Distance-protection performance under conditions

of single-circuit working in double-circuit

transmission lines
W. D. Humpage, B.Sc, Ph.D., C.Eng., F.I.E.E., and M. S. Kandil, M.Sc, Ph.D.

Indexing terms: Power-system protection, Transmission networks, Relays

Abstract
When double-circuit transmission lines are operated with one of the circuits isolated and earthed at both
ends, relaying conditions can arise that influence the choice of the forward-reach settings of distance pro-
tection. Earth-fault conditions during single-circuit working in this way give rise to apparent-impedance
values presented to the protection that are generally less, and to errors in impedance measurements that
are correspondingly greater, than for the same fault conditions during normal operation, when both circuits
are in service together. The paper reports computer studies which seek to compare the discriminative per-
formance of distance protection under earth-fault conditions during double-circuit and single-circuit
operation and which, in particular, provide an account of the relaying conditions likely to be encountered in
single-circuit operation. Apparent impedance values and associated relaying errors are summarised in
tabular form for fault and prefault conditions relevant to a typical 400kV interconnection, on the basis of
which an assessment of the discriminative performance of distance protection in single-circuit working is
made.

List of principal symbols overhead-line configuration, the computer assessment method

Z b Z 2 , Z o = transmission-circuit impedances in the positive-, on which the present and earlier investigations3 have been
negative- and zero-phase sequences, respec- based is easily adapted to any type of overhead line. In addi-
tively tion to the parallel-connected form of double-circuit line
analysed here, the method may equally well be applied to
Zmo = intercircuit mutual impedance in the zero-phase doubl&-circuit looped3 and direct teed4 network intercon-
sequence nections.
/,, /2, / 0 = transmission-circuit currents in the positive-,
negative- and zero-phase sequences, respec-
tively 2 Relaying conditions in single-circuit
]ra = compensated relaying signal operation
Zs, ZN = source impedances
Fig. 1 shows, in schematic form, a double-circuit line
Subscripts a, b and c denote quantities in the a, b and c phases, carrying a continuous earth wire with one of the circuits
respectively, of the circuit in service. A, B and G are the isolated and earthed at both ends. If the circuit in service
corresponding suffixes for quantities in the circuit that is sustains an earth fault, fault current, returning to the infeed-
isolated and earthed. ing source at the line end remote from that at which the fault
occurs, returns in part through the earth/earth-wire combina-
1 Introduction tion and in part through the conductors of the earthed circuit.
Previous papers1"3 have reported investigations into When both circuits are in service together and a fault occurs
the measuring accuracy of distance protection, and have at one end of the line, fault current in the two circuits flows
provided quantitative assessments of relaying conditions in the same direction in the conductors of the faulted phase or
relevant to single- and double-circuit transmission-line inter- phases. Under conditions of single-circuit working, on the
connections. So far as the authors are aware, however, no other hand, fault-current flow in the circuit in service and that
previous account of similar detail has been given of the in the isolated circuit are in opposite directions. Reduced to
particular case, of practical importance, in which one circuit its simplest terms, it is this, and, in particular, the corres-
of a double-circuit line is isolated and earthed while the ponding components of voltage appearing in the fault loop as
circuit remaining in service sustains an earth fault. It is this a consequence of the presence of intercircuit mutual coupling,
particular aspect of distance-protection application to which that gives rise to reduced apparent-impedance values. By
the present paper seeks to contribute, by providing a detailed comparison, the effect of intercircuit mutual coupling for the
study of the range of apparent impedances presented to same fault conditions when both circuits are in service is to
distance protection during the single-circuit operation of cause the apparent impedances to be greater than their actual
mutually coupled double-circuit lines. values. In addition, the partial cancellation of relaying errors
For these particular relaying conditions, it is shown here arising from the distinguishable error sources when both
that the apparent-impedance values with which the protection circuits are present,3 is disturbed. For a given set of relaying
is required to cope can depart considerably from those conditions, therefore, apparent-impedance values presented
occurring when both circuits are in commission together. In to distance protection in single-circuit working may be
particular, the reduced apparent-impedance values in single- expected to be lower, and the corresponding errors in im-
circuit operation have a bearing on the choice of protection pedance measurement to be greater, than those when both
forward-reach settings, where, as is frequently the case in circuits are in commission together. As the relaying conditions
practice, a single setting is used for single-circuit and normal are those of potential overreach, they are likely to represent
double-circuit operation. limiting conditions in the choice of protection forward-reach
While the studies relate to a specific and typical 400kV settings if a single setting is used indifferently for single- and
double-circuit working.
Paper 6132 P, first received 21st October 1969 and in revised form 27th To the effect of current flow in the conductors of the faulted
January 1970 phase in single-phase-earth fault conditions, and of the
Dr. Humpage is, and Dr. Kandil was formerly, with the Power Systems
Laboratory, Department of Electrical Engineering & Electronics, faulted phase pair in double-phase-earth fault conditions,
University of Manchester Institute of Science & Technology, PO Box should be added the effect of current flow in the remaining
88, Sackville Street, Manchester M60 1QD, England. Dr. Kandil is unfaulted conductors. When both circuits are in operation,
now with the Department of Electrical Engineering, University of
Libya, Tripoli, Libya this has a strong dependence on the magnitude and direction
766 PROC. IEE, Vol. 117, No. 4, APRIL 1970
of prefault power transfer in the interconnection, both for operating conditions, and an approximate value may easily
the unfaulted circuit and for the unfaulted conductors of the be found for it from symmetrical phase-sequence-component
faulted circuit. While a dependence on prefault power analysis.

*c circuit iiin service

*+
circuits mutually coupled L
SB

'NA

isolated circuit

Ir earth/earth-wire path

Fig. 1
Earth-fault condition during single-circuit working of double-circuit transmission line
One circuit is isolated and earthed; the circuit remaining in service sustains an earth fault
If = total current fed into fault
fr = current returning to infeeding source through earth/earth-wire path

transfer remains in earth-fault conditions during single-circuit 3.2 Phase-variable analysis

operation, the nearly equal cophasor currents flowing in the Following the preliminary fomulation of Section 8.1, a
conductors of the isolated, earthed circuit alter the form of direct phase-variable approach provides a basis for a more
the dependence, particularly under double-phase-earth fault detailed evaluation of relaying conditions. In this way,
conditions. These differences in the relaying conditions account may directly be taken of the asymmetries in the self-
relevant, on the one hand, to double-circuit operation, and, and mutual-impedance parameters and of the effect of the
on the other, to single-circuit operation, may be most clearly
seen from tabulations of apparent impedances in the two from
cases. Beyond this, it is required to formulate the greatest negative-phase-sequence
reductions in apparent impedance likely to arise in single- network
circuit working to provide a basis on which relay forward-
reach settings may be chosen.

Analysis of relaying conditions

3.1 Preliminary formulation
A clarification of the main parameters and variables
influencing the relaying conditions in single-circuit working
may readily be achieved from a preliminary analysis invoking positive- phase - sequence
symmetrical phase-sequence components. On this basis, the network
effects of intercircuit mutual coupling may be considered to Fig. 2
be confined to the zero-phase sequence, giving an equivalent Zero-phase-sequence circuit for single-phase-earth fault during single -
zero-phase-sequence circuit corresponding to the single- circuit working
circuit working of a double-circuit line, as shown in Fig. 2. It
The positive-, negative- and zero-phase-sequence networks are series-connected
is shown in Appendix 8.1 that, based on this circuit rep- at the point of fault
resentation, the apparent impedance Zr at the relay location
when the residual-current form of compensation is used, may
be expressed in the form
prefault power-transfer conditions at fault inception. For
2
these purposes, a model based on Fig. 1 may be adopted, or,
Jr. 7 alternatively, a 6-conductor representation may be used based
(1)
1 z on self- and mutual-impedance parameters including the
effect of the earth and earth-wire return paths. On the basis
in which Zx is the positive-phase-sequence impedance of the of this latter representation, that of an equivalent 6-conductor
line, on which basis the forward reach of the protection is set. model for analysis and for the 400 kV transmission-line para-
In this form, the simplified derivation of apparent im- meters summarised in Section 8.2, apparent-impedance values
pedance indicates that the zero-phase-sequence impedance for a range of fault and prefault operating conditions are
Z o of the circuit, and the mutual impedance Zmo between collected together in Tables 1-3. These relate to single-phase-
circuits in the zero-phase sequence may be used as an index and double-phase-earth faults at one end of the line, which
of the form Z^JZQ in assessing the reduced apparent-im- represents a fault location giving a limiting condition in
pedance values that might be encountered in single-circuit relation to the setting margins of the protection, to guard
operation. The ratio 7 0 // ra depends on the fault and prefault against possible overreaching.
PROC. IEE, Vol. 117, No. 4, APRIL 1970 767
4 Discussion of relaying conditions relay location. The errors in reactance measurement in Table 1
A comparison of the apparent impedances given in indicate the different margins available in normal double-
Table 1 indicates that the conditions that give rise to values circuit working and in single-circuit working. When both
greater than the actual values when both circuits are in circuits are in service together, there is a measure of balance
service together, are those for which apparent values are less between the different error sources, and, for a wide range of
than the actual values for single-circuit operation. In terms of system-fault and prefault operating conditions, the residual
the discriminative performance of the protection, the former errors are small and positive if the effects of fault resistance
conditions, those of positive errors in reactance measurement, are discounted. In single-circuit working, this partial canella-
correspond to the effective coverage of the protection being tion is disturbed. For typical operating conditions, errors in
less than that for which it is nominally set, whereas the cover- reactance measurement are significantly larger, and nega-
age extends beyond the setting when the errors in reactance tive, in comparison with those when both circuits are in
measurement are negative. In choosing the forward-reach service.
protection setting, it is required to allow a sufficient margin to The relaying errors given in Table 2 for different faults
ensure that, for the conditions for which the reduction in indicate that, in single-circuit working, the errors are not
apparent impedance is greatest, the effective coverage does strongly dependent on the fault levels at the circuit termina-
not extend beyond the circuit termination remote from the tions. For the remote-end fault condition to which the studies

Table 1
COMPARISON OF RELAYING CONDITIONS FOR 4 0 0 k V DOUBLE-CIRCUIT LINE

Both circuits in service One circuit isolated and earthed

System conditions
Apparent impedance Measuring errors Apparent impedance Measuring errors

a % Q %
Fault levels:
5000 MVA at relay end 4-49 +y50-37 46-84 +yl2- 84 2-82+740-48 -7-91 -y'9-33
20000 MVA at remote end
Prefault power transfer =' 0
Phase-a-earth fault relay
Fault levels:
20000 MVA at relay end 5-23 + 746-48 71-16+74-12 2-08 +739 13 -32-13 -712-35
5000 MVA at remote end
Prefault power transfer =
650 MW exported at relay end
Phase-c-earth fault relay
Fault levels:
5000 MVA at relay end 2-73 + 746-39 -10-85+73-93 4-12 +y36-96 34-65 -717-19
20 000 MVA at remote end
Prefault power transfer =
650 MW imported at relay end
Phase-c-earth fault relay

Residual current compensation

Positive-phase-sequence impedance of 100mile line section = 3-06 +j44-61

Table 2
MEASURING ACCURACY FOR SINGLE-PHASE-EARTH FAULT CONDITIONS IN SINGLE-CIRCUIT
OPERATION

System conditions Form of compensation Apparent impedance Measuring errors

n %
Fault levels:
15 000 MVA at both ends residual current 4-23 +73901 38-1 -y'12-60
Prefault power transfer =
650 MW exported at relay end sound phase 7-18+766-22 - 8 0 9 -712-29
Phase-a-earth fault relay
Fault levels:
5000 MVA at relay end residual current 4-33+738-49 41-48 -713-76
20000MVA at remote end
Prefault power transfer =
650 MW exported at relay end sound phase 7-35 +765-34 -5-83 -713-45
Phase-a-earth fault relay
Fault levels:
20000 MVA at relay end residual current 6-96 +737-41 127-5 - 7 1 6 1 9
5000 MVA at remote end
Prefault power transfer=
1600MW exported at relay end sound phase 11-83 +763-49 51-48 -715-89
Phase-a-earth fault relay
Fault levels:
5000 MVA at relay end residual current -1-61 +736-34 -152-3 -y'18-59
20 000 MVA at remote end
Prefault power transfer=
1600MW imported at relay end sound phase -2-73 +761-68 -134-9 -718-31
Phase-c-earth fault relay

Mean of conductor self impedances for lOOrriile section = 7-81 + j!5-44 Cl

Postive-phase-sequence impedance for 100mile section = 3-06 +y44-61Q
768 PROC. IEE, Vol. 117, No. 4, APRIL 1970
relate, the fault levels affect similarly the faulted-phase phase-earth fault conditions are not included in the Tables
component of the compensated relaying signal and the return for this reason.
currents in the earthed circuit, leaving the measured im- As is indicated by the errors summarised in Table 3,
pedance with little dependence on the actual fault-level values. double-phase-earth-fault conditions appear to give rise to
To the extent that the unfaulted-conductor currents are only fractionally different error values when compared with
related to the angular separation between the sources at the those for single-phase-earth fault conditions. However, the
two ends of the interconnection, the measuring errors depend dependence of the errors on the prefault power transfer is
on the magnitude and direction of prefault power transfer. altered, in that, for most conditions, the apparent impedance
Owing to the differences in the individual conductor im- is less than the actual impedance, irrespective of the direction
pedances given in Table 4 (Section 8.2), the dependence is of the prefault power transfer.
different for the different earth-fault relays. While the maxi- In comparison with the errors in reactance measurement,
mum errors of the phase-a and phase-c-earth-fault relays the errors in resistance measurement have appreciably less
are similar, they occur in the phase-o-earth-fault relay when significance in terms of the discriminative properties of the
the relaying end exports power, and in the phase-c-earth-fault protection unless fault resistance is added to the formulation
relay when the relaying end imports power. As the self on which Tables 1-3 are based. Depending on the value of
impedance of the line conductor in phase b corresponds the fault resistance, its presence can affect relaying conditions
closely to the mean value of the self impedances on which the substantially, but the pattern of errors to which this source
relay setting is based, the phase-6-earth-fault relay is affected gives rise is the same as in previous investigations.3 Therefore,
less in this context than the earth-fault relays of phases a and the effect of fault resistance is not separately tabulated in the
c. Error values for the phase-6-earth-fault relay in single- present paper.

Table 3
MEASURING ACCURACY FOR DOUBLE-PHASE-EARTH FAULT CONDITIONS IN SINGLE-CIRCUIT
OPERATION

System conditions Form of compensation Apparent impedance Measuring errors

n
Fault levels:
5000MVA at relay end residual current 14-21 +y4019 364-6 -y9-95
20000MVA at remote end
Prefault power transfer=
650 MW exported at relay end sound phase 24-16 +./68- 22 209-4-y9-64
c-o-earth fault relay
Phase-rt-earth fault relay

Preceding case residual current -3-38 +y38-25 -210-5 -yl4-29

Phase-c-earth fault relay sound phase -5-75 +y64-93 -173-7 -yl3-99
Fault levels:
5000 MVA at relay end residual current -4-22 + y41-06 -238-1 -y'8-01
20000 MVA at remote end
Prefault power transfer =
650MW imported at relay end sound phase -7-21 +y"69-71 -192-2 -y7-678
6-c-earth fault
Phase-6-earth fault relay

Preceding case residual current 3-26 +y36-88 6-79 -yl7-37

Phase-c-earth fault relay sound phase 5-55 +y62-60 -28-8 - y l 7 0 8

Mean of conductor self impedances for 100mile section = 7-81 +y"75-44fi

Positive-phase-sequence impedance for lOOmile section = 3-06 +y44-61H

Table 4
PARAMETERS OF 400kV DOUBLE-CIRCUIT LINE

a b c A B G

=
Zaa Zab = Zac ZaA ZaB = ZaG =
a 0-0798 + 0 0486 + 0-0472 + 00471 + 0 0486 + 0 0495 +
yO-7808 yO-3561 yO-2609 yO-2372 yO-2747 y0-3048
Zbb = Zbc = ZbA = ZbB = ZbG =
b Zba ==
Z ab 0-0781 + 0-0468 + 0 0467 + 0-0478 + 00486 +
y0-7632 yO-3081 yO-2478 yO-2667 y0-2747
Zcc = ZCA = ZcB = ZCG =
c Zca =
Zac Zcb =
Zbc 0 0765 + 0 0463 + 00467 + 00471 +
y0-7193 yO-2619 yO-2478 yO-2372
ZAA = ZAB = ZAG =
A ZAa =
ZaA ZAb = ZbA ZAC = ZCA 0 0765 + 0 0468 + 00472 +
yO-7193 yO-3081 yO-2609
ZBB = ZBG =
B ZBa = ZaB ZBb = ZbB ZBC = ZCB ZBA = ZAB 00781 + 0 0486 +
yO-7632 yO-3561
ZGG =
G ZGa ZaG ZGb = ZbG ZGC = ZCG ZGA = ZAG ZGB = ZBG 0 0798 +
yO-7808

PROC. IEE, Vol. 117, No. 4, APRIL 1970 769

5 Conclusions 8 Appendixes
Overall, the relaying conditions encountered in the 8.1 Apparent impedance presented to distance
single-circuit operation of double-circuit lines are pre- protection under conditions of single-circuit
dominantly those giving apparent reactance values less than working
the actual values. As such, the conditions relate to the In Fig. 2 is shown the equivalent zero-phase-sequence
selection of protection forward-reach settings that guard circuit of a double-circuit interconnection with one circuit
against the zone 1 relays responding to faults external to the isolated and earthed at both ends. In representing single-
circuit protected. In these terms, the paper provides an account phase-earth fault conditions, the circuit is series-connected
of the relaying errors that may arise in a particular line con- at the point of fault with the positive-, and negative-phase-
struction and form of interconnection for fault and prefault sequence networks. Of the total current flowing into the
operating conditions typical of the line. For this case, the circuit from the negative-phase-sequence network, component
errors in reactance measurement under earth-fault conditions 70 flows through the zero-phase-sequence path of the circuit
in which the effects of fault resistance are discounted can in service. The voltage V'o in the earthed circuit corresponding
reach 18-20%. More generally, for 400kV circuits of the to this is therefore given by
type analysed, of different lengths and in different applica-
tions, a range of 20-25 % could be regarded as typical maxi- Vo = hZmo (2)
mum values. The presence of fault resistance would add to In turn, this circulates a current IQ in the closed-path repre-
this, and its effect would follow the pattern reported in sentation of the earthed circuit, where
earlier work.3
Applications relating to lines of different construction may (.->)
require specific study, and the computer methods on which
the present studies have been based may be easily adapted for The voltage VQ at the relay location in the zero-phase sequence
these. In this context, the Z^JZQ ratio may represent a may therefore be formed as
useful index for preliminary checking purposes. For a typical
132kV double-circuit line, the ratio has a scalar value of (4)
0-36, whereas it is 0-48 for the 400kV circuit analysed. In-
creasing values of the ratio will, in general, be accompanied The positive- and negative-phase-sequence components of
by increasing discrepancies between the effective coverage voltage V\ and V2 at the relay location are given by
of the protection and the nominal forward reach to which it
is set in application. and V2 = I2Z2
Subject to the assumption that Zx = Z2, the phase-a con-
ductor-earth voltage Va for a single-phase-earth fault on
6 Acknowledgments phase a may then be expressed as
The authors are grateful to Prof. C. Adamson and to
Prof. L. M. Wedepohl for their interest and encouragement (6)
in this work, and for the facilities in the Power Systems
Laboratory, University of Manchester Institute of Science & In the residual-current method1*2 of relay-signal compensa-
Technology. They are grateful for discussions with J. Rushton tion, the relaying signal Ira takes the form
and D. W. Lewis, and to S. Manickavasagar for his co-
Zo Z (
operation in some of the preliminary work. 4 + A) (7)

in which Ia is the phase a current.

7 References The apparent impedance Zra presented to the phase-a
1 ADAMSON, c , and TURELI, A.: 'Errors of sound-phase compensation earth-fault relay, is formed from the ratio VJIra, and sub-
and residual-compensation systems in earth-fault distance relaying', stituting for Va from eqn. 6 and for Ira from 7 gives
Proc. IEE, 1965, 112, (7), pp. 1369-1382
x
2 DAVISON, E. B., and WRIGHT, A.: 'Some factors affecting the accuracy -7 0 *"om (Q\
of distance-type protective equipment under earth-fault conditions', ra ~
ibid., 1963. 110, (9), pp. 1678-1688 ha
3 HUMPAGE, w. D., and KANDIL, M. s.: 'Measuring accuracy of distance
protection with particular reference to earth-fault conditions on 8.2 400kV line parameters
400kV looped circuit interconnections', ibid., 1970, 117, (2),
pp. 431-438 The parameters on which the study results, summarised
4 HUMPAGE, w. D., and LEWIS, D. w.: 'Distance protection of teed in Tables 1-3, are based are collected together in Table 4.
circuits', ibid., 1967, 114, (10), pp. 1483-1498
5 LEWIS, D. w.: 'Discriminative properties of protection for e.h.v. In Table 4, impedance values are tabulated in Q/mile for
circuits and circuit groups'. Ph.D. thesis, University of Manchester, four conductors per phase each of 0-4in2 cross-sectional area,
6
1968
RUSHTON, J. : 'The discriminative bases of power system protection'.
for a conductor resistivity of 3-21 x 10~8Qm and an earth
Ph.D. thesis, University of Manchester, 1967 resistivity of lOOQm.

770 PROC. IEE, Vol. 117, No. 4, APRIL 1970