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Citation: Ghassemi, F. (1989). Adaptive digital distance protection for series compensated transmission lines. (Unpublished Doctoral thesis, City University London)
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0
ADAPTIVE DIGITAL DISTANCE PROTECTION FOR SERIES
COMPENSATED TRANSMISSION LINES
By
FOROOZAN GHASSEMI
Thesis Submitted To The City University
For The Degree Of Doctor of Philosophy
SEPTEMBER 1989
Power System Protection Laboratory Department Of Electrical, Electronic
And Information Engineering
City University Northampton Square
London EC1V OHB
I dedicate this thegig to my wife whose patience, encouragement and support
inspires me in every aspect of my life.
Co my daughter and on with love.
flo to the memory of our daughter Maryam,
toto came and passed away during the course of
this study.
). - +
LIST OF CONTENTS
page SYNOPSIS ACKNOWLEDGEMENTS ii
COPYRIGHT DECLARATION iii
LIST OF PRINCIPAL SYMBOLS iv
CHAPTER 1- INTRODUCTION AND LITERATURE SURVEY 1 1.1-Literature Survey 1 1.2-Summary Of The Thesis 16
CHAPTER 2-DIGITAL DISTANCE RELAY TECHNIQUES 20
CHAPTER 3-TIME SPACED SOLUTION DISTANCE PROTECTION
ALGORITHM 25
3.1-The Distance Protection Scheme Algorithm 25 3.2-Steady State Single Frequency Analysis 26 3.3-Application Of The Algorithm To Series
Capacitor Compensated Lines 27 3.4-Effect Of Sub-Synchronous Frequencies 29 3.5-Discrete Processing Solution 32 3.6-Computation Of Current Derivative 35
CHAPTER 4-DIGITAL DISTANCE RELAY 37 4.1-Primary System Interface 38
4.1.1-capacitor voltage transformer, C. V. T 38 4.1.2-current transformer, C. T 40
4.2-The Digital Distance Relay Struture 41 4.3-Digital Distance Relay Filtering Process 47
4.3.1-digital pre-filter 49 4.3.2-the Recursive Averager 54
4.4-Relay Characteristic And Decision Logic 58 4. Ä. 1-production of quadrilateral characteristic 58 4.4.2-directional reactance, XM 60 4.4.3-relay characteristic 62 4.4.4-decision logic 62 4.4.5-invoking the Recursive Averager 65
CHAPTER 5-EARTH FAULT COMPENSATION OF THE DIGITAL
DISTANCE RELAY 68
5.1-System With 70% Compensation And The C. V. T ON The Bus-Bar Side Of The Relay 71
5.1.1-residual current compensation 71 5.1.2-complex residual compensation factor 73 5.1.3-sound phase current compensation 74
5.1.4-compensation of errors due to the residual current compensation factor 75
5.1.5-modified residual compensation factor 76 5.1.6-modification of the relaying signal 80 5.1.7-comments on the compensation methods
explained in section 5.1.5 and 5.1.6 82 5.2-System With 70% Compensation And The C. V. T On
The Line Side Of The Relay 83 5.3-System With 50% Compensation At The Mid-Point
Of The Line 84
CHAPTER 6-RELAY RESPONSE FOR A LINE WITH 70%
COMPENSATION 90
6.1-Line With 70% Compensation And C. V. T On The
Source Side Of The Capacitor 91 6.1.1-relay trip characteristic 91
6.1.2-relay decision logic 92 6.1.3-the relay trip response 92
6.2-Line With 70% Compensation And C. V. T On The
Line Side Of The Capacitor 95 6.2.1-relay characteristic for line side C. V. T 95
CHAPTER 7-RELAY RESPONSE FOR A LINE WITH THE SERIES CAPACITOR AT THE MID-POINT OF THE LINE 97
CHAPTER 8-CONCLUSIONS AND FUTURE WORK 101
8.1-General Conclusions 101 8.2-Future Work 106
REFERENCES'' 110
APPENDICES 116
Appendix 3A 116
Appendix 3B 119
Appendix 3C 128
Appendix 4A 130
Appendix 5A
Appendix 5B
Appendix 5C
Appendix 5D
Appendix 5E
132
134
135
136
137
Published Papers
SYNOPSIS
Series capacitors offer considerable technical and economical advantages in long distance a. c. transmission. In particular, their excellent reliability and minimal maintenance requirements make series compensation the most cost effective method of enhancing the power transfer capability of an existing or proposed interconnection.
E. H. V. lines employing series capacitors however, pose difficult problems for the line protection relays, not encountered with plain feeders. One important cause of these problems is the resonance between the series capacitor and the line series inductance, which in turn imposes a sub-synchronous oscillation on the system signals. Also, the rapid changes in the circuit parameters, resulting from the operation of the capacitor protection equipment, namely the spark gaps, introduce some difficulties for the line protection schemes, especially an impedance measuring relay. These spark gaps are installed in parallel with the series capacitors to prevent the development of very high voltages across the capacitor which could cause excessive damage to the equip- ment.
The work presented herein describes a new digital distance relay suitable for series compensated line appli- cations.
The errors in the impedance measurement for a phase to earth fault when the spark gaps do not flash over, are discussed and new methods are proposed to compensate for these errors. The new concept of a complex residual compensation factor, as opposed to a real one, is also discussed.
A new adaptive filtering is incorporated in the relay in order to minimise the detrimental effect of the sub- synchronous oscillation on the relay decision logic.
Finally, the relay is thoroughly tested for many different system configurations, to fully evaluate the relay response.
i
ACKNOWLEDGEMENTS
The author wishes to express his sincere thanks to
professor A. T. Johns, D. Sc., Ph. D. B. Sc., C. Eng., FIEE,
SMIEEE, FRSA, for his guidance, invaluable advice and
encouragement throughout the course of study.
He would like to thank everyone at the power systems
research laboratory for their support and friendship,
especially Mr S. H. Lewis and Mr M. Gasparo for their
extremely helpful contributions to the preparation of the
thesis, and Dr P. J. Moore for friendly discussions
throughout the time he spent working on the project.
He is grateful to City University, London, and GEC
Measurement, Stafford, for providing the funding for the
project and would like to thank the engineers at GECM,
especially Mr E. P. Walker, Dr P. A. Crossley, Mr J. Weller
and R. Warren for very useful technical discussions.
Finally, he wishes to thank the staff of the school of
Electrical and Electronic Engineering, City University,
particularly Mrs L. Wilkinson, who have been extremely
helpful and encouraging during the studies.
ii
COPYRIGHT DECLARATION
I grant powers of discretion to the University Librarian
to allow this thesis (ADAPTIVE DIGITAL DISTANCE PROTECTION
FOR SERIES COMPENSATED TRANSMISSION LINES) to be copied in
whole or in part without further reference to me. This
covers only single copies made for study purposes, subject
to normal conditions of acknowledgement.
iii
LIST OF PRINCIPAL SYMBOLS
E. H. V extra high voltage.
Vg, VR line voltage at sending and receiving end of
a line respectively.
6 load angle (phase angle between the sending
and receiving end voltages).
P power transferred along a line.
v(t), i(t) time domain voltage and current.
v(k), i(k) discrete time voltage and current.
fs sampling frequency.
Ts sampling interval 1/fs.
h(t) impulse response.
Tw data window.
v(t), i(t) voltage and current derivatives.
0 phase angle between voltage and current.
0 angle between two points on voltage and
current signals.
WO fundamental angular frequency
wsu sub-synchronous frequency component.
Vsu, Isu magnitude of voltage and current of sub-
synchronous component.
ß phase angle between the fundamental and sub-
synchronous components.
C. V. T capacitor voltage transformer.
C. T current transformer.
V. T voltage transformer.
AT sampling time step.
t dummy time variable.
A/D analogue to digital converter.
iv
U. H. S ultra high speed.
S damping coefficient.
wn natural frequency.
TL relay trip level.
TC relay trip counter.
CRL1 relay control counter initiated by fault
detection.
CRL2 relay control counter initiated by first up-
count.
AVLL, AVLU lower and upper limit on reactance axis to
control the Recursive Averager.
R transmission line resistance.
L transmission line inductance.
C capacitance of the series capacitor.
L' equivalent inductance of transmission line.
ZLSr ZLM self and mutual impedance of transmission
line.
YLS, YLM self and mutual admittance of transmission
line.
pps positive phase sequence.
zps zero phase sequence.
ZL1, ZLO positive and zero phase sequence impedance of
transmission line.
YL1, YLO positive and zero phase sequence admittance
of transmission line.
RL1t RLO positive and zero phase sequence resistance
of transmission line.
XL1, XLO positive and zero phase sequence reactance of
transmission line.
a proportional fault position.
V
Z measured impedance by the relay.
Vsae phase "a" to earth voltage.
Isa phase "a" current.
Ires residual current.
Kc conventional residual current compensation
factor, CRCF.
Ks conventional sound phase current compensation
factor.
K(a) modified residual compensation factor.
K(ar) new residual current compensation factor,
NRCF.
ar fault position for a fault at the relay
zone-1 reach point.
vi
CHAPTER 1
INTRODUCTION AND LITERATURE SURVEY
1.1-Literature Survey
A transmission system comprising of short lines is
fairly stiff at the generator ends (bus-bars) because
there are a number of infeeding lines from other sources
connected to the bus-bar. As the line is short, both the
line reactance and line capacitance are relatively small,
and in fact the latter can be neglected. This means that
a generator can operate at a reasonably low load angle in
order to transmit an appreciable amount of power over the
line, so that the problem of generator instability due to
disturbances is reduced. Because of the stiffness of bus-
bars and the interconnection of the system even when a
line does go out due to a fault, the majority of faults
being transitory in nature anyway, a 3-phase autoreclosure
scheme is successfully employed without loss of stability
or any serious disruption. Moreover, the presence of a
second circuit helps to maintain stability during the
autoreclosure sequences of the faulted circuit.
On long lines, however, where the source of generation
is often remote from the load points, especially in
countries which employ hydro-power schemes, the system at
the generator end is relatively weak.
In such cases, the problem of maintaining stability of
the system becomes much greater. Double circuit lines are
often uneconomical to use because of the very long
distances involved.
Because the line is long, both the line inductance and
1
capacitance are large. The increase in line inductance
has the following main effects:
i-The power transfer capability of the line is reduced.
ii-Both the transient and steady-state stability margins
of the system for a given power transfer are lowered.
iii-The voltage drop along the line becomes excessive.
The power transfer capability, P, of a transmission
line is approximately given by Equation 1.1:
VS'VR P= sin ö 1.1
X
VS and VR are the sending and receiving end voltages
respectively and X is the inductive reactance of the
transmission circuit between the terminals, and 6 is the
phase angle between VS and VR. The power transfer
capability can be increased by either increasing Vg, VR or
6, or decreasing X. The maximum value by which VS and VR
can be increased to are normally fixed by the steady-state
and transient insulation limitations of the transmission
system itself. This includes the line and terminal
equipment. The value of X is determined by the
transmission line and terminal equipment (transformers,
generators, etc. ) reactances, the minimum value of which
is limited by the physical size of equipment and economic
consideration.
The inclusion of series capacitors in a. c.
transmission systems, particularly where long line
sections are involved, is an effective and economic means
of improving the power transfer capability and stability
of a system. Over the years, a series capacitor employed
2
in H. V. networks has evolved into a reliable element in
transmission systems, achieving an excellent performance
and reliability standard [1,2].
By electrically reducing the effective transmission
line lengths brought about by the cancellation of part of
the inductive reactance, series compensation offers the
following major technical advantages over uncompensated
system:
i-The steady-state power transfer capability of the
network becomes proportional to the degree of series
compensation. That is to say that for the maximum
level of series compensation encounterd in practice,
(typically 70%) the gain in power transfer capability
is around 233%. This implies that the same level of
power transfer can be achieved for a reduced load
angle between the generation voltages at the line
ends, thereby offering some improvement in terms of
systems stability [3].
ii-The voltage profile along the line is more evenly
distributed under normal load conditions. This leads
to a reduction in the reactive volt-drops along the
line, which for radially configured systems,
dramatically improves the voltage regulation and hence
the magnitude of the line voltages at the receiving or
load ends.
iii-Greater flexibility is introduced into the system.
Power losses depend upon the line cross sectional
areas and current distribution, and adjustment in the
level of series compensation helps to improve the X/R
ratio of the line such that transmission losses are
3
then minimised.
iv-The possibility of attaining more favourable load
distributions between different lines functioning in
parallel.
v-The series capacitor is the only static device with
true automatic regulation of the voltage and power.
vi-Extremely small losses and good reliability.
vii-providing a cheaper substitute (5,6] as an
alternative to construction of new lines.
In short, series capacitor compensation improves the
steady-state transmission characteristic of a power
network and reduces transmission losses and costs.
Since the cost of any power capacitor is roughly
proportional to the square of the voltage that it must
withstand, the series capacitor becomes extremely
expensive and uneconomical if it is required to tolerate
the large voltage which is developed across them during
system disturbances. In general when a capacitor is
subjected to any disturbances, abnormal changes take place
in the dielectric which result in breakdown or at least
produce fatique phenomena which causes ageing and shorten
its life.
To protect the capacitor bank in the presence of
severe over-voltages which may be developed across the
capacitors, particularly under fault conditions, three
main type of independent schemes are commonly applied
worldwide. These schemes can be classified as:
i-Single Gap Scheme (SGS).
ii-Dual Gap Scheme (DGS).
iii-Dual Gap with Non-linear resistor Scheme (DGNS).
4
These protection schemes remove or partially remove
the capacitor from the line, by diverting the line (or
some of the line) current from flowing through the
capacitor. This is carried out by connecting some form of
by-passes known as spark-gaps in parallel with the
capacitor unit. The gaps are set to breakdown and hence
to conduct when the voltage across the capacitor exceeds a
pre-set threshold, typically 2 to 3 times the nominal or
steady-state value which is developed across the capacitor
when maximum permitted load current flows through the
line.
Capacitor protection schemes are often provided with a
circuit breaker in parallel with the spark-gap and the
capacitor (5], to deionize the gap after flashing-over and
reinsert the capacitor back to the network immediately
after the capacitor voltage has reduced below the critical
value in order to improve the transient stability of the
system as a whole.
In the past decade, great technological advantages
have been made in the development of capacitor protection
equipments [6,7,8]. It seems likely that the DGNS will
become commonplace in future applications since many
publications highlight their stability boosting effect,
both from a by-passing and reinsertion standpoint [6,7].
In this scheme the capacitor is shunted in such a way
as to only partially remove the compensating reactance,
whilst retaining full protection against over-voltages.
This is achieved by inserting a non-linear resistor in
series with the dual gap branch to form the dual gap with
non-linear resistor scheme, DSNS. The impedance in the
5
shunt path varies with the voltage developed across the
capacitor/resistor combination, producing a self-
regulative action, holding the capacitor voltage to an
acceptable level, while merely reducing the compensation
as opposed to losing it altogether with the other schemes.
When a series capacitor is (partially) by-passed as a
result of operation of its spark-gaps, rapid changes occur
in the effective system impedances. Furthermore, it is
impossible to predict both the exact number and the
precise instant in time at which the various capacitor
gaps flash-over; the reason being the fact that under
fault conditions there are a vast number of variations
which affect the magnitude of over-voltages. These
include fault loop resistance, pre-fault loading, source
phase sequence ratios as well as capacities, point on wave
at which fault occurs, type of fault, etc [9].
The fundamental question of the location of the
capacitor in the system is another main problem which must be dealt with. Series capacitor can be placed either at
the line ends or at intermediate substation along the
line.
If the series capacitor is placed at the line ends
where there already exists a switching substation, the
need for extra station to install the capacitors is
obviated. Hence, the maintenance and operating cost is
reduced. However, it has the disadvantage of increasing
the short circuit level at the substation which implies
that more expensive intrupting equipments must be employed.
On the other hand, the advantages attributed to the
location along the line are easier protection [10].
6
However, location along the line means higher installation
and operating costs because special intermediate capacitor
stations have to be built at a distance from the switching
stations.
Differences of view of where the capacitors should be
located, either mid-point or at the lines ends, have
existed for many years.
In practice, the amount of compensation and the
location depends on various factors, including economy,
ease of protection, power transfer capability, etc [10].
The mid-point installation for about 50% (or less)
compensation tends to be Scandinavian practice, while the
USA manufacturers and utilities prefer to place the
capacitors in the vicinity of the line ends for a 70%
compensation (usually split up into two halves) [11].
The other factor which needs consideration is the
position of the voltage and current transducers which
supply the line protection gear. When the capacitors are
located at the line ends the user has a choice of taking
the voltage supply for the relay from either the bus side
or the line side of the capacitor bank (12].
The technique favoured in the USA has been to position
the current transformers on the bus side, and the voltage
transformers on the line side of the capacitor. With this
arrangement, the local capacitor effectively forms part of
the source impedance. Thus, the impedance seen by a
impedance measuring relay, i. e. distance relay, involve
only the inductive line impedance and therefore no
distortion due to the capacitor [13]. This is a notable
advantage of employing line-side voltage measurements.
7
However, maintaining the directionality of distance relays
becomes a major problem, and distance relays, depending on
methods of polarization being employed, become prone, to
different degrees, to reverse faults.
On the other hand, when voltage measuring equipment
(V. T. s) are installed on the source side of the capacitor,
the capacitor become part of the transmission line and may
be included in the protected zone of distance relays.
Also maintaining the directionality of the protective
equipments may not be as great as situations where the
V. T. s are connected to line side.
In general not all series compensated lines are
identical. The major variable for protection are the
degree of compensation, the capacitor position and whether
it is split into two parts, the type of over-voltage
protection and its operating level, and the location of
the relay measuring transformers.
Because of all these uncertainties and unsimilarities
among series compensated lines, these lines pose difficult
protection problems for line relays. Any mode of
independent tripping, without the use of communication
channels, linking the protection at the two end, is often
unsatisfactory. For example, distance relays can,
depending on their settings, either over-reach or under-
reach as a direct consequence of the operation of the
series capacitor protection equipments [14].
A method which is commonly used in practice is to use
a distance relay in which the setting is determined
assuming that the capacitor is always in the circuit under
fault conditions [12,15]. This method may not be
8
satisfactory due to the random nature in which a capacitor
flashes over under various fault conditions.
The other method is to set the relay assuming that the
capacitors have flashed over. Again, there will be a
tendency for the relay to over-reach if the capacitor's
protective gap does not flash-over under certain fault
conditions.
A method of protecting series compensated lines
involves the use of distance relays operating in a
directional comparison mode in conjunction with either
carrier or microwave signalling -channels. For systems
with less than 50% series compensation and a capacitor
located at the mid-point of the line, such a protection
scheme can offer secure and reliable operation [15].
However, when the capacitors are located at the line ends, directional comparison schemes using distance relays are
not very satisfactory (16]. For example, a low level
fault failing to cause capacitor by-passing, can result in
a loss of directionality arising as a result of voltage
reversal at the relay location. In the case of double
circuit applications, both voltage and current reversals
are quite common [11]. A distance relay employing an
expanded characteristic of the fully cross polarised mho
type (fcpm), goes some way to solving the inversion
problem, but the degree of expansion is very dependant
upon the type of fault and the impedance ratio of the
local source to the capacitive reactance [15].
Hinman and Gonnam [17] proposed a phase comparison
technique which compares the phase position of current in
each phase wire (and ground) separately. The comparisons
9
are based on square waves derived directly from the raw
(i. e. unfiltered) power system current. This is in
contrast to conventional phase comparison schemes which
compare a single square wave derived from a network of
sequence filters and a mixing transformer. The
conventional phase comparison technique incorporates
positive sequence and/or negative sequence network and
therefore has been vulnerable mainly to the problem of
phase impedance imbalance caused primarily by series
capacitor protective gaps flashing and re-inserting
unsymmetrically. The disadvantage of this approach is the
requirement for four separate pilot signal per terminal
[18].
Directional voltage blocking schemes have been
successfully implemented in conjunction with distance
relays to block any maloperation of the relay in the
presence of voltage inversion alone.
El-kateb and Cheetham (19] described a new technique
utilising the super-imposed voltages and currents, which
might over-come the problems of unwanted blockings of
distance relays due to operation of directional voltage
relays or the apparent capacitive source impedance,
utilising the fully cross-polarised mho relay.
Another method is a directional comparison protection
suitable for compensated and plain feeder systems which
utilises positive and negative sequence relays to detect
all types of fault [12], the former is a distance relay
with Mho characteristic which provides protection for
three phase faults and latter is a negative sequence
directional relay which protects the line against all
10
unbalanced faults. Each relay has a trip and block
element. It is designed such that for an internal fault,
the trip relay operates before the block relay and by-
passes any action taken by the latter. The opposite
procedure occurs for external faults. There is a
polarising quantity correction factor which is introduced
to neutralize the effect of polarising voltage inversion
at the relaying point. But this factor is dimensioned by
specific ratio of the source reactance to the series
capacitive reactance. This type of protection scheme may
not perform satisfactorily in a practical series
compensated system, since an effective value of source
impedance (impedance behind the relay) is not always known
and depends upon the infeeding lines and the number of
generators connected to the relaying terminal.
In recent years schemes utilising travelling wave techniques, suitable for series compensated lines, have
been developed [20], which are based on the work initially
carried out by Johns [21]. The basic relay operating
principle relies upon deriving two composite superimposed
signals using modal voltages and currents at each end of a
feeder. The use of modal quantities eliminates the mutual
coupling between the phases of a transmission line. The
criteria for determining the direction to fault is based
on the fact that for an internal fault (fault on protected
line) the superimposed modal voltage and current
components are of opposite polarities at each end of the
feeder. A forward fault indication is thus given by both
relay which is sent to the other end via a communication
link. Conversely, for an out of zone fault, although the
11
relay at one end gives a forward fault indication,
however, the modal voltage and current components at the
other end are of like polarity resulting in a reverse
fault indication by that relay which in turn sends a block
signal. Limited field experience is available on this
topic at present. Also the scheme relies heavily, as any
other directional comparison scheme, on the communication
link between the two ends of the line.
A commonly encountered problem in series compensated
line protection arises due to the presence of so called
sub-synchronous resonance that is introduced into the
system when capacitor protective gaps do not flash-over
[5,18].
If the sum of the electrical resonant frequency,
determined by the inductance and capacitance of the
system, and the mechanical resonant frequency given by the
masses of the turbine generator set and the torsional
properties of the shaft, is equal to the system frequency,
an unstable condition exists for which a small disturbance
can cause complex electrical and mechanical oscillation
[5]. Disasterous effects are possible with weak steam
turbine shafts since the high torsional stresses
associated with the sub-synchronous resonance are of
sufficient magnitude as to cause permanent shaft damage.
From the protection point of view, the interaction
between the total fault loop inductance (source and line)
and series capacitor can have a frequency bandwidth which
may exceed the power frequency, depending upon the fault
position (10). These extraneous frequencies, which are
usually underdamped (22) can cause considerable error in
12
small window calculations, and improper relay operation if
not catered for in the relay design.
Faults on any E. H. V. transmission systems have to be
cleared as soon as possible to avoid excessive damage.
Furthermore, fast fault clearance is essential to maintain
system stability and prevent the escalation of single
phase to earth fault to multi phase to earth faults. For
these reasons many studies have focused on Ultra-High-
Speed distance protection utilising digital technology.
When Ultra-High-Speed measurements are considered, the
waveforms from which measurements must be made can include
very significant travelling wave components, which are due
to the voltage step change on fault occurrence, in both
faulted and healthy phases. The amplitude and frequency
of these disturbances depend mainly on the line length,
fault inception angle and source termination [23].
The technique described by Gilcrest, et al [24] uses
the first and second differentiation of voltage and
current to calculate the transmission line impedance.
This has been done to minimize errors from the sub-normal
frequencies associated with the series capacitors (18].
However, this method is not favourable since higher
frequency transients caused primarily by travelling waves
are now accentuated.
The desirable features of any line protection scheme
for series compensated systems may be summarized as
follows:
i-High speed operation.
ii-Application independent
iii-Can detect the changes in the circuit as a result of
13
capacitor by-passing and adjust itself to the new
system condition.
iv-Can cope with the effect of resonance interaction
between the series capacitor and the loop inductances.
v-Can maintain its integrity when a voltage or current
reversal occurs.
As previously mentioned, in order to achieve fast
operating times, the majority of protection schemes which
are applied to series compensated systems are heavily
dependent upon the communication links between the line
ends.
Distance relays which have been successfully employed in plain feeder applications for many years, do not
provide a generally satisfactory response when applied to
series compensated lines. This is due to the fact that in
such lines the estimation of distance to fault from
measured impedance is very difficult, because of the
negative reactance of the capacitor and changes in the
system impedance as a result of capacitor protection gear
operation.
However, with the present day state of the art digital
technology, it will be possible to design an impedance
measuring device which can detect any changes in the
system states and adjusts its parameters according to the
new state of the system.
One of the advantages of distance schemes is the fact
that they can be employed in an independent mode, where
the relay trips irrespective of the information from the
other end of the line, as well as the unit protection
schemes where the tripping relies on the information from
14
the relay at the other end. Furthermore, since distance
relays, somehow compare the measured impedance with a pre-
determined boundary, it would be easy to change the relay
characteristic once the capacitor gap flash-over is
detected.
The new generation digital distance relays have a
distinct advantage over the older type of analogue and
hybrid analogue/digital relays in that the impedance is
calculated at any instant of time and the locus of the
impedance is available. Hence, any change in the measured
impedance may be detected, if a suitable filtering is
employed, and therefore appropriate steps may be taken by
the relay.
Since series compensated lines are usually long, the
long line transient effect caused by travelling waves may
be particularly troublesome, because the frequency of the
travelling waves, when considering a long line and
depending on sources at the line ends, may be as low as
250 Hz. Special attention must thus be given to this
phenomena when designing the filtering process of a
digital distance relay.
Distance protection algorithms have evolved over the
years. Algorithms based on conventional Fourier Transform
techniques (25,26,27) are effective in extracting the
fundamental components from highly distorted fault
waveforms, but their response to a fault is slow. The
response of the Fourier Transform method can be improved
by using a smaller data window, but small data windows
produce problems in current offset conditions and are
influenced by travelling wave components. However, the
15
Finite Fourier Transform can be satisfactorily implemented
if used with appropriate filtering [28].
The main disadvantage of the latter method is that the
magnitude response of the orthogonal filters are not the
same. Hence, they must be equalized at the power
frequency which means that any drift by the system
frequency from nominal frequency causes errors in the
impedance measurement. Furthermore, low order harmonics
in the relaying signals have a detrimental effect on the
performance [29].
A modified method uses two direct samples on the
relaying signals to solve for the resistive and reactive
components of the line impedance. This method has the
advantage of being immune to power frequency changes and
system harmonics [29].
1.2-Summary Of The Thesis
The problems associated with protection of series
compensated lines have already been mentioned. With
regard to distance protection, these problems can be
classified into two main areas:
i-When capacitors do NOT flash-over i. e. they remain in
the circuit. This situation arises from a low level
fault or high fault resistance [16,30]. Also, with
the new generation of Ultra-High-Speed protection, the
fault may be cleared in considerably less than one
cycle which can in turn be much shorter than capacitor
gap flash-over times [31]. In such situations
significant sub-synchronous resonance components are
often present. These components can be close to power
frequency and they can cause a significant slowing of
16
the protection and/or cause transient measuring errors.
Furthermore, in some system situations, the presence of
the capacitor affects the measuring accuracy of
distance schemes. Also, in applications where the
capacitors are located at the line ends, the first
independent zone of distance protection usually has to
be set to less than 80% in order to avoid possible
indiscrimination for remote end faults that do not
cause remote capacitor flash-over [13,32].
ii-When capacitors do flash-over, a relay may under-reach
significantly in applications where the voltage
transducer is located on the bus-bar (source) side of
the series capacitor.
The solutions to the foregoing problems are distinct.
Problem 1 may be solved by employing specially designed
signal processing filters applied to the basic measurands
and impedance estimates produced. A solution to problem 2
requires a dynamic adjustment to the relay characteristic
following the detection of gap flash-over.
In this thesis proposed solutions related to the
problems mentioned in group (i) are presented. Especial
attention is given to the situation where the capacitors
are located at line ends and the voltage transformers are
connected to the source side of the capacitor. A summary
of the thesis is now given.
A brief revision of digital distance relaying
techniques and algorithms is given in Chapter 2. The
discussion will mainly focus on the algorithms which are
related to the differential equation line model. A short
comparison between different methods is outlined.
17
Chapter 3 deals with the algorithm chosen for
implementation in the proposed digital distance relay.
The behaviour of the algorithm when applied to a series
compensated line is examined. In particular, the method
of differentiating the current signal and its effect in
reducing the high frequency oscillation caused principally
by the travelling wave is examined.
The digital distance relay structure and computer
simulation, together with a brief discussion on primary
system simulation is given in Chapter 4. The current and
voltage transducer simulations are also included in this
chapter. A detailed discussion on capacitor voltage
transformers (C. V. T. s) are presented and their effects on
distance relays are discussed. Different sections of the
simulated digital distance relay are explained in great
details. Particular attention is given to the filtering
process employed in the relay. In the analogue part of
the relay, the anti-aliasing filter and in the digital
section the digital pre-fault are thoroughly discussed.
The design and performance of a new recursive averager
implemented to cater for the sub-synchronous oscillation
on the final output of the algorithm is included in this
chapter, and finally the relay count regime and trip
decision logic is presented.
Chapter 5 is concerned with the accuracy in the
measurement of the distance relays when a phase to earth
fault occurs. It will be explained that if the
conventional methods of current compensation are used in
series compensated systems, the measurement will not be
accurate. A new method is proposed and implemented in the
18
relay. It will be shown that the accuracy of the relay is
greatly improved when the new method is employed in the
relay. The new concept of complex residual compensation
factor as opposed to the conventional real compensating
factor is also discussed.
The relay response for 70% series compensation, where
the capacitor is split into two halves and installed at
each end of the line is presented in Chapter 6. The relay
characteristic for source side and line side C. V. T. will
be shown and relay operating time for the fault inception
angle of 0 and 90 degrees are illustrated.
Chapter 7 includes the relay response for the
situations where the series capacitor is installed at the
mid-point of the line. In order to improve the relay
operating time response of the relay, a new relay
Quadrilateral characteristic is proposed and implemented
in the relay. The relay count regime and trip decision
logic suitable for such applications is presented in this
chapter.
The thesis will conclude in Chapter 8 and some propos-
als are given for future work.
19
CHAPTER 2
DIGITAL DISTANCE RELAY TECHNIQUES
During the past two decades, several algorithms for
distance protection have been proposed based on real time
impedance measurement. These techniques can be classified
into five main groups as follows:
1-Sample-and-derivative calculations.
2-Sinusoidal curve-fitting.
3-Fourier analysis of the relaying signals.
4-Least-squares curve fitting.
5-Solution of differential equation of the protected
system model.
The differential equation algorithms (group 5)
represent a major theme in line relaying. The algorithms
in groups 1 to 4 are mainly based on a description of the
waveforms. These algorithms attempt to estimate the
fundamental frequency components of currents and voltages
in order to compute the impedance to the fault [33]. The
differential equation algorithms, on the other hand, are
based on a model of the system rather than on a model of
the signal.
Consider the single-phase model of the faulted line
shown in Fig 2.1. The differential equation relating the
voltage and current seen by the relay is:
d V(t)=R i(t)+L ýt 1(t) 2.1
20
Since both v(t) and i(t) are measured, it is possible
that the parameters R and L and hence the distance to the
fault can be estimated.
McInnes and Morrison [25] proposed a solution to
Equation 2.1 by integrating over two consecutive
intervals:
tl tj V(t)dt=R i(t)dt +L [i(tl) - i(t0)] 2.2
to to
t2 ti
t+L [i(t2) - i(tl)) 2.3
t1 t1
The intervals in Equations 2.2 and 2.3 must be
approximated from the sample values. If the samples are
equally spaced at an interval T=1/fs (where fs is sampling
frequency), and the trapezoidal rule is used for the
integrals, viz:
tl TT
tÖ(t)dt= 2 [V(tl)+v(t0)] =2 [vl + vol 2.4
Then Equations 2.2 and 2.3 can be written for samples
at k, k+l, and k+2 as:
TT
2 (ik+l+ik) (ik+1-ik) R2 (uk+1+vk)
TT
2 (ik+2+ik+1) (ik+2-ik+l) L2 (vk+2+vk+1)
2.5
Then three samples of current and voltage are
sufficient to compute estimates of R and L as follows:
21
r (vk+l+vk)(ik+2-ik+l) - (vk+2+vk+1)(ik+1-ik) Rk 2.6
(ik+l+ik)(ik+2-ik+1) - (ik+2+ik+1)(ik+l-ik)
Tr (vk+2+vk+1)(ik+l+ik) - (vk+1+vk)(ik+2+ik+1) Lk-2 I 2.7
L (ik+l+ik)(ik+2-ik+l) - (ik+2+ik+1)(ik+l-ik)
Ranjbar and Cory (34] have proposed a related
algorithm in which the limits of integration have been
selected to introduce nulls at particular harmonic
frequencies. The method is very effective in this regard,
but does have a generally longer data window. Also, it
tends to ring on fault inception so that the results
oscillate severely until the window is completely filled
with fault data (35].
Sanderson et al [36] proposed a solution of Equation
2.1 in the form:
v(t)= R i(t) + L P(t) 2.8
v'(t)= R i'(t)+ Li" (t) 2.9
Where v' is the first derivative of voltage and il(t)
and ill(t) are the first and second derivatives of current
signal respectively. The use of the first and second
differentiations accentuates noise in the measured
parameters. In order to improve the system noise immunity
a digital smoothing process has been suggested by fitting
a second order polynomial to a data window of seven
samples as proposed by Savitzky et al (37].
Johns and Martin showd that the Fourier Transform
techniques can be used to solve Equation 2.1 and hence
calculate the line parameters [28].
Consider two filters having impulse responses hl(r)
22
and h2(r), defined over the same window width Tw. The
output of the filters are in the following forms:
TW V1(t) =
0V(t-r)hl(r) dt 2.10
Tw V2(t) =
0V(t-t)h2(t) dt 2.11
Defining the filter impulse responses hl(r) and h2(t)
as cos(wz) and sin(wr) respectively, Equations 2.10 and 2.11 can be written in the following form:
V(t) = v1(t) + jV2(t) 2.12
and
Tw V(t) °
J0V(t_t)E(_ih1t)dt
2.13
Figure 2.2 illustrates in schematic form the formation
of two orthogonal components from each input signal. Thus
v1(t) and v2(t) are orthogonal components derived from the
vector v(t), and similarly for il(t), i2(t) and i(t).
Application of Equations 2.10 and 2.11 to Equation 2.1
gives:
vl(t) =R i1(t) +L i'l(t)
V2(t) =R 12(t) +L i'2(t)
2.14
2.15
Which may be written in the matrix form of Equation
4.16:
vi (t)
V2(t) i2 (t)
i'l(t) R
10 2(t) L 2.16
23
Inverting the matrix 2.16 to solve for R and L gives:
R1 i'2(t) -i'1(t) Vi(t) 2.17
LD -i2(t) i1(t) V2(t)
where the determinant term is given by:
D= il(t) i'2(t) - i'1(t) 12(t) 2.18
The line parameters R and L from the relaying to fault
point are then given by:
vl(t) i'2(t) V2(t) i'l(t) R=
D
L= V2(t) il(t) - vl(t) i2(t)
D
2.19
2.20
In order to obtain two linearly independent equations from system signals similar to those given in Equations
2.14 and 2.15, two direct sample values from each input
measurand, which are spaced apart in time by n samples,
can be used [38]. This method, when compared to the
previous method, has the advantages of immunity to
harmonics or system frequency changes [29].
24
I (t) RL
V(t)
FIG 2.1- Relay Model Of Transmission Line
COS(wz) X1(t)
X(t
I SIN (wt) X2 (t)
FIG 2.2- Orthogonal Components Formation
CHAPTER 3
TIME SPACED SOLUTION DISTANCE PROTECTION ALGORITHM
In this chapter, first the application of the basic
distance protection algorithm to a plain feeder model is
discussed and then a series capacitor compensated line is
considered.
3.1-The Distance Protection Scheme Algorithm
The new distance protection scheme is based on a
modification of the method which was discussed in the
preceding chapter (25,34]. Consider the transmission
line model shown in Fig 3.1. The relationship between the
relaying voltage, v(t), and current, i(t), is given by the
expression,
d v(t)=Ri(t) +L
dt 1(t) 3.1
If the relay produces two linearly independent
equations from each relaying signal (v(t) and i(t)), then
it is possible to calculate the line parameters, R and L
[25,34,35]. This can be achieved by considering the
solution at two points on the relaying measurands which
are apart in time by e degrees thus avoiding
the process of integration (see Chapter 2). The two
simultaneous equations can then be written as:
vl(t) =R il(t) +L i'l(t)
V2(t) =R i2(t) +L i'2(t)
where: d
i'l(t)=dtil(t) and d
i'2(t)=ýti2(t)
3 .2 3.3
25
Which may be written in the matrix form of Equation
vl(t) il(t) i'l(t) R 3.4
v2(t) i2(t) i'2(t) L
Inverting the matrix 3.4 to solve for R and L gives:
R1 i'2(t) -if l(t) V1(t) - 3.5
LD -i2(t) i1ýtý v2(t)
where the determinant term is given by:
D= i1(t) V2(t) - M(t) i2(t) 3.6
The line parameters R and L from the relaying to fault
point are then given by:
V1(t) 1'2(t) - V2(t) i'1(t) R=3.7
D
V2(t) il(t) - vl(t) i2(t) L=3.8
D
3.2-Steady State Single Frequency Analysis
Let the voltage and current signals be expressed as
pure sinusoidal waveforms:
v(t)=V"sin(wot)
i(t)=I"sin(wot-P)
3.9
3.10
Where wo is the power system frequency and 0 is the
angle between the voltage and current at that frequency.
The relaying components vl(t), il(t), V2(t), and i2(t) of
Equations 3.2 and 3.3 can be written as:
26
vl(t)=V"sin(wot) 3.11
il(t)=V"sin(wot-0) 3.12
v2(t)=V"sin(wot-6) 3.13
i2(t)=V"sin(wot-0-®) 3.14
Where 8 is the delay angle which is used to produce
the second equation (see Fig 3.2).
Appendix 3A shows that R, L, and D are given by:
V R=
I "cos(O) 3.15
V L= -sin(O) 3.16
I"Wo
D=I2"wo"sin(8) 3.17
It is clear from equation 3.17 that if e assumes a
value corresponding to kn, where k=0,1,2, ..., then the
matrix 3.5 becomes singular and therefore no solution for
R and L can be expected.
3.3-Application Of The Algorithm To Series Capacitor
Compensated Lines
In series capacitor compensated lines a three phase
capacitor is inserted into each phase of the transmission
system. Thus the capacitor is in series with the line
resistance and reactance model as shown in Fig 3.3. This
model is valid for lines that are not extremely long,
permitting shunt capacitance of the line to be neglected.
In the case of series compensated lines, that are infact
normally relatively long, shunt admittance effects
introduce some errors but do not, in general, corrupt the
results exessively [35] (for line length<400 km no errors
were observed in steady state calculations).
27
Considering the effect of the series capacitor,
Equation 3.1 can be written as:
d1 V(t)=Ri(t) +L
ti(t) +c i(t) dt 3.18
Where C is the series capacitor capacitance.
Under steady state conditions, where there is only
power frequency present, Equation 3.18 can be expressed
as:
v(t)=R"I"sin(wot) +Ld ýtI"sin(wot) +1c I"sin(wot) dt
3.19 or
V(t)=R"I"sin(wot) + I"wo"L"cos(wot) -1 I"cos(wot) 3.20 wo"C
Equation 3.20 can be rearranged in the following form:
v(t)=R"I"sin(wot) + (wo"L -1 )"I"cos(wot) 3.21 wo"C
or
1d V(t)=R"I"sin(wot) + (L -2) dt I"sin(wot) 3.22
wo"C
During a fault however, the above condition is no
longer valid and other frequencies, such as sub-
synchronous frequency and long line transient effects are
likely to result in significant frequencies close to power
frequency being present. Hence there is a need for an
effective filtering of the system signals, which will be
discussed in the following chapter. By band-limiting the
voltage and current signals around power frequency, the
differential equation which is solved by the algorithm
28
returns to an equivalent form of Equation 3.23, where v(t)
and i(t) are band-limited versions of the signals.
V(t)=Ri(t) + L' dd
i(t) 3.23
where: L'=L - I Wo"C
1
3.4-Effect Of Sub-Synchronous Frequencies
The series capacitors, in series compensated lines,
form resonance circuits with the reactance of the
transmission line and the source system. This resonance
phenomenon, which is usually poorly damped [22], has
frequencies which are often lower than the fundamental
power frequency. In the next chapter this effect will be
discussed in more detail. Consider input signals of the
form:
v(t)=Vo"sin(wot) + Vsu"sin(wsut+ß) 3.24
and
i(t)=Io"sin(wot-00) + Isu"sin(wsut+ß-Osu) 3.25
where:
wo, wsu =power system and sub-synchronous frequency
respectively.
vo, 10 =voltage and current magnitude of the fundamental
components respectively.
vsu, Isu =voltage and current magnitude of the sub-
synchronous components respectively.
p =phase angle between the fundamental & sub-
synchronus components.
00 =phase angle between the power system fundamental
voltage and current.
29
*PSu =phase angle between the sub-synchronous voltage
and current.
It must be noted that in order to simplify the
analysis the decaying factor of the sub-synchronous
component has been ignored.
The relaying components v1(t), v2(t), il(t) and i2(t)
can thus be written as:
vl(t)=vo"sin(wot) + vsu"sin(wsut+p) 3.26
il(t)=Io"sin(wot-0o) + Isu"sin(wsut+p_f6u) 3.27
v2(t)=Vo"sin(wot-®) + Vsu"sin(wsut+p_©) 3.28 i2(t)=Io"sin(wot-0o) + Isu"sin(wsut+ß_osu_p) 3.29
Appendix 3B shows that the line parameters are given
by:
D=sin(®)"{wo'Iö+wsu-Isu
+ Io-Isu-(Wo+Wsu)"Cos[(Wo-Wsu)t-ß-(Oo-Osu)]} 3.30
D"R=sin(e)"{wo"Vo"Io"cos(oo)+wsu'Vsu'Isu'cos(osu)
+(AR+BR)"sin[(wo-wsu)t-ß+tan'1(AR/BR)]}
where:
AR=wsu'Vo'Isu"cos(4su) + wo'Vsu'Io'cos(Oo)
BR=Wo'Vsu'Io"cos(4o) + Wsu'Vo'Isu'cos(Osu)
and
3.31
D"L'=sin(e)"{Vo"Io"sin(oo)+Vsu-Isu-sin(osu)
+ (AX+BX)i"sin[(wo-wsu)t-ß+tan-l(AX/BX)]} 3.32
where:
Ag=vo'Isu"sin(osu) + vsu-Io-sin(io)
BX=Vo'Isu"cos(isu) - Vsu"Io"cos(, o)
The above analysis illustrates that when there are two
frequencies (power system and sub-synchronous) in the
30
relaying signal, the resultant measured values contain dc
and oscillatory terms which oscillate with a frequency
corresponding to the difference between the fundamental
and sub-synchronous frequencies. Also it is revealed that
the magnitude and phase angle of the ac components are not
the same and are independent of O. It should be noted
that the fault inception angle (point on wave when fault
occurs) has been ignored in the preceding analysis. This,
if included, may change the phase angle of the ac
component of the measured parameters but the frequency of
the oscillation will not be affected.
It has already been mentioned that the sub-synchronous
oscillation, caused by series capacitors in series
compensated systems, are usually under-damped [22] which
in turn causes errors in measurement during the time when
the Ultra-High-Speed digital distance relay must reach a
trip decision. Therefore there is a need for a special
filtering of signals and appropriate design for the trip
regime. It is also worth mentioning that during a fault
high frequency components, caused principally by
travelling waves, are also superimposed on the measuring
signals and the above analysis with three frequency
components (power frequency, sub-synchronous frequency and
the dominant travelling wave) on the relaying signals can
be applied to investigate the resulting effects on the
measured parameters. However, these components have
higher damping coefficients and diminish much faster than
the sub-synchronous oscillations. Nevertheless they also
make the relay decision making process more difficult
during the initial period after a fault and consequently
31
must be filtered from the relaying signals. The relay
filtering process will be discussed in more detail in the
next chapter.
3.5-Discrete Processing Solution
The need for faster and consistent tripping times has
promted an interest in discrete processing techniques. In
this technique, samples are fed to the process for
individual impedance estimates. The filtered voltage and
current can be made available as samples (using the
discrete variable k), at intervals Ts in time given by the
relay sampling frequency fs (Ts=l/fs).
In order to produce two simultanous equations, the
relay uses direct sample values from each input measurand
which are time spaced by n samples as shown in Fig 3.4.
Also since a given sample value contains no information
about the derivative at the sampling instant, the current
derivative can be approximated by computing the difference
between two consecutive samples. In the next section it
will be explained that a better result can be obtained if
the current derivative is computed over m number of
samples on each side of the point where a solution is
considered. In this method, since the relay has no
information about the future samples, the point of
solution is delayed so that the current derivative may be
calculated. Hence the two simultanous equations from the
line model can be expressed as:
vk-m-R'ik-m + L''i'k-m
vk-n-m-R-ik-n-m + L''i'k-n-m
3.33
3.34
32
where: ik - ik-2m irk-m-
2"m"TS
ik-n - ik-n-2m 2"m-Ts
Factors which determine the value of n are mainly as
follows:
1-'n' must not correspond to an angular displacement of
kn (k=0,1,2, ... ) of the fundamental component of the
relaying signals (see section 3.2).
2-In order to reduce the window width of the algorithm,
which in turn avoids long operating times by the relay,
'n' must be close to unity
3-To avoid ill conditioning of the algorithm under all
operating conditions (to preserve independance of the
solutions), when executed on a fixed word length
processor, 'n' must be greater than unity.
A value of 6 has been suggested for n [29] which
proved to be adequate for practical purposes and is used
in the digital distance relay.
In section 3.6 the method of differentiating the
current signals is explained and a value of 4 is suggested
for m. Therefore Equation 3.33 and 3.34 can be expressed
in matrix form:
Vk-4 ik-4
Vk-10 ik-10
iIk-4 R
i'k-10 3.35
33
where: ik - ik-8 i'k-4-
8"TS
ik-6 - ik-14 irk-10-
8-T5
Inverting the matrix 3.35 to solve for R and L'
yields:
R1 i'k-10 -i'k-4 Vk-4 = 3.36
L' Dk_4 -ik-10 ik-4 Vk-10
where:
D=ik-4'i'k-10 - irk-4'ik-10
R and L' can therefore be expressed as:
1 R- [vk_4'i-'k-10 - Vk-10'i'k-4] 3.37
Dk-4
1 L`= [uk-10'lk-4 - Vk-4'ik-101 3.38
Dk-4
Note that the algorithm has a window of 15 samples,
which corresponds to 3.75 msec at a sampling rate of 4
kHz.
The reactance is calculated by multiplying the
measured L' by the fundamental frequency of the power
system. Hence:
X=wo"LI
To avoid digital division in the relay, which is
considered to be undesirable in a real time calculation by
34
a microprocessor, the current derivatives can be
calculated without dividing by the term 2"m-Ts, but
instead multiplying X by the same term. Note that the
term is eliminated from the calculated D and R. Thus:
X=2"m"TS"wo"L'
3.6-Computation Of Current Derivative
In order to compute the current derivative, different
methods have been proposed [24,27,29]. The method
initially adopted in this work was based on the difference
between one point on each side of the point of interest
(the sample at which R and L' is calculated).
Fig 3.5 shows the frequency response of the difference
equation:
ik - ik-2 i'k-1- 3.39
2"T6
where Ts is the sampling period.
Examination of frequency response of different methods
has revealed that in order to suppress the high frequency
oscillations in the measured resistance and reactance,
caused by travelling waves, the current must be
differentiated using more points. Fig 3.6 illustrates the
frequency response of the current derivative when nine
points are used. The corresponding difference equation
being:
ik - ik-8 i'k-4
2"T8 3.40
Fig 3.7. a shows i', using one point on each side, for
35
a fault at 160 km (line length=300 km) and inception angle
of 90' where the travelling waves have the maximum effect
on the relay measurands. Fig 3.7. b shows the
corresponding measured X and R.
Fig 3.8. a illustrates the current derivative for the
same fault but for four points on each side of the point
where the solution is considered. Fig 3.8. b shows the
corresponding measured X and R.
Appendix 3C shows the error involved in taking more
points. By comparing Figures 3.7. b and 3.8. b it is
revealed that the high frequency oscillation has been
greatly reduced, whereas the actual dc values have not
been significantly affected. This is important,
especially for series capacitor compensated systems where
the lines are usually long.
For the foregoing reasons, it is decided to
differentiate the current over nine points, i. e., four
points on each side of the point in interest.
It must be said that for the results shown, the
relaying signals were filtered before the algorithm stage.
The filters used will be discussed in the next chapter.
36
i(t) R
V(t)
FIG 3.1- Relay Model Of Transmission Line
výtý or iýtý
wt
FIG 3.2-Solution Formation Using Time spacing
iýtý CRL
VM
FIG 3.3-Transmission Line Model With Series Capacitor
k
k-n I
ý- -n samples - -ý k
FIG 3.4-Solution Formation Using Discrete k Variable
XI O' LM MAIN R SPOt.
-11ý
td81 ýI
Ln
-11 -1
0 10 20 30 40 (Nair, Fr-tq F'G) x1 a-2
X 0, PHASE Re5PME
Cog)
50
0
X10-1 Ma4 Nss 24 1
1
4 10 20 20 f0 50 (Nor. M Frei FrF ) x10-2
X10-1 IhPUUE F SPOH$E
Fig 3.5-Frequency Response Of Equation 3.39
Note that the sampling frequency (fs) is 4 kHz
C Hceýh F"q Fo? F9) X IG-2 (N8. Pü1hu) xi O-l.
X1P1 LO3 PA RESPorZ
-1 .
-, t ) e{ t
-IW
tLO
-1 t
0 10 20 30 i0 60 (Na n, Fr-eq FrFS) X10-2
X fO1 PHASE R PO
(Dog)
CNa. Paints)
Fig 3.6-Frequency Response Of Equation 3.40
X
1 1 1 I 1
0 -1
Note that the sampling frequency (fs) is 4 kHz
0 10 20 20 +0 öo (NOM h Frei F'FF > X10-2
iö _1 IMML E RE$PVNSE
CHOM FMq F S) X1Q-2
X105 4C
tn d d
C 0
-4
d
C d 3
O
7
Fig 3.7. a-Current Derivative Using One Point On Each Side
U' E
0
d
C 0 U W IA .r ly
c
v a L 3 N d Cº
7
Fig 3.7. b-Measured X and R Using One Point On Each Side
SE SCL-5 GVA. RE SCL-35 GVA. No Load
Time ( sec) X10-2
f Time ( sec) X10'2
X105 12-
II J ei
i a,
C G
M
4-%
C$
C d 3 -'
0
-1: 7
Fig 3.8. a-Current Derivative Using Four Points On Each Side
112 N 20 E ä
18
=, 16 d 14 v ö 12
a 10 14 .. 8 ly 6 §4 d x2
0 a$ L :3 _2 ä
-4 o, = -s
X
i 5 67 8 9 10 11 12 13 14 15 16 1 Time ( sec) X10-2
Fig 3.8. b-Measured X and R Using Four Points On Each Side
7
SE SCL-5 GVA. RE SCI--35 GVA. No Load
Time (. sec) X10-2
CHAPTER 4
DIGITAL DISTANCE RELAY
Digital computers nowadays are very powerful tools in
engineering fields. They can be used to accurately
simulate and test a system or component before they are
actually built or manufactured.
The importance of digital computers in design and test
stages of the components of power systems is well known.
Advanced methods are now available for modelling and
testing complex power systems, such as series compensated
lines, on a digital computer [9,11,23,39]. These
simulation programes provide not only the steady state,
but also the transient response. They are of great values
to protective relays designers, for new designs can be
tested in laboratories before they are actually installed
on the system. In particular when considering Very and/or
Ultra-High-Speed protection schemes, when the measurement
is carried out in a very short time after fault inception,
the waveforms from which measurements are made must
contain all transient phenomena which occur in a real
system after a short circuit fault. These simulation
programs provide, in numerical forms, the voltage and
current waveforms at the relaying points.
The primary system simulation program which is used in
this study, employs the frequency domain analysis of
transmission lines. Full description of the technique and
the program is given in references 9 and 40.
The digital simulation of the primary system is run at
8 kHz sampling rate, which therefore yields accurate
37
information of up to 4 kHz. It is pointless extending
this bandwidth since the C. V. T. s which are used without
exception on EHV systems, have a very low cut off
frequency of typically 600 Hz. Most C. T. s however have a
very wide bandwidth, up to 10 kHZ, but an interface is
used in the current channel to convert the current to a
proportional voltage over a specified frequency range,
much less than 10 kHz. Moreover, an analogue low pass
filter (discussed later) is employed to pre-filter the
signals, with a cut off frequency well below 4 kHz. Hence
the requirement to provide very high frequency primary
system information, above 4 kHz, is obviated.
The primary system configuration which is simulated
thoughout this work is shown in Figure 4.1. Like the most
series compensated line constructions, a horizontally
constructed transmission line is considered. The complete
data of the line is given in Appendix 4A.
4.1-Primary System Interfaces
The primary system interfaces comprise the C. V. T. and C. T. transducers.
4.1.1-capacitor voltage transformer C. V. T.
It is now common practice to seek protective relay
operating times of about half a cycle from fault
inception. The high speed capability is conditional on
the quality of the input voltage signals. Although
electromagnetic voltage transformers (V. T. s) have a
performance which meets modern protection requirements,
the normal practice at transmission system voltages of 100
kV and above is to use capacitor voltage transformers
38
(C. V. T. s) for protection and measuring functions, these
being used in preference to electromagnetic V. T. s for
reasons of economy. Unfortunately, errors generated by
C. V. T. s during rapidly changing conditions can have
detrimental effects on the operation of protective relays
[18,41]. These C. V. T. errors result from energy storage
in the C. V. T. circuit, which causes a distorted output for
several cycles [18] of the system frequency when the
primary voltage changes suddenly, particularly when the
primary voltage falls to a small fraction of its rated
voltage.
While it is difficult , if not impossible, to make any
general statements about the effect of C. V. T. errors on
relay performance, one possible relay problem that has
been identified is the over-reach of first zone distance
relays.
Several solutions have been devised to overcome the
C. V. T. transient error problem as far as over-reach is
concerned [18]. The mechanism of the digital distance
relay trip decision logic, which will be discussed later,
is such that the relay operation is delayed for a few
millisecond after the fault detection. This method,
although not primarily designed for this purpose,
overcomes, to some extent, the measuring errors due to the
C. V. T. transients.
From the modelling point of view, the C. V. T. s have
well defined transfer functions derived from their circuit
elements and structures, from which corresponding time
domain impulse responses are obtained via inverse Fourier
methods.
39
The effect of any modifying function h(t), upon a time
domain variation x(t), may be determined using convolution
theorem, such that:
+CO y(t) = h(t) * x(t) = h(z) " x(t-z) " dt 4.1
J_Co
Where y(t) is the modified version of x(t), and r is
the dummy variable of integration.
If the time scale is divided into 'n' discrete samples
of width AT,, Equation 4.1 can be evaluated via simple
numerical integration, which gives:
n y(n) =E h(k) " x(n-k) "AT
k=0 4.2
Hence, the primary voltages at any sample 'n', are
found using a past history of the relevant impulse
response h(k), together with the profile of the input
signal. Figure 4.2. a and b illustrate the impulse and
frequency responses of the C. V. T. which was used in the
present study.
The three phase voltages are applied to the C. V. T. at
their pre-fault peak, to ensure that, at the fault
instance no transients are present except those generated
by the faults.
The C. V. T. ratio in the simulation is taken as
500x103/110 for the 500 kV system.
4.1.2-current tranformer C. T.
It is assumed that the C. T. has an ideal response over
the range of frequencies expected, and therefore is
simulated as a step down factor. The saturation of the
40
C. T. core is also neglected. The ratio is 2000/1.
4.2-The Digital Distance Relay Structure
The digital distance relay was simulated using a
standard Fortran program. The outputs from C. V. T. and
C. T. are fed to the relay program and the relay calculates
the impedance of the line from the relaying to fault
point.
The relay can be divided into two main parts:
(i) An analogue part which is mainly instrumentation and
signal filtering.
(ii) A digital part, which includes signal filtering,
the impedance measurement process and decision logic.
The relay must be capable of meeting conventional
distance protection accuracy, nominally 5% of the relay
reach, and go further in achieving the advantage of speed
and consistency of operation required for ultra fast fault
clearance. Tests on the discrete process simulation
showed that a sampling rate of 4 kHz is required for
U. H. S. performance [42,28]. Therefore, it was decided to
drive the relay at 4 kHz sampling rate. Figure 4.3 shows
the structure of the simulated relay. A description of the
relay is given below:
(i) Secondary voltage transformer: this is an
instrument voltage transformer used for the purpose
of signal level adjustment according to the
Analogue to Digital A/D converter requirements.
The frequency response of such a transformer is
taken to be ideal over the operating range of
interest.
41
(ii) Current interface (NOT simulated): this is to
convert the current into a proportional voltage.
There are different devices, such as the Hall
effect device or a transformer with an air gap
followed by an integrator, which can be employed.
This device is not simulated in the relay
simulation. Instead a simple scaling factor was
considered for signal level adjustment. The
scaling factor is introduced to limit the voltage
equivalents of the phase current inputs to ± 10
volts. The choice of the factor depends entirely
upon the setting philosophy adopted for the relay.
The range of current levels encountered in
integrated networks is extremely large and it is
necessary to limit or clip the input current if the
latter is very high. This permits larger a gain
for low current level faults, but introduces some
degree of non-linearity into the process. Also the
analogue filter used in the relay (discussed later)
can suffer from saturation in case the signal
exceeds the power supply level available.
Therefore, it is essential, at this stage , to
adjust the signal level such that saturation or
clipping is predicted under the worst possible
external fault conditions. Initial adjustments are
done so that clipping or saturation does not occur
for faults just outside the protected zone.
The residual current is formed, at this stage, by
adding the three phase currents.
42
(iii) Analogue filter: for a sampling frequency of fs the
Nyquist frequency is thus fs/2. All components
above fs/2, if unfiltered, will be mapped or
translated down into the dc to fs/2 Hz spectrum by
the digital process. This is known as aliasing.
The anti-aliasing analogue filter is used to filter
the frequencies above the Nyquist frequency. A
second order low-pass Butterwoth filter is
suggested, the transfer function of which takes the
standard form of:
w2 A G(B)=
s2+2 SwnS + wn
The choice of the cut-off frequency and required
attenuation largely depends upon the digital stages
of the relay. Figure 4.4. a shows the circuit
diagram for the proposed analogue filter and Figure
4.4. b illustrates the corresponding frequency
response. By cascading two such filters the
desired frequency response can be achieved. Figure
4.4. c shows the total frequency response of the
filter. From modelling point of view the method
explained in Section 4.1.1 was used to obtain the
equivalent impulse response of the filter.
(iv) Change in data sampling rate: although the relay
operates at 4 kHz sampling frequency, the primary
system simulation is derived at 8 kHz, allowing for
an accurate simulation of the anti-aliasing filter.
The sampling frequency of the relaying signals is
reduced in time to 4 kHz at this stage by taking
every other samples.
43
(v) Current clip detector: any current clipping is
detected at this stage. If the fault current is
very high (i. e. close up faults) and causes
saturation of the analogue electronic component of
the relay, the clip detector will indicate. This
may be used by the relay to initiate the trip
directly, irrespective of impedance measurement.
(vi) The Analogue to Digital converter: this is taken to
be of 14 bit (13+sign) structure. The eight
available signals, three phase voltages, three
phase currents and two neutral currents (one from
the main line and one from the parallel circuit)
are sampled simultaneously by eight sample and
holds and then scanned by a multiplexer to a single
A/D converter. This stage represents the link
between the analogue and digital parts of the
process. It must be said that, in computer
simulation terms, the difference in analogue and
digital quantities is only that the former is
perforemed with floating point arithmetic, and the
latter with integers. When using a fixed-point
representation of a binary number, truncation or
rounding errors exist in arithmetic multiplication
but not in arithmetic addition. In contrast, these
errors are present for multiplication or addition
of floating-point binary numbers. In fixed-point
format the dynamic range of the number is fixed,
and arithmetic addition and multiplication can
produce over-flow, thereby producing a result that
exceeds the valid dynamic number range. In
44
floating-point format however the dynamic number
range is relatively large and therefore overflow is
unlikely to occur.
13 bit converter (13 bit + sign) corresponds to
8192 quantisation levels representing the 10 v
input. The conversion gain of the A/D converter is
then simply 8192/10=819.2. The range from -10 to
+10 volt is thus represented by 16389 quantum
levels.
(vii) The residual current compensation process: a great
deal of work was carried out on the topic of the
residual compensation. This will be discussed in
the following chapters. The process which,
involves adding a scaled neutral current signals
from the main and parallel (if any) circuit to each
phase current, is performed digitally rather than
analogue wise. In this way a higher resolution is
obtained from 13 bit A/D converter for phase
current signals.
(viii) The digital pre-filter: it will be explained in
Section 4.3 that during the initial post-fault
period, the incoming power frequency signal is
contaminated by unwanted signals at other
frequencies which, in turn distort the impedance
measurements. In order to obtain a smooth and
accurate measurement it is essential to perform a
filtering process and possibly filter out all the
unwanted frequencies from the system frequency.
The filter and its response will be discussed in
Section 4.3.1.
45
(ix) Production of two relaying components: it was
explained in Section 3.5 of Chapter 3 that in order
to measure the line parameters from the relaying
point, two samples on each relaying signals, v(k)
and i(k), are considered. This is done by:
1-storing the incoming signal in a buffer. At the
instant of each system clock (relay sampling
clock) the samples in the buffer are shifted by
one location. In this way, the sample value in
the last location of the buffer is discarded and
the new sample is placed in the first location.
The length of the buffer depends on the delay
required by the algorithm (see Chapter 3).
2-to produce two signals from each signal, the
samples in the first and last location of the
buffer are considered. In this way, two
waveforms are produced which are identical but
separated in time by a specific delay. Figure
4.5. a and b illustrate the two relaying
components of the voltage and current signals
respectively.
(x) The relay algorithm and decision logic: it is well
known that the protection of series compensated
lines require special and delicate design
considerations. The method by which the relay
calculates the line parameters was explained in
Chapter 3. The relay tripping characteristic and
trip decision logic will be discussed later.
46
4.3-Digital Distance Relay Filtering Process
When a fault occurs on an overhead plain uncompensated
transmission line, the system voltages and currents are
distorted for a period after the fault. Transient
phenomena are super-imposed on the system frequency
signals. These transient effects can be classified into
two main groups:
(i) When a fault occurs on a transmission line the
voltage at the fault position is affected. As a
result, travelling waves of voltage and accompanying
current are initiated. The initial values of these
waves are dependent, amoung other factors, on the
voltage at the fault position at the instant of fault
occurrence. The change in voltage at the fault point
travels away from the fault towards the line ends.
At the point of discontinuity on the transmission
system, part of the wave is transmitted to the next
section and part of it is reflected. The method
known as lattice diagram and proposed originally by
Bewley [43] best analyses the effect of this
travelling phenomenon. Figure 4.6 shows a simple
Bewley lattice diagram for a fault on a simple
transmission line. Walker et al [44] reported
results in which it was shown that the frequency of
high frequency components were roughly inversely
proportional to the distance to fault. Swift [45]
explained that how the dominant travelling wave
frequency may be affected by the source impedances at
the line ends. Reference 46 shows the change in
dominant travelling wave for extreme cases of very
47
low and very high source capacities and different
line length.
(ii) A decaying exponential component may appear mainly on
the current after a fault occurs. This effect is due
to the fact that transmission systems contain
inductances and therefore the current state cannot be
changed instantly after the fault occurrence.
In series compensated systems however, in addition to
the well known fault generated travelling waves and dc
offset, the interaction between the total fault loop
inductance and the series capacitor create a resonance
circuit which causes an oscillation to be super-imposed on
the system frequency. In E. H. V systems, the resistance of
the lines are small and can be neglected. The resonance
frequency is thus given by:
11 fS
2n V,
L C 4.3
where: L=total inductance of the fault loop C=total capacitance of the fault loop
Figure 4.7 shows the equivalent circuit for a single
phase to ground fault, assuming the typical 70%
compensation, 35% at each end. Similar circuit with
capacitor location in the middle of the line can be used
for 50% compensation at the mid-point. The total
inductive reactance of the faulted path depends on the
fault position which in turn changes the resonance
frequency. Referring to Equation 4.3, it is clear that the
frequency of the resonance oscillation reduces as the
fault position moves away from the source. It must also
be noted that for sources with zps/pps impedance ratio of
48
less than unity the neutral impedance of the source, ZSN,
exhibits a negative and therefore capacitive reactance.
Also the frequency of resonance oscillation is higher than
the power frequency, if the total fault loop reactance is
capacitive at power frequency [10].
Figures 4.8 and 4.9 illustrate approximately, the
expected resonance (usually called sub-synchronous)
frequency for different system source and series
compensation. It is clear from Figures 4.8 and 4.9 that
the change in resonance frequency tends to be small when
the source symmetrical short circuit level becomes very
high.
It must be said that, the source termination
considered above are representative of a simple machine
providing all of the infeed at the busbar. This is a
reasonable assumption if the system behind the busbar
contains no series compensation.
4.3.1-digital pre-filter
The main pre-filtering process is performed by the
FIR (Finite Impulse Response) filters which have well
defined transient responses and steady state frequency
rejection characteristics. The filtering of the signals
is carried out digitally since the following advantages
are offered as opposed to analogue equivalent:
(i) Versatility: the weighting constants governing the
response of the filter are simply altered by
software re-programming.
(ii) Accuracy: background noise introduced by the
quantisation of analogue signals can be reduced to
well defined, acceptable levels by suitable
49
conversion gain in the A/D converter stage. Noise in
analogue circuits is difficult to quantify since it
largely depends upon component tolerances.
(iii) Freedom from drift: digital filters exhibit
precisely the same characteristics, no matter how
many times they are used. Analogue filters suffer
from component ageing and in many circumstances from
changes in temperature.
Ideally, the duty of the filtering process is to
filter out the dc component and all the frequencies
discussed earlier other than the system frequency.
However with Ultra-High-Speed operation in mind, the
filtering of all unwanted frequencies is very difficult to
achieve, since a long filtering process delays the
transition of signals from pre-fault to post-fault [46,
47].
It is decided to design a filter with the following
characteristics:
(i) The filter length must be as short as possible which
in turn makes the post-fault information available
for processing in a short time and therefore post-
fault impedance can be estimated in a short time
after the fault. The time allowed for filtering
depends upon the required minimum operating time by
the relay.
(ii) To have a zero at dc. This rejects any dc off-set.
Although the differential equation obtained from
transmission line model (see Chapter 3) recognises
the dc exponential component as a valid component,
but due to the fact that voltage and current
50
interfaces introduce some transients which are not
related to the line equation, the final impedance
measurement may be corrupted. It can be shown that
if the dc component in the signals is not true
reflection of dc transient in the line model, the
final impedance estimates oscillate at a frequency
equal to the power frequency . Moreover the
exponential component in current affects the
Determinant (D) term of matrix 3.36 (see Chapter 3)
which may, in turn, cause ill conditioning of the
solution [28]. Therefore it is essential to reject
any dc component from voltage and current.
(iii) To filter any travelling wave frequency. The main
pass-band must be as narrow as possible with the
second zero as close as possible to the system
frequency. The side lobes must also be small.
(iv) Possibly, it gives some attenuation at resonance
frequencies. It was shown earlier that the band
width of resonance (sub-synchronous) frequencies is
between approximately dc to 80 Hz for a typical
system. It is impractical to design a single filter
which, at 4 kHz sampling frequency and allowed time
for filtering, band limits the signals to around
system frequency. Therefore it is decided to impose
the filtering of the sub-synchronous components on
another filter which will be discussed in the next
section.
The required filter is constructed by combining two
filters. One with 9 points in impulse response which
gives dc rejection and also has four zeros at 0.5,1,1.5
51
and 2 kHz and has equal peaks at 0.25,0.75,1.25 and 1.75
kHz. Equation 4.4 gives the filter transfer function in
digital form. The other filter is a low-pass filter with
6 points in impulse response whose transfer function is
given in Equation 4.5.
Y(Z) = a0ZO+a8Z-8 4.4
X(Z)
Y(Z) = b0Z0+b1Z-1+b2Z-2
X(Z) +b3Z-3+b4Z-4+b5Z-5 4.5
where:
ap=1.428 and a8=-1.428
and
b0=0.1626, b1=0.1432, b2=0.2015
b3=b2, b4=b1, b5=bp
Using the convolution theorem the overall impulse
response of the filter can be obtained by convolving the
two impulse responses as given below:
+00 h(t)=hl(t)*h2(t) = hl(t)"h2(t-t) dt 4.6
J-00
in discrete form equation 4.6 can be written as:
n h(k) =kEOhl(k)-h2(n-k) 4.7
It must be noted that, as one of the convolution
properties of linear time-invariant system states, since
hl(k) and h2(k) are finite the resulting h(k) will be of
finite duration. Equation 4.8 gives the transfer function
of the overall filter in digital form. It can be deduced
52
that the filter has 14 points on its impulse response
which corresponds to 3.5 msec at sampling frequency of 4
kHz.
Ym = a0Z0+a1Z-1+a2Z-2+a3Z-3+a4Z-4+a5Z-5+a6+a7
X(Z) +aBZ-8+a9Z-9+a10Z-10+a11Z-11+a122-12+al3Z-13 4.8
where:
a0=0.2322, a1=0.2045, a2=0.2877, a3=a2, a4=alr a5-a0
a6=0.0, a7=0.0
a8=-a0, ag=-al, al0=-a2, a11=a10, a12=a9, a13=a8
Figure 4.10 shows the response of the 9 point filter
and Figure 4.11 the low-pass filter. Note that the zero's
of the low-pass filter have been arranged to,
approximately coincide with the peaks of the 9 point
filter. Figure 4.12 illustrates the impulse and frequency
response of the overall filter.
It can be seen, from frequency response, that the
side-lobes at high frequencies are not low enough compared
to the gain at the power frequency. However if the effect
of the anti-aliasing filter is considered it can be seen
that the overall frequency response is modified and higher
attenuation is observed at high frequencies. Fig 4.13
shows the overall frequency response of the pre-filter and
analogue anti-aliasing filter. Also, the frequency
components higher than the system frequency and lower than
approximately 0.4 kHz are amplified by the filter. These
components are usually associated with fault positions
which are far from the relay points (44,45,46).
Since these components are not filtered from the
53
system signals, the resulting measured reactance and
resistance are affected. The attenuation of these
frequencies is left to an averaging filter which will be
described in the next section.
The digital pre-filter described above is assumed to
be most suitable for the application and is employed in
the relay simulation.
4.3.2-the Recursive Averager
As explained earlier, when a fault occurs on a series
compensated line the interaction between the series
capacitor and the total fault loop inductance produce a
resonance oscillation which can have a frequency between 5
to 80 Hz depending on the degree of series compensation,
position of the series capacitor, system sources and fault
position [13,48,49].
If the protective gap of the series capacitor does not
operate after the occurrence of a fault (capacitors remain
in circuit), the relay performance may be greatly affected
by the resonance phenomenon especially for faults close to
zone boundaries. In such cases, the relay logic may
experience difficulty in deciding whether a fault is more
likely to be inside or outside the protected zone (and
thus maloperates) (11,18,49).
It was explained earlier that, it is very difficult to
design a short impulse response, very narrow band filter
to pass the power system frequency only. Therefore, it is
decided to attenuate sub-synchronous oscillation on the
output of the relay, i. e. the values DX, DR and D (see
Section 4.4) by applying a suitable filter which ideally
must have the following characteristics:
54
(i) It must attenuate or possibly reject any frequency
other than the dc, i. e. very sharp low-pass filter.
(ii) It must have the shortest possible impulse response.
It must be noted that although the filter is applied
to the output, a long impulse response may delay the
measurands to reach the steady state values and as a
result the relay may maloperate.
It has been proved to be very difficult to devise a
filter which perfectly meets both conditions
simultaneously. In this respect a lengthy study showed
that (i) can be satisfied by employing a recursive filter,
which is on contrary to (ii), since a very sharp low-pass
recursive filter with a very low cut-off frequency has a
relatively long impulse response. An extensive study of
various filters has revealed that a specially designed
Recursive Averaging filter described by Equation 4.9 is
best suited to this application.
1 n=M-1 Y(k)=
M (X(k) +nElY(k-n)]
where:
X(k)=present input sample
Y(k)=present output sample
Y(k-n)=Previous k-n output sample
M=number*of elements in the filter
4.9
The schematic diagram of this filter is shown in
Figure 4.14 The impulse and frequency response of the
filter for M=4,8,12 and 16 are shown in Figure 4.15. a,
b, c and d respectively. It is clearly evident from
Figures 4.15. a, b, c and d that as M increases the cut-off
frequency decreases and that the impulse response is
55
inversely proportional to M.
A compromise must be made in choosing a suitable
filter for the relay. With regard to frequency response,
the ac components, whose frequencies may be very low, is
best attenuated by a filter with larger M but the impulse
response become extermely long.
A lengthy test has shown that a filter with M=12 is
most suitable for this application. The Recursive
Averager with 12 locations has a relatively long impulse
response. Therefore it is not wise to apply the filter to
the measurands continuously, since the advantages of
applying the filter to the output is lost.
Figure 4.16 shows the measured reactance when the
Recursive Averager is not employed and Figure 4.17
illustrates the measured reactance when the averager is
applied continuously. It is clear that the output takes
relatively long time to reach its steady state value.
In order to reduce the effect of this problem, it is
necessary to apply the averaging filter after the
transition period of the measured X and R from pre-fault
to post-fault has expired. This requires that the
occurrence of the fault is detected by the relay as
described in Section 4.4.
To clearly understand how this very versatile filter
works, an array or buffer can be considered where the
present to last M-1 values of input samples are stored as
shown in schematic form in Figure 4.18. The switches SM
and S are analogous to the digital logics which are
controlled by the relay decision logic.
Under normal system conditions, i. e. pre-fault, the
56
switch SM is in the SMO position and S in SN position. In
this position gates SMO and SM2 are open and SM1 close,
which implies that the input samples are directly passed
to the output without any process being carried out on
them. The input samples are at the same time stored in
the buffer.
When it is required to apply the filter, i. e. after
fault, it can be set either to perform as a Recursive or
Non-recursive Averager. At the time it is applied switch
SM changes position from SMO to SMC, which makes gates
SMO, SM1, and SM2 close, open and close respectively. The
averaging process is thus started. When switch S is on
position SN, the averaging process is non-recusive, since
the output is the averaged value of M number of inputs
stored in the buffer. Figure 4.19 illustrates the
frequency response for a 12 point non-recursive averager.
On the other hand, if it is required to change the non-
recursive nature of the filter to recursive, switch S
changes position from SN to SR, which in turn places the
present output sample, Y(k), into the buffer. The next
averaging has M-1 inputs and one output. This process, if
continued, fills the buffer with output samples. The
present output will be based upon M-1 outputs and one
input. Thereafter the filter follows Equation 4.9.
The advantages of this Recursive filter are:
(i) It can be changed a to Recursive filter from Non-
recursive or vise-versa by changing the position of
switch S.
(ii) At the instant it is applied all inputs are averaged
, and if the filter is required to perform as a
57
recursive averager the starting value for recursive
action may be close to the actual steady state
value. This characteristic of the Recursive-
Averager may affect the overall performance of the
filter in terms of impulse response.
(iii) There is no weighting of samples involved. The
filter action is performed by simple addition of the
samples present in the filter buffer.
More details about implementation of the filter is
given in the next section.
4.4-Relay Characteristic and Decision Logic
4.4.1-production of quadrilateral characteristic
A conventional distance relay characteristic defines
the region where the fault loop impedance converges after
fault inception on a transmission line. It is usually
plotted on an impedance diagram with'R and jX axis.
Figure 4.20 shows a typical quadrilateral characteristic
for plain uncompensated feeders. The resistive reach is
expanded to cover high fault resistance.
A trip is initiated if:
Xo < WOL < Xr
Ro <R< Rr+woL"cOt4L1
4.10
4.11
where OL1 is the angle of the line's positive phase
sequense impedance. The directional stability is achieved
by satisfying the following condition:
XMA < woLM 4.12
where LM is the directional inductance. More details
58
about the directional element are given in Section 4.4.2.
Multiplying Equation 4.10 by D term and dividing by woT$
gives:
X0 DL Xr "D < (-) < "D 4.13
8-Tr, -Wo 8Ts 8-Ts-wo
multiplying Equation 4.11 by D gives:
DL Ro"D < (DR) < Rr"D+8"Ts-wo"(S )"COtOL1 4.14
To solve relationship 4.13 and 4.14 the term D,
DL/8Ts and DR are obtained directly from expressions (see
Chapter 3)
D=ik_4"i'k-10 - irk-4'ik-10 4.15
DR=vk_4"i'k-10 - Vk-10'ik-4 4.16
DL=Vk_10'lk-4 - Vk-4'ik-10 4.17
where: irk-4=ik - ik-8 4.18
irk-10°ik-6 -ik-14 4.19
It is apparent from above analysis that the digital
division process which is uneconomical and time consuming
has been eliminated from the relay boundary comparison.
Relationships 4.13 and 4.14 can be simplified in the form
of Equations 4.20 and 4.21.
DL Kgo. D <()< KXr"D 4.20
s
DL Ro"D < (DR) < Rr"D+KRr"( ) 4.21
8Ts
where the constants Kgo, KXr and KRO are given by:
59
Xo XXo- 4.22
8'Ts'Wo
Xr KXr=-- 4.23
8-Ts'Wo
KRr=8"Ts"wo"cotOL1 4.24
4.4.2-directional reactance XM
A distance protection relay must maintain consistency
of performance for faults within the protected zone.
However, the constraints of Equations 4.20 and 4.21 cause
unwanted operaton for reverse faults (faults behind the
relay). This is more important when the line is
compensated by series capacitors and the capacitor is
situated adjacent to the relay location (at each end). In
order to make the relay truly directional, the principle
of directional reactance XM must be implemented.
The relay designer is faced with 3 main options for
polarising signals:
(i) self (faulted voltage) polarising
(ii) memory voltage polarising
(iii) sound phase voltage polarising
Within a distance relay the function of the polarising
signal is to act as the phase reference signal. The
optimum polarising signal is one that maintains its
vectorial position regardless of what system parameters,
type of fault, fault location or fault resistance occurs
[50]. A thorough investigation is needed for choosing the
suitable polarising signal in XM calculations for series
capacitor compensated lines.
60
However, experience has shown that the use of memory
to store pre-fault voltage signal is normally adequate in
maintaining the directional stability of the relay.
The directional reactance measurement uses the delayed
samples of the voltage in conjunction with the undelayed
samples of the current component. This can be implemented
by using a voltage memory bank, to hold the pre-fault
samples of the voltage signals. Within the simulation a
memory of 5 power frequency cycles is used in the
directional reactance calculation.
The directional reactance XM is compared with the
directional reactance value XMA, and hence an additional
constraint is added to that of Equations 4.20 and 4.21 as
follows:
XMA < woLM 4.12 or
XM LMD "D < 4.25
8"Ts-wo 8T9
Equation 4.25 can be written as:
LMD KM"D < 4.26
8T6
where:
XMA KM= 4.27
8'Ts"wo
LID is directly obtained from expression:
LMD=Vk-6-N'ik-4 - Vk-N'ik-10 4.28
N corresponds to the delayed samples which in this
case is equal to 400 at 80 samples per cycle (50 Hz system
61
frequency). Figures 4.21 and 4.22 illustrate the
measured XM and X for reverse (at sending end busbar) and
forward (30% of the line length) faults respectively.
4.4.3-relay characteristic
In general, the shape of the quadrilateral
characteristics of the relay for protecting series
compensated lines are similar to the conventional
characteristic shown in Figure 4.20. However, there are
some practical considerations regarding the boundary
settings of the relay when applied to series capacitor
compensated lines [13,49] which will be discussed in the
appropriate chapters. Also, a new boundary characteristic
will be proposed for a system with the series capacitor
location in the middle of the line which will be explained
later.
4.4.4-decision logic
The measured impedance is compared with the pre-
determined characteristic of impedance which specifies a
zone in the impedance plane. The tripping criterion,
which is based on single impedance estimate can lead to
the degeradation in protection integrity because, in
practice, a significant fluctuation in impedance estimates
occurs after fault inception. Algorithm simulation shows
that a fault just beyond the relay reach can cause
impedance estimates falling within the relay
characteristic boundary [51]. The impedance transients
can be illustrated for voltage maximum faults, where the
relaying voltage signals are severly contaminated by
travelling wave harmonics, and voltage minimum faults
62
where the impedance estimates show a downward transient
droop.
The relay decision making process must be able to cope
with:
(i) long line transient effects: those travelling wave
components which are not sufficiently attenuated by
the pre-filters, cause a high frequency oscillations
on the final measured reactance and resistance.
(ii) the sub-synchronous oscillation which causes the
measurands to oscillate at a low frequency about the
dc values.
These phenomena are most critical when the faults are
around the boundary of the relay. For close up faults
(faults well inside the relay characteristic) the relay is
required to be fast because the damages caused by high
fault current are severe, and also the stability of the
integrated power system may be jeopardized. On the other
hand, for boundary faults (faults near the forward reach
of the relay) the relay must be accurate in deciding
whether the fault is inside or outside of the protected
zone. The speed of operation for such faults is the
second priority.
The foregoing principles are the main philosophy
behind the design of the decision logic for the digital
distance relay.
The relay trip mechanism comprises a main trip
counter, TC, which up-counts when any calculated impedance
sample falls within the characteristic and down-counts if
a sample is outside the relay boundary, and a trip level,
TL, which if the TC reaches that value the trip is
63
initiated [46,51].
The relay characteristic is divided into fast and slow
counting regions which in turn allows more time for the
relay to reach a trip decision for faults near the
boundary and at the same time produce fast operation for
close up faults. A typical characteristic with divided
counting zones is shown in Figure 4.23.
The trip decision making process starts by detecting
the disturbance. The fault detection is performed by
monitoring the measured DX and DR and determining when
they traverse a preset boundary that is larger than the
relay characteristic. The constraints applied for these
purposes are:
DL 1.2"KXo"D <()<1.2"Kgr"D 4.29
8To
DL 1.5"Ro"D < DR < 1.2"(Rr"D+KRr( )) 4.30
8Ts
When the relay detects a disturbance, the process of
decision making is started. The process can be generally
summarized as follows:
The Trip Level, TL, is set at 256. This means that
when the Trip-Counter, TC, reaches this value a trip is
initiated. The incremental values for top of the
characteristic are initially set at pre-set values. When
a fault is detected, a control counter CRL1 is
continuously incremented by 1. The Trip-Counter is kept
at zero for 4 msec (16 samples at fs=4 kHz) after the
fault detection (CRL1=16) even if the measured impedance
moves inside the boundary. This precaution is taken due
64
to uncertainty during the group delay of the pre-filters.
At the first up-count by the Trip-Counter the second
Control-Counter, CRL2, starts which is responsible for
resetting the counter and changing the incremental values
of the relay characteristic.
When CRL2 reaches a preset value and no trip has
occurred the counter will be reset to zero and the
incremental values of the top of the characteristic are
changed to a lower value. This ensures that for a close
up fault, where the measured impedance falls within the
fast counting region of the characteristic, the relay
response is very fast, whereas by resetting TC and
changing the incremental values at the top of
characteristic, more time is allowed for the relay to
reach a decision.
If CRL2 reaches the second preset value and still no
trip is initiated, the relay considers the fault as very
close to the boundary. Therefore it slows the counter by
changing the incremental values to even smaller values.
If a trip does not occur and CRL2 is greater than 10
and the Trip-Counter becomes zero for one msec(4 samples)
the relay considers this as an out of zone fault and
resets both Control-Counters, CRL1 and CRL2. The
incremental values are also reset to their initial values.
4.4.5-invoking the Recursive Averager
The Recursive Averager is applied when CRL1=16 (4 msec
after fault detection). This means that from the fault
instant to this time all filtering is done by the pre-
filters. However, because the main duty of the Recursive
Averager is to attenuate the sub-synchronous frequency on
65
the measurands, especially when it most affects the trip
decision process, i. e. around the reach point, it is
decided to introduce a mechanism so as to enable it to
change the averager nature to recursive when it is most
needed (for faults around the boundary). This is
performed by:
(i) when the filter is invoked (CRL1=16), it acts as'än
ordinary non-recursive averaging filter with 12
points in the impulse response.
(ii) at the same time, the relay checks whether the
reactance samples in the averager buffer (memory)
are within two boundaries around the forward
reactance reach of the relay, specified by AVLL and
AVLU.
(iii) if at least 8 reactance samples are not within these
limits, then the averager continues to act as a non-
recursive averaging filter, attenuating high
frequency components on the dc values (see Figure
4.19 for frequency response), i. e. the filter output
is not placed in the filter buffer (switch S remains
in SN position. see Figure 4.18).
On the other hand, each time at least 8 samples in
the buffer are within the specified boundary then
switch S changes position from SN to SR and hence
averager output is placed into the buffer. Hence
the filter acts as a recursive averager.
Values of 0.7"Xr and 2.0"Xr (Xr is the forward
reactance reach of the relay) are recommended for AVLL and
AVLU respectively.
The mechanism explained above, ensures that, if the
66
measurands are badly affected by the high frequency
oscillations caused by the travelling waves, the filter
acts as a non-recursive averager with a finite and short
impulse response (3 msec at fs=4 kHz). In such situations
the sub-synchronous oscillation may not be a problem. The
relay count regime will cope with the high frequency
oscillation on the measurands.
On the other hand, if the dominant oscillation on the
measured values are the sub-synchronous oscillation, then
the filter is changed to the Recursive Averaging filter.
By setting the lower limit (AVLL) closer to the
boundary than the upper limit (AVLU), it is ensured that
when the filter is changed to a recursive averager, the
initial averaged samples are in the slow-
counting/negative-counting region of the characteristic.
Hence relatively long transition of the measured reactance
(due to bad initial averaged values and relatively long
impulse response of the Recursive Averager) inside the
boundary is avoided. Figure 4.24 shows the flow chart for
the averager logic.
Figure 4.25. a shows the measured reactance for a fault
at 60% of the line length and assumed forward reach of 60%
of the line length and inception angle of 900, without
averaging filter and Figure 4.25. b illustrates the
measured reactance when the filter is applied. It is
clearly evident that without the Recursive Averager, the
relay may maloperate due to long incursion of the measured
reactance into the boundary. On the other hand, when the
filter is applied the incursion is reduced and confined to
the slow counting region of the characteristic.
67
6.85 m
:,..
Fig. 4.1 - Line construction
X10-2
(dB)
0
-10 -15 -20 -25 -30 -35
a, In c 0 CL o,
a, a
CL E
C
Fig 4.2. a-Impulse Response of the C. V. T. Used in the Simulation.
LOG MAGN RESPONSE x1o-1 12 1(ý ÖL
MAGN RESPONSE
0 10 20 30 40 50 (Norm Freq F/FS)X10-2
Fig 4.2. b-Frequency Response of the C. V. T. Used in the Simulation.
Note that fS=8 kHz.
Time ( sec) X10'3
0 10 20 30 40 50 (Norm Freq F/Fs)X10-2
is ib iý
I CALCULATE In
is ib ic in
RELAY CURRENT TRANSDUCER
4
ANTI -ALIASING FILTER
7
(\v3 TIME DECIMATION
(V) ANALOGUE CLIPPING
ANALOGUE TO (VI) DIGITAL CONY.
PRE-FILTER
IMPEDANCE MEASUREMENT
PROTECTION ALGORITHMS
RELAY TRIP OUTPUT
Va vb vc
RELAY VOLTAGE TRANSDUCER
3
8kHz sampling frequency
4kHz sampling frequency
Figure 4.3 Schematic Diagram of relay simulation
(i)
Note that the relaying signals (voltages & currents) are supplied to the relay after voltage and current transducers.
10 kA
82.5 kQ
1.5 pF
15 pF
FIG 4.4. a-Analogue filter circuit
2 0
-2 -4 M
"° -6 Z -8 ¢-10 m-12
-14 -16
0 -10
v-15 cm20
. u-25 -30
w-35 -J-40 z-45 <-50
C
LQG MAGN RESPONSE
PHASE RESPONSE X10-? MPULSE RESPONSE io 35 30 25 20 15 10 5
0 nc
No OF PAINTS
10 9 8 7
z6 5 4 3 2
Xt11 0-1 MAGN RESPONSE
01, º FO 0 10 20 30 40 X102
FREQUENCY <Hz)
Fig 4.4. b-Response of the Analogue Filter.
X102 FREQUENCY <Hz)
10 20 30 40
X102 FREQUENCY (Hz)
m D-1 v
Z-1
<-2 tD
_2 -3
X10' 10
r. 8 c6 a, 4 rn 2 °i 0- %_o -2 W -4 Z
-8 x-10 (
Inr MA(N P PnNSF
PHASE RESPONSE
X10-1 11 10 9 8 7
z6 5 4 3 2 1
MAGN RESPONSE
00 10 20 30 X102
FREQUENCY (Hz)
Ir1PULSE_RESPONSE 2
20 18 16 14 12 10 8 6 4 2 0
No OF POINTS
40
Fig 4.4. c-Total Response of Two Analogue Filters in Cascade.
X102 FREQUENCY (Hz)
10 20 30 40 X102
FREQUENCY (Hz)
X103
d a,
J C O
N -, 4 .0 G d
O
2
Fig 4.5. a-The Relaying Components of Voltage. a: the original signal b: delayed signal
X102 lie;
J
C O
3 d bi , M
4)
C d- 3
2
Fig 4.5. b-The Relaying Components of Currents. a: the original signal b: delayed signal
SE SCL=5 GVA. RE SCL=35 GVA, NO LOAD, FAULT INCEPTION ANGLE=90', LINE LENGTH=300 k., 70% SERIES COMPENSATION.
Time C , sec) X10"'2
Time ( sec) X10'2
, Li LZ
.y
iý k
ýý
, -% y
FIG 4.6- Bewley lattice diagram for a simple system
4-, mt. t-I Ll
F------------ H
F-------------H ZggýX /2 aZL1
r-,
ZSSN
aZLN
FIG 4.7-Equivalent circuit for an "a" phase- earth fault.
where:
ZSSN=1/3(ZSSO-ZSS1)
ZLN=1/3(ZLO-ZL1)
X101
N I
9
a.
L LL
U ä
N
N V
d u C d
d
Fig 4.8-Expected Sub-Synchronous Frequency VS Fault Position for 70% Series Compensation (35% at each end).
LINE LENGTH=300 km SE SCL (GVA) a=50. b=35, c=20, d=5, "=2.5, f=1.0
Fault Position (% Line length) X101
4n
N S v
Q a' L
LL
L U C
N
.0 3 N v N U C
C 0 W a tY
Fig 4.9-Expected Sub-Synchronous Frequency VS Fault Position for 50% Series Compensation at Mid-Point of the Line.
LINE LENGTH=300 km SE SCL (GVA) s=50, b=35, c=20, d=5, "=2.5, f=1.0
Not" that before the capacitor location, the capacitance present in the circuit is assumed to be infinite which results in zero Sub- Synchronous frequency.
Fault Position ( Line length) X101
X1101LOG MAGN RESPONSE 01 707 r
n
z -7
_c -1C -11 -12
xio2 FREQUENCY (Hz)
X101 PHASE RESPONSE 10 8
tA 6 L CA 2
o ý" -2 W -4 -j -6 Lo z -8 <-10
048 12 16 20 x102
FREQUENCY (Hz)
Fig 4.10-The Response of (differentiator).
X10-1 MAGN RESPONSE 30
z
I
X102 FREQUENCY (Hz)
X10-IMPULSE RESPONSE I1
=1ý No OF POINTS
9 Point Filter
0
InG MAN RESPONSE
n- m- -U- - v-
z- H-
(D
io 9 8 7
z6
3 2
X1tO-' MAGN RESPONSE
01 vv NJ !0048 12 16 20
X102 FREQUENCY (Hz)
X1101 PHASE RESPONSE
."8 6
rn 2 a s0 10
-Li
048 12 16 20 X102
FREQUENCY (Hz)
X10-ýpULSE RESPONSE 2 20 18 16 14 12 10
B 6 4 2 0.
--- 0 15 30 45 60 X10-1
No OF POINTS
Fig 4.11-The Response of 6 Point Low-Pass Filter.
X102 FREQUENCY (Hz)
xi I 01LOG MAGN RESPONSE
0 _1 _2 -3 °D -4 ý° -5 -6 -7 ~'
9 -10 -11 -12 48 12 16 20
X102 FREQUENCY (Hz)
X101 PHASE RESPONSE 10
r" 8 6
L2 N0
2 W -4 --1 -6 Z -$ <-10
X10-1 MAGN RESPONSE 26 24 22
18
X12
6 4 2 0 048 12 16
X102 FREQUENCY (Hz)
X10-PULSE RESPONSE 30 25 20 15 10 5
-5 -10 -15 -20 -25 301
%Eý
048 12 048 12 16 20 X102
FREQUENCY (Hz) No OF POINTS
Fig 4.12-The Response of the Digital Pre- Filter.
0
16
t
X101
1.
eN - m
v
C rn
-1
1
2
3
4
6-
7-
B
3
Frequency (Hz) X102 o
Fig 4.13-Overall Response of the Digital and Analogue Pre-Filter.
Fig 4.14-Schematic Diagram for Recursive Averager (Equation 4.9).
............................................................
ZM-1
.........................................................
LOG MAGN RESPONSE
Zr 1 CD
--1 -1
2 4 6 8 0 2 4 6 048 12 16 2
X102 FREQUENCY (Hz)
5 ,. 0
-5 a, -10 L-15 ßa, -20 D-25 "-30 W-35
-40 Z-45
-50
PHASE RESPONSE
0
ýo
X110-1 MAGN RESPONSE
z
cý
X102 FREQUENCY (Hz)
X10-ýpULSE RESPONSE 26 24 22 20 18 16 14 12 10 8 6 4 2 0
V
Fig 4.15. a-Response of the Recursive Averager for M=4.
X102 FREQUENCY (Hz)
48 12 16 20
xi 01 No OF POINTS
0 -2 -4
� -6 m -8
-10 -12
14 <-16 a-18
-20 -22 C
5 0
LA -5 ao-10 0-15 L-20 0-25 v-30
-35 J-45 CD-50 Z-55
-
LOG MAGN RESPONSE
PHASE RESPONSE
ýo
X10-1 MAGN RESPONSE 10 9
7
Z6 5 C4
3 2
0 048 12 16 20
X102 FREQUENCY CHzS
X10-ýpULSE RESPONSE 13 12
10 s 8 7 6 s 4 3 2
aý Q4s 12 16 2
Fig 4.15. b-Response of the Recursive Averager for M=8.
91 8 12 16 20 X102
FREQUENCY (Hz)
xio2 FREQUENCY (Hz)
X101 No OF POINTS
0 -2
_8 a-10 "-12 z-14 "-l 6
- 18 -20 -22 -24
LOG MAGN RESPONSE
o48 12 16 20
xio2 FREQUENCY (Hz)
X101 PHASE RESPONSE
0V -1
L -2 -3
" -4 L9 -5 Z < -7 nda 9'? 7c
xio2 FREQUENCY (Hz)
in
X110-1 MAGN RESPONSE
9 8 7
Z6 "5 L4
3 2 1L 0
nA0 17 Ic
X102 FREQUENCY (Hz)
X10IIaPULSE RESPONSE 4
0
Fig 4.15.0-Response of the Recursive Averager for M=12.
x101 No OF POINTS
0 LOG MAGN RESPONSE
-5 m-10 i7
z -20
LO-25
-30
X102 FREQUENCY (Hz)
X101 PHASE RESPONSE
p. IA N-
L 01 N-
J
(D Z
0 vv-., z 1
2 3 4 5 6 7 048 12 16 2
x102 FREQUENCY (Hz)
0
0
X10-1 MAGN RESPONSE 10 9 8 7
Z6 45
3 2
C
X102 FREQUENCY (Hz)
X10I1°II'ULSE RESPONSE 7 6
5
A
4
C
0
Fig 4.15. d-Response of the Recursive Averager for M=16.
xi 01 No OF POINTS
0 a L d
i O U a, 44
v x
'O d L
U'
a
8
Fig 4.16-Measured Reactance without the Recursive Averager.
2
1
1 0
«ti
V
V
x L
Qº
8
Fig 4.17-Measured Reactance with the Recursive Averager (M=12) when Applied Continuously.
SE SCL-StVA, RE SCL. 35 GVA, LINE LENGTH=300 km.
Time ( sec) X10'2
Time ( sec) X10-2
Fig 4.18-Schematic Diagram for switched Recursive Averager.
ZM-1
X1O1LOG MAGN RESPONSE
-2
m 'v -6
z -8
m-10
-121 1 048 12 16
xio2 FREQUENCY (Hz)
XX101 PHASE RESPONSE X1101
8 6
CD It rn 2
13 0 v -2 W -4 -J -6 z
-8 <-10 048 12 16
X102 FREQUENCY (Hz)
o
0
X110-1 MAGN RESPONSE
z 1-4
CD
B 7
5 4 3 2 1 D 0
X102 FREQUENCY (Hz)
X10IýPULSE RESPONSE 9 8 13
7 6 5 4 3 2
C
No OF POINTS
lo
Fig 4.19-The Response of the 12 point Non- Recursive Averager.
50 ItY
4C
3° ., L4 3C E o 2!
a 2C U cs 1V -fj d IC a,
C
_ý
-101 10
Solid fault line impedance locus for plain feeder
-5 Ua Iu I3 zu
Resistance (ohms) 43 30
Fig 4.20-Quadrilateral Characteristic for Plain Feeder.
5
O IA E t 0
_c T L d c-1C 0 u at
x maw-2C L 3 tA
wý2Z
-3C
XM
11 1 2 13 14 15 16 17 18 19 20 2 Time (. sec) X10-2
I
Fig 4.21-Measured XM and X for a Reverse Fault at Bus-Bar
is IA
IA E0
L ic
ä V CE 0 U a,
E X
0 L
2 tol d (it
-2
xM
If 1 2 13 Ii 15 16 17 18 19 20 2 Time ( sec) X10-2
Fig 4.22-Measured XM and X for a Forward Fault at 30% of Line Length.
SE SCL. 126VA, RE SCL-27 GVA. LINE LENGTH-300 km. 70% Series Compensation.
50
15
40
35
30
25
20
15
10
5
0
-5
Ui E
0
N u C a u d w
-101- -10 -5 05 10 15 20 25 30
Resistance (ohms)
Fig 4.23-Typical Relay Boundary with Different Counting Regions.
Solid fault line impedance locus for plain feeder
-- - ------- DEC2
-L ~ DEC1
X INC1
_
- INC2
- I
DEC2
INC3
Rol
rl Xo
IS NO
CRLI>24
YES
START AVERAGING BY CHANGING
SWITCH 'SM' POSITION FROM
SMO TO SMC
CHECK
THE REACTANCE BUFFER.
ARE AT LEAST 8 MEASURED X BETWEEN NO
AVLL & AVLU
(AVLL <X< AVLU)
PLACE THE AVERAGER O/P
INTO THE BUFFER. i. e. CHANGE
SWITCH'S' POSITION FROM
SN TO SR
Fig 4.24-Flow Chart for Applying the Recursive Averager.
20
tf
ö
a 1: L
Vis ÜE wE
X
d L U'
at
-E
Xr
jj I I
56789 10 11 12 13 14 15 16 1 ' '
Time ( sec) X10'2 7
Fig 4.25. a-Measured Reactance for a Boundary Fault (Fault at Forward Reach) without Invoking the Averager.
UI s 0
L d C 0 U Oi U'
v X
'U II L 3 IA cS a s
7
Fig 4.25. b-Measured Reactance for a Boundary Fault (Fault at Forward Reach) with Invoked Averager.
SE SCL-SGVA. RE SCLw35 GVA. LINE LENGTH. 300 km.
Time ( sec) X10'2
CHAPTER 5
EARTH FAULT COMPENSATION OF THE DIGITAL DISTANCE RELAY
The principle on which all distance relaying schemes
are based is that the impedance of the circuit between the
relaying point and the fault is proportional to the
distance between them (the impedance per unit length of
line is constant, hence the line impedance is proportional
to its length).
The distance relays are arranged to measure distance
in terms of the positive-sequence quantities for all types
of faults, assuming a fully transposed and balanced system
[52].
When an "a" phase to ground fault occurs on a
transmission system the phase-sequence components of
currents in the fault are equal (Il=I2=I0). This
relationship will also hold for the phase-sequence
components of currents in the line, when this constitutes
the sole path to the fault.
If, however, there are a number of paths to the fault,
as can occur when the system interconnects a number of
sources or when the system is multiple earthed, or when
both these conditions exist, the relationship I1=I2=IO no
longer holds for the line currents although it, of course,
still holds for the current in the fault.
Compensation methods are employed to make the relay
measure the positive phase sequence impedance of the fault
loop, which in turn makes it possible to specify a pre-
determined characteristic for the relay. An un-
compensated relay no longer measures a unique impedance
68
for any given fault position, the impedance seen by the
relay depending on the number of sources and the number of
earth neutrals available at the time. On the other hand
however, a compensated relay will, when applied to a plain
feeder, measure a unique impedance for any given fault
position regardless of source and neutral current return
paths (52].
The compensated methods which are used for earth fault
distance relays are (52,53,54]:
(i) Residual current compensation.
(ii) Sound phase current compensation.
Method (i) involves the addition of a fraction of the
residual (neutral) current to the phase currents and
method (ii) makes the use of, as the name implies, the
sound phase currents and addition to the faulted phase
current in order to make the relay measure a unique
impedance for any given fault position irrespective of the
system condition. The voltage signal used in both methods
is the phase to ground voltage.
In a plain uncompensated system the measured
impedances by the relay, when methods (i) and (ii) are
used, are given by:
(i)
Vsae Z= = aZL1
Isa+KcIres
where: Z=measured impedance
Vsae=phase voltage at relay point
Isa=faulted phase current at relay point
Ires=residual current
5.1
69
ZL1=total pps impedance of line
ZLO=total zps impedance of line
a=proportional fault position
Kc=conventional residual compensation factor
1 ZLO
_ -( 1-1 - 1) 5.2 3 ZL1
and (ii):
Vsae Z= = aZLS 5.3
Isa+Ks(Isb+Isc)
where:
Isb' Isc=sound phase currents (phase b and c)
Ks=the sound phase compensation factor
ZLM
_1 1 5.4 ZLS
Zj=mutual impedance of the line
=1/3(ZLO-ZL1)
ZLS=self impedance of the line
=1/3(ZLO+2ZL1)
Note that the compensation factors are assumed to be
real.
Errors in distance relay measurement when the above
compensation methods are used have been reported by
several authors [55,56]. It will be shown in this
chapter that, if any of the above methods, as they stand,
are used in distance protection of the series compensated
lines, there will be errors in the relay measurements of
the fault loop impedance, as long as the capacitors remain in the circuit.
70
In order to analyse the errors associated with
conventional current compensation, three general series
compensated line configurations are considered.
(i) 70% total series compensation where %35 is installed
at each end, with the voltage transducer located on
the bus-bar side of the series capacitor.
(ii) 70% total series compensation with 35% at each end
and the voltage transducer on the line side of the
series capacitor.
(iii) capacitor location at the mid-point of the line with
50% compensation.
5.1-System with 70% Compensation and the C. V. T. on the Bus-Bar Side of the Relay
Consider Figure 5.1 which shows a typical series
compensated line with 70% compensation (35% at each end).
The voltage signal for the relay is assumed to be taken
from the bus-bar side of the capacitor and sources are
represented by a simple generator.
5.1.1-residual current compensation
Appendix 5A shows that when an "a" phase-earth fault
occurs on a series capacitor compensated transmission line
and the conventional residual compensation factor is used,
the impedance measured by the relay is given by:
Vsae Isa Z= = aZL1 'J () Xc/2 5.5
Isa+KcIres Isa+KcIres
where: Xc=total capacitor reactance/phase
Kc=conventional residual compensation factor
=1( ZLO
I- 1) 3 ZL1
5.2
71
=0.774 (for the line under study)
Equation 5.5 shows that if the conventional residual
compensation factor, CRCF, is used the impedance measured
by the relay depends on the expression Isa/(Isa+KcIres)"
The response of the relay can be analysed by studying the
behaviour of the expression Isa/(Isa+KcIres) for different
system conditions.
Figures 5.2,5.3 and 5.4 illustrate the behaviour of
the expression Isa/(Isa+KcIres) with respect to the fault
position along the line and the receiving end bus-bar, for
pre-fault system load angles of -10', 0' and +10'
respectively. It must be noted that the load angles
represent the pre-fault phase angle between the sending
and receiving end voltages, the latter being the reference
voltage vector. Hence a negative phase angle represents
power being imported to the bus-bar and a positive load
angle implies an exporting power from the relaying
terminals.
It is clear from the Figures that the ratio varies
with the system source and pre-fault load situations.
Thus the measured impedance is affected.
Considering different system short circuit levels,
Figures 5.5. a, 5.5. b and 5.5. c show the measured
resistance versus pre-fault load angle for different fault
position. Figures 5.6. a, 5.6. b and 5.6. c illustrate the
corresponding measured reactance. It is clearly evident
that the measured impedance is affected by the system pre-
fault load. The source impedance affects the residual
current distribution which in turn affects the relay
72
measurement. The resistance measurement in particular is
affected more by the load current than is the reactance.
Figures 5.7. a, 5.7. b and 5.7. c illustrate the
variation in measured resistance with fault position, for
different load angles. Figures 5.8. a, 5.8. b and 5.8. c
show the corresponding measured reactance. Note that, if
the conventional residual compensation factor is used, a
distance relay may significantly under-reach if the
reactance reach is set at a value corresponding to the
equivalent fault loop reactance.
5.1.2-complex residual compensation factor
When calculating the residual compensation factor it
is common to assume that the zero and positive phase
sequence impedances of the protected line have the same
phase angle (LZLO°LZL1) " Therefore, the residual
compensation factor will be a real number.
However digital distance relays are particularly
suited to the implementation of a complex, rather than
real, residual compensation factor. Since samples of the
residual current are available at discrete instants of
time T=l/fs (where fs is the digital sampling frequency)
it is possible to effectively implement the phase shift
associated with the residual compensating factor LKc
(LZLOLZL1) by taking a sample n samples previous to any
measuring sample instant and multiplying it by the
magnitude of the compensation factor. For example, Kc is
calculated to be equal to approximately 0.782L-14.82'.
Thus, in a digital relay operating at a sampling frequency
of 4 kHz, on a power system having a nominal frequency of
50 Hz, one sample interval corresponds to a phase shift of
73
4.5'. A constraint is thus imposed on choosing the value
of n which, for the assumed sampling frequency (4 kHz) and
application illustrated, is equal to 3 which in turn
corresponds to -13.5°. For any particular relay and
application, the value of n that gives the closest
equivalent phase shift to the ideal value is used.
Figures 5.9. a, 5.9. b and 5.9. c show the measured
resistance versus fault position for different pre-fault
load. Figures 5.10. a, 5.10. b and 5.10. c illustrate the
corresponding measured reactance. It can be seen that
the variation in measured resistance and reactance with
respect to the system pre-fault load and source has been
reduced, but the relay still under-reaches.
The foregoing analysis illustrates that if
conventional residual compensation is used, the relay
measurement will not be accurate and the relay may
maloperate .
5.1.3-sound phase current compensation
Appendix 5B shows that if conventional sound phase
current compensation is used, the impedance measured by
the relay is given by:
Vsae Isa Z= = aZLS -] () Xc/2 5.6
Isa+Ks(Isb+Isc) Isa+Ks(Isb+Isc)
ZLN where: Ks=
ZLS
=0.442E-8.32' (for the line under study)
It is clear, from Equation 5.6 that, if conventional
sound phase current compensation is used the impedance
74
measured is affected by the expression
Isa/(Isa+Ks(Isb+Isc))"
Figures 5.11 and 5.12 show the measured resistance and
reactance respectively, when conventional sound phase
compensation is used. It can be seen that both measurands
are affected by the expression Isa/(Isa+Ks(Isb+Isc))" The
relay may significantly over-reach or under-reach due to
errors in reactance measurement which are caused mainly by
system source impedances. Pre-fault load current does
not, to any significant, affect the measurement. It must
be noted that for faults at the receiving end bus-bar
(beyond the remote end capacitor), the relay measures a
smaller reactance than the actual line reactance which
implies that the setting of the forward reactance reach is
even more restricted (see the next chapter).
The method which is commonly used in distance
protection schemes is residual compensation, and since
neither method has any advantage over the other when used
in series compensated lines, it was decided to use the
modified version of the residual current compensation.
This is described in the next section.
5.1.4-compensation of errors due to the residual current compensation factor
It was shown in Section 5.1.1 that if the conventional
residual compensation factor (CRCF) is used, the measured
impedance by the relay will not be accurate.
In order to ensure that the relay does not maloperate
and discriminates correctly between internal and external
faults, three methods may be considered:
(i) one may assume that the currents in the healthy
phases are much smaller than the faulted phase
75
current so that, for faults on phase "a", the
following relationships may be considered:
Isa"Isb and Isc
therefore: Isa'Ires
thus Equation 5.5 can be written as:
Vsae 1 Z= = aZL1 -j () Xc/2 5.7
Isa+KcIres 1+Kc
Hence the zone-i forward reactance reach can be set
at:
1 arXL1 -() Xc/2 5.8
1+Kc
where: XL1=total pps reactance of the line
ar=fault position for a fault at the zone-1
relay reach.
However it has been shown in Section 5.1.1 that the
expression Isa/(Isa+KcIres) cannot be considered as
a constant and varies with the system condition, and
that the measured impedance is not unique for a
given fault position.
(ii) to modify the residual compensation factor so that
the relay measures the equivalent fault loop
impedance, aZL1 -j Xc/2.
(iii) to modify the relaying signal so that the relay
measures the fault loop line impedance, aZL1"
5.1.5-modified residual compensation factor
Appendix 5C shows that in order to ensure that the
relay measures the equivalent pps impedance of the line
from the relay to fault point (for relay setting
76
purposes), the residual compensation factor must be set
according to the proportional fault position, a. The
measured impedance for a fault on the line is then given
by:
Vsae = aZLl-j Xc/2 5.9
Isa+K(a)'res
1 aZLO-7 Xc/2 where: K(a)= -( - 1) 5.10
3 aZL1-] Xc/2
and for a fault on the receiving end bus-bar:
Z= Vsae
= aZLI-j Xc 5.11 Isa+K(a)Ires
1 aZLO-j Xc where: K(a)= -( - 1) 5.12
3 aZL1-j Xc
This means that only if the fault position is known to
the relay will the measured value of impedance be
independant of source and pre-fault load current.
Figures 5.13. a and 5.13. b show the variation in
magnitude and argument of K(a) versus fault location for
the line under study. It must be noted that for a given
fault location and degree of series compensation, the
residual compensation factor is the same as that shown in
Figure 5.13. a and 5.13. b irrespective of the line length.
Also, it can be shown that the magnitude of K(a) has a
peak which always occurs at 35% of the line length.
It is clear that with the present generation of
digital equipment and Ultra-High-Speed operation in mind,
it is not possible to set the residual compensation factor
77
according to the fault position, since the location of the
fault is unknown to the relay.
Therefore it is proposed that the residual
compensation factor is set at a fixed value Kar, assuming
the fault position to be at the relay zone-1 reach
boundary, where the relay is required to be most accurate.
The procedure of calculating the residual compensation
factor is as follows:
1-decide about the relay zone-1 reach. Say it is set at
60% of line length.
2-look on graph of K(a) vs fault location, Figures 5.13. a
and 5.13. b, to find corresponding magnitude and argument
of K(a) for a=0.6.
Appendix 5D shows that the impedance seen by the
distance relay for faults on the line is then given by:
Vsae Isa+K(a)Ires Z= _ (aZLl-] Xc) 5.13
Isa+KarIres Isa+KarIres
where:
Kar=the residual compensation factor for fault at
the zone-1
1 arZLO-7Xc/2 Kar= (- 1) 5.14
3 arZLl-jXc/2
ar=proportional fault position for fault at the
relay zone-1 reach point.
Figures 5.14. a and 5.14. b illustrate the variation in
the magnitude and argument of the expression
(Isa+K(a)Ires)/(Isa+KarIres) with fault position for pre-
fault load angle of -10 degrees, for the relay zone-1
78
setting of 60% (ar=0.6). Figures 5.15. a, b and 5.16. a, b
show the corresponding graphs for pre-fault load angle of
0 and +10 degrees respectively.
It is clear that for a fault at the relay zone-1
boundary the expression has a magnitude of unity and
argument of zero (Isa+K(a)Ires)=(Isa+KarIres)r which
implies that the relay measurement is accurate at this
point only. It has been shown in Section 5.1.2 that a
complex residual compensation factor can be implemented in
a digital distance relay. It can be seen from Figure
5.13. a and b that, for a relay set with a forward reach of
60%, which in turn eliminates the possibility of
indiscrimination for faults beyond the remote capacitor
(see the next chapter), the new residual compensation
factor Kar is equal to approximately 1.82L-6.2'. A phase
shift of -4.5' (fs=4 kHz) is obtained by taking the first
previous sample of the residual current. Hence the
residual compensation factor which is used in the relay is
Kar=1.82L-4.5'.
Figure 5.17. a, b and c illustrate the variation in
measured resistance vs system pre-fault load for different
source configurations. Figures 5.18. a, b and c show the
corresponding reactance measurement. It is clear that the
measurement at the boundary (60%) are unaffected by the
pre-fault load. Furthermore variations in reactance
measurements with load for other fault positions,
especially those near the boundary, are minimal. This in
turn enables measuring accuracy to be maximised and avoids
both relay overreaching or underreaching.
Figures 19 and 20 show the measured resistance and
79
reactance vs fault position for different source short
circuit levels. The pps resistance and reactance of the
fault loop are also shown. Again the effect of the new
residual compensation factor NRCF on the measurement is
clear. In particular, note the constant and load
invariant measurement at the boundary (60%) for different
load currents. Note also that, the measured reactance for
faults at the receiving end bus-bar is larger than the
actual line reactance. This is due to the fact that the
relay is under-compensated (less current is given to the
relay, 1.82L-4.5' instead of 2.45L0.00), hence measuring a
larger value. This effect is one of the advantages of the
NRCF method since a bigger margin exists between the
measured reactance for receiving end faults and faults at
the relay forward reactance reach.
The modified residual compensation factor NRCF
provides a better representation of the primary system.
Figure 5.21. a shows the measured reactance when the
conventional residual compensation factor is used and
Figure 5.21. b when the NRCF is employed. It is clear that
the travelling wave effect and the sub-synchronous
oscillation have been greatly reduced.
5.1.6-modification of the relaying signal
It was shown in Section 5.1.1 that if the conventional
residual compensation factor is used, the measured
impedance is given by:
Vsae Isa Z= = aZL1 -J () Xc/2 5.5
Isa+KcIres Isa+KcIres
It is possible to modify the relaying voltage signal
80
so that the relay measures the fault loop line impedance,
aZL1"
If it is assumed that the capacitor's protective gaps do not operate and they remain in the circuit, the
relaying voltage Vsae can be compensated by adding a
component jIsaXc/2 to it, which in turn eliminates the
Isa term -j( )Xc/2 from the measured impedance.
Isa+KcIres
This method involves phase shifting the phase current
by 90' (represented by j) and multiplying it by the local
capacitor reactance which is known. The measured
impedance is then given by:
Vsae+]IsaXc/2 Vsae Isa Z= _+ j( )XC/2= aZL1
Isa+KcIres Isa+KcIres Isa+KcIres 5.15
Thus, the relay zone-1 forward reach can be set
according to the pps impedance of the line only, ignoring
the effect of the series capacitor.
It must be noted that the compensation signal jIsaXc/2
is obtained assuming the capacitor reactance at the system
frequency.
Figure 5.22. a, b and c illustrate the steady state
measurement of the resistance vs fault position for
different system pre-fault loading, when a complex Kc is
used. Figure 5.23. a, b and c show the corresponding
reactance measurement. It can be seen that the relay
measurenment, in particular the measured reactance is very
accurate for faults on the line.
However, the measurement for a fault at the receiving
end bus-bar is not accurate. This is due to the fact that
81
for such a fault two capacitors are in the circuit
(provided neither are by-passed by the gap flash over).
The measured impedance by the relay for this situation
is given by:
ysae+7IsaXc/2 Isa Z= = aZL1 - j( )Xc/2 5.16
Isa+KcIres Isa+KcIres
5.1.7-comments on the compensation methods explained in Section 5.1.5 and 5.1.6
The two methods explained earlier are meant to enhance
the accuracy of the digital distance relay measurement.
It has been shown that in the latter method the
measurement is accurate for all faults on the line up to
the remote end bus-bar, whereas the former method makes
the relay measurement accurate at only one point, the
zone-1 forward reach; for other faults the measurement may
be smaller or larger than the actual line impedance.
Figure 5.24. a shows the measured R and X when the NRCF
is used for a fault at 50% of the line length and fault
inception angle of 90'. Figure 5.24. b illustrates the
corresponding measurements when CRCF (complex) and voltage
compensation is used.
Figur 5.25 and 5.26 illustrate the corresponding
measurement for a fault position of 60% (assumed forward
reach) and fault inception angle of 90 and 0 degree.
It can be seen from these typical relay measurements
that the NRCF gives a better transient response and has an
inherent ability to reduce the travelling wave and sub-
synchronous oscillation for faults near the forward reach,
hence imposing less pressure on the relay decision logic
82
and the Recursive Averager (see Chapter 4).
Furthermore, as previously mentioned, in the voltage
compensation method the faulted phase current must be
phase shifted (displaced) by 900. The method adopted in
this study is to differentiate the current which in turn
introduces a 90' phase displacement. Due to the reasons
previously explained in Chapter 3, the differentiation is
carried out over 9 samples which introduces an extra delay
into the impedance measurement process. This is clearly
evident from Figures 5.24,5.25 and 5.26, where the relay
reaches the post-fault measurement faster, when the NRCF
is used.
Consider Figure 5.27 when the voltage transformer is
situated on the line side of the relay and the current
transformer on the bus-bar side of the relay. This is a
typical arrangment which effectively makes the local
capacitor part of the source.
Appendix 5E shows that the conventional residual
compensation factor, CRCF, must be used in the relay. The
measured impedance for faults on the line is given by:
Vsae Z= = aZL1
Isa+KcIres 5.17
If the fault position is on the receiving end bus-bar,
it is clear that the measurement is not accurate. The
measured impedance by the relay for a fault at the
receiving end bus-bar is given by Equation 5.5, Xc/2
being the remote end capacitor reactance.
83
Figures 5.28. a, b and c illustrate the measured
reactance versus fault position for different system
source and pre-fault load when a real residual
compensation factor is used (Kc=0.774). It is clearly
evident that the measurement varies with both the pre-
fault load and source, which affects the residual current
distribution in the system. The relay may, in this
situation, over-reach or under-reach.
Figures 5.29. a, b and c show the corresponding
measurement when a complex residual compensation factor is
used (Kc=0.78L-13.5'). The measured reactance is more
accurate and unaffected by the system condition.
5.3-System with 50% Compensation at the Mid-Point of the Line
Consider the system shown in Figure 5.30 with the
series capacitor situated at the mid-point. The
compensation at the mid-point may be less than 50% which
is considered to be less troublesome to the protection
gear. The mid-point compensation of more than 50% is
extremely rare.
Using a similar analysis as that given in Appendices
5E and 5A, for faults before and beyond the series
capacitor, it can be shown that, if the conventional
residual compensation factor is used, the impedance
measured by the relay for an as phase-ground fault,
before and after the series capacitor are given by:
Vsae Z= = aZL1
Isa+KcIres for a<0.5 5.18
84
Vsae Isa Z= = aZL1-j( )Xc for a>0.5 5.19
Isa+KcIres Isa+KcIres
where: Kc=conventional residual compensation factor
1 ZLO _(- 1)
3 ZL1 5.2
It is clear, from Equation 5.18 that for faults before
the mid-point of the line, the relay measurement is
accurate, whereas the relay measurement depends on and
varies with the expression Isa/(Isa+KcIres) when the fault
position is beyond the series capacitor. Figures 5.31,
5.32 and 5.33 illustrate the variation in magnitude and
argument of the expression Isa/(Isa+KcIres) versus fault
position for system pre-fault load angles of -100,0' and
+10' respectively. Note that for a fault position of less
than 50%, the expression has no effect on the measured
impedance (see Equation 5.18). However, it is clearly
evident that the current ratio varies with system pre-
fault load and source, thus affecting the measured
impedance for faults beyond the series capacitor.
Figures 5.34. a, 5.34. b and 5.34. c illustrate the
variation with fault position of the resistance, measured
for different load angles. Figures 5.35. a, 5.35. b and
5.35. c show the corresponding measured reactance. Note
that, if the conventional residual compensation factor is
used the relay measurement is accurate for faults before
the capacitor location. In particular, note the accurate
reactance measurement which does not vary with the system
source and pre-fault load. The d crepancy between the
measured resistance and the line locus for faults before
85
the capacitor location is due to the fact that the angle
of the residual compensation factor cannot be accurately
implemented in the relay (-13.5 instead of -14.82).
However, note that the impedance measurement, for a given
fault position beyond the capacitor location, varies with
the system source and pre-fault load.
In order to ensure that the relay measures the correct
value of pps impedance of the line from the relay to fault
point (for relay setting purposes) it has been shown that
in series compensated lines, the residual compensation
factor must be set according to the fault position a (see
Section 5.1.5). Considering a series compensated line
with 50% compensation at the middle of the line, it can be
shown that the impedance measured by the relay is given
by:
Vsae Z= = aZL1-JXce 5.20
Isa+K(a)'res
where: 1 aZLO-jXce
K(a)= (- 1) 5.21 3 aZL1-jXce
Xce=O for a<0.5
XCe=Xc for a>0.5
Figures 5.36. a and 5.36. b show the magnitude and
argument of K(a) versus fault position. It is evident
that K(a) stays at a constant value for fault positions of
less than 50% of the line length (capacitor location).
However note the variation in magnitude and argument of
K(a) with fault position, a, for faults beyond the series
86
capacitor.
It has been suggested in Section 5.1.5, that, since
the relay is required to be the most accurate at and
around the boundary, the residual compensation factor is
set at a fixed value Kar, assuming the fault position to
be at the relay zone-1 reach boundary. The measured
impedance by the relay is then given by (see Section
5.1.5):
Vsae Z= _
Isa+KarIres
where:
Isa+K(a)Ires
Isa+KarIres (aZL1-JXce) 5.22
Kar=the residual compensation factor for fault at
the zone-1
1 arZLO-7Xce Kar= (- 1) 5.23
3 arZL1-]Xce
Xce=O for a<0.5
XCe=Xc for a>0.5
If the relay independant zone-1 reach is considered to
be before the series capacitor, say at 45% of the line
length (ar=0.45) and a complex residual compensation
factor (assuming LZLOVLZL1) is considered in the relay,
the relay measures accurate impedances for all faults
before the mid-point of the line. But for faults beyond
the capacitor, the relay measurement will not be accurate.
If it is required to set the relay reach at a value
higher than 50%, then the relay measurement is accurate
only at the reach point. In this work it is decided to
set the relay zone-1 reach at 80% of the line length,
which is the common practice in plain uncompensated feeder
87
distance protection schemes. The required residual
compensation factor, for a boundary setting of 80%
(ar=0.8 )is, from Fig 5.36 .a and b, found to be
approximately equal to 2.015L-4.6°.
It is evident, from Equation 5.22 that the measured
impedance depends on and varies with the expression
(Isa+K(a)Ires)/(Isa+KarIres)" Figures 5.37,5.38 and 5.39
illustrate the variation in the current ratio with fault
position for pre-fault load angle of -10', 0' and +10'
respectively. It can be seen that the expression
(Isa+K(a)Ires)/(Isa+KarIres) has a magnitude of about 0.5
to 0.6 and an argument of between 0 to -10 degrees,
depending upon the system pre-fault load and source, for
faults before the capacitor location. If the current
ratio is considered in the form of a+jb, then the real and
imaginary part of the measured impedance for faults before
the capacitor is given by:
Z=(aaRL1-baXL1) + j(aaXL1+baRL1) 5.24
It can be seen that the dominant term in the reactive
component is aaXLl. For the system considered, a is very
close to the magnitude of the current ratio, i. e.
approximately 0.5 (since the argument is small), which
implies that the measured reactance is approximately half
the actual line reactance, for faults before the mid-
point of the line.
The expression (Isa+K(a)Ires)/(Isa+KarIres) has a
magnitude of unity and an argument of zero for a fault at
the relay zone-1 reach; which implies that the relay
measures the equivalent fault loop impedance, arZL1-7Xc"
88
Figure 5.40. a, b and c illustrate the variation in
measured resistance versus fault position for different
source configration and pre-fault load. Figures 5.41. a, b
and c show the corresponding reactance measurement. It is
clear that the measurements at the boundary (80%) are
unaffected by the pre-fault load.
Note that due to over-compensation of the relay
(2.015L-4.5' instead of 0.78L-14.820) the measured
reactance is smaller than the actual line reactance for
faults before the capacitor location. This is one of the
advantages of the new modified residual compensation
factor: when the the relay zone-1 reach is set at 80% of
the line length then faults before the capacitor are far
more likely to fall within the relay trip characteristic.
More will be said about this effect in the following
Chapters.
89
SE _jXc/2 Is
ZI
ZI
Vs M
_jXc/2 RE
d IEJ
VR
Fig 5.1-System Configuration with Source Side V. T.
X10-' 18,.. _
o1
L ºr U
d
r-ý
d H
º-I
(L 0
O; d
r. - ------------- " ..... ....... .
Fault Position (% oP line length) X10, I
Fig 5.2. a-Variation in Mag. Of Isa/(Isa+Kclres) VS Fault Position For Pre-Fault Load Angle of -iO Degrees
X101 1_
H L
r-+ U
+ -s d In
%d -4
d 84 -'9 U- D
01 < -E
-%
"r...
_ Iý11,1
Fault Position C% of Line length) X101
Fig 5.2. b-Variation in Arg. Of Isa/(Isa+KcIres) VS Fault Position For Pre-Fault Load Angle Of -10 Degrees
SE SCL-E OVA. RE SCL-315 OVA ----- SE SCL-35 OVA. RE SCL- OVA
.... SE SCL-10 OVA. RE SCL-10 OVA Line Length -300 km
xi 0-' 13
12r 1 ^I LA dI L 0-4 u
d
d N
as
C 0
= 2F
1
Fig 5.3. a-Variation in mag. Of Isa/(Isa+KcIres) Vs Fault Position For Pre-Fault Load Angle Of 0 Degrees
X101
L.
U
d N
d H
'-+
(1. O
O
I
Fig 5.3. b-Variation in Arg. Of Isa/(Isa+Kclres) VS Fault Position For Pre-Fault Load Angle Of 0 Degrees
SE SCL-15 GVA. RE SCL-3O GVA ---- SE SCL-35 GVA. RE SCL-O OVA .... SE SCL-10 QVA. RE SCL-10 OVA
Line Length -300 km
Fault Position (% of line length) X101
Fault Position (% of Line length) X101
X10'1 13 121
IA 4, L
8.4
u d
v
Ci. 0
d Z.
I
Fig 5.4. a-Variation in Mag. Of Iaa/(Isa+Kclrea) VS Fault Position For Pre-Fault Load Angle Of +10 Degrees
X101 4
H 0 L
º-I U
d tA
v
H
CL 0
Q1 L
1
Fig 5.4. b-Variation in Arg. Of Isa/(Isa+KcIres) VS Fault Position For Pre-Fault Load Angle Of +10 Degrees
SE SCL-O OVA. RE SCL-31S OVA ---- SE SCL-31S OVA. RE SCL- OVA .... SE SCL-10 OVA. RE SCL-10 OVA
Line Length -300 km
Fault Position (% of Line Length) X101
Fault Position (% of Line length) X101
-q Measured Resistance (secy. ohms) F' 1O -+N W-kLn0 V00W(8 NNW mN
" 'f (J1 n (D
1-1
(11 mr .4
U) 0 Po c r3
IA O K- 0 'D T //)
Cr
m
>Xr z
93 (n O
ro N n
O N O
O
01
O F-" tD
to ýr 5rt
0 (D G
Fi U1 CD 0) ýl rt P. º7 Oam
u P.
0 nCDm
CD 0
0 H- En
ow H CD
ýý CD rt En
r Cw as
Measured Resistance (secy. ohms) w
tn -v
Q
m r N0 t7 ä
1J N
ýo G) < vi
17 0 m '° N ob
r a
m G)
D
-n Measured Resistance (secy. ohms) No -ý N CJ -º (fl a) Vm lD o= IN
O
11 to QA
m
UI co
mrA N°1 nö
1: 3 2
V-
w 1O to C >n < >'m
z
o to
MÄ ro N
r
N
G) ö < D
0
-n Measured Reactance (secy. ohms)
to
N
0) -v
f 1p
r- C N
rn r ft.
N0 Q (7 a r> 43 N Om
G) ' << Dz
0 - rn M m n r P 0
ON O U1 Ö
N ÖC ý
N O
N
O
to
T L
V1
J
I
i i
0
A) A
N-
U,
0 P-0 b rt En
U) cn a ra 0 CD
Cl) hi 0 CD 0 fi 000 0<m
0 fi pq En 0
°äh
J CD
m rr ý'"r+ Ga° as
-q Measured Reac YY
F-' lo c
U O
Lq
I1 " 'f N ýÄ1
UI ö
m r N01 P n t" 4
UI `O
G7 c D cn
33 0 mI- O En tD
n r- oN L4 (A) K cn 0
D
C N N
ööm x
c
-q Measured Reactance (s rrrrrN
r to N
O UI
,91 "7 Uf
1m
r UI O
r No1 (7 ä cß
r 1 cu 'mo o [n m
DN
MÄO A
Nw n .. rN d UI Gö D
WN C` AN OD C3 o. ^ Q. ob be 030
,0 at
. ohms )
I
. ohms )
x
r_ z m r m z
s
r m
In
n
N m In n r I I-b
0 0 < D
m rn
n r I 0 C, < D
Measured Resistance (secy. ohms)
T P
'C O tA
Pý
0 1)
P"
iD 3
%0
v
O
:ý .ý ýý\ ýt ý :1 :_ :ý ., ;ýý ýý
ý
.ýý
;;. cý
-S
l"
rv'ovr 3 of "7 I1Io
iccca
o RttCC R
7rrr 1000 m" o oana 0 DDD x7a3 gone
/+ "M
+0 rr ono
ac a ". o 00
""
O P- (D b En
CD G Fi U1 cD
wa rt rr öýCD
N En ri-
Oen CD CD 0 ft o r"cn
11 O
0'i
vr fi
tic tD 0
wo rG
m
N
J
m
UI m N n r I UI 0
m U, n r I to C)
D
F+.
ü
N m N 0 r I U cn 0
m m N n r
0
a
Mea juc eed (Resistance (secy. ohms)
et-wfomý. ýºN0P.
34 0)m0P. 3-
Ii P
C4'
O H H c+ O
I'
0
w
ID
0
10ý« 7
X
O
r
Measured Resistance (secy. ohms)
T Q C r-
O
w
O
O
e- p. ob
r
J
'n
to En
in m In n r 0
0
D
m m U) 0 r I N 0
G)
D
Measured Reactance (secy. ohms)
P C
0 0 In
W 0 3
0
W
t"
X J Q
J
ftj N-
co
I ý. fte Iý
ruur cn n r '7 '7 r Q) CD
ööm ° `D po r r CD mccca It
rr ft m ä t)A
? rrr 00w 1oaa ft öä1,0 2
ää n<o a - DDD 0 7777
l rt, 3Io a +º13 0 U]
mmm ýý 0 +0 1 :j Iýd
p) .W aCL a
m nm a rt m"m 13 a mÖ
P. W
art 0 P. 00 N0
to
U1
N
N m U, 0 r I N
G)
D
71 m U, n r II w (n
D
ID
UI
in m U) n r I La cn 0
m m N C7 r cn L)
D
Measured Reactance (secy. ohms)
11 p C
c+
0
w C.
O
O
0. - Z O
r CD
x_ 0
Measured Reactance (sectA. ohms)
a c
c..
0 N r" c+. 0
\'
0 1)
sue.
ID
r- ID 7
In c"
X
0
..
-n Measured Resistance (secy. ohms) w m
to
to " .n Ic
UI -o rn
nö r3 O
r- ý D
I m
nx rd 1-
O
U,
O P" (D rr a
f f: ý f: f Nrtý
rt Miä7M
I n C a miI
:u 0 0 CD sau' r 9r .CCC0
rrK onC mit it a 0 x ;D
rt 3rrr 0 n ýiii n
O oCL CL IL 0 %
32 m x3 n
En genic ! +N r
s"e it
or' ft P. j + IV 0 v oý G D: O
r rP
a0 a 0. ö wý7ºti
(D O un cm to
P, Or 0 wo N0
Measured Resistance (secy. ohms) V lD
LB
to
P
ýc r m rn o Vk Ic w
r u UI
0 < D
7 rn rn N rx Go w N
0
-n Measured Resistance (secy. ohms)
U2
U1
to QP 1" r
c;
N -D
U] C r° 1 .. W ý. Ü] °
+n r
DÄ "r
-n M N" n r 1- U] C)
ýO ý" l
"\ t ýý
ýý
Ný
i Wý
.i ý ".
W t;
" i `
co i Ä
,
0
"n
to
LD
1.21 0
f)
In
m N n r i 0 0 < D
m
n r I IA 0 Gl
D
Measured Reactance (secy. ohms)
T P C
C'.
-U 0 IA w C.
O
0 1,
W
ID
I- ID
io
N-
Ui
0 nE ý O P" CD 5 rr a
i ý" m I '" En :: r (D ä CD ä r-a v-a r rt
0o 00 m OO CD
'AI _I :j El 0 r r CC Tý n mc Ö Ct Ki n a
it C
2rrr ön wvo5 oaaa C
DDD xCD cn sane rn (1 fti º+rr 0 F,.
"O +0 -4 ý3 1 -4 0) rr ö ö Iý r ýýro W CD 0
En En cn N" N- "arr
a0
'n F+ ID
Ln
0
N m N Cl r u
n
n r a t) tn G)
D
w U3
In
N O
Cr) m In r w
G) D
m rn N n r 9 In
Measured Reactance (secy. ohms)
11 P C 4- c+
O I" 4- c'"
O
O 0
r.
9D
e- CD
C'
v
x 0
Measured Reactance (secy. ohms)
T P C r C.
O
w
w 0
.\ 0
N
f
10
x 0
C < D
Measured gesistance (secy. ohms)
V
l0
Ln
-n p
nr
N
rn b 4 wö n3 r ,. I F0
0 1) G) <
ý c" rn ý N t7 0 r -a 1A 0 G) D
pi N- W
f-ri
r-ov -nr mmm7
it 1I1m qII
rmoor mccco 7Nf+F+o
ft rrft c
:r rrr 1000 wmmm onaa 0 DDD 70777 3micm
F+rN mmm 111
1 +0 I-º tº oao
m nm a m" m mm
O N" CD w tit
m H
uý m wrta ft 0 (D
ro zn 0rr 0
öb C) Mm
XC
. I-. ýý ct Na ý ro "c 0
ow °w
ýo cn a
Measured Resistance (secy. ohms)
t0
In
p Ol
c«
(A 0
M" w C"
N
n r a U) O
T) Gi r D
rn
nX r p Ld U)
0
D
Measured Resistance (secy. ohms) r l0
N H
-n rP C
(n 'o m
o` n3
o T)
Q
> 'm
fD Q M
n r D In a
i NON- 07 ON -> Q) 0)
w 1\ .\ 1\
\
\ %\ It
I
\\
to `.
0
�a
r t0
N
Ti -p I-
-D (p o mw
0 ri 3 F J% dx Fý 0
o -') 0- G
D r. m 3
c
m N
C) 0 r -- I
0
Measured Reactance (secy. ohms)
w
4F
01
0 ..
N-
Ln
II'' I ý.
r-u -a v -a r v'7 77r 7AAA7 mIIIm
"n I "q rop mmr Accca 7iI, o aft ft ft C "r m 7rrr t 00 n Wamm oaaa 0
DDD X: 3 ]7 gin on
Amm III +0 1 rP 0a
O P" CD ä rh CD G fi cn m ID
ö(Dýa GO
ö ö 'd, m
xc cn
0 (n hi "O Närt
ro 00
En
NO (D 0
71 Measured Reactance (secy. ohms)
l0
LA
Rl -n p
1 c' 0
m r.
N 0 r .. Ü1 p
0
D
ro
m Ul
r a -ý cI) to
0
rL
:ý ". e
" ̀ .
ý: ý
0
Measured Reactance (secy. ohms) t to
UI
N m QQ
1C C.
N rn °
W
na r U Ln o
<
D ro r ro
J
n r a
x C
V-
cs x
0 rn d
Fig 5.13. a-Variation in Mag. Of K(a) with Fault Position
X101 Is- I
l ci
Y CL O
Ol L
Fig 5.13. b-Variation in Arg. Of K (a) with Fault Position
Fault Position (: oP line Length) X101
Fault Position (% oP Line length) X10,
10-1 v L
H
L d
d
r. +
d L
v
d
H
V
CL
0
Q
30 28 26 24 i' 22- 20- Is- 16- 14- 12- 10 , rrr, +, 8 .. ". 6 4 2
I0123456789 10
Fault Position (% of line length) X101
Fig 5.14. a-Variation in Meg. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of -iO Degrees
ýxIo1 NI L
L
Ic d W
n N N L
v
d H v
U O
L
7
1 6 1
1
-1 '
. rrrr7.; --
1
Ö1234567B9 10 1 FauLt Position (% of Line Length) X10'
Fig 5.14. b-Variation in Arg. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of -10 Degrees
SE SCL- GVA, RE SCL-35 GVA
---- SE SCL-35 GVA. RE SCL-ö GVA SE SCL-30 GVA. RE SCL-10 GVA Line Length -300 km
.. .m W
L
L
v
IA n. 4 v
n IA as L
d v
d N
h+ v U- 0
a'
vv
28- 26- 24- 22- 20-
6
12- 14
6+
10-
4" ýýrrrrrr.
rr 2-
0 0123456789 10 1
Fault Position (% oP Line Length) X101
Fig 5. i5. a-Variation in Mag. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of 0 Degrees
X101 a, 14_ i
H L 12-
10-
vl 8 .r
6 a,
%. 01
d
cs 2
N0 r. 0 0
at o i
Fig 5.15. b-Variation in Arg. Of (Isa+K (a) Ires) / (Isa+K (er) Ires) with
Fault Position For Pre-Fault Load Angle of 0 Degrees
SE SCL-S OVA. RE SCL-35 OVA ---- SE SCL-35 OVA. RE SCL-5 OVA
... SE SCL-iO OVA. RE SCL-10" OVA Line Length -300 km
Fault Position (% of line length) X101
1o-' Oi L
.r
L d
d
N d L
d V
d in
H
Ci
O
Q' Fault Position (% of Line length) X101
Fig 5.16. a-Variation in Mag. Of (Xsa+K (a) Ires) / (Isa+K (er) Ires) with
Fault Position For Pre-Fault Load Angle Of +10 Degrees
X101 a1 L
a-4
Li
t1 d
nn
N Oi L
º-4
d
SG
CJ
v
O
01 L
:f I f
f .f
"I
Z ,I "I
^ "' i
FauLt Position (' of Line length) X101
Fig 5.16. b-Variation in Arg. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of +10 Degrees
--- SE SCL-5 GVA. RE SCL-35 GVA ---- SE SCL-35 OVA. RE SCL-E OVA
SE SCL-10 GVA. RE SCL-10 GVA Line Length -300 km
-q Measured Resistance (secy. ohms) O -+ NW -1. UI M -7 Co wO
O to
En C, 4 -j
vz!
n -n
U) r 0
(D ä n r' m apr
ý ro
G) ut >
rº "o OD ÄO
m ro N ... C) N r I o 0
6) < D
N"
cn
tD D. H" CD w rt`yu fio ý ýn rt CD :: r
xCD Qj n z(D .. CD E* oo rt to
i (no
ýi f. +. CD
a rro
Q fi nc) (D
0
rnCD
o)ý rt 0) t-4
rýo oa
CD 01
,n Measured Resistance (secy. ohms)
m
N
Fý .0 y
m ä
r `A N ro
D 7ä
ro a ro ro
n r I UI C)
ttt... itJN-ýO"+NLJ-aUIýVCOtDO"
N Op
WNp, "v CO em c2 O C, 0 CD O bx se 34 ýe o0
0p
314
P'
Om
r- m z
N O
'tt Measured Resistance (secy. ohms)
t0
N
I Q -n lQ
m (n ä
r e '2 () m tn ý C) > 1%
A
M ro
0 r N
C)
r W Ui ON V `o
m
0 C2 C3 XXXXX \\ - X a,
rC (n Ty
ý H
1
z cil O
0 0
A
Uý m
ýý
w
0
-n Measured Reactance (secy. ohms)
U3
N
"G co Ä
n -n 1 Cc
rn r 0 P N4 [] r ,3 0c
IA
0c <z
"o 9D Uo ID
rn go
C) r I N
0 t7
-a CO ON -ý 01 CD
VI AVA CO `0 Wo0o OXX ý /K XX
IX \/ oe r 17 C IN
r 1
O
0
Ln ,.
O
Or
m r
IJI z
00 h- Nie x N" a N" cn m rtp. G
0 h ft
ti (D (D
w CD z(D
n (D II rt
I. J.
ý-4 ro Un °ncn
oj 51
np rt ow
°`rto
ooa
Measured Reactance (secy. ohms) PQ NNN
n
'^ c
YI
"s u
m -ýn
'- c N mö N äu n r3 e 1°ý Ln ro
G) Ui D
ý< u
F' 0 71 ro m-
ro N n rü
t N
c C,
D
ONe, V CD N 70 O KKxK. N
0
.N
I C
O N
1 w O Z
n K
O T
r M
T
r
1
V
-n Measured Reactance (secy. ohms)
m
(TI
1 m
p c U) Mö UI CL n>
I '0 cn G) ` <Ä D "" "o
M N f) r I In
ON :Z 0I CD
W ON
Oo VM OOm
4 to KKö
I K
L, N C
O o N
1
UI 0 z
0 o
z A
N r- m
-I H
O
ne�ý�rpd Resistance (secy. ohr5)
to
UI
(0 -n p C1 r.
(p O mw Nö n r rO
o
1D
D , o- 3
31 & M :r
Nx J
no r- IA
O 1
J
Ö.
C,
D
P. to
UI
If
(D A) F'- (D I ' rt. ý
rr tn W I
- O'fS
ra r (D gal
, ammo m ýýým n rmmmr
m z
t mCCCC
' CD
o ft ft ft C m ý rt*
rrr Iaa0
a CD
moo 1 cn n oCL aCL , pP. CD
33 "a ( x ;C 3000 i» (! ä
~ smm Pj +01
- ar ü
Mº oao O
oý N
m°ým CD ao
" 'b
OO M E4 N
F'- r't
f, f" F- OO
(D ýO
-n Measured Resistance (secu. ohms)
m
In
LO -n p
1
(n O
m t O (1
r ,. to o T) 0r < r.
D
fD
rn
nx ro p
C)
D
0o -+ NW -º Cfl 0'1 ý7 CO (D O """ý N
,. 1
ý" i N
w1
In
m
ýt 1 `.
OD -
--------
11 Measured Resistance (secy. ohm )
t0
LD
ID m
Qc
c" U3
rn Vt ... Ui w
n0
r
cn n Cr
D
t0
M V.
N
r N
D
. 'ý\
4-
cn ý-
ý, "ý. 1 `. 1
ý `. .ý ý. 'ý,
1
0
(T) ý-
Mancured Reactance (secu. ohms) 'n r to
LA
N OT
n c
(n O rn in in p
r .. I. o O-
ý r" <Ä
m C.
rn ? ( oo r -- A
0 O
to ö to
o to ö
.n ö
lnn ö
U1
Co -
tD
N"
01
O
CD ) l- CD ," OOft w I to ft 0. m I ft ° K
r s ct CD .
r777ºý 7 AtCA7 CD
z(D raurar 11 10 ccc0 ý£ n a ft ft ft C
m ft
100ä hOn
oaaa H.
7C7]] .w Cn 310,30
mmm `r
ºýi +01 n CM G I. I. O0
11 Oý r1
Ol CD 0 010
O 0 En U! fh ýý / MD P.
Fý rt ft I-.. r.
O0 m :J :J
Measured Reactance (secy. ohms)
U3
N 0 -n p
m in
I. C' ö n r cn o
< D
rn C' Nv ra q (Al IA
0
'n Measured Reactance (secy. ohms)
to
UI
O . -n ff P
c* tn
rn 0 N K
0
r
cn 0 D
ro
Nx n r a cn
D
8 t 0
u a, IA
as U C
r-ý U cS d
d L
N t d
r-
Fig 5.21. a-Measured Reactance vs Time with Complex Kc (CRCF)
2R 21 a 22 2C
:, 18 U 1s
12
c 10 d8 ug a4
m2 ao L 3 -2 d -4 _ -6
0.6XL1 - X, /2
156789 1Q 11 12 13 14 15 16 17 1 Time (ursec) X 10-2
Fig 5.2i. b-Measured Reactance vs Time with Keir (NRCF)
SE SCLm5 GVA. RE SCL-35 GVA.
fault at 60% of line, Length
Kß'0.78/-13.5' Kar"1.82/-4.5'
8
3
Time (ursec) X10'2
Pleasured Resistance (secy. ohms)
IJ. NI
C) NWAt! I 0)
ID O
(
N -n p
n
No
U) ö C-3 :S CA
W. 0 0, O 'T)
< fD D r, M CD
rn w Nx' C7 o-
0 --
D
hi N" W
y: 0 r" CD bznm
a i (+ (D r, . ft ti
T -)-3ý ºtim : n' (D Hý"A' cn a ý+ M 7e 11 117 Aý µ
r2
r cö 0 00
mcc N
7Mº+t+n N NN C
0 ý. <, hI (D r} t
:i rrr 1000 o'> rC") h1 m en
oaaa wo0 cD
]Z2 gy X: ( p (D
K2nc p N0 Nm
0 FJC rt
01 +01
i1 o Q' o G o I CL 0
91 9vN fi
aa m" m
45 00 (
ao ~(
DÖ ' N- to U)
W + + wF " 1. " ft c1 rt f'" cn G f-- o "W0
-n Measured Resistance (secy. ohms)
r. ID
N
N N -n p m I-
0
m- wö C)
eN Üý p
r- m
m '° N
ro A 1) U1
I
0
D
i Measured Resistance (secy. ohms)
NW -A t11 03
(n
N
N p
c" W N0
II UA µý
r CA
w X, U1 % oý
ý3v D
I1 to rn vCD
Cl p ýc
U1
r C)
Measured Reactance (secy. ohms) "1 fº m
N m p
nC
(p o rn w t n r O
11
M N f7 0 r 8 N 0
L)
D
CA) .
8h 4
- Ul 0 (A O UI
0 (A
D UI 0 UI
N
tJ
UI
C)
-. 1.
C)
CO
r C
--
II" i i"
rv -a r r777º+ 7OA07 oIII0
raomr sccco ýº+rrn aft ft ft C ft a :y rrr Icoo w0va oaaa 0 DDD 70 33
in r"º+r "00 I11 +01 MM 00
hi N- W
U,
W
C: 1 OI"CD rt- ' äaºd : DM 0 cD cD G
+ ti ft n ýrorn ýr m H G" 1 CD a
rt XN00
0 ti ä N I-+ n
öwx r 00 D) n (Q %CC m (D rn
G Pl ft
o p- 0aGG
º JFýrt 0 (D Co GI (DO
ý*" arr
040 )0
N w
p mr
Co.
0
Mw C. N0 0 C r ,.
Üý p
D
r- lo M :5 m 'n C4,
n ro
Ln ci D
Measured Reactance (secu. ohms)
-q Measured Reactance (secy. ohms)
m
N
Nm
QQ co,
N
m0 W I. Nw n3 r 0^ tR (Jj O
0 r' < Dm "r
ID
M C- r 0x r I Ui
0 -.
15
10
-C 35
0 " 30
M u 25
20
°o 15
-0 10 L 5
N0
-5
Fig 5.24. a-Measured Reactance vs Time with Kar (NRCF)
i5
90
c 35 0 " 30
u 25
20
15
- 10 a, L 5
0
-5
t 1 1
t 1 1
1 j t t l
1 1 j 1 t l
1 1 6yL
ý. } .............. ."........................ ,
,
t t
t
1 4- 1 t t j/
, 41 ip ý . f
n, 1_ Jix ,1
t 1t
tl II
1 t
iS 789 10 11 12 13 14 15 16 17 1 Time C sec) X10-2
8
B
Fig 5.24. b-Measured Reactance vs Time with Complex Kc C Voltage Compensation
,,, forward reactive reach
--- measured reactance
---- measured resistance fault inception angle-90 degree
fault at SOX of line length
line length-300 km SE SCL-5 GVA. RE SCL-35 GVA. NO LOAD
I Time ( sec) X10'2
aCZ
IA E 0
u of SA
x
as
V a, L N d
Fig 5.25. a-Measured Reactance-vs Time with Ker (NRCF)
. 15
,. 4( LI
0 " 3(
T u N
x 2t
°a 1:
.0 1C a, L`
cS dC
-C
1 11 tl 11
7 tl
1 t
1 II $1
t It 11
/1
j. fj 1}
.... "" . ".... ".
1 Ir 11 Ir
h t
t r
11 t tr41A ilk 11 l
on. . %"..
11 t
li 11 1
6 788 10 11 12 13 l1151617 1 T Time C sec) X10'2
8
B
Fig 5.25. b-Measured Reactance vs Time with Complex Kc 6 Voltage Compensation
.... forward reactive reach ---- measured reactance ---- measured resistance fault inception enpla-9O degree fault at 60% of line length line 1sngth-300 km SE SCL-5 GVA. RE SCL-35 GVA. NO LOAD
f Time ( sec) X10-2
15
,-. .I L 35 0 " 30
u ei 25
x 20
°' 15 al
10 a, 35 LA a0
-5
+Ir
+11
+1+
+ +11 +r+ r +l+
+1+ + 1+1 + r+l 1 +l+ 1 +1+
1 +1+
+1+ +11
r 11+ ý
1+ .
56789 10 11 12 13 14 15 16 17 1 Time C sec) X10'2
Fig 5.26. a-Measured Reactance vs Time with Kar (NRCF)
45
4C
35 0 " 3C
u 2°
2C
1
IC
35
aC
-
11 t
11 11
tý
1.
t t . r r ...... ..... ... .ý...... .... ... .......... /
0.6XL1
t t
t
t t I.
ýýý 1 1 1i ý-\I 1 11 1
Ilt Itl
1- 1
tý t
56789 10 11 12 13 14 15 16 17 1 Time C sec) X10-2
6
8
Fig 5.26. b-Measured Reactance vs Time with Complex Kc 9 Voltage Compensation
.... forward reactive reach ---- measured reactance ---- measured resistance fault inception angle- 0 degree
fault at BOX of line length
line length-300 km SE SCL-5 GVA. RE SCL-35 GVA. NO LOAD
SE _i RE
Tc jXc/2
1-1-9 VR
Fig 5.27-System Configuration with Line Side V. T.
Measured Reactance (secy. ohms)
w t12
Ln
N CD >n p nC
c
U
No5
. 411-
Ln F
. I.
r-a -a ur Fº 77 '1 r 740Q7 mltlm
rmail r mccco 3*1wwn C ft ft AC ft m arrr Iooo I"O0 oaaa 0 DDD 70777 3moo
NON mmm il1 +01 r I- 00
I1
U,
rt Ö 4. z 0 P- CD
(D rl- ID
(D rt ä
rn :y aW f' (D CD
O CD
fti O 0)
C y( CD
OO W
En 0
n0
rt
J , hd d'CD 0 NN
H- c p.
rra 0
w ID
N
N m
1
N
m
n r n N
C,
m M
N n r U
N
G,
D
Measured Reactance (secy. ohms)
'T1 p C
C4.
-U 0
CIP r. 0
1
b 1)
r
ID
r ID
W
X
O
-tý Measured Reactance (secy. ohms) I» t0
In
N co
üg E
rn 0 NW no r d^ w No
< D
N
M C- n r I In n
r; rn
. 01 H
Measured Reactance (secy. ohms)
-n Fº
to
N lD 11 p nI
(n o m
C. a
n r No o -ý
D ro
M N 00 r -G O
D
-+ -' NNWW -a -º
_ÜI 0 UI 00 0(11 O UI 0 U1
N
W
4
(J1
O
J
a)
CD
O
hi N" W
N
ruv -a r 7mmm7 a1IIm
acCCD
nRRRC Ra irrr ROOD Waaa 0aaa 0 DDD 70777 glove
vº+r mmm t11 +01 $a I- 00
P. 0 P" (D rt 51 r'
10 ý
rt0 rt1 m
:x En pr (D m 0CD P"
r+ t-4 1- 0 ýa
CD bo wäx rr 5
CD00
"*CC C CD N Hu W0Orj
O Co r
i F- 00
~ (D O
-º to m wP. N-
Pi fi cn G P. 0 A) 0
-n 10
N (D -n p mC
C4" 0
rn u) r"
O 03
r r .ý O
0 r-
9D r
rn 'ý
0 ro N
G)
D
-n Measured Reactance (secy. ohms)
U3
Ui
N to
iJ P
N
m .. N
no r Ux Eo
0 <
D . r,
rn n r A In a D
Measured Reactance (secy. ohms)
SE IS -jXc RE
II 1-9
VS VR Relay
Fig 5.30-System Configuration with Compensation at the Mid- Point of Line.
X10-' 4n
I
a
L 6-4 U
d N
I -.
d In
H
iJ O
O; d
--------- ---
0123456789 10 1
Fault Position (% of line length) X101
Fig 5.31. a-Variation in Mag. Of Isa/(Isa+Kclres) Vs Fault Position For Pre-Fault Load Angle Of -i0 Degrees (50% series comp. )
.. L4 i U
d N
d U'
H
(1. 0
4 at <-1
-t
8
6
Q ý.
Ö123456789 10 1
Fault Position (% of Line length) X10,
Fig 5.31. b-Variation in Arg. Of Isa/(Isa+Kclres) VS Fault Position For Pre-Fault Load Angle Of -iO Degrees (50X series camp. )
SE SCL-S OVA. RE SCL-35 OVA ---- SE SCL-35 GVAj RE SCL-5 OVA
SE SCL-iO OVA. RE SCL-iO OVA Line Length -300 km
X10'' 10-
tA a L
H U
d Ui
d IA
H
Qt
Fig 5.32. a-Variation in Msg. Of Ise/ (Ias+KcIres) VS Fault Position For Pre-Fault Load Andle Of 0 Degrees (50% series comp. )
Q
N v L 6-4 u
d a
a IA H
(l. 0
L
7L
Fault Position (% oP Line length) X101
.' ýti
ý". -. ý '".
-. ý ". .ý", .ý .ý .ý ,ý .ý
ý, . .ý .ý:.
Fig 5.32. b-Variation in Arg. Of Iss/(Isa+Kclres) VS Fault Position For Pre-Fault Load Angle Of 0 Degrees (50X series comp. )
SE SCL- OVA. RE SCL-315 OVA ---- SE SCL-3S OVA. RE SCL-B OVA .,,. SE SCL-10 OVA. RE SCL-10 GVA
Line Length -300 km
Fault Position (% of Line length) X101
X10-' 10-
a, L
u
d K
d H
H
CL 0
CT d
SL
ýý, -
ýýý 7 ýýý
6 -------------------"-------.
ý. ý .......
5".............................
4L
2.
9 Fault Position (% of Line Length) X101
Fig 5.33. a-Variation in Mag. Of Ise/ (Iss+KcIres) vs Fault Position For Pre-Fault Load Angle Of +10 Degrees (50X series comp. )
30 28- 26
024 L 22 UU 20 d18 X16 X14
t412
(L 10
oý L9
Izs 't 5B7B3 10 11 Fault Position (% oP Line length) X101
Fig 5.33. b-Variation in Arg. Of Isa/(Ise+Kclres) VS Fault Position For Pre-Fault Load Angle Of +40 Degrees (50% series comp. )
SE SCL-n OVA. R SCL-35 OVA ---- SE SCL-35 OVA, RE SCL- OVA .,.. SE SCL-10 OVA, RE SCL-10 OVA
Lin. Length -300 km
-n Measur4d Resistance (secy. ohms)
F+. p -- N (1 -e cl1 a) -3 CO U3
Ln
n
n I-
C
(I, O
0 C) r cn
.. ". \
0 C7) .5 O
G) "t\ < D5\
3 5. i
tO 5.
N ,.
-C) ö;. el
r A
O
O
N-
Ln w
cn0Pco 0 El ft SD II ep kd ýf Ea I
" rn 0r 11 r -a -a -a r CD fn D 39M03 G+ PNc
mIIIm CD
rF n ýtj rm
®ö r MOm
O mccco 7wa+ro 0010
RRRC U1 ý El Pj CD rt.
7rrr 10 pý ýC SD 1oao äää
C ß'0 n ö
o (D O - 777 H
7C 3Nmw (D En 0
P4 rf-
401 0) it Oa 1-b Ilb ÖC0 rowN
. aura z .j t- rt
°mI. m° W CO
ahm ö ro; NEa °wäfi
c? U1 P) 0
Measured Resistance (secy. ohms) F' ONW -A Ui 01 V 00 U
.TN p
c1 c
N o0
0 r L' ---ý I IN: ;. un
D3 1"
Ö
rn t
cn ' nx
u --ö cn G
Measured Resistance (secy. ohms) ao
(B
l. J A
II p
c"
rn {UýI
µ
ºJ 0
r w to o G) <' D ID
I-
C-: r
N n r n cn
D
fleasured Reactance (secy. ohms) -n Fº to
Id
p
c-
No mw N" 0 () 3
r k% p C) -) 0
D-
m? ( (7 0 r -- 1 ku 0
rv -a -or 700A7 011Im
In *4 '1 roaco r mct CO
nRRRc Ra 7rrr 1000 1000 oaaa 0
sss x»> 3nnýo
mmm III +01 rM
00
Fº
t0
W
p Ul
H
M N 0 C) 3 r p ý. No
q Ci DZ
r-
rn *. ( %' n r e -- w cn C)
t7i N" w to -
w ýp
ýnE N C. n 0O rWtw W ÖP
po: 21 m UI
m C D ý' rs ma
N m 0Eg(D
o UI fi >k C) r (DO 0 fD mö0 n
n C C Ný C n G7
Oý ýºý D a ýI OG ct Oä
4 h" r rn "" 0 N
" (D -
n r o I- o wä
ý" cH" cn rcna0 , -- H: 6)
D
Measured Reactance (secy. ohms)
Measured Reactance (secy. ohms)
P C
O
C. r. O
O
0- ID
C.
x 0
..
x10-1 70-
G5 so- 55- 50
ti95 Yi0
tL 35 0 30-
c525 r-20 15 10
1
Fig 5.36. a-Variation in Mag. Of K (a) with Fault Position (50% series camp. )
xiol c
CL 0
Q; L
Fig 5.36. b-Variation in Arg. Of K(a) with Fault Position (5O% series comp. )
Fault Position (% of Line length) X101
Fault Position (/ of line length) X101
10-1 co 2s, _ L 124 L 22 +20 d N
IA d LI
r-i %
tl v
ti N
r-4
0
mQ d L
Fig 5.37. a-Variation in Mag. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of -10 Degrees
X101 ä; L
1 L ti
d bi
H
t4 CJ
H n ü
d UI
H
CL
O
-------------- L--------- --- -- I----. -.
L. Fault Position (% of Line length) X10'
Fig 5.37. b-Variation in Arg. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of -10 Degrees
---- SE SCL-S OVA, RE SCL-35 OVA
-""ý SE SCL-35 GVA. RE SCL-O OVA SE SCL-10 GVA, RE SCL-10 OVA Line Length -300 km
Fault Position (% oP line length) X101
K10-1 626- L
24
vL 22 + 20 1418
X16 r% H
V
U-
0
d 12-
10 Y8
d6 N rpr-r
mn d s
Fig 5.38. a-Variation in Mag. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of 0 Degrees
tn a, L
L b v
d
In GJ L
d In
L. O
L
X101 a
Fig 5.38. b-Variation in Arg. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle of o Degrees
-ýý SE SCL-5 GVA. RE SCL-35 GVA ---- SE SCL-33 GVA. Rd SCL-ö GVA
SE SCL-iO GVA. RE SCL-10 GVA Line Length -300 km
Fault Position (% of line length) X101
Fault Position (% of line length) X101
4o2s L "24 L 22
20
W18 1s
t414 X12
10 'U ac 8 da
ýL 2- 0 "0 rn 0 d
Fig 5.39. a-Variation in Mag. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of +10 Degrees
n If, C, L
r-a n L U v Y + CS N
H v n
0i L
n b v Y + ö
N V_
(J.
a
L 1
Fig 5.39. b-Variation in Arg. Of (Isa+K (a) Ires) / (Isa+K (ar) Ires) with
Fault Position For Pre-Fault Load Angle Of +1O Degrees
X101 c
SE SCL. -15 GVA. RE SCL-33 OVA ---- SE SCL-35 GVA. RE SCL-5 OVA
,... SE SCL-3O OVA. RE SCL-10 OVA Lins Length -300 km
Fault Position (i of Line Length) X101
Fault Position (% of Line length) X101
-ý M41 F+ to
UI
O -n p
nC
O 0
m 1"F
UI O (]
r .. i "" µO
o 0 r+. < Iýp
m N lý o r 1
0 -a
70as] /III/
rr /ccca o ft tºIt c ft zrrr ýaaa oaaa 0 DDD 7077 ] Sonn
º+ MM
+0I MM Oao
/ as a /"/ on
Iij
N" w
0
n9nroX 0KOOm
(D (D Uff!
Co cn F' II
a o(D
p. f o0
a N' , N" m rt IJ
(D a ft Ia
k' r F' O
(D'ý 'b0` CD A
CD to rtýnz
u CD C ýi :4
00 dp
0O CA
1m (D
, pI "hj n. as ~" to GC m "a k- m ft
UA ) -n He om
In
o -n p r.
Co.
rn o
., N 0 0 n r I Ln ". '
pq n D
r. 3 ro
rn ID
C-) r x
-Tl nE U3 N
A 0
ü 1
Nö m I, N C) 0
La ..
0
G) I < D
m Jo ID m n
I In
G
r
r 0
i r
N to
N
A N
Q
rn In C, r
0 cý D
m rn cn n r I w 0 a < D
Measured Reactance (secy. ohms)
-n p c r cº
0 VI
0 wo 3
n
O
r w 3 A
r 4 3
ýO
v X
O
N"
01
ct N" N N" cD i 0 rt W
(D r-r ýr En i: 0
r . III *r I (D I :: r
ro a %Q ý1 "'l n Fl- r1 x ýd
. ccc0 ft CD p) 7NNN0 n O ft ft ft C . ., U ry
? rrra p0
y0 0 loon
ocna -a N CD Fl-
337 ýIýQ'C x 3Com h' En
MNN 1'ý" Pw
... CD " hý tsj IÖ Nw ti 1 °nG OO ö0
rt
bnýro 0 CD No es ur
rt r P. t w H" o
0 ooýj
1) Fº 10
In
N
m N n r I N
6)
D
m
C) r W N
0
D
I P
Q Ili
U.
In m En n r I In
m m En n r I 0
D
treasured Reactance (secy. ohms)
P c
0 in cº 0
0 'I)
r
rD
A 3
%0
..
Measured Reactance (secy. ohms)
P C
0 h
CO, w 0
I' \"
0
r
r
1D
5 x r 0
CHAPTER 6
RELAY RESPONSE FOR A LINE WITH 70% COMPENSATION
When a transmission line is designed with a series
compensation of more than half of its series reactance,
say 70%, it is common practice to install half of the
series capacitance at each end of the line, e. g. 35% at each
end.
To apply distance protection to series compensated
lines demands a different setting philosophy than that
adopted on plain feeders. Basically the presence of a
capacitor in front of the relay will distort the reach of
an impedance measuring element.
As the zone-1 of the distance scheme trips
independantly of any additional information from the far
end of the line, it is vital that the element does not
over-reach. If there is a series capacitor in front of
the relay at the remote end bus-bar, then the worst case
assumption is to allow for that capacitor to be fully in
circuit. For this reason it has been suggested that the
zone-1 reach be set at 80% of the compensated impedance
[13], although some utilities have considered this
coverage as unsatisfactory and completely ignored
distance schemes for the first independant zone [32].
However, as explained in Chapter 5, for an "a"-phase-
ground fault, the measured reactance is bigger than the
actual line reactance for faults beyond the remote end
capacitor, if the new method of residual compensation
(NRCF) is used. Therefore, it is possible to set the
relay forward reactance reach at a value higher than 80%
90
of the compensated impedance, or 52% of line length. In
this study the relay forward reach is set at 60% of the
line length (or 92% of the compensated reactance).
6.1-Line With 70% Compensation And C. V. T. On The Source Side Of The Capacitor
Consider Figure 6.1 which shows a typical series
compensated line with 35% of the compensation at each end.
Since the C. V. T. is on the source side of the series
capacitor the line impedance locus will be in the fourth
and first quadrant of the impedance plane, as shown in
Figure 6.2.
6.1.1-relay trip characteristic
As previously mentioned, the relay forward reactance
reach setting is determined by the remote end capacitor.
Thus the forward zone-1 reactance reach is set at 60% of
the line length in order to exclude faults at the
receiving end bus-bar from the boundary.
The reverse reactance reach is, on the other hand, set
considering the effect of the local capacitor bank. The
relay trip characteristic may be arranged so that it
excludes the local capacitor, as shown in Figure 6.3.
This implies that some internal faults do not fall within
the relay trip characteristic as long as the capacitor
bank protection, namely the spark gap, does not flash-over
(i. e. capacitor remains in the circuit).
However, if it is ensured that the relay directional
ability is maintained for all reverse faults, irrespective
of system conditions, it is possible to include all faults
in front of the capacitor that are within the relay
boundary, as shown in Figure 6.4.
91
It has already been explained in Chapter 4 that the
directionality of the relay is maintained by the
directional reactance XM. Simulation tests have revealed
that the relay does not trip for reverse faults on the
sending end bus-bar.
It is common practice in distance protection to expand
the forward resistance reach to cater for the high fault
resistance. In general, it is preferred to set the
resistive reach as high as practicable and usually not
less than half of the load resistance.
6.1.2-relay decision logic
The principle of the relay trip decision logic and
count regime were explained in Chapter 4. The trip
characteristic is divided into three different counting
region, as shown in Figure 6.5. The incremental values
INC1 and INC2 are initially set at 8 and 32. They will be
changed twice after fault detection to 2 and 8 and then 1
and 4 respectively. Figure 6.6 shows the relay decision
logic flow chart suitable for a system with 70% series
compensation. Note that if a trip does not occur and CRL2
is greater than 60 and the Trip-Counter becomes zero for
one msec (4 samples) the relay considers the fault as an
out of zone fault and resets both Control-Counters, CRL1 a
CRL2. INC1 and INC2 are also reset to their initial
values of 8 and 32 respectively.
The counter is decremented by DEC1=8 or DEC2=32 (see
Figure 6.5) after fault detection for any sample falling
outside the trip characteristic.
6.1.3-the relay trip response
Since the main objective of the work presented here is
92
to improve the distance relay response when the capacitors
are (or remain) in circuit, the operating time response
of the digital distance relay, specifically designed for
series compensated line applications is examined when it
is assumed that the capacitors are permanently in the
circuit. This is achieved by adjusting the capacitors'
spark-gap threshold at a very high value.
Figures 6.7 to 6.16 illustrate the corresponding
relay operating time response. Different system source,
pre-fault load and line length have been considered.
It is clearly seen that the relay operating time is
about 10 msec for fault positions of up to 65% of the
relay reach, for all system condition considered. The
relay, generally operates in less than 20 msec for faults
between 65% and 80% of the relay reach. But operating
times of up to 30 msec is observed for some faults in this
region. These are associated with situations in which the
local source is much stronger than the remote source and
load is imported. In such situations the measured
impedance takes a longer time to enter the relay
characteristic, thus delaying initiation of count up. No
relay over-reach was observed.
The relay was tested for faults at the receiving end
bus-bar (behind the remote capacitor), which showed no
maloperation.
A lumped parameter program has been used to simulate
the primary system. This program has been used to test
the relay for many different situations and fault
inception angles (in excess of 2000 runs) when the
capacitors' spark-gaps flash-over was prevented. The
93
lumped parameter program was used merely because it has a
much faster excution time than a distributed parameter
program. The relay performance is shown in Figures 6.7 to
6.16. No relay over-reach/under-reach was observed.
The distributed parameter simulation [9] was used to
briefly examine the relay response when the capacitors
protective gaps operate.
Figures 6.17 and 6.18 show the typical relay operating
time versus fault position when the capacitors' gap flash-
over has been considered.
None of the capacitors in healthy phases were by-
passed for all faults considered.
It can be seen that the relay operating times are
generally less than 15 msec for faults up to 50% of the
relay reach, and that the relay trip times for faults with
the inception angle of 0 degree are longer than the faults
with the inception angle of 90 degree.
This is caused by a high exponential component in the
current signal (when the fault inception angle is around 0
degree) which in turn causes the voltage across the
capacitor (or spark-gap) to build up much faster than the
case when the current is not offset by exponential term
(i. e. for inception angle of around 90 degree).
The flash-over, also introduces a transient in the
measurement. Thus, depending upon the window of the
algorithm, the measured reactance (and resistance) takes a
finite time to reach its post flash-over values. Hence
delaying the trip initiation.
Also, it can be seen that for faults with inception
angle of 90 degree the relay has initiated trips for
94
faults up to the approximately 70% of the relay reach in
about 10 to 12 msec. This is due to the fact that the
relay trips before the capacitor spark-gap flashing over
(see Tables 6.1 and 6.2).
Throughout the test the sources were considered to
have X to R and zps to pps impedance ratio of 30 and 0.5
respectively. Also in all tests the C. V. T. response was
included in the simulation.
The residual compensation factor considered in the
relay was equal to 1.82L-4.5'.
6.2-Line With 70% Compensation And C. V. T. On The Line Side Of The Capacitor
In this section, the voltage supply for the relay is
assumed to be taken from the line side of the capacitor
bank (see Figure 6.19) and the relay behaviour is
examined.
Since the capacitor bank, in the line side C. V. T.
case, can be assumed to be part of the local source, the
flash-over of the protective gap will not affect the relay
impedance measurement. Furthermore, the line model
equation which the relay algorithm solves return to the
plain feeder model which consists of only the line
resistance and inductive reactance. It follows that the
capacitor has a very insignificant effect on the
measurands with regard to the sub-synchronous oscillation.
6.2.1-relay characteristic for line side C. V. T
The relay characteristic for a line side voltage
transducer is shown in Figure 6.20. Note that the local
capacitor reactance exhibits a positive reactance to the
relay and is inside the characteristic. The nearby
95
external faults are also within the protected zone and are
therefore detected by the relay. For these (reverse)
faults however, the directional reactance measurement, XM
(see Chapter 4), prevents relay maloperation. Figure 6.20. a
shows the measured X and XM for a reverse fault at the
sending end bus-bar.
The forward reactance reach of the relay is, as
mentioned in Section 6.1.1, determined by the remote end
capacitor and, therefore set at 60% of the line length to
exclude the faults at the receiving end bus-bar.
It was explained in Chapter 5 that in order to improve
the measurement accuracy of the relay a complex residual
compensation factor must be used in the relay, which is
calculated to be equal to 0.78L-13.5' (see Chapter 5,
Section 5.2).
Figures 6.21 to 6.27 show the relay operating times
versus the relay reach, for different system pre-fault
load and source conditions.
It is evident that although the count regime and trip
logic had originally been designed for the source side
C. V. T. configuration with very much stronger sub-
synchronous resonance, it coped very well with the line
side C. V. T. situation.
The relay response is observed, from Figures 6.21 to
6.26 to be about 10 msec up to about 85% of the relay
reach. No relay over-reach was observed. Moreover, the
relay restrained for all faults on the receiving end bus-
bar (behind the remote capacitor).
96
SE -jxd2 Is
Vs
Relay
_jXc/2 RE
ZU
ZLO II VR
Fig 6.1-Line Configuration With' Series Capacitors At The Line Ends And Source Side C. V. T.
45
4C
3:
vý 3C E ö2°
U 2C a,
1°
Go 1C C
ý _c V
-ic
-15
solid fault line inpedance locus for plain feeder
solid fault line irtpedance locus for series amp. Line
-1 0 1234567891 Resistance (secy ohms)
0
Fig 6.2-Impedance Locus For A Line With 70% Comp. And Source Side C. V. T.
45
1o
35 r, ýn 30 a ö 25 U 20 a,
15
Ü 10
5
0
-5
-10 -15
solid fault line inpedence loan for plain feeder
solid fault line ii edance locus for series coop. Line
-4 -2 O2468 10 12 14 16 Resistance (secy ohms)
Fig 6.3-Impedance Locus And Relay Characteristic (the local cap. is NOT included in the boundary
45
4o 35
30 L 25 0
20
15 " 10 a
5
0 u
-5 a -10 -15
-20
solid fault line inpedaice
Locus for plain feeder
solid fault line inpedu=
Locus for series cone. Line
-4 -2 0246a 10 12 14 16 Resistance (sect' ohms)
Fig 6.4-Impedance Locus And Relay Characteristic (the local cap. is included in the boundary
30
z=
2c
r% V
in E r- 0 1c
U V1
5
N U
0
U
°' -5
-10
-15
-201 -10 -6 -2 26 10 1't 18
Resistance (secy. ohms) Fig 6.5-Relay Quadrilateral Characteristic
And Count Regime For 70X Camp.
INC1 see section 6.1.2
INC2
DEC1= -8 DEC2= -32
solid fault line inpedsce locus for series cartp. Lire
CEC2
1. SXr ..... ----- ---- --------------------- Xr ......
I DECI
0.85Xr.... ----- --- ---- LUr., 1..... -.... --- iNC2
0.7Xr .... ---- --- ----------------- -
+32
i R Rr 1.2Rr
Xo
No
NO
Is CRU 0
IS 7<DX<l. i
<DR<1.7
x YES
CRL1= CRLI +1
YES
IS CRU>16
NO
INCREMENT COUNTER
IF COUNTER > TL COUNTER = TL
&
NO
CRL1 =0 INC1 =4 CRL2=0INC2= =32
COUNTER =0
NO
IS TRIP-0
reS
IS CRL2 >0
ICOUNTER >
rEs
DECREMENT COUNTER
IF COUNTER <0 COUNTER -0
YES
CRL2 = CRL2 +i
IS YES CRI3 =48
TRIP =0
NO INC1 =1 INC2 =4
CRL. 2 - 10 YES TRIP -0
NO COUNIERIRCBSE
2TO ZL-RO
INC2-8
IS > 60&
-OFORlmsec 1P -0 YES
NO
COUNTER -0 CRLI -0 CRL2 -0 INC1 -8 INC2 - 32
Fig 6.6-Flow Chart For The Relay Decision Logic"
X10' n
IV
9 u -4) 9 tA S ,7 w _
.6 I- C z <4
w n- 0 >- 2 J w
a
i r º
------ - -- -----
01 2 3 4. 5 6 7 8 9 10 1 FAULT POSITION (% OF RELAY REACH) X101
Fig 6.7-ROlay Operating Time VS Fault Position For.,
Sit SCL-5, RE SCL-38' Load eng. -O dep.. LL-300 km 70% Series Compensation
Relay Set At 60X Of Line Length Xr-rO. 1, Xo--16,0 secy. ohms Rr-13. O. Ro--b. 0 secy. ohms
Fault Incep. Anp. -0 deg
---- Fault Incep. Anp. -90 deg
x1ol
u a, E
w
F- c, z F-
w CL 0
J w ce.
9
8
7 H
6 '
5 '
3 '
2 `
------ -----
Ö 1 2 3 1 5 6 7 8 9 10 1
FAULT POSITION (% OF RELAY REACH) X101
Fig 6.6-Relay Operating Time VS Fault Position For.
SE SCL-5. RE SCL-38 Loso anp. -+10 dep.. LL-300 km 70"X Series Compensation
Relay Set At 60X Of Line Length Xr-1Q. 1. X0--16.0 secy. ohm$ Rr-13.0. Ro--3.0 secy. ohms
Fault Incep. Anp. -O deg ---- Fault Incep. Ang. -90 deg
X10' 10-
'u v e
w r_ I- F- co Z F-
w a- 0
J w
Fig 6.9-Relay Operating Time VS Fault Position For:
SE SCL-35. RE SCL-5 Load anD. -O dep.. LL-300 km 70% Series Compensation
Relay Set At 60% Of Line Length Xr-i0. i. Xo--16.0 secy. ohms Rr-13.0. Ro--3, O secy. ohms
Fault Incep. Anp. -O dog -ý-- Fault Incep. Anp. -90 deg
FAULT POSITION (% OF RELAY REACH) X101
x101 IV
9 .. u ag Lq E
w
E- C' z <4
w o- 3 0
<2 J
0
'0 It I
i
------------------- ---------------------
123456789 10 1 FAULT POSITION (' OF RELAY REACH) X101
Fig 6.10-Relay Operating Time VS Fault Position For:
SE SCL-38, RE SCL-a Load anp. --i0 dep.. LL-BOO km 70% Series Compensation
Relay Set At 60X Of Line Length Xr-10.1. Xo--18.0 secy. ohms Rr-13.0. Ro--3.0 secy. ohms
Fault Incep. Anp. -O deg
---- Fault Incap. Anp. -BO dap
x1ol In I
u a, E
w
i-- co z F-
w 0
J w m
9
8
7
6
5
3
" 2 ,
-
Ö 12 3 4 5 6 7 8 9 10 1
FAULT POSITION (' OF RELAY REACH) X101
Fig 6.11-Relay Operating Time VS Fault Position For.
SE SCL-3. RE SCL-35 Load ang. -O dep.. LL-400 km 70X Series Compensation
Relay Set At BOX Of Line Length Xr-13.6. Xo--20,0 secy. ohms Rr-14.0. Ro--3.0 aecy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep,. Anp. -90 dop
X10' n
I
u v UI E
w s .r I- co z F-
w 0 0 >- J w W-
9
8
7
6
5
4
3
2 '
01 2 3 4 5 6 7 8 9 10 1
FAULT POSITION ( OF RELAY REACH) X101
Fig 6.12-Relay Operating Time VS Fault Position For:
SE SCL-35, RE SCL-5 Load ang. -+5 deg.. LL-400 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-13.6, Xo--20.0 secy. ohms Rr-14.0. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
x1o1
u v E
w s i-- LD z E-
w a- 0 >- J w
0
9
7
6 '
5
3
-------------- ------ -
0 12 3 4 5 6 7 89 10 1
FAULT POSITION (% OF RELAY REACH) X101
Fig 6.13-Relay Operating Time VS Fault Position For:
SE SCL-35. RE SCL-5 Load ang. -+iO deg.. LL-400 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-13.6. Xo--20.0 secy. ohms Rr-14.0. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
X101 n
I
U a, N E
v W
I-
(0 Z r-4 F-
W a. O
J W
9
8
7 º
6 º
º 3 ot l º
-- ------- ------- ------ ------ ------ ------ --
01 2 3 4 5 6 7 8 9 10 1
FAULT POSITION (% OF RELAY REACH) X101 1
Fig 6.14-Relay Operating Time VS Fault Position For:
SE SCL-35. RE SCL-5 Load eng. --5 deg.. LL-200 km 7OX Series Compensation Relay Set At 60X Of Line Length Xr-6.79. Xo--9.5 secy. ohms Rr-11.0. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -9O deg
X101 10_
Ir%
u
5
W
r. + F-
CD Z
I--
ce. W CL 0
J W m
1
Fig 6.15-Relay Operating Time VS Fault Position For:
SE SCL-5. RE SCL-35 Load ang. -O deg.. LL-200 km 70X Series Compensation Relay Set At 60% Of Line Length Xr-6.79. Xo--9.5 secy. ohms Rr-11. O. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
FAULT POSITION (% OF RELAY REACH) X101
X101 10_
U II Ut E
v w r_
H
(D Z
F-
W
0
-J W W,
10 FAULT POSITION (< OF RELAY REACH) X101
Fig 6.36-Relay Operating Time VS Fault Position For.,
SE SCL-3. RE SCL-7 Load ang. -O dep.. LL-300 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-10.1. Xo--16 secy. ohms Rr-13.0. Ro--3.0 secy. ohms
--- Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -9O deg
x1o1
u 4) N E
w
I CD z F-
LU IL 0
J w
0 9
8
7
5
4
3
2
Ö 1 2 3 4 5 6 7 8 9 10 1
FAULT POSITION (% OF RELAY REACH) X101
Fig 6.17-Relay Operating Time VS Fault Position With Cap. Flash-Over (SGS) For.
SE SCL-5. RE SCL-35 Load ang. -O deg., LL-300 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-10.1. Xo--16 secy. ohms Sr-13.0. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
fault iti
gap flash-over time, after fault (ursec) rB on ' of line
th L fault incep. ang. 0' fault incep. ang. 90
eng SE cap. RE cap. SE cap. RE cap.
0 5.25 7.75 4.075 15.4 10 5.50 7.50 4.125 15.375 20 6.00 7.25 4.875 15.125 30 6.50 7.00 5.75 14.75 40 6.875 6.75 7.0 6.25 50 7.375 6.25 15.75 5.375 60 7.75 5.875 16.625 4.75
Table 6.1-Cap. Gap Flash-Over Time For Different Fault Position For:
SE SCL=5 GVA, RE SCLa35 GVA, Load Angle=0, LL=300 km, Single Gap Scheme (SGS),
X101
u
Ui E
ui
H
co z rý F-
Q. ' W C- 0
J W cy-
0 9
8
------- ----- --- ------- -
Q 1 2 3 4 5 6 7 8 9 10 1
FAULT POSITION (% OF RELAY REACH) X101
Fig 6.1e-Relay Operating Time VS Fault Position With Cap. Flash-Over (SGS) For:
SE SCL-3. RE SCL-7 Load ang. -O deg., LL-300 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-10.1. Xo--16 secy. ohms Rr-13. O. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -9O deg
fault gap flash-over time, after fault (ursec) Bition r ' of line
L th fault incep. ang. 0' fault incep. ang. 90
eng SE cap. RE cap. SE cap. RE cap.
0 6.00 8.25 4.35 16.90 10 6.25 8.125 4.375 16.875 20 6.75 7.875 6.25 16.625 30 7.125 7.625 15.50 16.125 40 7.625 7.375 16.375 15.625 50 8.0 7.0 17.25 7.00 60 8.375 6.625 18.375 5.875
Table 6.2-Cap Gap Flash-Over Time For Different Fault Position For:
SE SCL=3 GVA, RE SCL=7 GVA, Load Ang1e=0, LL=300 km, Single Gap Scheme (SGS),
SE _jXca
RE Is ZL1
ZLO
VS VR
Relay
Fig 6.19-Line Configuration With Series Capacitors At The Line Ends And Line Side C. V. T.
15
4C
L 3C 0 vº 2! u
2C
U 1: C d u 1C ci
C
-51 I1 -4 -2 0
solid farlt lire iipacirn loss
44 4- 4- 2468 10 12 14 16 18 20 Resistance (secy ohms)
Fig 6.20-Impedance Locus And Relay Characteristic For 7O Comp. And Line Side C. V. T.
20
U' 1 E t 0
L d
0
x-'11
IA-2, d31 m =-3
-41
5
D
T
X . r^'
D
D
2 Time (sec) X10'2
0
Fig 6.20. a-Measured Reactance VS Time For Reverse Fault At SE Bus-Bar
For 70X Series Compensation (35% At Each End)
And Line Side C. V. T And With SE SCL-35 GVA. RE SCL-5 GVA Load eng. -O deg.. LL-300 km Inception Ang. -90 Deg. No Cap. Flash-Over
X10' 10_
U Oi
8 v W
F-
C7 Z
H
W a- 0
J W w
1
Fig 6.21-Relay Operating Time VS Fault Position For Line Side C. V. T.
SE SCL-12. RE SCL-2/ Load ang. -O deg.. LL-300 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-'24.4. Xo--3 secy. ohms Rr-13. O. Ro--3.0 secy. ohms ---- Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -9O deg
FAULT POSITION (% OF RELAY REACH) X101
X101 10_
u Co U' E
w
H
co z . -4 }-
W LL O
J W w
1
Fig 6.22-Relay Operating Time VS Fault Position For Line Side C. V. T.
SE SCL-35. RE SCL-5 Load an8 -+10 deg.. LL-300 km 70X Series Compensation Relay Set At BOX Of Line Length Xr-24.4. Xo--3 secy. ohms Rr-13.0. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 dog
FAULT POSITION (% OF RELAY REACH) X101
x191
U 0º
E
w
F-
Z
W 0 0
J W x
V
9
8
7
6 '
5
4
3
2
1
ö 1 2 3 4 5 6 7 8 9 10 1
FAULT POSITION (4 OF RELAY REACH) X101
Fig 6.23-Relay Operating Time VS Fault Position For Line Side C. V. T.
SE SCL-S. RE SCL-35 Load ang. -O deg.. LL-400 km 70X Series Compensation
Relay Set At 60% Of Line Length Xr-32.6. Xo--3 secy. ohms Rr-14.0. Ro--3.0 secy. ohms
--- Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
X101 1o-
U
N E
v
w C
F- c7 z F-
w a- 0
J w w
Fig 6.24-Relay Operating Time VS Fault Position For Line Side C. V. T.
SE SCL-5. RE SCL-35 Load eng. --10 deg.. LL-400 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-32.6, Xo--3 secy. ohms Rr-14.0. Ro--3.0 secy. ohms --- Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
FAULT POSITION (% OF RELAY REACH) X101
xi 0' 1o_
U d N E
v W r_
t-
2
F-
W a- O
J W
I
Fig 6.25-Relay Operating Time VS Fault Position For Line Side C. V. T.
SE SCL-35. RE SCL-5 Load ang. --5 deg.. LL-200 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-16.3. Xo--3 secy. ohms Ar-12. O. Ao--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
FAULT POSITION (% OF RELAY REACH) X101
xlo' 1o^
u a, U' E
v W
H
C7 Z
H
W 0- 0
J W w
I
Fig 6.26-Relay Operating Time VS Fault Position For Line Side C. V. T.
SE SCL-5. RE SCL-35 Load sn® . -O deg.. LL-200 km 70X Series Compensation Relay Set At 60X Of Line Length Xr-16.3. Xo--3 secy. ohms Rr-12. O. Ro--3.0 secy. ohms
Fault Incep. Ang. -O deg ---- Fault Inc p. Ang. -90 dog
FAULT POSITION (% OF RELAY REACH) X101
CHAPTER 7
RELAY RESPONSE FOR A LINE WITH THE SERIES
CAPACITOR AT THE MID-POINT OF THE LINE
Consider Figure 7.1 which shows a series compensated
line with the series capacitor situated at the mid-point
of the line. In such systems the degree of series
compensation is often less than 50%.
It has been explained in Chapter 5 that the new
modified residual current compensation can be used for a
line with the compensating capacitor installed at the mid-
point of the line. Furthermore, it was explained that if
the new modified residual compensation factor is used, the
measured reactance for faults before the capacitor
location is smaller than the actual line reactance.
If the relay independent zone-1 reach is considered to
be before the series capacitor, say at 45% (ar=0.45 see
Chapter 5) and a complex residual compensation f actor
(assuming LZLO#LZL1) is considered in the relay, the relay
measures accurate impedance for all faults before the mid-
point of the line. But for faults beyond the capacitor,
the relay measurement will not be accurate.
However if it is required to set the relay reach at a
value higher than 50%, then the relay measurement is
accurate only at the reach point.
In this work it was decided to set the relay zone-1
reach at 80% of the line length, which is the common
practice in plain uncompensated feeder distance protection
schemes. The required residual compensation factor, for
boundary setting of 80% (ar=0.8) is, from Figures 5.36. a
97
and b, found to be approximately equal to 2.015L-4.6'.
Figure 7.2 shows the Quadrilateral characteristic of
the relay. It can be seen that the line locus before the
capacitor location is outside the characteristic. However
as previously mentioned due to the new method of residual
compensation, the measured impedance falls within the
characteristic.
It has been explained in Chapter 4 that in order to
improve discrimination ability of the relay around the
forward reach, a longer time is allowed for the relay to
reach a trip decision by dividing the relay characteristic
into fast and slow counting regions. For the foregoing
reasons, although the steady state locus of the measured
impedance more likely fall within the relay
characteristic, high speed operation may not be achieved
for faults just before the capacitor bank. Relay
operating time of up to 60 msec was observed for some
system conditions, for a fault at 48% of the line length.
In order to improve the relay operating time response
a new modified relay characteristic suitable for lines
with mid-point compensation is proposed. The new relay
boundary requires a new counting strategy in order to cope
with the long line transient effects and the sub-
synchronous resonance. Figure 7.3 illustrates the new
relay characteristic with different counting regions.
The principle of fault detection and counting is
similar to that explained in Chapter 4. INC1 and INC2 are
initially set at 8 and 32 respectively and a is also set
to unity (see Figure 7.3). If trip is not initiated
within 2.5 msec after the first upcount, INC1, INC2 and a
98
are changed to 2,8 and 0.7 respectively. The counter is
also reset to zero. If the relay does not trip within 12
msec after the first upcount, INC1 is changed to 1 and
INC2 to 4.
It is essential to use a time graded characteristic as
explained to ensure that the relay maintains a fast
operating time for faults before the series capacitor, and
also does not over-reach for faults outside the
characteristic if the spark-gap across the capacitor does
not flash-over.
Figure 7.4 illustrates the characteristic and the locus
of the measured impedance on a R-X plane for a fault at
the relay reach. Although the measured impedance traverses
the relay characteristic, no trip is initiated. This is
due to the fact that the measured impedance remains in the
slow-counting region of the boundary and then moves
outside which results in the counter being decremented.
Figures 7.5 to 7.8 show the relay operating times
versus fault position for a system with 50% series
compensation at the middle of the line, when the capacitor
flash-over was prevented by adjusting the spark-gap
threshold at a high value.
Figure 7.9 shows the relay operating time response for
a system with 40% series compensation at the mid-point.
It is clearly evident that the relay maintains a fast
operating time for the majority of its reach.
Figure 7.10 illustrates the relay operating time
versus fault position when the capacitor flash-over is
considered. It can be seen that the relay operates in
about 11 msec for faults up to the mid-point where the
99
capacitor is situated. For faults beyond the capacitor,
the change in measured reactance following the gap flash-
over, causes the relay to under-reach.
100
SE Is -j? Cc RE
vs Relay
VR
Fig 7.1-System Configuration For A Mid-Point Compensation.
30
zI
N 2t
0 " 1:
U u) uI
vIr
a
U
(Ti Ü`
b 0 a
C
_5
solid fault line inpedance locus for series asp. Line with 5C coop. at mid-point
-fi -4 -2 0 246 13 10 12 14 IR IR7
Resistance (secy. ohms)
3
Fig 7.2-The Trip Characteristic And The Line Locus For Mid-Point Compensation.
30
2`
2C N
L 0
" ,c
U N LA
1C C ti U
N
0
-5 - -6
solid fault Line impedance locus for series cortp. line
with 5W. corp. at mid-point
Xr
Ob
INCS
-32 0.7% ----- --
INC2 INCI 0.5Xr. -- -r ------------------- 0. ffiXb
INC2
+32
yo "Rb Rn
Ro
-1 zb 10 1It 18 Resistance (secy. ohms)
Fig 7.3-The New Relay Trip Characteristic For Mid-Point Series Compensation
30
v z0.
-" 2c E
L 0
v
U 0) IA
V
ü 1c C ci u C) 5
0
-51_ -6 -2 16 10 11 16
Resistance (secy. ohms)
Fig 7.4-The New Trip Characteristic, Measured Impedance And Line Loci For A Fault At The Relay Reach (80% Of The Line Length).
solid fault line impedance loans for series ccep. Line
with 5C comp. at mid-point
º
--
º º -' -- -- -- - ---
X101 I
u a' t4 E
w r- F- t7 z I. H-
w 0 0
J w w
9
ö
1
Ö i
r J i
4
3
2 %
01 2 3 4 5 6 7 69 10 1
FAULT POSITION ( OF RELAY REACH) X10'
Fig 7.5-Relay Operating Time VS Fault Position With The Mid-Point comp. For:
SE SCL-5 GVA. RE SCL-35 GVA Load ang. -O deg.. LL-300 km
50X Series Compensation
Relay Set At S0X Of Line Length Xr-20.4. Xo--3 secy. ohms Rr-13.0. Ro--3.0 secy. ohms Rb-12.2. Ro-3.6 secy. ohms. and
----- Fault Incep. Ang. -0 deg
---- Fault Incep. Ang. -90 deg
-1O
X101 10
u a UI E v W
H O Z I--
CL O
J W cy-
Fig 7.6-Relay Operating Time VS Fault Position With The Mid-Point comp. For:
SE SCL-35 GVA. RE SCL-5 GVA Load ang. -O deg.. LL-300 km
50X Series Compensation
Relay Set At 60% Of Line Length Xr-20.4. Xo--3 secy. ohms Rr-13.0. Ro--3.0 secy. ohms Rb-12.2. Ro-3.6 secy. ohms. and -10
Fault Incep. Ang. -O deg
---- Fault Incep. Ang. -90 dog
FAULT POSITION (% OF RELAY REACH) X101
X101 10^
..
U
E v w
F-
O Z
F-
W 0 O
J W
I
Fig 7.7-Relay Operating Time VS Fault Position With The Mid-Point comp. For:
SE SCL-5 GVA. RE SCL-35 GVA Load ang. -+10 deg.. LL-300 km
50X Series Compensation
Relay Set At 60X Of Line Length Xr-20.4. Xo--3 secy. ohms Rr-13. O. Ro--3.0 secy. ohms Rb-12.2. Ro-3.6 secy. ohms. and -1O
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
FAULT POSITION (% OF RELAY REACH) X101
X101 10,
u
In E
W r_
F-
Z
F-
W 0_ O
J W m
I
Fig 7.6-Relay Operating Time VS Fault Position With The Mid-Point comp. For:
SE SCL-5 OVA. RE SCL-35 GVA Load ang. --10 deg.. LL-300 km
5OX Series Compensation
Relay Set At 60X Of Line Length Xr-20.4. Xo--3 secy. ohms Rr-13. O. Ro--3.0 secy. ohms Rb-12.2. Ro-3.6 secy. ohms. and -1O
Fault Incep. Ang. -O deg
---- Fault Incep. Ang. -9O deg
FAULT POSITION (i OF RELAY REACH) X101
X101 I
U a'
w
r-4 F-
t7 Z
F-
re w n- O
J W
0
9 , 8 ;
7 º
6 º i º e
5 º i º
4 S
3
1 2 0, 1
0 12 3 4 5 6 7 89 10 1
FAULT POSITION ( OF RELAY REACH) X10, 1
Fig 7.9-Relay Operating Time VS Fault Position With The Mid-Point Comp. For:
SE SCL-5 GVA. RE SCL-35 GVA Load ang. -O deg., LL-300 km
40X Series Compensation
Relay Set At BOX Of Line Length Xr-20.4. Xo--3 secy. ohms Rr -13.0. Ro--3.0 secy. ohms Rb-16.3. Ro-3.6 secy. ohms. and -10
Fault Incep. Ang. -0 deg
---- Fault Incep. Ang. -HO deg
,u
x1ol n I
u a, U' e
w
I--
cD z 4
w a_ 0 >- J w m
v
9 -
7 -
5
4 '
3
2
- ------ ---
0 1 2 3 ''t 5 6 7 8 9 10 1
FAULT POSITION (% OF RELAY REACH) X10'
Fig 7.10-Relay Operating Time VS Fault Position With The Mid-Point Comp. And Gap Flash-Over (SGS) For:
SE SCL-5 GVA, RE SCL-35 GVA Load ang. -O deg.. LL-300 km
50% Series Compensation
Relay Set At 80% Of Line Length Xr-20.4. Xo--3 secy. ohms Rr-13.0. Ro--3.0 secy. ohms Rb-12.2. Ro-3.6 secy. ohms. and -10
Fault Incep. Ang. -O deg ---- Fault Incep. Ang. -90 deg
CHAPTER 8
CONCLUSIONS AND FUTURE WORK
8.1-General Conclusions
The work presented in this thesis describes the design
and performance of a new digital distance relay suitable
for series compensated line applications. Based upon
impedance measuring techniques, it provides a satisfactory
response for lines with capacitors installed at the line
ends or mid-point.
The problems associated with the case when the
capacitors' protective gaps do not operate, i. e. the
capacitors remain in the circuit, or when flash-over times
are longer than the relay minimum operating times (which
as a result causes the relaying signals to be distorted)
were discussed.
It was explained that, since series compensated lines
are usually long, a special filtering process is required
to eliminate high frequency oscillations, caused by
travelling waves, from the relaying signals. A digital
band-pass filter with 14 points in its impulse response
was employed which attenuates the dc exponential and
frequencies above 500 Hz. However, for faults far from
the relay , the frequency of the travelling waves are so
low that they fall within the pass band of the filter,
hence affecting the final algorithm output.
Also, the interaction between the line inductance and
the series capacitor, as long as the capacitors remain in
the circuit, imposes a sub-harmonic oscillation on the
relaying signals. The bandwidth of this oscillation was
101
shown to be approximately between dc and 80 Hz, depending
on system source condition and fault position for a
typical series compensated line.
It was explained that the filtering of this frequency
from the system signals is very difficult to achieve.
Thus, it was found more appropriate to attenuate the
resonance oscillation on the final algorithm output, i. e.
measured reactance and resistance.
In order to attenuate any oscillation on the
measured reactance and resistance, an adaptive feature,
using a new recursive averaging filter was incorporated in
the relay. This is a low-pass filter with a very low cut-
off frequency, which attenuates any frequency component
but the dc. The filter is applied when the dominant
oscillation on the measurands is the sub-synchronous
oscillation. If the travelling wave effect is stronger
than the sub-harmonic oscillation, then the filter acts as
a non-recursive averager, with a finite impulse response,
and together with the relay count regime and decision
logic any relay maloperation is prevented.
The errors in the measurement when a single-phase to
earth fault occurs were discussed. It was shown that when
the capacitors are placed at the line ends, and the
voltage transformers are located at the source side of the
capacitors, the conventional current compensation
(residual current and sound phase current) methods do not
provide an accurate measurement.
Two new methods were presented and examined in
detail. One utilises the conventional residual
compensation factor, but it requires modification of the
102
relaying voltage signal in order to enable the relay to
measure the positive phase sequence impedance of the line
from the relaying to fault point. This method provides an
accurate measurement for all faults between the two
capacitors, i. e. on the line.
The other method uses a new residual compensation
factor which is calculated assuming the fault is always at
the relay zone-1 forward reach; hence it implies that the
measurement is accurate only if a fault occurs at that
point. In this method a complex residual compensation
factor is considered, which was explained in considerable
detail.
The latter method proved to have the advantage of
reducing the high frequency oscillation, caused by
travelling waves, and sub-synchronous frequency effect by
providing a better replica of the primary system. Thus it
was decided to use the new residual compensation factor in
the relay.
When the capacitors are situated at the line ends, a
new setting philosophy must be adopted. The presence of a
capacitor in front of the relay affects the reach of the
distance relay. In order to avoid relay operation for
faults at the receiving end bus-bar (or beyond), the relay
zone-1 forward reach must be set at a value less than the
conventional distance schemes for plain feeders. It was
shown that, with the improved relay performance (as a
result of using the new residual compensation factor and
the recursive averager which deals with low frequency
oscillations) the relay can be set at 60% of the line
length for 70% total series compensation (35% at each
103
end). Thus, theoretically a margin of 8% exists between
faults at the relay zone-1 forward reach and faults at the
receiving end bus-bar. However, due to the fact that the
measurement is not accurate for faults at any other points
but the boundary, the actual measurement for a fault at
the receiving end bus-bar is bigger than the actual line
locus. Therefore the margin between the measured
impedance for a fault at the zone-1 forward reach and a
fault at the receiving end bus-bar is even larger.
It was explained that, when the voltage transformers
are located on the line side of the capacitor banks, the
conventional residual compensation factor must be used.
However, a complex residual compensation factor provides a
better relay measurement and response. As mentioned
earlier, the forward reach setting is restricted to 60% of
line length.
It was shown that when the capacitors are situated at
the middle of the line and the residual compensation
factor is used, the relay measures correct impedance only
if a fault occurs before the series capacitor. For faults
beyond the capacitor location the relay measurement is not
accurate. However, if the new residual compensation
factor is used the relay forward reach can be extended to
include the series capacitor. In this study the relay was
set at 80% of the line length. In order to improve the
relay operating time response, a new characteristic was
proposed which greatly improved the relay operating time.
In order to maintain the discrimination ability of the
relay, a time graded characteristic with different
counting regions was used. The sub-synchronous phenomena
104 -n a, ko4
imposes a very difficult task on the trip decision logic.
The process of counting, following a fault, is initiated
by detecting the disturbance. The incremental values of
the characteristic are changed to a lower values after a
pre-set time has elapsed following the fault detection, to
allow more time to the relay to reach a decision. In this
way, a more stable performance was observed from the
relay.
A directional element was incorporated in the relay in
order to maintain the directionality of the relay. The
directional reactance element utilises the memory voltage
polarisation.
A double end fed, single circuit system was simulated
using a distributed parameter model of transmission lines.
The sources were represented by their impedances. In
order to examine the relay behaviour when the capacitors
remain in the circuit, the gap flash-over was prevented
by setting the gap threshold level at a very high value.
It was shown that the relay operating times were about
10 msec for the majority of the relay reach and
independent of fault inception angles. However, for
faults near the boundary, the relay operating time appears
to be dependent upon the fault inception angle.
The relay was also tested for faults at the receiving
end bus-bar, where a severe sub-synchronous oscillation
was superimposed on the measurands. No relay over-reach
was observed for these cases.
The relay restrained for all reverse fault tests at
the sending end bus-bar, for both source side and line
side C. V. T. This is particularly important for line side
105
C. V. T, where for a reverse fault the capacitor reactance
(or any other impedance behind it) looks positive to the
relay and hence falls inside the relay characteristic.
A few tests were carried out when the capacitor
protective gap flash-over is considered. A fixed relay
characteristic was assumed. The relay characteristic was
set assuming the capacitors are in the circuit.
With the capacitors situated at the line ends, the
relay operating time was about 15 msec for faults up to
30% of the line length, irrespective of the fault
inception angle. Also, the relay did trip for faults up
to 40% of the line length with the fault inception angle
of 90 degree. This is due to the fact that the gap flash-
over time was longer than the relay operating time and the
relay tripped before the capacitor is by-passed.
The gap flash-over was also considered for the
situation where the capacitors are placed at the mid-point
of the line. The relay operating time was, as expected,
about 10 msec for faults before the capacitor location,
since the capacitor gap flash-over has no significant
effect on the measured impedance. However, the relay
under-reaches for faults beyond the capacitor location
when the gap flashes.
8.2-Future Work
As mentioned earlier, when the capacitor banks are
situated at the line ends and the C. V. Ts are connected to
the source side of the capacitors, or in the cases where
they are placed at the mid-point of the line, they become
part of the line impedance, which is measured by the
relay. Thus, when the capacitor protective gaps flash
106
over, there is an increase in the measured reactance.
This causes the relay under-reach, if the relay
characteristic has been set assuming the capacitor to be
in circuit. Therefore, it is highly desirable to detect
the gap flash-over in order to dynamically change the
relay characteristic.
Different approaches may be adopted to overcome the
aforementioned problems. Since in a digital distance
relay the locus of the measured impedance is available at
any instant of time, it seems possible to detect the
change in the measured reactance following a gap flash-
over. However, it is known that when a gap flashes, as a
result of change in voltage and current, a travelling wave
phenomena is established in the system. This high
frequency oscillation is superimposed on the measured
resistance and reactance which in turn makes it difficult
, in most cases, to detect the change in the measured
reactance due to the capacitor by-passing. Figure 8.1
shows the measured reactance for a typical single phase to
earth fault, far from the relay. It is clearly evident
that the change in the measured reactance cannot be
determined. Therefore, it is necessary to design a
suitable filter to cope with such effects and also does
not impose any significant time delay to the process.
It must also noted that, when a phase to earth fault
occurs and the new residual compensation factor is used in
the relay, the measured impedance is only accurate for a
fault at the relay forward reach, as long as the
capacitors remain in the circuit. Following a gap flash-
over, the measurement is not accurate. Thus, the change
107
in the measured reactance is not equivalent to the
capacitor reactance, and therefore a comparison of the
measured reactance, before and after the gap flash over is
very difficult.
The other approach is to detect any low frequency
oscillation on the measured impedance. As previously
mentioned, as long as the capacitors remain in the circuit
a sub-synchronous oscillation is superimposed on the
measured resistance and reactance. When the capacitor is
by-passed, the magnitude of this oscillation is greatly
reduced (as some sub-synchronous effect still appears on
the system signals via the mutual coupling to the other
phases). In order to detect any low frequency component,
between 5 to 60 Hz (note that the algorithm produces an
oscillation on the measured impedance which has a
frequency equal to the difference of the system frequency
and the main sub-synchronous oscillation on the system
signals), an especial filtering process is required to
extract the low frequency components.
To design such a filter is extremely difficult,
bearing in mind that the relay must detect the flash over
in a relatively short time.
The other method which can be considered is the effect
of capacitor gap flash-over on the magnitude of the
voltage and current signals and the phase angle between
them. Algorithms are available which calculate the
magnitude of any sinusoidal signal in real time. The
phase angle between them can also be estimated.
When capacitor bank is by-passed as a result of the
gap flashing, the magnitude of the current decreases and
108
as a result the voltage at the relaying point increases.
Of course, the degree of the change depends on the source
impedance. The phase angle between the voltage and
current also changes and becomes approximately the line
angle.
if the signals were pure sine waves, it would not be
difficult to devise an algorithm to detect these changes.
However, in practice, the signals are contaminated with
travelling wave effects, making it extremely difficult to
achieve a satisfactory result. Particularly, it is known
that the algorithms available for calculating the signal
magnitudes and phases often accentuate high frequencies.
Also, if the source impedance is small the change in the
voltage is not great, which in turn makes it difficult to
detect the changes in the voltage magnitude in such cases.
As it appears in the thesis the relay has been
thoroughly tested for single phase to earth faults, for
different system conditions.
It is felt that, it is necessary to fully evaluate the
relay response for other type of faults, particularly a
double phase fault. In this situation if none of the gaps
flashes, two capacitors are in the faulted path which in
turn imposes a more severe sub-synchronous oscillation on
the measurands.
Finally, the relay must be tested for a double circuit
system, where there is another infeed route to the fault
point. It is envisaged that the relay perform correctly in
such systems.
109
X101 8_
LE 0
L d
'U C O U a a
x w a, 31
d
-1I ,nII
11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time ( sec) X10-2
Fig 6.1-Measured Reactance VS Time For 7OX Series Compensation (35% At Each End)
And Source Side C. V. T And With Cap. Flash-Over (SGS) For: SE SCL-3 GVA. RE SCL-7 GVA Load ang. -O deg., LL-300 km Inception Ang. -O Deg. Flash-Over Time- 9 msec After Fault
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115
APPENDIX 3A
Let the voltage and current signals be expressed as
pure sinusoidal waveforms:
v(t)=V"sin(wot) 3A1
i(t)=I"sin(wot-0) 3A2
where: wo=power system frequency.
O=phase angle between the fundamental voltage and
current.
The relaying signals can be expressed as:
vl(t)=V"sin(wot) 3A3
il(t)=I"sin(wot-0) 3A4
V2(t)=V"sin(wot-e) 3A5
i2(t)=I"sin(wot-J-0) 3A6
Where 0 is the delay angle which is used to produce
the second equation.
D, R and L are calculated using the following
equations.
D=il(t)i'2(t) - i'l(t)i2(t) 3A7
R= 1
[vl(t)i'2(t) - V2(t)i'l(t)] 3A8
L= D
[v2(t)il(t) - vl(t)i2(t)] 3A9
The current derivatives are calculated as: i'l(t)=I"wo"COS(wo-O) 3A10
i'2(t)=I'wo'COs(wo-4I-0) 3A11
116
Substituting for voltages and currents in Equation 3A7
D term can be calculated.
D=I"sin(wot-0) " I"wo"cos(wot-o-O)
-I"wo"cos(wot-o) " I"sin(wot-0-0) 3A12
Taking I2 wo common Equation 3A12 can be written as:
D=I2"wo"[sin(wot-o)"cos(wot-o-0)
- cos(wot-o)-sin(wot-4-o)] 3A13
Equation 3A13 can be expressed as:
D=12'wo"{1/2[sin(wot-o-wot+0+0) + sin(wot-o+wot-o-0)]
- 1/2(sin(wot-o+wot-4-o) - sin(wot-o-wot+o+o)]} 3A14
or
D=I' wo"{1/2[sin(O) + sin(2w0t-20-O)]
- 1/2[sin(2wot-20-O) - sin(O)]} 3A15
Note that the double frequency components are
eliminated from the expression. Equation 3A15 can be
written as:
D=I' wo"sin(0) 3A16
The measured resistance is given by Equation
3A8. Substituting for voltages and currents yields:
R= 1D
[V. sin(wot) " I"wocos(wot-o-0)
- V"sin(wot-0) " I"wo"cos(wot-4)] 3A17
Taking V"I-wo common and use similar method as above,
Equation 3A17 can be written as:
117
V"I"wo R= D
{1/2[sin(O+O) + sin(2wot-O-O)]
- 1/2[sin(O-O) + sin(2wot-o-O)]} 3A18
Note the double power system frequency oscillation
which are cancelled from the expression. Rewriting
equation 3A18 yields:
V"I"wo R=
D [sin(¢+0) - sin(O-0)] 3A19
Substituting for D and expanding Equation 3A19 gives:
V R= COS(O) 3A20
The line model inductance is calculated by:
D [V"sin(wat-o) I"sin(wot-0)
- V"sin(wot) I"sin(wot-o-0)] 3A21
Equation 3A21 can be written as:
V"I L=
D {1/2[cos(¢-O) - cos(2wot-0-O)]
- 1/2[cos(. +O) - cos(2wot-4-O)]} 3A22
Note the double power system frequency oscillations
which are eliminated from the expression. Rewriting
equation 3A15 gives:
V"I L=
D [cos(¢-0) - cos(O+0)) 3A23
Substituting for D and expanding Equation 3A23 gives:
V L= sin(0)
I-wo 3A24
118
APPENDIX 3B
Consider input signals of the form:
v(t)=vo"sin(wot) + vsu"sin(wsut+ß) 3B1
and
i(t)=1o"sin(wot-0o) + Isu"sin(wsut+ß-osu) 3B2
where:
wog wsu =power system and sub-synchronous frequency
respectively.
Vo, 10 =voltage and current magnitude of fundamental
components respectively.
Vsu, Isu =voltage and current magnitude of sub-synchronous
components respectively.
P =phase angle between the fundamental & sub-
synchronus components.
, 00 =phase angle between the power system fundamental
voltage and current.
q5su =phase angle between the sub-synchronous voltage
and current.
The relaying components vl(t), v2(t), i1(t) and i2(t)
can thus be written as:
vl(t)=vo"sin(wot) + vsu"sin(wsut+p) 3B3
il(t)=Io"sin(wot-0o) + Isu"sin(wsut+ß-''su) 3B4
v2(t)=Vo"sin(wot-O) + Vsu"sin(wsut+ß-e) 3B5
i2(t)=Io"sin(wot-0o) + Isu-sin(wsut+ß-osu'O) 3B6
Where e is the delay angle which is used to produce
the second equation.
D, R and L' are calculated using the following
119
equations.
D=il(t)i'2(t) - i'l(t)i2(t) 3B7
R= D
[vl(t)i'2(t) - V2(t)i'l(t)] 3B8
L'= D
[v2(t)il(t) - vl(t)i2(t)] 3B9
The current derivatives are calculated as:
i'l(t)=wo"Io"cos(wot-0o) + wsu'Isu"cos(wsut+p-0su) 3B10
i'2(t)=wo"Io"cos(wot-00-0) + wsu"Isu"cos(wsut+p-Osu-0) 3B11
Substituting for voltages and currents in Equation 3B7
D term can be calculated.
il(t)"i'2(t)=[Io"sin(wot-0o) + Isu"sin(wsut+p-osu]
[wo"I0"cos(wot-4o-o) + Wsu"Isu"cos(wsut+ß-osu-©)] 3B12
i'l(t)"i2(t)=[wo"IO"COB(wot-00) + wsu"Isu"CO8(wgut+p-Osu)'
(I0"sin(wot-0a-0) + Isu"sin(wsut+ß-Osu-0)] 3B13
Rearranging Equations 3B12 and 3B13 yield:
il(t)"i'2(t)=wo"I0"sin(wot-oo)"cos(wot-/o-0)
+ wsu"Isu"Io"sin(wot-¢o)"cos(wsut+A-osu-0)
+ wo-Isu"Io"sin(wot+0-osu)"cos(wot-oo-0)
+ wsu"I$u-sin(wsut+p-Osu)"cos(wsut+ß-Osu_e) 3B14
i'l(t)'i2(t)=wo'IO2 "cos(wot-oo)'sin(wot-oo-0)
+ wo"Io"Igu"cos(wot-oo)-sin(wsut+p-OBU-O)
+ wsu'Io'Isu'cos(wsut+P-q5su)'sin(wot-oo-0)
+ wsu ASU cos(wsut+p-osu)"sin(wsut+, B-9su-O) 3B15
120
Equation 3B14 and 3B15 can be expressed as:
il(t) i'2(t) Wo2I0[sin(0)+sin(2wot-200-0)]
Wsu'Isu'Io +2 {sin[(wo-WSU)t-ß-(ýo-ýsu)+O]
+ sin[ (Wo+Wsu)t+P-(ýo+ýsu)-0]}
Wo' I2u Io + {-sin[(wo-wsu)t-ß-(0o-Osu)-0]
+ sin[(wo+wsu)t+P-(Oo+4su)-off}
wsu'Isu +2 [sin(©)+sin(2wsut+2ß-20su-O)] 3B16
. i'l(t)"i2(t)=
wo
2 (-sin(e)+sin(2wot-240-o)]
+ wsu'2su'Io{sin[(w
-w t- 0 o su) A-(Oo-osu)-]
+ sin[(wo+wsu)t+ß-(oo+osu)-o]}
+ wo" Isu Io{-sin[(wo-wsu)t-p-(oo-osu)+O]
2 + sin((wo+wsu)t+p-(Oo+osu)-0)}
wsu'Ia su +2 [-sin(O)+sin(2wsut+2p-20. u-O)] 3B17
Note that there are four frequency components in
il(t) "i'2(t) and i'l(t)"i2(t) which are given by, 2wo,
2wsu, wo-wsu and wo+wsu. The determinant term D, is given
by Equation 3B7. Thus:
D=il(t)"i'2(t)-i'1(t)"i2(t)
D=wo"I02"sin(0) + wsu"Isu"sin(O)
wsu'Io'Isu +2 {sin[(wo-wsu)t-ß-(Oo-osu)+0]
- sin[(wo-wsu)t-ß-(oo-osu)-OJ}
121
- wo. Isu Io{sin[(wo-wsu)t-P-(Oo-Osu)-E)]
2
- sin[(wo-wsu)t-ß-(Po-Osu)+0]} 3B18
Note that frequency components of 2wo, 2wsu and wo+wsu
have been eliminated from the D term. Expanding and
taking sin(0) common Equation 3B18 can be expressed as:
D=sin(O)"{wo'I0 + Wsu'Isu
+ Io'Isu-(wo+wsu)-Cos[(wo-wsu)t-P-(Oo-Osu)]} 3B19
It is evident from Equation 3B19 that, the D term
oscillates about a dc level given by wo"Iö + wsu'Isu with
a frequency of wo-wsu.
Measured R is given by Equation 3B8. Cross multiply D
Equation 3B8 can be written as:
D"R=vl(t)"i'2(t) - V2(t)'i'l(t) 3B20
Substituting Equations 3B3 to 3B6 into Equation 3B20
gives:
v1(t)"i'2(t)=(V0*sin(wot) + Vsu"sin(wsut+p)]
[wo"io"cos(wot-oo-o) + wsu"Isu. cos(wsut+P-osu-e)) 3B21
and
v2(t)"i'l(t)=[Vo"sin(wot-e) + Vsu"sin(wsut+ß-0)]
[wo"Io"cos(wot-0o) + wsu"Isu"cos(wsut+P-Osu)] 3B22
Equations 3B21 and 3B22 can be expanded and written in
the following form:
V1(t) i'2(t)=wo Vo 1. sin(wot) cos(w0t-ý0-0)
+ wsu'vo'Isu-sin(wot)-cos(wsut+ß-Osu-O)
+ wo-vsu-Io-sin(wsut+ß)"cos(wot-oo-0)
122
+ wsu"Vsu"Isu"sin(wsut+ß)"cos(wsut+ß-0su-O) 3B23
V2(t)"i'l(t)=wo"Vo"Io"sin(wot-O)"cos(wot-0o)
+ wsu"vo'Isu-sin(wot-e)"cos(wsut+ß-Osu)
+ wo. Vsu'Io"sin(wsut+p-0)"cos(wot-0o)
+ wsu"Vsu"Isu"sin(wsut+ß-o)"cos(wsut+ß-osu) 3B24
Equation 3B23 and 3B24 can be written in the form of
Equation 3B25 and 3B26.
v1(t)'i'2(t)=wo 2o
Io(sin(00+o) + sin(2wot-00-O)]
wsu'Vsu'Isu +2 [sin(osu+©) + sin(2wsut+2a-osu-0)]
wsu'Vo'Isu +2 {sin[(wo-wsu)t-Q+osu+e]
+ sin((wo+wsu)t+P-osu-o)]}
wo'Vsu'Io +2 {-sin[(wo-wsu)t-p-0o-o]
+ sin[(wo+wsu)t+p-¢o-e)]} 3B25
wo - Vo'Io V2(t)"i'l(t)= 2
[sin(0o-0) + sin(2wot-00-0)]
wsu'Vsu'Isu +2 [sin(q5su-o) + sin(2wsut+2p-osu-O)]
wsu-Vo - Isu +2 {sin[(wo-wsu)t-P+osu-O)
+ sin((wo+Wsu)t+P-osu-e)]}
Wo'Vsu'I0 +2 {-sin[(wo-Wsu)t-P-ýo+e]
+ sin[(wo+wsu)t+p-oo-0)]} 3B26
Note that there are four frequency components in
vl(t)"i'2(t) and v2(t)"i'l(t) which are given by, 2wo,
123
2wsu, wo-wsu and wo+wsu.
calculated. Thus:
Using Equation 3B20, D"R is
D"R=WO wo-v22 Io[sin(oo+©)
- sin(oo-O)]
Wsu'Vsu'Isu + [sin(osu+o) + sin(osu-o)] 2
Wsu - Vo - Isu +2 {sin[(Wo-Wsu)t-P+osu+0]
- sin((wo-wsu)t-P-tsu-O)]}
wo'Vsu'I0 +2 {-sin[(wo-wsu)t-ß-0o-O]
+ sin((wo-wsu)t-ß-oo+o)i} 3B27
It is clear from Equation 3B27 that the ac components
whose frequencies are given by 2wo, 2wsu and wo+wsu are
eliminated. Expanding Equation 3B27 and taking sin(O)
common yields:
D"R=sin(o)"{wo"vo"Io"cos(oo) + wsu'Vsu. Isu"cos(osu)
+ [WSU'vo'Isu'COs(Osu) + Wo'Vau'Io"cos(Oo))
"cos[(wo-wsu)t-P)] + [wo-vsu-Io"sin($o) + Wsu-vo-Isu-sin(Isu)]
"sin[(wo-wsu)t-P)]} 3B28
Equation 3B28 can be expressed as:
D"R=sin(o)"{wo"Vo"Io"cos(0o)+wsu"Vsu"Isu"cos(¢su)
+(AR+BR)i"sin((wo-wsu)t-ß+tan'1(AR/BR)II
where: 3B29
AR=wsu'Vo'Isu'cos(Osu) + Wo'Vsu'Io'cos(Oo) 3B30
BR=Wo'Vsu'Io'cos(Oo) + Wsu'Vo'Isu'cos(Osu) 3B31
It is evident from Equation 3B29 that the measured D"R
124
consists of dc and ac components and frequency of the ac
part is given by wo-wsu"
Measured L' is given by Equation 3B9. Cross multiply
D Equation 3B9 can be written as:
D"L'=V2(t)"il(t) - vl(t)"i2(t) 3B32
Substituting Equations 3B3 to 3B6 into Equation 3832
gives:
v2(t)"il(t)=[Vo"sin(wot-o) + Vsu"sin(wsut+p-0)]
(I0"sin(wot-00) + Isu"sin(wsut+ß-Osu)] 3B33
and
vl(t)"i2(t)=(Vo"sin(wot) + Vsu"sin(wsut+ß)]
(I0"sin(wot-00-8) + Isu-sin(wsut+ß-osu-0)] 3B34
Equations 3B33 and 3B34 can be expanded and written in
the following form:
V2(t)"il(t)=V0"Io"sin(wot-o)"sin(wot-00)
+ Vo'Isu-sin(wot-0)"sin(wsut+ß-osu)
+ Vsu"Io-sin(wsut+)3-o)-sin(wot-00)
+ Vsu"Isu"sin(wsut+p-0)"sin(wsut+p-osu) 3B35
vl(t)"i2(t)=Vo"Io"sin(wot)"sin(wot-00-0)
+ Vo. Isu-sin(wot)"sin(wsut+p-Osu-O)
+ Vsu"Io"sin(wsut+p)"sin(wot-oo-0)
+ Vsu"Isu"sin(wsut+p)"sin(wsut+p-osu-p) 3B36
Equation 3B35 and 3B36 can be written in the form of
Equation 3B37 and 3B38.
125
Vo"I0 v2(t) il(t)=
2 (cos(O0-0) - cos(2wot-0o-0)]
Vsu'Isu +2 [cos(, Osu-0) - cos(2wsut+2ß-Osu'O)]
+ Vo-Isu
cos (w -wr )t- +0 2{[ouß
Hsu-"]
- cos[(Wo+WSU)t+ß-osu-O))}
Vsu'Io +2 {COB((wo-wsu)t-P-oo+0]
- COs[(Wo+Wsu)t+p-oo-0)]} 3B37
vl(t)"i2(t)= 2 [cos(oo+o) - cos(2wot-oo-O)]
Vsu'Isu +2 [cos(osu+0) - cos(2wsut+2p-osu-0)]
Vo'Isu +2 {cos[(wo-wsu)t-ß+0su+e]
- COB[ II Vsu"I0
+2 {CO8((Wo-Wsu)t-P-$o-O]
- COS((Wo+Wsu)t+A-oo-O)]} 3B38
Note that there are four frequency components in
v2(t)"il(t) and vl(t)"i2 (t) which are given by, 2wo, 2wsu,
wo-wsu and wo+wsu. Using Equation 3B32, D"L' is
calculated. Thus:
Vo'I0 D"L'=
2 [cos(¢o-0) - cos(0o+0)]
Vsu'Isu +2 (CO8(Osu-o) - COS($su+O)]
Vo - Isu +2 {CO8((wo-wsu)t-ß+isu-O]
- COS[(Wo-wsu)t-ß+osu+O)]}
126
+ Vsu2Io{COs[(WO-Wsu)t-ß-oo+e]
- COS[(Wo-WSu)t-ß-Oo-0)]} 3B39
It is clear from Equation 3B39 that the ac components
with the frequencies of 2wo, 2wsu and wo+wsu are
eliminated. Expanding Equation 3B39 and taking sin(0)
common yields:
D"L'=sin(O)"{V0"Io"sin('o) + Vsu'Isu-sin(osu)
+ [vo-Isu"cos(Osu) - vsu"Io"cos(Oo)]
"sin((WO-WSu)t-Q)]
+ [vsu"Io"sin(oo) + vo"Isu"sin(4su)]
"sin[(wo-wsu)t-ß)]} 3B40
Equation 3B40 can be expressed as:
D"L'=sin(o)"{vo"Io"sin(po)+vsu. isu-sin(osu)
+ (AX+Bg)1"sin[(wo-wsu)t-, B+tan-l(Ax/Bx)]}
where: 3B41
Ag=Vo'Isu-sin(osu) + Vsu"Io"sin(oo) 3B42
BX=Vo'Isu'cos(Osu) - Vsu-Io"cos(Oo) 3B43
It is evident from Equation 3B41 that the measured
D"L' consists of dc and ac components and frequency of the
ac part is given by wo-w$u.
127
APPENDIX 3C
Consider an to be the approximation to the
differential i'.
i(k+n)-i(k-n) an= 3C1
2nh
Using Taylor expansion formula yeilds:
(nh)2 (nh)3 i(k+n)=i(k)+nhi'(k) i"(k)+
3! isle (k)+---- 3C2
(nh)2 (nh)3 i(k-n)=i(k)-nhi'(k)_T-i11(k)_
3! ioil (k)+.... 3C3
21
Subtracting 3 from 2 and ignoring the higher order of
h gives:
2 (nh) 3 i(k+n)-i(k-n)= 2nhi'(k)+
3! i"'(k) 3C4
Substituting 3C4 into 3C1 gives:
(nh)2 a(n)=i'(g) +
3! iýýý(k) 3C5
Using one point on each side of sample k gives:
h2 al=i'(k)+ 3!
1"'(k) 3C6
Using four points on each side gives:
128
16h2 a4=i' (k) +
3! iýý' (k) 3C7
It can be seen that the error term is proportional to
h2, and is 16 times bigger when 4 points on each side is
used.
129
APPENDIX 4A: Line data
The line is horizontally constructed and discretely
transposed. An earth plane resistivity of 100 A"m is
assumed and due to the horizental construction, the
material of the earth wires is alumoweld, which is known
to be approximately 25 times more resistive than ACSR
phase conductors. The following power frequency (50 Hz)
parameters are then applicable:
Phase conductor resistance = 0.0339 A/km
Phase conductor reactance = 0.0078 Q/km
Phase conductor radius = 9.05 cm (Two conductors per phase)
Earth wire resistance = 1.882 Q/km
Earth wire reactance = 0.388 Q/km
Earth wire radius = 1.8 cm
The above parameters, together with the tower arrangements
and earth plane effects, produce the following parameters:
Self impedance ZLS= 0.1223 + jO. 5358 Q/km
Mutual impedance ZLM= 0.0878 + jO. 2268 0/km
Self admittance YLS= j0.354.10-5 A'1/km
Mutual admittance YLM= jO. 298.10-6 0'1/km
The positive and zero phase sequence impedances and
admittances of the line are calculated by:
ZL1=ZLg-ZLM
ZL1= 0.0345 + jO. 309 n/km
ZL1= 0.3109 L+83.629' Q/km
and
ZLO=ZLS+2ZLM
ZLO= 0.2979 + jO. 9894 Q/km
130
ZLO= 1.033 L+73.243' cl/km
YL1= YLS+YLM S2/km
YL1- j0.384.10-5 R-1/]m
YLO= j0.294.10-5 iä-1/km
131
APPENDIX 5A
Figure 5A. 1 shows the symmetrical component network
connection for an "a"-phase-ground fault. During a phase
fault to ground, for the source side VT the phase
potential Vsae at the relay location consists of the
following drops in the sequence networks:
Vsae-Ist(aZL1-]Xc1/2)+Is2(aZL2-]Xc2/2)+Is0(aZLO-Jxc0/2) 5A. 1
But ZL1=ZL2 for lines and Xcl=Xc2=XcO=Xc for the
capacitor banks. Therefore:
Vsae-(Isl+Is2)(aZL1'7Xc/2)+IsO(aZLO'7Xc/2) 5A. 2
The phase current is given by:
Isa-Isl+Is2+IsO 5A. 3
rearranging 5A. 3 gives:
Ist+Is2=Isa-IsO 5A. 4
Substituting 5A. 4 into 5A. 2 yields:
Vsae-(aZL1-jXc/2)Isa+I(aZLO-jXc/2)-(aZL1-jXc/2)JIsO 5A. 5
The residual current can be calculated from:
Ires-Isa+Isb+Isc°3ISO 5A. 6
Therefore equation 5A. 5 can be written as:
Vsae-(aZL1-jXc/2)Isa+ 1/3[(aZLO-jXC/2)-(aZL1-]XC/2)]Ires 5A. 7
or ZLO
Vsae-aZLlIsa-]Xc/2Isa+1/3( -1)aZLlIres 5A. 8 ZL1
The impedance measured by the relay, when conventional
132
residual compensation is used, is thus given by:
Vsae Isa Z= = aZL1-J () Xc/2
Isa+Kclres Isa+KcIres
where:
Kc= 1/3(l ZLO
ZL1
ZLO -1) = 1/3( -1)
ZL1
5A. 9
133
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to
cn O `4
(D
ý r. rn rt CD
cn n O
Hb
(DO ti cn O p- :j
art CD <0
O 0 rt 0
0 h
ä
tic
m
Ift c c n1 r X y r
v Ci
I
;5 -if Vý1"
Iry
V"
"I
APPENDIX 5B
Equation 5A. 7 can be rewritten as:
Vsae-(aZL1-jXc/2)Isa+ 1/3(aZLO - aZL1)Ires
but the mutual impedance of the line is given by:
ZLM=1/3(ZLO-ZL1)
5B. 1
5B. 2
Substituting Equations 5A. 6 and 5B. 2 into Equation
5B. 1 gives:
Vsae°aZL1Isa']Xc/2lsa+aZLM(Isa+Isb+Isc) 5B. 3
or
Vsae=aZLllsa']Xc/2lsa+aZLMIsa+aZLM(Isb+Isc) 5B. 4
Equation 5B. 4 can be written as:
Vsae'a (ZL1+ZLM)Isa-jXc/2Isa+aZLM(Isb+Isc) 58.5
but ZL1+ZLM is equal to the self impedance of the line.
ZLS ZL1+ZLM 5B. 6
Substituting Equation 5B. 6 into Equation 5B. 5 gives:
Vsae=a ZLSIsa'7Xc/2lsa+aZLM(Isb+Isc) 5B. 7
Equation 5B. 7 can be written as:
aZj Vsae-a ZLS[IsaT (Isb+Isc)]-]Isaxc/2 5B. 8
aZLS
The measured impedance by the relay is given by:
Z_ Vsae
=a ZLS -j Isa
Xc/2 5B. 9 Isa+Ks(Isb+Isc) Isa+Ks(Isb+Isc)
where: aZLm ZLM Ks- = 5B. 10
aZLS ZLS
134
APPENDIX 5C
Equation 5A. 7 can be rewritten as:
aZLp-jXC/2 Vsae-(aZL1-7XC/2)Isa+l/3( -1)"(aZL1-jXC/2)Ires
aZL1-]XC/2 5C. 1
or
Vsae-(Isa+K(a)Ires)(aZL1-]Xc/2) 5C. 2
where: aZLO-jXc/2
K(a)= 1/3( -1) 5C. 3 aZLl-7Xc/2
Thus:
Vsae Z= = aZL1-JXC/2 5C. 4
Isa+K(a)'res
135
APPENDIX 5D
The voltage at the relaying point is given by equation
5C. 2. Using the new method of residual compensation, the
measured impedance for any fault along the line is given
by:
Vsae 5D. 1
Isa+KarIres
where:
arZLO- 7Xc/2 Kar=1/3( -1) 5D. 2
arZLi- JXc/2
ar=proportional fault position for a fault at the
zone-1 reach point. Note that ar is constant (relay
forward reach).
Substituting equation 5C. 2 into equation 5D. 1 gives:
Z_Isa+K(a)Ires (akl- 7Xc/2) Isa+KarIres
5D. 3
136
APPENDIX 5E
Figure 5E. 1 shows the symmetrical component network
connection for an "a"-phase-ground fault. During a phase
fault to ground, for the line side VT the phase potential
Vsae at the relay location consists of the following drops
in the sequence networks:
Vsae-Is1(aZL1)+Is2(aZL2)+Is0(aZLO) 5E. 1
but ZL1=ZL2 for lines Therefore:
Vsae-(Isl+Is2)(a2L1)+IsO(aZLO) 5E. 2
The phase current is given by:
Isa=Ist+Is2+Isp 5E. 3
rearranging 5E. 3 gives:
Is1+Is2-Isa-IsO 5E. 4
Substituting 5E. 4 into 5E. 2 yields:
Vsae°(aZL1)Isa+(aZLO-aZL1)IsO 5E. 5
The residual current can be calculated from:
Ires-Isa+Isb+Isc=3Is0 5E. 6
Therefore equation 5E. 5 can be written as:
Vsae-(aZL1)Isa+ 1/3(aZLO-aZL1)Ires 5E. 7
or ZLO
Vsae-aZLlIsa+1/3( -1)aZLlIres 5E. 8 ZL1
The impedance measured by the relay, when the
conventional residual compensation is used, is thus given
137
by:
Vsae Z= = aZL1
Isa+KcIres
where: ZLO
Kc= 1/3( -1) ZL1
5E. 9
5E. 10
138
PUBLISHED PAPERS
IEEE POWER ENGINEERING SOCIETY SUMMER MEETING
JULY 1989, LONG BEACH, USA
PAPER No 89SM 725-3 PWRD
INVESTIGATION OF ALTERNATIVE RESIDUAL CURRENT COMPENSATION FOR IMPROVING SERIES COMPENSATED LINE DISTANCE PROTECTION
F. GHASSEMI A. T. JOHNS Senior Member
The City University London - UK
ABSTRACT
In this paper the results of investigations into methods of improving the
measuring accuracy of distance protection
applied to series compensated lines is given.
It is shown that in order to compensate the
error in impedance measurement under earth-
fault conditions, an alternative to
conventional residual current compensation
must be used. The effect of load and source impedances on the measurands, when the
conventional and alternative compensation factors are used, is given.
RESIDUAL CURRENT COMPENSATION TECHNIQUES
Consider the system shown in Figure 1 with typical series compensation of 70%. Line data is given in Appendix A.
SE -ice Is -j'ß! 2 R[
74.1 o-1111
Z D
vs1(-P- I VR Relay
INTRODUCTION
Series capacitors have become an important
component in economical long distance power transmission[ 1,2]. The economical location for
any capacitor bank is generally in the
vicinity of the line end and hence it may
represent a part of the terminal substation. This paper concentrates on a transmission
system with compensation at each end.
The series capacitors and their over-
voltage protection introduce fairly well known
difficulties in protecting series compensated lines. This is particularly so when distance
schemes are applied(3,4]. It is known that,
there are system conditions that do not result in capacitor protection gear operation after the occurrance of a fault[5]. Also with the
new generation of Ultra-High-Speed protection, the fault may be cleared in considerably less
than one cycle which can in turn be much
shorter than capacitor gap flash-over
times[6]. Therefore it is highly desirable
that distance protection schemes perform the impedance measurements with the highest degree
of accuracy with capacitor banks in circuit.
one of the problems which arises, - when capacitors are in the circuit, is the effect of the residual compensation on the accuracy
of the distance relay when an earth fault
occurs. The authors reported some preliminary investigation into this effect in reference 7. In this paper, a more detailed investigation is presented and a proposed solution is given.
I'. 1C t sys, rE I CUNF CUUATIUN
It is well known that in distance protection, for phase to ground faults, compensation methods are used to allow the relay to measure the positive phase sequence (pps) impedance of the line from the relaying to fault point[8]. The most commonly used method employs residual current compensation, where a fraction of the residual current is added to the phase currents. It is shown in Appendix B that if the conventional residual compensation factor (CRCF) is used, the impedance seen by the distance relay is given by:
Vsae Isa Zr= aZLl-) ( )Xc/2 (1)
Isa+KcIres Isa+KcIres
where: Zr=measured impedance
Vsae=phase voltage at the relaying point Isa=faulted phase current at the
relaying point Ires=residual current
ZL1=total pps impedance of line Xc=total capacitor reactance/phase
a=proportional fault position Kc=conventional residual compensation
factor
I ZLO
- 1) (2) =1( 3 ZI, 1
From equation (1) it is clear that the impedance measured depends on and varies with the value of Isa/(1sa+KcIres). Figs 2. a and 2. b illustrate the variation in magnitude and argument of the ratio Isa/(Isa+Kcires) for different source capacities and pre-fault load. In the case where the source capacities at the line ends are equal(10 GVA symmetrical short-circuit level) and the system is pre- fault unloaded the ratio stays approximately at a constant value, for fault positions of up to 80%. However, note the large variation in the current ratio for situations where the
local source is much weaker than that at the
remote end or when the system is loaded. This implies that the relay will measure different impedances for different source and load
situations.
X10-1 I
1
1
1
0
i
2;
;
0'
n 8
I
-- ---------------------
oI23t5G789 10 1 FAULT POSITION W00 1% OF LINE LENCTN) X1 0 *1
? IG 2. a VARIATION IN ýIsa/(Isa*Kclres)I WITH FAULT POSITIO
Xto1
v y
ü
ü
ü
ýA
0 s+ s. ý C,
1R -2
,11I iI 1ý
-3
Id -1
-s -s -7
p123456789 10 1 FAULT POSITION tsI00 (% OF LINE LENGTH) X1 0"''
FIG 2. b VARIATION IN /Isa/llsa+Kczres) WITZ) FAULT POSITION Be SCL-! B OVA, Re SCL-O OVA. LOAD ANO--tO a. ß
.......... SC SCL-! O ßV A, RC SCL-40 OVA, LOAD AN -0 O. 0
----- Se OCL-O OVA. All GCL-30 OVA. LOAD ANG-. 90 O. O
.......... Se SCL-5 OVA. All SCL. 3 OVA, LOAD ANG-O O. O
In order to ensure that the relay measures the equivalent pps impedance of the line from
the relay to fault point(for relay setting, purposes)
it is shown in Appendix C that the
residual compensation factor must be set according to the proportional fault position a. The measured impedance is then given by:
Vsae Zs aZL1-j Xc/2 (3)
Isa+K(a)Ires
1 aZLO-j Xc/2 where: K(a)- -( - 1) (4)
3 aZL1-j Xc/2
This means that only if the fault position is known to the relay will the measured value of impedance be independant of source and load current.
Figures 3. a and 3. b show the variation in magnitude and argument of Kea versus fault location for the line under study. It must, however, be noted that for a given fault location and degree of series compensation the residual compensation factor is the same as that shown irrespective of the actual line length.
X10-1
C C W
0 F
C, CJ i
15 I0 5
FAULT POSITION WOO lt Of LINE LHNCTS) xi 0+ I
FIG 3. a VARIATION OF IK(a)l WITH FAULT POSITION
xlo1
0 H w
2
PAUL? POSITION "tION I1 OP LINE LENGTH) X 10+ 1
FIG 3. b VARIATION OF /K1(, ) WITH FAULT POSITION
Modified Residual Compensation For Series compensated Lines
Because the fault position is unknown, it is not possible to set the residual compensation factor according to the fault position, it is proposed that the residual compensation factor is set at a fixed value K(ar), assuming the fault position to be at the relay zone-i reach boundary. Appendix D shows that the impedance seen by the relay is then given by:
Iaa+K(a)Ires Zra ( aZL1- jXc/2) (5)
Isa+K(ar)Ires
1 arZLO-]Xc/2 where: K(ar)- -( - 1) (6)
3 arZL1-]Xc/2
ar=proportional fault position for fault at the relay zone-1 reach point.
Figures 4. a and 4. b illustrate the
variation in the expression (Iaa+K(a)Ires)/(Isa+K(ar)Ires) with fault
position for an assumed zone-1 forward reach of 60% (ar=0.6) and different source and load
situations. It is revealed that, at the forward reach, the expression has a magnitude of unity and angle of zero for all situations considered. With reference to equation 5, this
means that the relay measures a unique and constant impedance for a fault at the zone-1 boundary (60% for the reach assumed).
It is evident from Figures 4. a, b that the source impedance affects the measurement of the fault location; this is primarily due to the fact that the residual current distribution is affected to a small degree by the remote source impedance.
X10-1 7A
d ä s0
N W
A
W O W
i+ I.. K c? i
Lb ý 24 i
II
I0
FAULT POSITION a, 100 It OF LINE LCNCTl) X1 Ot1 FIG 4. a VARIATION OF
(lsa'K(a)Ires)/(IsafK(ar)Ires)I WITH FAULT POSITION
SC SCL-35 OVA. nG SCL-S OVA. LOO ANO.. -$Q 0. g .......... tit! SCL-10 OVA. fit! SCL-1O OVA. LOAD ANO-O O. O ----- SC 6CL. 5 OVA. ne SCL-Sy OVA. LOAD ANO-$O qý0
.......... ttr SCL-A OVA. NL' SCL-35 OVA. LOAD ANGýO OHO
X101 14
v
K
0
C,
PULT POSITION ad100 lt OF L1N6 LUNCT11) X10+
FIG 4. b VARIATION OF I(Isa'K(a)Ires)/(Is., +K(ar)Ires) WIT)1 FAULT POSITION
5H CCL: y9 OVA, R! CCL"! OVA, LOAD ANOýýtO tlop """""""""" YK YCL-*U OVA, n. L' CLIO UVA, LUAU ANY-O O. p ----- YC I: CL.. d OVA, qK SCL-JV OVA, LUAU ANO. ý$0 Yip " """""-""" UL SL"L-5 OVA. NK SCL-3t% UVA, LUAU ANü-O Y. p
IMPLEMENTATION IN DICITAL DISTANCE 1ErAYS
A large number of papers have described and investigated the performance of digital distance relays of which those given in reference 9,10 and 11 are typical. These are particularly suited to the implementation of a complex, rather than real, modified residual current compensation factor of the type proposed in the previous section. Since samples of the residual current are available at discrete instants of time AT-i/fs (where fs is the digital sampling frequency) it is possible to effectively implement the phase shift associated with the modified residual compensating factor LK(ar) by taking a sample n samples previous to any measuring sample instant. For example, it can be seen from Fig 3 that, for a relay set with a forward reach of 60%, which in turn eliminates the possibily of indiscrimination for faults beyond the remote capacitor, the modified compensating factor K(ar) is equal to approximately 1.82L-6.2". Thus, in a digital relay operating at a sampling frequency say 4 kiiz, on a power system having a nominal frequency of 60 tiz, one sample interval corresponds to a phase shift of approximately -5.4". A constraint is thus imposed on choosing the value of n which, for the assumed sampling frequency (4kHz) and application illustrated, is equal to unity. For any particular relay and application, the value of n that gives the closest equivalent phase shift to the ideal value (LK(ar)) is used.
It will be evident from Fig 3. b that for all zone-1 setting above about 50% the argument of the modified residual compensation factor is small and it has been found that little error occurs if K(ar) is assumed real. Since in most practical application the zone-1 reach exceeds 50% the need to implement an
effective phase-shift by the means described is often obviated. In the results that follow, which relate to an application with a nominal zone-1 reach setting of 60%, the value K(ar has thus been taken as real (K(ar)=1.82LO. 0
EVALUATION OF IMPROVEMENT IN ACCURACY
A good illustration of the improvement in
accuracy made possible by implementing the modified residual compensating factor developed can be obtained by considering a system with 5 GVA and 35 GVA symmetrical short-circuit level sources at the sending and receiving ends respectively. In all cases, the line is subjected to a single-phase to ground fault. The prefault load angle is defined by the argument of the ratio VS/VR (see Figure 1)
so that a positive value of LVg/VR is
associated with pre-fault load exporting from the relay location and a negative value prefault load importing.
Figures 5. a and 5. b show the measured resistance and reactance versus load angle for
different fault positions when the
conventional residual compensation factor
(CRC? ) (given in equation 2) is used. The
change in measured impedance for different load angles is clearly evident. The resistance measurement in particular is more affected by
the load current than is the reactance. When Quadrilateral Distance relay characteristics are used, the variation of measured reactance, particularly for faults near the boundary of the zone-1 reach can be particularly troublesome because errors of measurement with pre-fault load can cause either overreaching or underreaching. Figures 6. a and 6. b, show the corresponding performance when the new modified residual compensation factor (NRCF) is used. In this 'case , the
measurements at the boundary (60%) are unaffected by the pre-fault load. Furthermore
variations in_reactance measurements with load for other fault positions, especially those
near the boundary, are minimal. This in turn enables measuring accuracy to be maximised and avoids both overreaching and underreaching in Quadrilateral relay applications.
Figures 7 and 8 illustrate the variation with fault position of the resistance and reactance measured for different load angles when CRCF and NRCF are used respectively. The
pps resistance and reactance of the fault loop
are also shown. Again the effect of NRCF on the measurement is clear. In particular, note the constant and load invariant measurement at the boundary (60%) for different load currents when NRCF is used. Note also that, when CRCF is used, a relay with a Quadrilateral
characteristic will significantly underreach if the reactance reach is set at a value corresponding to the fault loop reactance for
a fault at the zone-1 reach boundary. It is also evident from Fig 7. b in particular that some variation in measurement accuracy (and hence relay reach) occurs with pre-fault cicuit loading.
ii
ö
ü `ý. s-
w
A
-z _,
-6
FAULT P S111011% Of LIEF LENCIE) ox
7oX
OX
OX
30X
9 0X
FIG 5. a VARIATION OF MEASURED RESISTANCE WITH PRE-FAULT LOAD ANGLE WITH CRCF
c
FAULT POSITION It or Lima UNGTuI
1
90%
70%
ß-60X
---50%
-- ý30X
cu -i: ) -iu -: I uS 10 15 20 LOAD ANCLI I/VsIVN) degree
WAD A«GL6 IIVS/VQI degree
FIG 5. b VARIATION OF MEASURED REACTANCE WITH PRE-FAULT LOAD ANGLE WITH CRCF
7 FAULT POSITIONIt OF LINE LENCiN) 90Xý
6 ©OX\ Y
Ö^
M
'Ö
O
W
rt
t. 3
W
sox
30
LOAD ANCLL I/VgjVRI degree
FIG 6. a VARIATION OF MEASURED RESISTANCE WITH PRE-FAULT LOAD ANGLE WITH NRCF
26
21 FAULT POSITIONIt Of LINE LENCTNI
22 20 90X
Is -
t4 Box 70X 12
10 6O
$ 50
6
4 30X
2
20 -IS -10 -S 0 5 10 15 2 0
t
(AAO AAG! L UYSIVg degree
FIG 6. b VARIATION OF MEASURED REACTANCE WITH PRE-FAULT LOAD ANGLE WITH NRCF
LOAD ANGLE ILVSIVg) 2
10 +1
0.
ý ýaLl
2-
0
-iö
34567891
c
u
r-
s u
9 c
FAULT POSITION 9,100 lt Of LINE LERCS9) X10- 1
FIG 7. a VARIATION OF MEASURED RESISTANCE WITH FAULT POSITION WITH, CRCF
40
35- WAD ANGLE ILVSIV&I
30 1 +10
25-
20.1s
10 oIL1-3IC/2
5.000
0 -5 34567891 2
w s 0
v
.n
z
FAULT POSITION 4-100 It OF LINE LENGTH) X1 OT '
FIG 7. b VARIATION OF MEASURED REACTANCE WITH FAULT POSITION WITH CRCF
FIG 8. a VARIATION OF MEASURED RESISTANCE WITH FAULT POSITION WITH NRCF
i
21 ICED AAC66 (/VS/V11 -10
22
20 t10O 18
16
14
12
10
&ILI-jlc/7
FAULT P0SITIOX ä100 (L OF LINE UNTO) X10+1
FIG 8. b VARIATION OF MEASURED REACTANCE WITH FAULT POSITION WITH NRCF
CONCLUSIONS
The effect of the residual compensation factor on the measuring accuracy of distance protection measurements when an earth fault occurs on a series compensated line has been investigated. It has been shown that when conventional residual compensation is used, there will be an error in impedance measurement which depends on the ratio Isa/(Isa+Kclres)" It has also been shown that this expression depends on load current and source conditions at the line ends.. In consequence, errors of measurement and concomitant overreaching/underreaching can occur when conventional residual compensation methods, as applied to plain feeders, is used in series compensated applications. An alternative method of compensation has therefore been developed. This has been found to improve accuracy of measurement at the boundary and also improves relay measurement integrity for other fault positions in series compensated line applications.
5
ACKNOWLEDGEMENT
The authors would like to thank The City University, London, UK, and the Science and Engineering Research Council UK for the provision of facilities and support for this research.
Reactance of capacitor/phase at each end= 32.44 n primary.
14.27 A secondary Line Length-300 km
Appendix B REFERENCES
(1. ] R. S. Seymour, E. C. Starr, "Economic aspect of series capacitors in high voltage transmission, "AIEE Trans, PAS, Vol 70, pp. 1660-1670,1951-
[2] G. Jahnke, N. Fahlen, O. Nerf, "Series capacitors in power system, "IEEE Trans, PAS-94, No 3, pp. 915-925, May/June 1975.
[3] M. M. Elkateb, W. J. Cheetham, "Problems in the protection of series compensated lines, " IEE Conference publication on power system protection, No 185, pp. 215-220,1980.
[4] M. Shafik, F. Ghassemi, A. T. Johns, "Performa-
nce of digital distance protection for
series compensated systems, "Universities Power Engineering Conference, SUNDERLAND- UK, April 1987.
(5] J. Berdy, "Protection of circuits with series capacitors, "AIEE Summer general meeting, DENVER-COLO, June 1962.
[6] Y. Mansour, T. G. Martinich, J. E. Drakos, "B. C. Hydro series capacitors bank staged fault test, "IEEE Trans, PAS-102, No7, pp. 1960- 1969, July 1983.
(7] A. T. Johns, F. Ghassemi, "Analysis and compensation of errors in distance protection measurement for series compensated systems, "Universities Power Engineering Conference, NOTTINGHAM-UK, September 1988.
(g] W. A. Lewis, S. L. Tippett, "Fundamental basis for distance relaying on three-phase systems, "AIEE Trans, pp. 694-709, January 1947.
[9] ß. J. Mann, I. F. Morrison, "Relaying a three phase transmission line with a digital computer, "IEEE Trans, PAS-90, No 2, pp. 742-749, March/April 1971.
[10]G. D. Rockefeller, E. A. Udren, G. Gilcrest, "High speed distance relaying using a digital computer, " Parts 1&2, IEEE Trans. PAS-91, No 3, pp. 1235-1258, May/June 1972
(11]A. T. Johns, M. A. Martin, "Now Ultra High speed distance protection using finite transform techniques, "Proc. IEE, Vol 131, pt. C No 5, pp. 188-196, May 1983.
Figure B1 shows the symmetrical component network connection for an "a"-phase-ground fault. During a phase fault to ground, for the line side VT the phase potential Veae at the relay location consists of the fpllowing drops in the sequence networks:
Vsae=Isl(aZLl-7 Xcl/2)+Is2(aZL2-7 Xc2/2)+ Is0(aZLO-j Xc0/2) (B1)
But ZL1-Z 2 for lines and XcloXc2uXc0®Xc i for the capac tor banks. Therefore:
Vsae®(Isl+is2)(aZLl-j Xc/2)+IßO(aZLO-J Xc/2) (B2)
The phase current is given by:
Isa'Is1+Is2+IsO (B3)
Rewriting B3 gives:
Ist+Is2°Isa-Is0 (B4)
Substituting B4 into B2 yields:
Vsae°(aZL1'] Xc/2)Isa+((aZLO. j Xc/2)- (aZL1-J Xc/2))Is0 (B5)
The residual current can be calculated : Ires°Isa+Isb+Isc=3Is0 (B6)
Therefore equation B5 can be written as:
Vsae-(aZL1-j Xc/2)Isa+ 1/3((SZLO-J Xc/2)- (aZLl-j Xc/2))Ires (B7)
or
Vsae-aZLlIsa-j Xc/21sa+1/3( ZLO
-1)aZLlIres ZL1 (Be)
The impedance measured by the relay, when conventional residual compensation is used, is thus given by:
usae 'Ba Zr- m aZLl-J (
sa ) Xc/2 (B9)
Isa+KcIres Isa+KcIres
APPENDIX A: SYSTEM DATA
The line is horizontally constructed and discretely transposed. System voltage is 500 y. V. The pps and zps impedances of the line are:
7-L1° 0.3109(83.62' n/km primary 0.1367(83.62' n/km secondary
ZLOm 1.033L73.24' n/km primary 0.4545(73.24" n/km secondary
where:
Kc- 1/3( I ZLO
I -1) a 1/3( ZLO
-1) ZL1 ZL1
Gse CRe
ZSSi
-SE RE-
-jXci/2 jXc, n
aZLI (1-ot)zil
Isl IR1
F, trE=
FIG B1 SYMMETRICAL COMPONENT CONNECTION FOR AN "a"-PI! ASE-GROUND FAULT
C APPENDIX
Equation B7 can be rewritten as:
Vsae-(aZL1-i Xc/2)Isa+1/3i
(aZL1-j Xc/2)Ires
aZLO-j Xc/2 -1)*
aZLl-j Xc/2 (Cl)
or
V0ae-(Isa+K(a)Ires)(CZL1_i Xc/2) (C2)
where: aZLO-j Xc/2
K(a)= 1/3( -1) (C3) aZL1-] Xc/2
Thus: usae
Zrs s aZL1-j XC/2 (C4) Isa+K(a)Ires
APPENDIX D
The voltage at the relaying point is given by equation C2. Using the new method of residual compensation, the measured impedance for any fault along the line is given by:
Vsae Z r=
(Dl) Ie. K(ar)Ires
Where: arZLO- j Xc/2
K(ar)-1/3( -1) (D2) arzLl' j Xc/2
and proportional fault position for a fault at the zone-1 reach point.
Substituting equation C2 into equation Dl gives:
Isa+K(a)Ires Yr (aZL1- j Xc/2) (D3)
Isa+K(ar)Ires
Foroozan Chassemi was born in Abadan, Iran in September 1958. He obtained his Master of Science degree in Power Systems Technology from University of Bradford, Bradford, UK. in November 1985. He joined the Power System Protection Research Group at City University, London, UK. in January 1986 and is working towards his PhD degree. His main area of
interest is the reactive power compensation and protection of transmission lines.
Allan Thomas Johns (SMIEEE, 1908) is Head of the Department of Electrical, Electronic and
' Information Engineering, and Professor of Electrical and Electronic Engineering at City University, London, England, UK.
+ Professor Johns is best known for his work on the protection, simulation and control of Power Systems and he is the author
of over 100 papers on these topics. He is a fellow of the Institution of Electrical Engineers and in 1982 was awarded the degree of Doctor of Science by the University of Bath, UK. for an original and substantial contribution to knowledge of Electrical Engineering.
7
UPEC 1987, SUNDERLAND, UK
1
PERFORMANCE OF DIGITAL DISTANCE PROTECTION FOR SERIES COMPENSATED SYSTEMS.
M. Shafik F. Ghassemi A. T. Johns
The City University, London.
ABSTRACT
Research is being performed into the use of modern digital signal processing technology in the design and engineering of next generation digital distance
protection for application to series compensated systems. This paper reviews the work being performed aril in particular details the performance which is
obtained under practical fault operating conditions in typical compensated feeder systems. The effect of series capacitor gap flashover on the performance is
investigated together with investigations into the
effect of subsynchronous resonance phenomena. The
paper concludes with a discussion of the prospective performance benefit in relation to present day
equipment.
INTRODUCTION
The use of series capacitors to compensate long
transmission lines has became an increasingly common
practice during the last decade. This is mainly to: -
relays) to maloperate.
(b) Subsynchronous Resonance - The existence of series capacitors in the transmission circuit gives rise to a resonance phenomenon with a frequency between 0 and 60 Hz. When combined with the characteristics of a synchronous machine, it can create the possibility of sustained or poorly damped subsynchronous oscillations. These can result in an oscillating torque and torsional vibrations in the turbo-generator shaft. To a protection scheme, such as distance protection. these oscillations can again result in maloperation.
(c) Loss of Directionality of Relays - When conventional distance relays are used with series capacitor compensated lines, the leading fault current may cause the relay to lose its directional discrimination abilty and, as a result, the relay may block instead of tripping or vice versa.
(a) Increase the carrying capacity of transmission lines.
(b) Reduce the losses associated with transmission lines.
(C) Improve both the transient and steady state stability of transmission systems.
(d) Control the load flow between parallel circuits.
(e) Obtain a desired voltage profile.
Series capacitors are either located in the middle of the line for less than 502 compensation or at both its ends for compensation greater than that limit. Capacitors are usually protected against over-voltage by means of spark gaps across the terminals and by-pass breakers. Different techniques are now in use to operate capacitor protection schemes, each having different operational advantages [Jancke (1) and Ahl, ren (2)1.
On the other hand, the use of capacitors and their
over-voltage protection has introduced some difficulties in protecting long series compensated lines. The object of this paper is to investigate
these difficulties especially, with the introduction
of digital relays and outline the facilities they can provide to this practice.
operational Problems with Series Compensated Lines
During the last few years, a number of publications tackled the common protection problems of long series compensated lines (Bendy (3), El-Kateb (4) and Ballance (5)]. These can be summarised as follows: -
(a) Transient Stability - The operation of the capacitor protection gear (namely the spark gap) results in the loss of the capacitor when it is most needed, thus jeopardizing the systems stability. To compensate for that, by-passed capacitors are reinserted back into the system as soon as the fault is cleared. The process of by-passing the capacitor and reinserting it again in the circuit often results in system disturbances that can cause line protection schemes (especially distance
Digital Relays
Recent advances in the field of microprocessors have resulted in a great improvement in their reliability. increase in their speed and reduction of their cost. Current research clearly shows that the next generation of protection relays is likely to be implemented using microprocessors. The following advantages are clear: -
(a) Flexibility of implementation is provided through the use of software to implement the relaying functions. This leads to the use of standard hardware to achieve an economical design.
(b) The use of modern high speed microprocessors capable of addressing large high speed memory facilitates the implementation of very complex relaying functions which can substantially improve the performance (e. g. intelligent relays). This can be easily done using currently available high level languages (e. g. C).
(c) Ease of communication between different equipment through the use of standardised, high speed communication links.
(d) The use of high capacity storage devices allows data logging for off-line analysis and performance evaluation.
In the study outlined below, a digital distance relay based on the 'Phase Modified Fourier Transform Principle' is considered for evaluation with a capacitor compensated long transmission line. The theory and development of that relay is outlined in several recent publications (e. g. Johns (6)1. The relaying process is based on solving the plain feeder circuit equation: -
v(t) " Rai(t) +L -1(t)
where Ra and L,,, are the line resistance and inductance up to the fault point while v(t) and i(t) are the voltage and current at the relaying point. For series compensated lines the equation to be solved by the relay is: -
J
2
v(t) - RQi(t) + l. aýti(t) C Ji(t)dt 2
The relay algorithm contains a number of digital filters and signal processing operations for signal conditioning and mathematical manipulations.
RELAY PERFORMANCE EVALUATION
The study is performed using a digital computer simulation which is divided into primary and secondary
stages as follows: -
Irim_arySystem Simulation
IliPhly accurate digital simulations for faulted,
series compensated lines were used to produce voltage
and current waveforms for different types of faults on
a given line configuration. These programs were developed within the Power Systems Measurement and Protection Group and are described in ref. (Aggarwal
(7)1. Due to the length and memory requirement,
primary system simulation was performed on a main frame computer and the resulting wave forms data files
weie down-line loaded to a PDP 11/23 microcomputer
where the relay simulation was performed. It should be noted that both the current transformer and the capacitor voltage transformer simulations are included
with the primary system.
Secondary System Simulation
The digital relay used for the study was simulated
according to the block diagram of Fig. I where: -
(a) Linear current and voltage interfaces are considered.
Cli
CVT" VT LPF
(b) The low pass antialiasinb filter is realised by the impulse response of a second order Butterworth with 1 kHz bandwidth.
(c) A 12-bit AID converter is considered with 2 10 V input limits. Both the current and voltage interface gains are adjusted according to that limit.
(d) r 16-bit microprocessor was considered during the sinulation for the relay realization.
(e) The characteristics of the preconditioning filter stage used is shown in Fig. 2 where it is required to block both the dc offset and the travelling wave components from the measured signals.
(f) The two orthogonal components of each current and voltage waveforms are obtained using the two orthogonal filters with the impulse responses shown in Fig. 3.
(g) The quadrilateral relay characteristics for the line represented by the parameters of Appendix 1A) are shown in Fig. 4. From the figure it is clear that in order that the relay would not respond to faults occuring at the receiving end busbar, the protected zone has to be reduced to 58% of the line length. In order to protect this reduced zone (including the sending end capacitor), the reverse reach is extended to -40% of the line length, as shown.
The relay operation is based on determining an estimate of the line impedance up to the fault from the waveforms of the line voltages and current at the
wb ý4 9)
v4a fin 0) 4v9w .H QäNM mmmmp Ei
F. a
-. -- Analog Side I Digital Side ý Fig. 1 Block Diagram For the Digital Distance Relay
. -_a_ IAI
80
60
40
20
0.0
-20.
-40.
-60.
:)
Fig 2 Frequency Responce of the Digital Prefilter.
0 BG(- U. OJ
-- 1 -.
ý' 1 10 010.5
Iimcros z 0.5 --- -- '
=
Fiy 3 Impulse Responce for the SIN and COS Orthogonal Filters.
T
XI °I
XR
x (n)
Solid Fault Impedance Locus for the Plain Feeder.
Solid Fault Impedance Locus for the Compensated Feeder.
ZL1
RR
-xo
Fig 4 Quadrilateral Tripping characteristics.
R (A)
3
relaying point. These values are compared with the
boundaries of the protected zone. A counter, which is
implemented in the relay software is incremented every
time the impedance is found to be inside the protected ozone and decremented if found outside. A trip signal
is issued when the trip counter reaches a certain
piespecified level.
Simulation Results
In the following part some examples are given for the
performance of the digital distance relay using the
test transmission line outlined in Appendix (A]: -
(a) Plain Feeder Applications - Fig. 5 shows the
relay performance when connected to the test
line with no compensation (i. e. plain feeder)
following voltage maximum, solid "a"-earth
faults at different locations on the line. The
figure clearly shows how the measured resistance
and reactance converge inside the protected zone
and the corresponding trip counter behaviour.
n
12.
8.
4.
0.
40
30
'0
to
0
n
40 30.
20.
10.
0.
Fig 5 Relay Performance for Plain Feeder.
(b) Series Compensated Line Application - When the same line was compensated using two capacitors at both ends, each with 35% of the total line reactance, the following performance was obtained: -
(i) Effect of Subsynchronous Resonance - When the protective gaps were prevented from flashing over (by setting their sparking level to a very high value), the effect of subsynchronous resonance on the measured line impedance to the fault can be clearly seen from Fig. 6. It is clear that the relay performance can be greatly affected by this phenomenon especially for faults close to zone boundaries. In such cases, the relay logic may experience difficulty in deciding whether a fault is more likely to be inside or outside the protected zone (and thus maloperate).
x
R
lt
20.
16.
12.
8.
4.
0.
-4.
-8.
K
9)
Fig 6 Effect of Subsynchronous Resonance. (ii) Effect of Protective Gap Flashover - When the flashover level was set at 2.5 p. u. of the rated capacitor voltage and the relay was tested with the test line subject to a maximum voltage fault on the "a"-phase, at 10% of the line len t the performance shown in Fig. 7 was obtained. (The figure shows the behaviour of the measured reactance when the flashover occurs as compared to the case with no flashover). It is clear that the measured reactance changes as soon as the capacitor is bypassed by the flashover gap. and the relay can under-reach in this case.
A
28.
24.
20.
16.
12.
8.
4.
0.
x
X
AS)
Fig 7 Effect of Capacitor Gap Flashover.
General Discussion
In order that the digital relay can operate correctly with series compensated lines, the following recommendations are to be considered: -
X
R
0 (a) The relay should be capable of detecting
protective gap flashover and take necessary action to compensate for any under-reach.
(b) The relay logic has to be modified to cater for the effect of subsynchronous frequency
(a) 20% Fault, Trip time 5 ms. a
ms. (b) 40% Fault, Trip Time -5 ms.
MS.
(C) 60% Fault, Trip Time - 4.75 ms.
components in the measured line impedance. It is clear that filtering out such low frequencies in the vicinity of the power frequency is not practical given the requirement of ultra high speed operation of the relay. When aa_averaging process was employed before the trip counter, a
rea improvement in the relay performance was achieved. Fig. 8 shows the inverse relay c aracteristics with the simple counter regime while Fig. 9 shows the same characteristics with the averaging process.
Operatimg Time (ms)
20.
16.
12.
8.
4.
L!
ý-z
V
0
c 0 N
0.10 20 30 40 50 60 70 % Distance
f 90o Fault, Without Gap Flashover.
0 Oo Fault, Without Gap Flashover.
900 Fault, with Gap Flashover
Fig 8 Relay Responce With the Simple Count Regime
11
APPENDIX A
Main line length is 300 km, the line is horizontally constructed and discretely transposed. The line can have 70% compensation using two capacitor banks at its ends. The line self and mutual impedances are given below: -
ZS - 0.1223 + J0.5358 Q/km Zm - 0.0878 + j0.2268 A/km
The positive and zero phase sequence impedances of the line were calculated: -
Z1 =ZS - Zm . ". Z1 - 0.0345 + jO. 309 2/km
Z1 - 0.3109/83.629 and Z0 - Zs + 2Zm
ZO - 0.2979 + j0.9894 2/km ZO - 1.033/73.243
The relay's quadrilateral characteristics can be defined by the following parameters: -
Xc - 32.445 2 Xr - 21.321 ß Xa - -37.08 Q Rr - 13.0 2 Ro - -3.0 2 Line angle t" 83.622
Faults were single phase to earth fault (phase 'a') and applied at phase 'a' peak voltage.
REFERENCES
1. G. Jancke, N. Fahlin, 0. Nerf, July 15-20 1973, 'Series Capacitors in Power Systems'. IEEE/PES Summer Meeting and EHV/U}IV Conference, Vancouver. B. C., Canada, 915-925.
20.
16.
12.
a.
4.
0.
Fig 9 Relay Responce with The Averaging Count
Regime.
CONCLUSIONS
In this paper, some aspects of the performance of a
digital distance relay are studied when operated with
series compensated lines. Major operational problems
are outlined to investigate the possible research
directives to improve the performance.
the study showed the potential of digital distance
relays in the field of series compensated lines.
Research is currently in progress to overcome the
problem-s outlined and to develop a modified version of
the relay suitable for these difficult applications.
ACKNOVLED(; E MENTS
the authors are grateful for the provision of
facilities at The City University, London and G. E. C.
M,. asuremcnts Ltd.. Stafford. Especial thanks are due
engineers at G. E. C. Measurements Ltd. for helpful
si"ussions . The support of the U. K. Science and
p, 11oncerinA Research Council and G. E. C. Measurements
1tij, are greatly acknowledged.
2. L. Ahigren, N. Fahlen. K. E. Johanson, February 4-9 1979, 'EHV Series Capacitors With Dual Gaps and Nonlinear Resistors Provide Technical and Economical Advantages'. IEEE/PES Winter Meeting, New York, NY.
3. J. Gerdy, June 17-22 1962, 'Protection of Circuits With Series Capacitors'. ATEE Summer General Meeting, Denver, Colorado, 929-935.
j 4. M. M. El-Kateb, W. J. Cheetham, 1980, 'Problems in the Protection of Series Compensated Lines', TEE Conference Publication on Power System Protection No. 185,215-220.
5. J. W. Ballance. S. Goldberg. January 28 - February 2 1973. 'Subsynchronous Resonance in Series Compensated Transmission Lines'.. IEEE/PES Winter Meeting. New York, N. Y.. 1649-1658.
6. A. T. Johns, M. A. Martin, May 1983, 'New Ultra High Speed Distance Protection Using Finite Transform Techniques', IEE Proc., Vol. 130, Pt. C. No. 3, May, 127-138.
7. R. K. Aggarwal, A. T. Johns. A. Kalam, September 1984. 'Computer Modelling of Series Compensated EIIV Transmission Systems', Proc. IEE, Vol. 131, Pt. C, No. S. 188-196.
10 20 30 40 50 bu 1 %
VDisGance
A, 900 Fault, Without Gap Flashover.
0 00 Fault, Without Gap Flashover.
A 90o Fault, With Gap Flashover.
UPEC 1988, NOTTINGHAM, UK
ANALYSIS AND COMPENSATION OF ERRORS IN DISTANCE PROTECTION MEASUREMENT FOR SERIES COMPENSATED SYSTEMS
A. T. Johns and F. Chassemi
City University, London, UK
ABSTRACT
This paper investigates the operation and accuracy of a digital distance relay when used on series compensated systems. Residual compensation factor was found to be one source of error in measurement for phase to earth faults. New method of residual compensation is proposed and relay performance is investigated.
INTRODUCTION
As shown in appendix (B), if the residual compensation factor is set according to fault position, the relay will measure: -
Zr la + K(a)lres ' aZhl - JZc
This means that only if the fault position is known to the relay will the measured value be very close to the positive sequence value of the line.
Series capacitors have proven to be an important component in economical long distance power transmission (1,2,31. The capacitor banks are either located at line ends or in the middle. each scheme has its own merits and disadvantages. From a protection point of view the former proves to be more difficult to deal with. For this reason this paper considers a transmission line with 102 compensation (3S2 at each end). Series capacitors introduce some difficulties in protecting such lines especially in distance schemes 14, S. 61. One of the difficulties which arises is the effect of residual compensation on accuracy of the distance relay for earth faults. The object of this paper is to investigate this effect and propose a method to enhance the digital distance relay accuracy. %
RESIDUAL COMPENSATION
it is well known that in distance protection, for phase to earth faults, compensation methods are used to allow the relay to measure the positive sequence impedance of the line from relaying to fault points (7]. One of these methods is residual compensation, where a fraction of the residual current is added to the phase currents as shown by equation 1: -
Vae (1) Zr ' Is + Klres - UZL1
Where: Zr measured impedance K residual compensation factor -
-50 -Lai - 1)
Vae faulted phase voltage at relay la phase current Tres residual current ZLI, ZLp positive and zero sequence
impedance of line a fault position
Appendix [AI shows that if the same residual compensation factor is used. when protecting series compensated lines. the relay would not measure the positive sequence impedance of the line to the fault point and an error will exist in the measurement. This error depends on the expression
a Ia ' Klres
if the relay is required to measure the positive sequence impedance of the line (for relay setting purposes) a modification to residual compensation factor is needed.
Proposed Method for Residual Compensation
Clearly. knowing the fault position to carry out the measurement is neither realistic nor practical. Since the relay is required to be most accurate at and around the boundary. it is proposed that the fault position (a) in equation D3 is set at a fixed value assuming the fault is at the boundary of the relay. Thus accuracy of the relay will be max for faults at and around the forward reach. It is clear that when capacitor flashover occurs the residual compensation factor must be modified to the plain feeder value.
RELAY PERFORMANCE EVALUATION
The study is performed using a digital computer simulation which is divided into primary and seccondary stages as follows: -
Primary System Simulation
A horizontal configuration, single circuit line was simulated, using highly accurate computer program. The program is described in reference [8). The line data is given in appendix [C).
To observe the effect of the capacitor. the action of the capacitor protection tear was prevented by adjusting the gap threshold setting to a high value.
Digital Relay
The digital distance relay used in the study is* based on the work which was originally carried out by Johns and Martin [9). A number of papers have since described and investigated the performance of this relay for both series compensated and plain lines [6.10). The relay has a quadrilateral characteristic which is set according to positive sequence impedance of the line.
Unlike plain feeder distance protection schemes, where the forward reach of the relay is set at 80%. in series compensated lines the forward reach of the first independent zone is set. at a lower value to exclude the remote end busbar and to allow for errors in discrimination. Fit. I shows the relay characteristic and the line locus. The forward reach was set at 60% of the line to exclude the receiving end busbar. The relay protects the local capacitor bank.
ANALYSIS OF TU RELAY PERFORMANCE
In distance relaying the accuracy of the resistance measurement is not important to the decision making logic. Accordingly. only reactance measurements are illustrated here.
Using conventional methods. the residual compensation factor was calculated to be 0.77. When the new method was used it was calculated to be 1.82 by putting a-0.6 in
equation B3 (assuming the fault position to be at the boundary). Fig. 2 illustrates the variation of measured reactance versus magnitude of K, for different fault positions. No load was considered on the system. The marked values on the reactance axis are th& actual line reactances for the shown fault positions.
The error in measurement IS clear when K-0.77. However, for faults at the boundary (60% of line length). the measurement is very close to the line reactance when K-1.82. Fit. 3 illustrates the variation of measured reactance versus fault position and the line reactance locus. - if K-0.77 there is an error in measurement and the relay under-reaches. But if K is calculated according to the new method, the measurement is very accurate at the boundary.
Simulation Results
Fig, 4 shows the measured reactance by the relay for a fault at 50% of the line length. It is clear that when K is calculated conventionally, the relay has under-reached and did not trip. However setting K-1.82, the measured value is inside the boundary and the relay responded correctly.
fig. 5 illustrates that the accuracy of the relay has greatly increased for a fault at the boundary. The strong subsynchronous oscillation was dealt with by filtering and suitable decision logic. A number of tests were carried out to evaluate the relay response ,
for different load and fault inception angle situation. No maloperation was observed and the relay responded correctly for faults close to the reach point.
Fib. 6a and 6b show operating time versus the relay reach for 2 load situation.
CONCLUSION
In series compensated lines, the presence of the series capacitor causes inaccuracy in distance protection scheme. One source of inaccuracy in earth fault measurements is the residual compensation factor. A new method of residual compensation was proposed. The results presented, show that the accuracy and hence deserimination ability of the relay has improved. In the new method the capacitor flash over must be detected to modify the compensation factor to maintain the accuracy in measurement.
ACKNOWLEDGEMENTS
The authors would like to thank City University. London. GEC Hensurements, Stafford and the Science and Engineering Research Council for the provision of facilities and support for this research.
APPENDIX A During a phase fault to ground the phase potential Vae at the relay consists of the following drops in the sequence networks.
Vae ' I1(aZL1 - 1X1) + I2(aZL2 -J) 22
+ IO(QZLO - JXCO) (Al)
But 2LI - ZL2 for lines and ZCl ' XC2 - XCO
for capacitor banks XCI
therefore V8e - (Il + I2)(a2yl - Ji)
+ IO(aZLO - JX2-? ) (A2) The phase current is given by
11 +I+ I0 (A3) Rewriting A3 gives
Il + 12 - Ia - I0 (A4) Substituting A4 into A2 yields
Vae " (aZLI - JXZI)Ia + ((aZt, O -J )C21)
- (42L1 - JK`Z'1)110 (A5) The residual current can be calculated as follows
Ires ' la + Ib * Ic - 310 (A6)
therefore equation AS can be written as
Vae " (aZLI -J I)Ia
+ 3I(aZLp - JXZI)
(aZLI - 1x? ))]Ires(A7)
or Vae ' aZLIIa - ?
X2IIa + j(ZLO -1)aZLllres(AS)
The measured impedance by the relay is riven by equation A9
Zr -V- la
la +Klres aZLI - Sj- la +Klres (A9)
where K- 3(IZLOl-I)
APPENDIX B
Equation Al can be rewritten as
Vde (0ZL1 - 1X21)Ia
)(CI
+ 3(a2L2 - 1)(aZLI - ,
1! 1 )Ires (BI)
or Vae - (Ia ' K(a)Ires)(aZLI -1
1) (82)
XC)
where k(a) 1(a2L1 -'- 1) (B3)
Thus Vae XC1 Zr y; -; K(a)ltes - aZL1 - J-2 (84)
APPENDIX C
Hain line length is 300 km, the line is horizontally constructed and discretely transposed. System voltage is 500 kV. Local and remote sources capacities are S and 3S GVA respectively. The positive and zero phase sequence impedances of the line are: -
zl - 0.0345 " j0.309 0/km or
yI - 0.3109/83.629 0/km
10 - 0.2979 + jO. 9894 0/km
or y0 - 1.033/73.243 2/km
The relay's quadrilateral characteristics in terms of secondary values can be defined by the following parameters: -
ICr - 10.19 Q x0 - -16.0 a Etc - 13.0 0 Ito - -3.0 ß Line angle 4- 83.629'
iteact3nce o of
St capacitor at each end: -
14.275 0 secondary
BEFE_ REHCES
1. Seymour. R. S. and Starr, E. C., 1951, "Economic aspect of series capacitors in high voltage transmission", AIEE Trans. Power Apparatus and Systems, 70, 1660-1670.
2. Maneatis. J. A., Hubacher. E. J., Rothenbuhler. W. N. and Sabath. J., 1971, "500 kV series capacitor installations in California". IEEE Trans PAS, PAS90. 1138-1149.
3. Jahnke. C., Fahlen. N. and Nerf, 0., 1975. "Series capacitors in power system". IEEE Trans PAS, PAS94,915-925.
4. Berdy, J.. 1962, "Protection of circuits with series capacitors". AIEE Summer General Meeting, Denver, Colorado, 929-935.
5, El-Kateb. M. H. and Cheetham, V. J.. 1980, "Problems in the protection of series compensated lines". IEE Conference Publication on Power System Protection, N0. I85,215-220.
b, Shatik. M.. Chassemi, F. and Johns, A. T.. 1987. "Performance of digital distance protection for series compensated systems", OPEC. Sunderland.
7. Lewis. W. A. and Tippett. S. L., 1947. "Fundamental basis for distance relaying on three-phase system", AIEE Trans.. 694-709.
8. Abbarwal, R. K.. Johns, A. T. and Kalam. A.. 1984, "Computer modelling, of series compensated EHV transmission systems", Proc IEE, Rat. PtC, NO. 188-196.
9. Johns, A. T. and Martin. M. A., 1983, "New ultra-high-speed distance protection using finite-transform techniques". Proc ZEE. 130. PtC. NO. 127-138.
10. Moore. P. J. and Johns. A. T.. 1987. "The performance of new ultra-high-speed distance protection", OPEC. Sunderland.
T I
x) cI
XA
x (a)
Sol4d Fault Impedance Locus for the Plain Feeder.
Solid Fault Impedance Locus for the Compensated Feeder.
LLZZL--I--
RR
-XD
Figure 1 Quadrilateral Tripping Characteristics.
24.0
20.0
oy V
16,0 ,I
i4 'a
N
8.0
4.0
40
0.0
iý 80%
'tom, 70% 1
60%
50%
4---40%
0.8 1.0 1.2 1.4 1.6 1.8 2.0 k Residual compensation factor
R (A)
Figure 2 Measured Reactance Vs Residual Compensation Factor
i
30
25
20
i5
10
x0 0 u
-S u N
-10
-15
ö
d V C d
V
v
N
O
Y V C
U A u
d
Fig 3. Variation of reactance vs fault position
1 2L0 kl 3
Cý ZLl
I- 1,
1 fOIr. ZLO - 7Xc k2
3 Oir. ZLl - jXc - 1)
whereCtr - 0.6
pol
aº
N E
N 6i
H
C M N b w N
O
ro
v a
b
Fault Position (% relay reach)
Fig 6a. Relay response for no load condition
a) Fault inception angle 90 b) Fault inception angle 0
X101
a
a' N '0 4
d 6
b
Fault Position relay reach) Fig 6b. Relay response for +10 load angle
a) Fault inception angle 90
b) Fault inception angle 0
xio,
I Fault Time (ms)
Fig 4. Measured reactance vs time -
a) Measured reactance when k-0.77
b) Measured reactance when k=1.82
Time (ms) xlO-l
Fig S. Measured reactance vs time
a) Measured reactance when k-0.77
b) Measured reactance when k-1.82
UPEC 1989, BELFAST, UK
PERFORMANCE OF EARTH FAULT ELEMENTS OF DIGITAL DISTANCE RELAYS APPLIED TO SERIES COMPENSATED LINES
GHAT I AND A. T. JOHNS
THE CITY UNIVERSITY. LONDON
This paper investigates the operation and accuracy of distance relay when applied to series compensated systems with 50% compensation at the mid-point of the line. The new modified residual compensation factor proposed by the authors in earlier papers is implemented in a distance relay. It is shown that, to modify the response of the distance relay a new relay characteristic may be employed.
INTRODUCTION
Series capacitors are well known for improving the cost and operation of the EHV transmission lines. Series compensated lines have always been considered to require special protective relays and schemes. The performance of the relays, especially distance relays, depends on capacitor location and its
percentage compensation with respect to the
associated transmission line. It is known that, there are system
conditions that do not result in capacitor protection gear operation after the occurance of a fault (1). Also, with the new generation of the Ultra-High-Speed protection, the fault
may be cleared in considerably less than one cycle which may be much shorter than capacitor gap flash-over times (2). Therefore it is highly desirable that distance protection schemes perform the impedance measurements with the highest degree of accuracy with capacitor banks in circuit. several papers have investigated the difficulties associated with protection of series compensated lines (3,4,5,6]. One of these problems is the effect of the residual compensation factor
when an earth fault occurs. Reference 5 and 6 have investigated this effect for systems with 70% compensation and proposed a new method to improve the distance relays performance when capacitors are assumed in the circuit. In this paper the application of the new modified residual compensation factor to series compensated
lines with 50% series compensation at the mid-point of the line is investigated.
ggcTOUAL CURRENT COMPENSATION FACTOR
Consider the system shown in Fig. 1 with series capacitor situated at the mid-point (line data is given in Appendix A).
SE Is -ix( RE
V5 výý Relay
Fig 1: SYSTEM CONFIGURATION
It is well known that in distance protection, for phase to earth faults, compensation methods are used to allow the relay to measure the positive phase sequence (pps) impedance of the line from the relaying to fault point [7]. The most commenly used method employs residual current compensation, where a fraction of the residual current is added to the phase currents. It has been revealed in reference 5 and 6 that, if the conventional residual compensation factor (CRCF) is used, the impedance measurement by the distance relay is not accurate. When the series capacitor bank is located at the middle of the line and using similar analysis as reference 6, it can be shown that the impedance seen by the distance relay for faults before and after the series capacitor are given by Eqn. 1 and 2 respectively:
Vsae 2r= " a2Ll for a<0.5
Isa+Kcires
Vsae Isa Zr= " aZLl-j()Xc
Isa+Kclres Isa+KcIres for a>0.5
Where: Zr=measured impedance
Vsae=phase voltage at the relaying point Isa=faulted phase current at the relaying
point Ires=residual current=Isa+Isb+Isc
ZL1=total pps impedance of the line Xcatotal capacitor reactance/phase
a=proportional fault position Kc=conventional residual compensation
factor 1. ZLO
°- (I I- 1) 3 ZL1
Figs 2 and 3 show the measured impedance by distance relay on impedance (R-X) plain for different source and pre-fault load. Note that the relay measurements are not accurate, even for faults before the capacitor bank. This is due to the fact that the angle of the line zero phase sequence (zps) and ppa impedances in Eqn. 3 are assumed to be the same. However, it can be seen that the measured resistance is more affected than the reactance. Fig 4 shows the measured reactance versus fault position which confirms that for faults before the capacitor location the discrepancy in the measured reactance and the actual line reactance is minimal if the impedance ratio ZL0/2U1 is taken as real.
In order to ensure that the relay measures the correct value of pps impedance of the line from the relay to fault point (for relay setting purposes) it has been shown that in series compensated lines, the residual compensation factor must be set according to the fault position a [6]. Considering series compensated line with 50% compensation at the middle of the line it can be shown that the measured impedance by the relay is given by:
Zrs Vsae
aZL1 -] Xce 4 Isa+K(a)Ires
where: 1 aZLO-] Xce
K(a)= -(- 1) 5 3 aZLI-j Xce
XCe= 0 for a<0.5 XCe= Xc for a>0.5
Figs 5. a and S. b shows the magnitude and argument of K(a) versus fault position. It is
evident that K(a) stays at a constant value for fault positions of less than 50% of the line length (capacitor location). However note the variation in magnitude and argument of K(a) with fault position, a, for faults beyond the series capacitor.
30
2 ö Zý T ö1
v
0 11 v
W u Z
r U C W oC
-101 1 6 -$ -2 Ol46 10
RESISTANCE (secondary ohms)
Fig 2: Measured Impedance For Different System Sources With CRCF (Kc=0.774L0')
a: Line Locus b: SE SCL"S GVA, RE SCL"35 GVA, Load Angle-0' c: SE SCL"35 GVA, RE SCL+S GVA, Load Angle=0'
30
z w
2
a ä
9 C Ö1 4 N
W I
u W K
-10 Bý G- -2 oita to RESISTANCE (secondary ohms)
Fig 3: Measured Impedance For Different System Load With CRCF (Kc=0.774L0')
a: Line Locus b: SE SCL-5 GVA, RE SCL-35 GVA, Load Angle=+10'
c: SE SCL-S GVA, RE SCL-35 GVA, Load Angle--10'
S
ý e ýq f
i ý
5 mit
f 'Id
b
. ý f
'a
i
i
i
1
FAULT POSITION (% OF LINE LENGTH) X101
Fig 4: Measured Reactance With CRCF (Kc=0.774LO')
--- Line Locus
---- SE SCL 5 GVA, RE SCL 35 GVA, Load Angle-O'
-- SE SCL 35 GVA, RE SCL-5 GVA, Load Angte"0'
"""" SE SCL-S GVA, RE SCL-35 GVA, Load Angle--10'
Y LL O
ül O
LO t
nua. i uaaaun f. ur a_anr_ ýa. nunnv
Fig 5. a: VARIATION OF IK(a)l WITH FAULT POSITION
X101
5-
i
3 a 0
2 z U)
V)
0
J
i FAULT POSITION (% OF LINE LENGTH) %101
Fig 5. b: VARIATION OF LK(a) WITH FAULT POSITION
Modified Residual Compensation Factor For Series Compensated Line
It has been suggested that, since the relay is required to be the most accurate at and arround the boundary, the residual compensation factor is set at a fixed value K(ar), assuming the fault position to be at the relay zone-1 reach boundary [5,6). If the relay independant zone-1 reach is considered
to be before series capacitor, say at 45% (ar=0.45) and a complex residual compensation factor (assuming L71,0 L0L1 ) is considered in the relay, the relay measures accurate impedances for all faults before the mid-point of the line. But for faults beyond the capacitor, the relay measurement will not be accurate.
If it is required to set the relay reach at a value higher than 50%, then the relay measurement is accurate only at the reach point [5,6). In this work it was decided to set the relay zone-1 reach at 80% of the line length, which is the common practice in plain uncompensated feeder distance protection schemes. The required residual compensation factor, for boundary setting of 80% (ar=0.8) is, from Fig 5. a and b, found to be
approximately equal to 2.015L-4.6'.
Figs 6 and 7 illustrate the measured impedance on an impedance plain for different
source and load condition when the new residual compensation factor (NRCF) is used. It can be clearly seen that the measured impedance at the boundary is independant of source and pre-fault load. Also, due to over- compensation of the residual current in the relay (2.015L-4.6' instead of 0.782L-14.82') for faults before the capacitor bank, the
measured reactance is smaller than the actual line reactance.
3C
21
20
a 15
0 ü 10 I, M
W3 C3
W
a -5
-1O -ý -o4 lo
RESISTANCE Csecondary ohms) Fig 6: Measured Impedance For Different
System Sources With NRCF (K(ar)-2.015(4.6')
e: Line Locus b: SE SCL 5 GVA, RE SCL=35 GVA, Load Angle-0'
c: SE SCL"35 GVA, RE SCL-S GVA, Load Angle=0'
30
2ý N
t 20 0
ä I5 9 C 0 10 4
w u
r u
-5
6 -4 -2 02468 10 RESISTANCE (secondary ohms)
Fig 7: Measured Impedance For Different System Load With NRCF (K(ar)=2.015L4.6*)
a: Line LOCUS b: SE SCL-S GVA, RE SCL-35 GVA, Load Angle- +i0-6: SE SCL. 5 GVA, RE SCL-35 GVA, Load Angte=-10'
e
c
a t
ý a b ;'/
!ýc :ý
ý, Gý . ýi
i .i i
RELAY CHARACTERISTIC
The new residual compensation factor was implemented on a digital distance relay described by reference 8 and 9. The relay forward reactance reach was set at 80% of the line length. Reference 6 has described how a complex residual compensation factor can be implemented in a digital relay. At the relay sampling frequency of 4 kHz, the first previous sample of the residual current is added to the phase current which corresponds to an angle of -4.5'.
The relay characteristic which was initially adopted in this work, the line actual impedance and the measured impedances for different source and pre-fault load are shown in Fig B. It must be said that, in order to improve discrimination ability of the relay around the forward reach longer time is allowed for the relay to reach a trip decision by dividing the relay characteristic into fast and slow counting regions (10). For the foregoing reasons, although the steady state locus of the measured impedances fall within the relay characteristic, high speed operation may not be achieved for faults just before the capacitor bank. Relay operating time of up to 60 msec was observed for some system conditions, for a fault at 48% of the line length.
0 0 a L
0 uu
W Li z
u w a
to i RESISTANCE (secondary ohms)
Fig 8: Quadrilateral Trip Characteristic And Measured Impedances With NRCF (K(ar)=2.015L4.5')
--- Line Locus
---- SE SCL"5 GVA, RE SCL"35 GVA, Load Angle-0'
-- SE SCL-5 GVA, RE SCL"35 GVA, Load Angle--10'
"""" SE SCL-35 GVA, RE SCL-5 GVA, Load Angle-O'
To improve the relay operating time response the relay characteristic was modified to Fig 9. The new characteristic has the advantages of improving transient as well as steady state, and operating time responses of the relay. Figs 10 and 11 illustrate typical relay operating time for different source and load conditions. The primary system simulation is described in Reference 11.
30
2: N E
0 2C
a V 15 0 v Y N 10
W U
z5 H u wp oc
-5 s -t -2 o2t6e io 12 it is ie 20 RESISTANCE (secondary ohms)
Fig 9: New Relay Trip Characteristic And Measured Impedances With NRCF (K(ar)=2.015L4,5')
--- Line Locus
---- SE SCL"5 GVA, RE SCL-35 GVA, Load Angte-0'
-- SE SCL"5 GVA, RE SCL-35 GVA, Load Angle--10'
"""" SE SCL"35 GVA, RE SCL-S GVA, Load Angle=0*
u 4 N E
w
r to z r
a w
d
i
ý /
ý' ! +%
Y
a
FAULT POSITION (% OF RELAY REACH) X10'
Fig 10: Relay Operating Time vs Relay Reach
SE SCL-35 GVA, RE SCL-5 GVA, Load AnglomW *: Fault Inception Angle=0' b: Fault Inception Angle=90'
XI0' 12_
uý 4
E
t7 Z I- r oc W
tl 1Ie
FAULT POSITION (: OF RELAT REACH) X101
Fig 11: Relay Operating Time vs Relay Reach
SE SCL=S GVA, RE SCL-35 GVA, Load Angte-10' ": Feutt Inception Angte-0'
b: Fautt Inception Angte=90'
Zr,, g USSLOONS
The new method of the residual current Compensation proposed in references 5,6 was
investigated for a series compensated line with 50% compensation at the mid-point of the line. It was shown that the relay reach can be set at 80% of the line length with the highest degree of accuracy in impedance measurement at the reach point. The new method was implemented in a digital distance relay and it was shown that to improve the relay operating time, a modified relay characteristic may be used.
ACKNOWLEDGEMENT
The authors would like to thank The City University, London, GEC Measurements, Stafford-UK, and the Science and Engineering Research Council UK for the provision of facilities and support for this research.
APPENDIX A: SYSTEM DATA
The line is horizontally constructed and discretely transposed. System voltage is 500 kV. The pps and zps impedances of the line are:
ZL1= 0.3109L83.62' Q/km primary = 0.1367(83.62' 0/km secondary
ZLO= 1.033L73.24' Q/km primary = 0.4545(73.24' 0/km secondary
Xc/phase = 46.353 0 primary. = 20.390 Q secondary
Line Length=300 kin
RGFERENCGS
[1] J. Berdy, "Protection of circuits with series capacitor, "AIEE Summer general meeting, DENVER-COLO, June 1962.
[2] Y. Mansour, T. G. Martinich, J. E. Drakos, "B. C. Hydro series capacitors bank staged fault test, "IEEE Trans, PAS-102, N07, PP. 1960- 1969, July 1983.
[3] M. M. Elkateb, W. J. Cheetham, "Problems in the protection of series compensated lines, " IEE Conference publication on power system protection, NO 185, PP. 215-220,1980.
[4] M. Shafik, F. Ghassemi, A. T. Johns, "Performa- nce of digital distance protection for series compensated systems, "UPEC, 1987.
(5) A. T. Johns, F. Ghassemi, "Analysis and compensation of errors in distance protection measurement for series compensated systems, "UPEC, 1988.
[6] F. Ghassemi, A. T. Johns, "Investigation of alternative residual current compensation for improving series compensated line distance protection, "Accepted for presentation in the IEEE summer meeting, California, July 1989.
(7) W. A. Lewis, S. L. Tippett, "Fundamental basis for distance relaying on three-phase system, "AIEE Trans, PP. 694-709,1947.
[8] A. T. Johns, M. A. Martin, "NeW Ultra High Speed distance protection using finite transform techniques, "Proc. IEE, Vol 131, ptc No 5, PP. 168-196,1983.
[9] P. J. Moore, A. T. Johns, "Impedance measurement techniques for digital EHV line protection", UPEC, 1988.
[10]P. J. Moore, A. T. Johns, "Adaptive digital distance protection, "Forth international conference on developments in power system protection. Edinburgh, April 1909.
[11]R. K. Aggarwal, A. T. Johns, A. Kalam, "Computer modelling of series compensated El1V transmission systems", Proc. IEE, Vol. 131, PtC, No3, pp. 127-138.
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