Z = V/I Does Not Make a Distance Relay
J. Roberts, A. Guzman, and E. O. Schweitzer, III
Schweitzer Engineering Laboratories, Inc.
Presented at the
48th Annual Georgia Tech Protective Relaying Conference
Atlanta, Georgia
May 4–6, 1994
Previously presented at the
47th Annual Conference for Protective Relay Engineers, March 1994
Originally presented at the
20th Annual Western Protective Relay Conference, October 1993
z
=
v II DOES
NOT
MAKE
A
DIST
ANCE
RELA
y
INTRODUCTION
Distance relays can provide effective transmission line protection. Their characteristics have
usually been created from comparators and various combinations of voltages and currents.
The mho characteristic, for example, is a popular design because it can be made from a single
comparator, has well-defined reach, is inherently directional, and can be made to tolerate fault
resistance quite well without serious overreaching errors due to load .
Quadrilateral characteristics traditionally require four comparators; e.g., one for each side of
the characteristic.
Because of the variety of fault types possible on a three-phase circuit, distance relays must be
available to respond to the voltages and currents associated with six different fault loops.
The number of relay elements required for complete schemes is usually quite large. For
example, a four-zone phase and ground mho distance relay requires 24 comparators.
Quadrilateral characteristics require even more.
One approach to making a distance relay with a computer is to calculate the apparent
impedance Z = V 11, and then check if that impedance is inside some geometric shape, like a
circle or box. The hope is that one impedance calculation (per loop) might be useful for all
zones.
Although relays have been made using this approach, their performance suffers under many
practical conditions of load flow and fault resistance.
This paper examines the z = V II approach, and shows the degradations due to load flow and
fault resistance. It shows us that calculating Z = V II and testing Z against a circle passing
through the origin is equivalent to a self-polarized
mho element --generally
a poor performer
for distance protection.
This paper shows some much better methods used in numerical relays, and emphasizes that
these methods have their roots in better polarization methods.
z
=
v II AS
A
DIST
ANCE
MEASUREMENT
Consider the making of a distance relay by calculating the apparent impedance and comparing
the result against some geometric shape. In this paper, we refer to this approach as the
Z = VII method. This method is appealing in that it only requires one impedance calculation
per fault loop. Multiple zones (or geometric shapes) only require more geometric tests of the
result. These apparent impedance equations are listed in Table I.
1
Table I:
Z = VII Apparent Impedance Equations
Fault Loop
Equations
First look at the AG element performance for an AG fault on the radially configured system
in Figure I. The A<p voltage at Bus S is:
v = m.Z .
(1
tL
+
k O .I
A
\
R1
+
R
.1
F
Equation
F
where:
v
= A<t> voltage
m = per-unit
ZlL
measured
distance
= positive-sequence
IR = residual
IF = total
current
from
Bus S
line impedance
IA = A<t> current measured
kO = (ZoL -ZlL)/(3.Z1J
RF = fault
at Bus S
to the fault
at Bus S
(ZoL = zero-sequence
measured
line
impedance)
at Bus S
resistance
current
flowing
through
RF
ELcS
0-
215
Z 05
PTR
CTR
m
kV
= Z1L .(0,1)
= 3 ' Z 15
= 3500:1
= 320'1
= 0,85
= 400
Z1L =10+j.110!2pri.
= 0.91 + j 10.06 Q sec
Z OL = 3. Z 1L
Figure 1: System Single Line Diagram
2
21R =215
2 OR = 2 os
1
Convert Equation
1 into an impedance measurement by dividing
kO.IJ.
I = (IA + kO.IJ,
This yields:
every term by I, where
=
~v = m
.Z
+ R .~
= -=
m.Z1L
I
lL
F I
I
Z
Z
Equation
Equation
z includes the line impedance to the fault plus RF.(IF/I).
RF"(IF/I}"
Z
For the radial system,
If =
L IF
2
2
L I
fault. Figure 2 shows the resistance and
and Z accurately measures the reactance to the fault,
reactance impedance measured by the relay for an AG fault at m = 0.85, with ~ = 4.60
secondary (or 500 primary
Im(V/I)
= m.
m" I X1L I,
given PTR/CTR
3500/320}.
= 3500/320),
Rf"(IF/I} is all real,
Because RF.(IF/I)
regardless the magnitude of RF,
RF.
Jm(+)
RF'(-1fj
E
Re (+
Figure
Figure 2:
2:
AG Apparent
AG
Apparent
)
Impedance Method
Impedance
Method Correctly
Correctly Measures
Measures Reactance
Reactance to Fault
Fault
for a Radial
for
Radial Line
Line
This suggests that we can define a zone of ground distance protection
resistance thresholds;
with two reactance and
i.e., the geometric test is a rectangle.
i,e.,
Figure 3 shows how these threshold checks enclose AG faults up to m = 0.85 with ~
less
than 9.20 secondary .Reactance Threshold 2 and Resistance Threshold 2 define the desired
reactance and resistance reach thresholds respectively.
Reactance Threshold 1 and Resistance
Threshold 1 restrict the zone definition to mostly the first quadrant in the impedance plane.
Their small negative settings accommodate slight measurement errors near either axis (Im[V /1]
or Re[V/I]).
These later thresholds must be replaced with a separate directional element to
insure directional
security ,
II approach is not inherently
Thus, the first major problem to note is the Z = V /1
ground faults.
3
directional
for
~
Im(~)
(+)
Im
RESIST
ANCE
THRESHOLD
1 ~
II
,\-RESISTANCE
:
\
RESISTANCE
THRESHOLD
2
: r
:I
:
,
r
THRESHOLO2
;1
m=1
m=1
~
10
,
I
;I
II
!
~
I
9
---[':':':':':':':'. ~:':':':':' :,:,~:,:,:,:,:,:,:,:,:,:':':':':':':':':':':':':':,:,:,:,:,:,:,:,~:,:,r---.~~~~~~r-",~~,~~~~,~~~~,~,,~,.
!
"
"
'1
::~~::~
N.
"
:::;::]
:-:7
u
'1
--:'
'1
:~::::.~..7:..0:J~::::::~:::::::::~::::
..
Q)
If)
~
'"-'
J
,
J
00
,
~~~~J
'--
REACTANCE
THRESHOLD
2
(8596 .Z1U
...
w
:::~::~:
"""""""""
"""""."""
"
m
"
-"
05
"" ."
u
z
i<3::
1U
<3::
w
~
(1:
L~"
4..~
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~
~
:[
:
:
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[
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[
:
~
~
~
:
:
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:
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:
:
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::
[
:
[~
:
:
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~
~
:[
:
:
:
:
:
[
:
~
~
~:
:
:
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~
:[
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~
~
:
~
:
:
:
:
:j
J
i';-;
,',',
l'
l~""
!
,
:
:
:
:
:
:j
'J
~~~ :
.1::~
t""C1C
t;:;:;:;:;:;.;.;.
t~~~~~~:~i
Re
";r
t
"J...:.:.
:.. J
2
j
:4
S
[)
,
B
gJ
;~~.~~~:~~~~~:~.
~~~~:~~~~~~
~~~~~~~~~~~~~~:~:~
t
1D
\
RESISTANCE [.0. sec.]
'--
RESISTANCE[.0.sec
Figure 3:
Figure
3:
"
'--
(
J
(v-Yt
REACTANCE
REACTANCE
THRESHOLD
THRESHOLO1 1
AG Apparent Impedance Compared to Reactance and Resistance
Thresholds (Radial Case)
Load
Resistance Effects
Effects on
on Z
Load Flow
Flow and
and Fault
Fault Resistance
Z
What effect
effect does
does load
load flow
and RF
the Z = V II measurement?
measurement? Consider
Consider the
What
flow and
RF have
have on
on the
the faulted
faulted
system in Figure
Figure 1 again,
again, except
except now
now close
close the
the switch
Bus R and
and assume
load flows
flows
system
switch near
near Bus
assume load
from Bus
to Bus
Bus R with
with O
0 = 30°,
from
Bus S to
30°,
Figure 4a
4a shows
shows the
at Bus
Bus S overreaches
overreaches in that
that Im(V
Im(V II)
II) measures
measures a reactance
reactance less
less than
Figure
the relay
relay at
than
the line
reactance to
to the
the fault.
fault. This
This is because
IF and
and I are
not in phase
phase {Figure
(Figure 4b)
4b) and
and RF
the
line reactance
because IF
are not
RF
appears as
as a complex
impedance.
appears
complex impedance.
This overreach becomes more pronounced with increasing RF and 0,
0.
4
~
(V~
(l"
II
mlT)
fu
IF-R F
'F.RF
,
'.R L
'.R
L-.
Re(+)
a Impedance
ImpedancePlane
Plane
b. Voltage
Voltageand
and Current
Current Phasors
Phasors
b.
a
Figure 4: AG Apparent Impedance Overreach with R.. and Load Flow Out (0 = 300)
Figure
Figure 5 illustrates
illustrates underunder- and
and overreaching
overreaching of
of the
the Z = V
V II approach
approach for
for different
different ~ and
and
load
0.85. The
load flow
flow conditions.
conditions. The
The relay
relay reach
reach is
is set
set to
to r.ZlL'
r.ZlL' where
where r = 0.85.
The Z
Z = VII
VII
approach
approach underreaches
underreaches for
for incoming
incoming load
load (IF
(IF leads
leads I),
I), and
and overreaches
overreaches for
for load
load out
out (IF
(IF lags
lags I).
I).
Im(V/I)
Im(V/I)
20
20
0=.60 .
/
m=O.85
m::0,85
/
/
vv
(1)
(1)
In
tn
I
0:
0:
LJ.J
LJ.J
u
u
z
z
<1:
<1:
ffu
u
<I:
«
~
LJ.J
cx:
/
k
10
/
0.
=
6=0.
:
;:!
N-'
15=+30.
5=+60
8::+60 .
Re(V/I)
a
G
6+
8+ -+ LOAD OUT
68- -+ LOAD IN
-5
0
-5
-so
20
10
10
RESIST
RESIST ANCE
ANCE [Q
[..\2sec.]
sec.]
FAUL T RESIST ANCE LEGEND'
x RF=O..\2
Figure
5: AG Apparent
.RF::10..\2
Impedance
.RF::25..Q
Method
5
Performance
~
RF::50..Q PRI.
Depends on RF and 0
To better illustrate the under- and overreaching of this reactance measurement. compare
X = Im(Z)lIm(r.Z1J to unity for the same system conditions shown in Figure 5. The results
are shown in Figure 6 where the ideal X is unity .
5.0
m=O.85
w
Rf=50.QPRIMARY
u
z
' .,
./
!
.1
1
<!
I-z
u O
<!w 1-'
a:<!
1- 5'
zw-Ju
a:
11:6
O.J:
<!
.
",
~
-Rf=25.Q
--.<
u
,
\"
.
\,
C
--'.
,
~
,
a:
w
\
\
:\
1-<!
~
'.
F3!:=.1P-~
"
,-
w
CI:
'
0=
~---~'.,.
~
,
1.0
;,;:
-.""'-
Rf-O.Q
0.
t
SET
REACH
:1:
---:0.:::-.=::-.=-.:-.:-.:-.:-.=::::=.
~
~
~
0=
0
-60
.LOAD
IN
O
I
60
LOADOUT
~
O
-
Per-unit
AG Apparent
Apparent Impedance
Illustrates the
Amount of
Per-unit AG
Impedance Calculation
Calculation ~ Illustrates
the Amount
UnderUnder- and
and Overreach
Overreach with
with Fault
Fault Resistance
Resistance and
and Load
Load Flow
Flow
Figure 6:
Figure
6:
The overreaching problem can be minimized by restricting the reactive reach. For a zone 1
element, this means reducing the amount of instantaneous protective coverground distance element.
age. We could also restrict the resistive coverage to avoid the overreach which occurs for
line-end faults. However,
However. this penalizes the fault resistance coverage for all fault locations.
IMPROVED
IMPROVED
QUADRILA
QUADRILA
TERAL
TERAL
CHARACTERISTIC
CHARACTERISTIC
There
are much
the reactance
reactance to the
the fault,
the fault
fault resistance,
There are
much better
better ways
ways to
to estimate
estimate the
fault, and
and the
resistance,
than
than to use
use R + j.X
j.X = VII.
VII.
These better methods depend on proper selection of polarizing quantities
quantities.
Reactance
Reactance Element
Element
Reference 1 describes one means of obtaining an improved reactance characteristic using the
sine-phase comparator. This comparator measures the angle, e, between the operating (Sop)
and polarizing (SPOJ
(SpQJ signals. The torque of this comparator is defined by Im(Sop.SPOL
*);
where * indicates the complex conjugate. For 00 ~ e ~ 180°, the characteristic is a
6
straight line, and the torque is positive. The angles e = 00 and e = 180° define the
boundary line in the impedance plane.
The reactance element comparator has the following input signals:
SOP== oV
oV
Sop
SPOL
SPOL== Ip
Ip
where:
where:
oV
oV
r
ZlL
ZlL
I
V
Ip
Ip
=
=
=
=
=
=
=
(r.ZlL.I
(r.ZlL .1 -V),
-V), line-drop
line-drop compensated
compensated voltage
voltage
per-unit
per-unit reach
reach
positive-sequence line
positive-sequence
line impedance
impedance
IA
IA + kO.
kO.IR
IR
A<1>
A<1>
measured
measured voltage
voltage
polarizing
polarizing current
current
Figure 4 shows that the faulted phase current is not always in-phase with the total fault
current, IF. Thus, phase current makes a poor choice for the polarizing reference signal,
signal.
Negative-sequence or residual currents are much better choices.
Equation 3 illustrates why IR is an appropriate polarizing choice. In this equation, the residual
current measured at Bus S is expressed in terms of the total fault current, 4. For systems
where the L Zos
Z05 = L ZOL= L ZOR(homogeneous systems), the L IR equals the L IF regardless of the load condition or fault resistance magnitude.
I
=
I
=
R
R
[
(l-m).Z OL +Z OR.]
Z +Z + Z
05 OL OR
I
Equation
Equation
F
33
By
By selecting
selecting Ip
Ip = IR,
IR, the
the reactance
reactance element
element measurement
measurement is
is insensitive
insensitive to
to load
load flow
flow condiconditions.
tions. Equation
Equation 4 defines
defines the
the reach
reach of
of a residual
residual current
current (IR)
(IR) polarized
polarized reactance
reactance element
element of
of
reach
reach r for
for a boundary
boundary fault
fault condition.
condition.
! =
Im(V.IR .) .Equation
Im(I.ZlL.IR )
Equation
In
In Equation
Equation 4,
4, r is
is equal
equal to
to the
the reach
reach setting
setting r for
for a fault
fault on
on the
the boundary
boundary of
of a zone.
zone. For
For
faults
faults internal
internal to
to a zone,
zone, r < r .
To
To show
show the
the improved
improved performance
performance of
of the
the IR
IR polarized
polarized reactance
reactance element
element for
for different
different RF
RF and
and
load
load flow
flow conditions,
conditions, compare
compare the
the per
per unit
unit reach
reach result
result of
of Equation
Equation 4 to
to unity;
unity; where
where per-unit
per-unit
reach,
reach, r' = r/r.
rlr. These
These results
results are
are shown
shown in
in Figure
Figure 7.
7.
From the figure, notice this reactance element does not have the under-and overreaching
problems we saw earlier with the Z = V II method.
7
7
4
4
5.DI
U.J
u
z
<
1U
<
U.J
0:
O
U.J
N
5:
<
-J
~
-0:
1z
=>
d:
U.J
0.
I
I
I
I
I
I
I
m=O85
~
z
Q
1<1:
-'
=>
u
..J
<1:
u
~
\
::I:
u
«
w
c:
c:
w
O
z
=>
SAME LINE FOR Rf:O, 10, 25, AND 50.Q PRIMARY
J:
\
u
<1:
LU
0:
1,lI -\1
SET REACH
::I:
u
«
w
I
I
I
,
I
I
I
c:
~ -c:
-60
O
-LOAD
Figure
Resistive
7:
IN
I
60
LOAD OUT
w
>
--0
Per-unit Improved Reactance Reach Calculation (r') Shows IR Polarization
Not Affected by O and Fault Resistance in Homogeneous Systems
Elements
The job of a resistive element is to limit the resistive coverage for a quadrilateral zone of
protection.
Some resistive elements measure the line resistance plus RF. Reference 1
describes a resistance element which limits its measurement to RF alone. Reference 1 also
shows the derivation
of the following
equation for RF:
The greatest advantage of this fault resistance element is that its measurement is not appreciably affected by load flow conditions. This allows setting the resistive boundary (or threshold) greater than the minimum load impedance. The resulting quadrilateral characteristic and
its response to different load flow and RF conditions for an AG fault at m = 0.85 is shown in
Figure 8.
8
LU
U
Z
~
fu
~
LU
cr
O
LU
N
u
Q)
(/1
9
f-I
=>
(/)
LU
a:
Z
Q
cr: f~
<!
-'
-I
=>
~ U
-I
CX~
U
RF CALC
Figure 8: Improved Quadrilateral
MHO
Characteristic Performance Does Not Depend on O
CHARACTERISTIC
The typical means of obtaining a mho characteristic is to use the cosine-phase comparator .
This comparator measures the phase angle, e, between the operating and polarizing signals.
For -90 o ~ e ~ 90 0, the characteristic is circular .The angle e = -90 ° and e = + 90 °
defines the boundary of the characteristic
The mho characteristic
Sop = oV
comparator
in the impedance plane.
has two inputs: operating (Sop) and polarizing
SPOL = Vp
where:
oV
r
ZlL
I
V
Vp
=
=
=
=
=
=
(r.ZlL .1 -V), line-drop compensated voltage
per-unit reach
positive-sequence line impedance
IA + kO.IR
A<t>measured voltage
polarizing voltage
9
(SPOL):
Reference 1 describes the torque expression for this cosine-phase comparator,
p
=
Re(SOp.SPOL
*)
=
Re[(r.ZlL.I
-V).Vp*]
Equation
All points where p = O define the boundary of a mho characteristic
Self-Polarized
Mho
labeled P, as:
5
of reach r.Z1Lo
Characteristic
Earlier we checked the Z = V II result against a rectangular
against a self-polarized
For a self-polarized
mho characteristic
mho characteristic,
characteristic.
Let's now test Z
to see how it performs.
Vp = V.
To determine the boundary characteristic
of
this element, set p = 0, substitute V for Vp in Equation 5, and solve for z:
Re[(r.ZtL.I
Re(r.ZtL.I.V*)
Let r.Z1L
=
I r.Z1L
-V).V*]
= O
-I
V I 2 = 0
where eL = positive-sequence
ev = angle of V
el = angle of I
I L eL
=
and <I>= (ev -el
I Z I L <1>= VII
When I/> = eL,
I Z I =
Z
line angle
Re {1.1 L eL.v*)
I r.Z1L
I
6
I v 12
=
r.ZlL
Next, let Z =
Equation
I
=
I r.Z1L I.
I
r.ZlL
I
.COS(eL-
<1»
)
Equation
Equation 7 describes a mho circle passing through the
origin and r.Z1L on the impedance plane (Figure 9). Equation 7 also shows the self-polarized
mho distance element is equivalent to testing Z = V II against a circular characteristic in the
impedance plane.
10
7
~
n(V/IJ
20
~
"'
9.
10
w
u
z
<
1U
<
w
a:
Re(V/I)
0
.5
Figure 9: Self-polarized Mho Characteristic
with Reach r.Z1L
Figure 10 shows the Z = VII AG apparent impedance values tested against the self-polarized
mho characteristic for different load flow and fault resistance conditions. With load flow and
fault resistance, this relay has severe underreaching problems and slight overreaching
problems. As compared with the rectangular characteristic, the overreaching problem is
reduced because there is less resistive coverage.
-so
10
20
RESISTANCE [.Q sec.]
FAUL T RESISTANCE LEGEND:
X
RF=O.Q
.RF=10.Q
.RF=25.Q
~
RF=50.Q PRI.
Figure 10: Self-Polarized Mlo Performance Depends on ~ and O
11
Solving Equation 6 for the minimum reach required to just detect a fault, instead of Z, results
in the following expression:
Re
Re (v.v.)
(V.V.)
r =
-Re Re (IoZlLoV.)
(I.Z1L.V.)
To determine if the fault is inside or outside the characteristic, compare the r calculation
against r (same process as for the reactance element). The per-unit self-polarized mho
element reach result, r', in Figure 11 shows the amount of under- and overreach for various
RF and load flow conditions for the system shown in Figure 1. The source impedance ratio
(SIR) for this example equals 0.1 (SIR = Z1S/(r.Z1J).
ZIS/(r.Z1J).
SO,
5.0
~.:~!2-P-~~ARY'
O
I
~
~
O
I
~
O
O
w 1UJ
N
N
-I 1..J
0=
...1
cr
4:
~
::.
<1:
-.J1n
-.J (I)
~
w
UJ
, cr
a:
~
u.I :r:
u.
-'
-' uu
w
UJ
In «4:
U)
~ UJ
a:
f- cr
,I.
,
,
m=~8S
r
'
I
m=O.BS
,
-, .,
,,
,,
Rf=25.Q
Rf=25.Q
,
'"
:I:
u
<
:I:
u
<
w
,
---w
w
-'
~
c:i:
w
ci
UJ
a..
0..
,
Rf=5O.Q
PRIMARY
.,/ ~
,/
'"
I
'.
.,
.,I'
~!-=-:~~---
---,
',
0:
---~
0:
t
---,
Rf=10.Q
---'---
:--~--~---:
10
1.-Rf=O.Q
I::> t
~~
:-:--- -
Rf=O.Q
I
u
:I:
SET REACH
REACH
SET
~
<
0
O
~
~
a:
,
I
-60
-60
~
~
Figure 11:
II:
Figure
:
I
I
-".
LOADININ
LOAO
8
I
I
I
I
I
LOADOUr
-
I
LOADOUT -
8
60
60
ffi
w
>
>
0
o
Per-unit Self-polarized Mho Reach Result Illustrates the Amount of Underand Overreach (for SIR = 0.1)
Positive-seouence
Positive-seouence Memorv
MemorY Polarized
Polarized Mho
Mho Characteristic
Characteristic
The biggest disadvantage of using V for the polarizing signal is the lack of security for zero
voltage faults. For these faults the polarizing signal has no definite phase angle.
The ideal polarizing signal should be available at all times, and not disappear with the fault.
One thing we know is that if the system is energized prior to the fault, the prefault voltage is
available. We must memorize this prefault voltage and use it for the polarizing signal.
Table 2 compares the self-polarized and phase-voltage memory-polarized cosine-phasecomparator results for an AG fault at m = 0. Notice the eov -evPRE is available (not
indeterminate) and less than 90° for all cases. This shows memorized prefault voltage is
excellent polarization.
12
12
Table 2: Memory Polarization is Better than Self-Polarization for Close-in Faults
If we use memorized positive-sequence voltage (Vlmem) for Vp, the polarizing signal is
present even if the memory has expired for all fault types except three-phase faults .Another
benefit of V p = V 1mem is the improved security during open-pole conditions in single-pole
tripping
schemes .
To obtain the boundary equation for the positive-sequence memory-polarized mho characteristic, set Vp = Vlmem in Equation 5, and solve for the boundary condition. This yields:
Equation
Figure 12 shows the per-unit reach calculation (r') for different RF and load flow conditions
for a SIR = 0.1. Notice there is not much difference between the performance of the
V1mem and V polarized mho elements for AG faults at m = 0.85. This is due to the
relatively strong source behind the relay. What happens if we increase the SIR?
13
8
~
5.0
5.0
I
o
O
I~
~
0
O
UJ
UJ
N
t:::!
-1a:
a:
~,
~
~
--1
O
O
0.
0.
1--I'
-J
~
~
tn
tn
w
w
a:
0:
~
:I:
:I:
u
u
~
.-UJ ~
.> UJ
a:
>
0:
I
,
a:
a:
w
UJ
0.
0.
,
I
I
I
m=O.BS
m=0.85
-,
,
,
, -,
r
I
-,-
Rf=2S.Q
'"
Rf=25.Q.
'
,
--
---'--
Rf=10.Q
--0,0
Rf=10.Q.
ffi
0-0'0
,
,
1.0
1.0
:1:
:x:
uu
..<
w
w
0:
c:
c:
w
o
O
zz
"
:
::>
:)
:~;:;~::::::-~~:
Rf=O.Q
Rf=O.Q.
0 I
0
t
:I: ~
:::::::::-:
SET
REACH
SET REACH
L>
<
w
0:
I
I
-6U
-60
-LOAD
-LOAD
Figure 12:
12:
Figure
I
,-
,
1-
!=
z:5
=>
I
Rf=SO.Q PRIMARY
PRIMARY
Rf=50..Q
I
IN
IN
I
15
8
I
I
I
Il
60
60
ffi
>
o
LOADOUT
OUT-LOAD
Mlo Reach Result Illustrates the Same Amount
Per-unit V1mem Polarized !\fi1o
Mlo (for SIR = 0.1)
of Under- and Overreach as the Self-polarized !\fi1o
Figures 14 and 15 show the amount of underreach for the self- and positive-sequence memory
polarized relays for a AG fault at m = 0.85 on the system in Figure 13 (SIR = 1.2). From
these figures, you can see the V1mem relay performance is better than the self-polarized relay
because its underreach is much less. This improvement increases with increasing SIR.
EL15
BUSS
BUSR
ELO
7777
zZ1S
15 =
Z 1L
=Z1L
Z
OS
ZOS
PTR
CTR
m
kV
=
3 .Z 15
=3.Z1s
=
3500:1
=3500:1
= 320:1
= 0.85
= 400
zZ1L
1L =
2 + j ,22 .Q.pri.
=2+j-22.Qpri.
=
0.18 + j'2.01.Q. sec.
=0.18+j-2.01.Qsec.
ZOL=3Z1L
Z
OL= 3 Z 1L
Figure 13: System Single Line Diagram (SIR = 1.2)
14
14
zZ1R
1R =
z 15
=Z1S
Z
OR= Z OS
Zo~=Zos
~
15.D
15.0
III
j
Rf=5D.Q
Rf=5D.QPRIMARY
PRIMARY
I
/ /
/
./.
/
I
m=085
m=085
/;/
0
:I:
,
~
..,
10.0
10,0
..:.
~
0
w
Q
w
N
1N
-",! 1-'
a:
:J
rr'
ii:
::>
-t
(/)
-t
tn
-'
w'/
-'
UJ
Oa:c::I:
-/
I:i
~
u:. :t
u:.
-'
u
u
-'
w
-t
<I:
w
(/) UJ
~
5.0
VJ
5.0
c:
1f-'zz,
=>
=>
a:
ci:
w
a.
w
I
~
-.'.
/
,
:,
,
,,
,
/
.,/
,
,
,
,,
,
n
Rf=25n
---
1"1=
f
25
J:
~n
-----u
--w
0.
--a:
t
Rf=10.Q.
~f-=-1-0-~
1.0
D
0
-60
-60
-~
SET REACH
Rf=O.Q.-1---
III
I
IN
LOADIN
Selr-Polarized
Self-Polarized
M1o
Mlo
5 I
i ,
I
O
5
~-LOAD
Figure
Figure 14:
14:
I
60
60
II
LOAD OUT
LOADOUT
Underreach
Underreach
-~
Increases
Increases Dramatically
Dramatically
with
with Increasing
Increasing SIR
SIR
(SIR
(SIR shown
shown == 1.2)
1.2)
1S.0
15.0 r
I
I
I
I
I
I
m=0.85
I
m=0.85
~
10.0
~
10.0
L:
Rf=50.Q
L:
Rf=50.Q PRIMARY
PRIMARY
o
0
w
N
~ 1a:
-' r I.-. .~
1a:
..1 r
<fEu
-'
O
a.
(j) ~
If)
w
=>
<f
<I:
::>
In
w
0:
I
E
u
1
-a:
z>
E
<11 w
<
E
w
0:
."
-'
O
Q.
"
,"
S."0
'.
Rf=25.Q
-'
c
:I:
5.0
'.
>
1-
Rf=25.Q.
:)"
Z
:)
a:
ci:
w
w
a.
Q.
-'-.-
u
w
1
~
w
Rf=10.Q
Rf=10.Q.
Rf=O.Q
§
SET
SET REACH
REACH
1.0
1.0
Rf=
0
0
1---
I
-60
-60
04
..LOAD
Figure
Figure 15:
15:
I
I
I
I
6
O
LOAD IN
IN
II
:I:
I
60
60
LOAD
our
----~
LOADOUT
u
i
~
i
I
>
0
V1mem Polarized M1o Underreach is Less than Selr-polarized M1o with
Increasing SIR (SIR shown = 1.2)
15
15
THE
V1mem
POLARIZED
DIRECTIONAL
ELEMENT
MHO
DENOMINATOR
TERM
IS A
In Equation 8, V in the numerator could be zero for close-in faults. Therefore, we cannot
rely on the sign of r to dependably indicate direction. Fortunately, the denominator of
Equation 8 defines a directional element. This directional element measures the angle e
between the operating signal {I.Z1J and the polarizing signal (Vlmem).
(V1mem). The angle e = -90°
and e = 90 ° defines the zero torque threshold.
Label the denominator term for the AG mho distance element as MAGD.
MAGD is defined as:
From Equation 8,
MAGD
.(V1mem)*]
MAGD = Re[l.Z1L
Re[I°ZlL"(Vlmem)*]
Equation 9
9
Equation
Figure 16 shows the inputs to this denominator for forward (16a) and reverse (16b) AG
faults. For simplicity of illustration, this example assumes O = 00,
0°, RF = 0, and a 90°
system angle.
90.
90.
90.
V1mem
V1
V1 mem
Z1L.1
Z1L.1
270.270
.
270.
a.
ForwardAG
AGFault
a. Forward
Fault
b. Reverse
Reverse AG
AG Fault
Fault
b.
Figure 16: AG Mho
l\D1o Denominator Term Inputs for Forward and Reverse AG Faults
The sign of MAGD is positive for forward faults and negative for reverse faults. Because the
sign changes with fault direction, we can use the denominator as a directional element.
CAN
CAN SUPERPOSITION
SUPERPOSITION
IMPROVE
IMPROVE
THE
THE Z =
= V
V IIII PERFORMANCE?
PERFORMANCE?
v II method under- and overreaches for resistive ground faults with load because I
The zZ = V
(IAPRE)from the faulted phase
and IF are not in phase. Subtracting balanced prefault current {lAPRE)
(IJ results in a current (1')
current {lJ
{1') which is in phase with the total fault current, IF, assuming
balanced prefault load. This I' current is referred to as the superposition current. Let's
analyze the approach of substituting I' for the faulted phase current in the AG equation shown
in Table 1 and check its performance.
16
16
Figure 17 shows the superposition current apparent impedance calculation (Z') results for AG
faults at m = 0.85 and various RF and load flow conditions. This modification of the
apparent impedance relay has severe under- and overreaching tendencies. One difference
between the distance measurement results shown in Figure 17 and those shown in Figure 10,
is the load flow conditions which cause under- and overreach are exactly opposite. The
superposition apparent impedance relay underreaches for load out, and overreaches for
incoming load flow, where the simple apparent impedance relay underreached for incoming
load and overreached for load out.
Im(Z')
~
"
8=+30"
8=0 "
x
8=-30 "
Re(Z')
8=-60 "
FAULT RESISTANCELEGEND'
X RF=O.Q
.RF=10.Q
.RF=25.Q
~ RF=50.QPR(,
Figure 17: Superposition Apparent Impedance Performance Depends on RF and O
Also notice the right-hand resistance threshold must be set almost ten times greater than the
line resistance value to just detect an AG fault with zero fault resistance during heavy
incoming load flow conditions (0 = -600).
-60°). While it is desirable to detect these faults, this
large resistance reach makes the relay susceptible to overreach for lower incoming load
conditions (eg. 0 = -30°) with fault resistance.
These
These last
last points,
points, coupled
coupled with
with those
those noted
noted earlier
earlier for
for the
the Z = V II calculation
calculation results,
results,
emphasizes
not an
emphasizes that
that an
an apparent
apparent impedance
impedance relay
relay is
is not
an acceptable
acceptable alternative
alternative to
to properly
properly
polarized
polarized distance
distance elements.
elements.
17
17
WHEN
CAN
WE
USE
V II CHARACTERISTICS?
One
One example
example where
where Z == VII
VII can
can be
be useful
useful is
is the
the detection
detection of
of balanced
balanced conditions,
conditions, such
such as
as
load.
load. For
For example,
example, we
we can
can define
define incoming
incoming (ZLOADIN)
(ZLOADIN) and
and outgoing
outgoing (ZLOADoUT)
(ZLOADoUT) load
load
regions
regions with
with thresholds
thresholds and
and check
check the
the V II calculation
calculation result
result against
against these
these thresholds.
thresholds. These
These
regions
regions define
define the
the Load-Encroachment
Load-Encroachment Characteristics.
Characteristics. If the
the calculated
calculated V
VIIII is
is inside
inside either
either of
of
these
these regions,
regions, the
the load-encroachment
load-encroachment logic
logic blocks
blocks the
the phase
phase distance
distance elements
elements from
from tripping.
tripping.
A load
load condition,
condition, a three-phase
three-phase mho
mho (3P21)
(3P21) and
and relay
relay load-encroachment
load-encroachment characteristics
characteristics are
are
shown
shown in
in Figure
Figure 18.
18. For
For this
this heavy
heavy load-out
load-out condition,
condition, the
the 3P21
3P21 element
element is
is blocked
blocked from
from
operating
operating because
because load
load also
also resides
resides inside
inside the
the LOADoUT
LOADoUT load-encroachment
load-encroachment characteristic.
characteristic.
Im(V/I)
35
35
I
T
u
(1)
~
9.
~
v
IJ)
U1
3P21 TIME
TIME
DELAYED
DELAYED
3P21
ZLOAD
ZLOAD OUT
OUT
LOAD
Re(V/I)
W
.uU~
Z
«
1U
«
W
a:
ZLOAD
ZLOAD IN
IN
1U
~
L
ZLOAD
OUT
52A
!
:
-35
-35
II52A
-35
35
35
35
RESIST
ANCE [.Qsec
RESISTANCE
[.Qsec.]
Z1S=(0.1).Z1L
Z1s=(0.1).Z1L
Figure 18:
18:
Figure
6=60.
6=60"
zZ = VII
VII Load-Encroachment
Load-Encroachment
ZR
= 3. Z1L
ZR=3.Z1L
Characteristic
Characteristic
Prevents
Prevents Phase
Phase Distance
Distance
Element
Element from
from Operating
Operating Under
Under Heavy
Heavy Load
Load Conditions
Conditions
SUMMARY
SUMMARY
1.
1.
The apparent impedance calculation result (Z = V /1)
II) compared with geometric characteristics (box or circle) presents serious under- and overreaching problems when load flow
and fault resistance are combined.
2.
2.
The
The zZ = VII
VII method
method has
has the
the same
same performance
performance deficiencies
deficiencies as
as self-polarized
self-polarized relays.
relays.
18
18
3
The z = v 1I approach is not improved
4.
Writing the torque equation for a properly polarized relay characteristic, setting it equal
to zero, and solving for the minimum reach required to just detect the fault yields a result
which we can test against scalar thresholds (Reference I). This method achieves the very
desirable result of offering one calculation (per fault loop) for all zones with the
performance of properly polarized relay elements.
5
We present ground-fault-resistance elements which estimate the fault resistance. This
estimate rejects the load-influenced positive-sequence current, can be used for multiple
zones, and can be set greater than the minimum load impedance.
6.
The z = v II calculation
encroachment
by using superposition
can be used to detect load conditions,
characteristic
current.
as in the new load-
(Reference I).
In conclusion, the Z = V 1I calculations have some use in elements intended to measure load,
but perform poorly compared to properly polarized relay element calculations, as represented
by the equations given for r and RF"
REFERENCES
1.
Edmund 0. Schweitzer III and Jeff Roberts, Distance Element Design, 19th Annual
Western Protective Relay Conference, October 1992, Spokane, W A, USA.
2.
A. R. Van C. Warrington, Protective Relays: Their Theory and Practice, Chapman and
Hall, 1969, Volumes I and II.
.
3.
v.
4.
Paul M. Anderson, Analysis of Faulted Power Systems, The Iowa State University Press,
1983.
Cook,
Analysis
of Distance
Protection,
19
John Wiley
and Sons Inc.,
1985
BIOGRAPHIES
Edmund 0. Schweitzer. III is President of Schweitzer Engineering Laboratories, Inc.,
Pullman, Washington, U.S.A., a company that designs and manufactures microprocessorbased protective relays for electric power systems. He is also an Adjunct Professor at
Washington State University. He received his BSEE at Purdue University in 1968 and MSEE
at Purdue University in 1971. He earned his PhD at Washington State University in 1977.
He has authored or co-authored over 30 technical papers. He is a member of Eta Kappa Nu
and Tau Beta Pi.
Jeff B. Roberts received his BSEE from Washington State University in 1985. He worked for
Pacific Gas and Electric Company as a Relay Protection Engineer for over three years. In
November, 1988 he joined Schweitzer Engineering Laboratories, Inc. as an Application
Engineer. He now serves as Application Engineering Manager. He has delivered papers at
the Western Protective Relay Conference, Texas A&M University, Georgia Tech and the
Southern African Conference on Power System Protection. He holds multiple patents and has
other patents pending.
Armando Guzman received a BSEE degree from University Autonomous of Guadalajara
(UAG), Mexico, in 1979. He received a Fiber Optics Engineering Diploma from Monterrey
Advanced Studies Technological Institute (ITESM), Mexico, in 1990. He served as Regional
Supervisor of the Protection Department in the Western Transmission Region of Federal
Electricity Commission (the electrical utility company of Mexico) for 13 years. He lectured
at the University Autonomous of Guadalajara in power system protection. Since 1993, he has
been with Schweitzer Engineering Laboratories, Inc., where he is currently an Application
Engineer. He has authored or co-authored several technical papers.
Copyright © SEL 1993, 1994
All rights reserved.
20