CHAPTER 4

DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL

TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS

4.1 INTRODUCTION

Around the world, environmental and cost consciousness are forcing utilities to install
more and more parallel lines to increase the power transmission capabilities. In the
transmission systems, it is very common to find parallel transmission towers transmitting
power in narrow physical corridors. There are also places in the power systems where single-
circuit towers run in parallel in wide corridors. These are the examples of parallel
transmission lines. While transmitting power by the parallel transmission lines during normal
or faulty conditions; the presence of mutual impedances between the lines modify the voltage
and current profile measured by the protective relays protecting each line. This is one of the
most critical problems of the distance relay used for the protection of parallel transmission
lines. The close arrangement of the transmission lines leads to a higher fault rate and that
influences the results provided by the protective relays.
In power system design and operation, various types of fault analysis including short-
circuit calculations are performed in order to obtain the symmetrical and phase components
of bus voltages and branch currents in all predictable fault situations. Among all the different
types of fault analysis, one of the most troublesome problems is the solution of the faulted
network involving two or more faults that can occur simultaneously. Occurrence of such
simultaneous faults may be the result of some events, such as a stroke of lightning or a
catastrophic accident. These simultaneous faults may be any combination of two different
types of series and parallel faults occurring on the same phase or different phases, at the same
point or at different points in the power system. The series faults are: one open phase and two
open phases. The parallel faults are: single line-to-ground fault, double line fault, double line-
to-ground fault, triple line fault and triple line-to-ground fault.
Formally, because of the limitations of the methods of analysis and computational
equipment, it was impossible to handle such complicated problems. Therefore, the fault
analysis studies were limited to the simple (or simplified) cases of the power system faults,
such as a single-phase grounding or single-phase open circuit. Recently, there have been
developed numerous power system fault analysis methods based on the applications of digital

56
computers and sophisticated mathematical techniques. However, as soon as the mutual
coupling effects are encountered in the zero-sequence network, the computational procedures
become more complex. Before few decades, some methods of incorporating the effect of
mutual coupling have been developed for short-circuit studies.
In this chapter, the discussion starts with determining the mutual impedances between
the parallel transmission lines and investigating the effect of mutual coupling between the
parallel lines for a single line-to-ground fault. Afterwards, specific features of the mutually
coupled lines are examined and the same method is extended to analyze a typical type of
simultaneous fault, namely an inter-circuit fault occurred on the mutually coupled
transmission lines. The essential object of the analysis is to perform the fault calculations
using local end voltages and currents to design an appropriate protection scheme to protect
the parallel transmission line network. The contents of this analysis should be of direct
benefits to the engineers to study the behaviour of the protection system during different
types of simultaneous faults.

4.2 SELF AND MUTUAL IMPEDANCES OF TRANSMISSION LINES

Figure 4.1 shows the circuit of a fully transposed transmission line situated at a
specific distance above the ground-return path. The ground-return path for In is sufficiently
away for the mutual effect to be ignored. The self and mutual impedances are called primitive
impedances. They are combined to determine the total phase impedances of the transmission
line [59], [118].

Figure 4.1 Mutually coupled transmission line

Referring to Figure 4.1, the KVL equations can be written as follows:

Va  Va '  jX aa I a  jX ab I b  jX ac I c (4.1)

57
Vb  Vb '  jX ab I a  jX bb I b  jX bc I c (4.2)

Vc  Vc '  jX ca I a  jX bc I b  jX cc I c (4.3)

The same equations can be written in matrix form as follows:

Va  Va '  X aa X ab X ca   I a 

V   V '  j  X ab X bb X bc   Ib  (4.4)
 b  b 
Vc  Vc '  X ca X bc X cc   I c 

 Vabc  Vabc ' X abc  I abc (4.5)

Multiplying both sides of equation (4.5) by T 1 yields equation (4.6),

T 1Vabc  T 1Vabc '  T 1 X abc  I abc (4.6)

where,

1 1 1
T   1 a 2 a 
1 a a 2 

Thus, equation (4.6) can be written as follows:

V012  V012 '  T   X abc T  I 012

1
(4.7)

 V012  V012 '  X 012  I 012 (4.8)

 X 00 X 01 X 02 
where,  X 012   T 
1
X abc T    X 10 X 11 X 12  (4.9)
 X 20 X 21 X 22 

For a fully transposed line, the self and mutual inductive reactances are given by,

X aa  X bb  X cc  X s (4.10)

X ab  X bc  X ca  X m (4.11)

Thus, equation (4.9) can be written as follows:

 X 00 X 01 X 02   X s  2 X m 0 0 
X 012   T 1
X abc T    X 10 X 11 X 12    0 Xs  Xm 0  (4.12)

 X 20 X 21 X 22   0 0 X s  X m 

58
 The results of equation (4.12) obtained in the form of reactance can be extended in the
form of impedance in equation (4.13) as follows:

 Z 00 Z 01 Z 02   Z s  2 Z m 0 0 
Z 012    Z10 Z11 Z12    0 Z s  Zm 0 

(4.13)
 Z 20 Z 21 Z 22   0 0 Z s  Z m 

4.3 FORMULA FOR MUTUAL IMPEDANCE

When the overhead transmission lines follow parallel paths, the effect of mutual
coupling exists between the lines. For the distance protection scheme, it is possible to
compensate the influence of mutual coupling between the parallel lines with the help of
knowledge of the transmission line self and mutual impedances. Magnetic flux linkages
between the parallel transmission lines depend on the total current flowing in one line and the
magnetic flux linkage of this line with the other line. Thus, positive- and negative-sequence
currents are induced between the two lines, whose magnitudes are related to the degree of
asymmetry between the two lines. Practically, the induced positive- and negative-sequence
currents are negligible because of the symmetry between the two lines.

During ground faults, the three-phase currents do not add to zero, but rather a
summation of all the currents is corresponding to the current passing through the ground path.
Hence, the zero-sequence currents flowing in one of the lines are significantly high. As a
result, the zero-sequence flux linking to the other line is also equally high. Analysis of
transmission line impedance formulas can provide interesting data to the protection engineer.
To perform the analysis, the paralleled lines are modeled by two parallel single conductors
with an earth return path, for which the mutual coupling impedance is required to be
calculated. It is calculated using equations (4.14)-(4.16), given as follows [157], [186]:

  0 D 
ZM '   f  j  0  f  ln e   (4.14)
4 Dab  km 

 s 
 0  4  10 4    (4.15)
 km 


De  k D (4.16)
f

59
 where,

De = Depth of penetration in ground

f = Frequency in Hz

ρ = Specific resistance in Ω-m

Dab = Spacing in meters between the two conductors

The constant kD is approximately 2160 or 660 for units of length in feet or meters,
respectively. The value of De depends on ρ, the resistivity of soil. Table 4.1 gives a range of
values. When actual earth resistivity data is unavailable, it is not uncommon to assume the
earth resistivity of 100 µ-m, which corresponds to the values given in Table 4.1.

Table 4.1 De for various resistances at 50 and 60 Hz

Return Earth Resistivity ρ, Ω-m De in ft @ 50 Hz De in ft @ 60 Hz

Condition
Sea water 0.01 – 0.1 9.3 – 93.05 27.9 – 279
Swampy ground 10 – 100 294 – 930.5 882 – 2790
Average damp earth 100 931 2790
Dry earth 1000 2943 8820
Pure slate 10 7 294300 882000
Sandstone 10 9 2943000 8820000

4.4 ESTIMATION OF MUTUALLY COUPLED VOLTAGES FOR PARALLEL

TRANSMISSION LINES

Figure 4.2 shows a three-phase circuit of mutually coupled parallel transmission lines.
The three-phase parallel transmission lines have mutual coupling among all the conductors in
both the circuits.

Figure 4.2 Three-phase circuit of mutually coupled parallel lines

60
 The current Ia flowing in transmission line 1 induces voltage in transmission line 2.
Hence, the voltage Vb induced in line 2 is the product of the current flowing in line 1 and the
mutual impedance between the lines, and it is given by [157],

Vb  I a Z m  3I a 0 Z m (4.17)

Therefore, the zero-sequence mutual impedance can be defined as follows:

Va 0
Z m0   3Z m (4.18)
Ia 0

4.5 ANALYSIS OF MUTUALLY COUPLED PARALLEL TRANSMISSION LINES

Figure 4.3 shows a model of parallel transmission line. A single line-to-ground fault
has occurred in phase A of transmission line x. To develop an algorithm for such condition,
the circuit is required to be analyzed.

Figure 4.3 Model of a single line-to-ground fault

The voltage (Vax) of the faulted phase A of line x is defined as follows [213]:

Vax  pZ ss I ax  Z sm I bx  Z sm I cx   pZ m I ay  Z m I by  Z m I cy  (4.19)

where,

Zss = Self impedance of faulted phase

Zsm = Mutual impedance between phases of the same circuit

Zm = Mutual impedance between phases of the other circuit

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 After simplifying equation (4.19), it can be written as,

Vax  p Z ss I ax  Z sm  I bx  I cx   pZ m I ay  I by  I cy  (4.20)

It is known that zero-sequence current is I 0  1 / 3I a  I b  I c  , so equation (4.20) can

be written as follows:

Vax  p Z ss I ax  Z sm 3I x 0  I ax   3 pZ m I y 0 (4.21)

Referring to Figure 4.3, the relations between the self (s) and mutual (m) impedances
can be obtained from the zero- and positive-sequence data using the well known relations:

Z 0  Z ss  2Z sm , Z1  Z ss  Z sm (4.22)

Substituting equation (4.22) in equation (4.21), Vax is rewritten as,

Vax  p Z ss  Z sm I ax  Z sm 3I x 0   3 pZ m I y 0 (4.23)

Zsm can be determined by simplifying equation (4.22) and it is given by,

Z sm  1 / 3Z 0  Z1  (4.24)

Substituting equation (4.24) in equation (4.23), Vax is rewritten as,

Vax  p Z1 I ax  Z 0  Z1 I x 0   3 pZ m I y 0 (4.25)

Using equation (4.18), Vax is expressed as,

Vax  p Z1 I ax  Z 0  Z1 I x 0   pZ m0 I y 0 (4.26)

Dividing equation (4.26) by pZ1 and after manipulating it, pZ1 is given by,

Vax
pZ1  (4.27)
I ax  k 0 I x 0  k M I y 0

where,

Z 0  Z1 Z
k0  and k M  m 0
Z1 Z1

4.6 INTER-CIRCUIT FAULTS ON PARALLEL TRANSMISSION LINES

Figure 4.4 shows a condition of an inter-circuit fault, involving/not-involving ground,

present on an overhead parallel transmission line. Inter-circuit faults on parallel transmission
lines usually occur as a result of a lightning stroke to an earth-wire or tower, or due to a direct

62
lightning stroke to a phase conductor. An inter-circuit fault on the parallel transmission line
can give rise to operation of the phase and ground relays at locations J, K, L and M. Two
types of inter-circuit faults considered are: phase ‘a’ (line JK) to phase ‘b’ (line LM) (referred
to as phase-to-phase inter-circuit fault) and phase ‘a’ (line JK) to phase ‘b’ (line LM) to earth
(referred to as phase-to-phase-to-earth inter-circuit fault).

Figure 4.4 Inter-circuit fault

It is demonstrated that in many cases the inter-circuit faults result in unusual current
distributions between the parallel transmission lines. Therefore, the impedance measured by
the digital distance relay is not proportional to the length of the transmission line [8]. Inter-
circuit faults and close-in earth faults are also known to result in a loss of phase selectivity for
single-pole tripping schemes due to the addition of zero-sequence currents [123]. This can be
a serious problem for important circuits where system stability is of main concern. Further,
when an inter-circuit fault without ground occurs, each transmission line has zero-sequence
current, but no zero-sequence voltage at bus terminal. Hence, the traditional fault location
algorithm cannot able to determine the correct fault distance and fault location using just one-
terminal data [229].

4.7 TECHNIQUES USED IN COMMERCIAL RELAYS AND THEIR PROBLEMS

In order to enhance the reliability and security of bulk power transmission and to share
the same right of way, parallel transmission lines are commonly used in modern high voltage
transmission networks. The fault detection/fault location for parallel transmission lines thus
becomes an important subject in electrical power industry. Conventionally, distance
protection is one of the commonly used techniques in the protection of transmission lines.
However, while using distance relay to protect parallel transmission lines, a number of
problems caused by the presence of mutual coupling effect, ground fault resistance, pre-fault
system conditions, shunt capacitance, etc. cause performance degradation of the distance
relay [5], [6], [130], [138], [150].

63
 Many fault location algorithms for parallel transmission lines have been developed
[19], [82], [83], [103], [109], [115], [162], [189], [191], [217], [222]. These algorithms are
based on either one-terminal [82], [103], [115], [162], [191], [217], [222] or two-terminal
data [19], [83], [109], [189]. Although one-terminal algorithms are less precise than two-
terminal algorithms, they appear more attractive since they rely only on voltage and current
measurements at one common terminal. Hence, one-terminal algorithms do not require
communication links to transmit the data between two terminals of the transmission line.
Many researchers have developed different types of one-terminal data algorithms based on
lumped parameter line model [103], [115], [162], [191], [217], [222]. These algorithms
attempted to estimate the fault current contribution from the other terminal by solving the
Kirchhoff’s voltage law (KVL) equations around parallel lines loops. Since they are based on
lumped parameter line model, these algorithms do not fully consider the shunt capacitance
effect. This may lead to significant errors in fault location estimation, especially for long
transmission lines where the magnitude of the capacitive charging current can be comparable
to the fault current, particularly under high impedance fault conditions. Moreover, none of
these algorithms deals effectively with the inter-circuit faults, which are more likely to occur
on parallel transmission lines located on the same tower. Consequently, a one-terminal
algorithm based on distributed parameter line model has been developed, having high fault
locating accuracy and treating satisfactorily most of the asymmetrical fault types that can be
encountered in parallel transmission lines [82]. However, it cannot be used to locate
asymmetrical faults between two lines, for example, a fault involving phases A and B of the
two lines at the same instant.

Contrary to one-terminal algorithms, there are few two terminal algorithms for parallel
transmission lines developed by different researchers [19], [83], [109], [189]. The voltage and
current measurements from all four measuring ends of a parallel transmission line are
considered in [19]. Although this algorithm is based on distributed parameter line model and
is capable of locating inter-circuit faults, it requires a great amount of data to be transferred
from all line ends. There is also one two/multi-terminal algorithm based on lumped parameter
line model [189] and two other algorithms based on distributed parameter line model [83],
[109]. These last two algorithms utilize only current measurements from all four ends of the
transmission line, which adversely affects their accuracy due to the errors produced by the
current transformers.

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4.8 CURRENT STATE-OF-THE-ART

Some methods have been proposed for improving the distance protection performance
of parallel transmission lines [5], [6], [150], [222]. These techniques are very instructive and
achieve some degree of improvement for the distance protection of parallel lines. However,
most of them possess some errors inherently due to the assumptions during the development
process of those algorithms. For example, Jongepier et al. [6] used artificial neural networks
to estimate the actual power system conditions and to calculate the appropriate tripping
impedance. Hence, inaccuracy in the distance protection caused by the continuously changing
power system state is compensated. However, the fault resistance effect has not been taken
into account in it, thus the accuracy of fault location may be influenced by the presence of
fault resistance in the ground path. In order to increase the accuracy of fault distance
estimation for distance protection, a new method that is independent of fault resistance,
remote infeed and source impedance is proposed by Liao et al. [222]. Nevertheless, the shunt
capacitance is neglected, which introduces errors for long transmission lines. Moreover, all
studies mentioned above do not consider the influence of line parameter uncertainty, system
frequency fluctuation and system noise on the accuracy of the proposed schemes.
To ensure system stability, modern power systems require high speed protective
relaying. An increase in power transfer of parallel transmission lines thus calls for faster
protective relaying schemes. With regard to this, traveling-wave-based or differential
equation-based protection schemes may be a way to decrease the fault clearing time and thus
increase reliability [7], [20], [124], [129]. However, in the traveling-wave algorithms, it is
very difficult to decide from the first arriving waves that whether the traveling-waves are
generated by a fault or by any other disturbance [129].
IEEE has also made the standard synchrophasors for power systems [216]. Aiming
such a trend, some synchronization measurement techniques have been proposed for
transmission line protection systems [91], [94], [95], [133]. These techniques use
synchronized data from the two terminals and the performance & accuracy of protection
systems have been partially improved over those algorithms which use local data. Based on
the previous work [94], [95], researchers have developed an adaptive phasor measurement
unit (PMU)-based technique for parallel transmission lines. This technique eliminates many
of the associated problems typically encountered in this area. However, such techniques
require communication channels to acquire the remote end data.

65
 Very few papers have been published by researchers to analyze the problems of inter-
circuit faults on parallel transmission lines using various fault analysis methods, such as
sequence-domain method and phase-domain method [33], [35], [102], [165], [199]. But none
of the papers have presented the complete solution to measure the correct value of fault
impedance during inter-circuit faults between parallel transmission lines considering the
effect of mutual coupling, remote infeed/outfeed and fault-resistance.

4.9 INTER-CIRCUIT FAULTS ON PARALLEL TRANSMISSION LINES

In regions where large blocks of power are being transferred over parallel transmission
lines, the occurrence of an inter-circuit fault because of conductor geometry, could initiate
serious system instability [48], [137], [138]. A brief introduction of two types of inter-circuit
faults, namely, phase-to-phase inter-circuit fault and phase-to-phase-to-ground inter-circuit
fault, present on a parallel transmission line is provided as follows:

4.9.1 Phase-to-Phase Inter-Circuit Fault

The schematic diagram of faulted tower with its equivalent three-phase circuit for a
phase-to-phase inter-circuit fault is shown in Figure 4.5. For such type of inter-circuit fault
not involving ground, the conventional ground distance relays, located at A and B, may mal-
operate unnecessarily. Further, they are not in a position to measure the correct value of fault
impedance [8].

(a) Schematic diagram of faulted tower, (b) Equivalent three-phase circuit

Figure 4.5 Phase-to-phase inter-circuit fault

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4.9.2 Phase-to-Phase-to-Ground Inter-Circuit Fault

Figure 4.6 shows the schematic diagram of faulted tower with its equivalent three-
phase circuit for a phase-to-phase-to-ground inter-circuit fault. For such type of inter-circuit
fault involving ground, the conventional phase distance relays, located at A and B, may mal-
operate unnecessarily and measure fault impedance with high percentage of error [8].

(a) Schematic diagram of faulted tower, (b) Equivalent three-phase circuit

Figure 4.6 Phase-to-phase-to-ground inter-circuit fault

4.10 ANALYSIS OF INTER-CIRCUIT FAULTS ON PARALLEL TRANSMISSION

LINES

For all the analysis, positive- and negative-sequence impedances (ZL1 and ZL2) of the
transmission lines are assumed to be equal. Also, in the equations throughout the entire
discussion subscripts 1, 2 and 0 represent positive-, negative- and zero-sequence components,
respectively. It is to be noted that phase-to-phase inter-circuit fault (between A phase of line x
and B phase of line y) has occurred between fault locations F′ and F″ at p percentage from
bus S (Figure 4.5). Further, as shown in Figure 4.6, phase-to-phase-to-ground inter-circuit
fault (between A phase of line x and B phase of line y to ground) has occurred between fault
locations F′ and F″ to ground at p percentage from bus S.

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4.10.1 Impedance Measured by the Conventional Ground Distance Relay

For both types of inter-circuit faults, the value of apparent impedances (Zax and Zby)
measured by the conventional ground distance relays, considering the effect of zero-sequence
mutual coupling impedance (ZLM0), is given by equation (4.28) as follows [32], [137], [139]:

Vax Vby
Z ax  and Z by  (4.28)
I ax  k 0 I x 0  k M I y 0 I by  k 0 I y 0  k M I x 0

where,

Z L 0  Z L1 Z
k0  , k M  LM 0
Z L1 Z L1

4.10.2 Impedance Measured by the Proposed Scheme

In the proposed scheme, Eaxf and Ebyf are the voltages produced at the fault points F′
and F″ on transmission lines x and y, respectively. Iax and Iby are the fault currents measured
at the relaying points A and B, respectively.

Symmetrical components of the voltage Eaxf at the fault point F′ on line x can be
expressed as follows:

E xf 1  E x1  pZ L1 I x1 (4.29)

E xf 2  E x 2  pZ L1 I x 2 (4.30)

E xf 0  E x 0  pZ L 0 I x0  pZ LM 0 I y 0 (4.31)

Adding equations (4.29), (4.30) and (4.31) yield,

Eaxf  E xf 1  E xf 2  E xf 0 (4.32)

  E x1  E x 2  E x 0   pZ L1  I x1  I x2   pZ L 0 I x 0  pZ LM 0 I y 0

 E ax  pZ L1 I a x  p Z L 0  Z L1 I x 0  pZ LM 0 I y 0 (4.33)

Similarly, symmetrical components of voltage Ebyf at the fault point F″ on line y can be
expressed as follows:

Ebyf  Eby  pZ L1 Iby  pZ L 0  Z L1 I y 0  pZ LM 0 I x 0 (4.34)

It is to be noted with reference to Figures 4.5 and 4.6 that the value of arc resistance is
very small during the early stage of an arc and hence, its value does not exceed 0.5 Ω for both

68
types of inter-circuit faults [130]. Moreover, the voltage drop produced by an arc resistance is
neglected. Therefore, both the fault points F′ and F″ are assumed to be at the same potential,
i.e. Eaxf = Ebyf. Considering this assumption and after algebraic manipulation of equations
(4.33) and (4.34), the compensated value of impedance (Zc) of the faulted portion of the
transmission line using the proposed scheme is given by,

E ax  Eby 
(4.35)
Z c  pZ L1 
  Z L 0  Z L1  Z LM 0  
I ax  I by    I x 0  I y 0 
  Z L1  

The imaginary part of impedance mentioned on the right side of equation (4.35)
indicates compensated value of reactance (Xc) of the faulted portion of the parallel
transmission line provided by the proposed method. It is given by,

 
 

X c  imaginary 
 Eax  Eby   (4.36)
   
 I ax  I by    Z L 0  Z L1  Z LM 0 I x 0  I y 0  
   Z L1 
   
It is well known that the ratio of reactance (X) to resistance (R) of the transmission line
remains constant. Therefore, the compensated value of resistance (Rc) of faulted portion of
parallel transmission line is determined by using the values of (Xc) and is given by,
R
Rc  X c (4.37)
X

4.11 RESULTS AND DISCUSSIONS

In this section, two types of inter-circuit faults on 400 kV parallel transmission lines
have been simulated. The system and line parameters are given in Appendix C. Throughout
the entire discussion Zax, Zby and Zc represent the impedances measured by the conventional
ground distance relay at A, at B and by the proposed scheme, respectively. Rax, Rby and Rc
represent the resistive part of impedances measured by the conventional ground distance
relay at A, at B and by the proposed scheme, respectively. Xax, Xby, Xc represent the reactive
part of impedances measured by the conventional ground distance relay at A, at B and by the
proposed scheme, respectively. Ract and Xact represent actual values of the resistive part and
the reactive part of impedance of the faulted portion of the transmission line. %RE and %XE
indicate percentage error in the resistive part and reactive part of the measured value of
impedance. δ and RF represent power transfer angle between two buses (S and R) and fault

69
resistance present in the faulted path, respectively. Rarc represents the resistance of arc that is
present between the faulted phases of the transmission lines. The value of arc resistance is
considered to be 0.5 Ω for both types of inter-circuit faults [132]. As the ground path is
involved in the phase-to-phase-to-ground type of fault, the value of fault resistance plays a
key role in the measurement of apparent impedance. Therefore, different values of fault
resistance (25, 50 and 200 ) have been considered for this fault.

4.11.1 Phase-to-Phase Inter-Circuit Fault

Tables 4.2 and 4.3 show the values of apparent impedances Zax, Zby and Zc measured
by the conventional relays and the proposed scheme, respectively, at different fault locations
(0% to 80% in steps of 10%) having different values of δ (30º and 15º) with Rarc = 0.5 .

Table 4.2 Impedance measured by the conventional scheme and the proposed scheme at
δ = 30º
p Zact Zax (at A) Zby (at B) Zc (by proposed method)
(%) Ract Xact Rax %RE Xax %XE Rby %RE Xby %XE Rc %RE Xc %XE
(Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω)
0 0 0 4.2  0.31  3.42  0.35  0.002  0.02 
10 0.3 3.33 6.73 2143 3.08 7.51 4.9 1733 3.64 9.31 0.302 0.500 3.35 0.601
20 0.6 6.66 9.36 1460 6.62 0.60 6.33 1155 6.85 2.85 0.601 0.200 6.68 0.300
30 0.9 9.99 12.09 1243 10.29 3.00 7.71 957 9.97 0.20 0.901 0.100 10.01 0.200
40 1.2 13.32 14.94 1145 14.17 6.38 9.08 857 13 2.40 1.203 0.275 13.37 0.375
50 1.5 16.65 17.95 1097 18.23 9.49 10.41 794 15.94 4.26 1.505 0.320 16.72 0.420
60 1.8 19.98 21.15 1075 22.54 12.81 11.74 752 18.8 5.91 1.808 0.450 20.09 0.551
70 2.1 23.31 24.63 1073 27.16 16.52 13.06 722 21.55 7.55 2.112 0.586 23.47 0.686
80 2.4 26.64 28.54 1089 32.23 20.98 14.5 704 24.18 9.23 2.420 0.838 26.89 0.938
Average % error  1291  7.63  959  2.17  0.409  0.509

Table 4.3 Impedance measured by the conventional scheme and the proposed scheme at
δ = 15º
p Zact Zax (at A) Zby (at B) Zc (by proposed method)
(%) Ract Xact Rax %RE Xax %XE Rby %RE Xby %XE Rc %RE Xc %XE
(Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω)
0 0 0 3.98  0.62  3.55  0.64  0  0 
10 0.3 3.33 6.25 1983 2.34 29.73 5.22 1840 4.32 29.73 0.298 0.700 3.31 0.601
20 0.6 6.66 8.49 1315 5.26 21.02 6.91 1252 8.08 21.32 0.597 0.550 6.63 0.450
30 0.9 9.99 10.72 1091 8.11 18.82 8.63 1059 11.9 19.12 0.895 0.600 9.94 0.501
40 1.2 13.32 12.94 978 10.92 18.02 10.44 970 15.82 18.77 1.193 0.550 13.26 0.450
50 1.5 16.65 15.18 912 13.67 17.90 12.29 919 19.83 19.10 1.492 0.520 16.58 0.420
60 1.8 19.98 17.44 869 16.34 18.22 14.22 890 23.96 19.92 1.790 0.550 19.89 0.450
70 2.1 23.31 19.78 842 18.92 18.83 16.29 876 28.24 21.15 2.089 0.529 23.21 0.429
80 2.4 26.64 22.28 828 21.35 19.86 18.55 873 32.76 22.97 2.386 0.588 26.51 0.488
Average % error  1102  20.30  1085  21.51  0.573  0.474

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 It is to be noted that the average percentage error in the measurement of resistive part
of the impedances (Rax and Rby) by the conventional ground distance relays at A and B is
1196.5% and 1022%, respectively. This clearly indicates that the conventional ground
distance relays measure the resistive part of impedances (Rax and Rby) with a very high
percentage of error. Moreover, it has also been observed from Table 4.3 that the conventional
ground distance relays measure the reactive part of the impedances (Xax and Xby) with
percentage error in the range of 30%. On the other hand, the average percentage error in the
measurement of resistance (Rc) and reactance (Xc) of faulted portion of parallel transmission
line by the proposed method is within 0.573%, which clearly indicates the effectiveness of
the proposed scheme in terms of accuracy.

Figure 4.7 represents the simulation results of apparent impedances Zax, Zby and Zc
measured by the conventional ground distance relays and the proposed scheme, respectively,
for phase-to-phase inter-circuit fault with wide variations in system and fault parameters.

Figure 4.7 Impedance measured by the conventional scheme and the proposed scheme at
different values of δ (phase-to-phase inter-circuit fault)

It is to be noted from Figure 4.7 that the conventional distance relay located at A is
able to sense only those phase-to-phase inter-circuit faults which occur approximately up to
30% of the complete line section from the relaying point. While, the conventional distance
relay located at B fails to sense such inter-circuit faults as the operating point lies in the
second quadrant of R-X plane (out of the zone of protection for quadrilateral characteristic of

71
the conventional ground distance relay). On the other hand, the proposed digital distance
relaying scheme measures the correct values of resistance and reactance of the faulted portion
of the transmission line for all cases.

4.11.2 Phase-to-Phase-to-Ground Inter-Circuit Fault

Tables 4.4 and 4.5 show the values of apparent impedances Zax, Zby and Zc measured
by the conventional ground distance relays and the proposed scheme for different values of δ
(30º and 15º) with Rarc = 0.5  and RF = 50 .

Table 4.4 Impedance measured by conventional and proposed scheme at δ = 30º with
RF = 50 Ω
p Zact Zax (at A) Zby (at B) Zc (by proposed method)
(%) Ract Xact Rax %RE Xax %XE Rby %RE Xby %XE Rc %RE Xc %XE
(Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω)
0 0 0 3.76  0.47  3.69  0.72  0.002  0.02 
10 0.3 3.33 5.77 1823 2.52 24.32 5.35 1883 4.7 41.14 0.302 0.500 3.35 0.601
20 0.6 6.66 7.75 1192 5.52 17.12 6.93 1255 8.74 31.23 0.601 0.200 6.68 0.300
30 0.9 9.99 9.79 988 8.57 14.21 8.44 1038 12.7 27.13 0.901 0.100 10.01 0.200
40 1.2 13.32 11.96 897 11.75 11.79 9.96 930 16.49 23.80 1.203 0.275 13.37 0.375
50 1.5 16.65 14.38 859 15.08 9.43 11.49 866 19.98 20.00 1.505 0.320 16.72 0.420
60 1.8 19.98 17.15 853 18.65 6.66 13.05 825 23.1 15.62 1.808 0.450 20.09 0.551
70 2.1 23.31 20.46 874 22.61 3.00 14.63 797 25.74 10.42 2.112 0.586 23.47 0.686
80 2.4 26.64 24.6 925 27.22 2.18 16.18 774 27.84 4.50 2.420 0.838 26.89 0.938
Average % error  1051  10.54  1046  21.73  0.409  0.509

Table 4.5 Impedance measured by conventional and proposed scheme at δ = 15º with
RF = 50 Ω
p Zact Zax (at A) Zby (at B) Zc (by proposed method)
(%) Ract Xact Rax %RE Xax %XE Rby %RE Xby %XE Rc %RE Xc %XE
(Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω) (Ω)
0 0 0 3.57  0.72  3.81  1.09  0  0 
10 0.3 3.33 5.36 1687 1.98 40.54 5.55 1950 5.64 69.37 0.298 0.700 3.31 0.601
20 0.6 6.66 7.03 1072 4.61 30.78 7.17 1295 10.52 57.96 0.597 0.550 6.63 0.450
30 0.9 9.99 8.66 862 7.18 28.13 8.64 1060 15.6 56.16 0.895 0.600 9.94 0.501
40 1.2 13.32 10.31 759 9.75 26.80 10.12 943 20.73 55.63 1.193 0.550 13.26 0.450
50 1.5 16.65 12.06 704 12.3 26.13 11.67 878 25.81 55.02 1.492 0.520 16.58 0.420
60 1.8 19.98 13.99 677 14.82 25.83 13.42 846 30.71 53.70 1.790 0.550 19.89 0.450
70 2.1 23.31 16.2 671 17.33 25.65 15.50 838 35.33 51.57 2.088 0.571 23.2 0.472
80 2.4 26.64 18.87 686 19.81 25.64 18.02 851 39.57 48.54 2.386 0.588 26.51 0.488
Average % error  890  28.69  1083  55.99  0.579  0.479

It is to be noted from Tables 4.4 and 4.5 that the average percentage errors in the
measurement of resistance and reactance of the faulted portion of the transmission line

72
(Rax and Xax) by the conventional ground distance relay at located A are 970.5% and
19.62%, respectively. Whereas, the conventional ground distance relay located at B
measures resistive part and reactive part of the impedance (Rby and Xby) with an average
percentage error of 1064.5% and 38.86%, respectively. On the other hand, the average
percentage error in the measurement of resistance (Rc) and reactance (Xc) of the faulted
portion of the transmission line using the proposed scheme is within 0.579%.

Figure 4.8 represents the simulation results of apparent impedances Zax, Zby and Zc
measured by the conventional ground distance relays and the proposed scheme for phase-to-
phase-to-ground inter-circuit faults at different fault locations (0% to 80% in steps of 10%)
having δ = 15º with Rarc = 0.5  and varying fault-resistances (25, 50 and 200 Ω).

Figure 4.8 Impedance measured by the conventional scheme and the proposed scheme at
different values of fault-resistance with δ = 15º (phase-to-phase-to-ground inter-circuit fault)

It is clear from Figure 4.8 that the conventional ground distance relay located at A is
able to sense only those inter-circuit faults which occur approximately from 35% to 60% of
the complete line section for different values of fault resistance. Whereas, the conventional
distance relay located at B completely fails to detect phase-to-phase-to-ground inter-circuit
faults that occur at any point on the line section. On the other hand, the proposed digital
distance relaying scheme is immune to the said problems and measures correct value of
impedance of the faulted portion of the transmission line even against wide variations in
system and fault parameters.

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4.12 ADVANTAGES OF THE PROPOSED SCHEME

1) In the proposed digital distance relaying scheme, there is no need to extend the
boundary of the quadrilateral characteristic of digital distance relay against wide
variations in the values of fault resistance.

2) The reach of the proposed scheme is not affected by the zero-sequence mutual
coupling impedance present between the parallel transmission lines.

3) The proposed scheme is not influenced by the loading effects of the transmission
lines, as it measures the correct value of impedance of the faulted portion of the
transmission line even during presence of large disturbances in power transfer
angles (δ) between two buses.

4) The proposed technique is highly accurate and robust against large disturbance in
system conditions and fault parameters, as it does its duty of fault impedance
measurement with an average percentage error of 0.579%.

5) As the derivation of final equation of compensated fault impedance is very simple,

the computational requirements are very less.

4.13 CONCLUSION

In this chapter, a new digital distance relaying scheme has been proposed for parallel
transmission lines, which effectively compensates the error present in the measurement of
apparent impedance by the conventional ground distance relay during inter-circuit faults. The
proposed scheme is based on digital computation of the compensated value of impedance
using symmetrical components of voltages and currents. The proposed scheme does not
require data from remote end and hence, it is very simple compared to the other techniques
which require remote end data in order to change relay characteristic in case of variation in
external system conditions. The proposed digital distance relaying scheme has been simulated
using MATLAB/SIMULINK software. The proposed scheme is highly accurate as it
measures correct values of resistance and reactance of the faulted portion of the transmission
line having percentage error within 0.579%. Moreover, it remains stable during inter-circuit
faults against wide variations in system and fault conditions.

74