Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 2
,
A
p
r
il
201
5, p
p
.
17
7
~
18
8
I
S
SN
: 208
8-8
7
0
8
1
77
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
/
IJECE
A Novel Meth
od for F
req
uenc
y Estimation
Consid
ering
Instrum
e
nt T
r
an
sient Ef
f
ect
Mohsen T
a
jdi
n
ian,
Me
hdi Z
a
reian
Jahr
omi, Mojtab
a
Jalalp
our
Dept. of
Electrical
Engineering
,
Am
irkabir Univ
ersity
of
Techno
log
y
No. 424, Hafez
Avenue, Tehr
an
1591634311, Ir
an
e-m
a
il:
ja
la
lpur
@aut.
ac.
ir
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 12, 2014
Rev
i
sed
Jan 10, 201
5
Accepte
d
Ja
n 26, 2015
Large dis
t
urb
a
n
ces
in power s
y
s
t
em
s
cause deviation in th
e frequency
from
the nom
inal valu
e. S
i
nce the freq
u
enc
y
is
an im
portant fa
ctor in t
h
e ele
c
tri
c
a
l
network par
a
meter measurements
, it ca
n cause m
a
lfunction of
the protection
s
y
stem
. In addi
ti
on, Bec
a
use of d
eca
yi
ng DC and oscilla
tor
y
com
p
onents that
introduced b
y
CCVT in response of
voltage variation during the fau
lt
occurren
c
e
,
caus
e
ch
anges
in
th
e value
of
r
e
ceived voltage o
f
primar
y
sid
e
o
f
CCVT. An im
proved least sq
uare me
thod
fo
r estimating fr
equency
is
presented
in th
is paper. In or
der to
redu
ce t
h
e effe
ct of
th
is
trans
i
en
t
component, phasor estimation method has
been improved by
u
s
ing the leas
t
square technique and utilizing kn
owledge
of CC
VT design. Th
e
capab
ility
of
the proposed method was verified b
y
se
ver
a
l case studies
gener
a
ting signals
in P
S
C
AD/EM
TDC. The r
e
s
u
lts
s
how the accu
ra
c
y
, s
p
eed
and c
a
p
abili
t
y
of
the proposed
method.
Keyword:
CCVT tran
sient
Fre
que
ncy
est
i
m
at
i
on
Least
sq
uare
t
e
chni
que
Phas
or estim
a
t
ion
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
:
Mo
j
t
ab
a Jalalpo
u
r,
Dept
.
o
f
El
ect
r
i
cal
Engi
neeri
n
g,
Am
i
r
kabi
r
U
n
i
v
e
r
si
t
y
of
Te
chn
o
l
o
gy
N
o
.
4
2
4
,
H
a
f
e
z Av
enu
e
, Teh
r
an
1
591
634
311
,
I
r
a
n
Em
a
il: j
a
lalp
u
r
@au
t
.ac.ir
1.
INTRODUCTION
The m
o
st
im
port
a
nt
de
vi
ces u
s
ed f
o
r
po
wer
sy
st
em
security, are protective re
lays. in the prese
n
ce of
faul
t
,
t
h
e
s
e de
vi
ces m
u
st
i
d
ent
i
f
y
t
h
e fa
ul
t
y
sect
i
on
or c
o
m
ponent
c
o
r
r
e
c
t
l
y
and q
u
i
c
kl
y
and i
s
ol
at
e i
t
so t
h
at
ot
he
r sect
i
o
ns
of t
h
e net
w
o
r
k
have
a m
i
nimum
im
pact
. Thi
s
sim
p
l
e
and
basi
c re
q
u
i
r
em
ent
i
s
ha
rd t
o
a
c
hi
eve
in presence of
transient c
o
m
pone
nts
due
t
o
fault, which is
prese
n
t in
voltage a
nd c
u
rre
n
t signals recei
ved by
the protective
device. T
h
e coupling ca
p
acito
r
vo
ltag
e
transform
e
r (CCVT)
i
s
one
o
f
t
h
e m
a
i
n
de
vi
ces w
h
o
s
e
t
r
ansi
ent
r
e
sp
o
n
se i
m
pact
s on pe
rf
orm
a
nce
of a di
st
a
n
ce
rel
a
y
.
Al
t
h
o
u
gh t
h
e v
o
l
t
a
ge
out
put
o
f
C
C
VT at
steady-state condition is acc
urate, its
beha
vior during
transient ca
uses inaccuracy
in phasor calcul
a
tion.
M
o
re
ove
r F
r
e
que
ncy
i
s
a si
gni
fi
cant
o
p
er
at
i
ng pa
ram
e
t
e
r o
f
a p
o
we
r
sy
st
em
. Preci
se
m
oni
t
o
ri
ng
of t
h
e
fre
que
ncy
of
a
p
o
we
r sy
st
em
i
s
i
m
port
a
nt
t
o
opt
i
m
al
oper
a
t
i
on,
especi
al
l
y
a real
-t
i
m
e preci
se est
i
m
at
ion
o
f
the m
a
in frequency is necess
a
ry for electric
a
l param
e
te
r
measurem
ents. T
h
is is beca
use
num
erous numerical
m
e
thods
for electrical param
e
ter m
easurem
en
ts are
se
nsitive to
fre
que
ncy
fluctuations
.
Seve
ral m
e
thods
for estim
ating freque
ncy
have
bee
n
m
e
ntione
d i
n
the
technical literature
[1-18].
Zero
-cr
o
ssi
ng
m
e
t
hods
are
t
h
e m
o
st
wi
del
y
use
d
m
e
t
hod
s f
o
r
est
i
m
at
i
ng
fre
que
ncy
[1
, 2]
.
H
o
weve
r,
t
h
ei
r
p
e
rform
a
n
ce i
s
Im
p
r
essiv
e
to
switch
i
ng
-t
yp
e tran
sien
ts. Th
e Kalm
an
filter h
a
s als
o
b
e
en
u
tilized
for
fre
que
ncy estim
ation in power system
[3, 4], but it is
highly affect
ed by the i
n
itial conditions
and its
per
f
o
r
m
a
nce i
s
not
r
o
bust
du
e t
o
de
vi
at
i
ons
i
n
t
h
e i
n
t
e
r
n
al
param
e
t
e
rs of
t
h
e m
odel
.
A t
h
ree-
p
h
ase,
p
h
ase-
locke
d
loop (PLL) prepa
r
es quick an
d r
o
b
u
s
t
freq
u
ency
est
i
m
a
ti
on f
o
r bal
a
nced t
h
ree-
p
h
a
se net
w
o
r
ks and
ha
s
been
wi
del
y
use
d
f
o
r est
i
m
a
t
i
ng fre
qu
e
n
cy
[
5
–
7
]
.
N
e
vert
hel
e
ss, i
t
s
per
f
o
r
m
a
nce i
s
pr
one t
o
err
o
r i
n
unbalance
d
c
o
nditions.
diffe
r
ent a
p
proa
ches, consist
of
least
squa
re m
e
thods [10, 11], DFT
s
[14–16],
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
17
7 – 1
8
8
17
8
Newt
on
-
b
ased
al
go
ri
t
h
m
s
[12
]
, and t
h
e m
a
xi
m
u
m
l
i
k
el
i
hoo
d a
p
p
r
oac
h
[1
7
]
,adapt
i
v
e
ne
u
r
al
net
w
o
r
ks
(
A
N
N
)
[8, 9
]
, co
m
p
lex
Pron
y an
alysis [13
,
18
] h
a
v
e
also
b
e
en
utilized
fo
r frequ
e
n
c
y estim
a
t
i
o
n
o
f
p
o
wer syste
m
si
gnal
s
.
A ne
w
dy
nam
i
c fre
que
ncy
est
i
m
a
ti
on m
e
t
hod i
s
su
g
g
est
e
d
i
n
t
h
i
s
pa
per
.
T
h
i
s
m
e
t
hod w
h
i
c
h i
s
base
d
on l
east
sq
uare
t
echni
q
u
e use
s
t
h
e
CCVT tran
sien
t in
formatio
n
in
th
e voltag
e
wav
e
form wh
ich
is d
i
sp
layed
during tra
n
sie
n
t condition.
Som
e
case studies such as
sig
n
a
l test and also
sign
ifican
t cases for fau
lt in
transm
ission line are
pres
ent
e
d. Si
gnal is generate
d
b
y
PSCAD/EMTDC so
ftware.
With
CCVT in
form
at
io
n
and
propose
d
algorithm
,
the
results
show that speed of c
o
nve
rgence a
n
d
accuracy has been im
proved in the
fre
que
ncy
.
2.
BA
C
KGR
OUN
D
2.
1.
E
ffec
t
i
v
e Fact
ors
o
n
t
h
e
T
r
ansi
en
t Re
spon
se of a C
CVT
The m
o
st significant factors that im
pact th
e CCVT
trans
i
ents response
ar
e the powe
r factor and
m
a
gni
t
ude
of s
econ
d
a
r
y
bu
rd
en, t
h
e i
n
ci
de
n
ce angl
e of
fau
l
t
,
vol
t
a
ge cha
nge m
a
gni
t
ude
and Fer
r
o
res
ona
nc
e
Su
pp
ressi
on
C
i
rcui
t
(
FSC
)
o
f
C
C
V
T [
2
1]
, [
2
2]
.
2.
1.
1.
B
u
r
d
e
n
M
o
st
C
C
V
T
m
odel
s
gi
ve
pr
ope
r
per
f
o
r
m
a
nce
du
ri
n
g
t
h
e
t
r
ansi
e
n
t
st
at
e fo
r
b
u
r
d
en
s l
o
wer t
h
an
t
h
e
nom
inal burde
n.
Whe
n
eve
r
, t
h
e powe
r fact
or
decreases
, CCVT tran
sien
t respon
se b
e
co
m
e
s wo
rse.
Parallel
R
L
ci
rcui
t
s
’ b
u
r
de
ns f
o
r t
h
e s
a
m
e
vol
t
-
am
pere an
d p
o
w
er
factor
give the
worse tra
n
sient
response tha
n
Series
RL [21]. The i
n
ductive
burde
n
s found
in electrom
echanical relays cause m
o
re CCVT transients state than the
resistiv
e b
u
rd
en
s foun
d
in
d
i
gital
an
d
n
u
m
erical
relays
[2
3
]
.
2.
1.
2.
F
a
ul
t
I
n
ci
dence
An
gl
e
Inci
dence a
ngl
e of t
h
e faul
t
causes cha
n
ge
s i
n
C
C
V
T t
r
ansi
ent
be
havi
o
r
. [
23]
. F
o
r a vol
t
a
ge
peak
tran
sien
t, th
e
resu
ltin
g simila
r is an
u
n
d
e
r da
m
p
ed
system
th
at will cau
se
a tran
sien
t vo
ltag
e
th
at
o
s
cillates at
a fre
quency la
rger tha
n
the
power freque
ncy. A
voltage ze
ro tra
n
sients
ca
use a
n
overs
hoot voltage t
h
at
dam
p
s
to
zero
i
n
a few cycles. In
t
h
is case, th
e sub
s
id
en
ce vo
ltag
e
will resu
lt i
n
a red
u
c
ed
v
o
ltag
e
m
a
g
n
itu
de and
shi
f
t
e
d
p
h
ase
a
ngl
e
[
24]
.
Fa
ul
t
s
at
zer
o c
r
os
s
i
ng
o
f
t
h
e
pri
m
ary
v
o
l
t
a
ge
ca
use si
gni
fi
cant
t
r
ansi
e
n
t
e
r
r
o
r
s
t
h
at
resu
lt in th
e operatio
n of co
ve
r
e
d pr
o
t
ectiv
e relays [
2
5
]
.
2.
1.
3.
F
S
C
T
y
pe
There a
r
e t
w
o
t
y
pes of FC
S
s
, '
p
assi
ve'
t
y
pe, w
h
i
c
h d
o
n
o
t
st
ore e
n
er
g
y
and ‘act
i
v
e
’
t
y
pe, whi
c
h
st
ores e
n
er
gy
[
20]
,
[2
1]
.
Act
i
v
e fe
rr
ore
s
o
n
a
n
ce s
u
p
p
re
ssi
o
n
ci
rc
ui
t
s
(A
F
S
C
)
ha
ve
paral
l
el
conn
ect
i
on
of i
r
o
n
co
re ind
u
c
t
o
rs and
cap
acitors,
wh
ich is
ad
ju
sted
to
the po
wer
frequ
en
cy. Th
ese circu
its con
s
isten
tly
co
nn
ected
o
n
CCVT secon
d
ary sid
e
[23
]
, [2
6
]
. Th
e AFSC b
e
h
a
v
e
s
lik
e a b
a
n
d
-pass filter an
d
cau
ses
additional tim
e delay in t
h
e C
C
VT sec
o
nda
r
y out
put. The
e
n
ergy stora
g
e c
o
m
pone
nts in t
h
e
AFSC
pa
rticipate
to the inte
nsity of t
h
e CCVT
transients [23].
Passive ferroresonance
-s
uppression circ
uits (PFSC
) c
onsis
t of a
consistently c
o
nnected loa
d
i
ng re
sistor and a saturabl
e
in
du
ctor
.Th
e
satu
r
a
b
l
e indu
ctor
is d
e
sign
ed
to
satu
rate at ab
ou
t 150
%
o
f
rat
e
d
v
o
ltag
e
to
ho
ld
up
a su
stai
n
e
d ferro
r
esonan
ce co
nd
itio
n [23
]
. Th
ese FSCs do
not
c
h
a
nge
t
r
a
n
si
ent
res
p
o
n
se
o
f
C
C
V
T
u
n
l
e
ss an
o
v
e
r
v
o
l
t
a
ge
occu
rs
[
26]
.
2.
1.
4.
Ma
gni
t
ude of V
o
l
t
ag
e
Ch
an
ge
Th
e fau
lt v
o
l
t
a
g
e
m
a
g
n
itu
d
e
lev
e
l is th
e sig
n
i
fican
t
facto
r
th
at affects th
e in
ten
s
ity o
f
CCVT
tran
sien
ts. In
t
h
e lo
wer vo
ltag
e
lev
e
l, th
e tran
sien
t
res
p
on
se of Sec
o
n
d
ar
y
vol
t
a
ge wa
v
e
of C
C
V
T i
s
m
o
re
het
e
r
oge
ne
ous
i
n
du
ri
n
g
t
h
e
f
a
ul
t
.
T
h
e
v
o
l
t
a
ge c
h
a
nge
m
a
gni
t
ude
depe
n
d
s
t
o
so
urce
t
o
l
i
n
e i
m
pedance
rat
i
o
(SIR
)
v
a
lu
e, fau
lt lo
cation
,
an
d fau
lt resist
an
ce
[23
]
.
A
hig
h
e
r SIR cau
s
es in
to
a larg
er m
a
g
n
itu
d
e
vo
ltag
e
ch
ang
e
at t
h
e
relay lo
catio
n
on
th
e on
set
o
f
a fau
lt [22
]
,
wh
ich
can
resu
lt i
n
h
i
gh
er
o
v
e
rreach
d
i
fficu
lties.
2
.
2
. Equi
va
lent
C
i
rcuit
of
a CC
V
T
A g
e
n
e
ral coup
lin
g
cap
acitor v
o
ltage tran
sform
e
r
(CCVT) in
clud
es a cap
acitiv
e v
o
l
t
a
g
e
d
i
v
i
d
e
r,
tuning react
or, step-down
transform
e
r and Ferro reso
na
nce suppressi
on circuit.
Duri
ng fa
ult condi
tions,
because of the voltage drops, th
e
r
e is no threat of over pa
ssing
the knee-point
of
the m
a
gnetizing
characte
r
istic of the ste
p
-down tra
n
sf
orm
e
r, s
o
a
C
C
V
T
can
be e
x
p
r
ess
e
d
by
t
h
e
eq
ui
val
e
nt
l
i
n
ea
r ci
rcui
t
as
illu
strated
in Fi
g
u
re
1
.
In
th
is
p
a
p
e
r t
h
e CCVT m
o
d
e
l sh
o
w
n
in Figure
1
.
Th
e lin
ear ci
rcu
it
of
Fi
g
u
re 1
can
be
f
u
r
t
h
e
r
sim
p
lif
i
e
d
as show
n in Figu
r
e
2. Th
e
param
e
ters in t
h
e circ
uit o
f
Figu
re
2 a
r
e:
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8-8
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8
A N
o
vel
Met
ho
d f
o
r Fre
q
uenc
y Est
i
m
at
i
o
n C
onsi
d
eri
n
g
I
n
st
rume
nt
T
r
a
n
si
e
n
t
Ef
f
ect
(Mo
jta
ba
Ja
la
l
p
ou
r)
17
9
Fi
gu
re
1.
Eq
ui
val
e
nt
ci
rc
ui
t
d
i
agram
of a C
C
VT
Fi
gu
re
2.
Si
m
p
l
i
f
i
e
d m
odel
o
f
a C
C
V
T
f
r
om
Fi
gu
re
1
C
eq
is su
m of the stack capaci
tances,
L
eq
and
R
eq
are equi
va
l
e
nt
i
nduct
a
nce
and resi
st
ance
respect
i
v
el
y
,
of t
h
e
tuning react
or
and the Ste
p
down transform
e
r,
Z
0
i
s
bur
de
n im
pedance
,
f
is subscri
p
t for pa
ram
e
ters
of the
anti-res
o
nance
circuit.
As m
e
nt
i
one
d i
n
[1
9]
, t
h
e
t
r
a
n
sfer
f
unct
i
o
n
o
f
a C
C
VT
deri
ved
f
o
r
t
h
e m
odel
o
f
Fi
g
u
re
2
i
s
:
*
11
2
3
**
11
2
2
3
CCVT
Ks
z
s
z
s
z
s
z
Gs
s
ps
p
s
p
s
p
s
p
(1)
Whe
r
e
z
i
s is zero
s of CCVT tran
sfer
fun
c
tion and
p
i
s a
r
e
pol
es o
f
C
C
V
T t
r
a
n
sfe
r
fu
nct
i
o
n
and:
11
1
pj
(2)
22
2
pj
(3)
33
p
(4)
Whe
r
e
p
1
i
s
l
o
w f
r
e
que
ncy
p
o
l
e
,
p
2
i
s
hi
gh
f
r
eq
ue
ncy
p
o
l
e
and
p
3
is dc
pole.
3.
PROP
OSE
D
METHO
D
In
or
der t
o
i
n
v
e
st
i
g
at
e t
h
e be
havi
or
of C
C
VT, t
h
e C
C
V
T
i
n
p
u
t
si
g
n
al
has bee
n
c
o
n
s
i
d
ere
d
d
u
r
i
n
g
fau
lt
o
ccurren
c
e h
a
s b
e
en
consid
ered
as fo
llowing
:
10
2
sin
sin
t
i
N
ii
i
vt
B
e
A
t
A
i
t
(5)
Whe
r
e
B
i
s
t
h
e am
pl
i
t
ude a
nd
is t
h
e time constant
of decaying
dc
signal,
A
i
s are harm
onic
com
pone
nt
s i
n
cl
udi
n
g
si
gnal
fu
n
d
am
ent
a
l
com
pone
nt
,
0
i
s
fu
ndam
e
nt
al
ang
u
l
a
r
fre
q
u
e
ncy
w
h
i
c
h
0
=2
f
0
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I
S
SN
:
2
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-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
17
7 – 1
8
8
18
0
and
f
0
is th
e
main
freq
u
e
n
c
y o
f
th
e system
.
Th
e expo
n
e
n
tial DC ter
m
o
f
sig
n
a
l is created
wh
en
fau
lt occu
rs i
n
t
h
e net
w
o
r
k a
n
d t
h
e
ot
her
si
n
u
soi
d
al
e
x
p
r
ess
i
ons
are
seco
n
d
a
n
d
hi
ghe
r
or
der
ha
rm
oni
c o
f
si
g
n
al
of
v
o
l
t
a
ge.
As ha
s bee
n
m
e
nt
i
one
d i
n
[
1
9
]
, t
h
e C
C
V
T a
m
pli
t
ude fre
q
u
e
ncy
res
p
o
n
se
i
s
such t
h
at
D
C
com
pone
nt
and
hi
g
h
-
fre
q
u
e
ncy
com
pone
nt
s el
im
i
n
at
es
and al
s
o
st
ren
g
t
h
e
n
s o
r
wea
k
en
s fre
q
u
enc
y
of ar
ou
n
d
t
h
e po
we
r
fre
que
ncy
.
The
fi
ft
h-
or
der
t
r
a
n
sfe
r
f
unct
i
o
n can be use
d
t
o
rep
r
ese
n
t
C
C
V
T beha
vi
o
r
[1
9
]
. Accor
d
i
n
g t
o
t
h
i
s
m
odel
,
t
h
e
out
put
si
g
n
al
f
r
om
C
C
V
T i
s
ge
ne
ral
l
y
t
o
be
co
ns
i
d
ere
d
as
f
o
l
l
o
ws:
11
22
11
1
22
1
22
ˆ
sin
cos
s
i
n
ci
os
os
s
n
c
dc
tt
t
tt
ri
ri
ri
d
c
vt
V
t
V
t
Ve
t
V
e
t
Ve
t
V
e
t
V
e
(6)
Whe
r
e
V
r
and
V
i
are
real a
n
d
im
aginary
par
t
s of
v
o
ltage
p
h
as
or
o
f
f
u
nda
m
e
ntal com
ponents
,
α
1
and
1
and
α
2
and
2
are real and i
m
aginary part
s and
α
dc
is dc
com
pone
nt p
o
le of the tr
ans
f
e
r
f
unctio
n
of C
C
VT.
Utilizing Taylor se
ries,
si
n(
t)
,
cos(
t)
can be e
xpa
n
d
ed
as
belo
w :
2
2
00
0
sin(
)
s
in
(
)
c
o
s(
t)
sin
(
)
2
t
tt
t
t
(7)
2
2
00
0
c
o
s(
)
c
os(
)
si
n(
t
)
c
o
s(
)
2
t
tt
t
t
(8)
By substituting Taylor series expa
nsi
on in (6), th
e out
put signal of the C
C
VT can be re
prese
n
ted as
follow:
11
22
22
11
22
11
22
ˆ
sin
sin
s
in
cos
s
i
n
co
co
s
c
ss
i
n
os
co
s
dc
ri
r
ir
i
ri
ri
d
c
tt
t
tt
vt
V
t
V
t
V
t
Vt
V
t
V
t
Ve
t
V
e
t
Ve
t
V
e
t
t
e
t
t
V
t
(9)
3.1.
Cal
c
ul
at
i
o
n of P
h
as
or
Dam
p
ing oscillatory com
ponents an
d
dc de
caying c
o
m
ponent
of t
h
e vol
t
age signal w
h
ich is creat
e
d
du
rin
g
t
h
e fa
u
lt occu
rre
nce,
cause t
h
e
uns
u
ccessf
ul estim
a
tion
with
bas
i
c least squa
re
m
e
thod
. in
o
r
der
to
ove
rc
om
e this pr
o
b
lem
,
it
m
u
st be c
o
nside
r
ed that
the c
o
m
ponents
of
t
r
ansie
n
t re
sp
o
n
se C
C
VT
ha
s bee
n
extracted
f
rom
the e
qui
valen
t
circuit sectio
n
2.
1,
ph
aso
r
estim
a
tion ca
n
be im
pro
ved
by
the least s
qua
res
m
e
thod. Acc
o
rding to the
e
quation (9)
ca
n be
w
r
itten:
ˆ
11
1
1
1
1
Vm
D
m
E
(10
)
whe
r
e:
12
3
4
ˆ
ˆˆ
ˆ
ˆ
ˆ
T
m
V
vt
vt
vt
vt
vt
(11
)
12
3
4
5
11
3
3
2
1
2
mm
m
m
m
m
Dd
d
d
d
d
(12
)
''
'
'
'
'
11
2
2
rr
r
i
i
i
d
c
i
T
rr
i
VV
V
V
V
V
V
V
V
V
V
E
(13
)
whe
r
e i
n
(12)
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8
A N
o
vel Met
h
o
d
fo
r Fre
q
uenc
y Estimatio
n C
onsi
d
erin
g
I
n
strume
nt T
r
a
n
sie
n
t Effect
(Mojtaba Jalal
p
our)
18
1
11
1
22
2
33
2
11
2
22
2
1
33
2
3
co
s
c
o
s
c
o
s
co
s
c
o
s
c
o
s
co
s
c
o
s
c
o
s
cos
c
os
cos
m
mm
m
m
tt
t
tt
t
tt
t
t
tt
tt
d
tt
tt
tt
(14
)
11
1
22
2
33
2
11
2
22
2
2
33
2
3
sin
s
in
sin
si
n
s
i
n
s
i
n
sin
s
in
sin
sin
s
in
sin
m
mm
m
m
tt
t
tt
t
tt
t
t
tt
tt
d
tt
tt
tt
(15
)
1
2
3
3
dc
dc
dc
dc
m
t
t
t
t
e
e
e
e
d
(16
)
11
11
12
12
13
13
11
11
1
1
12
12
13
1
4
31
1
cos
s
i
n
cos
s
i
n
cos
s
i
n
co
s
s
i
n
mm
tt
tt
tt
tt
mm
et
e
t
et
e
t
et
d
et
et
e
t
(17
)
21
21
22
22
23
2
3
22
21
2
1
22
2
2
23
2
5
32
2
cos
s
i
n
co
s
s
i
n
cos
s
i
n
cos
s
i
n
mm
tt
tt
tt
tt
mm
et
e
t
et
e
t
et
d
et
et
e
t
(18
)
In the equation
(10)
ܸ
and
E
ar
e v
a
lu
e o
f
kn
own
and
unkn
own
f
actor
s
resp
ectiv
ely
and
D
is the
matr
ix
o
f
known v
a
lu
es. Th
e equ
a
tio
n (19
)
is ob
tain
ed
b
y
usin
g th
e m
e
th
od
o
f
least squ
a
res (
L
S)
:
1
TT
ED
D
D
X
(19
)
By calculating
this m
a
trix, re
al and im
aginary values
of
the signals will
be obtained.
ri
VV
j
V
(20
)
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I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 5, No
. 2, A
p
ril 20
15
:
17
7 – 1
8
8
18
2
3.
2.
Freque
ncy Es
timation
In
practice, three phase fa
ult
doe
sn’t
occur
constantly. Act
u
ally the co
ntinuity of single
phase faults
whic
h are
m
u
ch m
o
re com
m
on causes
phase-phase a
n
d
th
ree phase
faults
a
nd
al
so
vo
ltag
e
un
balan
ces.
Solvi
n
g this
problem
,
positiv
e sequence of the voltage
signals ca
n
be
use
d
[27]. In
ot
her words, voltage
positive sequence is al
ways available
unde
r balanced
and unba
lanced conditions.
Referri
ng
to above reasonable
assum
p
tions, t
h
e
positive sequen
ce of voltage
si
gnal can
be
con
s
idere
d
i
n
to
two
o
r
th
o
g
o
n
a
l
com
pone
nts a
s
f
o
llows:
co
s
rm
Vt
V
t
(21
)
si
n
m
i
Vt
V
t
(22
)
By diffe
rentiation
of equations (21) and
(22) and
the
place
m
e
nt in each
ot
her, the
followi
ng e
q
uation
is obtained:
22
2
im
re
im
r
e
re
i
m
Vt
V
t
V
t
V
t
f
Vt
V
t
(23
)
Also for created
calculation
error by approxi
m
a
te differe
ntiation, it can
be
written:
23
2
0
2
3
er
r
o
r
f
T
f
(24
)
As a
result, the
fre
quency ca
n
be calculate
d a
s
follows:
est
i
m
a
ted
e
rro
r
f
ff
(25
)
3.3. Algorithm
Implementati
on
and
Computati
o
n Pr
ocess
The p
r
op
ose
d
algo
rithm
is describe
d in p
r
evio
us
sectio
n.
C
o
m
puting p
r
oces
s of t
h
e
algo
rithm
is
sho
w
n in
Fi
gu
r
e
(
3
):
Figu
re
3.
Stage
s
o
f
phas
o
r a
n
d
fre
q
u
ency
e
s
tim
ation
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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ECE
I
S
SN:
208
8-8
7
0
8
A N
o
vel Met
h
o
d
fo
r Fre
q
uenc
y Estimatio
n C
onsi
d
erin
g
I
n
strume
nt T
r
a
n
sie
n
t Effect
(Mojtaba Jalal
p
our)
18
3
4.
CASE ST
UDY
Dynam
i
c conditions a
r
e a
n
alyzed using the
Elect
rom
a
gnetic Transients Program
(PSCAD/EMTDC
)
to sim
u
late the sim
p
le syste
m
. As
m
e
ntioned in sec
tion
3; the
f
r
eq
ue
ncy
res
p
ons
e
of t
h
e C
C
VT,
contain
s
attenuated
hig
h
o
r
der
harm
onic com
p
o
n
ent
s
. Ne
vert
hele
s
s
, to
pre
v
ent t
h
e p
r
ese
n
ce
of
hig
h
o
r
der
ha
rm
onic
com
pone
nts, the second order butterw
ort
h
low
p
ass filte
r with 360
Hz cutoff frequec
ny has been use
d
. Als
o
the
5 KHz sa
m
p
ling
f
r
e
que
ncy
has bee
n
selected.
I
n
order t
o
eval
uva
te the perform
ance of the
propose
d
m
e
thod (
P
M
)
,
the results o
f
the PM
have
be
en com
p
ared
with N
onlinea
r
Least Squa
res
(NLS
) [
9
]
,
R
ecursi
v
e
Discrete F
o
uri
e
r T
r
ans
f
orm
(R
DFT)
[
1
4]
a
n
d
A
d
a
p
tive
M
e
tho
d
(
A
M
)
[1
1]
.
As s
h
ow
n in
fi
gu
re
(4
),
seve
ral
dy
nam
i
c
con
d
itions ha
ve bee
n
selected: d
o
uble p
h
ase-
t
o
-
g
r
o
un
d
faults,
three
p
h
ase
-
to-
g
r
o
un
d a
n
d
singl
e
pha
se-to
-
gr
ou
n
d
faults in
di
ffe
rent l
o
cation
s
.
Figure 4.
Four kinds of
dy
nam
i
c
c
onditions: double phase-to
-ground fault
s
,
three pha
se-t
o-ground and single
pha
se-to
-
gr
ou
n
d
faults in
di
ffe
rent l
o
cation
s
4.
1.
Case
1
Figure
(5) shows t
h
e tim
e response
of t
h
e
pha
se
A
vo
ltage signal for LL
G
fault condi
tion
with
a
fault i
n
cide
nc
e an
gle
o
f
0
°
de
g
r
ees.
A
m
a
gnitude
o
f
voltage
ch
an
ge
o
f
24%
(=
1
0
0
%
–
7
6
%
)
o
f
the p
r
e-
fault am
plitude was
observed
at this lo
cation
of the
powe
r syste
m
selected.
Figures
6 illust
rates the
frequency of t
h
e
vol
tage ph
asor has been estim
at
ed
using t
h
e (PM).
As ca
n
b
e
seen
in
f
i
gur
e (
6
)
,
pr
opo
sed
app
r
o
ach ca
uses esti
m
a
ted f
r
eque
ncy converg
e to origi
n
a
l
value after 1 cycle.
The res
u
lts show that AM
, R
D
FT a
nd
NLS
m
e
thods
have
m
o
re sensitivity to Transient
com
pone
nt produce
d
by
C
C
V
T
in
v
o
ltage si
gnal
.
That’s
the
reas
on
that
fre
q
u
e
n
cy c
o
nverge
to
ori
g
inal
value afte
3 t
o
5 c
y
cles
whe
n
CC
VT i
m
pact is not conside
r
ed.
Figu
re
5.
A
-
p
h
a
se v
o
ltage
wa
vef
o
rm
of
the l
o
w
resista
n
ce LLG fa
ult
stag
es
o
f
pha
so
r
a
n
d fre
que
ncy
esti
m
a
t
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 5, No
. 2, A
p
ril 20
15
:
17
7 – 1
8
8
18
4
Figu
re
6.
C
C
V
T im
pact on F
r
eque
ncy
du
ri
ng
first cycles after fa
ult occ
u
rrence
4.
2. C
a
se2
Figure (7) s
hows the tim
e response
of t
h
e pha
se
A
volta
ge sig
n
al fo
r L
LLG
fault condition
with a
fault incide
nce
angle of
90
° d
e
grees
. A m
a
gnitude
of v
o
ltage cha
nge
of 5
6
%
(= 1
0
0
%
–
44%
) of the p
r
efa
u
lt
am
plitude
was
obs
er
ved
at thi
s
locatio
n
of t
h
e p
o
we
r sy
ste
m
selected.
Figure
7. A-phase voltage
wa
veform
of the l
o
w resista
n
ce
LLLG fa
ult
Figure (8) illustrates th
e frequency of the voltage
phasor
which has
been estim
ate
d
usi
ng the
pr
o
pose
d
m
e
thod
.
As ca
n b
e
seen i
n
fi
gu
re
8, alt
h
o
u
gh t
h
e stres
s
es
pr
o
duce
d
i
n
volta
ge sig
n
al
have
bee
n
increase
d
, the
pr
o
pose
d
a
p
p
r
oach e
s
tim
a
ted fre
que
ncy
co
n
v
er
ges to
ori
g
i
n
al value a
f
ter
1 cy
cle. As s
h
ow
n in
figure 8, without
considera
tion of CCVT im
pact, it takes 3 to 6 cycles
f
o
r f
r
eq
ue
ncy
to
con
v
e
r
ge t
o
o
r
iginal
value.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
A N
o
vel Met
h
o
d
fo
r Fre
q
uenc
y Estimatio
n C
onsi
d
erin
g
I
n
strume
nt T
r
a
n
sie
n
t Effect
(Mojtaba Jalal
p
our)
18
5
Figu
re
8.
Im
pact on
F
r
eq
ue
nc
y
du
rin
g
first c
y
cles after faul
t occurre
nce
4.
3. C
a
se3
Fig
u
r
e
(9
)
shows th
e ti
m
e
r
e
s
p
on
se of
th
e ph
ase
A voltage signal for LG
fault condition with a fault
incidenc
e
an
gl
e
of 3
0
° deg
r
e
e
s.
A
m
a
gnitu
de
o
f
voltage
chan
ge of 6
4
%
(=
1
0
0
%
– 36
%
)
of
t
h
e
p
r
e-
fault
am
plitude
was
obs
er
ved
at thi
s
locatio
n
of t
h
e p
o
we
r sy
ste
m
selected.
Figu
re
9.
A
-
p
h
a
se v
o
ltage
wa
vef
o
rm
of the l
o
w resista
n
ce
LG
fault
Figure (10) illustrates the
fre
que
ncy of the
voltage
phasor estim
a
ted using the propose
d
m
e
thod.
As
it is shown fi
gure
10,
when fault locati
o
n approaches
to the
generator bus, st
re
sses in
voltage wa
veform
increse.
Ne
ve
rtheless estim
ated f
r
e
que
ncy
of
the
pr
op
ose
d
m
e
thod c
o
nve
r
g
es to
o
r
igi
n
al value
after
1
cy
cle
with m
i
ni
m
u
m error.
As the results of the
proposed
m
e
thod
sho
w
, c
onsi
d
e
r
ation
of C
C
V
T im
pact results hig
h
precisio
n
i
n
tra
n
sient
peri
od
i
n
c
o
m
p
arison
with the
ot
her
m
e
thods
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 5, No
. 2, A
p
ril 20
15
:
17
7 – 1
8
8
18
6
Figu
re 1
0
. Im
pact
on
F
r
eq
ue
n
c
y
du
rin
g
first cy
cles
after fau
lt
occu
rre
nce
4.
4. C
a
se4
Figure
(11) illustrates t
h
e tim
e response
of the
ph
ase A voltage
si
gnal for
LG
fault
condition with a
fault inci
de
nce
an
gle
of
9
0
°
d
e
grees
.
A m
a
gnitude
of
v
o
lta
ge
c
h
a
nge
o
f
9
0
%
(= 1
00%
– 10
%
)
o
f
the
pr
e-fa
ult
am
plitude was
percei
ved at th
is location of t
h
e p
o
we
r sy
st
em
selected. as
can be see
n
in figure 11, tension in
voltage
wa
ve
fo
rm
have
been
e
nha
nce
d
.
Fig
u
r
e
11
.
A-ph
ase vo
ltag
e
wav
e
fo
r
m
of
the low resistance
LG fault
Figure (12) illustrates th
e
frequency of the
voltage
phasor esti
m
a
ted usi
ng proposed
approach. As
sh
own
in
f
i
gu
re 12
, pr
opo
sed app
r
o
a
ch
cau
s
es estim
a
t
ed
fr
eque
ncy
c
o
nve
rge
to
o
r
ig
inal value after
1
c
y
cle.
Despite
of te
ntion inc
r
em
ent, the
proposed approach has m
o
re
significa
nt accuracy in com
p
arison
with the
othe
r m
e
thods.
Evaluation Warning : The document was created with Spire.PDF for Python.