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1.
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NT
RO
D
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N
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h
e
cu
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ax
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lo
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s
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ased
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th
is
m
an
n
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s
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ar
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at
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th
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ea
s
o
n
,
p
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s
f
o
r
m
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s
ar
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th
e
m
o
s
t
s
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itab
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ch
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ice.
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h
er
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ar
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m
an
y
ty
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es
o
f
tr
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s
f
o
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m
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s
an
d
tr
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s
f
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s
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av
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m
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y
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s
es.
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u
t
th
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asic
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r
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tr
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s
f
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en
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v
o
ltag
e
at
th
e
en
d
o
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th
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co
n
s
u
m
er
[
1
]
,
[
2
]
.
T
h
e
m
is
m
atch
b
etwe
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t
r
an
s
f
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s
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iately
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s
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lit
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to
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ical
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ts
[
1
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-
[
1
1
]
.
T
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m
o
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el
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th
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tr
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s
f
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m
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is
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im
p
o
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tu
d
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ab
n
o
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m
alities
p
h
en
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m
e
n
a
as
well
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s
th
e
d
esig
n
p
r
o
ce
s
s
.
T
h
e
m
o
r
e
ac
cu
r
ate
th
e
m
o
d
e
l,
th
e
m
o
r
e
r
eliab
le
an
d
ac
cu
r
ate
th
e
r
esu
lts
[
1
2
]
.
Var
io
u
s
r
esear
ch
er
s
u
s
e
o
p
ti
m
izatio
n
ap
p
r
o
ac
h
es
to
s
o
lv
e
m
an
y
p
r
o
b
lem
s
b
y
esti
m
atin
g
p
ar
am
eter
s
[
1
3
]
-
[
1
6
]
.
Ma
n
y
tech
n
i
q
u
es
ar
e
u
s
ed
to
im
p
r
o
v
e
th
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esti
m
atio
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o
f
th
e
tr
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s
f
o
r
m
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r
'
s
p
ar
am
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s
b
y
em
p
lo
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g
v
a
r
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u
s
o
p
tim
izatio
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s
tr
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f
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r
esti
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atin
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e
p
ar
a
m
eter
s
f
r
o
m
s
ea
r
ch
s
p
ac
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co
n
s
tr
ain
ts
,
an
d
o
b
jectiv
e
f
u
n
ctio
n
s
[
1
7
]
-
[
1
9
]
.
T
h
e
esti
m
ated
co
y
o
te
o
p
tim
izatio
n
alg
o
r
ith
m
(
C
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Evaluation Warning : The document was created with Spire.PDF for Python.
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J
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&
C
o
m
p
Sci
,
Vo
l.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
3
9
-
6
4
7
640
p
ar
am
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s
lead
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a
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s
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th
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ex
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ith
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[
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r
ee
w
in
d
in
g
T
r
a
n
s
f
o
r
m
er
p
r
o
tectiv
e
ci
r
cu
its
[
2
0
]
.
T
h
e
p
ap
er
d
escr
ib
es
th
e
m
eth
o
d
f
o
r
d
eter
m
in
in
g
th
e
p
ar
am
eter
s
o
f
th
e
n
o
n
-
lin
e
ar
cu
r
r
en
t
-
f
l
o
w
r
elatio
n
wh
ich
ch
ar
ac
ter
izes
th
e
s
atu
r
atio
n
.
T
h
ey
s
u
it v
er
y
well
with
th
e
an
aly
tical
r
o
le
f
o
r
m
o
d
if
y
in
g
th
e
ex
p
e
r
im
en
tal
m
ea
s
u
r
em
en
ts
[
2
1
]
.
T
o
o
p
tim
ize
th
e
tr
an
s
f
o
r
m
er
p
ar
a
m
eter
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
u
s
e
m
an
ta
r
ay
o
p
tim
izatio
n
an
d
ch
ao
tic
m
an
ta
r
ay
.
I
n
c
o
n
tr
ast
with
th
e
ap
p
r
o
ac
h
s
u
g
g
ested
in
th
e
p
r
e
v
io
u
s
ar
ticle,
th
e
p
r
o
p
o
s
ed
o
b
jectiv
e
f
u
n
ctio
n
d
o
es
n
o
t
r
eq
u
ir
e
an
y
lo
s
s
in
th
e
esti
m
atio
n
p
r
o
ce
s
s
.
T
h
e
ap
p
r
o
x
i
m
ate
p
ar
am
eter
s
o
b
tain
e
d
th
r
o
u
g
h
th
e
p
r
o
p
o
s
e
d
o
p
tim
izatio
n
an
d
o
b
jectiv
e
f
u
n
ct
io
n
ar
e
co
m
p
ar
ed
with
th
e
v
alu
es
o
b
tain
ed
u
s
in
g
th
e
cl
ass
ical
I
n
s
ti
tu
te
o
f
E
lectr
ical
an
d
E
lectr
o
n
ics
E
n
g
in
ee
r
s
(
IEEE
)
test
p
r
o
to
c
o
l
an
d
th
e
v
alu
es
d
er
iv
ed
u
s
in
g
th
e
liter
atu
r
e
p
r
ev
io
u
s
ly
i
n
tr
o
d
u
ce
d
.
T
h
e
m
ea
s
u
r
em
en
ts
o
f
t
h
e
ex
p
e
r
i
m
en
tally
d
ef
in
e
d
tr
an
s
f
o
r
m
er
p
ar
am
eter
s
s
h
all
b
e
p
er
f
o
r
m
ed
to
d
em
o
n
s
tr
ate
th
e
ef
f
ec
ts
o
f
th
e
p
r
o
p
o
s
ed
p
ar
am
eter
esti
m
atio
n
alg
o
r
ith
m
an
d
th
e
co
r
r
elatio
n
s
h
all
b
e
s
tu
d
ied
[
2
2
]
.
T
h
e
p
r
o
p
o
s
ed
tu
r
b
u
len
t
f
l
o
w
o
f
wate
r
-
b
ased
o
p
tim
izatio
n
(
T
FW
O
)
alg
o
r
ith
m
u
s
ed
to
esti
m
ate
th
e
tr
an
s
f
o
r
m
er
p
ar
a
m
eter
s
o
f
th
e
p
o
wer
tr
an
s
f
o
r
m
er
f
r
o
m
its
n
am
e
p
late
d
ata
a
n
d
th
e
ac
cu
r
ac
y
an
d
r
eliab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
h
ig
h
er
th
an
th
e
o
th
er
alg
o
r
ith
m
s
.
T
h
e
f
o
llo
win
g
is
h
o
w
th
is
p
a
p
er
is
s
tr
u
ctu
r
e
d
;
s
ec
tio
n
2
ex
p
lain
s
th
e
an
al
y
s
is
o
f
o
b
jectiv
e
f
u
n
ctio
n
th
at
s
o
lv
es
p
r
o
b
lem
f
o
r
m
u
lati
o
n
.
Sectio
n
3
co
n
tain
s
th
e
d
et
ails
o
f
th
e
p
r
o
p
o
s
ed
T
FW
O
alg
o
r
ith
m
s
.
Sectio
n
4
an
aly
s
es
th
e
r
esu
lts
o
f
th
e
ca
s
e
s
tu
d
y
an
d
th
e
co
n
clu
s
io
n
is
in
s
ec
tio
n
5
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
AND
O
B
J
E
C
T
I
V
E
F
UN
CT
I
O
N
2
.
1
.
T
ra
ns
f
o
rm
er
mo
del
T
h
e
eq
u
iv
alen
t
cir
c
u
it
r
ef
er
r
e
d
to
th
e
p
r
im
ar
y
s
id
e
o
f
a
s
in
g
le
-
p
h
ase
two
-
win
d
in
g
tr
an
s
f
o
r
m
er
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
c
o
n
v
en
tio
n
al
m
eth
o
d
o
f
esti
m
atio
n
o
f
tr
an
s
f
o
r
m
er
p
ar
a
m
eter
s
r
e
q
u
ir
es
u
s
u
ally
o
p
e
n
cir
cu
it
an
d
s
h
o
r
t
cir
c
u
it
test
ex
p
e
r
im
en
tal
d
ata.
I
n
th
is
p
ap
er
,
th
e
ch
allen
g
e
is
to
e
s
tim
ate
tr
an
s
f
o
r
m
er
p
ar
am
eter
s
b
y
o
n
ly
u
s
in
g
th
e
n
am
ep
late
d
ata
with
o
u
t
p
er
f
o
r
m
in
g
test
s
.
T
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
is
b
ased
o
n
a
r
ed
u
ctio
n
in
th
e
s
q
u
a
r
e
er
r
o
r
o
f
th
e
n
o
m
i
n
al
tr
an
s
f
o
r
m
e
r
n
am
ep
late
p
ar
am
eter
s
an
d
th
e
co
r
r
esp
o
n
d
in
g
p
ar
am
eter
s
ca
lcu
lated
in
Fig
u
r
e
1
.
Use
th
e
cir
cu
it
laws
o
f
Kir
ch
h
o
f
f
b
y
s
o
lv
in
g
s
e
v
er
al
m
ath
em
atica
l
eq
u
atio
n
s
[
23
]
.
T
h
e
to
tal
im
p
e
d
an
ce
o
f
tr
an
s
f
o
r
m
er
is
as f
o
ll
o
ws:
=
1
+
×
(
́
2
+
́
)
+
́
2
+
́
(
1
)
w
h
er
e
:
1
=
1
+
1
,
́
2
=
́
2
+
́
2
,
an
d
=
×
+
f
r
o
m
Fig
u
r
e
1
,
t
h
e
p
r
im
a
r
y
cu
r
r
en
t is:
1
=
1
(
2
)
a
n
d
th
e
s
ec
o
n
d
ar
y
cu
r
r
e
n
t is
:
́
2
=
+
́
2
+
́
×
1
(
3
)
t
h
e
s
ec
o
n
d
ar
y
v
o
ltag
e
ca
lcu
lated
as:
́
2
=
́
2
×
́
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
E
s
tima
tio
n
o
f th
e
tr
a
n
s
fo
r
mer p
a
r
a
mete
r
s
fr
o
m
n
a
mep
la
te
d
a
ta
u
s
in
g
tu
r
b
u
len
t
…
(
A
mir
Ya
s
s
in
Ha
s
s
a
n
)
641
W
h
er
e:
1
=
́
2
=
1
=
́
2
=
=
=
1
=
́
2
=
1
=
ℎ
́
2
=
=
−
́
=
Fig
u
r
e
1
.
R
ef
er
r
e
d
to
th
e
p
r
im
ar
y
s
id
e
tr
an
s
f
o
r
m
er
eq
u
iv
alen
t c
ir
cu
it [
1
4
]
2
.
2
.
T
he
o
bje
ct
iv
e
f
un
ct
io
n o
f
estim
a
t
io
n
T
h
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
ar
e
u
s
ed
i
n
ex
t
r
ac
tin
g
t
h
e
p
a
r
am
eter
s
o
f
th
e
d
if
f
er
e
n
t
r
ati
n
g
s
o
f
th
e
tr
an
s
f
o
r
m
er
(
4
k
VA,
1
0
k
VA,
an
d
1
5
k
VA)
,
th
ese
tech
n
iq
u
es
n
ee
d
an
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
p
er
f
o
r
m
in
g
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
Min
im
i
zin
g
th
e
s
u
m
o
f
s
q
u
ar
e
er
r
o
r
(
SS
E
)
is
th
e
o
b
jectiv
e
f
u
n
ctio
n
o
f
th
e
o
p
tim
izer
tech
n
iq
u
e.
T
h
e
SS
E
f
u
n
ctio
n
in
clu
d
es
th
e
s
u
m
m
atio
n
o
f
th
e
s
q
u
ar
e
er
r
o
r
f
o
r
th
e
p
r
im
ar
y
cu
r
r
en
t
an
d
s
ec
o
n
d
ar
y
cu
r
r
en
t
a
n
d
v
o
ltag
e
r
ef
er
r
in
g
to
th
e
p
r
im
ar
y
.
T
h
e
m
ath
em
atica
l
f
o
r
m
u
la
to
co
m
p
u
te
SS
E
is
as
f
o
l
lo
w:
=
(
1
.
−
1
.
)
2
+
(
2
.
′
−
2
.
′
)
2
+
(
2
.
′
−
2
.
′
)
2
(
5
)
w
h
er
e
th
e
f
ir
s
t
ter
m
i
n
th
e
SS
E
is
th
e
d
if
f
er
e
n
ce
b
etwe
en
t
h
e
p
r
im
ar
y
ac
tu
al
an
d
esti
m
ated
cu
r
r
e
n
t,
th
e
s
ec
o
n
d
ter
m
is
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
ac
tu
al
an
d
esti
m
a
ted
s
ec
o
n
d
ar
y
c
u
r
r
en
t,
a
n
d
th
e
th
i
r
d
te
r
m
is
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
s
ec
o
n
d
ar
y
ac
t
u
a
l
an
d
esti
m
ated
v
o
ltag
e.
T
h
e
o
p
tim
izatio
n
alg
o
r
ith
m
n
ee
d
s
b
o
u
n
d
a
r
ies
lim
it;
th
ese
b
o
u
n
d
ar
ies ar
e
ex
p
lain
e
d
in
T
ab
le
s
1
-
3
[
2
2
]
,
[
2
3
]
.
T
ab
le
1
.
T
h
e
ex
tr
ac
ted
p
ar
am
e
ter
s
b
o
u
n
d
a
r
ies f
o
r
4
k
VA
P
a
r
a
me
t
e
r
s
Lo
w
e
r
b
o
u
n
d
U
p
p
e
r
b
o
u
n
d
0
.
2
0
.
6
0
.
1
0
.
3
′
0
.
2
0
.
4
5
′
1
.
5
2
.
5
1
4
0
0
1
5
0
0
7
0
0
7
5
0
T
ab
le
2
.
T
h
e
ex
tr
ac
ted
p
ar
am
e
ter
s
b
o
u
n
d
a
r
ies f
o
r
1
0
k
VA
P
a
r
a
me
t
e
r
s
Lo
w
e
r
b
o
u
n
d
U
p
p
e
r
b
o
u
n
d
0
.
3
1
0
.
2
1
′
0
.
1
1
′
0
.
2
1
5
0
0
1
0
0
0
2
0
0
5
0
0
T
ab
le
3
.
T
h
e
ex
tr
ac
ted
p
ar
am
e
ter
s
b
o
u
n
d
a
r
ies f
o
r
1
5
k
VA
P
a
r
a
me
t
e
r
s
Lo
w
e
r
b
o
u
n
d
U
p
p
e
r
b
o
u
n
d
1
.
2
2
.
5
1
.
3
3
.
5
′
1
.
3
2
.
2
′
1
.
8
2
.
3
99
,
000
12
,
0
0
0
0
9
,
0
0
0
9
,
2
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
3
9
-
6
4
7
642
3.
T
F
WO
ANA
L
YS
I
S
A
cir
cu
lar
s
h
ap
e
is
f
o
r
m
ed
f
r
o
m
th
e
tu
r
b
u
len
t
f
lo
w
o
f
wate
r
;
th
is
cir
cu
lar
f
o
r
m
is
ca
lled
a
wh
ir
lp
o
o
l.
g
r
av
ity
f
o
r
ce
is
af
f
ec
ted
o
n
th
i
s
wh
ir
lp
o
o
l
s
o
th
at
wate
r
f
o
r
m
s
a
s
p
ir
al
p
ath
[
2
4
]
.
T
h
e
r
an
d
o
m
n
atu
r
e
b
eh
a
v
io
r
in
o
ce
an
s
,
r
iv
er
s
,
a
n
d
s
ea
s
is
th
e
f
ea
tu
r
e
o
f
th
e
wh
ir
lp
o
o
l
p
h
en
o
m
en
o
n
.
T
h
e
s
u
c
k
h
o
le
th
at
s
u
ck
s
th
e
o
b
jects
in
th
e
ce
n
ter
o
f
th
e
wh
ir
l
p
o
o
l.
At
f
ir
s
t,
th
e
in
itial
p
o
p
u
latio
n
(
0
,
co
m
p
r
is
in
g
m
em
b
er
s
)
o
f
th
e
alg
o
r
ith
m
is
d
iv
id
ed
eq
u
ally
b
etwe
en
ℎ
g
r
o
u
p
s
o
r
wh
ir
lp
o
o
l
s
ets,
an
d
th
en
th
e
s
tr
o
n
g
est
m
em
b
er
o
f
ea
c
h
wh
ir
lp
o
o
l
s
et
(
T
h
e
b
etter
o
b
jectiv
e
v
al
u
e
m
e
m
b
er
(
)
is
s
ee
n
as a
n
o
b
ject
p
u
ll
wh
ir
lp
o
o
l (
,
in
clu
d
i
n
g
-
ℎ
o
b
ject
s
)
)
.
E
v
e
r
y
w
h
ir
lp
o
o
l
(
W
h
)
b
eh
av
e
s
as
a
s
u
ck
in
g
well,
an
d
ten
d
s
to
u
n
if
y
th
e
lo
ca
tio
n
s
o
f
o
b
je
cts
in
s
id
e
its
s
et
(
X)
with
its
ce
n
tr
al
p
o
s
itio
n
b
y
ap
p
l
y
in
g
a
ce
n
tr
ip
etal
f
o
r
ce
o
n
th
e
m
,
an
d
p
u
s
h
th
em
in
to
its
well.
T
h
u
s
,
th
e
jth
wh
ir
lp
o
o
l
a
n
d
th
e
lo
ca
l
p
o
s
itio
n
o
n
ℎ
co
m
b
in
e
th
e
ith
o
b
ject
p
o
s
itio
n
(
)
with
its
elf
(
=
ℎ
)
.
Ho
wev
er
,
o
th
er
w
h
ir
lp
o
o
ls
p
r
o
d
u
ce
s
o
m
e
d
e
v
iatio
n
s
(
∆
)
b
ec
a
u
s
e
o
f
t
h
e
d
is
tan
ce
am
o
n
g
th
e
m
(
ℎ
−
ℎ
)
an
d
its
o
b
jectiv
e
v
alu
es
(
(
)
)
as
well.
Acc
o
r
d
in
g
ly
,
th
e
n
ew
p
o
s
itio
n
o
f
th
e
ℎ
o
b
ject
b
ec
o
m
es
=
ℎ
−
∆
.
an
d
th
e
o
b
jects
(
)
tr
av
el
t
h
r
o
u
g
h
th
eir
wh
ir
lp
o
o
l'
s
co
r
e
an
d
to
war
d
it
with
th
eir
u
n
iq
u
e
an
g
l
e
(
)
.
Hen
ce
,
t
h
is
an
g
le
at
ea
ch
it
er
atio
n
is
ch
an
g
i
n
g
ac
co
r
d
in
g
to
(
6
)
:
=
+
1
∗
2
∗
(
6
)
t
o
m
o
d
el
an
d
ca
lcu
late
t
h
e
f
a
r
th
est
an
d
n
ea
r
est
wh
ir
lp
o
o
ls
(
∆
),
in
(
7
)
d
e
p
icts
th
e
wh
ir
lp
o
o
l
s
with
th
e
least
weig
h
ed
d
is
tan
ce
f
r
o
m
all
o
b
j
ec
ts
,
an
d
th
en
∆
is
ca
lcu
lated
u
s
in
g
b
o
th
in
(
8
)
.
In
(
9
)
is
u
s
ed
to
u
p
d
ate
t
h
e
p
o
s
itio
n
o
f
t
h
e
p
ar
ticle.
∆
=
(
ℎ
)
∗
|
ℎ
−
(
)
|
0
.
5
(
7
)
∆
=
c
os
(
)
∗
(
1
.
)
∗
(
ℎ
−
)
−
s
in
(
)
∗
(
1
.
)
∗
(
ℎ
−
)
)
∗
(
1
+
|
c
os
(
)
−
s
in
(
)
|
)
(
8
)
=
ℎ
−
∆
(
9
)
wh
er
e
ℎ
an
d
ℎ
m
an
if
est
th
e
w
h
ir
lp
o
o
ls
with
m
in
im
u
m
an
d
m
ax
im
u
m
o
f
∆
,
r
esp
ec
tiv
ely
,
wh
ile
ch
ar
ac
ter
izes
th
e
ℎ
o
b
ject’
s
an
g
le.
C
en
tr
if
u
g
al
f
o
r
ce
(
)
s
o
m
etim
es
o
v
er
co
m
es
th
e
ce
n
tr
ip
etal
o
f
th
e
wh
ir
lp
o
o
l,
a
n
d
r
an
d
o
m
ly
tr
a
n
s
f
er
s
th
e
o
b
ject
t
o
a
n
ew
l
o
ca
tio
n
.
T
h
e
ce
n
tr
if
u
g
al
f
o
r
ce
is
m
o
d
eled
as
illu
s
tr
ated
in
(
1
0
)
,
wh
ic
h
r
an
d
o
m
ly
o
c
cu
r
s
in
o
n
e
d
im
en
s
io
n
o
f
t
h
e
d
ec
is
io
n
v
ar
iab
les.
T
h
e
ce
n
tr
if
u
g
al
f
o
r
ce
is
d
eter
m
in
ed
b
ased
o
n
th
e
an
g
l
e
b
etwe
en
th
e
wh
ir
lp
o
o
l
an
d
th
e
o
b
ject,
as
s
h
o
wn
in
(
1
0
)
,
an
d
if
th
is
f
o
r
ce
is
g
r
ea
ter
th
an
a
r
an
d
o
m
v
alu
e
in
th
e
r
an
g
e
[
0
,
1
]
,
th
e
ce
n
tr
i
f
u
g
al
ac
tio
n
is
p
er
f
o
r
m
ed
f
o
r
r
an
d
o
m
ly
s
elec
ted
d
im
en
s
io
n
,
as sh
o
wn
in
(
1
1
)
.
T
h
is
p
h
en
o
m
en
o
n
ca
n
b
e
ex
p
r
ess
ed
m
ath
em
atica
lly
as f
o
llo
ws:
=
(
(
c
os
(
)
)
2
∗
(
s
in
(
)
)
2
)
2
(
1
0
)
.
=
+
∗
(
−
)
(
1
1
)
t
h
e
wh
ir
lp
o
o
ls
co
llid
e
an
d
d
is
p
lace
o
n
e
an
o
th
e
r
.
T
h
is
p
h
en
o
m
en
o
n
ca
n
b
e
m
o
d
eled
as th
e
s
am
e
as th
e
im
p
ac
t
s
o
f
wh
ir
lp
o
o
ls
o
n
th
e
o
b
jects,
wh
er
e
ev
er
y
w
h
ir
lp
o
o
l
ten
d
s
to
p
u
ll
o
th
e
r
wh
ir
lp
o
o
ls
an
d
i
m
p
ly
th
e
ce
n
tr
i
p
etal
f
o
r
ce
o
n
th
em
.
As s
h
o
wn
i
n
(
12
)
,
th
e
clo
s
est wh
ir
lp
o
o
l c
an
b
e
m
ath
em
atica
lly
r
ep
r
esen
ted
u
s
in
g
th
e
m
in
im
u
m
s
u
m
an
d
its
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
en
,
t
h
e
wh
ir
lp
o
o
l’
s
p
o
s
itio
n
ca
n
b
e
u
p
d
ated
ac
co
r
d
in
g
t
o
(
1
3
)
a
n
d
(
1
4
)
:
∆
=
(
ℎ
)
∗
|
ℎ
−
(
ℎ
)
|
(
1
2
)
∆
ℎ
=
(
1
.
)
∗
|
c
os
(
)
+
s
in
(
)
|
∗
(
ℎ
−
ℎ
)
(
1
3
)
ℎ
=
ℎ
−
∆
ℎ
(
1
4
)
w
h
er
e
r
ep
r
esen
ts
th
e
ℎ
wh
ir
lp
o
o
l
h
o
les
an
g
le
v
alu
e.
Fin
ally
,
th
e
s
tr
o
n
g
est
m
em
b
er
o
f
t
h
e
n
ew
m
em
b
er
s
o
f
th
e
wh
i
r
lp
o
o
l'
s
s
et
is
ch
o
s
en
as
th
e
n
ew
w
h
ir
lp
o
o
l
f
o
r
th
e
n
ex
t
iter
atio
n
wh
en
th
e
v
a
lu
e
o
f
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
less
th
an
th
e
p
r
ec
e
d
in
g
wh
ir
lp
o
o
l.
T
h
e
T
FW
O
f
lo
wch
ar
t is d
ep
icted
in
Fig
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
E
s
tima
tio
n
o
f th
e
tr
a
n
s
fo
r
mer p
a
r
a
mete
r
s
fr
o
m
n
a
mep
la
te
d
a
ta
u
s
in
g
tu
r
b
u
len
t
…
(
A
mir
Ya
s
s
in
Ha
s
s
a
n
)
643
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
T
FW
O
alg
o
r
ith
m
4.
ANALY
SI
S O
F
R
E
SU
L
T
S
T
h
is
s
ec
tio
n
p
r
esen
ts
an
an
al
y
s
is
o
f
th
e
p
ar
am
eter
s
ex
t
r
ac
ted
u
s
in
g
th
e
p
r
o
p
o
s
ed
T
FW
O
alg
o
r
ith
m
f
o
r
v
a
r
io
u
s
tr
an
s
f
o
r
m
er
s
r
ati
n
g
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
i
s
ap
p
lied
in
th
is
p
a
p
er
o
n
t
h
e
m
ain
p
r
o
p
o
s
ed
alg
o
r
ith
m
T
FW
O
an
d
it
'
s
ap
p
lied
also
o
n
th
e
C
u
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
(
C
SA)
[
2
5
]
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
T
FW
O
i
s
v
alid
ated
b
y
co
m
p
a
r
is
o
n
o
f
its
r
esu
lts
with
th
is
C
SA
an
d
o
th
er
alg
o
r
ith
m
s
f
r
o
m
th
e
p
r
ev
io
u
s
wo
r
k
s
u
ch
as
g
en
etic
alg
o
r
ith
m
(
G
A)
,
p
r
ac
ti
ca
l
s
war
m
o
p
tim
izat
io
n
(
PS
O)
[
1
8
]
,
im
p
e
r
ialis
t
co
m
p
etitiv
e
alg
o
r
it
h
m
(
I
C
A)
,
an
d
g
r
av
itatio
n
al
s
ea
r
c
h
alg
o
r
ith
m
(
GSA)
[
1
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
3
9
-
6
4
7
644
4
.
1
.
Resul
t
s
f
o
r
t
r
a
ns
f
o
rm
er
t
y
pes
I
n
th
is
s
u
b
s
ec
tio
n
,
th
e
d
etails
o
f
e
x
tr
ac
ted
p
ar
am
eter
s
an
d
th
e
b
est
o
b
jectiv
e
f
u
n
ctio
n
b
y
T
FW
O
i
s
p
er
f
o
r
m
ed
.
T
h
e
p
r
o
p
o
s
ed
T
F
W
O
alg
o
r
ith
m
is
co
m
p
ar
ed
with
th
e
cu
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
(
C
SA)
f
o
r
3
0
in
d
ep
en
d
en
t
r
u
n
s
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
test
is
ap
p
lied
to
tr
an
s
f
o
r
m
e
r
s
r
ated
at
4
k
VA,
1
0
k
VA,
an
d
15
k
VA,
an
d
th
e
r
esu
lts
ar
e
co
m
p
ar
ed
to
ex
is
tin
g
ap
p
r
o
ac
h
es
.
4.
1
.
1.
T
he
t
ra
ns
f
o
rm
er
o
f
ra
t
ing
4
k
VA
Par
am
eter
s
wer
e
ex
tr
ac
ted
f
r
o
m
a
s
in
g
le
-
p
h
ase
tr
an
s
f
o
r
m
er
b
ased
o
n
th
e
a
n
aly
s
is
in
s
ec
tio
n
two
an
d
th
r
ee
.
T
a
b
le
4
ex
p
lain
s
th
e
v
al
u
e
o
f
th
e
p
a
r
am
eter
s
f
o
r
th
e
4
k
VA
tr
an
s
f
o
r
m
er
.
T
ab
le
5
ex
p
lain
s
th
e
cu
r
r
en
t
1
an
d
′
2
an
d
t
h
e
v
o
ltag
e
V
2'
f
o
r
th
i
s
tr
an
s
f
o
r
m
er
b
ased
o
n
th
e
p
a
r
am
eter
s
ex
tr
ac
ted
f
r
o
m
ea
c
h
alg
o
r
ith
m
at
th
e
b
est
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
e
v
alu
e
o
f
th
e
b
est
SS
E
f
o
r
ea
ch
alg
o
r
ith
m
is
illu
s
tr
ated
in
T
a
b
le
6
.
T
h
e
s
tatis
tical
r
esu
lts
o
f
3
0
r
u
n
f
o
r
T
FW
O
an
d
C
SA
alg
o
r
ith
m
s
ar
e
p
r
esen
ted
in
T
ab
le
7
.
Fro
m
th
e
r
esu
lts
in
T
ab
les
4
-
6
,
it
ca
n
b
e
o
b
s
er
v
e
d
th
at
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
T
FW
O
is
th
e
b
est
alg
o
r
ith
m
in
e
x
tr
ac
t
tr
a
n
s
f
o
r
m
er
p
ar
a
m
eter
s
an
d
th
e
C
SA
alg
o
r
ith
m
is
th
e
s
ec
o
n
d
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.
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2
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I
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G
RAP
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AUTH
O
RS
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ir
Ya
ss
in
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ss
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re
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h
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S
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wit
h
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ra
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e
with
h
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ri
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v
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g
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t,
in
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n
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h
e
jo
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e
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th
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e
c
tro
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ics
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se
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rc
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stit
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te
(E
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s
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rtme
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t
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o
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fr
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t
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t
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h
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tri
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s
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n
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n
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rc
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wa
s h
o
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d
a
s
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t
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a
t
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fo
r
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e
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rs
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6
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a
n
d
2
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sp
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ti
v
e
ly
a
lso
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t
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g
y
p
ti
a
n
En
g
in
e
e
rs
S
y
n
d
ica
te.
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m
a
jo
r
in
tere
sts
a
re
:
e
lec
tri
c
a
l
d
riv
e
s
c
o
n
tr
o
l,
m
o
d
e
li
n
g
a
n
d
sim
u
latio
n
o
f
e
lec
tri
c
a
l
sy
ste
m
s,
a
rti
ficia
l
in
te
ll
ig
e
n
c
e
,
t
h
e
rm
a
l
m
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ll
in
g
a
n
d
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lec
tri
c
a
l/
h
y
b
ri
d
v
e
h
icle
s
m
o
d
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li
n
g
,
sim
u
lati
o
n
,
a
n
d
c
o
n
tro
l
.
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c
a
n
b
e
c
o
n
tac
ted
a
t
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m
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:
a
m
ir@eri.
sc
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e
g
.
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k
h
t
a
r
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re
c
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S
c
.
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e
x
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n
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with
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r
d
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re
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tri
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g
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o
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c
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ty
o
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g
,
F
a
y
o
u
m
Un
i
v
e
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E
g
y
p
t,
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n
Ju
n
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0
0
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d
o
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tain
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S
c
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fr
o
m
fa
c
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lt
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g
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g
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a
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m
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iv
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y
p
t
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p
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g
y
p
t,
in
2
0
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.
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is
m
a
jo
r
o
f
in
tere
sts
is:
m
o
d
e
li
n
g
a
n
d
sim
u
latio
n
o
f
e
lec
tri
c
a
l
sy
ste
m
,
e
lec
tri
c
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l
d
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e
s
c
o
n
tro
l
a
n
d
o
p
ti
m
iza
ti
o
n
o
f
re
n
e
wa
b
le
e
n
e
rg
y
sy
ste
m
.
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c
a
n
b
e
c
o
n
tac
ted
a
t
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m
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:
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si0
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m
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g
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d
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re
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s
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it
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l
p
r
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tec
ti
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n
fro
m
Ca
ir
o
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n
iv
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rsit
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Ca
iro
,
E
g
y
p
t,
in
2
0
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n
d
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0
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wo
rk
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d
f
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t
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rs
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r
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re
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