5

Nonpilot Distance Protection

of Transmission Lines

5.1 Introduction
Distance relays are normally used to protect transmission lines [1]. They respond to the
impedance between the relay location and the fault location. As the impedance per mile of
a transmission line is fairly constant, these relays respond to the distance to a fault on the
transmission line – and hence their name. As will be seen shortly, under certain conditions
it may be desirable to make distance relays respond to some parameter other than the
impedance, such as the admittance or the reactance, up to the fault location. Any of the
relay types described in Chapter 2 can be made to function as a distance relay by making
appropriate choices of their design parameters. The R –X diagram is an indispensable tool
for describing and analyzing a distance relay characteristic, and we will examine it initially
with reference to a single-phase transmission line. Similar principles are applicable in case
of a three-phase transmission line, provided that appropriate voltages and currents are chosen
to energize the distance relay. This matter of energizing voltages and currents in three-phase
systems will be considered in detail later.

5.2 Stepped Distance Protection

Before describing the specific application of stepped distance protection, the definitions
of underreach and overreach must be addressed. “Underreaching” protection is a form of
protection in which the relays at a given terminal do not operate for faults at remote
locations on the protected equipment [2]. This definition states that the relay is set so that
it will not see a fault beyond a given distance (e.g., an instantaneous relay should not see
the remote bus, as discussed in Section 4.4). The distance relay is set to underreach the
remote terminal. The corollary to this definition, of course, is that the relay will see faults
less than the setting. “Overreaching” protection is a form of protection in which the relays
at one terminal operate for faults beyond the next terminal. They may be constrained from
tripping until an incoming signal from a remote terminal has indicated whether the fault

Power System Relaying, Fourth Edition. Stanley H. Horowitz and Arun G. Phadke.
© 2014 John Wiley & Sons, Ltd. Published 2014 by John Wiley & Sons, Ltd.
108 Power System Relaying

is beyond the protected line section [2]. Note the added restriction placed on overreaching
protection to avoid loss of coordination.
The zone of distance relays is open at the far end. In other words, the remote point
of reach of a distance relay cannot be precisely determined, and some uncertainty about
its exact reach must be accepted. This uncertainty of reach is typically about 5% of the
setting. Referring to Figure 5.1a, the desired zone of protection is shown with a dotted line.
The ideal situation would be to have all faults within the dotted area trip instantaneously.
Owing to the uncertainty at the far end, however, to be sure that we do not overreach the
end of the line section, we must accept an underreaching zone (zone 1). It is customary to
set zone 1 between 85% and 90% of the line length and to be operated instantaneously.
It should be clear that zone 1 alone does not protect the entire transmission line: the area
between the end of zone 1 and bus B is not protected. Consequently, the distance relay is
equipped with another zone, which deliberately overreaches beyond the remote terminal of
the transmission line.
This is known as zone 2 of the distance relay, and it must be slowed down so that for
faults in the next line section (F2 in Figure 5.1a), zone 1 of the next line is allowed to
operate before zone 2 of the distance relay at A. This coordination delay for zone 2 is
usually of the order of 0.3 s, for the reasons explained in Chapter 4.
The reach of the second zone is generally set at 120–150% of the line length AB. It
must be borne in mind that zone 2 of relay Rab must not reach beyond zone 1 of relay Rbc ,
otherwise some faults may exist simultaneously in the second zones of Rab and Rbc , and may
lead to unnecessary tripping of both lines. This concept, of coordination by distance as well
as by time, leads to a nesting of the zones of protection, and is illustrated in Figure 5.1b.
It should be noted that the second zone of a distance relay also backs up the distance
relay of the neighboring line. However, this is true for only part of the neighboring line,
depending upon how far the second zone reaches. In order to provide a backup function
for the entire line, it is customary to provide yet another zone of protection for the relay

A B C
Rbc
Rab Zone 1
F2
Zone 2
Zone 3
(a)

A B C

Rab Rba Rbc Rcb

(b)

Figure 5.1 Three-zone step distance relaying to protect 100% of a line and back up the neigh-
boring line
Nonpilot Distance Protection of Transmission Lines 109

at A. This is known as the third zone of protection, and usually extends to 120–180% of
the next line section. The third zone must coordinate in time and distance with the second
zone of the neighboring circuit, and usually the operating time of the third zone is of the
order of 1 s. The three zones of protection of the two line sections AB and BC are shown
in Figure 5.1b.
It should also be mentioned that it is not always possible to have acceptable settings for
the two overreaching zones of distance relays. Many of these issues will be discussed in
greater detail in the later sections. However, it is worth noting some of the limiting causes
at this time. First, a complication is caused by dissimilar lengths of adjacent lines. If the
length of a downstream line is less than 20% of the line being protected, its zone 2 will
certainly overreach the first zone of the shorter line. Similarly, the zone 3 of the first line
may overreach the zone 2 of the next line. The guidelines for setting the reach of zones
mentioned above must be considered to be approximate, and must be adjusted to meet a
specific situation at hand. Zone 3 was originally applied as a remote backup to zones 1
and 2 of an adjacent line in the event that a relay or breaker failure prevented clearing the
fault locally [3]. The reach setting, however, is a complex problem and is the subject of
many ongoing studies and suggestions that will be discussed in detail in Chapters 5, 10,
and 11. Briefly, however, the zone 3 characteristic must provide protection against faults
but should not operate for normal, albeit unusual, system conditions such as heavy loads or
stability swings. Computer relaying makes provision for identifying heavy loads or stability
swings through its load encroachment feature that is discussed further in Chapter 11. Another
consideration is the effect of the fault current contributions from lines at the intermediate
buses. This is the problem of infeed, and will be discussed in greater detail later.

Example 5.1
Consider the transmission system shown in Figure 5.2. The relay Rab is to be set to protect
the line AB and back up the two lines BC and BD. The impedances of the three lines are as
shown in Figure 5.2. (Note that these impedances are in primary ohms – i.e., actual ohms
of the transmission lines. Normally, the settings are expressed in secondary ohms, as will
be explained in Section 5.3.) Zone 1 setting for Rab is 0.85 × (4 + j 30) or (3.4 + j 25.5) .
Zone 2 is set at 1.2 × (4 + j 30) or (4.8 + j 36) . Since the relay Rab must back up relays
Rb and Rbd , it must reach beyond the longer of the two lines. Thus, zone 3 is set at
[(4 + j 30) + 1.5 × (7 + j 60)] or at (14.5 + j 120) . The time delays associated with the
second and third zones should be set at about 0.3 and 1.0 s, respectively.
It should be noted that if one of the neighboring lines, such as line BD, is too short, then
the zone 2 setting of the relay Rab may reach beyond its far end. For the present case, this

B C
(7 + j 60)
A
(4 + j30) Rbc

Rab D
(2 + j20)

Rbd

Figure 5.2 System for Example 5.1

110 Power System Relaying

Seal-in Z1 Z2 Z3
unit

T2 T3

Target Target Target

Seal-in T2 T3
unit timer timer
TC
Breaker
aux. contact
−

Figure 5.3 Control circuit for a three-zone step distance relay

would happen if the impedance of line BD is smaller than [(4.8 + j 36) − (4.0 + j 30)] =
(0.8 + j 6) . In such a case, one must set zone 2 to be a bit shorter to make sure that it
does not overreach zone 1 of Rbd , or, if this is not possible, zone 2 of the relay Rab may
be set longer than zone 2 of relay Rbd or it may be dispensed with entirely and only zone
3 may be employed as a backup function for the two neighboring lines.

The control circuit connections to implement the three-zone distance relaying scheme are
shown in Figure 5.3. The seal-in unit contact shown is typical for all three phases, and the
seal-in coil may be combined with the target coils in some designs. The three distance-
measuring elements Z1 , Z2 , and Z3 close their contacts if the impedance seen by the relay is
inside their respective zones. The zone 1 contact activates the breaker trip coil(s) immediately
(i.e., with no intentional time delay), whereas the zones 2 and 3 contacts energize the two
timing devices T2 and T3 , respectively. Once energized, these timing devices close their
contacts after their timer settings have elapsed. These timer contacts also energize the breaker
trip coil(s). Should the fault be cleared before the timers run out, Z2 , Z3 , T2 , and T3 will
reset as appropriate in a relatively short time (about 1–4 ms).
We should remember that the zone settings for zones 2 and 3 are affected by the contri-
butions to the fault current made by any lines connected to the intervening buses, that is,
buses B and C in Figure 5.1. This matter has been dealt with in the discussion of infeed
and outfeed in Section 4.3, and similar considerations apply here as well. The problem is
caused by the different currents seen by the relays as a result of the system configuration.
As shown in Example 4.6, the operating currents in the upstream relays change significantly
if parallel lines are in or out of service.

5.3 R –X Diagram
In general, all electromechanical relays respond to one or more of the conventional torque-
producing input quantities: (i) voltage, (ii) current, (iii) product of voltage, current, and
Nonpilot Distance Protection of Transmission Lines 111

the angle θ between them, and (iv) a physical or design force such as a control spring
[4]. Similar considerations hold for solid-state relays as well. For the product-type relay,
such as the distance relay, analyzing the response of the relay for all conditions is difficult
because the voltage varies for each fault or varies for the same fault but with different
system conditions.
To resolve this difficulty, it is common to use an R –X diagram to both analyze and
visualize the relay response. By utilizing only two quantities, R and X (or Z and θ ), we
avoid the confusion introduced using the three quantities E, I , and θ . There is an additional
significant advantage, in that the R –X diagram allows us to represent both the relay and
the system on the same diagram.
Consider an ideal (zero resistance) short circuit at location F in the single-phase system
shown in Figure 5.4. The distance relay under consideration is located at line terminal A.
The primary voltage and current at the relay location are related by
Ep
Zf,p = (5.1)
Ip
where the subscript “p” represents primary quantities. In terms of the secondary quantities
of voltage and current transformers (CTs), the relay sees the primary impedance Zf,p as Zf,s ,
where
E n
Zf,s = s = Zf,p i (5.2)
Is ne
where ni and ne are the CT and voltage transformer (VT) turns ratios. It is customary to
suppress the subscript “s,” with the understanding that the secondary quantities are always
implied. Thus, we will mean Zf,s when we use Zf .

ZF

S A B
(1:n i ) F
R + jX

Zs Rba

Rab

(1:n e )
Es

q Ep

Is
Ip

Figure 5.4 Voltage, current, and impedance as seen by the relay

112 Power System Relaying

Example 5.2
Consider a distance relaying system utilizing a CT with a turns ratio of 500 : 5 and a VT
with a turns ratio of 20 000 : 69.3. Thus, the CT ratio ni is 100, while the VT ratio ne
is 288.6. The impedance conversion factor ni /ne for this case is (100/288.6), or 0.3465.
All primary impedances must be multiplied by this factor to obtain their secondary values.
Thus, the line in Example 5.1 with an impedance of (4 + j 30)  primary would appear to
be (1.386 + j 10.395)  secondary.
The zone 1 setting for this line would be 85% of this impedance or (1.17 + j 8.84) 
secondary. Of course, the actual setting used would depend upon the nearest value that is
available on a given relay.

Although we have defined Zf under fault conditions, it must be borne in mind that the
ratio of E and I at the relay location is an impedance under all circumstances, and when
a fault occurs, this impedance assumes the value Zf . In general, the ratio E/I is known
as the apparent impedance “seen” by the relay. This impedance may be plotted as a point
on the complex R –X plane. This is the plane of (apparent) secondary ohms. One could
view the impedance as the voltage phasor, provided that the current is assumed to
be the reference phasor, and of unit magnitude. This way of looking at the apparent
impedance seen by a relay as the voltage phasor at the relay location is often very useful
when relay responses to changing system conditions are to be determined. For example,
consider the apparent impedance seen by the relay when there is normal power flow in the
transmission line. If the load current is of constant magnitude, and the sending end voltage
at the relay location is constant, the corresponding voltage phasor, and hence the impedance,
will describe a circle in the R –X plane. Lighter loads – meaning a smaller magnitude of
the current – produce circles of larger diameters. Similarly, when the load power factor is
constant, the corresponding locus of the impedance is a straight line through the origin.
Figure 5.5 shows these contours for varying load current magnitudes and power factors.
Note that when the real power flows into the line, the corresponding apparent impedances
lie in the right half of the plane, while a reversed power flow maps into the left half-
plane. Similarly lagging power factor load plots in the upper half-plane, while a leading
power factor load plots in the lower half-plane. Zero power transfer corresponds to points
at infinity. A line open at the remote end will have leading reactive current, and hence the
apparent impedance will map at a large distance along the negative X axis.
Now consider the fault at location F as shown in Figure 5.4. The corresponding apparent
impedance is shown at F in Figure 5.5. As the location of the fault is moved along the
transmission line, the point F moves along the straight line AB in Figure 5.5. Thus, the
transmission line as seen by the relay maps into the line AB in the R –X plane. The line AB
makes an angle θ with the R axis, where θ is the impedance angle of the transmission line.
(For an overhead transmission line, θ lies between 70◦ and 88◦ , depending upon the system
voltage, the larger angles being associated with higher transmission voltages.) When the fault
is on the transmission line, the apparent impedance plots on the line AB, for all other faults
or loading conditions, the impedance plots away from the line AB. Often it is convenient
to plot the source impedance Zs also on the R –X diagram, as shown in Figure 5.5.
Nonpilot Distance Protection of Transmission Lines 113

X
Power into bus Power into line

Light load

B E
Heavy load Load with
F
ZF q lagging pf

A I R
S ZS
Load with
leading pf

Line charging

Figure 5.5 R –X diagram as a special case of the phasor diagram (pf, power factor)

Example 5.3
Let the rated load for the transmission line shown in Figure 5.4 be 8 MVA. This corresponds
to 400 A at the rated voltage of 20 000 V. The apparent impedance corresponding to this
load is (20 000/400) = 50  primary. In terms of secondary ohms, this impedance becomes
50 × 0.3465 = 17.32 . Thus, a load of 8 MVA at 0.8 pf lagging is 17.32 × (0.8 + j 0.6) =
(13.86 + j 10.4)  secondary. This is shown as L1 in Figure 5.6. A load of 8 MVA with
a leading power factor of 0.8 is (13.86 − j 10.4)  secondary, which maps as point L2 .
Similarly, 8 MVA flowing from B to A maps into L3 and L4 for leading and lagging power
factors, respectively.
The line impedance of (1.39 + j 10.4)  secondary maps into point B, while the zone
1 setting of (1.17 + j 8.84)  maps into the point Z1a . A similar relay located at B would
have its zone 1 map at Z1b . If we assume the equivalent source impedances as seen at buses
A and B to be j10 and j8  primary, respectively, they will be j3.46 and j2.77  secondary,
respectively, as shown by points S1 and S2 in Figure 5.6. If the line charging current is
15 A, the apparent impedance seen by the relay at A when the breaker at terminal B is open
is −j (20 000/15) = −j 1333 primary, or −j 461.9 secondary. This is shown as the point
C, on a telescoped y axis in Figure 5.6. The zones of protection of a relay are defined in
terms of its impedance, and hence it is necessary that they cover areas in the immediate
neighborhood of the line AB. As the load on the system increases, the possibility of it
encroaching upon the protection zones becomes greater. Ultimately, at some values of the
load, the relay is in danger of tripping. The R –X diagram offers a convenient method of
analyzing whether this is the case. A fuller account of the loadability of a distance relay is
considered in Section 5.11.
114 Power System Relaying

S2 (1.39 + j13.17)

B (1.39 + j10.4)
L 4 (−13.86 + j 10.4) Z 1a (1.17 + j8.84) L 1 (13.86 + j 10.4)

A Z 1b (0.22 + j1.16)

S1

L 3 (−13.86 − j 10.4) L 2 (13.86 − j 10.4)

C (−j 461.9)

Figure 5.6 R –X diagram for Example 5.3

5.4 Three-Phase Distance Relays

On a three-phase power system, there are 10 distinct types of possible faults: a three-phase
fault, three phase-to-phase faults, three phase-to-ground faults, and three double-phase-to-
ground faults. The equations that govern the relationship between voltages and currents at
the relay location are different for each of these faults. We should therefore expect that it
will take several distance relays, each of them energized by a different pair of voltage and
current inputs to measure the distance to the fault correctly. It is a fundamental principle of
distance relaying that, regardless of the type of fault involved, the voltage and current used
to energize the appropriate relay are such that the relay will measure the positive-sequence
impedance to the fault [5]. Once this is achieved, the zone settings of all relays can be based
upon the total positive-sequence impedance of the line, regardless of the type of the fault.
We will now consider various types of fault, and determine the appropriate voltage and
current inputs to be used for the distance relays responsible for each of these fault types.

5.4.1 Phase-to-Phase Faults

Consider a fault between phases b and c of a three-phase transmission line. We may consider
this to be the fault at location F in Figure 5.4, provided we view that figure as a one-line
diagram of the three-phase system. The symmetrical component representation for this fault
is shown in Figure 5.7. The positive- and negative-sequence voltages at the fault bus are
equal, and are given by
E1f = E2f = E1 − Z1f I1 = E2 − Z1f I2 (5.3)