n
uous
c
ur
r
e
nt
mode
(
C
C
M
)
.
T
he
inducta
nc
e
va
lue
of
b
uc
k
c
onve
r
ter
is
:
m
i
n
(
1
)
2
SW
DR
L
f
−
=
(
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
460
-
469
462
whe
r
e
m
i
n
L
is
the
mi
nim
um
inducta
nc
e
va
lue,
D
is
the
duty
c
yc
le,
R
is
the
output
im
pe
da
nc
e
,
SW
f
is
s
witching
f
r
e
que
nc
y.
o
V
is
output
vo
lt
a
ge
r
ippl
e
.
T
he
c
a
pa
c
it
a
nc
e
va
lue
f
or
the
output
c
a
pa
c
it
or
of
a
buc
k
c
onve
r
t
e
r
is
:
(
)
2
1
8
o
o
S
W
D
C
L
V
V
f
−
=
(
3)
F
or
the
f
lybac
k
c
onve
r
ter
,
the
mi
nim
um
inducta
nc
e
is
:
2
2
1
m
i
n
2
(
1
)
2
SW
N
DR
L
fN
−
=
(
4)
(
a
)
(
b)
(
c
)
F
igur
e
2.
C
onve
r
ter
s
with
powe
r
ba
lanc
e
c
ontr
ol
te
c
hnique
(
a
)
f
lybac
k
c
onve
r
ter
,
(
b
)
buc
k
c
onve
r
ter
,
a
nd
(
c
)
bidi
r
e
c
ti
ona
l
c
onve
r
ter
T
he
output
c
a
pa
c
it
a
nc
e
of
the
f
lybac
k
c
onve
r
ter
is
:
=
⋅
(
)
(
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
De
s
ign
and
s
imulat
ion
of
DC
dis
tr
ibut
e
d
pow
e
r
s
upply
w
it
h
…
(
Uthe
n
K
amnar
n
)
463
T
he
mathe
matica
l
model
o
f
the
modul
e
s
in
the
s
ys
tem
ha
s
be
e
n
de
r
ived
to
s
im
ulate
a
nd
s
tudy
the
dyna
mi
c
r
e
s
pons
e
obtaine
d
f
r
om
M
AT
L
AB
/
S
im
uli
nk,
a
s
we
ll
a
s
to
a
na
lyze
the
c
ompatibi
li
ty
f
or
c
o
nne
c
ti
ng
the
modul
e
s
in
a
ll
pr
opos
e
d
c
onne
c
ti
on
s
tr
uc
tur
e
s
in
the
DC
dis
tr
ibut
e
d
powe
r
s
upply.
I
f
1
=
u
is
the
ON
s
tate
of
the
s
witching,
0
=
u
is
the
OF
F
s
tate
of
the
s
wit
c
hing,
a
nd
1
−=
uu
,
the
inducto
r
c
ur
r
e
nt
e
qua
ti
on
o
f
the
f
lybac
k
c
onve
r
ter
is
:
1
2
1
(
)
(
)
(
)
=−
L
i
n
o
N
i
s
u
V
s
u
V
s
s
L
N
(
6)
T
he
output
c
a
pa
c
it
or
volt
a
ge
e
qua
ti
on
o
f
the
f
lybac
k
c
onve
r
ter
is
:
1
2
1
(
)
(
)
(
)
=−
C
L
R
N
V
s
uI
s
I
s
s
C
N
(
7)
T
he
inductor
c
ur
r
e
nt
e
qua
ti
on
of
the
buc
k
c
onve
r
ter
is
:
1
(
)
(
)
(
)
=−
L
i
n
o
I
s
u
V
s
V
s
sL
(
8)
T
he
output
c
a
pa
c
it
or
volt
a
ge
e
qua
ti
on
o
f
the
buc
k
c
onve
r
ter
is
:
1
(
)
(
)
(
)
=−
C
L
R
V
s
I
s
I
s
sC
(
9)
2
.
2.
Ave
r
age
s
m
all
s
ign
al
an
alys
is
T
he
p
r
opos
e
d
s
ys
tem
c
ontr
ol
tec
hnique
is
ba
s
e
d
o
n
the
idea
o
f
powe
r
ba
lanc
e
,
whic
h
s
tate
s
that
the
input
a
nd
ou
tput
powe
r
of
the
s
ys
tem
is
e
qua
l.
S
u
ppos
e
that
the
s
ys
tem
is
los
s
les
s
,
thus
,
the
a
ve
r
a
ge
s
mall
-
s
ignal
model
of
the
powe
r
ba
lanc
e
e
qua
ti
ons
of
bu
c
k
a
nd
f
lybac
k
c
onve
r
ter
s
c
a
n
be
obtaine
d
a
s
f
o
ll
o
ws
:
F
or
load
s
pli
tt
ing,
a
nd
nor
mal
s
tr
uc
tur
e
:
1
=
=
ii
in
B
L
o
o
i
V
k
I
V
I
(
10)
F
or
s
our
c
e
s
pli
tt
ing
,
a
nd
pa
r
a
ll
e
li
ng:
1
=
=
i
i
i
o
lo
a
d
in
B
L
i
VI
V
k
I
N
(
11)
whe
r
e
in
V
is
the
inpu
t
volt
a
ge
,
o
V
is
the
outpu
t
volt
a
ge
,
L
I
is
inductor
c
ur
r
e
nt
,
l
o
a
d
I
is
load
c
u
r
r
e
nt
,
N
is
a
number
of
output
bus
pa
r
a
ll
e
l
-
c
onne
c
ted
modul
e
s
,
a
nd
B
k
is
the
duty
c
yc
le
,
whic
h
is
c
ons
ider
e
d
a
s
loop
ga
in
.
F
r
om
the
powe
r
ba
lanc
e
e
qua
ti
ons
,
the
r
e
f
e
r
e
nc
e
i
nduc
tor
c
ur
r
e
nt
e
qua
ti
on
c
a
n
be
de
ter
mi
ne
d
by
the
inductor
c
ur
r
e
nt
c
a
lcula
tor
.
PBC
i
is
the
inducto
r
c
u
r
r
e
n
t
that
is
c
a
lcula
ted
ba
s
e
d
on
load
c
u
r
r
e
nt,
ou
tput
volt
a
ge
,
input
volt
a
ge
,
a
nd
the
number
of
pa
r
a
ll
e
le
d
modul
e
s
N
.
T
he
pe
a
k
va
lue
o
f
PBC
i
c
a
n
be
de
r
ived
a
s
:
=
o
l
o
a
d
P
B
C
B
i
n
Vi
i
k
V
N
(
12)
whe
r
e
r
e
f
L
i
is
the
va
lue
of
the
inducto
r
c
ur
r
e
nt,
VR
i
is
the
c
or
r
e
c
ti
ng
s
ignal
of
the
P
I
c
ontr
oll
e
r
,
PBC
i
is
the
pe
a
k
va
lue
of
the
inductor
r
e
f
e
r
e
nc
e
c
ur
r
e
nt
.
T
he
pe
a
k
v
a
lue
of
the
inductor
c
u
r
r
e
nt
is
:
re
f
L
P
B
C
V
R
i
i
i
=+
(
13)
T
he
dyna
mi
c
e
qua
ti
on
o
f
the
output
vo
lt
a
ge
is
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
460
-
469
464
1
N
o
Li
lo
a
d
i
dv
i
C
i
dt
=
=+
(
14)
P
e
r
f
or
mi
ng
the
pe
r
tu
r
ba
ti
ons
a
nd
s
mall
-
s
ignal
a
ppr
oxim
a
ti
on
in
(
10)
to
(
14)
yields
:
,,
=
=
=
in
B
re
f
B
in
o
V
k
z
o
o
o
B
k
n
I
k
n
V
I
G
G
G
V
V
V
k
n
,
2
,,
=
=
=
o
i
n
o
l
o
a
d
o
l
o
a
d
l
o
a
d
V
V
B
i
n
B
i
n
in
V
I
V
I
F
F
F
k
n
V
k
n
V
V
T
he
output
c
ur
r
e
nt
,
the
pe
a
k
va
lue
of
the
inducto
r
r
e
f
e
r
e
nc
e
c
ur
r
e
nt,
a
nd
output
inducta
nc
e
c
a
n
be
e
xpr
e
s
s
e
d
a
s
:
=
+
−
in
o
V
i
n
k
r
e
f
z
o
i
G
v
G
i
G
v
(
15)
=
+
−
+
o
i
n
P
B
C
lo
a
d
lo
a
d
v
o
V
in
i
F
i
F
v
F
v
(
16)
1
()
==
−
o
L
o
l
o
a
d
v
ZS
C
s
i
i
(
17)
F
r
om
(
15
)
to
(
17)
a
nd
the
output
volt
a
ge
e
qua
ti
o
n
c
a
n
be
wr
it
ten
a
s
a
block
d
iagr
a
m
a
s
s
hown
in
F
igur
e
3.
F
r
om
F
igu
r
e
3,
a
pplyi
ng
M
a
s
on's
ga
in
method,
the
output
volt
a
ge
loop
c
a
n
be
s
hown
in
F
igur
e
4.
T
he
powe
r
ba
lanc
e
c
ontr
ol
tec
hnique
c
ons
is
t
ed
of
a
n
inductor
c
ur
r
e
nt
c
a
lcula
t
ion
block
a
nd
P
I
c
ont
r
o
ll
e
r
.
T
he
output
volt
a
ge
will
be
c
ompa
r
e
d
with
the
de
s
ir
e
d
r
e
f
e
r
e
nc
e
volt
a
g
e
.
T
he
inductor
c
ur
r
e
nt
c
a
lcula
t
i
on
block
c
omput
e
s
the
r
e
f
e
r
e
nc
e
input
c
ur
r
e
nt.
T
he
n,
th
e
e
r
r
or
s
ignal
wi
ll
be
c
ompens
a
ted
by
the
p
r
o
pos
e
d
P
I
c
ontr
oll
e
r
.
T
he
n,
t
he
output
s
umm
a
ti
on
s
ignal
wil
l
be
c
ompar
e
d
with
the
input
inductor
c
u
r
r
e
nt.
F
in
a
ll
y,
t
he
r
e
s
ult
c
omm
a
nd
s
ignal
will
be
pr
oc
e
s
s
e
d
by
puls
e
width
modul
a
ti
on
(
P
W
M
)
o
r
hys
ter
e
s
is
c
ur
r
e
nt
c
ontr
ol,
ge
ne
r
a
ti
ng
the
s
ignal
to
the
ga
te
dr
ive
c
ir
c
uit
to
c
ontr
ol
the
s
witch
.
T
he
pr
opos
e
d
c
ontr
ol
tec
hniqu
e
c
a
n
be
s
im
ply
im
pleme
nted
by
a
na
log
a
nd
digi
tal
c
ir
c
uit
s
.
F
igur
e
3
.
B
lock
diagr
a
m
of
a
c
onve
r
ter
in
the
pr
op
os
e
d
s
ys
tem
with
powe
r
ba
lanc
e
c
ontr
ol
tec
hnique
F
igur
e
4
.
B
lock
diagr
a
m
of
the
output
volt
a
ge
loop
W
he
r
e
VR
G
is
the
P
I
c
ont
r
oll
e
r
a
nd
fb
k
is
the
f
e
e
dba
c
k
ga
in,
the
ou
tput
volt
a
ge
c
a
n
be
e
xpr
e
s
s
e
d
a
s
:
o
V
R
B
i
n
o
V
R
B
i
n
f
b
r
e
f
V
G
k
N
V
V
C
S
G
k
N
V
k
V
=
+
(
18)
T
he
ope
n
-
loop
tr
a
ns
f
e
r
f
unc
ti
on
(
OL
T
F
)
o
f
the
out
put
volt
a
ge
c
a
n
be
e
xp
r
e
s
s
e
d
a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
De
s
ign
and
s
imulat
ion
of
DC
dis
tr
ibut
e
d
pow
e
r
s
upply
w
it
h
…
(
Uthe
n
K
amnar
n
)
465
in
fb
o
Vk
O
L
T
F
V
CS
=
(
19)
2
.
3
.
Cont
r
ol
s
t
r
at
e
gy
T
he
c
ontr
ol
s
tr
a
tegy
r
e
quir
e
s
a
f
e
e
dba
c
k
c
ompens
a
ti
on
pr
oc
e
s
s
to
r
e
gulate
the
output
volt
a
ge
ove
r
the
output
load
va
r
iation
a
nd
input
volt
a
ge
.
T
he
f
r
e
que
nc
y
ga
in
a
nd
loca
ti
on
o
f
the
z
e
r
o
mus
t
be
s
e
lec
ted
f
or
the
c
ompens
a
ti
on
ne
twor
k
,
the
s
tea
dy
-
s
tate
e
r
r
or
of
the
output
volt
a
ge
s
hould
a
ls
o
be
a
s
s
mall
a
s
pos
s
ibl
e
.
F
r
om
the
pr
opos
e
d
s
ys
tem
output
volt
a
ge
t
r
a
ns
f
e
r
f
unc
ti
ons
c
a
n
inves
ti
ga
te
us
ing
B
ode
d
iagr
a
m
s
t
o
ge
t
the
de
s
ir
e
d
f
r
e
que
nc
y
a
nd
pha
s
e
s
hif
t.
T
he
e
qua
ti
on
of
P
I
c
ontr
ol
ler
f
o
r
vol
tage
r
e
gulation
is
:
()
Z
V
R
C
G
s
K
S
=+
(
20)
F
igur
e
s
5
a
nd
6
s
how
the
B
ode
diagr
a
m
s
o
f
the
pr
opos
e
d
s
ys
tem
’
s
output
volt
a
ge
,
the
P
I
c
ontr
oll
e
r
s
,
a
nd
ope
n
-
loop
tr
a
ns
f
e
r
f
unc
ti
ons
.
E
a
c
h
pa
r
t
ha
s
a
bou
t
85
-
90
de
gr
e
e
s
of
pha
s
e
mar
gin
,
e
nough
to
s
tabili
z
e
the
s
ys
tem.
(
F
ly
ba
c
k#1)
(
F
ly
ba
c
k#2)
(
F
ly
ba
c
k#3)
F
igur
e
5
.
B
ode
diagr
a
m
s
of
the
p
r
opos
e
d
s
ys
tem
s
(
380
Vdc
bus
)
(
F
ly
ba
c
k#4, #5)
(
B
uc
k#1)
(
B
uc
k#2)
(
B
uc
k#3)
(
B
uc
k#4)
F
igur
e
6
.
B
ode
diagr
a
m
s
of
the
p
r
opos
e
d
s
ys
tem
s
(
100,
60,
48,
24,
a
nd
12
Vdc
bus
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
460
-
469
466
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
F
igur
e
7
s
hows
t
he
s
im
ulation
r
e
s
ult
s
of
the
p
r
op
os
e
d
s
ys
tem
.
T
he
tr
a
ns
ient
r
e
s
pons
e
e
f
f
e
c
ti
ve
ne
s
s
of
the
s
ys
tem
is
inves
ti
ga
ted
by
M
AT
L
AB
/
S
i
mul
ink
to
ve
r
i
f
y
the
c
ontr
o
l
a
lgo
r
it
hm
a
nd
e
va
luate
the
pe
r
f
or
manc
e
of
the
s
ys
tem
,
us
ing
the
c
a
lcula
ted
s
pe
c
if
ica
ti
on
s
hown
in
T
a
ble
1
.
F
igur
e
7
(
a
)
s
hows
the
r
e
s
pons
e
s
of
bus
vo
lt
a
ge
a
nd
load
c
ur
r
e
nt
a
t
the
3
80
V,
100
V
,
60
V,
48
V
,
24
V
,
a
nd
12
V
bus
.
F
ig
ur
e
7
(
b
)
s
how
s
the
s
tate
of
c
ha
r
ge
,
c
u
r
r
e
nt
,
a
nd
volt
a
ge
o
f
t
he
ba
tt
e
r
y.
F
r
om
0
-
0.
1
s
,
the
s
ys
tem
ini
ti
a
l
iza
ti
on
s
tar
ts
a
nd
ha
s
f
ull
load
a
t
100
%
a
s
de
s
igned.
At
0
.
1s
,
a
s
ud
de
n
s
tep
down
of
the
s
ys
tem’
s
load
f
r
om
100
%
(
1
kW
)
to
10%
(
100
W
)
oc
c
ur
s
.
At
0.
2s
,
a
s
udde
n
s
tep
up
of
the
s
ys
tem’
s
load
f
r
om
10%
(
100
W
)
to
100
%
(
1
kW
)
oc
c
ur
s
.
T
he
n,
a
t
0
.
3s
,
a
s
udde
n
c
ut
of
f
of
the
s
ys
tem
main
s
our
c
e
s
oc
c
ur
s
,
then
the
bidi
r
e
c
ti
ona
l
c
onve
r
ter
with
e
ne
r
gy
ba
lanc
e
c
ontr
o
l
tec
hnique
c
onne
c
ted
to
the
ba
tt
e
r
y
maintains
the
s
tabili
ty
o
f
the
volt
a
g
e
a
t
the
24
V
a
nd
12
V
bus
.
T
he
n,
a
t
0
.
4s
a
nd
0.
5s
a
r
e
s
udd
e
n
s
tep
down
f
r
om
100%
(
400
W
)
to
10%
(
40
W
)
a
nd
s
tep
up
f
r
om
10%
(
40
W
)
to
100
%
(
400
W
)
o
f
the
load.
T
he
s
im
ulation
r
e
s
ult
s
de
mons
tr
a
ted
the
s
tabili
ty,
r
e
li
a
bil
it
y,
a
nd
f
a
s
t
dyna
mi
c
r
e
s
pons
e
s
of
the
s
ys
tems
with
the
p
r
opos
e
d
c
ontr
ol
tec
hnique.
(
a
)
(
b)
F
ig
ur
e
7.
S
im
ulation
r
e
s
ult
s
(
a
)
b
us
volt
a
ge
a
nd
c
ur
r
e
nt
a
nd
(
b)
b
a
tt
e
r
y
s
tate
o
f
c
ha
r
ge
(
S
OC
)
,
c
ur
r
e
nt
,
a
nd
volt
a
ge
T
a
ble
1.
De
s
ign
r
e
s
ult
s
P
a
r
a
me
te
r
V
a
lu
e
F
ly
bac
k
#1
F
ly
bac
k
#2
F
ly
bac
k
#3
F
ly
bac
k
#4
-
5
B
uc
k
#1
B
uc
k
#2
B
uc
k
#3
B
uc
k
#4
I
nput
vol
ta
ge
,
V
in
60 V
50 V
311 V
380 V
100 V
24 V
100 V
100 V
O
ut
put
vol
ta
ge
200 V
180 V
380 V
100 V
24 V
12 V
48 V
60 V
I
nduc
ta
nc
e
666
H
479
H
9.14 mH
195.90
H
136.80
H
25.5
H
3.8 mH
4.5 mH
O
ut
put
c
a
pa
c
it
a
nc
e
480
F
600
F
150
F
1600
F
800
F
1200
F
1300
F
800
F
O
ut
put
vol
ta
ge
r
ip
pl
e
0.5 %
0.5 %
0.5 %
0.5 %
0.5 %
0.5 %
0.5 %
0.5 %
S
w
it
c
hi
ng f
r
e
que
nc
y
20 kHz
20 kHz
20 kHz
20 kHz
20 kHz
20 kHz
20 kHz
20 kHz
T
ot
a
l
out
put
pow
e
r
200 W
300 W
500 W
850 W
400 W
200 W
150 W
150 W
C
K
,
Z
of
t
he
P
I
c
ont
r
ol
le
r
8, 800
8, 800
8, 800
4, 400
50, 5000
10, 2000
4, 400
4, 400
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
De
s
ign
and
s
imulat
ion
of
DC
dis
tr
ibut
e
d
pow
e
r
s
upply
w
it
h
…
(
Uthe
n
K
amnar
n
)
467
4.
CONC
L
USI
ON
T
his
wor
k
pr
e
s
e
nts
the
de
s
ign
a
nd
s
im
ulation
o
f
dis
tr
ibut
e
d
powe
r
s
upply
in
DC
a
r
c
hit
e
c
tur
e
with
powe
r
a
nd
e
ne
r
gy
ba
lanc
e
c
ontr
ol
tec
hnique
f
or
the
pr
opos
e
d
1
kW
dis
tr
ibut
ion
s
ys
tem
that
c
o
ntains
6
volt
a
ge
bus
with
volt
a
ge
r
a
ti
ng
s
o
f
380
,
100
,
60
,
48
,
24
,
a
nd
12
V
,
c
ons
is
ted
of
5
c
onne
c
ti
on
s
tr
uc
t
ur
e
s
.
T
he
pr
opos
e
d
a
ve
r
a
ge
s
mall
-
s
ignal
a
na
ly
s
is
a
nd
c
ontr
o
l
tec
hnique
is
a
ble
to
s
im
pli
f
y
the
pa
r
a
mete
r
s
de
s
i
gn
of
the
P
I
c
ont
r
oll
e
r
a
nd
s
olve
the
ba
s
ic
c
ontr
ol
li
mi
tat
ions
of
the
DC
-
to
-
DC
c
onve
r
ter
s
.
T
he
s
ys
tem
h
a
s
be
e
n
s
im
ulate
d
by
M
AT
L
AB
/
S
im
uli
nk
in
va
r
ious
s
c
e
na
r
ios
including
no
r
mal
ope
r
a
ti
on
wi
th
f
ull
load,
o
pe
r
a
ti
on
with
s
udde
n
load
c
ha
nge
including
s
tep
down
f
r
om
100%
to
10
%
a
t
0
.
1s
a
nd
0
.
4s
.
S
tep
up
f
r
om
10%
to
100%
a
t
0
.
2s
a
nd
0
.
5s
.
A
nd
in
the
e
ve
nt
that
the
m
a
in
s
our
c
e
s
s
top
pe
d
s
upplyi
ng
po
we
r
to
the
s
ys
tem
a
t
0
.
3s
,
the
ba
tt
e
r
y
s
tar
ted
to
s
upply
the
e
ne
r
gy
to
maintai
n
the
24
V
a
nd
12
Vdc
bus
volt
a
ge
with
the
e
ne
r
g
y
ba
lanc
e
c
ontr
ol
tec
hnique
.
T
he
s
im
ulation
r
e
s
ult
s
de
mons
tr
a
te
s
table
s
ys
tem
s
tabili
ty
a
nd
dyna
mi
c
r
e
s
pons
e
.
T
he
pr
opos
e
d
tec
hnique
c
a
n
a
ls
o
r
e
duc
e
the
s
ize
o
f
t
he
output
c
a
pa
c
it
or
due
to
the
r
e
duc
ti
on
of
outpu
t
volt
a
ge
r
ippl
e
in
the
s
tea
dy
s
tate
,
r
e
s
ult
ing
in
the
incr
e
a
s
e
of
the
powe
r
de
ns
it
y
o
f
the
s
ys
tem.
T
he
r
e
s
ult
s
f
r
om
th
is
wor
k
c
a
n
be
a
ppli
e
d
to
DC
dis
tr
ibut
ion
s
ys
tems
that
a
r
e
li
ke
ly
to
be
c
ome
p
r
e
va
lent
in
the
f
utur
e
.
AC
KNOWL
E
DGE
M
E
NT
S
T
his
wor
k
wa
s
s
uppor
ted
in
pa
r
t
by
a
n
I
nter
na
ti
on
a
l
R
e
s
e
a
r
c
h
P
a
r
tner
s
hip
“
E
lec
tr
ica
l
E
nginee
r
ing
–
T
ha
i
F
r
e
nc
h
R
e
s
e
a
r
c
h
C
e
nter
(
E
E
-
T
F
R
C
)
”
un
de
r
the
p
r
ojec
t
f
r
a
mew
or
k
of
the
L
or
r
a
ine
U
niver
s
it
é
d
'E
xc
e
ll
e
nc
e
(
L
UE
)
in
c
oope
r
a
ti
on
be
twe
e
n
Un
iver
s
it
é
de
L
or
r
a
ine
a
nd
King
M
ongkut's
Univ
e
r
s
it
y
of
T
e
c
hnology
Nor
th
B
a
ngkok
a
nd
in
pa
r
t
by
the
Na
ti
ona
l
R
e
s
e
a
r
c
h
C
ounc
il
of
T
ha
il
a
nd
(
NR
C
T
)
und
e
r
S
e
nior
R
e
s
e
a
r
c
h
S
c
holar
P
r
og
r
a
m
unde
r
G
r
a
nt
No
.
N42
A640328,
a
nd
in
pa
r
t
by
Na
ti
ona
l
S
c
ienc
e
,
R
e
s
e
a
r
c
h
a
nd
I
nnova
ti
on
F
und
(
NSR
F
)
unde
r
King
M
ongkut’
s
Unive
r
s
it
y
of
T
e
c
hnology
Nor
th
B
a
ngkok
unde
r
Gr
a
nt
no.
KM
UT
NB
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FF
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65
-
20.
RE
F
E
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NC
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S
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jr
i
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r
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s
i,
“
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n
O
ve
r
vi
e
w
of
D
ir
e
c
t
C
ur
r
e
nt
D
is
tr
ib
ut
io
n
S
ys
te
m
A
r
c
hi
te
c
tu
r
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ne
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“
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I
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E
E
I
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R
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a
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c
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ppl
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at
io
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I
C
R
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l,
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ma
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e
l
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v
ol
ta
ge
le
v
e
l
c
hoi
c
e
fo
r
s
ta
ndal
one
r
e
s
id
e
nt
ia
l
D
C
nanogr
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a
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P
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e
w
of
C
ont
r
ol
S
tr
a
te
gi
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s
a
nd
S
ta
bi
li
z
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ti
on
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e
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E
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a
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M
ic
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W
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e
ne
r
a
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a
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a
s
it
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pa
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A
ve
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lu
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onve
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te
r
f
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nda
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V
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ic
a
ti
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e
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C
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te
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d
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lo
op
tr
ip
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de
c
k
buc
k
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boo
s
t
c
onve
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te
r
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O
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ut
io
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V
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r
ol
f
or
D
C
M
ic
r
ogr
id
s
U
s
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g
F
uz
z
y
C
ont
r
ol
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G
a
in
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T
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e
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S
ta
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M
odul
a
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S
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T
r
a
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I
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e
r
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F
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r
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s
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i
v
e
Sy
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r
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P
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e
c
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[
25]
U
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s
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es
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r
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s
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,
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w
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e,
b
at
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,
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d
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u
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),
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o
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l
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ear
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.
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at
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:
p
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p
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t
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t
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ft
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k
m
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n
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.
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t
h
.
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o
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a
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IE
E
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)
w
as
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o
rn
i
n
A
l
g
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ers
,
A
l
g
er
i
a,
o
n
May
23
,
1
9
6
9
.
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e
recei
v
e
d
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n
g
i
n
eer
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i
p
l
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ma
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m
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at
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Po
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ech
n
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q
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f
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l
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s
(A
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i
n
1
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.
H
e
recei
v
ed
a
Mas
t
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o
f
Sc
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fr
o
m
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n
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en
r
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Po
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n
caré
(N
a
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an
d
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Ph
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fro
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s
t
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n
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(N
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n
ce
1
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h
e
h
as
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an
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Pr
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l
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,
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d
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m
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h
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as
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a
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Pro
fe
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o
r
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t
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n
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e
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o
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(E
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n
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l
ec
t
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c
al
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n
g
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n
eer
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g
.
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s
D
i
rect
o
r
o
f
t
h
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res
earc
h
cen
t
er
G
RE
E
N
:
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ro
u
p
o
f
Res
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l
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n
g
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n
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i
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g
o
f
N
a
n
cy
.
T
h
e
ma
i
n
t
each
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n
g
ac
t
i
v
i
t
i
e
s
d
ea
l
w
i
t
h
el
ect
r
i
cal
mach
i
n
e
s
,
el
ect
r
o
mag
n
et
i
cs
,
n
u
mer
i
ca
l
s
i
m
u
l
a
t
i
o
n
an
d
mat
h
ema
t
i
c
s
.
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i
s
mai
n
res
earch
act
i
v
i
t
i
es
are
fo
cu
s
ed
o
n
el
ect
r
o
mag
n
et
i
c
mo
d
el
i
n
g
o
f
mag
n
e
t
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c
d
e
v
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s
,
el
ect
r
i
cal
mach
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n
es
a
n
d
t
ran
s
fo
rmer
s
.
H
e
ca
n
b
e
co
n
t
ac
t
ed
a
t
emai
l
:
n
o
u
red
d
i
n
e.
t
a
k
o
ra
b
et
@
u
n
i
v
-
l
o
rra
i
n
e.
fr
.
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