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CHAPTER 5

DIGITAL DISTANCE RELAYING SCHEME FOR SERIES

COMPENSATED PARALLEL LINES DURING SIMULTANEOUS

OPEN CONDUCTOR & GROUND FAULT

5.1 INTRODUCTION

The main purpose of using series compensated transmission lines is to cancel out a

portion of the inductive reactance of the transmission line; thereby improving the power

transmission capability of the transmission line. There are several other reasons for favouring

the use of series compensated long EHV/UHV transmission lines. The benefits include:

increased transmittable power, improved system stability, reduced transmission losses,

enhanced voltage control, more flexible power flow control and cost benefits are the technical

reasons favouring the application of series compensated transmission lines.

For these reasons, the use of series compensated transmission lines has increased for

EHV/UHV transmission lines carrying huge amount of power for a long distance. Series

compensation is usually stated in terms of a percentage of the transmission line inductive

reactance, which is referred to as the “degree of compensation”. Typically, the series

capacitors are used to compensate for 25% to 75% of the inductive reactance of the

transmission line; it means that the degree of series compensation is 25% to 75%. Normally,

the series capacitors are located at the ends of the transmission lines as it is the least

expensive alternative, since no middle station is required. However, this alternative may

cause a distance relay to measure a negative reactance for a close-in fault.

The series capacitors essentially violate a fundamental principle upon which distance

protection is built; that is the apparent impedance varies proportionally with the distance to

the fault. The series capacitors are exposed to a wide range of currents, which can result in

the development of large voltages across the capacitors. Generally, it is uneconomical to

design the capacitors to withstand these over-voltages, thus additional equipment, namely

metal oxide varistor (MOV) is usually provided to protect the series capacitors. Obviously,

the non-linear characteristic of this MOV is of concern to the protection engineers. Because,

the majority of distance relays respond to more (security) or less (speed) accurately filtered

fundamental frequency components. Therefore, it becomes necessary to understand relations

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between the fundamental frequency voltage and current of a typical arrangement of series

capacitors and their overvoltage protection devices.

5.2 SERIES CAPACITORS: THEORY AND OPERATION

5.2.1 Aim of Series Compensation

The main objective of providing series compensation to the EHV/UHV transmission

lines is to reduce the inductive reactance of the transmission line by the addition of series

capacitors. Further, it increases the line loading capacity and stability margins of the power

system. This is apparent by reviewing the basic equation of power transfer between two buses

by the series compensated transmission line, and it is given by [76],

CL XXEEP

sin21 (5.1)

Where, P is the amount of power transfer by the series compensated transmission line,

is the angle between the E1 and E2 voltages, XL is the inductive reactance of the

transmission line and XC is the capacitive reactance of the series capacitor. It is to be noted

from equation (5.1) that XC reduces the total transfer impedance thus allowing increased

power flow for the same system angle; or a reduction in the power transfer angle for the

same power transfer level, thus increasing the stability margins [76].

5.2.2 Series Compensated Transmission Line

Figure 5.1 shows a typical arrangement of a series compensated transmission line.

Generally, the series capacitor (SC) is protected against over-voltages by air gaps or metal

oxide varistors (MOVs) or both.

Figure 5.1 Typical configuration of a series compensated transmission line

Under normal operating conditions of the power system, voltage drop across the series

capacitor is well below the voltage protection level. As a result, neither the air gap nor the

MOV conduct any current. Therefore, the equivalent reactance of SC/MOV parallel

combination is equal to the reactance of the actual (physical) capacitor. Whereas, during a

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fault and depending on the fault current magnitude, both SC and MOV will conduct a portion

of the fault current; thereby modifying the impedance of the capacitor bank.

5.2.3 Series Capacitor Bypass Systems

a) Series Capacitor with Bypass Gaps

Figure 5.2 shows the simplest type of circuit in which the series capacitor is protected

by a self-triggered spark gap. The spark gap is set to flashover at a given voltage, usually in

the range of 2.0 to 3.5 per unit (where 1.0 per unit is equal to the crest voltage produced

across the series capacitor at rated current). But, the spark gap may not fire for low-current

faults. Therefore, the line protection scheme must also perform properly with the series

capacitor still in operation. The bypass breaker is used by an operator to remove the capacitor

bank from the service for maintenance and for reinserting the capacitor bank into the service

following these intentional removals [157].

Figure 5.2 Typical circuit for spark gap protected series capacitor

b) Series Capacitor with MOV and Bypass Gaps

Figure 5.3 shows a typical arrangement for capacitor protection using Metal Oxide

Varistor (MOV). MOV clamps the voltage and change the series capacitor impedance in a

non-linear fashion.

Figure 5.3 Typical circuit for MOV protected series capacitor

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The MOV operation does not fully remove the series capacitor as it does not conduct

the whole current during the faulty conditions. However, this scheme includes MOV energy

monitoring devices that bypass series capacitor and MOV both completely, when the MOV

energy level exceeds a threshold [157].

5.2.4 Operation of Series Capacitor Bypass Systems

Normally, during faulty conditions, the MOV (Metal Oxide Varistor) starts conducting

immediately, after the instantaneous voltage (v) across the capacitor exceeds a protective

voltage level (Vpl). The highly non-linear characteristic of the MOV makes it ideal for

maintaining the voltage across the capacitor within a specified limit. The basic VI

characteristic of the MOV is approximated by the single exponential model as given by

equation (5.2) as follows [157]:

plMOV V

vIi max (5.2)

where,

iMOV - MOV current

Imax - maximum current that cause the gap to flashover

α - characteristic constant, whose value is between 30 to 50

Vpl - protective voltage level of MOV: plcpl IXV 2

Ipl - protective current level of MOV: ,kII npl k = 2 to 2.5

Xc - capacitive reactance

In - maximum load current

The MOV is a resistive device that absorbs substantial amount of energy for high-

current faults like those near a series capacitor bank. In such conditions, to protect the MOV

from overheating, a triggered gap controlled by a special circuitry is used in parallel with

MOV to rapidly bypass the MOV and series capacitor if the absorbed energy level reaches to

a preset value. The triggered gap control and the MOV energy absorption capability are

normally coordinated so that the gap may fire only during in-zone faults. In addition to this, a

bypass switch is provided in parallel with the whole arrangement, which inserts and removes

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the capacitor bank from the service and also provides protection to the complete assembly for

failures or imbalances.

The MOV protection is designed to hold the capacitor voltage at or below the peak

value even for the highest fault currents. It has been observed from the results of field tests

and simulations involving MOV-protected series capacitors that even though the capacitor is

paralleled by a highly nonlinear device, the resulting total current through the SC/MOV

combination remains remarkably sinusoidal. This effect can be attributed to the system

inductance which is the major component in determining the fault current.

Considering the total current to be sinusoidal and the external system having a linear

impedance, the SC/MOV combination is approximated by Goldsworthy’s equivalent linear

impedance (ZC'). This equivalent impedance is then broken down into components of

resistance (RC') and reactance (XC') connected in series as shown in Figure 5.4. This new

linearized equivalent impedance in series with the system impedance produces the same

magnitude and phase angle of fault current. In Figure 5.4, ipu represents per-unit value of the

fault current (i) passing through SC/MOV with respect to the capacitor protective level

current (Ipl). XC represents capacitive reactance of the capacitor bank.

Figure 5.4 Goldsworthy’s model of SC/MOV combination

Referring to Figure 5.4, for ipu > 0.98, the values of Goldsworthy’s equivalent

resistance RC′ and reactance XC′ are expressed by equations (5.3) and (5.4) as follows [49]:

pupupu iiiCC eeeXR 4.15243.0 6.03549.00745.0' (5.3)

puipuCC eiXX 8566.0088.2005749.01010.0' (5.4)

5.2.5 Series Compensation Model

Figure 5.5 shows a single-phase series compensation model used for MATLAB

simulation. The three-phase module consists of three identical subsystems, one for each phase

of a three-phase transmission line. Subsection 5.2.4 describes the method of calculation of the

capacitor value and the MOV protection level. A gap is also connected in parallel with the

MOV block. The gap fires when the energy absorbed by the MOV exceeds the threshold. The

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energy dissipated in the MOV is calculated by integrating the power (product of the MOV

voltage and current). A damping R-L circuit is connected in series with the gap to limit the

rate of rise of the capacitor current when the gap is fired [200].

Figure 5.5 Single-phase series compensation model

5.3 PROTECTION ISSUES OF SERIES COMPENSATED LINES

The different protection issues related to series compensated EHV/UHV transmission

lines are given as follows:

5.3.1 Malfunctioning of Distance Relay

The addition of capacitor bank, along with metal oxide varistor (MOV), in series with

the transmission line reactance creates certain complexities in the effective functioning of the

digital distance relays. Generally, during a faulty condition, the distance relay measures the

fault impedance which is proportional to the length of the transmission line and tries to

compare it with the set impedance. If the measured impedance is less than the set impedance,

the distance relay considers it to be an in-zone fault. But, because of the non-linear behaviour

of SC/MOV parallel combination, the fault impedance measured by the digital distance relay

is not proportional to the impedance of the length of the transmission line. Hence, it is

difficult for the digital distance relay to decide that whether the fault is inside or outside the

zone boundary. Therefore, for most of the cases, the digital distance relay over-reaches for

the faults on the series compensated transmission lines.

The concept of equivalent impedance measured by the digital distance relay allows

grasping the basics of the overreaching phenomenon. If the series capacitors are located

between the fault point and the relaying point, the fault loop contains the line-to-fault

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impedance, fault resistance and the equivalent impedance of the SC/MOV parallel

combination. According to Goldsworthy’s equations the equivalent impedance of the

SC/MOV parallel combination is resistive-capacitive in nature, and hence, it shifts the

apparent impedance measured by the digital distance relay down and to the right as shown in

Figure 5.6.

Figure 5.6 Distance element overreaching due to series compensation

Overreach is the primary consequence of the situation depicted in Figure 5.6. In the

worst case, for low-current faults, the equivalent impedance of the SC/MOV parallel

combination is a pure capacitive reactance shifting the apparent impedance down by the

entire capacitive reactance of the physical capacitors. As the transmission lines are typically

compensated in the range of 25% to 75% of the total length, the overreach may be as high as

25% to 75%. Whereas, for high-current faults, the equivalent impedance of the SC/MOV

parallel combination shifts the apparent impedance only slightly to the right. Hence, the

overreaching of the digital distance relay is minimum for high-current faults [25].

During medium-current faults on the series compensated transmission line, the

apparent impedance may be shifted to the right by more than half of the capacitive reactance

of the capacitors. This relocation may be high enough to push the apparent impedance outside

the operating characteristic, particularly if the load encroachment characteristic is used [25].

Another observation that can be derived from this simplified characteristic of the series

compensated transmission line is a failure of a distance protection scheme to respond to a

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low-current close-in fault. During a low-current close-in fault, the apparent impedance moves

to the fourth quadrant of the impedance plane resulting in problems with directional

discrimination [25].

5.3.2 Sub-synchronous Resonance

The series combination of the capacitive reactance of the series capacitors and the

inductive reactance of the system sets up a series resonant circuit, the natural frequency nf

of which can be calculated by [76],

L

Cn X

XfLC

f 2

1

(5.5)

In which, f is the system frequency, XC is the capacitive reactance of the series

capacitor and XL is the total system inductive reactance. Since, XC/XL is typically in the range

of 0.25 to 0.75, fn will be a sub-harmonic of the power frequency.

Any system disturbance produced due to occurrence of a fault, insertion/removal of the

capacitor bank, switching of any series element, etc. will result in the excitation of the system

at the sub-harmonic frequency, which, in turn, can give rise to transient currents. These

transients are typically damped out after a few cycles, but in certain cases, it may last for a

significantly longer duration [76].

The presence of such transients may also excite one or more of the natural torsional

frequencies of the mechanical shaft system of the generators. This complex phenomenon is

known as sub-synchronous resonance (SSR). Depending upon the degree of damping and

resonance, the torsional oscillations may be severe enough to cause damage to the shaft of the

generators and failure of the capacitor bank [76].

5.3.3 Voltage Inversion

Voltage inversion will occur for a close-in fault after a capacitor bank, during which,

the net fault impedance measured at the relaying point is capacitive rather than inductive. As

a result, the voltage applied to the digital distance relay will be shifted approximately by 180º

from its normal position. It means that voltage inversion causes the relay to see a fault on the

protected line to be in a reverse direction. Since, the conventional digital distance relays are

designed to work properly only on inductive system, the voltage inversion will have a

negative effect on the performance of the protective relaying [76].

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Consider a system shown in Figure 5.7 in which, a digital distance relay is located at

Station A before the capacitor XC and it is looking towards Station B. A three-phase fault F1 is

assumed to be present at fault location F1 near Station A. Therefore, the voltage applied to the

potential coil of a digital distance relay will be the drop across the capacitor. Consequently, it

will be reversed from the position normally encountered in an inductive system. Figure 5.8

shows a negative sequence network of a typical power system considering a three-phase fault

present at fault location F1. For a fault at F1, if the voltage drop across the capacitor XC

exceeds the voltage drop of the faulted portion of the transmission line then the voltage

measured by the digital distance relay will be negative as shown in Figure 5.9.

5.3.4 Current Inversion

A current inversion is said to occur when the fault current appears to be entering at one

end and leaving at the other end of the transmission line, just as it would occur during an

external fault. As shown in Figure 5.10, current inversion can occur for the fault at fault

location F1 (just after the capacitor), if the source impedance XS is less than the capacitive

reactance XC of the capacitor. This may be the impractical condition for a bolted fault, since

the large fault current would ensure rapid bypassing of the capacitor. However, in the case of

a fault with large fault resistance, the fault impedance can reduce the fault current below the

bypass level. The protective relaying schemes that use current only for operation will be

blocked by the fault current reversal depicted in Figure 5.7 unless they are modified to obtain

reliable operation [76].

Figure 5.7 Typical series compensated power system

Figure 5.8 Negative sequence network of a power system

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Figure 5.9 Voltage profile for fault at F2

Figure 5.10 Current distribution for fault at F1

5.4 TECHNIQUES USED IN COMMERCIAL RELAYS AND THEIR PROBLEMS

Protection of the series compensated transmission lines is considered to be one of the

most difficult tasks for relay manufacturers and utility engineers [45], [67], [214]. The typical

problems faced by the digital distance relays have been addressed in many publications;

which include different phenomena, such as voltage and/or current inversion, sub-harmonic

oscillations and additional transients caused by the air gaps triggered by thermal protection of

the MOVs [39], [45], [67], [141], [214]. However, the reach measurement problems for the

fault detection and fault location applications are difficult to solve with the conventional

approaches.

For the fault detection applications, it is not required to detect the exact fault location.

In order to overcome these problems, accurate modeling of the capacitor installation is

required for the fault location application. Further, the identification and classification of

faults on a transmission line are essential for relaying decision and auto-reclosing

requirements. A conventional approach classifies the fault based on fundamental frequency

only [7], [153], [167]. However, in a series compensated transmission line, the load current

level may be of the order of fault current, which will lead to wrong classification and

malfunction of the digital distance relay.

Some studies are associated with the simplified analysis of series compensation device

models [1], [56], [142]. However, these algorithms must need to consider the model of series

compensation device to compute voltage drop, which limits the accuracy of fault location

algorithm. For example, the protection functions of series compensation devices are too

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simplified in [56], [142]; while the analysis given in [1] ignores the switching among

different operation modes that initiates from the protection function. Thus, those algorithms

inevitably suffer from the errors produced due to inaccuracy of the adopted models.

To overcome the above problems, various protective schemes utilizing traveling wave

principles have been suggested. The high frequency components in the fault waveform

present undesirable effects for most of the fault location algorithms [14], [29]. A fault

detection/fault location algorithm derived from traveling wave principles can handle the

problems of high frequency transients. Fault location methods based on traveling waves are

independent of network configurations and installations. Thus, these methods are suitable for

the series compensated transmission line [96]. However, identifying the desired high

frequency signal becomes problematic. Additionally, the need for a high sampling rate for

identifying the signal also limits the application of the traveling wave based method.

The synchronized PMU-based fault detector/locator technique has been proven

effective for the relaying of transmission line without series compensation device [94], [95],

[135]. However, when the series compensation device is installed in the transmission line,

this technique must be incorporated with the series compensation device model to estimate

voltage drop of the series compensation device in fault location computation.

5.5 CURRENT STATE-OF-THE-ART

For series compensated transmission lines, the problems faced by the distance relay

and some of the solutions to these problems are published in [25], [43], [45], [49], [55], [67],

[184]. The reach settings for the different zones of protection with respect to some of the

typical problems and adaptive approach have been discussed in [13], [22], [88], [136], [154],

[163], [166], [193], [225], [231].

Many researchers have proposed a number of fault location methods for the

transmission lines with series compensation devices [1], [11], [42], [56], [64], [108], [142],

[215], [218]. Most of them have used impedance-based approach [1], [42], [108], [142].

Differential equation based algorithms are introduced in [64]. Wavelet Transform is also

effectively used for fault recognition of series compensated transmission lines [11]. In [56],

[218], application of artificial neural networks combined with the impedance-based approach

to fault location has been presented. Consequently, the use of artificial neural networks

combined with discrete wavelet transform for fault location on thyristor controlled series

compensated lines has also been considered [215]. In turn, [182] presents the usage of

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wavelet packet for digital protection of series compensated transmission line. However, these

algorithms use direct or indirect measurement of impendence to locate the fault, which would

fail in case of series compensated transmission line due to the non-linear operation of the

capacitor bank.

Spoor and his colleagues [48] suggested the use of carrier aided permissive over-reach

transfer tripping scheme or a carrier blocking scheme to detect inter-circuit faults. However,

this scheme requires communication channel, which increases cost and reduces reliability in

case of failure of link. Agrasar and his co-workers [123] discussed the effect of inter-circuit

faults on the conventional distance relay for parallel transmission lines. However, they have

not considered the effect of simultaneous open conductor and ground fault on series

compensated parallel transmission lines. Saha and his co-workers [141] proposed an

algorithm to protect series compensated transmission lines against various types of phase and

ground faults. But, they have not considered the impact of simultaneous faults. Further, they

have not analyzed the effect of zero-sequence mutual impedance and fault resistance.

Afterwards, Evrenosoglu et al. [44] presented different options for traveling wave

method for locating faults on teed circuits with mutually coupled lines and series capacitors.

Use of traveling wave based fault location algorithms is expanding. They are insensitive to

the fault resistance, power flow and source impedance. In addition, they are more accurate

compared to impedance based methods [3]. However, conventional traveling wave methods

are sensitive to the fault inception angle, noises and faults occurred on the other lines [122],

[207].

Relay design progressing is concerned with the improvement of conventional relay

algorithms based on phasor concepts. The complexities discussed in the protection

performance of the series compensated transmission lines calls for the early fault detection

and high-speed distance relays with good accuracy. One can find some of the advanced

techniques with respect to the early fault detection and phasor estimation proposed in [16],

[64], [141]. Adaptive reach settings of the distance relays for faults involving high arc

resistance have been presented in [37], [108], [155]. Methods for on-line corrections of the

trip boundaries are presented using the wavelet transform in [179], [182], [227] and method

for the development of integrated protection systems is presented in [228].

The conventional digital distance relay system is not able to detect and trip High

impedance faults (HIFs) occurred on series compensated lines. The failure of HIF detection

may lead to potential hazards to human beings and fires [192]. HIFs on the electrical

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transmission and distribution networks involve arcing and/or nonlinear characteristics of the

fault impedance. Therefore, the main objective of most of the fault detection schemes is to

evaluate the special features in patterns of the voltages and currents in HIFs. In recent years,

several researchers have presented many techniques to detect the HIFs more effectively.

These techniques include discrete wavelet transform with other different methods [17], [148],

[192], down-conductor fault detection via a voltage based method [117] and development of

a fuzzy inference system based on genetic algorithm [143].

Recently, the application of series compensated transmission lines has increased to

transmit bulk power for a long distance. Therefore, it is worth to undertake an effort to

simulate the transient conditions for series compensated transmission line applications, to

fine-tune & verify settings and finally to test the relaying system using digital simulators.

5.6 SIMULTANEOUS OPEN CONDUCTOR AND GROUND FAULT ON SERIES

COMPENSATED PARALLEL TRANSMISSION LINES

5.6.1 Simultaneous Open Conductor and Ground Fault

Figure 5.11 shows a model of series compensated parallel transmission line with half

series compensation provided at each end of both transmission lines. XG and XH are the values

of capacitive reactance of SC located at G and H, respectively. XC is the value of capacitive

reactance of SC with respect to full series compensation provided to each transmission line.

Therefore, XG = XH = XC/2. Further, VG120, IG120, ZG120 and VH120, IH120, ZH120 are the sequence

(positive, negative and zero) components of voltages, currents and impedances of SC/MOV

combination located at G and H, respectively.

A simultaneous open conductor and ground fault has occurred on line x at fault

location F, which is at p percentage from the relaying point G. During a simultaneous open

conductor and ground fault, phase A of line x on Bus S side has broken and fallen to ground,

whereas phase A of line x on Bus R side has broken but is being held by the suspension

insulators. In this situation, because of the presence of zero-sequence mutual impedance

between parallel transmission lines, the ground unit of the conventional digital distance relay

located at G with a facility of series compensation may under-reach/over-reach. Conversely,

the conventional digital distance relay located at Bus R with a facility of series compensation

completely fails to detect an open-circuit fault [205].

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Figure 5.11 Model of a simultaneous open conductor and ground fault

5.6.2 Linearized Equivalent Model of SC/MOV

During a simultaneous open conductor and ground fault, if the solid ground fault will

occur, then a very high amount of fault current (ipu > 0.98) will pass through the capacitor

bank located at G and connected to the grounded phase A of line x. Therefore, the MOV will

start conducting a portion of fault current. Hence, Goldsworthy’s equations can be applied

during this condition to determine equivalent resistance RC′ and equivalent reactance XC′ of

SC/MOV (refer Figure 5.12).

Figure 5.12 Goldsworthy’s equivalent model considering open conductor and ground fault

But, if high resistance ground fault will occur, then a low value of fault current

(ipu < 0.98) may pass through the capacitor bank located at G and connected to the faulted

phase A. As a result, the value of series capacitor will not change (refer Figure 5.12).

Furthermore, for both the aforementioned situations, the magnitude of currents passing

through the remaining healthy phases (phases B and C) of line x will always be less than rated

current of the capacitor bank (i.e., ipu < 0.98) and hence, the value of SC connected in healthy

phases will not change.

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5.6.3 Effect of Mutual Coupling for Simultaneous Open Conductor and Ground Fault

In case of series compensated parallel transmission lines, the series capacitor

compensates the zero-sequence self impedance of the two lines. But the zero-sequence

mutual impedance between series compensated lines remains the same as that of

uncompensated lines. Therefore, the relative effect of series compensation becomes more

pronounced than that observed in the uncompensated line [157].

Figure 5.13 depicts the effect of zero-sequence mutual coupling on series compensated

parallel transmission line. It is clear from Figure 5.13 that the reactance of series capacitor

affects only to the self impedance of two lines, whereas mutual impedance remains

unchanged with reference to the uncompensated case [157].

(a) Mutually coupled parallel transmission lines, (b) Equivalent using 1:1 transformer

Figure 5.13 Equivalent circuit of zero-sequence mutual coupling

5.6.4 Effect of Simultaneous Open Conductor and Ground Fault

A simultaneous open conductor and ground fault creates voltage and current unbalance

in the SC/MOV parallel combination. In this situation, the symmetrical components of

voltages and impedances of SC/MOV parallel combination are expressed by equations (5.6)

and (5.7) as follows [25]. In which, ZA, ZB and ZC are Goldsworthy’s equivalent impedances

of SC/MOV combination connected in phases A, B and C, respectively, and ‘a’ is 120º phase

shift operator.

012012012 IZV (5.6)

CBACBACBA

CBACBACBA

CBACBACBA

ZZZZaaZZaZZaZaZZaZZZZZaaZZZaaZZaZZaZZZZ

Z22

22

22

012 31 (5.7)

During a simultaneous open conductor and ground fault, the fault currents are not

equally distributed among the three phases of transmission line. Therefore, Goldsworthy’s

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equivalent impedances of SC/MOV connected in the three phases are not equal, as they

depend on the values of fault current [49].

5.7 ANALYSIS OF SIMULTANEOUS OPEN CONDUCTOR AND GROUND FAULT

For all the analysis, positive- and negative-sequence impedances (ZL1 and ZL2) of

parallel transmission lines are assumed to be equal. ZLM0 is the zero-sequence mutual coupling

impedance present between the two lines. Eax and Iax are the voltage and current of phase A of

line x measured at the relaying point G, respectively. Further, Ex120, Ix120 and Ey120, Iy120 are the

sequence (positive, negative and zero) components of voltages and currents of lines x and y

measured at the relaying points G and H, respectively. In all 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 during a simultaneous open conductor and ground fault, Bus S

side conductor has been assumed to be broken and fallen to the ground. Since a ground path

is involved in this situation, the fault resistance (RF) plays a key role in the measurement of

apparent impedance. Hence, different values of RF (25, 50, 100 and 150 ) have been

considered in the fault analysis. The ground units of the conventional digital distance relay

located at G, having facility of series compensation, measures incorrect value of impedance

of the faulted portion of the transmission line.

Further, during a simultaneous open conductor and ground fault, the other end of the

conductor (Bus R side) has been assumed to be hanged on the tower without touching to the

ground. The conventional phase and ground distance relays located at Bus R completely fail

to detect this open conductor fault. To solve this problem of conventional digital distance

relays, a new scheme has been proposed in this thesis. A detailed analysis of the conventional

digital distance relaying scheme having a facility of series compensation and the proposed

scheme are given in the following subsections.

5.7.1 Impedance Measured by the Conventional Scheme

As shown in Figure 5.11, during a simultaneous open conductor and ground fault, the

ground unit of the conventional digital distance relay at G sees this fault as a single-line-to-

ground fault and measures apparent impedance (Zapp) as follows:

000 yMxax

SCaxapp IKIKI

VEZ

(5.8)

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where,

VSC = voltage drop across series-capacitor bank

1

100

L

LL

ZZZK

and 1

0

L

LMM Z

ZK

On the other hand, Bus R side conventional (phase and ground) digital distance relays

completely fail to detect this type of fault.

5.7.2 Impedance Measured by the Proposed Scheme

During a simultaneous open conductor and ground fault, the open conductor fault can

be sensed by checking the following two conditions:

1) The positive-sequence current is divided between the negative-sequence and zero-

sequence currents, i.e. 021 III [70].

2) The phase current of the opened phase is zero.

Hence, in this chapter, the open conductor fault is not discussed further.

The main objective of this analysis is to measure the correct value of impedance of the

grounded section of the transmission line. In this situation, the magnitude of fault current

passing through the SC/MOV parallel combination located at G and connected in phase A

depends on the value of fault resistance. Based on that value of fault current, an equivalent

impedance of SC/MOV located at G and connected in phase A is given by,

'' GGGA jXRZ for 98.0pui (5.9)

GGA jXZ for 98.0pui (5.10)

Furthermore, during the same situation, the magnitude of fault current passing through

other healthy phases on line x (phases B and C) is always less than the SC/MOV reference

current setting (ipu < 0.98). Hence, the impedances of SC/MOV connected in phases B and C

of line x are given by,

GGCGB jXZZ (5.11)

The positive-, negative- and zero-sequence components of impedances of SC/MOV

(ZG120) located at G are determined by substituting the values of ZGA, ZGB and ZGC in equation

(5.7). Hence, the sequence (positive, negative and zero) components of voltages of SC/MOV

(VG120) located at G are determined by,

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120120120 GGG IZV (5.12)

Using equations (5.9)-(5.12), the voltage VGA appeared across SC/MOV located at G

and connected in phase A is given by,

axGGGGGA IjXVVVV 021 for 98.0pui (5.13)

axGGGGGGA IjXRVVVV ''021 for 98.0pui (5.14)

Referring to Figure 5.11, during a simultaneous open conductor and ground fault,

symmetrical components of voltages (Ex1, Ex2 and Ex0) at relaying point G on line x are

expressed by,

11111 xFxLGx IRIpZVE (5.15)

22122 xFxLGx IRIpZVE (5.16)

0000000 yLMxFxLGx IpZIRIpZVE (5.17)

Now, voltage Eax at the relaying point G on line x can be determined by adding

equations (5.15)-(5.17) as follows:

axFyLMxLLaxLGAax IRIpZIZZpIpZVE 000101 (5.18)

Therefore, the actual value of impedance (Zact) that should be measured by the

proposed scheme is given by,

axFGAaxK

PLact IRVEI

ZpZZ 1

1 (5.19)

where,

000 yMxaxK IKIKII

A simultaneous open conductor and ground fault is reflected as a single-line-to-ground

fault at G. The apparent impedance (Zapp) measured by the conventional ground distance

relay at G is shown in Figure 5.6 [25]. Hence, the actual impedance (Zact) that should be

measured by the proposed scheme is given by,

FSCappPact ZZZZZ (5.20)

Comparing equations (5.19) and (5.20), impedances Zapp, ZSC and ZF can be defined as,

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K

axapp I

EZ , K

GASC I

VZ and K

axFF I

IRZ (5.21)

Now, in order to obtain Zact, impedance ZSC (determined in equation (5.21)) is

subtracted from Zapp. Afterwards, vector ZF is extended up to point A on the reactance axis

(Figure 5.6). Now, OA is determined by,

tan BCOBOA (5.22)

where, the argument α is the angle between Iax and IK

Hence, Zact is determined at the intersection point of two straight lines C-A and O-Z.

Here, O-Z represents the impedance vector of line x. Now, assuming R and X as resistance

(Ω/km) and reactance (Ω/km) of line x, impedance of the faulted portion of line x is given by

[220],

1

BCOAOB

RX

OApRL (5.23)

BCOAOB

RX

OApX L RX 1 (5.24)

5.8 RESULTS AND DISCUSSIONS

In this section, a simultaneous open conductor and ground fault on a 400 kV, 300 km

long series compensated parallel transmission line has been simulated considering wide

variations in fault location (0% to 80% in steps of 10%), different degrees of series

compensation (30%, 50% and 70%), different values of zero-sequence mutual coupling

impedance (50%, 60% and 70% of zero-sequence self impedance of the line), different values

of power transfer angle (+15º, 0º and 15º) and different values of fault resistance (25, 50,

100 and 150 Ω). The system and line parameters are given in Appendix D. Throughout the

entire discussion, Zapp and ZP represent impedances measured by the conventional ground

distance relay and the proposed scheme, respectively. Rapp and Xapp represent the resistive part

and reactive part of fault impedance measured by the conventional scheme, respectively. RP

and XP represent the resistive part and reactive part of fault impedance measured by the

proposed scheme, respectively. Ract and Xact represent actual values of the resistive part and

reactive part of fault impedance of line x, respectively. δ and RF represent the power transfer

angle between two buses (S and R) and fault resistance present in the faulted path,

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respectively. KC represents the degree of series compensation (in percent) provided to each

line. It is defined as the ratio of capacitive reactance of series capacitor (XC) connected to the

line to the inductive reactance (X) of the complete section of the line. εRapp and εXapp indicate

the percentage error in the measurement of resistive part and reactive part of the fault

impedance given by the conventional scheme, respectively. εRP and εXP indicate the

percentage error in the measurement of resistive part and reactive part of the fault impedance

given by the proposed scheme, respectively. These errors are defined as follows:

% 100

act

actappRapp R

RR , % 100

act

actappXapp X

XX (5.25)

% 100

act

actPRP R

RR , % 100

act

actPXP X

XX (5.26)

The simulation results are discussed in the next subsections.

5.8.1 Change in Fault Location and Power Transfer Angle

Table 5.1 represents the performance of the proposed scheme in terms of error in the

measurement of resistance and reactance of the faulted portion of line x for a simultaneous

open conductor and ground fault at different fault locations (0% to 80% in steps of 10%)

having different power transfer angles (+15º, –15º), with KC = 70%, KM = 70% and

RF = 50 Ω. It is to be noted from Table 5.1 that for δ = +15º, the percentage error (for most of

the cases) in the measurement of resistance and reactance of the faulted portion of line x by

the proposed scheme decreases as the fault location moves away from the relaying point.

Subsequently, for δ = –15º, the percentage error is positive for local end faults, whereas it

becomes negative and increases for remote end faults. Still, the maximum percentage error is

within 4.19%.

Figure 5.14 shows the simulation results given by the conventional ground distance

relay and the proposed scheme for a simultaneous open conductor and ground fault at

different fault locations (0% to 80% in steps of 10%), different power transfer angles (–15º,

0º, +15º), with KC = 70%, KM = 70% and RF = 50 Ω. It is to be noted from Figure 5.14 that

irrespective of the direction of power flow, the conventional ground distance relay located at

G completely fails to detect the faults occurring after 30% of the line length from bus S. On

the other hand, the proposed scheme provides very accurate results for all fault locations

having different power transfer angles. The fault impedance given by the proposed scheme

exactly coincides with the actual impedance of the faulted portion of line x.

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Table 5.1 Effect of change in p and δ on resistance and reactance measurement

p (%)

Ract (Ω)

Xact (Ω)

δ = +15º δ = 15º RP (Ω)

εRP (%)

XP (Ω)

εXP (%)

RP (Ω)

εRP (%)

XP (Ω)

εXP (%)

0 0 0 0.1 1.06 0.11 1.18 10 0.994 10.27 1.04 4.16 10.7 4.19 1.02 2.65 10.51 2.34 20 1.987 20.54 2.05 3.15 21.16 3.02 1.99 0.13 20.52 0.10 30 2.981 30.81 3.03 1.64 31.33 1.69 2.93 1.71 30.26 1.79 40 3.975 41.08 4.02 1.14 41.5 1.02 3.87 2.64 40.05 2.51 50 4.969 51.35 5.01 0.84 51.76 0.80 4.83 2.79 49.93 2.77 60 5.962 61.62 6.02 0.97 62.19 0.93 5.8 2.72 59.95 2.71 70 6.956 71.89 7.04 1.21 72.73 1.17 6.75 2.96 69.73 3.00 80 7.950 82.16 7.99 0.51 82.53 0.45 7.67 3.52 79.31 3.47

Figure 5.14 Fault impedance measurement with varying p and δ

5.8.2 Variation in Zero-Sequence Mutual Coupling Impedance

Tables 5.2 and 5.3 show the performance of the proposed scheme in terms of error in

the measurement of resistance and reactance of the faulted portion of line x for a

simultaneous open conductor and ground fault at different fault locations (0% to 80% in steps

of 10%) having different percentage of zero-sequence mutual coupling impedance (50%,

60% and 70%) with δ = +15º, KC = 70% and RF = 25 Ω. It has been observed from Tables 5.2

and 5.3 that the maximum percentage error in the measurement of resistance and reactance of

the faulted portion of line x given by the proposed scheme remains within 2.65%.

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Table 5.2 Effect of change in KM on resistance measurement

p (%)

Ract (Ω)

KM = 50% KM = 60% KM = 70% RP (Ω) εRP (%) RP (Ω) εRP (%) RP (Ω) εRP (%)

0 0 0.05 0.05 0.05 10 0.994 1.02 2.65 1.02 2.65 1.01 1.64 20 1.987 2.02 1.64 2.02 1.64 2 0.63 30 2.981 3.03 1.64 3.02 1.30 3 0.63 40 3.975 4.02 1.14 4.02 1.14 3.99 0.38 50 4.969 5.01 0.84 5.01 0.84 4.98 0.23 60 5.962 6.02 0.97 6.02 0.97 5.98 0.30 70 6.956 7.05 1.35 7.04 1.21 6.99 0.49 80 7.950 8.1 1.89 8.09 1.77 8.03 1.01

Table 5.3 Effect of change in KM on reactance measurement

p (%)

Xact (Ω)

KM = 50% KM = 60% KM = 70% XP (Ω) εXP (%) XP (Ω) εXP (%) XP (Ω) εXP (%)

0 0 0.52 0.52 0.52 10 10.27 10.52 2.43 10.51 2.34 10.45 1.75 20 20.54 20.87 1.61 20.84 1.46 20.65 0.54 30 30.81 31.27 1.49 31.25 1.43 31 0.62 40 41.08 41.52 1.07 41.51 1.05 41.2 0.29 50 51.35 51.79 0.86 51.79 0.86 51.43 0.16 60 61.62 62.21 0.96 62.18 0.91 61.76 0.23 70 71.89 72.82 1.29 72.77 1.22 72.26 0.51 80 82.16 83.7 1.87 83.59 1.74 82.98 1.00

Figure 5.15 shows the simulation results provided by the conventional ground distance

relay and the proposed scheme for a simultaneous open conductor & ground fault at different

fault locations (0% to 80% in steps of 10%) having a different percentage of zero-sequence

mutual coupling impedance (50%, 60% and 70%) with δ = +15º, KC = 70% and RF = 25 Ω.

Figure 5.15 Fault impedance measurement with varying p and KM

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It is to be noted from Figure 5.15 that the loci of fault impedance provided by the

conventional ground distance relay located at G are far away from the actual impedance

locus. On the other hand, the loci of fault impedance of the proposed scheme get

superimposed on the actual impedance locus.

5.8.3 Change in Degree of Compensation

Tables 5.4 and 5.5 show the simulation results in terms of percentage error in the

measurement of resistance and reactance of the faulted portion of line x given by the

proposed scheme, respectively, for a simultaneous open conductor & ground fault at different

fault locations (0% to 80% in steps of 10%) having different degrees of series compensation

(30%, 50% and 70%) with δ = +15º, KM = 70% and RF = 50 Ω.

Table 5.4 Effect of change in KC on resistance measurement

p (%)

Ract (Ω)

KC = 30% KC = 50% KC = 70% RP (Ω) εRP (%) RP (Ω) εRP (%) RP (Ω) εRP (%)

0 0 0.06 0.08 0.1 10 0.994 1.03 3.65 1.035 4.16 1.035 4.16 20 1.987 2.01 1.14 2.03 2.14 2.05 3.15 30 2.981 2.99 0.30 3.01 0.97 3.03 1.64 40 3.975 3.97 0.12 3.99 0.38 4.02 1.14 50 4.969 4.97 0.03 4.98 0.23 5.01 0.84 60 5.962 5.92 0.71 5.99 0.47 6.02 0.97 70 6.956 6.91 0.66 6.93 0.37 7.04 1.21 80 7.950 7.92 0.37 7.92 0.37 7.99 0.51

Table 5.5 Effect of change in KC on reactance measurement

p (%)

Xact (Ω)

KC = 30% KC = 50% KC = 70% XP (Ω) εXP (%) XP (Ω) εXP (%) XP (Ω) εXP (%)

0 0 0.58 0.82 1.06 10 10.27 10.67 3.89 10.7 4.19 10.7 4.19 20 20.54 20.77 1.12 20.96 2.04 21.16 3.02 30 30.81 30.88 0.23 31.08 0.88 31.33 1.69 40 41.08 41.04 0.10 41.23 0.37 41.5 1.02 50 51.35 51.32 0.06 51.5 0.29 51.76 0.80 60 61.62 61.2 0.68 61.9 0.45 62.19 0.93 70 71.89 71.4 0.68 71.64 0.35 72.73 1.17 80 82.16 81.83 0.40 81.82 0.41 82.53 0.45

It is to be noted from Tables 5.4 and 5.5 that for low degrees of series compensation

(KC = 30% and 50%), the percentage error given by the proposed scheme is initially positive

and decreases as the fault location moves away from the relaying point up to a certain portion

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of line length (say p = 30% for KC = 30% and p = 60% for KC = 50%). Afterward, it becomes

negative for remote end faults. Further, for a high degree of series compensation (KC = 70%),

as the fault location moves away from the relaying point, the percentage error in the

measurement of resistance and reactance of the faulted portion of line x by the proposed

scheme decreases. However, the percentage error for all the cases stays within 4.19%.

Figure 5.16 shows simulation results given by the conventional ground distance relay

and the proposed scheme for a simultaneous open conductor & ground fault at different fault

locations (0% to 80% in steps of 10%) having different degrees of series compensation (30%,

50% and 70%) with δ = 15º, KM = 70% and RF = 50 Ω. It has been observed from Figure 5.16

that as the degree of compensation increases, the locus of fault impedance provided by the

conventional ground distance relay located at G moves away from the first zone boundary.

Further, for faults after 20% of line length, the loci of fault impedance move outside the first

zone boundary. Conversely, the proposed scheme always measures the correct value of

impedance for all fault locations and for different degrees of series compensation.

Figure 5.16 Fault impedance measurement with varying p and KC

5.8.4 Change in Fault Resistance

Figure 5.17 shows simulation results provided by the conventional ground distance

relay and the proposed scheme for a simultaneous open conductor and ground fault at

different fault locations (0% to 80% in steps of 10%) having different values fault resistance

(25, 50, 100 and 150 Ω) with δ = +15º, KM = 50% and KC = 70%.

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Figure 5.17 Fault impedance measurement with varying p and RF

It has been observed from Figure 5.17 that for low value of RF (up to 25 Ω), even

though the locus of fault impedance provided by the conventional ground distance relay lies

within the first zone boundary, it is far away from the actual impedance locus. In addition, the

same relay partially or completely loses its first zone coverage for a simultaneous open

conductor and ground fault with other higher values of RF. On the other hand, the proposed

scheme measures the correct value of impedance of the faulted portion of line x for all fault

locations having different values of fault resistance.

Table 5.6 and Figure 5.18 show the simulation results in terms of reactances XP and

Xapp measured by the proposed scheme and the conventional scheme, respectively, for a

simultaneous open conductor and ground fault on line x at different fault locations (0% to

80% in steps of 10%) having different values of fault resistance (100 Ω and 150 Ω) with

δ = +15º, KM = 50% and KC = 70%.

It is to be noted from Table 5.6 and Figure 5.18 that, as the value of fault resistance

increases, the percentage error in the measurement of reactance of the faulted portion of line x

given by the conventional scheme also increases. It has been observed from Table 5.6 that the

value of percentage error is –5.71% for RF = 100 Ω, whereas it increases up to –14.03% for

RF = 150 Ω. Conversely, the maximum percentage error in the measurement of reactance of

the faulted portion of line x given by the proposed scheme remains within 3.23% even in

case of higher values of fault resistances (RF = 100 Ω and 150 Ω).

100

Table 5.6 Effect of change in RF on reactance measurement

p (%)

Xact (Ω)

RF = 100 Ω RF = 150 Ω Xapp (Ω) εXapp (%) XP (Ω) εXP (%) Xapp (Ω) εXapp (%) XP (Ω) εXP (%)

0 0 0.16 0.05 0.12 0 10 10.27 9.74 5.16 10.14 -1.27 9.45 7.98 10.41 1.36 20 20.54 19.53 4.92 20.56 0.10 18.9 7.98 20.99 2.19 30 30.81 29.29 4.93 31 0.62 28.2 8.47 31.46 2.11 40 41.08 39.05 4.94 41.47 0.95 37.32 9.15 41.78 1.70 50 51.35 48.77 5.02 51.94 1.15 46.21 10.01 51.89 1.05 60 61.62 58.23 5.50 62.37 1.22 54.8 11.07 61.67 0.08 70 71.89 68.01 5.40 72.73 1.17 62.98 12.39 70.95 -1.31 80 82.16 77.47 5.71 82.94 0.95 70.63 14.03 79.51 -3.23

Figure 5.18 Error in reactance measurement with varying p and RF

5.8.5 Close-in and Remote End Faults

It is to be noted from Figures 5.14-5.17 that the conventional ground distance relay

located at G sees a simultaneous open conductor and ground fault occurring just after the

relaying point with a very high percentage of error. Furthermore, for most of the cases, the

conventional ground distance relay sees the remote end fault outside the first zone boundary.

On the other hand, the proposed scheme always measures the correct value of impedance of

the faulted portion of line x during close-in and remote end faults.

5.8.6 SC/MOV and Proposed Scheme Performance during Fault

The performance of SC/MOV and the proposed scheme are shown in Figure 5.19

considering a simultaneous open conductor and ground fault at 80% of the line length, having

δ = +15º, KM = 70% and KC = 70%. Further, the fault is assumed to occur at 0.02 sec.

101

Figure 5.19(a) shows equivalent resistance (RC) and equivalent reactance (XC) of the

SC/MOV determined by Goldsworthy’s equations before (0.005 to 0.02 sec) and after (0.02

to 0.04 sec) the instant of fault. Furthermore, Figure 5.19(b) shows the fault impedance locus

given by the proposed scheme on R-X plane considering the same situation.

(a) SC/MOV impedance locus (b) Line fault impedance locus

Figure 5.19 SC/MOV and proposed scheme performance before and after fault

It is to be noted from Figure 5.19(a) that during pre-fault condition; only SC will

conduct the current, whereas MOV will not conduct the current. In this situation, the

magnitude of XC is the maximum, whereas the magnitude of RC is zero. Therefore, as shown

in Figure 5.19(b), the impedance locus given by the proposed scheme will settle down very

far from the first zone boundary of a digital distance relay. Conversely, after the occurrence

of a fault, SC and MOV both will conduct the fault current. Therefore, the magnitude of RC

increases whereas the magnitude of XC decreases. Hence, the locus of fault impedance begins

to move towards the first zone boundary and settles down within the first zone boundary.

5.9 ADVANTAGES OF THE PROPOSED SCHEME

1) The proposed scheme is not affected by a change in degree of series compensation

of the parallel transmission lines.

2) The reach of the proposed scheme is not influenced by the zero-sequence mutual

coupling impedance present between two lines.

3) The proposed scheme avoids the problem of incorrect operation of ground units of

the conventional digital distance relay having a facility of series compensation

during open conductor and ground fault and measures the correct value of fault

impedance.

102

4) The proposed scheme is not affected by the variations in the system loading

conditions and measures the correct value of fault impedance for different values of

the power transfer angles.

5) The proposed scheme is said to be accurate and robust against wide variations in

system and fault parameters, since the value of percentage error is found to be

within 4.19%.

5.10 CONCLUSION

A new digital distance relaying scheme presented in this chapter provides adequate

protection to series compensated parallel transmission lines during a simultaneous open

conductor and ground fault. The proposed scheme is based on derivation of the compensated

values of impedance using the symmetrical components theory. It measures the correct value

of fault impedance for different fault locations, different values of fault resistance, various

zero-sequence mutual coupling impedance, different degrees of series compensation and

various system loading conditions. Further, it does not require remote end data. A

comparative evaluation of the proposed scheme and the conventional scheme indicates that

the proposed scheme is highly accurate and robust against wide variations in system and fault

parameters as its percentage error is within 4.19%.