Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 10
88
~1
098
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p10
88-
1098
1
0
88
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Sim
u
link model of transform
e
r di
fferential protection using
phase angle differen
ce based al
gori
thm
N
a
ssim A
.
Iqte
it
1
, Kh
ali
d
Y
a
h
y
a
2
1
De
pa
rtme
n
t
o
f
El
ec
tric
a
l
E
ngi
n
e
e
r
i
ng,
P
a
lesti
n
e Polyt
e
chnic
Un
iver
si
ty, Palesti
n
e
2
De
pa
rt
me
nt
of Me
c
h
a
t
r
onic
E
n
g
i
n
e
e
r
i
n
g
,
Ista
n
bul
Ge
lisim
Uni
v
e
r
si
ty
,
T
u
rke
y
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Se
p 3
,
20
19
Re
vise
d N
o
v
9
,
20
19
Acc
e
pt
e
d
Fe
b 16
, 20
20
An a
p
pl
ic
a
t
i
o
n
of p
h
a
se
-a
n
g
l
e
-d
iffe
re
nc
e b
a
se
d a
l
g
o
r
it
hm
wit
h
pe
rce
n
ta
ge
different
ial
r
e
lays is presented
i
n
th
is pa
pe
r.
In t
h
e
situation where t
h
e
t
r
ansform
e
r
differential relay is un
der
magnetiz
ing
in
rus
h
current
,
t
h
e
a
l
g
o
ri
th
m
wil
l
b
e
u
t
iliz
e
d
t
o
bl
oc
k
t
h
e
proc
e
s
s.
In
t
h
i
s
st
ud
y,
th
e
t
echn
i
qu
e
is
mod
e
led and
i
m
ple
m
en
ted
u
s
in
g S
i
mu
link in
teg
r
ated with
MATL
AB. T
h
e re
a
l
c
i
rc
ui
t
m
o
de
l
of p
o
we
r tra
n
sforme
r a
n
d c
u
rre
nt
tran
sfo
r
m
e
rs
a
r
e
con
s
idered
in
th
e simulatio
n
m
o
del.
Th
e r
e
su
lt
s co
nfirm
e
d
th
e effe
ctiv
en
es
s of the
te
ch
niq
u
e in
diffe
rent op
eratio
n
mod
e
s
;
su
c
h
as
,
magnet
izing i
n
rush currents
,
current
transfor
mers sat
u
r
a
ti
on and
i
n
ternal
t
r
ansform
e
r
fa
u
l
t
s
.
Ke
yw
ords:
D
i
f
f
e
r
e
n
tia
l re
la
y
In
rus
h
cu
rre
nt
Int
e
r
n
a
l
fa
ult
P
h
ase ang
l
e
d
i
ff
er
en
ce
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
N
a
ssim
A
.
Iq
teit,
Depa
rt
me
nt o
f
Ele
c
t
r
i
c
a
l
Engi
ne
eri
n
g
,
P
a
l
e
st
in
e
Po
ly
t
e
c
h
n
i
c Un
iv
er
sity
,
H
e
bro
n
-
W
a
d
i
A
l
h
a
r
e
a Bu
ild
in
g P
O
BOX
:
19
8, Pa
le
sti
n
e
.
Ema
i
l
:
n
a
ssi
m_
e
ng8
3@p
p
u
.
e
d
u
1.
IN
TR
O
DUCTION
Tran
sformers
are a
vit
a
l a
n
d
e
xpe
nsi
v
e
c
o
mp
one
nt
o
f
el
e
c
t
r
i
cal
p
o
w
er s
y
ste
m
s. T
h
e
pr
ote
c
t
i
on
of
t
r
ans
f
o
r
me
rs
i
s
e
s
se
nti
a
l t
o
ac
hie
v
e
hig
h
q
u
a
l
it
y performa
n
ce i
n
m
o
dern e
l
ec
tric
ne
tw
o
r
k
s
. T
h
e
w
i
n
d
i
n
g
faul
ts
on p
o
we
r tran
sfo
r
me
rs
ca
u
s
ed by hi
gh
se
nsi
t
ivi
t
y, sel
e
c
t
i
v
i
t
y and
fa
st
resp
o
n
se wi
ll
be det
e
rre
d b
y
t
h
e
di
ffe
re
nt
i
a
l
prot
ec
ti
on
rel
a
y
[1
]. Tra
n
sf
o
r
m
e
rs w
i
t
h
a
hi
g
h
c
a
p
ac
it
y a
r
e
us
ual
l
y
p
r
ot
e
c
t
e
d
by
a
har
m
o
n
i
c
r
e
s
t
r
a
in
t
p
e
r
cen
ta
g
e
d
i
ff
ere
n
t
i
al
r
e
l
a
y
[2
].
Th
e f
a
u
l
ts
th
a
t
o
c
c
u
r in
t
r
a
n
sfo
r
m
e
r
s
ar
e e
i
t
h
er
:
in
te
rn
al
i
n
ci
p
i
en
t
fa
ult
s
o
r
i
n
t
e
rn
a
l
sho
r
t
c
i
rcui
t
faul
ts [
3
]. S
h
o
r
t
ci
rc
uit
fa
ult
s
con
s
t
i
tut
e
a
b
o
u
t
70-
8
0
%
of t
r
ans
f
orme
r fa
i
l
ures
,
a
n
d
t
h
ese ca
n be (1
)
ph
a
s
e-
t
o
-ground fault
or (2)
turn
-t
o-t
u
r
n
fa
ult
s
[4
].
D
u
e
to
t
h
e
n
o
n
li
nea
r
i
t
ie
s
i
n
t
h
e tra
n
s
f
o
r
me
r c
o
re,
o
r
i
n
t
h
e C
T
c
o
re
o
r
i
n
bot
h ca
se
a s
ubsta
nti
a
l
d
i
f
f
e
ren
tia
l
cu
rr
en
t
ma
y f
l
ow
,
wh
en t
h
e
r
e
is
n
o
fau
l
t
.
Th
e
s
e f
a
l
s
e d
i
f
f
er
e
n
t
i
a
l
c
u
rr
en
ts ar
e
g
e
n
e
r
a
ll
y suf
f
i
c
i
en
t
t
o
c
a
use a
perc
ent
a
ge
di
ffe
r
e
n
ti
al
re
l
a
y t
o
trip. S
o
me
o
f
t
h
ese
phe
no
me
na are ma
g
n
et
i
z
i
ng in
rush c
u
rre
n
t
du
ri
n
g
e
n
er
g
i
z
a
t
i
on
or
faul
t
rem
oval
,
t
r
a
n
sfo
r
me
r o
v
e
r
-e
xc
it
a
t
i
on a
nd
C
T
sa
t
u
rat
i
o
n. Ho
we
ve
r, in
mo
der
n
di
git
a
l
rel
a
y
s
s
o
me
a
l
go
ri
t
h
m
s
we
re
devel
o
ped
t
o
a
v
oi
d
the
fal
s
e
t
r
i
p
pi
ng
i
n
pe
rce
n
t
a
ge
diffe
r
e
n
t
i
a
l
re
l
a
ys.
Some
of t
h
e
s
e
al
gori
t
h
m
s
h
a
ve bee
n
d
e
ve
lope
d
base
d o
n
dif
f
ere
n
t
t
e
c
hni
que
s, suc
h
a
s
, art
i
fi
ci
al
n
e
ura
l
net
w
orks, fuz
z
y
l
ogi
c
,
wa
vel
e
t
t
r
an
sfor
ms and
pri
n
ci
pa
l
co
mp
on
e
n
t
anal
y
s
is [5-
8
]
.
Th
ese a
p
p
r
o
a
c
h
e
s
h
a
v
e
l
i
mi
ta
t
i
ons tha
t
ma
y
a
ffe
ct
t
h
ei
r spee
d o
f
o
p
e
r
at
i
o
n,
de
pe
nda
bi
l
i
t
y an
d se
curi
t
y
. T
h
ey a
l
so re
qui
re
c
o
mpl
e
x
c
o
mp
u
t
ati
o
n
s
an
d
ar
e su
sce
p
tib
le
to
ch
a
n
ge
s in
tr
a
n
sfo
r
me
r
p
a
rame
te
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Si
m
u
li
nk
mo
de
l
o
f
tra
n
sf
o
r
m
e
r di
f
f
e
r
ent
i
al
prot
ec
ti
on
usi
n
g
p
has
e
an
gle
di
f
f
e
r
ence
…
(N
a
ssi
m A.
Iqt
e
i
t
)
1
089
The
di
ffe
rent
i
a
l
prote
c
t
i
on
on
mag
n
et
i
z
i
n
g i
n
rus
h
c
u
rre
n
ts
can
be
a
v
erte
d b
y
ma
ny
e
f
fect
i
v
e
met
h
o
d
s
[9-
1
2
]
.
O
n
e
of t
h
ose
met
h
o
d
s is
ma
ki
ng t
h
e
pha
se
vol
ta
ge
as a
co
nt
rol
si
gnal
.
A
n
d t
h
i
s
wa
y
gua
ra
nte
e
t
h
at
t
h
e
prot
e
c
t
e
d
tr
ansfo
r
mer
i
s
e
xpl
ic
i
t
l
y
decre
a
se
d
i
n
t
h
e
te
rmina
l
vol
t
a
ge
. A
l
so,
i
m
ple
m
e
n
ti
ng
a
core
-fl
ux
o
r
tr
ansfo
r
mer
whi
c
h i
s
eq
ui
val
e
nt
c
i
rc
ui
t
for e
l
e
c
t
i
ng i
n
rush
from
i
n
t
e
rna
l
f
a
ul
t
cu
rre
n
t
s
c
oul
d
be
anot
her
rema
rka
b
le
me
t
h
o
d
.
T
hose
wa
ys c
oul
d achi
e
ve
ma
jor
s
u
c
cess
conc
e
r
ni
n
g
the
i
r ap
pl
ic
at
ions
i
f
t
h
e
tr
a
n
sf
orm
e
r
te
rmin
a
l
vo
l
t
ag
e
me
a
s
ur
ed
and
th
e
me
asu
r
e
m
en
t p
r
o
c
e
ss
w
i
ll b
e
qu
ite
co
s
tly
[1
3]
.
A
d
d
i
t
i
on
a
lly
,
com
puta
t
io
na
l
bur
den
o
n
t
h
e
diffe
r
e
n
t
i
a
l
rel
a
y
wo
ul
d
be
i
n
crease
d
so
t
h
at
ca
uses
a
slo
w
mot
i
o
n i
n
w
i
ndin
g
shor
t
circuits [14-16]
.
Ph
a
s
e a
n
g
l
e
d
i
ff
eren
c
e
t
ech
n
i
q
u
e
,
pr
opose
d
by [1
] i
s
use
d
to av
o
i
d
l
i
mi
ta
tio
n
s
i
n
p
r
e
v
i
o
u
s
t
echni
q
u
es
, an
d t
o
i
m
prove t
h
e
rel
i
a
bi
l
i
t
y
a
n
d
fast
res
p
onse
i
n
pe
rcent
a
ge
di
ffe
r
ent
i
a
l
re
la
y.
In t
h
is p
a
per
t
o
d
i
s
c
r
i
m
i
n
a
t
e
ma
g
n
e
t
i
z
i
ng
in
ru
s
h
c
u
rre
n
t
s a
n
d shor
t
c
i
r
c
u
it fa
u
lts
in power
t
r
an
sfor
me
r,
t
h
e P
A
D
te
c
h
n
i
qu
e
wi
th pe
rc
e
n
t
a
g
e
diffe
r
e
n
t
i
a
l
rel
a
ys wil
l
be
mo
de
le
d
a
nd s
i
mula
te
d usin
g
Si
mu
l
i
n
k
pac
k
age i
n
MAT
L
A
B
so
f
t
w
a
r
e
.
A
l
so
,
th
e r
e
a
l
ci
rcuit
mo
d
e
l of
p
o
w
e
r
t
r
an
sfo
r
mer
an
d
C
T
s
tr
a
n
sfo
r
me
r w
ill
b
e
co
nsi
d
er
ed
in
th
e
si
mu
la
tio
n
mod
e
l
in
bo
th
ca
se
s.
2.
M
E
THOD
OLOG
Y
OF D
I
FFER
ENTIA
L
R
E
LAY WITH PAD
2.1.
Pe
rce
nta
g
e
d
i
ffer
en
tial
(87T
)
ch
ar
ac
ter
i
sti
c
Pow
e
r
tr
a
n
sforme
r
s
th
a
t
ar
e
ra
te
d a
bov
e
10
MV
A ar
e
mo
st co
mm
on
ly p
r
o
t
ec
ted
w
ith
p
e
r
c
en
t
a
g
e
di
ffe
re
nt
i
a
l
rel
a
y (
8
7T) for t
h
e p
u
r
p
o
s
e
s
of
avoi
din
g
i
n
t
e
rn
a
l
sho
r
t
c
i
rc
ui
ts. T
h
e
87T
-re
l
a
y
has
bee
n
fo
un
d t
o
o
f
f
e
r
imp
o
r
t
a
n
t
gr
oun
d
an
d sp
ee
d p
h
a
s
e
p
r
o
t
e
c
t
i
o
n
fo
r 2
an
d 3
w
i
nd
in
g pow
e
r
t
r
an
sfor
me
rs
[
17]
.
The
r
e
la
y
fe
at
ure
s
a
n
ad
d
i
t
i
ona
l ha
rmo
n
i
cs re
st
ra
i
n
t
un
it
i
n
w
h
ic
h ma
ssi
ve t
r
ans
f
ormer
ma
g
n
e
t
iz
ing
i
n
ru
sh
i
s
p
r
ese
n
t
as
w
e
ll a
s
r
a
tio
m
a
tc
h
i
ng
tap
s
. Th
e un
i
t
p
r
e
v
en
ts
re
lay
op
er
at
io
n on
tra
n
sf
or
mer m
a
gn
e
t
i
z
i
n
g
i
n
ru
sh
cu
rre
n
t
.
The
se
c
o
nd
ha
rmoni
cs rest
rai
n
t
u
n
i
t
is
fact
o
r
y cal
i
b
rat
e
d
to re
st
rai
n
1
5
%
se
co
nd
ha
rm
oni
c cu
rre
n
t
,
b
u
t
may
be a
d
j
u
ste
d
i
f
requi
re
d. A
n
u
n
r
e
s
t
r
a
i
ne
d
i
n
st
ant
a
ne
ou
s u
n
i
t
w
h
ic
h ope
rat
e
s
o
n
ma
gni
t
ude
of
dif
f
ere
n
ce
c
u
rre
n
t
i
s
provi
ded t
o
ba
ck
u
p
t
h
e
p
e
rcent
a
ge
di
ffe
r
e
n
ti
a
l
u
n
i
t
. The
uni
t
is adj
u
sta
b
l
e
from a
p
pro
x
i
m
a
t
e
l
y
8
t
o
2
0
t
i
mes t
a
p
[18
]
.
The
c
h
a
r
ac
te
ri
sti
c
of
pe
rce
n
t
a
ge
di
ffe
r
e
n
t
i
al
rel
a
y i
s
p
r
o
v
i
d
i
n
g
fol
l
owi
n
g
i
n
Fi
g
u
re
1
[1
9,
2
0
]
.
Th
e
c
h
a
r
ac
ter
i
sti
c
I
n
th
is c
a
s
e
th
e
d
i
f
f
e
r
e
ntia
l c
u
rr
en
t is
f
a
lse
,
th
ey
sti
ll c
a
n
c
a
us
e a
tr
ip
in
a
p
e
r
cen
ta
ge
di
ffe
re
nt
i
a
l
re
la
y.
S
o
me
ti
mes
d
u
ri
ng
en
e
r
gi
zat
i
on i
n
rus
h
c
u
rrent
i
s
ma
g
n
e
t
i
z
e
d. T
h
e si
t
u
a
t
ion
c
a
n
a
l
s
o
oc
c
u
r
du
ri
n
g
t
r
a
n
sf
o
r
me
r
ove
r-e
x
ci
t
a
t
i
o
n, or fa
ul
t re
moval
,
o
r
CT
sat
u
ra
ti
o
n
.
Ho
we
ver,
re
ce
ntl
y
, al
go
ri
t
h
ms ha
v
e
bee
n
de
ve
lo
pe
d t
o
a
voi
d
t
h
e
fa
lse
t
r
i
p
pi
ng
i
n
pe
rce
n
t
a
ge
di
ffe
r
e
n
t
i
al
re
l
a
ys.
Vari
ous
te
chni
q
u
es
suc
h
as
pri
n
ci
pal
co
m
p
o
n
e
n
t
a
n
al
ys
is, fuzz
y
lo
gi
c a
nd a
r
t
i
f
i
c
i
a
l
ne
ura
l
ne
tw
ork
s
he
l
p
e
d
to
t
o
de
vel
o
p t
h
es
e
a
l
g
o
r
ith
m
s
. The
s
e
te
c
h
n
i
qu
e
s
h
a
v
e
t
h
eir p
a
r
a
me
te
rs in Fi
gure 1
ar
e as
fo
llo
ws
:
I
diff
:
i
s
ma
gni
t
ude
o
f
5
0
H
z
c
o
mpo
n
e
n
t
for
diffe
r
e
n
t
i
a
l
cur
r
ent
.
I
re
s
:
i
s
m
a
g
n
i
t
u
de
of
5
0
Hz
c
o
mp
one
nt
fo
r
re
s
t
rai
n
t
c
u
rre
nt.
I
op
1
: is th
e
m
i
n
i
m
u
m op
e
r
a
tio
n c
u
rr
en
t.
I
op
2
:
i
s
t
h
e
ad
j
u
ste
d
mi
n
i
m
u
m o
p
e
ra
ting
cu
rr
en
t
I
re
s, min
: is minimum
r
e
s
t
r
a
int
current.
k
:
g
r
ad
ie
n
t
of
t
h
e
fun
c
ti
on
al
ch
ar
a
c
t
e
r
i
st
ic
wh
ic
h
a
r
e
,
10
,
20
o
r
40
%.
Fi
gu
re
1.
Pe
rce
n
ta
ge di
f
f
e
re
nti
a
l rel
a
y
(8
7T
)
cha
r
ac
te
ri
s
t
i
c
I
diff
w
ith
t
r
an
sfo
r
m
a
ti
o
n
r
a
tio o
f
n
i
s
de
fi
ne
d by
(1), whi
l
e
I
re
s
at
the
same
ra
ti
o
i
s
gi
ve
n b
y
(2).
d
iff
I
res
t
I
2
op
I
1
op
I
mi
n
,
res
I
slope
k
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
88
–
1
0
98
1
090
,
∅
⃗
,
∅
⃗
,
∅
(1)
,
∅
⃗
,
∅
⃗
,
∅
/2
(2)
Whe
r
e,
⃗
,
∅
: is tr
an
sfor
mer
pr
im
ary
c
u
rr
e
n
t
a
t
ph
as
e
∅
(n
a
m
el
y,
A
,
B
or
C).
⃗
,
∅
:
i
s
t
r
a
n
s
f
orme
r
se
co
n
d
ar
y c
u
r
r
ent
a
t
p
h
ase
∅
(namely,
A
,
B or
C).
Th
e p
e
rc
en
ta
ge
d
i
f
f
er
en
tia
l
op
er
a
t
ing
ch
ar
act
er
ist
i
c
p
r
e
v
e
n
t
s
op
er
at
i
o
n
un
til
t
h
e
d
i
ff
er
en
tia
l
cu
rr
e
n
t
i
s
grea
te
r t
h
an
a
certa
i
n
pe
rc
e
n
t
a
ge
o
f
t
h
r
ough
c
u
rre
n
t.
(3)
as s
h
ow
n
p
r
o
v
i
d
es
t
h
e
o
p
er
at
ing c
h
ara
c
t
e
ri
st
ic
o
f
one
p
h
ase
di
ffe
rent
i
a
l
e
l
e
m
ent
.
T
h
e t
h
resh
ol
d val
u
e
Io
p
1
bi
ases
the
di
ffe
r
e
n
t
i
a
l
opera
ti
ng
current
.
The t
h
res
h
old
val
u
e must
b
e
ch
ose
n
base
d o
n
the
ma
g
n
et
i
z
i
n
g
c
u
rre
nt’s ma
gni
tu
d
e
,
a
n
d
t
h
e
di
ffere
nti
a
l
c
u
rre
n
t
, wh
ic
h r
e
su
lts
from
on-
lo
ad
tap
-
ch
a
n
g
i
ng
wh
ic
h o
c
c
u
rs d
u
r
i
ng
n
o
rm
al
t
r
an
sfo
r
mer
l
o
ad
in
g
cond
iti
o
n
s
[2
1, 2
2
].
T
h
e s
econ
d
i
n
e
q
ual
i
t
y
mo
de
ls the
sl
ope
o
f
t
h
e tra
n
sfo
r
me
r di
ffe
re
nt
i
a
l
rel
a
y.
,
(3)
The
mi
ni
mum ope
rat
i
n
g
c
u
rre
n
t
Io
p1
i
n
a
m
p
e
res ca
n
be cal
cul
a
t
e
d
wi
t
h
t
h
e
f
o
ll
owi
n
g
rel
a
t
i
on
[1
1]:
(4)
R:
is
ad
j
u
stab
le
m
i
n
.
r
e
s
t
r
a
in
t se
tt
in
g
,
R
[1-3].
T: i
s
t
a
p
se
tting
in
a
m
p
e
re
s.
2
.
2
.
Fa
ult
discrimina
t
i
on
t
ech
niq
u
e
s
in po
w
er t
r
a
n
sfo
r
m
e
r
s
2.
2.1.
Tr
a
n
sfo
r
m
er cu
rr
e
n
t t
r
a
n
s
i
en
t
co
m
p
o
n
e
n
t
s
te
ch
ni
que
The
desc
ribe
d
te
ch
ni
q
u
e i
s
uti
l
i
zed t
o
di
sce
r
n
bet
w
ee
n
ext
e
rna
l
a
n
d
i
n
te
rnal
fa
ul
ts
wi
t
h
i
n
po
w
e
r
tr
a
n
sf
orm
e
r
s
.
Th
e ph
a
s
e tr
ansie
n
t
c
u
rr
en
t
s
(a
ll t
h
re
e) of
t
h
e
t
r
an
sfo
r
me
r go
th
rou
g
h
c
onve
rsi
o
n
i
n
t
o
th
e mod
a
l
c
u
rre
n
t
com
pon
en
ts by
w
a
y
of
Clark
e
's
tr
ansfor
ma
ti
on
t
o
g
i
v
e
g
r
ou
nd
mo
de
I0
, a
r
e
a
l
mo
de
I1
as
w
e
ll
as
a
r
e
a
l
mode
I2
.
Hig
h
and
lo
w
t
e
nsi
o
n
si
des of
t
h
e
t
r
ans
f
orme
r gi
v
e
t
r
an
si
ent
mo
da
l c
u
rrent
s
w
h
i
c
h
are
use
d
wi
t
h
t
h
e
F
a
u
l
t
D
i
sc
ri
mi
n
a
ti
o
n
Equ
a
t
i
on
(
F
D
E
)
,
wh
i
c
h
i
n
tu
rn is ab
l
e
to
d
i
sc
e
r
n
in
te
rn
a
l
fr
om ex
t
e
rn
a
l
f
a
u
lts
b
a
se
d on
p
o
l
ar
ity
o
f
it
s
o
u
t
p
u
t
. Th
e
po
lar
i
t
y
of t
h
e FD
E, fo
r i
n
terna
l
fa
u
l
t
s
,
w
ill r
e
g
i
ste
r
n
e
g
a
tiv
e wh
er
e
a
s it
w
i
ll
b
e
la
r
g
el
y po
s
itive
fo
r
e
x
t
e
rn
a
l
fa
u
lts
.
Th
e f
o
llow
ing
eq
u
a
t
i
on
p
r
ov
i
d
es
t
h
e
fau
l
t
d
i
s
c
r
i
min
a
t
i
o
n
equ
a
ti
on
:
∙
∙
∙
(5)
Whe
r
e,
(
I
0
)
th
, (
I
0
)
tl
: a
r
e
th
e
cu
rre
n
t
s (tr
a
n
s
ie
n
t
g
r
ound
mod
e
) on
h
i
gh
an
d on
l
o
w
te
n
s
ion
si
d
e
s.
(
I
1
)
th
, (
I
1
)
tl
: a
r
e
t
h
e c
u
rrent
s
(t
ra
nsi
e
nt a
e
ria
l
mo
de
)
1 on
hi
gh
a
n
d o
n
lo
w
te
nsio
n side
s.
(
I
2
)
th
, (
I
2
)
tl
:
are
t
h
e c
u
rrent
s (t
ra
n
s
i
e
nt
a
e
ria
l
mo
de
)
2 on
hi
gh
a
n
d o
n
l
o
w
te
nsio
n si
de
s.
2.
2.2.
Fau
l
t
d
e
te
cti
o
n pr
ocess in
p
o
wer
tr
ans
f
or
m
ers a
p
p
l
y
i
ng
th
e
D
i
sc
re
te Wa
ve
le
t
T
r
an
sfor
m
Th
e Di
scr
e
te
W
a
v
e
le
t Tr
ansf
orm
te
chn
i
qu
e
is u
s
ed
for
on-
lin
e
f
a
u
lt d
e
te
ct
io
n
w
i
th
in
p
o
wer
tr
a
n
sf
orm
e
r
s
.
W
a
v
e
le
t te
ch
niq
u
e
is a
ti
me
-s
ca
le
do
ma
in
a
p
pro
a
ch,
w
h
i
c
h
is app
l
i
e
d
to
lo
c
a
t
e
shor
t
c
i
r
c
u
i
t
f
a
u
l
ts
a
n
d in
cip
i
en
t
f
a
u
l
ts
th
rou
gh
co
mp
ari
s
on
o
f
p
e
rfor
m
an
ce
du
rin
g
n
o
rm
al
op
e
r
at
io
n o
f
t
h
e
p
o
wer
tr
a
n
sf
orm
e
r
.
Th
e
f
o
ll
ow
ing
s
t
e
p
s
ou
t
lin
e
t
h
e f
a
u
l
t
d
e
te
c
tio
n
al
g
o
r
ith
m [2
3]
:
Step 1: Obtain
and r
e
c
o
rd
c
u
rrent s
i
gn
als from
power
tr
ansf
ormer
te
r
m
inals.
St
ep
2:
A
n
al
yz
e
t
h
e
si
g
n
al
a
p
pl
y
i
n
g
a
wa
ve
l
e
t
t
a
ke
n
from
a
wa
ve
le
t
famil
y
, f
o
r
the
req
u
i
r
ed
l
e
vel
o
f
dec
o
mp
osi
t
i
o
n.
St
ep 3:
Asses
s
t
h
e ap
pr
oxi
m
a
t
e
c
o
effic
i
e
n
ts a
n
d det
a
i
l
of
Di
sc
re
te
Wav
e
le
t Trans
f
o
r
m
wi
t
h
ti
me
th
ro
ugh
f
i
r
s
tly
p
l
o
t
tin
g a samp
le
—c
o
e
ff
ic
ien
t
grap
h.
Ste
p
4
:
Lo
ca
te
t
h
e
fau
l
t
v
i
a
wav
e
le
t
co
ef
fi
cien
t
in
t
e
rp
r
e
ta
ti
on
.
St
ep
5:
Di
ffer
ent
i
at
e fa
ul
t
c
u
rrent
(i
nci
p
i
e
nt
),
fro
m
i
n
t
e
rnal
sh
ort
ci
rc
ui
t
cu
rre
n
t
a
nd
ordi
n
a
ry
ope
ra
t
i
o
n
c
u
rre
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Si
m
u
li
nk
mo
de
l
o
f
tra
n
sf
o
r
m
e
r di
f
f
e
r
ent
i
al
prot
ec
ti
on
usi
n
g
p
has
e
an
gle
di
f
f
e
r
ence
…
(N
a
ssi
m A.
Iqt
e
i
t
)
1
091
D
i
scret
e
wa
vel
e
t
transfo
r
m i
s
a
l
so a
t
e
ch
ni
que
t
h
a
t
i
s
use
d
.
It c
a
n
be a
ppl
i
e
d
t
o
get
h
e
r
wi
t
h
bac
k
p
r
op
a
g
at
ion n
e
u
r
a
l
n
e
t
w
or
ks
and
is
a
p
p
l
ie
d
to
c
l
as
sify
d
i
ff
e
r
en
t
i
n
te
r
n
al f
a
u
lt
typ
e
s in
a
t
h
r
ee-
ph
ase
tr
a
n
sf
orm
e
r
[24
]
.
2.3.
P
h
ase
a
n
gle
dif
f
er
ence
(PAD)
pri
n
c
i
p
l
e
techni
q
u
e
To di
ffe
rent
i
a
t
e
t
h
e i
n
te
rnal
fa
ult
cu
rre
n
t
from a di
ffe
r
e
n
t
di
st
u
r
ba
nce
in a po
we
r trans
f
orme
r,
th
e
PAD
i
n
t
h
e fu
nd
a
m
en
t
a
l
fre
qu
en
cy
co
mp
on
en
ts wi
ll
be u
s
e
d
as th
e gu
id
e
[25
,
26
].
It is
no
t n
e
c
e
s
sary
th
a
t
th
e
ex
a
c
t PAD
is
u
s
e
d
.
The
lo
ca
tion
of
re
la
tiv
e
to
t
h
e
PAD
s
c
h
e
me
o
p
e
ra
ti
ng
c
h
ar
a
c
ter
i
st
ic
ca
n
be
est
i
m
a
t
e
d
t
o
fi
nd
the
st
at
us o
f
a gi
ve
n p
o
we
r
t
r
a
n
sf
o
r
mer.
F
i
gu
res 2
a
n
d 3
hi
g
h
l
i
ght
s
t
h
a
t
t
h
e ope
rat
i
n
g
m
o
de
of t
h
e p
o
w
e
r
t
r
ansfo
r
me
r i
s
th
e
ma
i
n
det
e
rmi
n
ant
of t
h
e
pri
n
ci
pl
e
of
Phas
e
An
gle
Di
ffe
renc
e.
U
n
d
e
r n
o
rmal
o
p
e
r
a
ti
on
a
s
we
ll
as
in
e
x
t
e
rn
a
l
f
a
u
l
t,
t
h
e
lin
e
cu
rr
e
n
ts
f
l
o
w
ar
e p
a
ra
ll
el
w
ith
t
h
e
v
a
rian
c
e
i
n
p
h
a
ses
b
e
i
n
g
a
l
mo
s
t
zero
a
s
show
n Figu
res 2(b
)
an
d
2
(
e) re
sp
e
c
t
i
v
e
l
y
.
H
o
w
e
v
e
r,
du
r
i
n
g
t
h
e
ma
gn
e
tiz
in
g inr
u
sh c
u
rr
en
ts,
th
e
PA
D
is app
r
ox
ima
t
e
l
y
9
0
o
sin
c
e
i
t
is
lar
g
e
l
y
in
du
ct
iv
e
as
see
n
i
n
Fi
g
u
r
e
2(
a).
Sub
j
ec
tin
g
th
e tr
ans
f
or
mer
to
w
i
nd
ing
shor
t c
u
r
r
en
t
r
e
v
e
rse
s
e
i
th
e
r
, if the
tr
an
sfo
r
me
r is e
xpo
sed
to a
wi
nd
ing
sh
o
r
t
c
i
r
c
u
it,
ei
th
er
I1
o
r
nI2 cu
rre
n
t
.
In
t
h
is ca
se the
PAD
bec
o
me
s g
r
eat
er tha
t
9
0
o
in t
u
rn-t
o-t
u
rn
fa
ult
an
d t
u
rn
-t
o-gro
u
n
d
fa
ul
t
as is
vi
si
bl
e i
n
F
i
g
u
r
e
s
2(c
)
a
nd
2(d
)
.
N
o
w
,
t
h
ro
ug
h usi
n
g Idi
f
f an
d Ire
s
, we
c
a
n est
i
mat
e
P
A
D
w
i
t
h
o
u
t
pl
ac
ing
muc
h
st
ra
in
o
n
t
h
e
rel
a
y
wit
h
grea
t
c
o
m
put
at
i
o
n
s
whi
c
h
w
o
uld
i
n
t
u
rn
sl
ow
i
t
s resp
o
n
se
.
Fi
gu
re
3
sh
o
w
s ho
w
t
o
est
i
m
a
t
e
P
A
D in
a po
we
r tr
ansfo
r
mer
o
n
d
i
ffere
n
t
ope
ra
ti
on
mode
s.
Fi
gu
re
2. P
A
D bet
w
e
e
n
the
5
0
H
z c
o
m
p
o
n
e
n
t
s
o
f
phas
e
A
respective
currents
.
(a
)
Magnetizing
i
n
rus
h
.
(b)
N
o
r
mal
l
o
a
d
i
n
g. (c
)
T
u
r
n
-t
o- gr
oun
d
faul
t
(d
)
T
u
r
n
-t
o-t
u
r
n
fa
ult
a
n
d
(e
) e
x
t
e
rna
l
fa
ult
(
A
C-G)
Fi
gu
re
3. P
h
a
s
o
r
di
a
g
ram
for
com
put
in
g
PA
D respe
c
t
i
ve
l
i
ne c
u
rre
n
ts:
N
o
rma
l
l
o
a
d
i
n
g,
ext
e
rna
l
fa
ul
t
s
,
ma
g
net
i
zi
n
g
i
n
rus
h
a
n
d
i
n
te
rn
al
f
a
ul
ts
2
nI
1
I
re
s
I
2
2
nI
d
iff
I
re
s
di
f
f
o
I
I
2
90
2
nI
1
I
re
s
I
2
2
nI
di
f
f
I
re
s
dif
f
o
I
I
2
90
2
nI
1
I
re
s
I
2
2
nI
di
f
f
I
re
s
diff
o
I
I
2
90
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
88
–
1
0
98
1
092
3.
M
O
D
E
L
I
NG OF
P
O
WER SY
S
TEM C
O
M
P
ON
EN
TS
3.1. Si
mu
li
n
k
m
o
del
of
p
o
w
e
r
sy
stem
F
i
gure
4
i
l
l
u
st
ra
te
s t
h
e
po
we
r s
y
st
em
’s
si
n
g
l
e
-l
i
n
e
dia
g
ra
m
use
d
i
n
t
h
e
st
ud
y.
T
h
e
sou
r
ces
E
s
∟
0
o
and
E
r
∟
be
hi
nd
s
e
ri
es
i
m
pe
danc
e
s
re
prese
n
t
t
r
a
n
s
m
i
ssio
n
and
di
st
ri
b
u
t
i
o
n
net
w
o
r
ks.
B
A
an
d BB
a
r
e
ci
rc
ui
t
br
eakers with
resistance
0.001
Ω
.
F
i
gu
re 4.
S
i
ngl
e-l
i
ne
di
ag
ra
m
of
si
mula
t
e
d p
o
we
r
s
y
st
e
m
F
i
gure 5 s
h
ow
s t
h
e S
i
mul
i
n
k
mo
de
l of t
h
e
el
eme
n
t
s
o
f
th
e
po
wer
syst
e
m
wi
t
h
the
pro
t
ec
ti
on re
la
y
.
Th
e pow
e
r
sy
ste
m
pa
r
a
m
e
ters in
Fi
g
u
r
e 5 (a
) ar
e
g
i
v
e
n i
n
t
h
e
A
p
pe
ndi
x. T
h
e
p
o
we
r
tra
n
sformer
i
n
Si
mul
i
n
k
mode
l
in
Fi
g
u
re 5(a
)
, ca
n
be
not
e
d
as i
n
Y/
Y t
o
get
h
e
r
s
h
o
w
i
n
g a
gro
u
n
d
e
d
neut
ra
l
t
oge
the
r
wi
t
h
a
2
5
M
V
A
ra
te
d c
a
pac
i
ty
and
13
8
k
V
/
13
.
8kV
rat
e
d
volt
a
ge
s. A
s
s
h
ow
n i
n
F
i
gu
re
5
(
b
)
,
t
h
e
p
o
we
r
t
r
a
n
sf
o
r
mer i
s
m
odel
e
d
f
o
r
c
a
l
cu
l
a
t
i
ng d
i
ff
er
en
t
o
p
e
ra
tin
g
mod
e
s, su
ch a
s
: in
te
rn
al fa
u
lts
,
no
rmal o
p
e
r
a
tion
and
magn
et
izi
n
g
in
ru
sh
c
u
rre
n
t
s.
W
e
can
simu
lat
e
the
op
e
r
ati
o
n
s
t
h
r
oug
h pow
e
r
tr
a
n
sfo
r
m
e
r
con
t
ro
l
sw
itch
e
s
S
1
,
S2
, S3
, S01
and
S0
2
wi
th B
A
a
n
d
BB
c
i
rc
ui
t b
r
ea
ke
rs.
Fi
gu
re
5. P
o
we
r
s
y
st
em wi
t
h
8
7
T
rel
a
y a
n
d P
A
D
sche
me:
(a
) t
h
ree
pha
se
di
agra
m (S
imul
i
n
k
mode
l
)
a
n
d
(b
)
Po
we
r t
r
a
n
sf
or
m
e
r
mo
de
l
(
p
h
a
s
e
A
)
o
s
E
0
o
r
E
Line
,
1
I
,
2
I
o
kV
0
13
8
o
kV
20
8
.
13
A
I
,
1
A
I
,
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Si
m
u
li
nk
mo
de
l
o
f
tra
n
sf
o
r
m
e
r di
f
f
e
r
ent
i
al
prot
ec
ti
on
usi
n
g
p
has
e
an
gle
di
f
f
e
r
ence
…
(N
a
ssi
m A.
Iqt
e
i
t
)
1
093
The
c
o
res a
n
d
wi
ndi
ngs
of t
r
ans
f
orme
r
i
s
mo
del
e
d
b
y
eq
ui
val
e
nt
ci
rc
ui
t
i
l
l
ust
r
a
t
ed
i
n
Fi
gu
re
6
(
a)
.
The (c
u
rre
nt–
fl
u
x
) c
h
a
r
a
c
t
eri
s
ti
c
s
of p
o
w
e
r
t
r
ans
f
o
r
me
r an
d CTs a
r
e sh
ow
n in
F
i
gu
re
s 6(
b) an
d 6
(
c)
.
The
ca
l
c
ul
at
io
ns
o
f
t
r
a
n
sf
orme
r are
re
fe
rred t
o
t
h
e
rel
a
y
si
de
(I1
,
nI
2).
A
si
n
g
le
π
-sec
ti
on
mo
d
e
ls t
h
e
tr
ansmissi
on line.
Fi
gu
re
6.
(a
) P
o
we
r
t
r
a
n
s
f
o
r
m
e
r si
n
g
l
e
pha
s
e
eq
ui
va
l
e
nt
ci
r
c
ui
t (
b
)
Po
we
r t
r
a
n
s
f
o
r
m
e
r c
u
rr
e
n
t
–
fl
u
x
ch
a
r
a
c
t
eri
s
tic
s an
d (
c
)
C
T
s cur
r
e
n
t
–
fl
u
x
c
h
a
r
ac
t
e
ri
s
t
ic
s
3.2. Si
mu
li
n
k
m
o
del
of
P
A
D
sch
e
me
an
d d
i
ffe
ren
ti
al
r
e
l
a
y
The
de
vel
o
pe
d
d
i
ffe
r
e
n
ti
a
l
re
la
y
w
i
t
h
PA
D sc
heme
i
s
i
m
pl
eme
n
t
e
d in
Si
m
u
li
nk
s
o
ft
wa
re
,
fo
r
e
v
al
uat
i
n
g
it
s per
f
o
r
ma
nc
e at
di
ffere
nt
o
p
e
r
at
i
n
g c
o
ndi
t
i
ons
o
f
t
h
e
p
o
w
e
r
t
r
a
n
sf
orme
r.
A
bl
oc
k
di
a
g
ra
ms
of
t
h
e
p
r
o
p
ose
d
dif
f
ere
n
t
i
a
l
rel
a
y
i
s
sh
o
w
n
i
n
Fi
gu
res
7
a
n
d
8. F
i
g
u
re
7 i
n
cl
ude
a
m
pe
r 2p
u
bl
oc
k
t
o
c
o
n
v
e
r
t
t
h
e p
h
ase sa
mpl
i
ng c
u
rre
nts
from CT
1&C
T
2 (
pha
se
A)
t
o
p
u
-va
l
ue
s.
The rel
a
y +
P
AD
bl
oc
k
of
p
h
a
s
e A
re
prese
n
t
s
t
h
e
di
ffe
re
nt
i
a
l
rel
a
y (
8
7
T
)
wi
t
h
a
ssoci
at
ed P
AD sc
heme
s.
Sc
o
p
e1 i
n
Fi
g
u
re
7 i
s
o
n
ly
use
d
to
d
e
te
rm
i
n
e
th
e
p
h
a
se
a
n
g
l
e
d
i
ff
ere
n
c
e
b
e
tw
een
I1
, A an
d nI2,
A
.
Th
e b
a
s
e
c
u
rr
en
t
fo
r t
h
e HV
-sid
e
i
s
5.23
A
,
w
h
il
e th
e
b
a
se
c
u
rre
nt
for t
h
e
LV
-
s
i
d
e is
4.
358 A.
Fi
gu
re 7.
Si
m
u
li
n
k
B
l
oc
k di
a
g
ra
m of
p
r
ot
ec
t
i
on
s
y
st
em (P
hase
A)
The
mo
de
l o
f
pe
rce
n
ta
ge
di
fferent
i
a
l
rel
a
y e
l
e
m
e
n
ts (p
ha
se
-A e
l
e
m
e
n
ts)
wi
t
h
P
A
D
rest
rai
n
t
sc
heme
i
s
de
pi
ct
ed i
n
Fi
gu
re
8, w
h
e
r
e t
h
e
ma
g
n
i
t
u
d
e
va
l
u
e
s
of Idi
f
f
(I1-
n
I2) and 2I
res
(I1
+nI
2
) a
r
e
co
mpu
t
ed u
s
ing
‘F
o
u
ri
er
a
n
al
y
z
e
r’ S
i
mul
i
n
k mo
de
l.
T
h
e
di
ffe
r
ent
i
a
l
rel
a
y char
act
e
r
i
s
t
i
cs
gi
ve
n b
y
(3
)
a
r
e
rep
r
e
s
e
n
t
e
d by
com
p
ara
t
o
r
s
2
an
d 3 al
on
g
wi
t
h
S
i
m
u
l
i
nk
em
bed
d
e
d
funct
i
o
n
f(
u
)
t
o
ge
ne
ra
t
e
X
a
n
d
Y
s
i
gnal
s
.
The di
ffe
r
e
n
ti
a
l
rel
a
y c
h
a
r
a
c
t
e
ri
st
ic
sho
w
n i
n
Fi
g
u
re
1 ha
s
bo
u
nda
ry
val
u
es:
Iop
1
i
s
0.2 p
u
, I
op2
is
0.
3 p
u
,
Ire
s
,
mi
n i
s
0.6
pu
a
n
d t
h
e sl
op
k e
qual
t
o
0.2. T
h
e
di
fferent
i
a
l
el
eme
n
t al
so i
n
v
o
l
v
es
i
n
st
ant
a
ne
o
u
s trip
fu
nct
i
o
n
u
s
i
n
g
com
p
ara
t
or
1
t
h
at
cre
a
t
e
s t
h
e
un
rest
ra
i
n
t
sig
n
a
l
UR
if
t
h
e
c
ondi
t
i
on:
Idi
ff
≥
20 pu
,
i
s
sat
i
sfie
d.
The
PAD
sc
he
me
i
s
c
h
aract
e
r
iz
ed b
y
c
o
mpa
r
at
or 4
to
p
r
o
d
u
ce
bl
oc
ki
n
g
o
r
rel
easi
n
g
si
g
n
al
PAD ac
co
rdi
n
g to
0
0.
2
0.
4
0.
6
0.
8
1
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
C
u
rr
en
t
(
pu)
F
l
ux
(
p
u)
0
0.
2
0.
4
0.
6
0.
8
1
0
2
4
6
8
10
12
C
u
rre
n
t
(p
u
)
F
l
ux
(
pu)
(
a
)
(
b
)
(
c
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
88
–
1
0
98
1
094
t
h
e trip
pi
n
g
c
r
i
t
e
ri
on
of
t
h
e
sc
he
me
. T
h
e fu
n
c
t
i
on f1
(u
)=
Id
i
f
f
-
0
.0
00
1
i
s
use
d
onl
y as
a
c
o
rre
c
t
i
on
fu
nc
ti
on t
o
co
rrect
som
e
mism
at
ch
Simu
lin
k
v
a
lu
es
. Th
e o
u
t
pu
t
signal o
f
AND1
g
a
t
e
i
s
u
s
ed
to
g
e
n
e
rate
8
7
T
d
i
f
f
er
en
t
i
al
re
la
y
si
gnal
.
Fi
nal
l
y
,
t
h
e
o
u
tp
ut
of OR
ga
te
i
s
use
d
t
o
gene
rat
e
t
h
e
fi
na
l t
r
i
p
si
gnal
(Tri
p_
A)
Fi
gu
re
8. Di
ffe
r
ent
i
al
rel
a
y (8
7T) wit
h
P
A
D
sc
heme
4.
SIM
U
LAT
I
ON
RE
SUL
T
S
AN
D A
N
A
L
Y
S
IS
Th
e
pow
er t
r
ansf
or
mer
in S
i
mu
lin
k
mod
e
l i
s
si
mu
la
te
d i
n
no
rma
l
l
o
a
d
in
g, in
te
r
n
al f
a
u
l
t an
d ex
te
rn
al
fa
ult
as
wel
l
a
s
ma
gne
ti
z
i
n
g
i
n
rush
o
p
e
r
at
i
ng mo
des.
The
foll
owi
n
g
Fi
g
u
res
9
-
13
dis
p
l
a
y t
h
e
p
h
ase
A
seco
nda
ry
c
u
rre
n
t
s
o
f
C
T
1 (a
),
an
d CT
2 (b)
i
n
p
u
val
u
es. The same
fi
gu
res
sh
o
w
the
o
u
t
p
ut sig
n
a
l
of
87T
di
ffe
re
nt
i
a
l
rel
a
y (c
), P
A
D
sc
heme (d
),
a
nd fina
l t
r
i
p
sig
n
a
l
of p
h
ase
A (e
). T
h
e si
mul
a
t
i
on ti
me
of
ou
r
mo
del
is
20
0
ms.
4.1. P
o
wer
tr
ans
f
orm
er
wi
th n
o
r
m
al
l
o
ad
i
n
g
In
no
r
m
al
load
ing
mo
d
e
,
the
co
nn
ec
ted
sw
it
ch
e
s
w
i
th
p
o
w
e
r
tr
ans
f
o
r
me
r
a
r
e
in
‘off’
po
si
tio
n,
and t
h
e
b
r
e
a
k
e
r
s BA
a
nd BB
a
r
e swit
c
h
e
d
on 2
5
ms a
f
t
e
r
t
h
e ru
n
n
in
g p
r
o
g
ra
m. In t
h
i
s
mo
de o
f
o
p
e
r
at
i
on,
t
h
e i
n
put
cu
rrent
s t
o
p
r
i
m
ary
have
the
sa
me
di
rect
i
o
n
of
the
c
u
rre
n
t
flo
w
from
t
h
e
se
co
n
d
ar
y
o
f
p
o
w
e
r
t
r
ans
f
o
r
me
r. F
o
r
t
h
is
re
a
s
o
n
, the
out
put
sig
n
a
l
s
of 8
7
T a
n
d
PA
D
are
z
e
r
o ca
u
s
i
n
g
t
h
e
fi
nal
t
r
ip
to
be
ze
ro,
a
s
s
how
n i
n
F
i
g
u
r
e
9
.
F
i
g
u
re 9
.
R
e
sp
ons
e of
t
h
e
P
A
D
-
b
a
s
ed
a
l
gor
it
h
m
t
o
nor
ma
l lo
a
d
ing
4.2. P
o
wer
tr
ans
f
orm
er
wi
th ma
gn
e
t
i
z
i
n
g i
n
r
u
sh
cu
rre
nt
Th
e tr
an
sf
or
me
r mo
d
e
l i
s
pr
ov
id
ed
wi
th
a
n
on-l
i
n
e
ar
i
n
du
c
t
or
L
m
c
onne
ct
e
d
a
s
sh
ow
n i
n
t
h
e
Fi
gu
re
6(a
)
f
o
r
eac
h
p
h
a
s
e.
L
m
i
s
use
d
t
o
a
c
c
ou
nt
m
a
g
n
et
i
z
i
ng c
u
rre
nt re
pre
s
e
n
ta
t
i
on
. T
h
e
po
we
r t
r
a
n
sfo
r
me
r
cha
r
ac
te
ri
sti
c
s (
curr
ent
–
f
l
ux
) of
L
m
a
r
e
de
pi
ct
ed i
n
F
i
gu
re
6(b). T
h
e
ma
gne
t
i
z
i
ng
i
n
rus
h
c
u
rre
n
t
c
a
n
b
e
0
0.
0
5
0.
1
0.
1
5
0.
2
-2
0
2
i
a
1 (
pu)
0
0.
0
5
0.
1
0.
1
5
0.
2
-2
0
2
(b
)
ia
2
(
p
u
)
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
1
2
(c
)
87
T r
e
l
a
y
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
1
2
(d
)
PAD
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
1
2
(e
)
Ti
m
e
F
i
n
a
l T
r
ip
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Si
m
u
l
i
n
k
m
o
d
e
l
of
t
r
a
n
sfo
r
me
r
di
ff
ere
n
ti
al
p
r
ot
ect
i
o
n
usi
n
g
p
has
e
angl
e
di
ff
e
r
e
n
ce
…
(
N
a
s
sim
A.
I
q
t
e
i
t
)
1
095
si
mula
te
d
b
y
s
w
it
c
h
i
n
g
o
f
f
al
l
swi
t
c
hes
a
n
d
brea
ker
s
on t
h
e
LV
si
de
of
pow
er
t
r
a
n
sf
o
r
me
r, a
n
d cl
osin
g
c
i
rc
uit
br
ea
ke
r
B
A
.
F
i
gu
res
10(
a
)
a
n
d
10
(
b
)
co
m
p
ar
es
t
h
e
pr
op
ose
d
Si
muli
n
k
m
odel
a
n
d
E
M
TP
-R
V
si
m
u
la
ti
on
p
a
c
k
ag
e
[1]
i
n
th
e ca
se
o
f
i
n
ru
s
h
c
u
rr
e
n
t
s
,
w
h
er
e
th
e r
e
sul
t
s w
e
r
e
fo
un
d clo
s
e
to
e
a
c
h
o
t
h
e
r
.
In th
e ob
ta
in
e
d
re
su
lt
s
of
Fi
g
u
r
e
1
0
(
a
), th
e br
ea
k
e
r
B
A
was
sw
itch
e
d on af
te
r
on
e
cy
c
l
e of
r
unn
in
g
mo
d
e
l.
A
ma
gn
e
t
iz
in
g
in
ru
sh
cur
r
e
n
t
o
f
amp
lit
ud
e
up
to
8
tim
es t
h
e
tr
an
sfor
mer
ra
te
d
c
u
r
r
en
t is
si
mu
la
te
d
.
I
t
i
s
ob
v
i
o
u
s
t
h
at
su
ch
in
ru
sh c
u
rr
en
t
ca
u
s
es th
e
mal
-
op
e
r
at
ion
o
f
th
e
d
i
ff
er
en
tia
l re
la
y
.
N
e
v
e
rt
h
e
le
ss, th
e
ou
t
p
u
t
sign
a
l
o
f
PAD
sch
e
me is ze
ro log
i
c
and th
e
P
A
D
d
e
c
i
sion is sta
b
le a
nd ind
e
p
e
nd
en
t
o
f
t
h
e mag
n
itud
e
o
f
th
e i
n
ru
sh
cu
rre
n
t
.
Fin
a
ll
y
,
t
h
e
tr
an
sfo
r
mer
bre
a
ker
s
w
ill
n
o
t
t
r
ip.
F
i
g
u
r
e
10.
R
e
s
p
o
n
se
o
f
t
h
e
P
A
D
-
ba
se
d al
g
o
r
i
t
h
m t
o
ma
g
n
e
t
i
z
i
ng
i
n
rus
h
c
u
r
r
e
n
t,
(a
) P
r
op
ose
d
Si
m
u
li
n
k
mo
del
,
(b
) E
M
TP-R
V
si
m
u
l
a
t
i
on
pac
k
a
g
e
[
1
]
4.
3.
P
o
we
r
t
r
an
sf
orm
e
r
w
i
t
h
tur
n
to
gr
ou
n
d
f
a
ul
t
Fi
gu
re
11
p
r
e
s
ent
s
t
h
e
pe
r
f
o
r
m
anc
e
o
f
t
h
e
p
e
rc
ent
a
ge
di
ff
e
r
e
n
ti
a
l
re
l
a
y
8
7
T
a
n
d the
P
A
D
sche
me
t
o
a
tu
rn-
t
o-
gr
oun
d
fau
l
t
o
ccu
rr
e
d
wh
en
t
h
e
sw
it
ch
e
s
S
1
&S
01
a
r
e c
l
o
s
ed
.
F
i
g
u
r
e
1
1
(
a)
sh
ow
s th
e
r
e
su
l
t
s of t
h
e
pr
opose
d
Si
m
u
li
nk
m
o
del
w
h
er
eas
F
i
gu
re
11
(
b
)
i
l
l
u
st
rat
e
s
the
res
u
l
t
s
o
f
usi
n
g
t
h
e
E
M
TP
-
R
V
si
m
u
la
t
i
o
n
p
a
c
k
ag
e and
ap
p
l
y
i
ng
PAD [1
].
Th
e
r
e
su
lt
s
o
f
bo
th
m
e
th
od
s
w
e
re
sim
ilar
to
e
a
c
h
o
t
h
e
r. Th
e fa
u
l
t
is i
n
itia
te
d
at
ti
me
t
= 25
ms
w
ith
ze
ro
fau
l
t r
e
sist
an
c
e
. B
o
th
d
i
ffe
r
e
n
tia
l r
e
lay
an
d
PAD
sc
h
e
m
e
h
a
v
e
t
h
e
ab
i
lity
t
o
d
e
t
e
c
t
th
e
f
a
u
lt,
b
u
t
w
ith
d
i
ff
er
en
t
time
in
st
an
ts
a
s
a
p
p
ear
e
d
in
th
e
fi
gure
.
Th
e
d
i
f
f
er
en
t time
in
sta
n
ts
i
s
d
u
e
to
th
e
ut
i
l
i
z
at
ion of
Di
scre
te
F
o
ur
i
e
r
T
r
ans
f
orm
(
D
FT
) f
o
r
c
a
l
c
ul
at
i
ng
t
h
e
ma
gni
tu
de
val
u
es
of
the
dif
f
er
e
n
t
i
a
l
and
re
str
a
in
t cu
rrents
.
Th
e
fi
n
a
l t
r
ip
sign
a
l
is r
e
lease
d
o
n
l
y
for
th
e
fau
lte
d
ph
ase
,
le
a
d
ing
t
o
th
e
d
i
s
c
on
n
e
c
t
i
o
n of
t
h
e p
o
w
er t
r
an
sfo
r
me
r from
t
h
e tot
a
l
po
we
r
syste
m
.
F
i
gu
r
e
1
1
.
R
e
s
p
o
n
se
o
f
t
h
e
P
A
D
-
ba
sed
al
g
o
r
i
t
hm t
o
tu
r
n
-t
o-
gr
o
u
n
d
f
a
ul
t.
(
A
)
Pr
op
ose
d
Si
muli
n
k
m
o
de
l
,
(B
)
EM
TP
-RV
si
mu
la
tio
n
p
ac
ka
g
e [1
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 10
88
–
1
0
98
1
096
4.4. P
o
wer
tr
ans
f
orm
er
wi
th tu
r
n
to
tu
r
n
faul
t
Tu
rn-
t
o
-
t
u
rn
fa
u
lt
is te
ste
d
i
n
Fig
u
r
e
12
wh
e
n
S
1
o
f
Ph
ase
-
A
is
cl
o
s
ed at
tim
e
t =
2
5
ms.
I
n
t
h
e
simul
a
t
i
on
res
u
l
t
bot
h
di
ffe
r
ent
i
a
l
rel
a
y
an
d P
AD sc
he
me
ca
n see
t
h
e
fa
ult
,
b
u
t
wi
th
diffe
r
e
n
t
ti
me
inst
ant
s
.
In t
h
i
s
ca
se
, P
A
D
sc
he
me si
gnal
i
s
t
h
e sa
me fi
nal
trip
pi
ng
si
g
n
al
a
n
d
it
ca
n
l
e
a
d
t
o
di
sc
o
n
n
ect
the
pow
e
r
tr
a
n
sf
orm
e
r
from to
t
a
l pow
e
r
sy
st
em
w
ith
f
a
s
t
r
e
sp
on
se
.
Fi
g
ur
e
12
.
Res
p
on
se of
t
h
e
P
A
D-
b
ased a
l
g
or
ith
m
to
turn
-
t
o
-
t
u
rn
fa
u
lt
4.
5.
Ex
te
rn
al
fau
l
t
(A
C
G
f
a
ul
t)
The
PA
D ba
se
d
al
gori
t
hm
i
s
al
so t
e
st
ed
fo
r
ext
e
r
n
al
fa
ult
(ACG). Thi
s
fa
ult
i
s
l
o
ca
te
d
o
n
t
h
e l
o
w-
vol
ta
ge
te
rmin
a
l
s o
f
the
po
we
r
t
r
a
n
sform
e
r, a
n
d
i
t
i
s
i
n
i
t
i
a
t
e
d
a
t
25
ms, wi
t
h
fa
ul
t re
si
st
ance
0.
0
0
1
Ω
.
The
sta
t
us
o
f
t
h
e
pro
p
o
s
ed
re
l
a
y i
s
s
h
ow
n
in
F
i
g
u
re
13
. A
s
see
n
, the
fi
na
l
t
r
i
p
si
gnal
i
s
z
e
r
o
l
ogi
c
be
ca
use t
h
e
CT
1
a
nd
CT
2
c
u
r
r
ent
s
flo
w
i
n
t
h
e sa
me
di
re
ct
ion a
n
d le
ss t
h
a
n
20
pu.
Fi
g
ur
e
13
.
Re
s
p
on
se of
th
e PAD-
b
a
s
ed
al
g
or
ith
m
to
A
C
-G
ex
t
e
rn
a
l
f
a
u
lt
5.
CO
NCL
U
S
I
O
N
In
t
h
i
s
pa
per
t
h
e t
r
a
n
sfo
r
me
r di
ffe
r
e
n
t
i
al
prot
ect
i
on
wit
h
P
A
D
base
d
al
gori
t
hm i
s
mo
del
e
d by
Si
muli
n
k
pac
k
a
g
e.
I
n
S
i
mul
i
nk mo
del
,
t
h
e
po
we
r
t
r
a
n
s
f
ormer a
nd
a
l
l
cu
rrent
tra
n
sfo
r
m
e
rs a
r
e
re
p
r
ese
n
t
e
d by
re
al
e
q
uiva
l
e
n
t
c
i
rcui
t
.
Al
so, n
o
n
-l
ine
a
r
i
n
duct
a
nc
e is
us
ed t
o
re
pre
s
en
t
t
h
e
ma
gne
ti
z
a
t
i
on e
f
fec
t
s.
Thi
s
n
o
n
l
in
e
a
r
ity
c
a
u
s
es
ma
l-op
e
r
ati
o
n i
n
p
e
r
cen
ta
g
e
d
i
ff
e
r
en
ti
a
l
r
e
la
y.
Th
e
a
l
g
o
r
ith
m
o
f
tr
an
sfo
r
m
e
r d
i
ffer
e
n
t
ia
l
prot
ec
ti
on
re
la
y
was
de
vel
o
p
e
d
b
y
a
ddi
n
g
P
A
D
based
a
l
g
o
r
i
t
hm; t
h
i
s
i
m
p
r
o
v
eme
n
t
i
s
use
d
t
o
s
o
l
v
e
t
h
e
mal
-
ope
ra
t
i
o
n
of t
r
ans
f
orme
r
dif
f
ere
n
t
i
a
l
p
r
ote
c
t
i
on
o
n
m
a
g
n
et
i
z
i
n
g
i
n
rus
h
c
u
r
r
e
n
t
s
. T
h
e S
i
m
u
l
i
nk
m
odel
is
simul
a
t
e
d at
di
ffe
r
ent
m
o
des:
no
rma
l
l
o
a
d
i
n
g
,
inr
u
sh cu
rre
n
t
s
a
nd
i
n
t
e
rna
l
a
n
d e
x
t
e
rnal
fa
ul
t
s
. The si
mul
a
t
i
on
re
sul
t
s
s
h
o
w
th
a
t
t
h
e
pr
o
pose
d
a
l
go
ri
t
h
m has
go
od re
li
a
b
i
l
i
t
y,
l
a
r
g
el
y
i
nde
pe
nde
nt o
f
ha
rmo
n
i
c
co
nt
ent
s
i
n
t
h
e
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
0
10
i
a1 (
pu)
0
0.
0
5
0.
1
0.
1
5
0.
2
-2
0
2
(b)
i
a
2 (
p
u)
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
1
2
X
:
0.026
39
Y:
1
(c
)
87
T r
e
l
a
y
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
1
2
X
:
0.
0371
5
Y:
1
(d)
PAD
0
0.
0
5
0.
1
0.
1
5
0.
2
-1
0
1
2
(e)
Ti
m
e
F
i
n
a
l T
r
ip
0
0.
05
0.
1
0.
1
5
0.
2
-20
0
20
ia
1
(
p
u
)
0
0.
05
0.
1
0.
1
5
0.
2
-20
0
20
(b
)
ia
2
(
p
u
)
0
0.
05
0.
1
0.
1
5
0.
2
-1
0
1
2
(c
)
87
T
rel
a
y
0
0.
05
0.
1
0.
1
5
0.
2
-1
0
1
2
(d
)
PAD
0
0.
05
0.
1
0.
1
5
0.
2
-1
0
1
2
(e
)
Ti
m
e
Fi
n
a
l
Tr
i
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Si
m
u
li
nk
mo
de
l
o
f
tra
n
sf
o
r
m
e
r di
f
f
e
r
ent
i
al
prot
ec
ti
on
usi
n
g
p
has
e
an
gle
di
f
f
e
r
ence
…
(N
a
ssi
m A.
Iqt
e
i
t
)
1
097
di
ffe
re
nt
i
a
l
c
u
rre
n
t,
a
n
d
tra
n
sformer pa
ramet
e
rs. Si
m
u
li
nk
mo
de
l s
h
ows
t
h
a
t
t
h
e
pro
pos
ed al
go
ri
thm
d
o
es
not
re
qui
re
c
o
mpl
e
x c
o
m
puta
t
i
o
n a
n
d
c
a
n
be
ea
si
l
y
inc
o
rp
orat
e
d
int
o
e
x
i
s
t
i
n
g d
i
gi
ta
l di
ffe
rent
i
a
l
re
l
a
ys.
APPE
NDI
X
Tabl
e 1
P
o
wer Syst
em
P
a
ra
m
e
t
e
rs
Pa
ram
e
t
e
r
s
va
l
u
e
Sour
ce
1:
Sour
ce
2:
Pow
e
r
Tr
an
s
f
o
r
mer
CT
1: 100/5 A
CT
2: 1200/5A
L
i
ne pa
ram
e
t
e
r
s
E
s
=
138
kV
∟
0o /50H
z ,
R
+
=
7.
1
Ω
,
L
+
=
53.
99
m
H
R
0
=7.
159
6
Ω
,
L0=115.
45m
H
E
r
=13.
8kV
∟
20o /50H
z ,
R
+=1.
4
Ω
, L
+
=5.
6m
H
R
0
=1.
498
Ω
,
L
0=11.
975m
H
25M
V
A
,
1
38kV
/13.
8kV
,
R
1=0.
908
Ω
,
R2=
0
.
0091
Ω
L
1
=
7
8
.
51m
H
,
L
2
=
0
.
7851m
H
,
Rc=
1
.
19M
Ω
L
m
=fl
u
x/
cur
r
e
n
t (pu
)
/ F
i
gure
6(b)
.
25V
A
,
0.25/
5
V
,
50H
z,
R1=
2
.
5
μΩ
, R
2
=1
m
Ω
L
1
=
0
.31831
μ
H
,
L
2
=0.
1273
2m
H
,
Rc
=
0
.
2
5
Ω
L
m
=fl
u
x/
cur
r
e
n
t (pu
)
/ F
i
gure
6(c).
25V
A
,
0.020833/
5
V
, 50Hz
,
R1=
17.361n
Ω
, R
2
=1
m
Ω
,
L
1
=
2
.2105nH
,
L
2=0.
12732m
H
R
c
=
1
.7361m
Ω
, L
m
=f
lu
x
/
c
u
rr
en
t
(p
u
)
/
F
i
gure
6 (c
).
R
0
= 0.
1437
Ω
,
R1 = 0.
3101
Ω
L
0
= 1
1
.
45 m
H
,
L
1
= 2.
41 mH
,
C0
=
5.
6
35 nF
,
C1 = 26.
8 nF ,
le
n
g
th= 1km
.
RE
FERE
NC
E
S
[1]
A. H
o
sn
y,
an
d
V.K
.
S
ood
,
“
T
ra
ns
former
d
i
ffere
n
t
ial pro
t
ec
tion
w
i
th ph
as
e
an
gle
di
ffer
e
n
c
e bas
e
d inrush
res
t
r
a
int
”
El
e
c
tri
c
P
o
w
e
r
S
y
st
ems
Res
e
ar
ch
,
vo
l.
11
5, p
p
.
57-6
4
,
20
14.
[2]
S.H. Horowitz
,
A.G
.
Phadke
, Po
we
r
Sy
ste
m
Re
layi
ng
,
3
r
d e
d
.
,
Jo
hn
W
i
ley
&
So
ns
L
t
d
,
pp
.19
5
-2
01
, 20
08
.
[3]
N.
Ya
dai
a
h, a
n
d
N.
Ra
v
i
,
“
I
nte
r
n
a
l fa
ult
de
te
c
tion
t
e
c
h
ni
que
s
fo
r p
o
w
e
r
tra
n
sform
e
rs”
,
Appl
i
e
d Soft
C
o
mputi
n
g
,
vo
l. 11
pp
.
52
59
-52
69,
20
11
.
[4]
A.
M.
Ma
hm
ou
d
,
M
.
F.
E
l
-
N
a
g
gar,
a
nd E.H.
Sh
e
h
a
b
_
E
l
d
i
n
a, “A N
e
w Tech
niqu
e
f
o
r
P
o
wer Tr
ans
f
ormer P
r
otect
io
n
Based on
Tran
s
i
ent
Co
mpo
n
e
n
ts”,
Int
e
rn
atio
n
a
l
Co
nf
erenc
e
on
Adv
a
n
ces
in
En
erg
y
Eng
i
neer
in
g, IC
AEE
,
p
p
.
31
8
-
32
4
,
201
1.
[5]
Wiszn
i
ews
k
i, A
.
and
Kaszt
e
nn
y, B.
“A
mu
lti
-
crit
eria
d
i
ff
ere
n
tial
tr
ans
f
orme
r rel
a
y b
a
s
e
d
o
n
fu
zzy
log
i
c”
.
IE
EE Transacti
o
n
s on P
o
wer Delive
r
y
,
10
(4),
p
p
.1
78
6-1
7
9
2
,
1
995.
[6]
Tripa
t
h
y
,
M
.
“P
o
w
er Trans
f
orm
e
r D
i
ffer
e
nt
ial
P
r
otec
tio
n
B
a
sed
on
Neu
r
al N
e
tw
ork
P
r
in
cip
a
l Co
m
p
on
ent
An
aly
s
is,
Harmoni
c
R
e
st
r
a
int
a
n
d Pa
rk
's Pl
o
t
s”
.
Advances
in A
r
t
ificial Intel
l
i
g
ence
, pp
.1
-9, 201
2
.
[7]
Krishn
amurthy
,
S
.
,
E
l
eng
a
Ban
i
ng
ob
era,
B.
I
E
C6
18
50
“stand
ard
-
bas
e
d
har
m
o
n
i
c
blo
c
king
s
c
h
e
me fo
r po
we
r
t
r
ansformers
”.
Pro
t
Co
nt
ro
l M
od Po
we
r Sy
st
,
4,
1
0
, 20
19
.
[8]
Go
uda, O.E., El
Dein, A.Z. &
M
o
u
k
h
t
ar, I
.
“P
erforman
ce
of trans
f
ormer different
i
a
l
r
e
l
a
y at
di
fferent neutral
g
r
ou
nd
i
n
g
re
si
sta
n
c
e
b
a
se
d on
w
a
v
e
le
t
tra
n
sform”
.
El
ectr
En
g
9
9
,
27
5-28
4,
20
17.
[9]
Krs
t
ivojevi
c
,
J
.
,
& D
j
u
r
ic
,
M
.
“
A
n
e
w
algo
rith
m
for
av
oid
i
ng
malo
p
e
rat
i
on
o
f
trans
f
orm
e
r r
e
s
t
rict
ed
ear
th
f
a
u
lt
pro
t
ec
tion
c
a
us
ed b
y
the
tra
n
s
f
ormer
magn
eti
z
in
g
in
ru
sh
cur
r
ent
and
curren
t
trans
f
or
mer
satur
a
tio
n
”
.
Tu
rk
i
s
h J
o
u
r
na
l
o
f
El
e
c
t
r
i
c
al Engi
ne
e
r
i
ng &
Compu
t
e
r
Sc
ie
nc
e
s
,
24
, 5
0
2
5
-
50
42
, 20
16
.
[10]
Kau
r
, A., Br
ar
, Y
., &
G
.
,
L.
“Fau
lt
de
te
ction
in
pow
er
tr
an
sformers
us
ing
rand
o
m
n
e
ural
n
e
tw
ork
s
”.
I
n
t
e
rna
t
i
o
n
a
l
Jo
ur
na
l Of
El
e
c
tr
i
c
al
An
d C
o
m
p
u
t
er E
n
g
i
n
e
er
in
g (
I
J
EC
E
)
, 9(1
)
, 78
. do
i: 10
.
1
15
91
/ije
ce
.v
9i1
.
p
p
.
78
-8
4
,
20
19.
[11]
Ou
tzgu
in
r
i
m
t
,
H., C
h
r
a
y
g
an
e, M
.
,
Laha
me
, M
.
,
Ou
mgh
a
r
,
R
.
, B
a
t
i
t
,
R
.,
& Fer
f
r
a, M
.
“M
od
el
i
n
g o
f
t
h
r
e
e-
l
i
m
b
th
ree-ph
as
e tr
an
s
f
o
r
mer rel
a
tes
t
o
shu
n
t co
re u
s
i
n
g
in
in
dus
tri
a
l
microw
av
e
gen
e
rators
w
i
th
n=2
mag
n
e
t
ro
n
per
ph
ase”.
Inte
rnat
io
na
l J
o
u
r
nal o
f
E
l
e
c
t
r
i
c
al an
d
Comput
e
r
En
gi
n
e
e
r
i
n
g
(IJ
E
CE
)
,
9
(
6),
45
56
.
d
o
i
:
10
.11
5
9
1
/ijec
e.
v
9
i6.
pp
45
56-4
5
6
5
, 201
9
.
[12]
J.K
.
B
l
ad
ow,
A
.
“M
on
to
ya
Ex
p
e
r
i
en
c
e
s wi
th
p
a
r
a
ll
el
EHV
phas
e
shifting
tr
ans
f
ormer I
E
EE Trans
”
.
P
o
w
e
r De
l
i
v
.,
6
(3), pp
.
1
0
9
6
-
1
1
00
,
19
91.
[13]
Alsh
a
r
if,
M., Y
a
hy
a
,
K.
and
G
eem,
Z.,
“S
trate
g
ic M
a
rk
et
G
r
owth and
P
o
licy
Recomm
en
da
tio
n
s
fo
r
S
u
stain
a
b
l
e
S
o
lar En
ergy
De
ploy
ment
in
S
o
u
t
h
Ko
rea”.
Jou
r
n
a
l
of
El
ec
trical
En
gine
er
ing
&
T
ech
nolog
y
,
2
019
.
[14]
Je
bu
r,
I.
a
n
d
H
a
m
e
e
d
, K.
“
E
valu
a
t
i
on a
n
d
im
p
r
o
v
e
m
e
n
t
of th
e m
a
in
in
sula
ti
o
n
st
ru
c
t
u
r
e
of 33
kV di
st
ri
bu
ti
on
tran
sformer
base
d
o
n
FEM
”
.
Indo
ne
sia
n
J
o
urna
l o
f
Ele
ct
ri
c
a
l E
ngi
ne
e
r
in
g
a
n
d
Co
mpu
t
e
r
S
c
ie
nc
e
(IJEECS)
, 15(1)
,
p. 36
,
20
19
.
[15]
Kareem
, O.,
A
d
ekitan, A. and Awelewa
, A.
“Power dist
ribu
t
i
on
s
y
s
t
em
faul
t
m
o
nit
o
ri
ng device for suppl
y
network
s
in Nig
e
ria
.
In
terna
t
ion
a
l Jou
r
n
a
l
of
El
e
c
trical
an
d
Com
p
uter Eng
i
neer
in
g (IJEC
E)
,
9
(
4),
p. 2
8
0
3
,
20
19
.
[16]
Badri,
R
.
and
H
o
cine,
L.
,
“D
iagn
os
is
w
i
n
d
ing
sh
ort-c
i
rcu
it
fa
ults
o
f
p
o
wer
tran
sformer”
.
Glo
b
a
l
J
o
urna
l
of
Com
puter Scien
ces:
T
h
eory
and
Resear
ch
,
8(2)
,
pp
.70
-
78
,
2
018
.
Evaluation Warning : The document was created with Spire.PDF for Python.