Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 3
,
Sep
t
em
b
e
r
2015
, pp
. 42
3
~
42
8
I
S
SN
: 208
8-8
6
9
4
4
23
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Analysis
of
M
o
deling of
Current Differenti
al P
r
otection
D
e
nis B. So
lovev
,
A
n
g
e
lina I. Ma
keeva
Engineering Sch
ool, Dep
a
rtment
of
Innovatics, Far Eastern Fed
e
ral Univer
sity
(FEFU), Russian Federation
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 21, 2015
Rev
i
sed
May 13
, 20
15
Accepte
d
J
u
n 5, 2015
Anal
y
s
is of tran
sients in longitu
dinal
diff
erential protection schemes is given
basing on results obtained
b
y
simulati
on. Simulation d
i
agr
a
m for modeling
differen
tial protection with
cur
r
ent tr
ansformers with non-linear cores is
proposed. Main
shortcomings of using
current transformers as measuring
transducers
are s
hown. Solutions
of the problem r
e
vealed
are prop
osed.
Keyword:
B
u
sba
r
pr
ot
ect
i
o
n
Cu
rren
t tran
sform
e
rs
Differen
tial p
r
o
t
ectio
n
Ro
go
wsk
y
co
ils
Transien
t sim
u
latio
n
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Deni
s
B
.
S
o
l
o
v
e
v,
En
gi
neeri
n
g
sc
ho
ol
,
De
part
m
e
nt
o
f
In
n
ovat
i
cs,
Far Ea
stern Fe
deral
Un
iv
ersity (FEFU),
City o
f
Vlad
ivo
s
tok
,
Ru
ssk
y
Island
, R
u
ssian Fed
e
ration
.
Em
a
il: so
lo
v
e
v.db
@dv
f
u
.
ru
1.
INTRODUCTION
Cu
rren
t d
i
fferen
tial
p
r
o
t
ectio
ns
are
p
r
o
t
ection
s
with
ab
so
l
u
t
e
selectiv
ity co
m
p
arin
g
cu
rren
ts eith
er at
th
e term
in
als
o
f
an
elem
en
t
to
b
e
p
r
o
t
ected
or in
p
a
rallel circu
its o
f
el
ectric in
stallati
o
n
s
. Th
e first typ
e
of
su
ch
pro
t
ectio
n
s
is called long
itu
d
i
n
a
l curren
t d
i
fferen
tial
p
r
o
t
ectio
n wh
ile th
e
o
t
h
e
r
–
tran
sv
erse d
i
fferen
tial
pr
ot
ect
i
o
n
[
1
–2
]
.
Transv
erse d
i
fferen
tial p
r
o
t
ectio
n
con
t
ro
ls
th
e equ
a
lity o
f
cu
rren
ts in
p
a
rallel tran
sm
is
sio
n
lin
es
o
r
p
a
rallel bran
ches of
wind
ing
s
in
la
rg
e transfo
r
m
e
rs or
ro
tat
i
n
g
m
ach
in
es.
Lon
g
itud
i
n
a
l
differen
tial pro
t
ectio
n
is
m
o
re widespread tha
n
the trans
v
erse
o
n
e.
I
t
i
s
used for
pr
ot
ect
i
on o
f
l
i
n
e
s
, bu
sba
r
s, rea
c
t
o
rs, a
nd wi
n
d
i
n
gs
of
t
r
an
sf
orm
e
rs an
d
ot
he
r el
ect
ri
c m
achi
n
es.
That
i
s
why
o
n
l
y
l
ongi
t
u
di
nal
pr
ot
ect
i
o
n
i
s
di
scusse
d
bel
o
w.
In m
o
st
exi
s
t
i
ng di
f
f
ere
n
t
i
a
l
prot
ect
i
o
ns m
e
asurem
ent
of cu
rre
nt
s i
s
done
wi
t
h
cur
r
e
n
t
t
r
ansf
o
r
m
e
rs
(CTs). T
h
e CT
s connected at
the term
inals of
protected
elemen
t m
u
st h
a
ve id
en
tical p
a
ra
m
e
ters su
ch
as rated
v
a
lu
es of
p
r
imar
y and
second
ar
y cu
rr
e
n
ts,
core
sizes, a
nd core m
a
terial.
Th
e ex
cep
tion
s
with
t
h
e rule are
di
ffe
re
nt
i
a
l
prot
ect
i
ons
of t
r
ansf
o
r
m
e
rs where C
T
s i
n
st
al
l
e
d o
n
HV
, M
V
, an
d LV si
d
e
s of t
h
e t
r
an
s
f
o
r
m
e
r
have
di
f
f
ere
n
t
t
r
ans
f
o
r
m
a
ti
on
rat
i
o
s.
Im
pl
em
ent
a
t
i
on feat
ures
o
f
t
r
an
sf
o
r
m
e
r di
ffere
nt
i
a
l
pr
ot
ect
i
ons
are wel
l
kn
o
w
n
f
r
om
co
urse
b
o
oks
[
1
–
2
]
an
d
n
o
t
di
sc
usse
d i
n
t
h
i
s
a
r
t
i
c
l
e
.
2.
THE PROPOSED
METHOD
C
u
r
r
ent
di
ffe
re
nt
i
a
l
pr
ot
ect
i
ons are
us
ual
l
y
base
d o
n
t
h
e
schem
e
wi
t
h
ci
rcul
at
i
ng c
u
rr
ent
s
. I
n
t
h
i
s
case the secondary
windings
of t
h
e CT
s on
the term
inals of the
protected
ele
m
ent are connected t
o
the relay
terminals so that the secondary curre
nt
s of th
ese CTs are i
n
op
po
site d
i
rectio
n
relativ
e to
th
e relay termin
als
[
1–2
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
42
3 – 428
42
4
During norm
al ope
ration
of the protected el
e
m
ent wh
en c
u
rre
nts at its en
ds are equal and fall withi
n
t
h
e rat
e
d
ra
nge
t
h
e seco
n
d
ary
cur
r
ent
s
of
b
o
t
h
C
T
s are
ap
pr
oxi
m
a
t
e
l
y
equal
.
The c
u
r
r
en
t
fl
owi
ng t
h
r
o
u
gh t
h
e
relay is called
"i
m
b
alan
ce cu
rren
t".
It is neg
lig
ib
ly sm
all
an
d is d
e
term
in
ed
b
y
th
e
d
i
fferen
ce
b
e
tween
the
m
a
gnet
i
z
i
ng c
u
r
r
ent
s
o
f
t
h
e
C
T
s. T
h
i
s
di
ff
erence i
s
caus
e
d
by
som
e
di
ffe
rence
bet
w
e
e
n t
h
e
pa
ram
e
ters
o
f
their c
o
res
at low e.m
.
f.
of t
h
e secondary
windi
ngs.
In case
o
f
in
sulatio
n
fau
lt in
th
e pro
t
ected
ele
m
en
t sh
ort circu
it curren
t
i
SC
starts to
flow fro
m
th
e
faulty elem
ent
to the ea
rth
or
othe
r phases
, a
n
d the
pr
im
ary curre
n
ts of the CTs bec
o
m
e
une
qual.
As a
result
the im
balance curre
nt,
i
р
, fl
o
w
s t
h
ro
ugh
th
e relay. It is ap
prox
im
ate
l
y eq
u
a
l to
i
SC
/
n
, w
h
e
r
e
n
is th
e CT
tran
sform
a
t
i
o
n
ratio
.
The im
balance current also
appea
r
s i
f
due
t
o
a sh
ort
ci
r
c
ui
t
out
si
de t
h
e pr
ot
ect
ed el
em
ent
hi
g
h
currents
flow t
h
rough t
h
e ele
m
ent.
In
th
is case th
e
p
r
im
ary cu
rren
ts
o
f
bot
h t
h
e
C
T
s
are e
qual
a
n
d
cause
satu
ration
o
f
the CT co
res.
As th
e sat
u
ration
cu
rv
es
of th
e co
res canno
t
b
e
fu
lly co
i
n
cid
e
nt i
m
b
a
lan
ce curren
t
will flo
w
throu
g
h
t
h
e relay. Th
is cu
rren
t will b
e
e
q
u
a
l t
o
alg
e
b
r
aic
d
i
fferen
ce
o
f
CT m
a
g
n
e
tizin
g
cu
rrent
in
stan
tan
e
ou
s v
a
lu
es [3
]. Th
e o
r
d
e
r of th
is cu
rren
t is d
e
termin
ed
b
y
th
e o
v
e
rcu
r
ren
t
ratio
and
th
e
m
i
s
m
atch
o
f
t
h
e C
T
m
a
gnet
i
zi
ng c
u
r
v
es.
3.
R
E
SEARC
H M
ETHOD
Let u
s
d
i
scu
s
s
th
e resu
lts
o
f
si
m
u
la
tio
n
o
f
a t
r
an
sien
t in long
itu
d
i
n
a
l
d
i
fferen
tial p
r
o
t
ection
in case of
sh
ort circu
it th
at is ex
tern
al
relativ
e to the ele
m
ent protected. T
h
e sc
hem
e
used
for sim
u
lation of the
pr
ot
ect
i
o
n
i
n
M
i
cro-C
a
p e
n
v
i
ro
nm
ent
[4]
i
s
sh
ow
n i
n
Fi
g
u
r
e
1.
Fi
gu
re
1.
Si
m
u
l
a
t
i
on di
a
g
ram
of
l
o
ngi
t
u
di
nal
di
f
f
ere
n
t
i
a
l
p
r
ot
ect
i
on
usi
n
g
C
T
s wi
t
h
n
o
n
-l
i
n
ear c
o
re
s
The si
m
u
l
a
t
e
d
ci
rcui
t
repres
ent
s
cur
r
ent
di
ffe
rent
i
a
l
pr
ot
ect
i
on of
HV a
e
ri
al
l
i
n
e of 2
20
kV p
o
w
e
r
n
e
two
r
k
.
Th
e
pro
t
ected
elem
e
n
t is represen
ted
b
y
su
bstitu
tio
n
ci
rcu
it in
clud
ing
serially co
nn
ected
resist
o
r
R
2
(R
=0,
0
11
O
h
m
)
and i
n
d
u
ct
or L
6
(
L
=0
,0
6
7
m
H
). T
h
e cu
rre
nt
t
r
ans
f
or
m
e
r i
n
st
al
l
e
d at
t
h
e begi
nni
ng
of t
h
e
lin
e, CT1, is si
m
u
la
ted
as two
indu
ctan
ces,
L3
an
d L4
, t
h
a
t
are inductively coup
led th
rou
g
h
no
n-lin
ear co
re
K1. T
h
e
stray i
n
ductance
of CT1 s
econdary
winding a
n
d
its ohm
i
c resistance a
r
e
represe
n
ted by elem
e
n
ts
L
2
and R1. T
h
e
pa
ram
e
ters of the
s
e elem
ents
and the
core
of the CT are
as
fol
l
ows:
-
m
ean l
e
ngt
h
of
m
a
gnet
i
c
fl
ux
l
i
n
e o
f
t
h
e
co
re
–
2,
6
6
m
(PA
T
H =
2
6
6
cm
);
-
core
cr
oss
-
sect
i
on
–
4
6,
0
1
0
m
2
(AREA =
6
cm
2
);
-
o
h
m
ic r
e
sistance of
seco
nd
ary w
i
nd
ing
–
R
2
= 2,11
Oh
m
;
-
reactance a
n
d s
t
ray inductance
of sec
o
nda
r
y
winding
–
X
2
=
0,
8 O
h
m
and
L
2
=
2,55 m
H
;
-
dom
ai
n wal
l
s
i
rre
versi
b
l
e
de
f
o
rm
at
i
on co
nst
a
nt
–
K
=
25
А
/m
[1–
2
]
.
;
-
dom
ain border
elastic displace
ment constant
–
C
= 0,001
[1–
2
]
.
It is presum
ed that the core of trans
f
orm
e
r
C
Т
1 i
s
m
a
de of st
eel
341
1 o
f
bet
t
e
r gra
d
e.
Acco
r
d
i
n
g t
o
d
a
ta g
i
v
e
n in
[5
] su
ch
steel
has th
e
fo
llowing
p
a
ram
e
ters: satu
ration
m
a
g
n
etizatio
n
MS
1
=
1,
5
3
·
10
6
А
/m,
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Ana
l
ysis o
f
Mod
e
lin
g o
f
C
u
rren
t Differen
tia
l
Pro
tection
(Den
is B. So
lo
vev)
42
5
hysteresisless magnetization curve form
factor A
1
=
17
4
А
/m
. These
pa
ram
e
ters are used
for sim
u
lation
of
th
e m
a
g
n
e
tic co
re in
Micr
o-C
a
p
en
vi
r
o
nm
ent
.
Th
e curren
t
tran
sfo
r
m
e
r in
stalled
at th
e en
d
of th
e lin
e, CT2
,
is si
m
u
la
ted
as two
in
du
ctances, L8
and
L9
, t
h
at ar
e ind
u
c
tiv
ely coupled
th
rou
g
h
n
o
n
-
lin
ear
cor
e
K1
. I
t
is
p
r
esu
m
ed
th
at th
e co
re o
f
tr
an
sf
or
mer
C
Т
2
i
s
m
a
de of st
ee
l
34
11
of
wo
rs
e gra
d
e.
Acco
r
d
i
n
g t
o
dat
a
gi
ven i
n
[
5
]
such
st
eel
has t
h
e f
o
l
l
o
wi
ng
para
m
e
t
e
rs:
satu
ration
m
a
g
n
e
tizatio
n
MS
1
= 1,31·10
6
А
/
m
, and hy
st
ere
s
i
s
l
e
ss
m
a
gnet
i
zat
i
on cu
r
v
e f
o
rm
fact
or A
1
=
1
66
А
/
m
. Ot
her
par
a
m
e
t
e
rs of
C
T
2 a
r
e si
m
i
l
a
r t
o
t
h
o
s
e
of C
T
1.
In
accordance
with recomm
e
ndations
of
Mi
cro-C
a
p
th
e ind
u
c
tiv
e elem
e
n
ts
o
f
t
h
e tra
n
sform
e
rs are
connected via
resistors R
3
a
nd R6
whose
resi
stance is
denot
e
d as
1/
GMIN
(i.e.
10
12
Ohm
)
.
Acco
r
d
i
n
g t
o
t
h
e sc
hem
e
of ci
rcul
at
i
ng c
u
r
r
ent
di
ffe
re
nt
i
a
l
pr
ot
ect
i
on t
h
e seco
nda
ry
w
i
ndi
n
g
s
o
f
C
T
1 an
d C
T
2
fo
rm
a
l
oop
of
el
em
ent
s
L4, L2, R
1
, L
9
, L
7
, R
5
. The e
n
ds o
f
t
h
e
wi
n
d
i
ngs a
r
e co
nn
e
c
t
e
d t
o
co
mm
o
n
no
d
e
s 5 and 7. Th
e r
e
lay co
nn
ect
ed
t
o
th
e sam
e
no
d
e
s actuates th
e t
r
ipp
i
ng
cir
c
u
it of
t
h
e
cir
c
u
i
t
brea
ker
po
we
r
i
ng t
h
e p
r
ot
ect
ed l
i
n
e. I
n
t
h
e
sim
u
l
a
t
e
d
circu
it th
e relay is
rep
r
esen
ted
by serially-co
n
n
ected
in
du
ctor
L5
(
L
=3
,0
6 m
H
)
and r
e
sistor
R
4
(
R
=1
,2
8 Oh
m
)
.
The l
o
a
d
co
nn
ect
ed t
o
t
h
e en
d o
f
t
h
e l
i
n
e i
s
sim
u
l
a
t
e
d as i
nduct
o
r L
1
0 (6
7
m
H
) and
resi
s
t
or R
7
(
2
8,
2
Ohm
)
.
In t
h
e si
m
u
l
a
t
i
on
di
ag
ram
sh
ow
n i
n
Fi
g
u
re
1 t
h
e si
nus
oi
d
a
l
vol
t
a
ge so
ur
ce, V1
, has t
h
e fol
l
o
wi
n
g
param
e
t
e
rs:
vo
l
t
a
ge am
pl
i
t
ude –
2
220000
3
V, fre
que
ncy –50
Hz,
s
o
urce i
n
ternal
resistance
-
0,17 Ohm
(this value is
entere
d into the box of setting
param
e
ters of source V1 along
with voltage am
plitu
de and
fre
que
ncy), and source internal reactance
X
1
=
3,
1
7
O
h
m
.
In t
h
e si
m
u
l
a
t
i
on di
a
g
ram
t
h
e react
i
v
e com
pone
nt
cor
r
es
po
n
d
i
n
g
t
o
t
h
e l
a
st
val
u
e i
s
re
prese
n
t
e
d
by
el
em
ent
L1
havi
ng
i
n
duc
t
a
nce o
f
1
0
m
H
.
Resistance of
R2 and induct
ance of
L6 re
prese
n
t
i
n
g t
h
e
prot
ect
e
d
line are negligi
b
ly s
m
all when
com
p
ared to the values of R7
and L
1
0 re
pres
enting t
h
e
load connected to t
h
e end of
the line. T
h
e steady
-
state
lo
ad
cu
rren
t is
3
,
4
6
kA, th
at is 8
6
,5% of th
e
rated
curr
en
t of th
e CT prim
a
r
y wind
ing
.
The r.m
.
s. v
a
lu
e
o
f
th
e
sho
r
t
ci
rc
ui
t
cu
rre
nt
pe
ri
o
d
i
c
c
o
m
pone
nt
i
s
4
0
kA
.
The si
m
u
l
a
t
e
d
sho
r
t
ci
rc
ui
t
p
r
ocess
occ
u
rs
af
t
e
r m
a
ki
ng
of
e
i
t
h
er
of t
h
e t
w
o ci
rc
ui
t
b
r
ea
k
e
rs
(S
W1
o
r
SW2
)
. For each
of th
em
m
a
k
i
n
g
tim
e an
d
resistan
ce in
clo
s
ed
and
o
p
e
n
con
d
ition
s
are set
.
Th
e co
rresp
o
n
d
i
ng
values
of the
s
e
resistances
are
set
t
o
0,
0
0
1
O
h
m
and
1 M
O
h
m
.
During
sim
u
latio
n
o
f
th
e
s
h
ort circuit
pr
ocess within t
h
e pr
otected z
o
ne
th
e switch
SW1
closure
ti
m
e
is set to
a v
a
lu
e ex
ceed
i
ng
th
e
d
u
rat
i
o
n
o
f
t
h
e tran
sien
t, so
th
e
switch
rem
a
in
s o
p
en
for th
e who
l
e
si
m
u
latio
n
ti
me. Th
e clo
s
u
r
e
ti
m
e
o
f
switch
SW2
for th
is
m
o
d
e
is assu
med
to b
e
0
,
04
s. By th
is ti
m
e
t
h
e lo
ad
en
erg
i
zing
transien
t will start
(at ti
m
e
e
q
u
a
l t
o
zero) and
v
i
rtu
a
lly ter
m
in
ate. At
t
= 0
,
04
s a sh
o
r
t circu
it in
th
e
p
r
o
t
ected
zon
e
o
ccurs. In
th
is case th
e in
itia
l v
a
lu
e o
f
t
h
e ap
eri
o
d
i
c co
m
p
on
en
t o
f
th
e sh
ort circu
it curren
t is
close to the am
plitude of the
peri
odic com
pone
nt there
o
f
while the m
a
xim
u
m
fault cu
rrent will be reached in
ap
pro
x
i
m
a
tel
y
0
,
01
s after
b
e
g
i
n
n
i
n
g
o
f
th
e
p
r
o
cess.
Th
is m
a
x
i
m
u
m
will b
e
app
r
ox
im
a
t
ely eq
u
a
l to
t
h
e
maxim
u
m
pos
sible val
u
e i.e. the i
n
rush s
h
ort-circ
uit
curren
t
.
During
t
h
e
who
l
e sim
u
lati
o
n
ti
m
e
switch
SW2
rem
a
ins in the
closed state.
Th
e resu
lts of
si
m
u
latio
n
o
f
t
r
an
sien
ts du
ri
ng
en
erg
i
zi
n
g
of th
e lo
ad
and
su
bsequ
e
n
t
sho
r
t circu
it in
th
e pr
o
t
ected
zo
n
e
ar
e sh
own in
Figu
r
e
2
.
In
Figu
r
e
2
,
а
are shown t
h
e
curves
of
th
e fo
llowing
variab
les:
sou
r
ce cu
rre
nt
I
(L
1) t
h
at
i
s
alm
o
st
equal
t
o
cu
rre
nt
I
(
L
3
)
of C
T
1 p
r
i
m
ary
wi
n
d
i
n
g (l
oad a
nd s
u
bse
que
nt
sho
r
t-circ
uit c
u
r
r
ent
)
a
n
d
im
balance c
u
rre
n
t
(relay
cu
rre
nt
) I
(L
5
)
w
h
ile
in Fig
u
r
e
2,
b
– c
u
r
r
ents
I
(L
4)
an
d
I
(L9)
of
C
Т
1
and C
Т
2 sec
o
n
d
a
r
y
wi
n
d
i
n
gs. T
h
e i
m
balance cu
rre
nt
i
s
sho
w
n i
n
ver
t
ed t
o
si
m
p
l
i
f
y
vi
sual
co
m
p
ariso
n
of
th
is curren
t
w
ith
th
e CT
s
e
cond
a
r
y cu
rr
en
ts
.
а
)
b)
a)
wave
fo
rm
s of
so
ur
ce I
(L
1
)
a
n
d
im
balance I
(L
5) c
u
rre
nts;
b)
wa
vef
o
rm
s
of
cu
rre
nt
s
I (
L
4)
an
d
I
(L9
)
o
f
C
Т
1 a
n
d
C
Т
2
second
ar
y w
i
nd
ing
s
Fi
gu
re
2.
Ene
r
gi
zi
ng
o
f
l
o
ad
and
s
ubse
q
uent
sh
ort
ci
rcui
t
i
n
t
h
e
pr
ot
ect
ed z
one
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
42
3 – 428
42
6
As it can
b
e
seen
, in
th
e in
t
e
rv
al fro
m
0
s to
0
,
0
4
s lo
ad
en
erg
i
zation p
r
o
cess o
c
curs with
th
e
am
pl
i
t
ude o
f
t
h
e f
o
rce
d
c
o
m
p
o
n
e
n
t
bei
n
g
4
,
9
kA . T
h
e s
econ
d
a
r
y
cur
r
e
n
t
s
o
f
C
Т
1 a
n
d C
Т
2 a
r
e pra
c
tically
equal
.
The am
pl
i
t
ude
of t
h
e f
o
rce
d
c
o
m
pon
ent
o
f
t
h
ese c
u
rre
nt
s i
s
6,
1
k
А
. T
h
e im
bala
nce curre
nt sta
y
s equal
to zero. At i
n
s
t
ant
t
=
0,04
s
th
e sh
or
t cir
c
uit o
ccur
s
.
Th
e
a
m
p
litude of t
h
e forced co
m
p
on
en
t of
t
h
e
sh
or
t
circuit cu
rre
nt
is 8
5
kA.
It
rea
c
hes its m
a
xim
u
m
(10
1
,
5
k
A
)
in
half a
pe
rio
d
(at
t
=
0,
05
s)
.
The
n
t
h
e sec
o
nda
ry
cu
rre
nt
of C
T
2
becom
e
s cl
ose
to ze
ro. T
h
e a
b
s
o
lut
e
values
of the im
balance
current
and C
T
1 sec
o
ndary
current
are
clo
s
e to eac
h
ot
he
r (t
he
first
pea
k
o
f
th
e
second
ar
y cu
rr
en
t is 63
,7
А
wh
ile th
at
of the i
m
b
a
lan
ce curren
t
– 63
,6
А
).
Al
m
o
st
al
l
of
seco
nda
ry
cur
r
e
nt
of C
T
1 fl
ows t
h
r
o
u
g
h
t
h
e rel
a
y
due t
o
hi
g
h
i
m
pedance of C
T
2
seco
nda
ry
wi
n
d
in
g.
It re
sults
fr
om
th
e f
act
th
at cur
r
e
n
t
does no
t f
l
o
w
thro
ugh
CT2
p
r
i
m
ar
y w
i
nd
ing
an
d its
core is dem
a
gnetized so the re
actance of CT
2 m
a
gnetizi
ng loop is
m
u
ch highe
r than
the leakage
reactance of
the sec
o
ndary
winding as
wel
l
as its resistance.
The cu
rre
nt
wa
vef
o
rm
of C
T
2
secon
d
ary
wi
n
d
i
n
g an
d t
h
e re
l
a
y
i
s
hi
ghl
y
di
st
ort
e
d
.
As t
h
e
aperi
o
di
c
com
pone
nt
de
cay
s t
h
e wav
e
fo
rm
of t
h
ese curre
nt
s im
pr
o
v
es b
u
t
rem
a
i
n
s cl
earl
y
no
n-si
nus
oi
d
a
l
.
Suc
h
d
i
sto
r
tion
s
are cau
sed
b
y
deep
sat
u
ration of CT1
co
re. Ev
en
tu
ally the po
sitiv
e and n
e
g
a
tiv
e
p
e
ak
s
o
f
im
balance current and CT1 se
conda
r
y curre
n
t equa
lize and
becom
e
close to the values
of 69,2
А
a
nd
6
9
,
3
А
.
The im
balance current c
onsi
d
er
ably excee
ds
the rated
value of CT sec
ond
ar
y cu
rr
en
t (5 A
)
, so
th
e
r
e
lay
m
u
st
ope
rat
e
a
n
d
di
s
c
on
nect
t
h
e
pr
ot
ect
ed l
i
n
e
f
r
o
m
t
h
e so
urce
.
In
Fi
g
u
re
3 ar
e sh
ow
n t
h
e
r
e
sul
t
s
o
f
si
m
u
lation of loa
d
energizing and conseque
nt
sh
o
r
t circu
it
out
si
de t
h
e pr
o
t
ect
ed zone
. In
th
is case circu
it b
r
eak
er SW1
will clo
s
e at
t
= 0
,
04
s and
sho
r
t circu
it will o
ccur
outsi
de the
protected zone. The circuit
brea
ker SW2 rem
a
in
s op
en
for th
e
who
l
e tim
e.
а
)
b)
а
) s
o
urce c
u
rre
n
t I (L
1) and i
m
balance curre
n
t I (L
5);
b
)
CT1 secondar
y
cur
r
e
n
t
I (
L
4
)
.
Fi
gu
re
3.
W
a
v
e
fo
rm
s at
l
o
ad
ener
gi
zat
i
o
n
w
i
t
h
su
bse
que
nt
faul
t
out
si
d
e
t
h
e p
r
ot
ect
ed
zo
n
e
In Fi
gu
re
3 ar
e sho
w
n wa
ve
fo
rm
s of t
h
e f
o
l
l
o
wi
ng
va
ri
abl
e
s:
so
urce c
u
r
r
ent
I
(
L
1
)
(
F
i
g
u
r
e 3
,
a)
,
im
bal
a
nce cu
rr
ent
I
(L
5)
(
F
i
g
ure
3
,
a)
, a
n
d
C
T
1 sec
o
nda
ry
cu
rre
nt
I
(L
4)
(Fi
g
ure
3
,
b)
.
As in Figure 2
it can be seen t
h
at
i
n
t
h
e i
n
t
e
r
v
al
fr
om
0 s t
o
0,0
4
s l
o
a
d
e
n
er
gi
zat
i
on
pr
o
cess occ
u
rs
with the am
plitude of the forced c
o
m
pone
nt
being 4,9
kA. T
h
e secondary currents
of C
Т
1 an
d C
Т
2 are
pract
i
cal
l
y
eq
u
a
l
.
The
am
pl
i
t
ude
of
t
h
e
f
o
rc
ed c
o
m
pone
nt
of
t
h
ese
cu
rre
n
t
s i
s
6
,
1
k
А
. T
h
e im
balance c
u
rrent
stays equal to zero. At instant
t
=
0
,
04
s th
e sh
ort circu
it o
ccu
rs. Th
e
amplitude of the forced c
o
m
ponent of
t
h
e s
h
o
r
t
ci
rc
ui
t
cur
r
ent
i
s
8
5
kA
. It
reac
hes i
t
s m
a
xim
u
m
(101
,5
k
A
)
i
n
hal
f
a
peri
od
(at
t
= 0
,
05
s)
.
If
bo
th
t
h
e CTs h
a
d
co
res
with
fu
lly id
en
tical p
a
ram
e
ters the sec
o
nda
ry
cur
r
ents
o
f
CT
1 a
n
d
CT
2
wo
ul
d
be t
h
e sam
e
and t
h
e im
bal
a
nce cur
r
ent
w
oul
d be
zero both in case of exte
rnal fault and at load.
Ho
we
ver
d
u
ri
n
g
s
h
ort
ci
rc
ui
t
t
h
e
pri
m
ar
y currents a
r
e
highe
r
th
at at
procee
ding load, s
o
t
h
e c
o
res
of C
T
1 a
n
d
C
T
2 sat
u
rat
e
.
Thei
r m
a
gnet
i
z
i
ng c
u
r
r
e
n
t
s
r
i
se but
t
o
di
f
f
e
r
ent
e
x
t
e
nt
s. T
h
e m
a
gnet
i
z
i
ng cu
rre
nt
of C
T
2 ri
se
s
to
a
h
i
gh
er
v
a
lu
e as CT2 cor
e
is m
a
d
e
of
steel o
f
wo
rse gr
ad
e. Th
erefo
r
e th
e
secondar
y
cur
r
e
n
t
o
f
CT1
becom
e
s highe
r
tha
n
t
h
at of
CT2.
In
this ca
se there
appea
r
s noticeable
di
ffe
rence
of the
s
e curre
nts ca
used
by
th
e m
easu
r
em
e
n
t error of th
e d
i
fferen
tial p
r
o
t
ectio
n
.
Th
is
diffe
re
nce res
u
lts in non-ze
ro im
balance current.
Th
is cu
rren
t
h
a
s th
e ap
p
e
arance o
f
altern
ating
sh
ort pu
ls
es
with
wav
e
form clo
s
e to
t
r
iangu
lar.
Th
e
first
p
u
l
se
h
a
s
n
e
g
a
ti
v
e
po
larity and
th
e larg
est am
p
lit
u
d
e
of
9
,
8
A. Th
e fo
llowing
p
u
l
se h
a
s po
sitiv
e
po
larity
and
t
h
e
least a
m
p
litu
d
e
n
o
t
ex
ceed
i
ng
0
,
1
A. Ev
en
t
u
ally th
e a
m
p
litu
d
e
s
o
f
po
sitiv
e
p
u
l
ses
rise
wh
i
l
e th
o
s
e
o
f
n
e
gativ
e
pul
ses
fad
e
. B
y
appr
o
x
i
m
at
el
y
0,2
s t
h
e a
m
pli
t
ude o
f
ne
gat
i
v
e p
u
l
s
es
f
a
l
l
s
t
o
1 A.
T
h
en t
h
e am
pl
i
t
ude
s o
f
p
o
s
itiv
e and
n
e
g
a
tiv
e
p
u
l
ses eq
u
a
lize at lev
e
l of ab
ou
t
0
,
1
A.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Ana
l
ysis o
f
Mod
e
lin
g o
f
C
u
rren
t Differen
tia
l
Pro
tection
(Den
is B. So
lo
vev)
42
7
Th
e
ob
tain
ed resu
lt shows that th
e cu
rre
nt
di
ffe
re
nt
i
a
l
pr
o
t
ect
i
on ha
s t
h
e
fol
l
owi
n
g
sh
o
r
t
c
om
i
ng. I
t
can gi
ve
fal
s
e t
r
i
p
s at
hi
g
h
fa
u
l
t
current
s ca
us
ed by
sh
ort
ci
r
c
ui
t
s
occu
rri
ng
out
si
de t
h
e
pr
ot
ect
ed zo
ne e
v
en i
f
t
h
e cu
rre
nt
s at
bot
h e
n
d
s
of t
h
e
protected element are e
qual.
To
avo
i
d
su
ch false trip
s (at su
ch
fau
lts ov
er
c
u
r
r
e
n
t
pr
o
t
ect
i
on sh
oul
d
operat
e
) a de
l
a
y
m
a
y
b
e
in
trodu
ced
to
av
o
i
d
tripp
i
ng
th
e p
r
o
t
ected
ele
m
en
t b
y
th
e
first p
u
l
se hav
i
n
g
th
e larg
est a
m
p
litu
d
e
. Also
, th
e
sen
s
itiv
ity o
f
th
e pro
t
ection
may b
e
red
u
c
ed
. Th
e pro
t
ect
i
o
n
sho
u
l
d
no
t o
p
e
rate at relativ
ely lo
w pu
lses after
th
e d
e
lay elapses. Th
e pro
t
ectio
n
with
redu
ced sens
itiv
ity will n
o
t
tri
p
th
e
pro
t
ected
elem
en
t u
n
til th
e
in
su
lation
b
r
eak
dow
n do
es not d
e
v
e
lop
an
d t
h
e
f
a
u
lt cu
rr
en
t b
e
co
m
e
s h
i
g
h
er th
an th
e
op
eratio
n thresho
l
d
.
In
th
is case th
e
d
a
mag
e
cau
sed
by th
e sho
r
t circu
it cu
rren
t w
ill b
e
co
n
s
i
d
erab
l
y
h
i
g
h
e
r th
an
i
n
case
o
f
tri
p
p
i
n
g
at
th
e first stag
e of in
su
latio
n fault d
e
v
e
lop
m
en
t.
As can be se
en from
Figure 4 the current
m
easurement error of the
d
i
fferen
tial p
r
o
t
ection
co
nsid
erab
ly rises in
th
e fo
llo
wi
n
g
situ
ation
.
In
th
e b
e
g
i
nn
ing
a sh
ort circu
it in
th
e p
r
o
t
ected
zon
e
occu
rs.
Aft
e
r i
t
has be
en cl
eared a
n
o
t
her sh
ort
ci
rc
ui
t
out
si
de
the
protecte
d
zone occurs.
The t
i
m
e
interval between
t
h
e t
w
o
faul
t
s
i
s
not
e
n
o
u
gh
f
o
r t
h
e C
T
c
o
re
s t
o
dem
a
gne
tize. So
b
e
fo
re th
e b
e
g
i
nn
ing
of th
e seco
nd
fau
lt th
e
cores
have
re
m
a
nent
m
a
gne
t
i
zat
i
on. As a resul
t
t
h
e
core
s becom
e
m
o
re saturated causing the m
easurem
ent
erro
r (im
b
alan
ce curren
t
) and th
e
false trip prob
ab
ility to
rise.
As in
t
h
e fi
rst
case (Fi
g
ure
2
)
sho
r
t circu
it in th
e
p
r
ot
ect
ed z
one
(
b
et
wee
n
C
T
1 a
nd C
T
2
)
occu
rs a
f
t
e
r
0
,
0
4
s fr
o
m
en
er
g
i
zation
o
f
t
h
e lo
ad. A
t
in
stan
t t
=
0
,
0
8342
s th
is f
a
u
lt w
a
s clear
ed
. Th
i
s
in
stan
t co
rr
esp
ond
s
to
zero
cro
s
sing
o
f
t
h
e sh
ort
circu
it curren
t
. Selectio
n
o
f
su
ch fau
lt clearan
ce tim
e si
mp
lifies th
e simu
latio
n
d
i
agram
as
in
t
h
is case it is
n
o
t
n
ecessary to
in
tro
d
u
ce ele
m
ents represe
n
ting pro
ces
ses cause
d by electric arc
du
ri
n
g
t
r
i
ppi
ng
t
h
e ci
rc
ui
t
b
r
e
a
ker
.
а
)
b)
а
) s
o
urce c
u
rre
n
t I (L
1) and i
m
balance curre
n
t I (L
5);
b
)
cur
r
e
n
t
s
I
(L4
)
and
I
(
L
9)
of
CT1
an
d CT2 second
ar
y
w
i
nd
ing
s
.
Fi
gu
re 4.
C
l
ear
i
ng fa
ul
t
o
u
t
s
i
d
e protected zone after clea
ring
fau
lt with
in pro
t
ected
zon
e
At in
stan
t t
=
0,11
s n
e
w sh
ort circu
it o
ccu
rs b
e
h
i
n
d
CT
2. It
can be seen that
the second short-circ
ui
t
cur
r
ent
ha
s ne
gat
i
v
e ape
r
i
o
di
c com
ponent
i
.
e. i
t
s
pol
ari
t
y
is i
nverse as c
o
m
p
ared t
o
suc
h
com
pone
nt
o
f
t
h
e
first s
h
o
r
t circ
u
it curre
nt.
During
th
e fi
rst fau
lt th
e i
m
b
a
lan
ce cu
rren
t ap
p
e
ars at th
e sa
m
e
ti
me an
d
h
a
s th
e sam
e
wav
e
fo
rm
an
d
in
stan
tan
e
ou
s
v
a
lu
es as in
t
h
e fi
rst case (Fig
ure
2
)
. During
th
e second
fau
lt th
e
wav
e
fo
rm
o
f
t
h
e first
i
m
b
a
lan
ce cu
rren
t
pu
lse is similar to
th
at in
th
e secon
d
case (Figu
r
e
3
)
. Bu
t th
e am
p
litu
d
e
o
f
th
is
p
u
l
se
is 2
8
,
7
A i
n
st
ea
d
of
9
,
8
A t
h
at
i
s
al
m
o
st
t
h
ree t
i
m
e
s hi
ghe
r.
The
n
as i
n
t
h
e sec
o
n
d
ca
se t
h
e
a
m
pli
t
udes
of
n
e
gat
i
v
e
an
d po
sitiv
e i
m
b
a
lan
ce cu
rren
t pu
lses equ
a
lize at
lev
e
l of
0
,
1
A after
rather long
tim
e.
The si
m
u
l
a
t
e
d
im
bal
a
nce curr
ent
wave
fo
rm
s obt
ai
ne
d fo
r f
a
ul
t
s
out
si
de t
h
e prot
ect
e
d
zon
e
i
nvol
vi
n
g
deep sat
u
ration of the CT core
s are
si
m
i
lar to
th
e i
m
b
a
lan
ce
cu
rren
t wav
e
fo
rm
gi
ven i
n
[
3
]
.
These wa
vef
o
rm
s
were cal
c
u
l
a
t
e
d by
c
o
m
put
er
usi
n
g a
p
p
r
oxi
m
a
t
i
on of t
h
e
C
T
core m
a
gn
et
i
zat
i
on cur
v
e
wi
t
h
t
h
ree st
r
a
i
ght
seg
m
en
ts i.e. with
ou
t con
s
ideratio
n
o
f
th
e
h
y
steresis.
Us
e of M
i
cro
-
C
a
p en
vi
r
onm
ent
wi
t
h
t
h
e sam
e
pu
r
pose
g
r
eatly sim
p
lifi
e
s th
e calcu
latio
n
s
an
d prov
ides b
e
tter accuracy.
4.
DIS
C
USSI
ON
Fo
r i
n
creasi
n
g th
e sen
s
itiv
ity o
f
curren
t
differen
tial p
r
o
t
ectio
n
and
redu
ctio
n
o
f
false o
p
e
ration
p
r
ob
ab
ility
in
case
of fau
lts o
u
t
si
d
e
th
e p
r
o
t
ected
zon
e
a nu
m
b
er
o
f
meth
od
s
was
offered [5
] e.g
.
use of
a
relay with
saturab
l
e curren
t
tran
sform
e
r. In
th
is case
th
e sen
s
itiv
ity is red
u
ced
du
ring
actio
n
of th
e ap
eriod
i
c
com
pone
nt
of
im
bal
a
nce cur
r
e
nt
. The
ot
he
r
way
t
o
red
u
c
e
t
h
e i
n
fl
ue
nc
e of hi
gh c
u
r
r
e
nt
s d
u
ri
n
g
ex
t
e
rnal
fau
lts is t
o
u
s
e
cu
rren
t
d
i
fferen
tial relays wit
h
m
a
g
n
e
tic rest
rain
t
o
r
restrai
n
t b
a
sed on
electron
ics.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
42
3 – 428
42
8
The
usi
n
g
o
f
t
h
e
di
scus
sed
m
e
t
hods
res
u
l
t
s
i
n
c
o
m
p
l
i
cati
on
o
f
di
ffe
re
n
t
i
a
l
prot
ect
i
o
n
devi
ces
an
d
d
e
terioration
of th
eir respo
n
se ti
m
e
.
5.
CO
NCL
USI
O
N
The above shortcom
ings can
be overc
o
m
e
by use
of s
o
m
e
innovative
sol
u
tio
ns e.g. by
replacem
ent
o
f
CTs fo
r Rog
o
wsk
y
co
ils av
o
i
d
i
ng
u
s
e of in
teg
r
ating
filters [6-10
]
. In
th
is case th
e weigh
t
o
f
th
e
cu
rren
t
tran
sd
u
c
ers is
g
r
eatly red
u
c
ed
an
d
t
h
e
p
r
o
t
ectio
n
d
e
v
i
ce
sch
e
m
a
t
i
c is si
mp
lified
.
Th
e
pro
b
a
b
ility o
f
fal
s
e trips
i
s
al
so g
r
eat
l
y
red
u
ce
d as R
o
go
ws
ky
coi
l
s
d
o
n
o
t
sat
u
rat
e
.
B
e
si
des t
h
e i
m
pact
o
f
ape
r
i
o
d
i
c com
ponent
s
of t
h
e
measu
r
ed
cu
rren
t
s
is red
u
c
ed as th
e d
e
riv
a
tiv
e o
f
su
ch
co
mp
on
en
ts is
m
u
c
h
sm
a
ller th
an
th
e a
m
p
litu
d
e
v
a
lu
es
of
t
h
e
peri
odi
c
com
pone
nt
s (R
og
o
w
sky
c
o
i
l
s
m
easure
deri
va
t
i
v
es o
f
c
u
r
r
ent
s
i
n
st
ead
o
f
c
u
r
r
ent
s
a
s
s
u
ch
).
REFERE
NC
ES
[1]
S.
H.
Horowitz,
et al.
, “Power
Sy
stem Relay
i
ng”, Third Edition,
J
ohn Wiley
& Sons, Ltd,
Chich
e
ster, UK, ISBN:
978-047-07-5878-6; 2008. http://dx.doi.org
/ 10
.1
002/9780470758786.ch7.
[2]
“Power
Sy
stem Protection
:
Principles
and components”. Ed
itor:
Electricity
Trainin
g
Association, UK, ISBN: 978-
184-91-9442-6; 1995.
http://dx.d
o
i.org/10
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B
PO905F.
[3]
A. Wright,
et
al.,
“Electrical Po
wer S
y
stem Protection”, P
ublisher Springer US,
ISBN: 978-1-4615-3072-5; 1993
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http://dx.doi.org/10.1007/978-1-4
615-
3072-5. Av
ailable from: http://li
nk.spring
er
.com/book/10.10
07/978-1-4615-
3072-5.
[4]
Spectrum-soft.
http://www.
sp
ectrum-soft.
c
om/index.
shtm.
[5]
A. W
r
ight, Current Trans
f
orm
e
rs
: Their Tr
ans
i
ent and S
t
e
a
d
y
-
s
tate P
e
rform
an
ce (M
odern El
e
c
tri
cal S
t
udi
es
).
Publisher: Ch
apm
a
n and
Hall; 1St E
d
ition
ed
ition
.
ISBN: 978-0-4120-8850-6;
1968. http:
http://www.amazon.com/Curr
ent-Transformers-S
tead
y
-
state-Per
f
o
rmance-
Electrical
/dp/04120885
09.
[6]
L. Kojovi
c, “
R
o
gowski Coils Suit
Relay
Protection and Measurement”,
IEEE C
o
mputer Applications in Pow
e
r
,
Vol. 10
, No. 3, p
p
. 47-52
, July
19
97. http://dx.doi.o
rg/ 10.1109
/67.595293.
[7]
L. Kojovic, “PC
B
Rogowski co
ils benefit rela
y
protection”,
IEEE Computer Applications in Power
, vol. 15. pp
.
50–53, 2002
. ht
t
p
://dx.do
i.org
/
1
0
.1109/MCAP.2002.1018823.
[8]
D. B. Solovev
,
et al
.,
“
I
ns
trum
ent curr
ent tr
ans
ducers
with Ro
gows
k
i coils in
protective relay
i
ng applications”,
International Jo
urnal of Elect
rical Power and Energy Systems
, Vol. 73C, pp. 107-113, 2015. http://dx.doi.org
/
10.1016/j.ijepes.2015.04.011
.
[9]
P.
Pe
tit,
et a
l
.
,
“Basic MOSFET Based vs Couplecoils Boost
Con
v
erters for Photo
voltaic Gener
a
to
rs”,
Internationa
l
Journal of Power Electronics
an
d Dr
ive S
y
s
t
ems
(
I
JPEDS)
, Vol.
4, pp
. 1-11
, 201
4.
[10]
P.
L
i
,
et
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,
“High Frequency
C
h
aracte
ristic Of
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TELKOMNIKA Indonesian Jou
r
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l
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, Vol. 10
, pp
. 2209-2
214, 2012
.
BIOGRAP
HI
ES OF
AUTH
ORS
De
nis B.
Solov
e
v
is a graduat
e
of Far Easter
n State Te
chni
c
a
l Universit
y
(
D
iplom
a
with
honours), Vladiv
ostok, Russia. In
2011 he receiv
e
d
a PhD in
electric
engineering
.
From 2011 to
2015 he took internship in
the lead
ing Russian
and internatio
nal univ
e
rsities and research
laboratories: M
A
TI - Russian
State Technolog
ic
al University
named after K.E. Tsiolkovsk
y
,
Moscow; Universit
y
of Maastr
i
c
ht, Ma
astrich
t
(Netherlands);
Laborator
y
o
f
the Ministr
y
of
Energ
y
of the U
n
ited S
t
a
t
es
of Am
erica, S
e
a
ttl
e and Richland
,
Washington.
H
e
i
s
c
u
r
r
e
n
t
l
y
t
h
e
head of the
ed
ucational progr
am “Innovatica” (c
luster of
energ
y
and electronics) at th
e
Engineering Sch
ool of
the Far
Eastern
F
e
der
a
l
Univers
i
t
y
,
Vl
adivo
s
tok, Rus
s
i
a.
An
gel
i
n
a I
.
M
a
kee
v
a
stud
ent of chair “Innovatica” (cluster
of
energ
y
and electronics) at th
e
Engineering Sch
ool of
the Far
Eastern
F
e
der
a
l
Univers
i
t
y
,
Vl
adivo
s
tok, Rus
s
i
a.
Evaluation Warning : The document was created with Spire.PDF for Python.