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]
an
d
[
1
1
]
is
:
(
5
)
3.
SI
M
UL
AT
I
O
N
A
ND
RE
SU
L
T
AN
AL
Y
SI
S
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
w
a
s
i
m
p
le
m
e
n
ted
i
n
th
e
s
o
f
t
w
ar
e
p
ac
k
ag
e
Ma
t
lab
/ Si
m
u
li
n
k
,
an
d
test
ed
f
o
r
a
tr
an
s
f
o
r
m
er
w
h
o
s
e
p
ar
a
m
eter
s
ar
e
s
h
o
w
n
i
n
T
ab
le
1
.
T
ab
le
1
.
No
m
in
a
l
D
ata
an
d
St
an
d
ar
d
P
ar
am
eter
s
o
f
t
h
e
T
h
r
ee
-
p
h
a
s
e
T
r
an
s
f
o
r
m
e
r
-
4
0
0
k
V
Su
b
s
tat
io
n
P
ej
a
3
–
Ko
s
o
v
o
D
a
t
a
V
a
l
u
e
R
a
t
e
d
p
o
w
e
r
p
r
i
mary
/
se
c
o
n
d
a
r
y
3
0
0
/
3
0
0
M
V
A
P
r
i
may
v
o
l
t
a
g
e
4
0
0
k
V
S
e
c
o
n
d
a
r
y
v
o
l
t
a
g
e
1
1
5
k
V
F
r
e
q
u
e
n
c
y
5
0
H
z
P
a
r
a
me
t
e
r
s o
f
p
r
i
mary
w
i
n
d
i
n
g
V
1
=
4
0
0
k
V
;
R
1
=
0
.
0
0
1
8
p
u
;
L
1
=
0
.
0
7
6
p
u
P
a
r
a
me
t
e
r
s o
f
se
c
o
n
d
a
r
y
w
i
n
d
i
n
g
V
2
=
1
1
0
k
V
;
R
2
=
0
.
0
0
1
8
p
u
;
L
2
=
0
.
0
7
6
p
u
S
h
o
r
t
c
i
r
c
u
i
t
v
o
l
t
a
g
e
1
2
.
5
%
A
co
m
p
u
ter
m
o
d
el
w
a
s
d
ev
el
o
p
ed
in
MA
T
L
A
B
/
Si
m
u
li
n
k
p
r
o
g
r
am
.
Fo
r
th
e
tr
an
s
f
o
r
m
er
m
o
d
el
is
u
s
ed
ele
m
e
n
t
n
a
m
ed
"
Satu
r
a
b
le
T
r
an
s
f
o
r
m
er
,
"
th
e
tr
an
s
f
o
r
m
er
w
it
h
t
w
o
w
i
n
d
in
g
s
.
T
h
e
m
o
d
el
ta
k
es
i
n
to
ac
co
u
n
t
t
h
e
w
i
n
d
i
n
g
r
esis
tan
ce
(
R
1
R
2
R
3
)
,
t
h
e
lea
k
ag
e
in
d
u
cta
n
ce
s
(
L
1
L
2
L
3
)
,
as
w
el
l
as
th
e
co
r
e
m
ag
n
etiza
tio
n
c
h
ar
ac
ter
is
tic.
T
h
e
tr
an
s
f
o
r
m
er
is
co
n
n
ec
ted
to
th
e
n
et
w
o
r
k
t
h
r
o
u
g
h
th
e
s
w
itc
h
t
h
at
co
n
n
ec
t
s
th
e
tr
a
n
s
f
o
r
m
er
at
a
g
iv
e
n
ti
m
e
m
o
m
e
m
t
an
d
t
h
u
s
s
i
m
u
l
ates
tr
an
s
ie
n
ts
o
f
al
l
t
h
r
ee
p
h
ase
s
.
Osci
llo
g
r
a
m
s
p
r
esen
t v
o
lta
g
e
,
cu
r
r
en
t a
n
d
th
e
f
lu
x
o
f
t
h
e
p
r
i
m
ar
y
w
in
d
i
n
g
.
Flu
x
-
cu
r
r
en
t
C
h
ar
ac
ter
is
tic
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
T
h
e
lay
o
u
t
o
f
th
e
M
A
T
L
A
B
/
Si
m
u
li
n
k
m
o
d
eled
tr
an
s
f
o
r
m
er
co
n
n
ec
ted
to
th
e
n
et
w
o
r
k
i
s
g
iv
e
n
in
Fi
g
u
r
e
2
.
Si
m
u
latio
n
s
w
er
e
p
ef
r
o
m
ed
f
o
r
s
ev
er
al
ca
s
es
o
f
p
o
w
er
tr
an
s
f
o
r
m
er
en
er
g
izatio
n
.
T
i
m
e
m
o
m
en
e
ts
o
f
en
er
g
izat
io
n
a
n
d
r
e
m
a
n
en
t
m
a
g
n
et
ic
f
lu
x
v
al
u
es
w
er
e
ta
k
en
i
n
to
ac
co
u
n
t.
T
h
e
s
i
m
u
la
tio
n
s
w
er
e
p
er
f
o
r
m
ed
f
o
r
th
r
ee
d
if
f
er
en
t
ti
m
e
m
o
m
e
n
ts
o
f
en
er
g
izatio
n
:
t
1
=0
.
0
2
s
;
t
2
=
0
.
0
1
3
4
s
;
t
3
=0
.
0
2
6
6
s
in
all
t
h
r
ee
p
h
ases
.
T
h
e
t
i
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
Tr
a
n
s
ien
t P
h
en
o
men
a
d
u
r
in
g
t
h
e
Th
r
ee
-
P
h
a
s
e
3
0
0
MVA
Tr
a
n
s
fo
r
mer E
n
erg
iz
a
tio
n
o
n
…
(
S
r
ete
N
iko
lo
vski
)
2501
m
o
m
e
n
t
t
1
co
r
r
esp
o
n
d
s
to
p
h
a
s
e
L
1
,
th
e
ti
m
e
m
o
m
e
n
t
t
2
c
o
r
r
esp
o
n
d
s
to
p
h
ase
L
2
an
d
t
h
e
ti
m
e
m
o
m
en
t
t
3
co
r
r
esp
o
n
d
s
to
p
h
ase
L
3
o
f
th
e
r
ea
l
th
r
ee
p
h
ase
tr
an
s
f
o
r
m
er
.
I
n
th
e
r
ea
l
th
r
ee
-
p
h
a
s
e
tr
an
s
f
o
r
m
er
en
er
g
izatio
n
tr
an
s
ie
n
ts
i
n
all
t
h
r
ee
p
h
ase
s
o
cc
u
r
at
th
e
s
a
m
e
ti
m
e.
Fig
u
r
e
1
.
Flu
x
-
c
u
r
r
en
t
C
h
ar
ac
t
er
is
tic
Fig
u
r
e
2
.
T
r
an
s
f
o
r
m
er
Mo
d
el
Dev
elo
p
ed
in
M
A
T
L
A
B
/
Si
m
u
li
n
k
So
f
t
w
ar
e
P
ac
k
ag
e
3
.
1
.
E
nerg
iza
t
io
n o
f
Si
m
ula
t
ed
T
ra
ns
f
o
r
m
er
M
o
del
a
t
t
he
T
im
e
M
o
m
e
nt
t
1
Fig
u
r
es
3
to
5
p
r
esen
ts
s
i
m
u
latio
n
r
es
u
lts
w
it
h
o
u
t
r
e
m
a
n
en
t
m
ag
n
eti
s
m
at
t1
.
T
h
is
i
s
t
h
e
ti
m
e
m
o
m
e
n
t
w
h
e
n
t
h
e
v
o
lta
g
e
v
al
u
e
p
ass
e
s
t
h
r
o
u
g
h
th
e
ze
r
o
-
p
o
in
t
a
n
d
th
e
m
a
x
i
m
u
m
m
ag
n
e
tic
f
l
u
x
i
s
eq
u
al
to
th
e
d
o
u
b
led
n
o
m
in
al
v
al
u
e.
E
n
er
g
izatio
n
o
f
t
h
e
s
i
m
u
la
ted
m
o
d
el
r
ep
r
esen
ts
tr
an
s
ie
n
ts
o
f
t
h
r
ee
p
h
ase
tr
an
s
f
o
r
m
er
th
r
o
u
g
th
e
f
ir
s
t
w
i
n
d
i
n
g
o
f
p
h
a
s
e
L
1
.
Oscill
o
g
r
a
m
s
in
Fi
g
u
r
es
3
,
4
an
d
5
s
h
o
w
th
e
c
h
an
g
e
i
n
v
o
ltag
e,
c
u
r
r
en
t
a
n
d
f
lu
x
i
n
t
h
e
ti
m
e
in
ter
v
al
o
f
a
o
n
e
s
ec
o
n
d
.
T
h
e
tr
an
s
f
o
r
m
er
e
n
er
g
iza
tio
n
en
tails
a
n
ad
v
er
s
e
ef
f
ec
t o
n
t
h
e
n
et
w
o
r
k
,
b
ec
au
s
e
in
th
is
ca
s
e
t
h
e
g
r
o
w
t
h
o
f
i
n
r
u
s
h
c
u
r
r
en
t is
u
p
to
ab
o
u
t 4
ti
m
es th
e
e
x
p
lo
itatio
n
.
T
h
e
v
o
ltag
e
o
n
t
h
e
p
r
i
m
ar
y
w
i
n
d
in
g
o
f
t
h
e
tr
an
s
f
o
r
m
er
h
as
a
n
o
n
s
i
n
u
s
o
id
al
s
h
ap
e
b
ec
au
s
e
o
f
h
ig
h
er
h
ar
m
o
n
ics
o
cc
u
r
e
n
ce
.
T
h
e
cu
r
r
en
t
o
n
t
h
e
p
r
i
m
ar
y
w
i
n
d
i
n
g
r
ea
ch
es
a
v
a
lu
e
o
f
2
.
3
p
u
.
T
o
i
n
d
u
ce
t
h
e
co
u
n
ter
v
o
tag
e
to
th
e
co
n
n
ec
ted
v
o
lta
g
e
U
1
,
a
s
in
e
f
lu
x
Ф
ap
p
ea
r
s
in
th
e
tr
an
s
f
o
r
m
er
co
r
e,
w
h
i
ch
lag
s
b
eh
in
d
t
h
e
ap
p
lied
v
o
ltag
e
f
o
r
9
0
0
.
Ma
g
n
etizin
g
cu
r
r
en
t
is
n
o
t
s
in
u
s
o
id
al,
as
th
e
h
al
f
p
er
io
d
is
s
y
m
etr
i
ca
l,
th
u
s
it
co
n
tai
n
s
o
d
d
s
in
e
an
d
co
s
in
e
h
ar
m
o
n
ics
[
1
]
.
Fig
u
r
e
3
.
Vo
ltag
e
o
n
P
r
i
m
ar
y
W
in
d
in
g
o
f
Si
m
u
lated
T
r
an
s
f
o
r
m
er
w
ith
o
u
t
R
e
m
a
n
e
n
t M
ag
n
eti
s
m
at
t
1
in
p
u.
Fig
u
r
e
4
.
C
u
r
r
en
t i
n
P
r
i
m
ar
y
W
in
d
in
g
o
f
Si
m
u
lated
T
r
an
s
f
o
r
m
e
r
w
ith
o
u
t
R
e
m
a
n
e
n
t M
ag
n
eti
s
m
at
t
1
in
p
u.
Fig
u
r
e
5
.
Flu
x
at
th
e
P
r
i
m
ar
y
o
f
Si
m
u
la
ted
T
r
an
s
f
o
r
m
er
w
ith
o
u
t
R
e
m
a
n
e
n
t M
ag
n
e
ti
s
m
at
t
1
in
p
u.
Fig
u
r
e
6
.
Vo
ltag
e
o
n
P
r
i
m
ar
y
W
in
d
in
g
o
f
Si
m
u
lated
T
r
an
s
f
o
r
m
er
w
ith
R
e
m
an
e
n
t
Ma
g
n
e
tis
m
V
al
u
e
o
f
0
.
7
5
p
u
.
at
t
1
in
p
u.
Fig
u
r
es
6
-
8
p
r
ese
n
t
t
h
e
r
e
s
u
l
ts
o
f
s
i
m
u
latio
n
s
w
i
th
r
e
m
a
n
e
n
t
m
a
g
n
etis
m
at
e
n
er
g
iza
tio
n
a
t
t
1
.
W
h
i
le
en
er
g
izi
n
g
th
e
tr
a
n
s
f
o
r
m
er
w
i
th
r
e
m
a
n
e
n
t
m
a
g
n
eti
s
m
,
h
i
g
h
er
v
alu
e
s
o
f
en
er
g
izatio
n
cu
r
r
en
t
o
cc
u
r
e
in
th
a
n
-1
-0.5
0
0.5
1
-1.5
-1
-0.5
0
0.5
1
1.5
Cu
rre
nt
(p
u)
F
l
ux
(pu
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
.
6
,
Dec
em
b
er
2
0
1
6
:
2
4
9
9
–
2
5
0
5
2502
w
it
h
o
u
t
r
e
m
an
e
n
t
m
ag
n
eti
s
m
.
I
n
th
e
co
n
s
id
er
ed
m
o
d
el
w
ith
r
em
a
n
en
t
m
a
g
n
et
is
m
,
s
o
u
r
ce
c
u
r
r
en
t
h
a
s
a
v
alu
e
ab
o
u
t
4
.
1
6
p
u
.
A
cc
o
r
d
in
g
to
eq
u
atio
n
5
,
t
h
e
m
a
x
i
m
u
m
f
lu
x
v
alu
e
i
s
i
n
cr
ea
s
ed
b
y
t
h
e
v
al
u
e
o
f
r
es
id
u
al
r
e
m
an
e
n
t
m
ag
n
eti
s
m
.
I
n
th
i
s
c
ase,
th
e
m
ag
n
etizi
n
g
cu
r
r
en
t
r
ea
ch
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f
ab
o
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t 4
.
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Fig
u
r
e
7
.
C
u
r
r
en
t i
n
P
r
i
m
ar
y
W
in
d
in
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f
Si
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lated
T
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an
s
f
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r
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er
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th
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e
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an
e
n
t
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g
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tis
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v
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f
0
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5
p
u
at
t
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p
u.
Fig
u
r
e
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.
Fl
u
x
at
th
e
Pr
i
m
ar
y
o
f
Si
m
u
la
ted
T
r
an
s
f
o
r
m
er
w
it
h
R
e
m
a
n
e
n
t M
ag
n
eti
s
m
Va
lu
e
o
f
0
.
75
p
u
at
t
1
in
p
u.
3
.
2
.
E
nerg
izing
o
f
t
he
Si
m
ula
t
ed
T
ra
ns
f
o
r
m
er
a
t
t
he
T
i
m
e
M
o
m
ent
t
2
Fig
u
r
es
9
to
1
1
s
h
o
w
th
e
p
o
w
er
tr
a
n
s
f
o
r
m
er
e
n
er
g
izatio
n
at
th
e
t
i
m
e
m
o
m
e
n
t
t
2
w
i
th
o
u
t
r
e
m
a
n
en
t
m
ag
n
eti
s
m
in
p
h
ase
L
2
.
I
n
r
u
s
h
cu
r
r
en
t t
h
r
o
u
g
h
th
e
p
r
i
m
ar
y
w
i
n
d
i
n
g
o
f
s
i
m
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lated
tr
an
s
f
o
r
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er
is
0
.
9
2
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u
.
Fig
u
r
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1
2
to
14
t
h
e
p
o
w
e
r
tr
an
s
f
o
r
m
er
e
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er
g
izatio
n
a
t
th
e
ti
m
e
m
o
m
en
t
t
2
w
it
h
r
e
m
a
n
en
t
m
ag
n
eti
s
m
i
n
p
h
ase
L
2
.
An
ev
id
en
t
d
is
o
r
d
er
o
f
t
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e
c
u
r
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s
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ce
a
m
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e
ap
p
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s
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ile
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e
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ax
i
m
u
m
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en
t v
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lu
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ea
c
h
es 1
.
3
ti
m
e
s
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al
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h
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w
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d
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1
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Fig
u
r
e
9
.
Vo
ltag
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o
n
P
r
i
m
ar
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in
d
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f
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lated
T
r
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f
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r
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e
r
w
ith
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u
t
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t M
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s
m
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Fig
u
r
e
1
1
.
Flu
x
at
t
h
e
P
r
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m
ar
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f
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m
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lated
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f
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er
w
ith
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t
R
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ag
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Fig
u
r
e
1
0
.
C
u
r
r
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t i
n
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m
ar
y
W
in
d
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g
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f
Si
m
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lated
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r
w
ith
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t
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t M
ag
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s
m
at
t
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in
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u.
Fig
u
r
e
1
2
.
Vo
ltag
e
o
n
P
r
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y
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in
d
in
g
o
f
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m
u
lated
T
r
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s
f
o
r
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er
w
ith
R
e
m
an
e
n
t
Ma
g
n
e
tis
m
V
al
u
e
o
f
0
.
7
5
p
u
at
t
2
in
p
u.
Fig
u
r
e
1
3
.
C
u
r
r
en
t i
n
P
r
i
m
ar
y
W
in
d
in
g
o
f
Si
m
u
lated
T
r
an
s
f
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e
r
w
ith
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e
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an
e
n
t
Ma
g
n
e
tis
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Val
u
e
o
f
0
.
7
5
p
u
at
t
2
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u.
Fig
u
r
e
1
4
.
Flu
x
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e
P
r
i
m
ar
y
o
f
Si
m
u
lated
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r
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er
w
ith
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g
n
e
tis
m
Valu
e
o
f
0
.
7
5
p
u
at
t
2
in
p
u.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
Tr
a
n
s
ien
t P
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2503
3
.
3
.
E
nerg
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o
f
t
he
Si
m
ul
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ra
ns
f
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r
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er
a
t
T
i
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M
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Fig
u
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0
s
h
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w
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3
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izatio
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cu
r
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w
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g
r
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s
0
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9
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u
r
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2
1
to
2
3
s
h
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w
tr
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n
s
f
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er
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izatio
n
a
t
th
e
t
i
m
e
m
o
m
en
t
t
3
w
ith
a
r
e
m
an
e
n
t
m
a
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is
m
v
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lu
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o
f
0
.
7
5
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u
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h
ase
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3
.
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iza
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n
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.
2
3
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Fig
u
r
e
1
5
.
Vo
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d
in
g
o
f
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m
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lated
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r
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f
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er
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ith
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t
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m
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t M
ag
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s
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t t
3
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Fig
u
r
e
1
6
.
C
u
r
r
en
t i
n
P
r
i
m
ar
y
W
in
d
in
g
o
f
Si
m
u
lated
T
r
an
s
f
o
r
m
er
w
ith
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u
t
R
e
m
a
n
e
n
t M
ag
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eti
s
m
a
t t
3
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u.
Fig
u
r
e
1
7
.
Flu
x
at
t
h
e
P
r
i
m
a
r
y
o
f
Si
m
u
lated
T
r
an
s
f
o
r
m
er
w
ith
o
u
t
R
e
m
a
n
e
n
t M
ag
n
eti
s
m
a
t t
3
in
p
u.
Fig
u
r
e
1
8
.
Vo
ltag
e
o
n
P
r
im
ar
y
W
in
d
i
n
g
o
f
Si
m
u
lated
T
r
an
s
f
o
r
m
e
r
w
ith
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m
an
e
n
t
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g
n
e
tis
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Va
l
u
e
of
0
.
7
5
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u
at
t
3
in
p
u.
Fig
u
r
e
1
9
.
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u
r
r
en
t i
n
p
r
i
m
ar
y
w
i
n
d
i
n
g
o
f
s
i
m
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lated
tr
an
s
f
o
r
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er
w
it
h
r
e
m
a
n
en
t
m
a
g
n
et
is
m
v
a
lu
e
o
f
0
.
7
5
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u
at
t
3
in
p
u.
Fig
u
r
e
2
0
.
Flu
x
at
t
h
e
p
r
i
m
ar
y
o
f
s
i
m
u
lated
tr
an
s
f
o
r
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er
w
it
h
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e
m
a
n
en
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m
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g
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0
.
7
5
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u
at
t
3
in
p
u.
3
.
3
.
Ana
ly
s
is
Res
ults
Si
m
u
latio
n
s
o
f
tr
a
n
s
f
o
r
m
er
e
n
er
g
izat
io
n
w
er
e
p
er
f
o
r
m
ed
a
t
d
if
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er
en
t
ti
m
e
m
o
m
en
t
s
a
n
d
d
if
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er
en
t
v
alu
e
s
o
f
r
e
m
a
n
en
t
f
l
u
x
.
I
n
t
h
e
ca
s
e
3
.
1
at
th
e
ti
m
e
m
o
m
e
n
t
o
f
en
er
g
izatio
n
,
t
h
e
c
u
r
r
en
t
i
s
an
d
th
e
c
u
r
r
en
t
i
p
f
r
o
m
eq
u
atio
n
3
h
av
e
t
h
e
s
a
m
e
v
al
u
e
b
u
t
d
i
f
f
er
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n
t
s
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g
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s
an
d
th
e
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lti
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u
r
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as
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h
e
s
u
m
o
f
th
o
s
e
t
w
o
cu
r
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en
ts
i
s
ze
r
o
.
T
h
is
co
r
r
esp
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to
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e
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p
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ted
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s
ical
p
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a
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th
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eg
i
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n
i
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g
o
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izatio
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,
b
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d
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ap
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)
(
1
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.
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ased
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(
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it
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n
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at
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e
tr
an
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m
p
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en
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f
th
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r
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ch
es
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ts
m
a
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v
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at
α
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w
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en
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tr
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to
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th
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w
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f
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r
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is
c
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eted
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.
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0
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eq
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,
th
e
tr
an
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r
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t
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izatio
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ep
en
d
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em
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m
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m
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izat
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w
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t
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p
r
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ar
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v
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v
al
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s
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
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6
,
Dec
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2
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1
6
:
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2504
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f
o
r
th
r
ee
d
if
f
er
e
n
t
v
a
lu
e
s
o
f
AC
s
i
n
e
v
o
lta
g
e.
T
h
e
en
er
g
izat
io
n
ca
n
o
cc
u
r
e
in
an
y
t
i
m
e
m
o
m
e
n
t,
o
r
ap
p
lied
v
o
ltag
e
v
al
u
e
f
r
o
m
eq
u
at
io
n
(
1
)
.
F
o
r
th
e
p
h
ase
L
1
s
i
m
u
lat
io
n
is
m
ad
e
w
h
en
t
h
e
v
o
ltag
e
v
alu
e
p
ase
s
th
r
o
u
g
h
th
e
ze
r
o
p
o
in
t
an
d
en
er
g
izatio
n
cu
r
r
en
t
v
alu
e
s
ar
e
th
e
h
ig
h
e
s
t,
w
h
ile
i
n
p
h
a
s
es
L
2
an
d
L
3
o
cc
u
r
e
i
n
cr
ea
s
e
o
f
in
r
u
s
h
cu
r
r
en
t
a
m
p
li
tu
d
e
v
al
u
e,
b
u
t
i
n
a
s
m
a
ller
a
m
o
u
n
t.
Au
t
h
o
r
s
o
f
p
ap
er
[
1
2
]
s
im
u
l
ated
a
tr
an
s
f
o
r
m
er
w
it
h
s
i
m
il
ar
p
ar
am
eter
s
a
n
d
o
b
tain
ed
t
h
e
h
ig
h
es
t
in
r
u
s
h
c
u
r
r
en
t
v
a
lu
e
o
f
2
.
5
9
p
u
(
o
n
th
e
p
h
ase
w
h
er
e
t
h
e
v
o
lta
g
e
p
ass
ze
r
o
p
o
in
t
at
th
e
m
o
m
en
t
o
f
en
er
g
izat
io
n
)
.
4.
CO
NCLU
SI
O
N
T
h
e
m
aj
o
r
in
f
lu
e
n
ce
o
n
t
h
e
in
r
u
s
h
c
u
r
r
en
t
m
a
k
e
t
h
e
v
al
u
e
o
f
co
n
n
ec
ti
n
g
v
o
lta
g
e
a
n
d
t
h
e
v
alu
e
o
f
t
h
e
r
e
m
an
e
n
t
m
a
g
n
e
tis
m
i
n
t
h
e
tr
an
s
f
o
r
m
er
co
r
e
at
t
h
e
m
o
m
e
n
t
o
f
t
h
e
e
n
er
g
izatio
n
.
T
h
e
in
r
u
s
h
c
u
r
r
en
t
v
al
u
e
ca
n
b
e
s
ev
er
al
ti
m
es
h
i
g
h
er
t
h
an
th
e
en
er
g
izatio
n
cu
r
r
en
t.
Su
ch
h
i
g
h
cu
r
r
e
n
t
v
al
u
e
s
ca
n
t
r
ip
th
e
tr
an
s
f
o
r
m
e
r
p
r
o
tectio
n
an
d
th
u
s
m
a
k
e
co
s
t
s
to
th
e
co
n
s
u
m
er
an
d
en
er
g
y
s
u
p
p
lier
.
Si
m
u
latio
n
s
in
t
h
is
p
ap
er
s
h
o
w
i
n
r
u
s
h
c
u
r
r
en
t
in
th
r
ee
d
if
f
er
e
n
t
t
i
m
e
m
o
m
e
n
ts
o
f
t
h
e
p
o
w
er
tr
an
s
f
o
r
m
er
en
er
g
izatio
n
.
Ma
x
i
m
al
in
r
u
s
h
cu
r
r
en
t
ap
p
ea
r
ed
at
th
e
ti
m
e
m
o
m
e
n
t
o
f
t
h
e
en
er
g
izatio
n
w
h
en
t
h
e
ap
p
lied
p
h
ase
v
o
ltag
e
v
alu
e
was z
er
o
w
it
h
r
esid
u
al
m
a
g
n
et
is
m
in
tr
a
n
s
f
o
r
m
er
ir
o
n
co
r
e.
RE
F
E
R
E
NC
E
S
[1
]
Do
len
c
,
―
T
ra
n
sf
o
r
m
a
to
ri
I
i
II
‖
,
S
v
e
u
č
il
ište u
Zag
re
b
u
,
E
lek
tro
teh
n
i
č
k
i
fa
k
u
lt
e
t,
Zag
re
b
,
1
9
8
7
,
[2
]
Đ.
Ka
li
ć
,
T
ra
n
sf
o
r
m
a
to
ri,
Zav
o
d
z
a
u
d
ž
b
e
n
ik
e
i
n
a
sta
v
n
a
sre
d
stv
a
,
Be
o
g
ra
d
,
1
9
9
1
.
[3
]
A
.
K.
A
l
-
Kh
a
li
fa
h
,
E.
F
.
El
-
S
a
a
d
a
n
y
,
―
In
v
e
sti
g
a
ti
o
n
o
f
M
a
g
n
e
ti
z
in
g
In
ru
sh
C
u
rre
n
t
i
n
a
S
i
n
g
le
-
P
h
a
se
T
ra
n
s
f
o
r
m
e
r
‖
,
1
-
4
2
4
4
-
0
5
5
7
-
2
/
0
6
/©
2
0
0
6
IEE
E
.
[4
]
N.
Ch
ies
a
,
B.
A
.
M
o
r
k
a
n
d
H.
K
.
Hø
i
d
a
len
,
―
T
ra
n
s
f
o
rm
e
r
M
o
d
e
l
f
o
r
In
r
u
sh
C
u
rre
n
t
Ca
lcu
lati
o
n
s:
S
im
u
latio
n
s,
M
e
a
su
re
m
e
n
ts
a
n
d
S
e
n
sit
iv
it
y
A
n
a
l
y
sis
‖
,
IEE
E
T
ra
n
s
a
c
ti
o
n
o
n
P
o
we
r De
li
v
e
ry
,
V
o
l.
2
5
,
No
.
4
,
Oc
t.
2
0
1
0
.
[5
]
M
.
S
teu
re
r,
K.
F
r
ö
h
li
c
h
,
―
T
h
e
Im
p
a
c
t
o
f
In
ru
sh
C
u
rre
n
ts
o
n
t
h
e
M
e
c
h
a
n
ica
l
S
tres
s
o
f
Hig
h
V
o
l
tag
e
P
o
w
e
r
T
ra
n
s
f
o
r
m
e
r
Co
il
s―
,
IEE
E
T
r
a
n
sa
x
ti
o
n
o
n
Po
we
r De
li
v
e
ry
,
Vo
l.
1
7
,
No
.
1
,
Ja
n
.
2
0
0
2
.
[6
]
Li
-
Ch
e
n
g
W
u
,
Ch
ih
-
W
e
n
L
iu
,
S
h
ih
-
E
n
Ch
ie
n
,
Ch
in
g
-
S
h
a
n
Ch
e
n
,
―
T
h
e
E
ff
e
c
t
o
f
In
ru
sh
Cu
rre
n
t
o
n
T
ra
n
sf
o
r
m
e
r
P
r
o
tec
ti
o
n
‖
,
P
o
we
r S
y
mp
o
si
u
m
,
2
0
0
6
.
NA
P
S
2
0
0
6
.
3
8
t
h
No
rt
h
A
m
e
rica
n
,
Ca
rb
o
n
d
a
le,
IL
.
[7
]
M
.
Na
g
p
a
l.
,
T
.
G
.
M
a
rti
n
ich
,
A
.
M
o
sh
re
f
,
K.
M
o
riso
n
,
―
A
ss
e
s
sin
g
a
n
d
L
im
it
in
g
I
m
p
a
c
t
o
f
T
r
a
n
sf
o
rm
e
r
In
ru
sh
Cu
rre
n
t
o
n
P
o
w
e
r
Qu
a
li
ty
‖,
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
P
o
we
r De
li
v
e
ry
,
Vo
l.
2
1
,
No
.
2
,
A
p
ril
2
0
0
6
.
[8
]
R.
Ya
c
a
m
in
i
a
n
d
A
.
A
b
u
-
Na
ss
e
r
,
―
Nu
m
e
ric
a
l
c
a
lcu
latio
n
o
f
in
ru
s
h
c
u
rre
n
t
i
n
sin
g
le
-
p
h
a
se
tran
sf
o
rm
e
rs
‖
,
El
e
c
tric
Po
we
r A
p
p
li
c
a
ti
o
n
s
,
IEE
Pro
c
e
e
d
in
g
s B
,
(
V
o
l
u
m
e
:
1
2
8
,
Iss
u
e
:
6
)
,
No
v
e
m
b
e
r
1
9
8
1
.
[9
]
K.
Ka
rsa
i,
D.
Ke
re
n
y
i,
L
.
Kiss
,
―
L
a
r
g
e
P
o
w
e
r
T
ra
n
s
f
o
r
m
e
rs
‖
,
O
x
fo
rd
1
9
8
7
.
[1
0
]
G
.
P
e
tro
v
ić,
T
.
Kili
ć
,
O.n
Be
g
o
,
―
Re
d
u
stio
n
o
f
In
ru
sh
Cu
rre
n
ts
a
t
T
h
re
e
-
p
h
a
se
P
o
w
e
rT
tran
s
f
o
r
m
a
r
Co
n
n
e
c
ti
o
n
‖
,
S
p
li
t
,
Cro
a
ti
a
,
J
o
u
r
n
a
l
o
f
En
e
rg
y
,
v
o
l.
5
7
(2
0
0
8
),
n
r.
3
,
p
a
g
e
s.
3
5
0
-
3
6
7
[1
1
]
S
.
D.
Bo
le,
―
M
it
ig
a
ti
o
n
o
f
In
ru
sh
Cu
rre
n
t
in
T
ra
n
sf
o
r
m
e
r
‖,
In
te
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
I
n
n
o
v
a
ti
v
e
T
e
c
h
n
o
l
o
g
y
a
n
d
Exp
lo
ri
n
g
E
n
g
in
e
e
rin
g
(
IJ
IT
EE
)
,
IS
S
N:
2
2
7
8
-
3
0
7
5
,
Vo
lu
m
e
3
,
Iss
u
e
7
,
De
c
e
m
b
e
r
2
0
1
3
[1
2
]
Jo
h
n
H.
Br
u
n
k
e
a
n
d
Kla
u
s
J.
F
r
ö
h
li
c
h
,
―
El
im
in
a
ti
o
n
o
f
T
ra
n
sf
o
r
m
e
r
In
ru
s
h
Cu
rre
n
ts
b
y
Co
n
tro
l
led
S
w
it
c
h
in
g
—
P
a
rt
I:
T
h
e
o
re
ti
c
a
l
Co
n
si
d
e
ra
ti
o
n
s
‖
,
I
E
EE
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r De
li
v
e
ry
,
V
o
l.
1
6
,
N
o
.
2
,
A
p
ril
2
0
0
1
.
[1
3
]
M
.
Bu
k
u
b
u
k
w
a
n
a
,
R.
Zi
v
a
n
o
v
ic,
―
In
ru
sh
C
u
rre
m
t
T
ra
n
sie
n
ts
Du
rin
g
En
e
rg
iza
ti
o
n
o
f
a
n
Un
lo
a
d
e
d
T
r
a
n
sf
o
r
m
e
ro
n
th
e
Esk
o
m
N
e
t
w
o
rk
,
CIRED
2
0
0
5
‖,
1
8
t
h
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
a
n
d
Ex
h
i
b
it
i
o
n
o
n
,
T
u
rin
,
Italy
.
[1
4
]
E.
Ca
z
a
c
u
,
V
.
Io
n
it
a
,
L
P
e
tres
c
u
,
―
A
n
I
m
p
ro
v
e
d
M
e
th
o
d
f
o
r
th
e
In
ru
sh
Cu
rre
n
t
Ev
a
lu
a
ti
o
n
in
S
in
g
le
P
h
a
se
P
o
w
e
r
T
ra
n
s
f
o
r
m
e
rs‖
,
A
d
v
a
n
c
e
d
T
o
p
ics
in
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
(AT
E
E),
2
0
1
3
8
th
I
n
tern
a
t
i
o
n
a
l
S
y
m
p
o
siu
m
o
n
2
3
-
25
M
a
y
2
0
1
3
,
B
u
c
h
a
re
st.
[1
5
]
S
.
A
.
M
.
M
irk
a
lae
i,
F
.
Ha
sh
ies
h
,
―
Co
n
tr
o
ll
e
d
S
w
it
c
h
in
g
to
M
it
ig
a
te
P
o
w
e
r
T
ra
n
s
f
o
r
m
e
rs
In
ru
sh
Cu
rre
n
t
P
h
e
n
o
m
e
n
o
n
‖
,
P
o
we
r
En
g
in
e
e
rin
g
Co
n
fer
e
n
c
e
(
UPEC)
,
2
0
1
5
5
0
t
h
In
tern
a
ti
o
n
a
l
Un
iv
e
rsiti
e
s,
1
-
4
S
e
p
t.
2
0
1
5
,
S
to
k
e
o
n
T
re
n
t
[1
6
]
Ya
c
a
m
in
i
R.
,
A
b
u
-
Na
ss
e
r
A
.
,
―
T
h
e
c
a
lcu
latio
n
o
f
in
ru
sh
c
u
rre
n
t
in
th
re
e
-
p
h
a
se
tran
sf
o
r
m
e
r
s
‖
,
El
e
c
tric
Po
we
r
Ap
p
li
c
a
ti
o
n
s,
I
EE
Pro
c
e
e
d
i
n
g
s B
,
Vo
l.
1
3
3
,
Iss
u
e
1
,
Ja
n
u
a
ry
1
9
8
6
.
[1
7
]
S
.
G
.
A
b
d
u
lsa
la
m
,
W
.
X
u
a
n
d
V
.
Din
a
v
a
h
i,
―
M
o
d
e
ll
in
g
a
n
d
sim
u
latio
n
o
f
th
re
e
-
p
h
a
se
tran
sf
o
r
m
e
rs
fo
r
in
r
u
sh
c
u
rre
n
t
stu
d
ies
‖
,
Ge
n
e
ra
ti
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CI
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Evaluation Warning : The document was created with Spire.PDF for Python.