Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Power System Protection
for Engineers
Transmission Line Distance
Protection
Part 2
Copyright © SEL 2004
Technical papers supporting this section:
6022.pdf, Z = V/I Does Not Make a Distance Relay by J. Roberts; A. Guzman; E.O.
Schweitzer, III
6063.pdf, Innovative Solutions Improve Transmission Line Protection (WPRC '97) by
Daqing Hou; Armando Guzman; Jeff Roberts
6010.pdf, Distance Relay Element Design by Jeff Roberts; Dr. Edmund O. Schweitzer
III
6065.pdf, Application Guidelines for Ground Fault Protection by Joe Mooney, P.E.;
Jackie Peer
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Transmission Line Distance
Protection (Part 2) Objectives
l
Discuss the Effect of Fault Impedance on
Distance Relays
l
Discuss the Load Encroachment Problem in
Distance Relays
l
Describe the Effect of Magnetic Mutual
Coupling on Ground Distance Relay
Performance
l
Describe and Compare Distance Relay
Polarizing Methods
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Distance Protection Problems
l
Infeed
l
Fault Resistance
l
Unequal Measured Impedances
During Faults
l
Evolving Faults
l
Load Encroachment
Transmission line protection is complex. Problems such as infeed, fault resistance,
unequal measured impedances during faults, load encroachment, and mutual coupling
affect the apparent impedance of distance relays. Fault resistance and mutual coupling
may also affect ground directional overcurrent relays. These problems may be
complicated by the evolving character of many faults.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Distance Protection Problems
l
Mutual Coupling
l
Simultaneous Faults
l
Cross-Country Faults
l
Power Swings
l
Three-Terminal Lines
All these problems may affect distance and directional overcurrent relays. Cross-country
faults, simultaneous faults, and CT saturation may also present a problem for differential
schemes.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Distance Protection Problems
l
Reactor-Compensated Lines
l
Short Lines
l
CT Saturation
l
CCVT Transients
l
Series-Compensated Lines
Three-terminal lines and short lines also have special protection requirements. The
ringdown at subharmonic frequency resulting from compensation reactors may also
create protection problems. Series-compensated lines are extremely difficult to protect.
All protection principles may have problems, because of the possibility of voltage and
current inversions. If the series-compensation capacitors are carefully selected, the
possibility of current inversions can be eliminated. In such a case, a differential
protection scheme may be the best option.
In this presentation, we will examine transmission line protection problems that exclude
CT saturation, CCVT transients, series-compensated lines, three-terminal lines, short
lines, and reactor-compensated lines.
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Fault Resistance
l
l
Phase Faults
t
Arc resistance
t
Other components (trees, etc.)
Ground Faults
t
Arc resistance
t
Tower and tower footing
t
Ground return path
t
Other components (trees, etc.)
Fault resistance affects all protection principles to some extent. For phase faults (threephase, line-line) fault resistance results largely from the resistance of the arc between the
faulted conductors. If the fault is initiated by a tree or something else in the line, its
resistance should also be considered.
Ground fault resistance includes the resistance of the arc between the conductor and the
tower, the tower and tower footing resistance, and the ground return path resistance.
Ground faults may also involve other objects such as trees.
Ground fault resistance values are typically much greater than phase fault resistances. For
transmission line faults involving trees, for example, the fault resistance may be on the
order of hundreds of ohms.
In distribution lines, an important component of ground fault resistance is the contact
resistance between the fallen conductor and ground. For a conductor falling on dry
asphalt, for example, the fault resistance could be close to infinity. The detection of fallen
conductors in overhead distribution systems is a very complex protection problem.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Arc Resistance
440 × L
R arc =
W
I
L: Arc Length in Feet
I: Arc Current in Amperes
Arc resistance is quite variable. A commonly accepted value for currents between 70 A
and 20,000 A is an arc voltage drop of 440 V per phase, independent of current
magnitude.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Arc Resistance
28710 × L
Rarc =
Ω
1.4
I
L: Arc Length in Meters
I: Arc Current in Amperes
This is another empirical expression for arc resistance with the arc length in meters
(instead of feet). Observe that there is a 1.4 exponent in the current in this expression.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Effect of Fault Resistance
l
Reduces Fault Current Values
l
Reduces Voltage Sag in the Faulted
Phase
l
Increases Measured Impedance
Values
l
Limits Protection Sensitivity
The general effect of fault impedance is reduction in protection sensitivity. Fault
impedance reduces the fault current values and the voltage sag in the faulted phases.
Fault impedance also increases the value of the impedance measured by distance relays.
Fault resistance limits the sensitivity of all protective relay types.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Fault Resistance
Radial Lines
V
mZL
R
I
F
21
Z = V I = mZ L + R F
Fault Resistance Produces Relay Underreach
The figure shows the effect of fault resistance on the impedance a distance element
measures in a radial system. The distance element measures the fault loop impedance,
including the fault resistance. The result is a distance estimate greater than the real
distance to the fault. This inaccurate distance estimate makes the distance element
underreach.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Fault Resistance
Looped Lines
V
mZL
I
RF
IF
21
V = I mZL + IFRF
Z = V I = mZ L +
IF
I
RF
An additional problem in looped lines is the infeed effect in the fault impedance. The
relay does not measure the current contribution to the fault from the remote-end source.
As a result, RF in the impedance estimate is multiplied by an infeed effect factor IF / I.
The effect of this factor is twofold. The infeed effect increases the value of the apparent
fault resistance (the magnitude of the factor is greater than unity). The infeed effect factor
is, in general, a complex number, so the apparent fault impedance is no longer purely
resistive.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Impedance Plane Diagram
X
IF
I
RF
mZL
Z
R
In this impedance plane representation, the effect of fault resistance in looped lines can
be seen. The distance element should measure an impedance mZL. However, the
measured impedance is Z. Observe that the infeed effect factor, IF / I, increases the value
and produces a phase shift in the fault resistance RF.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
System Single-Line Diagram
E Ðd
I
BUS S
ZS
(1-m)•ZL
m•ZL
RELAY
E Ð0
BUS R
RF
ZR
IF
Z1S = 2 Ð 80°
Z1L = 8 Ð 80°
Z1R = Z1S
Z0S = 3•Z1S
Z0L = 3•Z1L
Z0R = Z0S
The power system model shown will be used to study the effect of RF and the power
angle, d, on the apparent fault impedance. For simplicity, a homogeneous system (all
source and line impedances have the same angle) will be considered.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Effect of RF and δ
RF (W sec.)
8
d = -60°
6
d = -30°
4
2
d = 0°
X
d = +30°
d = +60°
Z1L
Reactance (W sec.)
10
Im (V/I)
0
-2
-2
0
2
4
6
8
X
=0
=1
=4
=8
Re (V/I)
10 12 14
Resistance (W sec.)
This figure shows the effect of RF and d on the impedance estimate. For bolted faults,
the distance element measures the correct impedance value. An increase in the value
of RF increases the measured impedance and produces relay underreach.
In radial lines, or when d = 0, the apparent impedance is purely resistive. A reactancetype characteristic would avoid relay underreach. However, for d ¹ 0, even a reactance
element may overrreach (d > 0) or underreach (d < 0). In other words, the direction of
the pre-fault power flow will determine the reactance element behavior.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Measured Impedances During
Faults
mZL
V
IF
I
21
ZX
C = I IF
A distance protection scheme has six basic relay elements. For the phase elements, the
line-line voltages and the differences of the line currents are used as input signals.
Ground distance elements receive the phase voltages and the compensated line currents
as input signals. The zero-sequence current is used to compensate the line current inputs
of ground distance elements. These connections ensure that the fault-loop element(s)
correctly measure the fault-loop impedance. For example, for an ABG fault, three
distance elements correctly estimate impedance: AB, AG, and BG elements. The
question is, what impedances do the other three elements measure for this fault? These
elements need to measure impedances with values no lower than the fault-loop
impedance. This ensures that the distance elements that measure the correct impedance
value will make the tripping decision.
The simple power system shown in the figure can be used for an analytical study of the
impedances measured by the different distance elements during faults. The idea is to
derive the expressions of the measured impedance using symmetrical component
techniques. In the figure, mZL is the impedance of the protected line section. The
positive-sequence value of this impedance, mZL1, is the correct value that the distance
elements measure. ZX is an impedance including mZL and the source impedance behind
the relay. The factor C expresses the infeed effect in the fault resistance.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Measured Impedances
Relay
Element
Fault Type
ABC
AB
m Z L1 +
BC
m Z L1 +
CA
m Z L1 +
BC
RF
C1
m Z L1 + 3 Z X 1Ð -90° +
RF
m Z L1 +
C1
RF
C1
RF
C1
Ð -60°
RF
C1
m Z L1 + 3 Z X 1Ð90° +
RF
C1
Ð60°
This table shows the expressions of the impedances phase distance elements measure for
two types of phase faults (ABC and BC faults). For ABC faults, all three elements
measure the loop impedance value, which unfortunately includes the fault impedance
term. For BC faults, only the fault-loop element BC correctly measures the impedance.
The other two elements (AB and CA) estimate higher impedances. This means that the
BC element will make the tripping decision for zone-end faults.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Measured Impedances
Relay
Element
Fault Type
ABC
AG
m Z L1 +
BG
m Z L1 +
CG
m Z L1 +
BC
RF
¥
C1
RF
C1
RF
C1
m Z L1 +
Z X1
R
Ð -90° + F Ð -30°
3
3C1
m Z L1 +
Z X1
R
Ð90° + F Ð30°
3
3C1
This table shows the expressions of the impedances measured by ground distance
elements for two types of phase faults.
For ABC faults, all three elements measure the fault-loop impedance. In other words,
ground distance elements may respond to three-phase faults unless, for example, their
operation is supervised with a zero-sequence overcurrent element. This tendency to
operate is also present for other system balanced conditions such as normal load or power
swings. For phase-to-phase faults, the ground distance elements measure impedance
values greater than the fault-loop impedance.
The effect of ground faults on ground distance elements is not presented in this analysis.
The result is the same as for the phase elements. That is, the fault-loop element correctly
measures the impedance, and the healthy phase elements estimate impedance values
greater than the fault-loop impedance.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Example Power System
m (per-unit of ZL)
ZS
ZL
Relay
SOURCE S
ZL1 = 8 Ohms
ZL0 = 24 Ohms
ZS1 = 1 Ohm
ZS0 = 3 Ohms
FAULT
Digital simulation is an excellent tool for studying the impedances that distance elements
measure during faults in complex power systems. The figure shows a power system
model that will be used for digital simulation studies.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Close-In Phase A-to-Ground Faults
Variable RF
X
Line Angle
Reach =
300%•Z1L
Characteristics
Self-Polarized
Expanded
4 CG
0
0
BG
2
4
AB
0 AG
0
R
CA
4
4
The figure shows the impedances all distance elements measure for a close-in A-phaseto-ground fault for different RF values (0 to 4 ohms).
Two mho-element characteristics are shown, a self-polarized mho characteristic (crosses
through the origin of coordinates) and a cross-polarized mho characteristic. As will be
seen in a future presentation, the effect of mho element polarization is to expand the
characteristic backwards in relation to the origin of coordinates for forward faults.
Polarization ensures mho element directionality for close-in bolted faults.
The figure indicates that only the AG distance element correctly measures the impedance
for this AG fault. It is also clear from the figure that a self-polarized mho element may
not see the fault. For a polarized mho element, the fault is well within the characteristic.
Other distance elements such as AB, CG, and CA may operate for this fault, so distance
element operation cannot be relied on to make single-pole tripping decisions. In this case,
for example, a three-pole trip would be issued instead of a single-pole trip for a singleline-to-ground fault.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Phase A-to-Ground Faults
Variable RF and Fault Location
X
AB
Line Angle
Reach = 300%•Z1L
100%
100%
50%
CA
AG
50%
CG
0
0
0
R
0
50%
50%
100%
100%
BG
The figure shows the effect of displacing the fault location along the protected line. The
result is the appearance of fault areas in the impedance plane. The impedance each
distance element measures will lie inside the corresponding fault area. The position for
the measurement depends on fault location and fault resistance. The sides of the fault
areas marked with dots are the locii of the measured impedances for bolted (RF = 0)
faults. The straight lines parallel to those sides are the locii of the measured impedances
corresponding to the maximum RF value (4 ohms.)
The basic conclusion is the same as for the previous figure: there are several distance
elements prone to operate for a single line-to-ground fault. For single-pole tripping, the
tripping decisions of the distance elements cannot be used. A separate algorithm is
needed to determine the fault type for single-pole applications.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
BCG Fault at Remote Terminal
X
15
CA
1
7
CG
7
-10
-5
NO LOAD
1
5
-15
Line Impedance
1
BC
AB
7
BG
5
7
10
15
CASE
1
2
3
4
5
6
7
RF
0.00 W
0.25 W
0.50 W
1.00 W
2.00 W
5.00 W
10.00 W
R
This figure shows the impedances the distance elements measure for a BCG fault at the
remote end of the relay reach. The dots on each fault locus represent different values of
fault resistance (0 to 10 ohms).
For bolted faults, three distance elements (BC, BG, and CG) see the fault exactly at the
end of the reach corresponding to each element. When the fault resistance increases, the
impedance the CG element measures moves away from the relay characteristic. On the
other hand, the BC impedance penetrates the relay characteristic. This element
overreaches, so it must be blocked from operation for this fault. For simplicity, the effect
of the fault resistance on the BC element impedance is not shown. It is clear, however,
that this impedance also leaves the operation characteristic.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Measured Impedances During Faults
l
Distance Elements Measure
Different Impedances
l
Ground Elements Can
Overreach for Line-LineGround Faults
l
Phase Elements Can Operate
for Close-in Line-Ground Faults
In summary, distance elements measure different impedances for unbalanced faults.
Phase elements can operate for close-in, line-to-ground faults, and ground elements can
overreach for line-to-line-to-ground faults. A separate algorithm is needed to determine
the fault type. The information on the fault type can be used to decide on single-pole
tripping and to block the operation of ground distance elements for line-to-line-to-ground
faults.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Evolving Faults
l
Variable RF and IF
l
The Fault Type Changes
(AG®ABG ®ABCG)
l
It Is Difficult to Detect Fault
Inception and Fault Type
Changes
Evolving faults present problems for all protection principles. Many faults evolve in
some way. The fault resistance RF may vary with time. As a result, the fault current is
variable. Another common type of fault evolution is a change of fault type. Many faults
initiate as line-to-ground faults and evolve into line-to-line-to-ground faults and/or threephase-to-ground faults.
For evolving faults, it is generally difficult to detect fault inception and fault type
changes.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Measured Impedance for Load
Conditions
V
I
P, Q
21
In Per-Unit:
SÐj = VIÐj = P + jQ
V
V2
Z = = Ðj =
Ðj
I
S
I
V
Both phase and ground distance elements measure impedance for normal load conditions.
As can be seen in the figure, the measured impedance depends on the load flow
conditions. An increase in the apparent power, S, transferred over the line reduces the
magnitude of the measured impedance
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Load Impedance Regions
X
Maximum
Load
Load OUT
Load IN
R
The impedance angle depends on the direction of P and Q. For positive values of P and Q
(both P and Q flowing into the line), j is between 0° and 90° and the measured
impedance lies on the first quadrant of the impedance plane. A negative Q value brings
the impedance to the fourth quadrant.
Accordingly, a negative P value will move the measured impedance to the other two
quadrants: to the second quadrant for a positive Q value and to the third quadrant for a
negative Q value.
The figure shows the possible regions of the measured impedance for normal load
conditions. For positive P values (Load OUT in the figure), the impedance is in the first
or fourth quadrants. For negative P (Load IN), the impedance is in the second or third
quadrants.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Load Encroachment
X
R
Checks for load encroachment problems can be performed by superimposing relay and
load characteristics on the impedance plane. In the figure, it can be seen that certain load
conditions result in penetration of the impedance in the relay characteristic.
A traditional solution to avoiding distance element misoperation is to shape the relay
characteristic to exclude the load impedance regions. A drawback of this solution is that
it limits the fault resistance coverage of the distance element.
A new solution is to create a relay load element having the same shape as the load
impedance regions. This new element may be used to block the distance element. In this
case, only a small section of the relay characteristic is lost.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Power Swings
Example Fault on Line A-B
A
B
p
L1
q
The relay is supposed to be protecting line L1, and its location is at Bus P. The fault
occurs on line A-B.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Power Swings
No Relay Misoperation
Second Clearing
t=t2
X
First Clearing
t=t1
t=0+
Fault
q
L1
p
t=t3
L1 Relay at p
Post-Fault
Power Swing
Pre-Fault
t=0R
The figure shows the impedance measured by a distance relay for an external fault. As
expected, the apparent impedance moves to an external point. After the fault clears, the
apparent impedance does not return instantaneously to the load equilibrium point, but
there is a post-fault “slow” oscillation, or swing. The characteristics of the oscillation
depend on many parameters of the power system. The case shown in the figure shows
that the oscillation does not produce any relay misoperation.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Power Swings
Relay Could Misoperate
Second Clearing
t=t2
X
First Clearing
t=t1
t=0+
Fault
q
L1
p
t=t3
L1 Relay at p
Post-Fault
Power Swing
Pre-Fault
t=0R
The figure shows a case where the post-fault power swing enters into the relay first zone
operation characteristic. This will produce an undesired operation of the relay.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Power Swing Blocking
Traditional Scheme
X
+
B
B
21
tD
T
LOAD
tB
AUXT
21
52/TC
AUX
R
l
For a Fault, tD-tB Is Almost Zero
l
For an Oscillation, tD-tB is Relatively Large
l
Time Relay “T” Is Set to Block the Tripping (21 Over
52/TC)
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Parallel Lines - Mutual Coupling
Parallel lines is a very common case in transmission systems. The magnetic field
produced by a faulted line influences the behavior of the voltages and currents of a
neighboring line. This influence is called mutual coupling between lines.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Zero-Sequence Mutual Coupling
I0M
Z0M
IR,
I0
Relay
The figure illustrates mutual coupling. For a ground fault on one of two double-circuit
lines, the zero-sequence current flowing at each line induces a voltage in the other line.
This effect modifies the voltage ground distance elements measure. If the mutually
coupled current flows in the same direction as the relay current, the measured voltage
will increase and the distance element will tend to underreach. On the other hand, if
the mutual current direction is opposite to that of the relay current, the relay element
will measure a lower voltage and tend to overreach.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Magnetic Mutual Coupling
l
Occurs in Double-Circuit Lines
l
Affects the Zero-Sequence
Network
l
Z0M= 50–70% of Z0
l
Very Low Coupling in the Positive
and Negative-Sequence Networks
(5–7%)
Magnetic mutual coupling between multiple-circuit lines affects distance and directional
ground relays. Typical values of the zero-sequence mutual coupling impedance, Z0M, are
on the order of 50 percent to 70 percent of the zero-sequence impedance, Z0. Very low
coupling occurs in the positive-sequence and negative-sequence networks.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Effect on Ground Distance Relays
(
)
V a = m Z1L I a + k 0 I res + m Z0 M I 0 M
Z=
Va
I a + k 0 I res
= m Z IL + m Z0 M
I0 M
I a + k 0 I res
Relay Underreaches When
I0M and I0 Flow in the Same Direction
These expressions show the effect of mutual coupling on the impedance ground distance
elements measure. I0M is assumed to be positive when it flows in the same direction as
Ires. The result is an increase in the apparent impedance, Z, and a relay underreach. A
negative value of I0M reduces the measured impedance, and the relay element
overreaches.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Parallel Lines With Mutual Coupling
C
D
mZ
(1-m)ZL
L
B
A
Z
2 ZL
ZC
ZL
ZA
ZB
0
0.2
0.4
0.6
0.8
1.0
m
The figure shows the ground distance element behavior for a ground fault on a doublecircuit transmission line with both lines connected in parallel. For simplicity, it is
assumed that the system is energized at one end only.
In the lower figure, the impedances ground distance elements measure at locations A, B,
and C are shown as a function of the distance, m, to the fault from location A. For relay
elements A and C, the apparent impedances, with mutual coupling, are represented by
full lines, and dotted lines are used to represent the measured impedances without mutual
coupling. The latter case gives the correct impedance values and serves as a reference for
analysis. For relay element B, the measured impedance plot without mutual coupling
would be a straight line from ZB = ZL at m = 0, to ZB = 0 at m = 1.
The effect of mutual coupling in this case is that none of the ground distance elements
correctly measure the distance to the fault. For relay elements A and C, the mutually
coupled current flows in the same direction as the relay current. These elements measure
higher impedance values and tend to underreach. For relay element B, the mutual current
flows opposite to relay current. The result is a lower apparent impedance value and a
tendency for the relay element to underreach.
Transmission Line Distance Prot II_r8
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Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Zero-Sequence
Mutual Coupling Compensation
(
)
Va = mZ1L Ia + k0 Ires + mZ0M I0M
æ
ö
Z0 M
ç
I0 M ÷
V a = m Z1L I a + k 0 I res +
ç
÷
Z1L
è
ø
I relay = I a + k 0 I res + k 0 M I0 M
k 0 M = Z0 M Z1L
The mutual-coupling error may be compensated for by providing the faulted-line relay
element with information on the mutually coupled current. These equations show that an
additional compensation term, k0M I0M, is needed in the relay current of the ground
distance element. The compensation factor, k0M, equals the ratio of the zero-sequence
impedance to the positive-sequence impedance of the protected line. Several commercial
distance relays have an additional current input for the mutually coupled current.
Transmission Line Distance Prot II_r8
36
36
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Mutual Coupling
Compensation Limitations
l
Provides Compensation Only to the
Faulted Line Relays
l
I0M is not Always Available at the Relay
Location
A limitation of mutual coupling compensation is that it eliminates the distance
measurement errors only for the faulted-line ground elements.
In the parallel-line case that was presented before, compensation works for relays at
locations A and B and fails for the relay at C. The problem with the relay at C is that the
level of compensation needed depends on the fault location, m.
Another limitation of mutual coupling compensation is that I0M is not always available at
the relay location.
Transmission Line Distance Prot II_r8
37
37
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Difficult System Arrangements
for Zero-Sequence Compensation
This figure shows cases in which the mutually-coupled current I0M is not available at
the relay location.
Transmission Line Distance Prot II_r8
38
38
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Case Where Compensation Fails
Experience shows that the first zone setting for the relay should be reduced to avoid
overreaching for severe cases of zero-sequence mutual coupling. In some cases, the first
zone may need to be reduced by 60 percent.
Transmission Line Distance Prot II_r8
39
39
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Introduction to
Distance Relay Polarizing
Transmission Line Distance Prot II_r8
40
40
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Basic Distance Element
Signal
V
I
S1
Phase
Forming
Signal
Trip
Comparison
S2
Forming
S1 = -V + Zr I
S2 = V
Operating Quantity
Polarizing Quantity
(
)
Operation Condition: l1 £ arg S1 S 2 £ l 2
Transmission Line Distance Prot II_r8
41
41
Power System Protection for Engineers – PROT 401
42
Section 21 - Transmission Line Distance Protection - Part II
Mho Characteristic
Mho Circle Threshold:
(
)
arg ( Z r - Z ) Z = ± 90
X
B
Zr
Zr-Z
90o
Z
A
R
It is convenient to use an impedance plane to represent the distance element operating
characteristic. There are three traditional distance elements: impedance-type, reactance-type,
and mho-type distance elements.
The figure shows the operation equation and the operating characteristic of the mho distance
element. The characteristic is the locus of all apparent impedance values for which the relay
element is on the verge of operation. The operation zone is located inside the circle, and the
restraint zone is the region outside the circle.
The mho characteristic is a circle passing through the origin of the impedance plane. The mho
element operates for impedances inside the circle, which is basically oriented toward the first
quadrant. This is the case for forward faults. For reverse faults, the apparent impedance lies in
the third quadrant of the impedance plane and represents a restraint condition. The fact that the
circle passed through the origin of coordinates is an indication of the inherent directionality of
the mho elements. However, close-in bolted faults produce deep voltage sags. The mho
element may lose the voltage polarizing signal for close-in faults. This fact needs to be
considered in selecting the appropriate mho element polarizing quantity.
There are only two settings in a mho element: the characteristic diameter, ZM, and the angle of
this diameter with respect to the R axis, jMT. This is equivalent to the maximum torque angle
of a directional element: the mho element presents the highest reach (highest sensitivity) when
the apparent impedance angle j coincides with jMT.
The value jMT should be set close to the protected line impedance angle. By doing this, it
ensures maximum relay sensitivity for faults and minimum relay sensitivity for load
conditions, in which j < j MT.
The other two conventional distance elements lack directionaly. The impedance-type
characteristic is a circle whose center is at the origin of coordinates. The reactance-type
characteristic is a straight line parallel to the R axis. Impedance-type elements need an
additional directional element. Reactance-type elements need a directional element and a
resistance element to limit the reach on both sides of the element characteristic.
Transmission Line Distance Prot II_r8
42
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Concept of Polarizing Quantity
X
F4
S1 = - V + Z r I
F3
S2 = V
S1 Phase Changes
S2 Phase Does Not Change
F1
F2
Transmission Line Distance Prot II_r8
R
43
43
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Loss-of-Polarization
for Close-In Bolted Faults
X
I
V
F2
F1
F1
21
F2
V = 0, S2 = 0
Transmission Line Distance Prot II_r8
44
R
44
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Polarization Alternatives
l
Self-Polarization
l
Dual-Polarization
t
Addition of healthy phase voltage
l
Cross-Polarization
l
Positive-Sequence
l
Memory
t
Transmission Line Distance Prot II_r8
Three-phase faults, voltage reversals
45
45
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Polarized Mho Relay
S1 = - V + Z r I
Self-Polarization: S 2 = V
Dual Polarization: S 2 = V + k p V p (Healthy Phases)
Cross Polarization: S 2 = k p V p (Healthy Phases)
Positive-Sequence
Polarization: S 2 = k p V p
Transmission Line Distance Prot II_r8
46
46
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Polarized Mho Relay Characteristic
S1 = - V + Z r I
S2 = V + k p V p
æ Z - Zr ö
÷£p
0 £ argç
çZ+Z ÷
p ø
è
A = -Z p = - k p V p I
Transmission Line Distance Prot II_r8
47
B = Zr
47
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Relay Characteristic: Forward Fault
m ZL
1
F
2
3
3
X
B
Zr Z r
2
A'
Transmission Line Distance Prot II_r8
A
R
1
48
48
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Relay Characteristic: Reverse Fault
m ZL
1 F
3
2
3
X
B
A''
Zr
2
A
R
1
Transmission Line Distance Prot II_r8
49
49
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Polarization Alternatives Summary
l
Self-Polarization
l
Healthy-Phase Cross
Polarization (With and Without
Memory)
l
Positive-Sequence Polarization
(With Memory)
Transmission Line Distance Prot II_r8
50
50
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Phase Element Self-Polarization
S1 = - V bc + Zr Ibc
S 2 = V bc
l
No Characteristic Expansion
l
Unreliable for Zero-Voltage Faults
l
Directionally Insecure for Reverse Bus
Faults During High Load. Requires
Additional Directional Element
Transmission Line Distance Prot II_r8
51
51
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Ground Element Self-Polarization
(
S1 = - Va + Zr Ia + k 0 I0
)
S2 = Va
l
No Characteristic Expansion
l
Unreliable for Zero-Voltage Single
Line-to-Ground Faults
l
Requires Directional Element
Transmission Line Distance Prot II_r8
52
52
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Phase Element Cross Polarization
S1 = - V bc + Zr Ibc
S2 = - j Va
l
Good Expansion for Phase-to-Phase
Faults
l
Unreliable for Zero-Voltage Three-Phase
Faults
l
Requires Directional Element
Transmission Line Distance Prot II_r8
53
53
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Ground Element Cross Polarization
(
S1 = - Va + Zr I a + k 0 I 0
)
S 2 = j Vbc
l
Good Expansion
l
Reliable Operation for Zero-Voltage
Single Line-Ground Faults
l
Requires Directional Element
l
Single-Pole Trip Applications Require
Study for Pole-Open Security
Transmission Line Distance Prot II_r8
54
54
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Phase Element
Cross Polarization With Memory
S1 = - Vbc + Zr Ibc
S2 = -j Va,mem
l
l
l
l
Transmission Line Distance Prot II_r8
Good Expansion
Reliable Operation for Zero-Voltage
Three-Phase Faults
Requires Directional Element
Single-Pole Trip Applications
Require Study for Pole-Open
Security
55
55
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Phase Element Positive-Sequence
Polarization With Memory
S1 = - Vbc + Zr Ibc
S2 = -j Va1,mem
l
Greatest Expansion
l
Reliable Operation for Zero-Voltage
Three-Phase Faults
l
Requires Directional Element
l
Best Single-Pole Trip Security
Transmission Line Distance Prot II_r8
56
56
Power System Protection for Engineers – PROT 401
Section 21 - Transmission Line Distance Protection - Part II
Ground Element Positive-Sequence
Polarization With Memory
(
S1 = - Va + Zr Ia + k 0 I0
)
S2 = Va1,mem
l
Greatest Expansion
l
Reliable Operation for Zero-Voltage
Faults
l
Requires Directional Element
l
Best Single-Pole Trip Security
Transmission Line Distance Prot II_r8
57
57