Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 3,
March 20
16, pp. 464 ~ 4
7
9
DOI: 10.115
9
1
/ijeecs.v1.i3.pp46
4-4
7
9
464
Re
cei
v
ed
No
vem
ber 5, 20
15; Re
vised
Febr
uary 10,
2016; Accept
ed Feb
r
ua
ry
20, 2016
Distance Relay Impedance Measuring Problems in
Presence of Wind Farms
Farhad
Nam
d
ari*, Fatem
e
h Soleimani, Esmaeel Rokrok
Dep
a
rtment of Electrical E
ngi
neer
ing, L
o
rest
an Un
iversi
y,
Khorram
aba
d, Loresta
n, Iran
*e-mail: Namdari.f@lu.ac.ir
A
b
st
r
a
ct
Enviro
n
m
enta
l
concer
ns al
on
g
w
i
th the incre
a
s
ing
d
e
m
a
nd o
n
electric
al
po
w
e
r, have le
d to pow
er
gen
eratio
n of
renew
abl
e s
ources l
i
ke w
i
nd. Con
necti
n
g
w
i
nd turbi
n
es in lar
ge s
c
ale p
o
w
e
rs w
i
th
transmissio
n
n
e
tw
ork makes
new
cha
l
l
eng
e
s
lik
e th
e i
m
pa
ct of thes
e r
e
n
e
w
able
so
urce
s on
p
o
w
e
r sys
tem
protectio
n
. T
h
i
s
pap
er stud
ie
s t
he i
m
p
a
ct
of fault res
i
sta
n
ce a
nd
its lo
cation
on v
o
lt
age
an
d curr
e
n
t
funda
menta
l
frequ
enci
e
s of faulte
d li
nes co
nnecte
d to
DF
IG based w
i
nd f
a
rms
and it w
ill
be de
monstrat
e
d
that bec
ause
o
f
the lar
ge
diffe
rences
betw
e
e
n
thes
e freq
ue
ncies, i
m
pe
dan
ce meas
urin
g of
distanc
e
re
l
a
ys
is inefficient. Hence in thes
e
pow
er system
s
using c
onventi
onal impedanc
e
m
e
asuremen
ts is not s
u
itable
any
mor
e
an
d n
e
w
imp
eda
nce
me
asuri
ng a
p
p
r
oach
e
s are re
quir
ed in d
i
stan
ce relays.
Ke
y
w
ords
: T
r
ans
missi
on l
i
n
e
, DF
IG-based
w
i
nd farm, imp
eda
nce
me
asu
r
ement
1. Introduc
tion
Incre
a
si
ng d
e
m
and o
n
ele
c
tri
c
al po
we
r,
fossil fu
el p
o
we
r pla
n
ts
environ
menta
l
issue
s
,
and high
cost of electricity have led to global
tren
d inclea
n an
d free ren
e
wable so
urce
s of
energy like
wind. Electri
c
ity generationo
f wind en
er
gy
in large
-
scal
es i
s
more e
c
onomi
c
al. Wi
nd
farms (WF
)
–that may consi
s
t of se
veral hun
dre
d
individual
KW or MW wind turbin
es-
aren
orm
a
lly l
o
cate
d at
the
rem
o
te
rea
c
hes of
th
e p
o
w
er
system.
This wi
nd
po
wer n
eed
s to
be
delivere
d
to load ce
nters
thro
ughlo
n
g
-
dista
n
ce
tra
n
smi
ssi
on li
n
e
s. M
o
st
co
mmon
gen
erator
techn
o
logy
u
s
ed
in
win
d
t
u
rbin
es (WT
s
)
wa
s
squi
rre
l ca
ge i
ndu
cti
on g
ene
rato
rs
(SCIG
)
in
the
past. De
spite
some drawb
a
cks,
be
ca
use of econo
mi
c co
ncern
s
these gene
rat
o
rs
con
s
titute
a
non-negli
g
ibl
e
share of
cu
rre
ntly
install
ed wind ene
rgy
ca
pa
city.
Wind
turbi
ne gene
rato
rs (WTG
)
equip
ped
with Do
ubly-Fe
d
Inductio
n
G
enerator
(D
FIG) with
adva
n
tage
s like
wide win
d
spe
ed
rang
e
o
p
e
r
ati
on
a
nd re
du
ced conve
r
ter power are
al
so wi
dely e
m
pl
oyed in
mo
de
rn
wind
e
nergy
sy
st
em
s.
Con
n
e
c
ting WF
s to transmissi
on net
works en
co
unt
ered u
s
with
some n
e
wch
a
lleng
es
basi
c
ally due
to unpredi
ct
able and int
e
rmittent
beh
avior of wind
energy. Tra
n
smi
ssi
on lin
es
prote
c
tion i
n
pre
s
en
ce
of
these
kin
d
s
of ene
rgy so
urces is
one
of these p
r
o
b
lems.
Wh
en
a
disturban
ce
o
c
curs in p
o
wer
system, WF termin
al wo
uld expe
rien
ce a voltage
d
r
op le
adin
g
to
a
large
current
flowing
thro
ugh
DFIG
st
ator a
nd
as
a con
s
equ
en
ce
(du
e
to th
e mag
netic field
intera
ction b
e
t
ween
stator
and rotor) rot
o
r ci
rcuit.
Thi
s
would
h
u
rt rotor circuit converte
r.
WF
s
were forme
r
ly protecte
d by simple und
er volt
age relay
i
ng duri
ng po
wer
system faults. Ho
wev
e
r
as a result of
the incre
a
se
d wind e
nerg
y
penetrati
on,
and in ord
e
r to increa
se
system
stabili
ty,
the ne
w
gri
d
code
s
re
q
u
ire
WF
s to
rem
a
in
co
n
necte
d to t
he p
o
wer n
e
tworks
duri
ng
disturban
ce
s.
Conve
n
tional
ly Fault analy
s
is
and
se
ttings of
prote
c
ti
ve relay
s
hav
e bee
n fou
n
d
ed
upon thi
s
fact
that power
systems
con
s
i
s
t mainly
of synchrono
us g
enerat
ors. Mean while, fault
behavio
r of the ne
wly integrated IG
s is different
fro
m
that of the SGs [1]. This differe
nce ca
n
dire
ctly affect
the perfo
rma
n
ce
of relay
s
, particula
rly the on
es th
at prote
c
t the lin
es
con
n
e
c
ted
to
IG bas
ed WFs
.
D
i
s
t
an
ce
r
e
la
ys
ar
e co
mmo
n
l
y us
ed
r
e
la
ys fo
r line
pr
o
t
ec
tio
n
e
i
th
er
as
pr
ima
r
y or
backu
p. Ref.
[1] is di
scu
s
sed a
bout t
w
o type
s of
WT g
ene
rat
o
rs ap
ply most in
WF,
and
prop
osed a
current wave f
o
rm ba
se
d tech
niqu
e
for impeda
nce measuri
ng
of
distan
ce rel
a
ys
with qua
drati
c
ch
aracte
rist
ic. In [2] an adaptive se
ttin
g
is propo
se
d
for distan
ce
relays p
r
ote
c
ting
lines conn
ect
ed to WFs. Ref. [3] also discu
s
ses an
adaptive set
t
ing for dista
n
ce relays wi
th
quad
ratic ch
ara
c
teri
stic u
s
ing neu
ral netwo
rks wi
t
hout con
s
ide
r
ing th
e type
of WT
s. Fa
ult
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 3, March 20
16 : 464 – 479
465
behavio
r an
d
sho
r
t ci
rcuit
studie
s
of
WT
s ha
s al
sore
ceived a great deal of
attention
in relay
s
e
ttings
.
Ref. [4] s
t
udies
different fac
t
ors
affec
t
i
ng
sh
ort circuit current of WF
s with variou
s
WT
types. While i
n
[5] sho
r
t circuit current contributio
n of
WTs i
s
expl
ored.
Ref. [6] has p
a
rticula
r
ly
discu
s
sed sh
ort circuit current cont
ributi
on of
DFIG in
compa
r
i
s
on
with indu
ction
machin
es.
The im
pa
ct o
ffault re
sista
n
c
e
and
its lo
cation
on
tra
n
smi
ssi
on
lin
e voltage
a
n
d
current
freque
nci
e
sconne
cted
to
DFIG-ba
s
ed
WF
s i
s
n
o
t st
udied
yet. Th
us i
n
the
prop
ose
d
p
ape
r, it will
be demo
n
strated that different voltag
e and cu
rre
n
t fundamen
tal frequen
ci
es will lea
d
to
inefficien
cy of
conve
n
tional
im
peda
nce
measurement
s that a
r
e u
s
ed
in di
stan
ce rel
a
ys. Section
2 will
briefly
describe
WTs
with DFIG modeling.
In section3 we
will take a look
at WF
simplification
s
. Section 4
will descri
b
e DFIG
short circuit beha
vior.Some an
alysis b
a
sed
on
simulatio
n
s d
one in PSCA
D
/EMTDC an
d investigatio
ns
of impa
ct of fault resist
or and its lo
cation
on fun
dam
en
tal freq
uen
cy
differe
nces
betwe
en volt
age
and
current will
b
e
d
e
mon
s
trate
d
in
section 5. Finally conclusions
will be presentedin secti
on 6.
2. WT Gene
r
a
tors
w
i
th Doubly
Fed Induction G
e
n
e
rato
rs Mod
e
ling
WT mod
e
ling
generally co
nsi
s
ts of thre
e part
s
. Aero
dynamic, d
r
ive-trai
n and in
ductio
n
gene
rato
r mo
deling.
2.1. WT Aer
o
d
y
namic
modeling
The ae
rodyn
a
mic mo
del o
f
a WT can b
e
ch
ara
c
te
rize
d by the well-kno
w
n
CP-
λ
-
β
curv
e
s
[7]. An empiri
cal relation
d
e
scrib
ed
(eq
uation
Err
o
r! Reference s
o
urce not found.
)
be
tw
ee
n
Cp
(roto
r po
we
r
coeffici
ent), tip sp
eed
ratio
(
λ
) a
nd bla
d
e
pitch
angle
(
β
) is
used f
o
r devel
opin
g
a
look-up tabl
e that provide
s
a value of
Cp
for a given value of wind
sp
eed an
d tip speed ratio [8].
,
(1)
1
1
0.08
0.035
1
(2)
The c
o
effic
i
ents
c
1
−
c
6
are prop
osed a
s
equal to:
c
1
= 0.5,
c
2
= 116,
c
3
=
0
.4,
c
4
= 0,
c
5
=
5,
c
6
= 21 [8] and
λ
i
s
de
scribed in
relati
on
Error! Re
ference s
o
urce
not found.
as
:
(3)
Whe
r
e
R
i
s
the bla
de le
n
g
th in m,
ω
t
is the WT
rotat
i
onal
spe
ed i
n
rad/
s, an
d
V
w
i
s
t
he
wind
spe
ed in
m/s, andthe
nume
r
ator
(
ω
t
×R) re
pre
s
e
n
t
s the blade ti
p spe
ed in m/s ofthe WT.
At a certain wind spee
d, there i
s
auniq
ue WT
rotatio
nal spe
ed to achi
eve the maximum
power coefficient,
C
Pm
, an
d there
b
y the
maximum m
e
ch
ani
cal (wi
nd) p
o
wer th
at is present
ed
with equ
ation
Error! Refer
e
nce
s
o
urce not
found.
:
1
2
.
.
.
(4)
Whe
r
e
ρ
i
s
th
e air d
e
n
s
ity in kg/m
3
, A
r
=
π
R
2
is the
area in m
2
swe
p
t
by the rotor
blade
s
[7].
2.2. Driv
e-Train
Modeling
The low
WT
speed i
s
co
nverted to a hig
h
spe
ed in order to rotate
DFIG roto
r th
roug
h a
gearbox with
sh
afts.
The
drive-train sy
stem
will
sim
p
ly be m
odel
eda
s a
sin
g
l
e
lump
ed-ma
ss
system
with the lumpe
d
in
ertiacon
stant H
m
, that is cal
c
ulate
d
by:
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Dista
n
ce Rel
a
y Im
pedan
ce Measuri
ng
Problem
s in
Presen
ce of Wind F
a
rm
s
(Farh
ad Nam
dari)
466
The ele
c
trom
ech
ani
cal dyn
a
mic eq
uatio
n is then give
n by
Error!
Reference s
o
urc
e
not
fou
nd.
:
2
(6)
Whe
r
e
ω
m
is
the rotation
al
spee
d of the
lumped
-ma
s
s sy
stem and
ω
m
=
ω
t
=
ω
r
, D
m
is
the dampin
g
of the lumped
system [7].
2.3. Inductio
n
Gener
a
tor
Modeling
The DFIG is
an indu
ction
machi
ne with
a wound rotor wh
ere the
rotor and st
ator are
both conn
ect
ed to ele
c
tri
c
al
sou
r
ces,
hen
ce the t
e
rm ‘d
oubly-f
ed’ Figu
re
1
[9]. The sta
t
or
windi
ng is
directly co
nne
ct
ed to gri
d
while roto
r wi
n
d
ing conn
ecti
on is th
rou
g
h
back to ba
ck
conve
r
ters.
Figure 1. Dou
b
ly-fed indu
ct
ion gen
eratio
n system p
o
wer flows [9].
Stator and rot
o
r equ
ation
s
are de
scri
bed
in matrix form at equation
s
Error! Re
fe
rence
source
n
o
t
fou
nd.
an
d
Error
!
Reference
s
o
urce not found.
.
(7)
′
′
′
(8)
Whe
r
e,
λ
i
s
the flux linka
ge, sub
s
cript
s
s an
d r st
and for vari
a
b
les a
nd pa
rameters
asso
ciated
with the stato
r
and
roto
r si
de respe
c
tively. Equation
Error! Refe
rence
source not
fou
nd.
rep
r
e
s
ents ma
chi
n
e
param
eters
whe
n
refe
rre
d
to the roto
r sid
e
. As it can b
e
se
en
in
relation
s
Err
o
r!
Reference
source not found.
a
nd
Er
ror!
Refere
nc
e source not
found.
voltag
es,
indu
ctan
ce
s
and
cu
rrentsare i
n
the
sta
t
ionary
ab
c
referen
c
e
fra
m
e. They
are
thus time-va
r
iant.
Applying Pa
rk tran
sform, t
he
ab
c
fra
m
e
qua
ntities
are conve
r
ted
i
n
qd
0 frame
quantitie
s a
s
in
Error!
Refere
nce source not found.
and
Error!
Refere
nce source not found.
. This
frame is
rotating
at the synch
r
onou
s freq
ue
ncy [8].
(9)
′
′
′
′
′
(10
)
ω
s
and
ω
r
are the rotation
al spee
d of the sy
n
c
hrono
usly rotating
qd0 fram
e an
d rotor
frame resp
ect
i
vely.
It has been
mentione
d that the three
pha
se roto
r
windi
ng
s are
con
n
e
c
ted to
electri
c
al
sou
r
ce a
nd a
r
e e
nergized
with three
-
p
hase current
s. The
s
e
rot
o
r
curre
n
ts e
s
tabli
s
h the
rotor
magneti
c
fiel
d. The
roto
r
magneti
c
fiel
d interact
s
wi
th the
stator
magneti
c
fiel
d to d
e
velop
torqu
e
[9]. The per-u
nit electro
m
a
gnetic torque
equatio
n is gi
ven by:
(11
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 3, March 20
16 : 464 – 479
467
The PSCA
D
/
E
MTDC software lib
ra
ry provide
s
th
e
stand
ard
mo
del of the
wo
und
rotor
indu
ction ma
chin
e, whi
c
hi
s used in this
study.
DFIG Co
nv
er
ters Mo
deling
This sectio
n descri
b
e
s
the
modeling of
a
back-to-b
ack conve
r
te
r system for
a DFIG
usin
g
field ori
ented cont
rol (FO
C
).
T
he converte
rs are
model
ed to
be voltage
so
urce
conve
r
te
rs
[8].
2.3.1. Grid-si
d
e Conv
erte
r Control
The grid
-side
converte
r co
ntrols the flo
w
of
real and
reactive po
wer to the grid,
through
the g
r
id i
n
terf
acin
g in
du
cta
n
ce
s. T
he
ob
jective of
the
gri
d
-side
co
nverter is to
kee
p
the
d
c
-l
ink
voltage con
s
t
ant rega
rdle
ss of the magn
itude and di
re
ction ofthe rot
o
r po
wer. Th
e vector control
method is u
s
ed, with a
referen
c
e fra
m
e orie
nted along
the stator
voltage vector
po
siti
on,
enabli
ng i
nde
pend
ent
cont
rol
of the
acti
ve and
rea
c
tive po
we
r flo
w
ing
bet
wee
n
the
gri
d
a
n
d the
conve
r
ter.
Th
e PWM
conv
erter is curre
n
t reg
u
lated,
with the
d-axis
cu
rre
nt u
s
e
d
to
regul
ate
the
dc-li
n
k voltag
e and the q-a
x
is curre
n
t co
mpone
nt to regulate the re
active po
wer.
Figure
2
sh
o
w
s the
schem
atic co
ntrol st
ructu
r
e of the
grid-sid
e co
n
v
erter.
Figure 2. Grid
side convert
e
r co
ntrol
The voltag
e
equatio
ns i
n
synchro
nou
sl
y rotating
dq
-axis refere
nce frame
are d
e
scrib
e
d
by
Error! Reference
s
o
urce not
found.
and
Error! Re
fe
rence
s
o
urce not
found.
:
(12
)
(13
)
Whe
r
e
v
cd
an
d
v
cq
are
d a
nd q axis
co
nverter
side
voltages.
R
a
nd
L
choke
are
interface
resi
sto
r
and i
ndu
ctan
ce wit
h
grid. The a
ngula
r
po
sitio
n
of the grid voltage is
cal
c
ulated a
s
t
an
(14
)
Whe
r
e
v
c
α
an
d
v
c
β
are
the
conve
r
ter
gri
d
-sid
e voltag
e
stationa
ry fra
m
e compo
n
e
n
ts. The
d-axis of the
refe
ren
c
e
frame i
s
ali
g
n
ed
with the
grid volta
ge
angul
ar
po
sition
θ
e
. Sinc
e the
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752
Dista
n
ce Rel
a
y Im
pedan
ce Measuri
ng
Problem
s in
Presen
ce of Wind F
a
rm
s
(Farh
ad Nam
dari)
468
amplitude
of the gri
d
voltag
e is
con
s
tant,
v
cq
is
ze
ro a
nd
v
cd
i
s
con
s
tant. The a
c
tive and
rea
c
ti
ve
power
will be proportional to
i
cd
an
d
i
cq
r
e
s
p
ec
tive
ly. As
s
u
me
th
e
gr
id-
s
id
e
tr
an
s
f
or
me
r
con
n
e
c
tion i
s
star, th
e con
v
erter
active
and
rea
c
tive
power flo
w
s
descri
bed
by
equatio
ns
Er
ror!
Refere
nce s
o
urce not
found.
and
Error! Reference s
o
urc
e
not
found.
.
3
3
(15
)
3
3
(16
)
Whi
c
h dem
o
n
strate
s that the real an
d reactive
po
we
rs from the g
r
id-sid
e conv
erter a
r
e
controlled by
the
i
cd
and
i
cq
compo
nent
s of
current
resp
ectively. To re
alize de
cou
p
led
co
ntrol,
simila
r
comp
ensation
s
a
r
e
introd
uced li
ke
wise in
eq
uation
s
Err
o
r
!
Re
ference s
o
urce not found.
and
Error
!
Reference s
o
urc
e
not
found.
:
∗
′
(17
)
∗
′
(18
)
The refe
ren
c
e
voltage
s
v
cd
*
and
v
cq
*
a
r
e
then t
r
an
sformed by
inverse-P
a
rk tran
sformation
to give3-p
h
a
s
e voltage
v
cabc
*
for the
final PWM signal ge
neration for the
conve
r
ter IG
BT
swit
chin
g.
2.3.2. Rotor
-
Side Conv
erter Co
ntr
o
l
The rotor
sid
e
co
nverte
r (i
nverter) of th
e DFIG i
s
co
nne
cted to th
e grid
sid
e
converte
r
(re
ctifier)
th
ro
ugh a DC
lin
k cap
a
cito
r. Actual
a
c
ti
ve
power i
s
co
m
pare
d
with th
e set-poi
nt va
lue
whi
c
h is d
e
termined by the wind
spe
ed. A PI controlle
r is u
s
ed, a
s
see
n
in
Figure
3
, to
gene
rate
the
re
quired val
ue of
I
dr
. Similarly
,
for th
e
re
activ
e
po
wer,
a PI
controlle
r is u
s
ed to g
ene
rate the re
quired
I
qr
. These
values of
I
dr
a
nd
I
qr
are tra
n
sformed b
a
c
k
into the
abc
frame to obtain
the requi
red
value of rotor
curre
n
ts. Also
seen in the
Figure
3
, is
a hysteresi
s
controlle
r used to
gen
era
t
e the swit
ch
ing se
que
nce
for the
IGBT swit
che
s
in the
rotor
side
conve
r
te
r. Req
u
ire
d
rotor current
s
obtaine
d in th
e
ab
c
frame
are
thus ge
nerate
d
by using hy
stere
s
i
s
co
ntrol. A hysteresis band of
0.1
%
is used for
the hystere
s
i
s
controlle
r.
Figure 3. Rot
o
r sid
e
co
nve
r
ter control [8]
3. WF Simplification in P
o
w
e
r Sy
stem Studies
In ord
e
r to
WFs
con
n
e
c
tio
n
to g
r
id fo
r
power
syste
m
studi
es, th
ere
are
some
com
m
on
simplification
s
. The
comm
on mod
e
ling
method fo
r d
oubly-fed
WF
dynamic
equ
ivalence can
be
divided i
n
to t
w
o
kin
d
s of
rep
r
e
s
entatio
ns:
si
ngl
e-m
a
chi
ne and
multi-ma
chin
e
representa
t
ion
method.
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752
IJEECS
Vol.
1, No. 3, March 20
16 : 464 – 479
469
3.1. Single-Machine Repr
esen
tatio
n
Method
Single-m
a
chi
ne rep
r
e
s
e
n
tation method
refers
to the whole
WF is represented
with one
WT ma
chin
e
as the eq
uivalent mod
e
l. Acco
rd
i
ng to
the differen
c
e of wind
sp
eed bet
wee
n
all
WT
s, the m
e
thod
ca
n b
e
fu
rther cl
assifie
d
into ‘’
1+1’
model
(n
amel
y one
WT
wit
h
on
e g
ene
ra
tor)
and “n
+1
” mo
del (na
m
ely n
WTs
with on
e gene
rato
r).
This
classification is given
in Figure 4.
Figure 4. The
classification
of single ma
chin
e rep
r
e
s
e
n
tation metho
d
.
a. 1+1 representation. b.
n+1 re
present
ation [10]
3.2. Multi-Ma
chine Re
pre
sentation Me
thod
Multi-ma
chin
e rep
r
e
s
entat
ion method i
s
aime
d to build the “n
+n
” model (n
am
elyn WT
plus n g
ene
rator) by intro
duci
ng the id
ea of co
h
e
re
ncy-b
a
sed eq
uivalents, whi
c
h is a
com
m
on
method fo
r d
y
namic e
quiv
a
len
c
e in th
e
power
sy
ste
m
, to the dynamic
equiva
lent modeli
n
g
of
the WF. The
method i
s
ba
sed o
n
the p
r
incipl
e of
unit
grou
p that WT
s have th
e sam
e
or
si
milar
operational p
o
int to combi
ne the sam
e
grou
p of units [10].
The employe
d
simplification method o
f
WF
s here, is “1+1” re
pre
s
entatio
n method
.
Paramete
r eq
uivalen
c
e is b
a
se
d on Tabl
e 1 Table
1
.
DFIG eq
uivalent model pa
rameters[11].
Table 1. DFI
G
equivale
nt model pa
ram
e
ters
Parameter
Equivalent
DFIG
MVA
n × detailed DFI
G
10
V
s
t
ator
(kV)
The same as det
ailed DFIG
p.u Paramete
rs
The same as det
ailed DFIG
4. Short Circ
uit Beh
a
v
i
or
of DFIG
s
Balanced faul
t current for a SCIG machi
ne is
co
nsi
s
te
d of a decayi
ng dc an
d a decayin
g
ac compo
nen
t, expressed
by equation
E
rror! Re
ference source not found.
:
1
1
′
1
1
.
5
′
cos
1
1
1
′
cos
(19
)
Whe
r
e
V
max
is the voltage
amplitude,
ω
1 is the fund
amental an
gu
lar freq
uen
cy,
s
is the
IG s
lip,
X
′
is the moto
r transi
ent rea
c
tance,
X
σ
s
an
d
X
ms
are the lea
k
ag
e a
nd ma
gneti
z
i
n
g
rea
c
tan
c
e
s
of the stator wi
nding,
T
′
is the sho
r
t-circuit
transie
nt ti
me constant, which is inversely
prop
ortio
nal t
o
the rotor
resi
stan
ce,
T
a
i
s
the
stator time con
s
tant, and
θ
i
s
the
fault inception
angle. Since the DFIG
s protect with cro
w
ba
r ci
rc
uits,
under
seve
re fault conditi
ons (li
k
e th
re
e
phase
balanced fault),
crowbar
circ
uit
will be activated, rotor
and
stator convert
e
rs
will be short
circuited
an
d
then th
e b
e
havior
of DFIGs
co
nceptu
a
lly is th
e
sa
me a
s
S
C
IG
s. Ma
chin
e
sl
ip of
the fault current in
Error!
Refere
nce s
o
urce not
found.
would affe
ct quit different i
m
pact o
n
sh
o
r
t
circuit
curre
n
t from di
stan
ce rel
a
ying p
e
r
sp
ective [1].
DFIG
s work unde
r
slip
range
s of
±30
%
,
comm
en
surate with wind
speed. Thu
s
(1-s) facto
r
he
re wo
uld not
be a negligi
b
l
e
term and in
60
Hz sy
stem
s,
cau
s
e
s
a ran
ge of
42–
78
Hz for DFIG
fault current
s. Thi
s
me
an
s
that fault current
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IJEECS
ISSN:
2502-4
752
Dista
n
ce Rel
a
y Im
pedan
ce Measuri
ng
Problem
s in
Presen
ce of Wind F
a
rm
s
(Farh
ad Nam
dari)
470
freque
ncy
wil
l
gen
erate
off
-
nomi
nal freq
uen
cy t
hat le
ads to im
ped
ance m
e
a
s
uri
ng
(ne
c
e
s
sary
for distan
ce p
r
otectio
n
) p
r
o
b
lems.
5. Impact An
aly
s
is of Fault Resis
t
or Size and its Lo
cation on Im
pedan
ce Me
asuring
In
th
is
s
e
c
t
io
n p
o
w
er
s
y
s
t
em p
r
es
e
n
t
ed
in
Figure
5
is
simulate
d in
PSCAD an
d a symmet
r
ical three ph
ase
-
g
r
ou
nd fault with
cha
ngin
g
re
sisto
r
i
s
ap
plied o
n
various l
o
cation
s of p
o
wer system. T
h
en fund
ame
n
tal
freque
nci
e
s
of voltage a
nd cu
rrent of
lines u
nde
r fault and the line conn
e
c
ted to WF are
c
o
ns
ide
r
ed
.
Figure 5. Single line diag
ram of the test powe
r
syste
m
[1]
A distan
ce
relay ope
rate
s ba
se
d on t
he fund
amen
tal freque
ncy
voltage an
d
curre
n
t
pha
sors. Fo
r example, t
he ph
ase A
-
groun
d el
e
m
ent of a
distan
ce
rel
a
y comp
utes the
impeda
nce b
y
relation
Error! Re
ference
source
not
found.
:
(20
)
Whe
r
e
V
ag
an
d
I
a
are th
e
fundam
ental
frequ
en
cy p
hasors for p
hase A volta
ge an
d
c
u
rrent,
k
is the zero-se
quen
ce
com
pen
sation fa
ctor, an
d
I
o
is the ze
ro
seque
nce cu
rrent.
Occu
rrin
g
a f
ault will result in frequ
en
cy excursio
n co
ndition
s. In order to m
odify adaptively wi
th
these
con
d
itions a
nd co
m
pute voltage and current
p
hasors accu
rately, distance relays
will be
equip
ped
wit
h
freq
uen
cy trackin
g
te
chn
i
que
s. It w
ill
be de
mon
s
trated that in t
he case of
DFIG
based WF
s
durin
g balan
ced faults, sin
c
e the volt
ag
e freque
ncy is dictated by
the bulk po
wer
system, this f
r
equency will
remain
within a
narro
w margin of 60
Hz. Ho
wever
current frequ
e
n
cy
signifi
cantly deviates fro
m
the nomin
al
frequ
en
cy. Thus
relatio
n
s such a
s
Error! Re
fer
e
nce
source n
o
t found.
i
s
not
hold tru
e
. To
validate this differen
c
e b
e
twee
n volta
ge an
d cu
rre
n
t
freque
ncy, ba
lanced thre
e pha
se faults
with ch
angi
ng
resi
stor
size and lo
cation i
s
appli
ed to line
12 and lin
e 2
4
.
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 3, March 20
16 : 464 – 479
471
Figure 6. Short circuit fault at 50m of bus2 on line2
4 graph
s
Whe
n
a
sho
r
t
circuit o
c
curs ne
ar
bu
s 2,
becau
se of t
he cro
w
ba
r a
c
tivation an
d
also th
e
non-negli
g
ibl
e
sli
p
te
rmin
DFIG
(eq
uati
on
Err
o
r!
Re
ference s
o
urc
e
not found.
),
fault current
in
line co
nne
cte
d
to WF is d
a
mped fa
sterin com
pari
s
o
n
with the further line (li
n
e
24). Fre
que
ncy
fluctuation
s
i
n
line 2
4
is
smaller th
an t
he line
co
nne
cted to
WF.
This
woul
d re
sult in in
accu
rate
impeda
nce m
easurin
g in li
ne 12
dista
n
ce rel
a
y, l
eadi
ng to ineffi
cie
n
cy of
conve
n
tional di
stan
ce
relay impe
da
nce me
asuri
n
g algorith
m
s.
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IJEECS
ISSN:
2502-4
752
Dista
n
ce Rel
a
y Im
pedan
ce Measuri
ng
Problem
s in
Presen
ce of Wind F
a
rm
s
(Farh
ad Nam
dari)
472
Figure 7. Short circuit fault on the middle
of lin 24 grap
hs
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 3, March 20
16 : 464 – 479
473
Figure 8. R
f
= 20 ohm at 50
m of bus 2 o
n
line 24
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