Fundamentals of Power System protection by Y.G.Paithankar and S.R.Bhide

Fundamentals of
Power System Protection
Y.G.Paithankar
Formerly Professor and Head
Electrical Engineering Department
Visvesvaraya National Institute of Technolorn
Nagpur
S.R. Bhide
Assistant Professor
Electrical Engineering Department
Visvesvaraya National Institute of Technology
Nagpur
- -.. - .I - - I L
Saeed Book Bank
-,f India
hc Delhi - 11
2003

Dependence of Modern Society on Electric Supply I
Faults and Abnormal Operating Conditions I
1.2.1 Shunt Faults (Short Circuits) 1
1.2.2 Causes of Shunt Faults 3
1.2.3 Effects of Shunt Faults 3
1.3 Classification of Shunt Faults 5
1.3.1 Phase Faults and Ground Faults 5
1.3.2 Phasor Diagram of Voltages and Currents During Various Faults 5
1.3.3 Series Faults 7
Abnormal Operating Conditions 9
1.4.1 Should Protective Relays Trip During Abnormal Operating
Conditions? 9
1.4.2 Can Protective Relays Prevent Faults? 9
.3 What are Protective Relays Supposed to Do? 9
volution of Power Systems 9
1.5.1 Isolated Power System 10
1.5.2 Interconnected Power System 10
1.5.3 Negative Synergy of a n Interconnected System 10
ates of Operation of a Power System 11
.5.5 From Natural Monopoly to the Deregulated Power System 12
Protection System and Its Attributes 13
.6.1 Sensitivity 14
.6.2 Selectivity 14 ?-
.6.4 Reliability and Dependability 14
ystem Transducers 14
.7.1 Current Transformer 15
nsforrner 16
iii

1.7.3 Circuit Breaker 17
1.7.4 Trip Circuit of a CB 1 7
17 5 Organization of Protection 1 7
1.7 6 Zones of Protection 19
1 7.7 Primary and Back-up Protection 20
1.7.8 Maloperations 22
1.8 Various Power System Elements That Need Protection 23
1.9 Various Principles of Power System Protection 23
Reuiew Questions 24
Problems 25
2 OVER-CURRENTPROTECTION OF TRANSMISSION LINES 26-56
2.1 Introduction 26
2 2 Fuse 26
2.3 Thermal Relays 27
2.4 0; er-current Relay 28
2.4.1 Instantaneous OC Relay 29
2.4.2 Definite Time Over-current Relay 30
2.4.3 Inverse Time Over-current Relay 30
2.5 Implementation of Over-current Relay Using Induction Disk 32
2.6 Application of Definite Time OC Relays for Protection of a
Distribution Feeder 35
2.7 Application of Inverse Definite Minimum Time Relay on a
Distnbution Feeder 37
2.7.1 Choice Between IDMT and DTOC Relays 42
2.8 Protection of a Three-phase Feeder 42
2.9 Directional Over-current Relay 44
2.9 1 Other Situations Where Directional OC Relays are Necessary 45
2.9.2 Phasor Diagram for Voltage and Current for Forward and
Reverse Fault (Single-phaseSystem) 47 1
2.9.3 Application of Directional Relay to a Three-phase Feeder 49
2.9.4 Directional OC Protection of a Three-phase Feeder 52
2.9.5 Directional Protection Under Non-fault Conditions
*(Reverse Power Relay) 53
2.10 Drawbacks of Over-current Relays 54
Reuzew Questions 55
Problems 56
3 DIFFERENTIAL PROTECTION 57-73
3.1 Introduction 57 j

3.2 Dot Markings 57
3.3 Simple Differential Protection 59
3.3.1 Simple Differential Protection: Behaviour During Load 59 I
3.3.2 Simple Differential Protection: Behaviour During External Fault 60 I
3.3.3 Simple Differential Protection: Behaviour During Internal Fault 60
3.3.4 Simple Differential Protection, Double-end-fed: Behaviour I
During Internal Fault 61

i3unr~11rs Y
3.4 Zone of Protection of the Differential Relay 62
3 5 Actual Behavlour of a Simple Dlfferentlal Scheme 63
3 5 1 Through Fault Stability and Stabillcy Ratio 64
3.5.2 Equivalent Circuit of CT 65
3.6 Percentage Differential Relay 67
3.6.1 Block Diagram of Percentage Differential Relay 70
3.7 Earth Leakage Protection 71
3.7.1 Earth Leakage Protection for Single-phase Load 71
3.7.2 Earth Leakage Protection for Three-phase Loads 72
Reuzew QuestLons 73
Problems 73
4 TRANSFORMER PROTECTION 74-100
4.1 Types of Transformers 74
4.2 Phasor Diagram for a Three-phase Transformer 75
4.3 Equivalent Circuit of Transformer 77
4.4 Types of Faults in Transformers 78
4 5 Over-current Protection 80
4.6 Percentage Differential Protection of Transformers 81
4.6 1 Development of Connections 81
4.6.2 Phase c-to-Ground (c-g) External Fault 82
4.6.3 Phase c-to-Ground (c-g) Internal Fault 84
4.7 Inrush Phenomenon 86
4.7.1 Percentage Differential Relay with Harmonic Restraint 89
4.8 High Resistance Ground Faults in Transformers 91
4.8 1 High Resistance Ground Faults on the Delta Side 91
4 8.2 High Resistance Ground Faults on the Star Side 92
4.9 Inter-turn Faults in Transformers 93
4 10 Incipient Faults in Transformers 93
* 4.10.1 Buchholz Relay 93
4.10.2 Analysis of Trapped Gases 95
4.11 Phenomenon of Over-fluxingin Transformers 95
4.11.1 Protection Against Over-fluxing 95
4.12 Transformer Protection Application Chart 96
4.13 An Illustrative Numerical Problem 97
Reuzew Questions 99
Problems 100
5 BUSBAR PROTECTION 101-117
.,
5.1 Introduction 101
5.2 Differential Protection of Busbars 102
5.2.1 Selection of CT Ratios in Case of Busbar Protection:
Wrong Method 102
5.2.2 Selection of CT Ratios in Case of Busbar Protection:
Correct Method 103

5 3 External and Internal Fault 104
.5.4 Actual Behaviour of a Protective CT 105
5.5 Circuit Model of Saturated CT 108
5.6 External Fault with One CT Saturated: Need for High Impedance
Busbar Protection 108
5.7 Minimum Internal Fault That Can Be Detected by the High
Impedance Busbar Differential Scheme 110
5.8 Stability Ratio of High Impedance Busbar Differential Scheme 112
5.9 Supervisory Relay 112
5.10 Protection of Three-phase Busbars 114
5.11 Numerical Example on Design of High Impedance Busbar Differential
Scheme 115
Review Questions 117
6 DISTANCEPROTECTION OF TRANSMISSION LINES 118-152
6.1 Drawbacks of Over-current Protection 118
6.2 Introduction to Distance Protection 119
6.3 Simple Impedance Relay 123
6.3.1 Trip Law for Simple Impedance Relay Using Universal
Torque Equation 123
6.3.2 Implementation of Simple Impedance Relay Using Balanced
Beam Structure 124
6.3.3 Performance of Simple Impedance Relay During Normal Load Flow 126
6.3 4 Effect of Arc Resistance on Reach of Simple Impedance Relay 126
6.3.5 Directional Property Exhibited by Simple Impedance Relay 127
6.3.6 Performance of Simple Impedance Relay During Power Swing 127
6.4 Reactance Relay 129
6.4.1 Trip Law for Reactance Relay Using Universal Torque Equation 129
6.4.2 Implementation of Reactance Relay Using the Induction
Cup Structure 131
6.4.3 Performance of Reactance Relay During Normal Load Flow 131
6.4.4 Effect of Arc Resistance on Reach of Reactance Relay 132
6.4.5 Directional Property Exhibited by Reactance Relay 133
6.4.6 Performance of Reactance Relay During Power Swing 134
6.5 Mho Relay 134
6.5.1 Trip Law for Mho Relay Using Universal Torque Equation 134
6.5.2 Implementation of Mho Relay Using Induction Cup Structure 135
6.5.3 Performance of Mho Relay During Normal Load Flow 135
6.5.4 Effect of Arc Resistance on Mho Relay Reach 136
6.5.5 Directional Property Exhibited by Mho Relay 137
6.5.6 Performance of Mho Relay During Power Swing 138
6.6 Comparison Between Distance Relays 139
6.7 Distance Protection of a Three-phase Line 139
6.7.1 Phase Faults 141
6.7.2 Ground Faults 142
6.7.3 Complete Protection of a Three-phase Line 144

...YIII C o i ~ r r f ~ t s
9 INDUCTION MOTOR PROTECTION 184-195 '
9.2 Various Faults and Abnormal Operating Conditions 184
9.3 Starting Current 185
9.4 Electrical Faults 186
9.4 1 Fault on Motor Terminals 186
9.4.2 Phase Faults Inside the Motor 186
9.4.3 Ground Faults Inside the Motor 188
9.4.4 Inter-turn Faults 189
9.5 Abnormal Operating Conditions from Supply Side 189
9.5.1 Unbalanced Supply Voltage 189
9.5.2 Single Phasing 191
9.5.3 Reduction in Supply Voltage 192
9.5.4 Reversal of Phases 192
9.6 Abnormal Operating Conditions from Mechanical Side 192
9.6.1 Failure of Bearing and Rotor Jam 192
9.6.2 Overload 192
9.7 Data Required for Designing Motor Protection Schemes 195
10 STATIC COMPARATORSAS RELAYS 196-221
10.1 Comparison vs Computation 196
10.2 Amplitude Comparator 196
10.3 Phase comparator 199
10.3.1 The Cosine-type Phase Comparator 199
10.3.2 The Sine-typePhase Comparator 200
10.4 Duality Between Amplitude and Phase Comparators 201
10.5 Synthesis of Various Distance Relays Using Static Comparators 204
10.5.1 Synthesis of Mho Relay Using Static Phase Comparator 204
10.5.2 Synthesis of Reactance Relay Using Cosine-type Phase Comparator 208
10.5.3 Synthesis of Simple Impedance Relay Using Amplitude Comparator 210
e
10.6 Development of a n Electronic Circuit for Implementing
a Cosine-type Phase Comparator 210
10.7 An Electronic Circuit for Implementing a Sine-type Phase Comparator 216
10.8 Synthesis of Quadrilateral Distance Relay 218
11 NUMERICAL PROTECTION
11.2 Block Diagram of Numerical Relay 223
11.3 SamplingTheorem 225
11.4 Correlation with a Reference Wave 228
11.4.1 Fourier Analysis of Analogue Signals 229
I 11.5 Least Error Squared (LES) Technique 237

--- Conrcnis vii .
. 6.8 Reasons for Inaccuracy of Distance Relay Reach 145
6.9 Three-stepped Distance Protechon 146
6.9.1 First Step 146
6.9.2 Second Step 146
6.9.3 Third Step 147
6.10 Trip Contact Configuration for the Three-stepped Distance
Protection 149
6.11 Three-stepped Protection of Three-phase Line against All Ten Shunt
Faults 150
6.12 Impedance Seen from Relay Side 150
6.13 Three-stepped Protection of Double-end-fedLines 151
e
7 CARRIER-AIDEDPROTECTION OF TRANSMISSIONLINES 153-167
7.1 Need for Carrier-aided Protection 153
7.2 Various Options for a Carrier 155
7.3 Coupling and Trapping the Carrier into the Desired Line Section 155
7.3.1 Single Line-to-ground Coupllng 157
7.3.2 Line-to-line Coupling 157
7.4 Unit Type Carrier-aided Directional Comparison Relaying 158
7.5 Carrier-aided Distance Schemes for Acceleration of Zone I1 160
7.5.1 Transfer Trip or Inter-trip 160
7.5.2 Permissive Inter-trip 161
7.5.3 Acceleration of Zone I1 161
7.5.4 Pre-acceleration of Zone I1 161
7.6 Phase Comparison Relaylng (Unit Scheme) 163
8 GENERATOR PROTECTION 168-183
8.2 Electrical Circuit of the Generator 169
8.3 Various Faults and Abnormal Operating Conditions 172
8.3.1 Stator Faults 173
8.3.2 Stator Phase and Ground Faults 173
8.3.3 Transverse Differential Protection 174
8.4 Rotor Faults 175
8.5 Abnormal Operating Conditions 176
8.5.1 Unbalanced Loading 176
8.5.2 Over-speeding 178
8.5.3 Loss of Excltation 179
8.5.4 Protection Against Loss of Excitation Using Offset Mho Relay 180
8.5.5 Loss of Prime Mover 181
Revzew Questions 183

~ .. Co~zrr~lts jx
11.6 Digital Filtering 239
11.6.1 Simple Low-pass Filter 239
11.6.2 Simple High-pass PLlter 240
11.6.3 Finite Impulse Response (XR) Filters 241
11.6.4 Infinite Impulse Response (IIR) Filter 242
11.6.5 Comparison Between FIR and IIR Filters 243
11.7 Numerical Over-current Protection 243
11.8 Kumerical Transformer Differential Protection 245
11.9 Numerical Distance Protection of Transmission Line 245 - ,
11.9.1 Mann and Morrison Method 245
11.9.2 Differential Equation Method 247
11.10 Algorithms and Assumptions 253
@ Appendix A-CT AND PTERRORS 255-267
A.l Introduction 255
A.2 CT Construction 255
A.3 Measurement CT and Protective CT 255
A.4 Steady State Ratio and Phase Angle Errors 256
A.4.1 Current Transformer 256
A.4.2 Potential Transformer 259
A.5 Transient Errors in CT 261
A.6 Transient Errors in CVT 264
A.7 Saturation of CT 265
A.8 CT Accuracy Classification 267
1
Appendix &POWER SWING 268-274
B.l Introduction 268
B.2 Stable and Unstable Power Swing 268
B.3 Impedance Seen by Relay During Power Swing 270
0. B.4 Out-of-stepBlocking Scheme 272
B.5 Out-of-stepTripping Scheme 274
Appendix CPROTECTION OF LONGESTAND SHORTEST LINES 275-279
C.1 Introduction 275
C.2 Longest Line That Can Be Protected 275
C.3 Shortest Line That Can Be Protected 277
REFERENCES 281-283
INDEX 285-287

Power System Protection is a fascinating subject. A protection scheme in a power
system is designed to continuously monitor the power system to ensure maximum
continuity of electrical supply with minimum damage to hfe, equipment, and property.
While designing the protective schemes, one has to understand the fault characteristics
of the individual power system elements. One should also be knowledgeable about the
tripping characteristics of various protective relays. The job of the protection engineer is
to devise such schemes where closest possible match between the fault characteristics
and the tripping characteristics is obtained. The design has to ensure that relays will
detect undesirable conditions and then trip to disconnect the area affected, but remain
restrained at all other times However, there is statistical evidence that a large number
of relay trippings are due to improper or inadequate settings than due to genulne faults.
It is therefore necessary that students should be equipped with sound concepts of power
system protection to enable them to handle unforeseen circumstances in real life.
Whenever a tripping takes place it has all the elements of intrigue, drama, and
suspense. A lot of detective work is usually undertaken to understand the reason behind
the tripping. It needs to be established why the relay has tripped. Whether it should
have tripped at all. What and where was the fault? These are some of the questions
required to be answered. This is because a power system is a highly complex and
dynamic entity. It is always in a state of flux. Generators may be in or out of sewice.
New loads are added all the time. A single malfunction at a seemingly unimportant
location has the potential to trigger a system-wide disturbance. In view of such possible
consequences, a protective system with surgical accuracy is the only insurance against
potentially large losses due to electrical faults.
Protective relays are meant to mitigate the effects of faults. This text treats the
entire spectrum of relays, from electromechanical to the state-of-the-art numerical relays,
for protection of transmission lines, turbo-alternators, transformers, busbars, and motors.
However, it is ironic that every additional protective relay also increases the possibility of
disturbance by way of its (relay's) own malfunction. This is possibly an area where
protection tends to become an art.The protection engineer has to strike a balance between
the threat perception and the security offered by the protective scheme.
xi

xii Prefncc
The book is focused on teaching the fundamental concepts and the related design -
aspects of protective relay schemes. Written in a simple, clear and down-to-earth style,
this state-of-the-art text offers students of electrical engineering a stimulating
presentation that is both friendly and refreshingly simple.
The text contains a wealth of figures, block diagrams, and tables to illustrate the
concepts discussed. The graphics are extensively annotated. The students are urged to
spend some time to read the annotations on the figures, so that learning becomes easy
and concepts are reinforced.
Though the book's audience consists mainly of final year electrical engineering
students, the practising engineers, interested in learning the fundamental concepts of
power system protection, will also find it useful. The authors will gratefully receive
suggestions and comments from the readers for improvement of the book.
XG. PAITHANKAR 0
S.R. BHIDE

1.1 Dependence of Modern Society on Electric Supply
The modem society has come to depend heavily upon continuous and reliable availability
of electricity-and a high quality of electricity too. Computer and telecomm~ication
networks, railway networks, banking and post office networks, continuo&s$rocess
industries and life support systems are just a few applications that just cannot function
without a highly reliable source of electric power. And add to this, the mind-boggling
number of domestic users of electricity whose life is thrown out of gear, in case the
electric supply is disrupted. Thus, the importance of maintaining continuous supply of
electricity round the clock cannot be overemphasized.
No power system can be designed in such a way that it would never fail. So, one has
to live with the failures. In the language of protection engineers, these failures are called
faults. There is no negative connotation to the word fault in this context. What is more
important is, how to prevent the faults and how to ~ e t h econsequences of the
faults. The- - -~ill effects of faults-" are-...minimized.. ---.. . by.-q",ck!y..isolating the-. faulty....~,. .element.. . . from~..~ .
the rest of the healthy systqm; th%.limiting the disturbance,.. ~ footprint to as~.small an ~qeea_
- ,- -
1.2 Faults and Abnormal Operating Conditions
1.2.1 Shunt Faults (Short Circuits)
When the path of the load current is cut short because of breakdown of insulation, we
i say that a 'short circuit' has occurred. The insulation can break down for a variety of
reasons, some of which are listed in Section 1.2.2.Figure 1.1shows a single line-to-ground
fault on a transmission line due to flashover of spark gap across the string insulator.
Such faults due to insulation flashover are many times temporary, i.e. if the arc path
is allowed to deionize, by interrupting the electrical supply for a sufficient period, then
the arc does not re-strike after the supply is restored. This p r o ~ ~ ~ f ~ ~
followed..... by intentional re-energization~ .-..,. .,
.-is. ~ .known as'ieclosure.I-In low-voltage systems up
1
yC .<<? 7 ' 3 ':c:<.

2 F~~r~damentalsof Power Systern Protection
--
Step-up
transformer
Arcing fault
(L-G fault)
'f
Figure 1.1 Single line-to-ground fault due to flashover of insulator string.
tp _thfee.recl~~re_s_-ar_eattem~ted~._aRerwhich t h ~ b r e a k e r,,,-~. .~~.-~-. is, locked out. The repeated
attempts at reclosure, at times, help in burning out the object which is causing the
breakdown of insulation. The reclosure may also be done automatically In EHV systems,

where the damage due to short circuit may be very large and the system stability at stake,
only one reclosure is allowed.
At times the short circuit may be total (sometimes called a dead short circuit), or it
may be a partial short circuit. A fault which bypasses the entire load current through
itself, is called a metallic fault. A metallic fault presents a very low, practically zero, fault
resistance. A partial short circuit can be modelled as a non-zero resistance (or impedance)
in parallel with the intended path of the current. Most of the times, the fault resistance
is nothing but the resistance of the arc that is formed as a result of the flashover. The
arc resistance is highly nonlinear in nature. Early researchers have developed models of
the arc resistance. One such widely used model is due to Warrington, which gives the arc
resistance as:
a where
S is the spacing in feet
u is the velocity of air in mph
t is the time in seconds
I is the fault current in amperes.
S~u~&..f&s~~e..basicall~~,~due_~to~fajl.u.reof insulation. The insulation may fail because
of its own weakening, or it may fail due to overvoltage. The weakening of insulation may
be due to one or more of the following factors:
- Ageing -
'i."
_ Temperature
;. Rain, hail, snow
' Chemical pollution
Foreign objects
Other causes
The overvoltage may be either internal (due to switching) or external (due to lightening).
1.2.3 Effects of Shunt Faults
If the power system just consisted of isolated alternators feeding their own loads, then the
steady-state fault currents would not be qpch of a concern. Consider an isolated
turboalternator with a three-phase short circuit on its terminals as shown in Figure 1.2.
Assuming the internal voltage to be 1 p.u. and a value of synchronous impedance,
Xd = 2 p.u., the steady-state short-circuit current would only be 0.5 p.u. which is too
small to cause any worry. However considering subtransient impedance, X: = 0.1, the
subtransient current would be 10 p.u. We must not, however, forget that in an

(a) Isolated generatorwith its load
(c) Subtransient
(b) Three-phasefault
-
(d) Transient (e)Steady state
Figure 1.2 Isolated generator experiences a three-phase fault.
1"
interconnected power system all the generators (and even motors) will contribute towards
the fault current, thus building up the value of the fault current to couple of tens of times
the normal full-load current.
Faults, thus, cause heavy currents to flow. If these fault currents persist even for
a short time, they will cause extensive damage to the equipment that carry these
currents. Over-currents, in general, cause overheating and attendant danger of fire.
Overheating also causes deterioration of the insulation, thus weakening it further. Not SO
apparent is the mechanical damage due to excessive mechanlcal forces developed during a
over-current. Transformers are known to have suffered rnechanlcal damage to their
windings, due to faults. This is due to the fact that any two current-carrying conductors
experience a force. This force goes out of bounds during faults, causing mechanical
distortion and damage.
Further, in an interconnected system, there is another dimension to the effect of
faults. The generators in an interconnected power system must operate in synchronism
at all instants. The electrical power output from an alternator near the fault drops
sharply. However the mechanical power input remains substantially constant at its pre-
fault value. This causes the alternator to accelerate. The rotor angle 6 starts increasing.
Thus, the alternators start swinging with respect to each other. If the swing goes out of
control, the alternators will have to be tripped out. Thus, in an interconnected power
system, the system stability is at stake. Therefore, the faults need to be isolated as
selectively and as speedily as possible

Introduction 5
1.3 Clussificafi~nof Shunf Fslulfs
1.3.1 Phase Faults and Ground Faults
Those faults, which involve only one of the phase conductors and ground, are called
ground faults. Faults involving two or more phase conductors, with or without ground,
are called phase faults.
Power systems have been in operation for over a hundred years now. Accumulated
experience shows that all faults are not equally likely. Single line to ground faults (L-G)
are the most likely whereas the fault due to simultaneous short circuit between all the
three lines, known as the three-phasefault (L-L-L), is the least likely. This is depicted
in Table 1.1
Table 1.1 Fault statistics with reference to type of fault
Fault Probability of occurrence (%) Severity
L-G 85% Least severe
L-L 8%
L-L-G 5%
L-L-L 2% Most severe
Total 100%
Further, the probability of faults on different elements of the power system are
different. The transmission lines which are exposed to the vagaries of the atmosphere are
the most likely to be subjected to faults. Indoor equipment is least likely to be subjected
to faults. The fault statistics is shown in Table 1.2.
Table 1.2 Fault statistics with reference to power system elements
Power system element Probabiliw of faults (9%)
Overhead lines 50
Underground cables 9
Transformers 10
Generators 7
Switchgem 12
CT, PT relays, control equipment, etc 12
Total 100%
The severity of the fault can be expressed in terms of the magnitude of the fault
current and hence its potential for causing damage. In the power system, the three-phase
fault is the most severe whereas the single line-to-ground fault is the least severe.
1.3.2 Phasor Diagram of Voltages and Currents During Various Faults
A fault is accompanied by a build-up of current, which is obvious. At the same time there

6 Fu~~da~,rentaLsof Power Systen~Protectio~l-
is a fall in voltage throughout the power system. If the fault is a metallic fault, the voltage -
at the fault location is zero. The voltage at the terminals of the generator will also drop,
though not drastically. If the source is ideal, there will be no drop in voltage at the
generator terminals. Normally the relay is away from the fault location. Thus, as seen
from the relay location, a fault is characterized by a build-up of current, and to a certain
extent, collapse of voltage.
Figure 1.3 depicts various ground faults as well as phase faults.
a
(a) L-Gfault (b) L-L fault
(c)L-L-G fault (d) L-L-L fault
I
a iI
i
I,;
1
!
(e) L-L-L-G fault
1.3 Various ground faults and phase faults.
-~ ~ .-.. -,~ , , ,, . . ,.

--
Introduction 7
Figure 1.4 depicts a radial power system with a fault near the remote end of the
transmission line. It can be seen from the phasor diagram that the voltage at the relay
location during fault is less in magnitude than that during the pre-fault condition and
also lags its pre-fault value. In order not to clutter the diagram, only phase a voltage is
shown. In Figure 1.5, the distortion in voltages during all the 11 shunt faults are
considered.
Eala = --
Zs + ZL
'b C=- Eb
zs + ZL
e Ec
I, = --
zs + ZL
Va=E,-IZ
8 S
Vb = Eb-lbZS
Vc = E, - I$s
Figure 1.4 Fall of voltage at the relaylocation shown on singlelinediagramof a three-phasesystem.
IZLIL @L
ZL
-----..-------------------------..---.
/ - Three-phaseline
Source
'b -lc - Three-phasefault
1.3.3 Series Faults
I
Series faults are nothing but a break in the path of current. Normally such faults do not
result into catastrophes except when the broken conductor touches other conductor or
Relay

8 F~mrla~nenmlsof Power Svsre,n Protecrio,l
Grounded
neutral
.-----.----------
7----
L-L fault
va
A, ;T'
. _ _ _ _ _______________ . _ _ _ - -_ _ ----_------
vc ,-*-N . ,,,N --... , *
I .---.'., I I-
,.-.,V C f l-----.------------------,----------------------A- vb A,--_-
---:A
v, b c faulta-b fault a-c fault
L-G fault
"a Va
,;,
I I
vc
a-g fault b-g fault c-g fault
a-b-g fault a-c-g fault b-c-gfault
I Figure 1.5 Voltages at the relay location during various faults.
I
some grounded part. It is observed in practice that most of the open conductor faults
sooner or later develop into some or the other short-circuit fault. However, there are some
instances where an open circuit can have dangerous consequences For example, the
secondary circuit of a current transformer and the field circuit of a dc machine if open
circuited, can have dangerous consequences.

1.4 Abnormal Operafjng Condifjons
The boundary between the normal and faulty conditions is noc crisp. There are certain
operating conditions inherent to the operation of the aower system which are definitely
not normal, but these are not electrical faults either. Some examples are the magnetizing
inrush current of a transformer, starting current of an induction motor, and the
conditions dunng power swing.
1.4.1 Should Protective Relays Trip During Abnormal
Operating Conditions?
How the protective system should respond to the abnormal operating conditions needs
careful consideration. It may or may not be required to take c_ognizanceof the abnormal',
,
operating condition. Some examples of abnormal operating conditions are starting
currents of motors, inrush currents of transformers and stable power swings. Magnitude-
wise, these currents may qualify as faults, but there is no need to provide protection from
them. Thus, the-- wtective system-. . ~.m u s t be able to discriminate between the normal~ ~ --- ~,~ -~ .
operating~~ . conditions,~.,~~ ~ .. ..~ ,,. abnormal~ operating... condi&io.as,and~~ faults.~,,. .
1.4.2 Can Protective Relays Prevent Faults?
It can be seen from the above discussion that protective relays cannot prevent faults. To
a certain extent, faults can be prevented by using the properly designed and maintained
equipment. However, it is not possible to totally prevent the occurrence of faults.
1.4.3 What are Protective Relays Supposed to Do?
The protective relays are supposed to detect the fault with the help of current and voltage
transformers, and selectively remove only the faulty part from the rest of the system by
a tripping an appropriate number of circuit breakers. This, the relay has to do with utmost
sensitivity, selectivity and speed. In a power system, faults are not an everyday
occurrence. A typical relay, therefore, spends all of its life monitoring the power system.
It must, therefore, be ready all the time in anticipation of a fault. It is said that a relay
operates far more number of times during testing and maintenance than during actual
fault! Thus, relaying is like an insurance against damage due to faults.
1.5 Evolution of Power Systems
Power systems have evolved from isolated feeding their own loads to huge
interconnected power systems spanning an entire country. The evolution has progressed
from low-voltage systems to high-voltage systems and low-power handling capacities to
high-power handling capncities. The requirements imposed on the protective system are
closely linked to the nature of the power system.

1.5.1 Isolated Power System
The protection of an isolated power system is simpler because firstly, there is no
concentration of generating capacity and secondly, a single synchronous alternator does
not suffer from the stability problem as faced by a multi-machine system. Further, when
there is a fault and the protective relays remove the generator from the system, the
system may suffer from a blackout unless there is a standby source of power. As shown
in Section 1.2.3,the steady-state fault current in a single machine power system may even
be less than the full-load current. Such a fault will, however, cause other effects like
speeding up of the generator because of the disturbed balance between the input
mechanical power and the output electrical power, and therefore should be quickly
attended to. Although, there are no longer any isolated power systems supplying
residential or industrial loads, we do encounter such situations in case of emergency
diesel generators powering the uninterrupted power supplies as well as critical auxiliaries
in a thermal or nuclear power station.
a
1.5.2 lnterconnected Power System
An interconnected power system has evolved because it is more reliable than an isolated
power system In case of disruption in one part of the system, power can be fed from
alternate paths, thus, maintaining continuity of service. An interconnected power system
also makes it possible to implement an economic load dispatch.
The generators in an interconnected system could be of varied types such as
turboalternators (in coal fired, gas fired or nuclear power plants), generators in
hydroelectric power plants, wmd-powered generators, fuel cells or even sol%-powered
photovoltaic cells
Figure 1.6 shows a simple interconnected power system. Most of the generators
operate at the voltage level of around 20 kV For bulk transmission of power, voltage levels
of the order of 400 kV or higher are used. At the receiving end, the voltage is stepped
down to the distribution level, which is further stepped down before it reaches the
consumers.
It can be seen that the EHV lines are the tte lines which interconnect two or more ()
generators whereas the low voltage lines are radial in nature which terminate in loads at
the remote ends
There is interconnection at various EHV voltage levels.
1.5.3 Negative Synergy of an Interconnected System I
There are other undesirable effects of interconnection. It is very difficult to maintain
stability in a massively interconnected system. Disturbances quickly propagate
throughout the system endangering the integrity of the whole system. Possibility of
cascade tripping due to loss of stability is always looming large. In addition to the angle
stability problem, an interconnected system also suffers from the voltage stability
problem. Further, undesirable effects, such as harmonic distortion, propagate throughout
the system rather than remain localized. Also, there is the possibility of cyber-attacks and
acts of malicious hacking, which have a greater footprint in the case of an interconnected

Generating
statlon A
m e20 kVl400 kV
Step-up
transformer
Load A
BusA A
Load 3
A Bus B
Generating
-'-A:..- 0
Double circuit
EHV line 400 kV 20 kV
EHV line
EHV line
/
J, ICEBus C
- 400 kV
Load C
-/-' 20 kV
Generating
station C
Figure 1.6 Single-line diagram of a simple interconnected power system
power system. This can be called the synergy, of the negative type, which inevitably
accompanies the interconnection. However, these are the perils of the so-called modern
way of life that we have adopted and have to be taken as an opportunity to devise newer
and novel methods of protection.
1.5.4 Various States of Operation of a Power System
A power system is a dynamic entity. Its state is likely to drift from one state to the other
as shown in Figure 1.7. When the power system is operating in steady state, it is said to
be in the normal operating state. In this state, there is enough generation capacity
available to meet the load, therefore, the frequency is stable around the nominal
frequency of 50 Hz or 60 Hz. This state is also characterized by reactive power balance
between generation and load. This is reflected as a flat voltage profile with normal voltage
throughout the system. The above is almost a theoretical proposition and a real power
system rarely finds itself in this state.

12 Firndunlcntals of Power System Protectiofl
n
Restorative -------- --------------- Alert
<I-
Figure 1.7 Various states of the power system.
Another possible state of the power system is the alert state. In this state, all the •parameters are within the limits but a major disturbing event is imminent, for example,
a mighty storm, accompanied by lightening, which threatens to put some major EHV tie
line out of service. From this state the system may hurtle into the in-extremis state, as
a result of major tripping, after passing through an emergency state. In the emergency
state there could be overloading in certain tie lines, the system frequency may take a
significant plunge or may surge and the voltage profile may be far from flat. The
emergency situation may lead to total ac failure as a result of cascade tripping. This is
indeed the nightmare and the system controllers at the load dispatch centres try their
best to avoid it.
What has all these states of the power system to do with relaying? A httle thought
will show that on the one hand relaying is profoundly affected by the state of the system
while on the other, the system's fate is decided by the settings of the relays. Ideally, relay
settings must be live to the system state and must change so as to operate in the best
interest of system stability and security. There are, however, certain other ground
realities which prevent us from implementing a totally adaptive online relay setting
philosophy. The relay engineers want their protective system to be as simple as possible.
There is overwhelming evidence that the simpler the systems are, the more reliable they
are. Thus the relay engineers follow the KISS philosophy; Keep It Simple, Stupid!
1.5.5 From Natural Monopoly to the Deregulated Power System
The electrical power system was always considered to be a natural monopoly Recently,
however, the world over, there is a paradigm shift. The industry is being deregulated. In
this scenario, big electric utility companies are no longer monopolizing the generation of
electric power. The field is open for smaller players. The customers have a choice to buy
electricity from the cheapest bidder (albeit through the distribution company). This has
opened many technical and administrative issues which, up till now, were non-existent.
The relaying engineer cannot remain unaffected by this change which IS sweeping
through the power industry. We shall, however, not discuss this aspect further in this
introductory text.

1.6 A Profection Sysfern and Its AHributes
Figure 1.8 shows a protection system for the distance protection of a transmission line,
consisting of a CT and a PT, a relay and its associated circuit breaker. Every protection
system will have these basic components. (In non-directional over-current protection, as
well as in differential protection, the PT will not be required.) The CT and the PT are
briefly discussed in Section 1.7.
Fault
Relay
Trip
uFigure 1.8 The protection system
At this stage, we can consider the relay as a black-box having current and voltage at
its input, and an output, in the form of the closure of a normally-open contact. This
output of the relay is wired in the trip circuit of the associated circuit breakerb) so as
to complete this circuit. The relay has another user settable input which is the setting of
the relay. The relay carries out the processing of information provided by the CT and the
PT in accordance with some predetermined logic to arrive at a discriminant, and
compares it with the settings to take a triplno-trip decision. The conceptual diagram of
a generalized relay is shown in Figure 1.9.
Setting
I
Current from CT 4 1 1
Current from PT 4Relay dTI Trip signal to CB
tSetting
Figure 1.9 Conceptual diagram of a relay.
I
Without entering into the discussion about how it is to be achieved, it is possible at
this stage to enumerate certain general properties that a protective system should
possess. This is more or less like a wish list, in the mind of a protection engineer.

7 -6.7 Sensitivity
The protective system must be alive to the presence of the smallest fault current. The
smaller the fault current it can detect, the more sensitive it is.
1.6.2 Selectivity
In detecting the fault and isolating the faulty element, the protective system must be very
- , ,. , selective. Ideally, the protective system should ~ o ~ i non the faulty element and isolate
it, thus causing minimum disruption to the system.
1.6.3 Speed
The longer the fault persists on the system, the larger is the damage to the system
and higher is the possibility that the system will lose stability. Thus, it helps a lot if the e
entire process of fault detection and removal of the faulty part is accomplished in as
! short a time as feasible. Therefore, the speed of the~protectionis very important. It
must, however, be mentioned that speed and accuracy bear an inverse relationship! The
high-speed systems tend to be less accurate. This is for the simple reason that the high-
speed system has lesser amount of information at its disposal than a slow-speed system.
The protection engineer has to strike a balance between these two incompatible
requirements.
..%
' 1.6.4 Reliability and Dependabilityt
! A protective system is of no use if it is not reliable. There are many ways in which
reliability can be built into the system. Good engineering judgement plays a great part in
1 enhancing the reliability of the protective system. In general, it is found that simple
1 systems are more reliable. Systems which depend upon locally available information, tend
to be more reliable and dependable than those that depend upon the information at the
remote end. However, in spite of best efforts to make the system reliable, we cannot rule
out the possibility of failure of the (primary) protection system. Therefore, we add
features like back-up protection to enhance the reliability and dependability of the
protective system.
1.7 System Transducers
Current transformers and voltage transformers form a very important link between the
power system and the protective system. These transducers basically extract the
information regarding current and voltage from the power system undcr protection and
pass it on to the protective relays. While doing this, they lnsulate the low-voltage
protective system (both personnel and protective apparatus) from the high-voltage power
system.

1.7.1 Current Transformer
The current transformer has two jobs to do. Firstly, it steps down the current to such
levels that it can be easily handled by che relay current cod.
The standard secondary current ratings used in practice are 5 A and 1A. This frees
the relay designer from the actual value of primary current. Secondly, it isolates the relay
circuitry from the high voltage of the EHV system. A conventional electromagnetic
current transformer is shown in Figure 1.10. Ideally, the current transformer should
faithfully transform the current without any errors. In practice, there is always some
error. The error creeps in, both in magnitude and in phase angle. These errors are known
as raho error and phase angle error.
Figure 1.10 Current transformer.
Transformer
CT Ratio = 1000/5 CT
, /
&t
l000A j Pr~mary i/-
Source - Bus - .- Secondary
.---------.-----.---..----*i 7Fault
Jt 5 A
5 A "
It may be pointed out here, that current transformers are used for metering purposes
as well. However, there is a very important difference between a metering CT and a
protection CT. A metering CT is so designecl (proportioned) that in case of faults, it will
saturate and thus save the instrument connected to its secondary from damage due to
excessive current On the other hand, a protective CT is designed to faithfully reproduce
the largest fault current. The operating po~nts,on the excitation charactenstics, for the
two types of CTs are shown in Figure 1.11.Further treatment of CT errors is given in
Appendix 1
Relay Output
14

I,i 16 F~~ncia~~~eiltolsof Power Svsre~nProrection A-
-"E
Measurement CT
m operating point
5
-5
c
m
51
ProtectiveCT
operating point
--f
Excitation, H(AT/m)
Protective CT
output
s
1
.. Slope= Cm
I Full- I
I l l l i l I ' 1 '
7load i4--
I / aMetering CT output
;current
Prirnaw current (rms)
Max~mumfaultcurrent
= 20 to 30 times
full-load current
Figure 1.11 Protective CT vs measurement CT.
1.7.2 Voltage Transformer
The voltage transformer steps down the high voltage of the line to a level safe enough for
the relaying system (pressure coil of relay) and personnel to handle. The standard
secondary voltage on line-to-line basis is 110V.This helps in standardizingthe protective
relaying equipment irrespective of the value of the primary EHV adopted.
-A PT primary is connected in parallel at the point where a measurement is desired,
unlike a CT whose primary is in series with the line in which current is to be measured.
A conventional electromagnetic VT is shown in Figure 1.12. The VT also suffers
from ratio and phase angle errors. Further treatment of VT errors can b e found in
Appendix 1.

Figure 1.12 Potential (voltage) transformer (PT or VT)
Another type of VT that is commonly used in EHV systems is the Capacitive Voltage
Transformer or CVT. This is dealt with in Appendix 1.
1.7.3 Circuit Breaker
The circuit breaker is an electrically operated switch, which is capable of safely making,
as well as breaking, short-circuit currents. The circuit breaker is operated by the output
of the associated relay. When the circuit breaker is in the closed condition, its contacts
are held closed by the tension of the closing spring. When the trip coil is energized, it
releases a latch, causing the stored energy in the closing spring to bring about a quick
opening operation.
1.7.4 Trip Circuit of a CB
The circuit breaker contacts are in a closed position by the force of a spring. Energy is
stored in the spring during the closing operation. In order to trip the circuit breaker, it
is necessary to release a latch either manually or by energizing the trip-coil of the circuit
breaker. The trip-battery supplies energy to the trip-coil for this operation. The relay
output contact is wired in series with the trip-battery and the trip-coil. Thus when the
relay operates, the trip-coil gets energized and the circuit breaker quickly parts its
contacts. The mechanical arrangement is quite complicated and only its essence is
depicted in Figure 1.13.
1.7.5 Organization of Protection
The protection is organized in a very logical fashion. The idea is to provide a ring of
security around each and every element of the power system. If there is any fault within
this ring, the relays associated with it must trip all the allied circuit breakers so as to
remove the faulty element from the rest of the power system. This 'ring of security' is
called the zone ofprotection. This is depicted in Figure 1.14 with the help of a simple
differential relay for the protection of a transformer. Without going into the detailed
working of the differential relaying scheme, we can make the following statements:

18 F~.!~~~ia~~lenrolsof Power Sysrrnl Prvieclior~
Step-up
transformer
Current Voltage
Trip battely
Trip coil Relay
B r e a k e r I
I 2 1 Trip
contact
Relay t r i r
CT HV
1output
I
I line
DT
contact 1 = 1
Figure 1.13 Trip circuit of a circuit breaker.
QOver-current
relay
differential protection
Figure 1.14 Zone of protection, external and internal faults.
Faults within the zone are termed internal faults whereas the faults outside the
zone are called external faults. External faults are also known as through faults.
Ideally, a relay looking after the protection of a zone should operate only for internal
faults. It should restrain from operating for external faults. The farthest point from the
relay location, which is still inside the zone, is called the reach point. The distance
, between the relay location and .he reach point is termed the reach of the relay.

It might be mentioned here, in passing, :hat though the zone of protection, as a
notion, is a very ciearly marked out area, in practice, it may become fuzzy and keep on
expanding and contracting. How far the zone is crisply carved out depends upon the
relaying principle used. In general, it can be said that the differential relaying gives a
much more crisply carved out zone than over-current or distance relaying. Directional
relaying creates a zone with infinite reach in the tripping direction.
1.7.5 Zones of Protection
Various zones, for a typical power system, are shown in Figure 1.15. It can be seen that
the adjacent zones overlap, otherwise there could be some portion which is left out and
Generatorzone
Transformerzone
Transmiss~onlinezone
Transformerzone
Generator zone
Figure 1.15 Various zones of protection for a power system

i1 20 F ~ i ~ ~ ~ i n ~ i r r ~ ~ t a l sof' Power Svsrrn~P~orecrioi~
I -
remains unprotected. At the same time, it must be realized that if the fault takes place
in the overlapped portion, more than the minimum number of circult breakers will trip,
causing a major dislocation to the system. Each of the zones may be implemented using
a different relaying principle. All the zones, in practice, may not be as well marked out
as they are shown in the figure and may contract or expand depending upon the various
system conditions.
1.7.7 Primary and Back-up Protection
As already mentioned there are times when the primary ~rotectionmay fail. This could
be due to failure of the CTIVT or relay, or failure of the circuit breaker. One of the
possible causes of the circuit breaker failure is the failure of the trip-battery due to
inadequate maintenance. We must have a second line of defence in such a situation.
Therefore, it is a normal practice to provide another zone of protection which should
operate and isolate the faulty element in case the primary protection fails. A little thought
will convince the reader that the back-up protection should not have anything in common
with the primary protection. It should also preferably be located at a place different from
where the primary protection is located. Further, the back-up protection must wait for the
primary protection to operate, before issuing the trip command to its associated circuit
breakers. In other words, the operating time of the back-up protection must be delayed
by an appropriate amount over that of the primary protection. Thus, the operating time
of the hack-up protection should be equal to the operating time of primary protection plus
the operating time of the primary circuit breaker.
Consider the radial system shown in Figure 1.16. Relay B, in conjunction with circuit
breaker CBB,provides primary protection to the line section B-C. Relay A with circuit
breaker CBAprovides back-up protection to the section B-C. Consider a fault in section
B-C as shown in Figure 1.16.

When a fault takes place, both the primary relay RBand the back-up relay ItA,szart
operating simultaneously. in case the primary protection (provided by RB+ CBB) operates
successfully, the line B-C gets de-energized but the loads on buses A and B remain
unaffected. Therefore, the back-up protectior 'provided by RA + CBAj resets without
issuing a trip command. The sequence of events in such a case is depicted in Figure 1.17.
However, in case the primary protection fails to operate, the back-up which is already
monitoring the fault, waits for the time in which the primary would have cleared the fault
and then issues the trip command to its allied circuit breakers.
When the back-up operates, the time for which the fault persists is longer and
disruption to the loads also lasts longer.
Fault
instant
Primary relay RB
operates Primary relay CBB
interrupts
the fault current
P-
Primary Primary CB
operating time
Pr~maryfault clearing time 3
Back-up relaying time > Primary fault clearing time
T A > TB + CBB
ePrimary protection provided by RB starts operating
I)
Back-up protection prov~dedby RA starts operating
/
Primary protection issues trip command to primary circuit breaker CBB
'Primary circuit breaker starts operating
/
Primary circuit breaker CBBtrips. Current returns to normal value
'Back-up protection provided by RA resets,
Figure 1.17 Primary and back-up protection: sequence o f events: normal operation

i 22 F~~ncla~nenralsof Power Sysrem Prorection
I
i 1.7.8 Maloperations
i
! There should be proper coordination between the operating time of primary and back-up
v
{
protection. Figure 1.18shows an instance of loss of selectivity between the primary and .
I, back-up protection. It can be seen that the back-up protection in this case issues trip
1 command to its breaker without waiting for the primary protection to do its job. This
1
1
results in operation of both the primary and the back-up, resulting in a longer and
1 unnecessary disruption to the system. It is said that with every additional relay used,
there is an increase in the probability of maloperation.
Time
Primary CBPrimary
relayingtime operating time?
*
Back-upCB
Back-uprelaying operatingtime4+operating timeJ
t.
6 Primary fault clearing time
Back-up relayingoperating time c Primary fault clearing time
TA-=TB+CBB
Fault instant
Primary protectionprovided by RBstarts operating
Back-upprotectionprovided by RAstarts operating
/ Primary protectionissues command to primary CB(RB +CBB)
'Primary CB, CBs, starts operating
,Back-up protectionissues command to back-up CB(RA+CBA)
'Back-upCB. CBA,starts operating
PrimaryCB, CBB,trips
Back-upCB, CBA,trips
Figure 1.18 Primary and back-up protection: sequence of events: loss of selectivity

1.8 Various Power System Elements That Need Projection
The power system consists of alternators; busbars, transformers for transmission and
distribution, transmission lines at various voltage levels from EHV to 11 k y cables,
induction and synchronous motors, reactors, capacitors, instrument and protective CTs
and PTs, various control and metering equipment, etc. Each of these entities needs
protection. Each apparatus has a unique set of operating conditions. For example, while
the transmission line is spread out geographically over a very long distance, the
transformer windings are localized to comparatively much smaller space. While the
alternator is a huge rotating mass with mechanical coupling to the turbine and electrical
coupling to the power system, the busbars present an entirely different scenario as far as
protection is concerned. Thus each apparatus needs a different kind of protective system
targeted to its unique set of anticipated faults and abnormal operating conditions. This
makes the field of power system protection a medley of relay operating principles and
schemes. However, it is possible to sort out this seemingly kaleidoscopic situation by
either focusing on the power system element that one is trying to protect or by focusing
on the protection principle involved. Both approaches are complementary and both should
be used.
1.9 Various Principles of Power System Protection
The most visible effect of fault is a sudden build-up of current. Thus, over-current relaying
is the most natural principle of relaying. However, fault current magnitude is a function
of type of fault and the source impedance. The source impedance, which depends upon the
number of generating units that are in service at a given time, keeps changing from time
to time. Therefore, the reach as well as the operating time of over-current relaying keep
changing from fault to fault, and time to time.
This has led relay engineers to think of other principles of protection. Another very
Q
natural and appealing principle is the differental protection. It is based on the premise
that the current entering a protected section must be equal to that leaving it. Any
discrepancy between the two indicates the presence of a fault. However, it is impractical
to apply this principle to a transmission line because the ends are far apart and it is not
easy to compare information at the two ends.
To get over the above problem, a distance relay compares voltage with current at the
same end. This, in effect, measures the impedance between the relay location and the
fault point. Since impedance of a transmission line can be considered to be directly
proportional to the distance along the line, this type of relaying is known as distance
relaying.
In case of a double-end feed system, or parallel lines, or a ring main system, a fault
gets fed from both sides. In order to be selective, the relay must be sensitive to the
direction of fault power flow. The relays which exhibit such property are termed
directional relays. The entire gamut of protection can be captured in Table 1.3.

The cells of the Table 1.3, where the principle meets the protected, in fact form tg
subject matter of the book. In chapters to come, we will try to fill up these cells or try
to understand why some of the cells remain vacant!
21 F[~i~d~~~ile,~rnlsof Power S?:sie~~rPr~rccriol~
Table 1.3 The gamut of power system protection
Principle I Won-directional Directional Differential Distance
Apparatus11- ouer-current ouer-current
Review Questions
Alternator
Busbar
Transformer
Transmission Line
Large Induction
Motor
Power systems are moving towards increasing complexity and demand equally
complex protection. Discuss.
Compare an isolated power system and an interconnected power system. How do
their protection requirements differ?
A single synchronous alternator does not suffer from loss of stability. Discuss.
What do you mean by zone of protection?
Primary
Protection
Primary
Protection
Primary
Protection
Primary
Protection
Primary
Protection
What do you mean by an internal and an external fault?
What is a through fault?
Why are adjacent zones made to overlap?
Why zone boundaries, in practice, tend to float?
J J J
I
J
J
J J J
J J
Explain the terms sensitivity and selectivity with respect to their use in the
protective relaying field.
Why is speed of protection so important?
C
Why is back-up protection needed?
What do you mean by maloperation of a relay?
What do you mean by maloperation due to loss of selectivity between the primary
and the back-up relaying?
What are the advantages of high-speed protection?
What are the pitfalls of high-speed protection?
Give an estimate of circuit breaker operating time.
Give an estimate of relay operating time.

Problems
1. The percentage impedance of a transformer is 8% Determine the short-circuit
current for a three-phase short circuit on the secondary terminals of the
transformer.
2. In the diagram of Figure 1.16, TB= 0.2 s. If the circuit breaker operating time
is 0.5 s, determine the operating time of relay RA so that there is no loss of
selectivity.
3. In the diagram of Figure 1.16, the operating time of relay RB = 0.3 s, operating
time of relay RA = 0.6 s. The circuit breaker operating time is 0.5 s. Investigate
whether there will be any loss of selectivity between the primary and the back-
up protection.
4. The load current in a system is 100 A. The short-circuit current for the smallest
fault is 1000 A. An over-current relay capable of carrying a current of 5 A
continuously is to be used.
(a) Suggest a suitable CT ratio.
(b) What will be the relay current for the smallest fault?
(c) Will the protective CT be able to faithfully reproduce the fault current?

2.1 Introduction
As already pointed out, the most obvious effect of a shunt fault is a sudden build up of
current. Therefore, it is only natural that the magnitude of current be utilized as a
positive indication of existence of a fault. It is no wonder, therefore, that the over-current
protection is the most widely used form of protection. In many situations, it may be the
only protection provided. This type of protection which depends on only the magnitude
of the current, without taking any cognizance of its phase angle, is known as the
non-directional over-current protection.
However, many times it is required to discriminate between faults rn front of the
breaker and faults behind the breaker. This is possible only if we take into account, not
only the magnitude of the current but also its phase with respect to the voltage at the
relay location. In such cases, the protection is known as the directional over-current
protection. A little thought will convince the readers that a directional over-current
protection affords greater selectivity than a non-directional over-current protection.
We must not forget that any type of protection is first a concept. Then, it needs to
be implemented. The vehicle of implementation is the relay. We can thus imagine a non0
directional over-current relay, which provides the non-directional over-current protection
and so on.
Historically, however, fuses have preceded the over-current relays for providing over-
current protection. We will, therefore, take a brief look at fuses in the next section.
2.2 Fuse
Fuses are the oldest protective devices that have survived from the dawn of the age of
electricity to the present times. This can be attributed to their intuitive simplicity The
fuse allows the normal current to flow but melts itself out, thus breaking the circuit,
when the current exceeds a certain magnitude for a certain amount of.time. It combines
the functions of sensing, comparing, and interrupting the current into one. Figure Z.l(a)
depicts the external appearance of a high rupturing capacity (HRC) fuse. The current
26

versus time characteristic of a fuse is shown in Figure Z.l(b,. The waveform of che short-
circuit current interrupted by a fuse is shown in Figure 2.l(c).where it can be seen that
the fuse interrupts the current even before it attains its peak value.
(a) External appearance of a HRC fuse
(b) Time-current characteristic of a fuse
/ Prospective peak
t 1,
Fault current
I
Instant of :,
interruption k,
I
, I
, ' J
_'
(c) Short-circuit current interrupted by a fuse
Figure 2.1 High rupturing capacity (HRC)fuse.
I
2.3 Thermal Relays
Thermal relays, of the bimetallic type, work on the principle of strain generated due to
unequal linear expansion of two different metals as a result of heat generated by the

28 F~tr~dainirrerirnlsof Power Svsrerrr Prvtecrion
passage of the fault current. Figure 2.2(a) shows a bimetallic relay consisting of strips AB .
and CD of two different materials. Both the strips get heated up by the same amount but
are deformed by diqering amounts. Figure 2.2(b) shows the rclay operation. The material .
with higher coefficient of expansion is at the outer surface of the curve while that with
lower coefficient is at the inner surface.
Low coefficient r - O
of expansion Heater coil
4 I / 'Trip c
High coefficient
of expansion
Figure 2.2 A bimetallic relay
Since the heating effect is propnrtional to the square of the current, the energy
dissipated is given by (1?R)t,where t is the time for which the current flows through the
relay. (i
Since accumulation of sufficient amount of heat depends on the thermal inertia of the
relay, which tends to be rather large, these relays are used where-~....very~ . .~q u i c k m a t i o n-
is not d e d f ~ .A typical- application of the thermal relay is to provide protection a g a w
prolonpeddo_ve~&a&ngo f m o t ~ p .The thermal overload relay thus let; the motor supply
overload for a preset amount of time before tripping it off.
2.4 Over-current Relay
An over-current (OC) relay has a single input in the form of ac current. The output of
the relay is a normally-open contact, which changes over to closed state when the relay
trips. The relay has two settings. These are the time setting and the plug setting. The
time setting decides the operating time of the relay while the plug setting decides the
current required for the relay to pick up. The name plug setting comes from the

~Izctromechanicdover-current relay. In these relays, we have io ~nserta shorting ?lug in
J. plug-setting bridge, so as to change che numher of turns of the operating cod to get a
particular pick-up value. The same terminologlv continues to be used in the modern
relays. The block diagram of an OC reldy is ahown in Figure 2.3.
Time setting
Input current Time over-current ~ r c poutput
relay aPlug setting (Pick-up)
Figure 2.3 Block diagram of an over-currentrelay.
The plug-setting multiplier, PSM, is defined as follows:
Irelay /PSM = -
PS
where Irelayis the current through the relay operating coil and PS is the plug-setting of
the relay. The value of PSM tells us about the severity of the current as seen by the relay
A PSM less than 1means that normal load current is flowing. At PSM > 1, the relay is
supposed to pick up. Higher values of PSM indicate how serious the fault is.
For example, let us consider a 1.0 A relay (i.e. a relay with current coil designed to
carry 1.0 A on a continuous basis) whose plug has been set at 0.5 A, i.e. at 50%. Assume
that, for a certain fault, the relay current is 5.0 A. The relay, therefore, is said to be
operating at a PSM of (5.0/0.5) = 10.
@ 2.4.1 Instantaneous OC Relay
It is to be noted that the word instantaneous has a different connotation in the field of
power system protection. Instantaneous actually means no intentional time delay.
Howsoever fast we want the relay to operate; it needs a certain minimum amount of time.
The operating time of an instantaneous relay is of the order of a few milliseconds. Such
a relay has only the pick-up setting and does not have any time setting. The construction
and the characteristics of an instantaneous attracted armature type relay is shown in
Figure 2.4,wherein it can be seen that as the armature of the relay gets attracted towards
the coil, the air-gap becomes smaller, and hence the reluctance becomes smaller. This
results in increased flux which causes the force on the armature to build up (force being
proportional to the square of the flux density). This is a positive feedback action which
results in the armature moving quickly in an instantaneous snap action. The operating
torque on the armature is proportional to the square of the current.

2.4.3 Inverse Time Over-current Relay
30 F~~~rclr~rr~e~~talsof Po~verSj~sreti7P,vr?crior~
-::C
0
0
a,
m.---.-
E-
E.--m
C.--E
d Operating lime
0
I
-
t
f
Current (amperes)
Pick-up value I
Figure 2.4 Instantaneous over-current relay characteristic.
a
2.4.2 Definite Time Over-current Relay
A definite time over-current relay can be adjusted to issue a trip output at a definite (and
adjustable) amount of time, after it picks up. Thus, it has a time-setting adjustment and
a pick-up adjustment. The characteristic and the block diagram are shown in
Figure 2.9.
Inverse time characteristic fits in very well, with the requirement that the more severe
a fault is, the faster it should be cleared to avoid damage to the apparatus. This type of
characteristic is naturally obtained from an electromechanical relay, which has led to its
:' widespread use and standardization. With the advent of microprocessor-based relays, it is
,,!I now possible to generate any imaginable time-current characteristic. However, in order to
I:,
r: maintain compatibility with the very large number of electromechanical relays, still in
, I
A
..
Time setting
m
E.--m
C
.-
t
d
0
@ ' -.
Current Trip output t
Plug setting .-
Plug setting
j.
?
Time setting Operating time 1
-----r---
J. (, 1
f
f Current
i
Pick-up value
+
Figure 2.5 Definite time over-current relay characteristic.

service, certain ifivrse time characteristics, described in the nesz sectior., have beer,
standardized.
Inverse definite minimum time (IDi)IT) oaer-current relay
This is possibly the most widely used characteristic. The characteristic is inverse in the
initial part, which tends to a definite minimum operating time as the current becomes
very high. The reason for the operating time becoming definite minimum, at high values
of current, is that in the electromechanical relays the flux saturates at high values of
current and the relay operating torque, which is proportional to the square of the flux,
does not increase substantially after the saturation sets in. Such a characteristic came
about because of the limitation of the electromechanical technology Ideally, we may
demand that the operating time be inverse in nature throughout the operating range. The
mathematical relation between the current and the operating time of IDMT characteristic
- can be written as
I I
where PSM is the plug-setting multiplier and TMS is the time-multiplier setting of the
relay. Thus, the operating time is directly proportional to the TMS and inversely
proportional to the PSM. The characteristics of the IDMT relay are shown in
Figure 2.6.
Plug-setting rnult~pller(relay current as a rnultlpie of plug setting)
Figure 2.6 Inverse definite minimum time relay characteristics (TMS= 1.0).
-

32 Funda~nenmlsoj Power Sysrern Prorectioi~
Very inverse time over-current relay
The inverseness of this characteristic is higher than that of the IDMT characteristic. The
mathematical relation between the current and the operating time of such a characteristic
can be written as
The characteristic of the relay is shown in Figure 2.6.
Extremely inverse time over-current relay
The inverseness of this characteristic is higher than that of the very inverse
characteristic. The mathematical relation between the current and the operating time of-
such a characteristic can he written as
80.0 (TMS)
It,; m .
(PSM)~- 1
The characteristic of the relay is shown in Figure 2.6.
2.5 Implementation of Over-current Relay Using Induction
Disk --I
In order to understand the working of an induction disk type relay; let u s first see how
,'
torque can be produced by two alternating fluxes acting on a common metallic but non-
i ,
magnetic rotor. Figure 2.7 shows two alternating fluxes and @2 having a phase
f
T difference of 0 between them.
Induced flux
f
hernating fluxes
Ed<-. -
//
1
I'
miniurn disc
'e 2.7 Operating principle of induction disc type relay.
alu
Figu

Over-crrrrcnr Protectlort of Traizsnris~ro~~Lines 33
Thus, we have
$1 = $,, sin ot
pz = h,sin (at + 8)
Each flux induces a voltage in the disc, and hence gives rise to induced currents ih and
'
Assuming that the eddy current path has negligible inductance, we can writeb ~ x
$2 = oh2cos (ot + 8)4 2 a 7
As shown in Figure 2.7, 4 interacts with i,, to produce force Fl. Likewise $2 interacts
with i,, to produce a force Fz. Assuming w to be constant, we have
@ F1 = $liCza sin wt cos (wt + 8)
F2 = hi,,a &,&, sin (wt + 8) cos wt
The net force (F2- Fl) is thus, given by
3'2 - FI a [sin (wt + 8) cos ot - cos (wt + 8) sin wt ]
which simplifies to
IF2 - F1 $m1&2 sin 81,
The following important conclusions can be drawn from the above expression for
torque:
Two alternating fluxes with a phase shift are needed for torque production,
i.e. a single alternating flux would not produce torque.
Maximum torque is produced when two alternating fluxes are shifted in phase
by 90".
The resultant torque is steady, i.e. it is not a function of time, as time t is not
involved in the expression for torque.
Since in an over-current relay, there is only one input quantity, it will not be possible
to produce torque unless two fluxes shifted in phase are produced.
The above principle has been used in the induction disc type over-current relay whose
construction is shown in Figure 2.8. Herein two fluxes shifted in time phase are obtained
from the input current, by using a shading coil. The flux in the shaded coil lags the main
flux. The torque thus produced by the interaction of the two fluxes, neglecting saturation,
is proportional to I2 since each of the flux is proportional to I. This is the deflecting
torque TdeneCtinpThe spiral spring provides the control torque TcontrollingThe control
: torque can be considered to be directly proportional to the angle 6, through which the
back-stop has been retarded from the trip position. The permanent magnet provides the
damping torque, which is active only when the disc is in motion and is thus proportional
to the rate of change of angle dFldt. The torque equation can therefore be written as

34 F~rrirln~ne~~talsof Power Syste~f~Protr.crioll
ThlS adjustment dial
Movable contact
. .
0---------,------5 - -
,
Figure 2.8 Constmction of an induction disc relay. ':,..
where K is deflection constant, S is the spring constant, and D is the damping constant.
All these constants depend upon the design of the relay.
When the disc is on the verge of deflection, we can equate the torques and write
i
d6 S K
-+ K,6 - ~~1~= 0, K, = and K2 = -
dt D
The solution of the above equation is of the form i
I
6 = K,e-" KK,
where K, and K4 are functions of K1 and K2, i.e. S, D and 1'. Now,
At t = 0; 6 = 6,,,t,,1
At t = top; 6 = 0
We can find the operating time by finding the value of time t for which 6 becomes
zero. The value of Finitial is decided by the time-multiplier setting.

The exact analysis of the dynamics of induction disc is quite involved. However, it can
be noted that by proper design of the magnetic circuit a wide range of characteristics from
extremely inverse to definite time can be obtained.
2.6 Application of Definite Time OC Relays for Protection
of a Distribution Feeder
Consider a three-phase feeder as shown in the single-line diagram of Figure 2.9, with two
line sections AB and BC. Assume that DTOC relays are used at buses A and B. There are
loads at all the three buses.
Three-phase line
Bus C
I
I
Fault location
Figure 2.9 Application of DTOC relays for feeder protection.
The protection problem can be stated as follows:
Given the magnitudes of all the loads and the fault currents at all the buses, how to
e set the DTOC relays at buses A and B so that the entire feeder gets over-current
protection arranged as primary and back-up protection.
The first step in designing the over-current protection is to select the ratios for all
the CTs. The secondary current of the CT is decided by the rating of the relay current
coil. The CT primary current is decided by the maximum load current to be carried by
the CT primary. Next we have to do the relay setting. It may be noted that setting of the
relay, where the DTOC relays are involved, means:
1. How to select the pick-up value of the relay?
2. How to set the operating time of the relay?
How to select the pick-up value of the relay?
The setting problem has been pictorially depicted in Figure 2.10.
We can set the pick-up value of the relay, keeping in mind, that the relay should allow
normal load as well as a certain degree of overload to be supplied. Thus the pick-up value

36 Fu,idrz~ui.rlmlsof Power S.vsterrz Protecriun
of the relay should be more than the allowable maximum load. At the same time, the relay
should be sensitive enough to respond to the smallest fault. Thus, the pick-up value
should be less than the smallest fault current. Therefore, we can write the foliowing rule,
as far as setting the pick-up value of the OC relay is concerned:
1IL,m a < Ipu< Ic,mln 1 -
Permissible ,I I
I
overload I
Minimum fault current --+ I
I
% Maximum fault current
Figure 2.10 The plug setting of DTOC relays
How to set the operating time of the relay
Here we are guided by the principle that a relay must get an adequate chance to protect
the zone under its primary protection. Only if the primary protection does'not clear the
fault, the back-up protection should initiate tripping. Thus as soon as the fault takes
place, it is sensed by both the primary and the back-up protection. ~aturallj!the primary
protectioil is the first to operate, its operating time being less than that of the back-up
relay. Figure 2.11 shows the relationship between the operating time of the primary relay
and that of the back-up relay. We have to allow for the overshoot of the primary relay, so
that there is proper coordination between the primary and the back-up. Overshoot time I)
If fault is cleared beyond this porn1 Overshoot
' time To,,.the relay RA does not reset '-"yL
Relay R, operating time. T,,,
v -Time
4
I
Fault instant +I Reiay RA
I trips
f I
Relay Re operating Circuit breaker B
time, T,,, perating time. Tc,, ,
< - TR,A' TR.B+ Tca.6 + TOSA -, 4, ,--+Time
Figure 2.11 The time setting of DTOC relays.

Over-currer~rProtecrio~lof Tro~r.vnissionLines 37
is defined as the time for which the relay mechanism continues to move, even after the
operating coil has been de-energized. Overshoot is because of the moment of inertia of the
moving system.
in the light of the above discussion, the correct procedure would be to start
the setting from the tail end of the feeder system. The relay, which is at the end of the
radial feeder, can be made to operate without any delay, as it does not have to coordinate
with any other relay. In the given example of Figure 2.9, iet us assume that the operating
time of RBis set to 0.1 6. Thus relay RA should wait for 0.1 s plus, a time equal to the
operating time of circuit at bus B (TCB,B)plus overshoot time of relay A (ToS,*).Thus,
we can write
TR,B= 0.1 s (fastest)
Assuming CB operating time = 0.5 s and overshoot time = 0.2 s, we have
TR,, = 0.1 + 0.5 + 0.2 = 0.8 s
The time step between the operating times of the two relays, which is equal to the sum
of the operating time of the circuit breaker at B and the overshoot time of relay A, is
essential for maintaining selectivity between relays at A and B. Hence this interval is
referred to as the selective time interval (STI). The worksheet for the settings of the relays
thus can be written as shown in Table 2.1.
Table 2.1 Purpose and setting of relays
Relay Purpose Pick-up value Time setting
Primary protection Fastest
of section BC IL,C< I p u 4 B < II,c,mln TR,U= 0.1 s
Ru Note: RB is at the
tail end of the system
Back-up protection of (IL,B+ IL,c)< Ipu4*< II,Cmin TR,A= TRB+ TCB,B+ TOS,A
section BC = 0.1 + 0.5 + 0.2
RA
Primary protection of = 0.8 s
section AB
Note that the setting process has to be started from the relay which is at the tail end
of the system. This is because this relay is not at all constrained by selectivity problems.
All other upstream relay settings are tied up with their downstream neighbours.
The result of this setting process is shown in Figure 2.12. It can be seen from this
figure that as the fault moves towards the source, the fault currents become larger and
the fault clearing time also becomes longer. This is because the relays nearer the source
are deliberately delayed so that they are selective with relays downstream Thus, the relay
nearest to the source is the slowest. This is not desirable. It can be shown that a
significant improvement in fault clearing time, as we move towards the source, is
obtained if we use the Inverse Definite Minimum Time (IDMT) relays.

38 F~rndu17ienralsof Power Systrln Prorecrio~i
Three-ohase line
Fault location
r''2
2 0.8 s
w
n
0
ST1 = 0.7 s
Operating time
X
m- of Ra = 0.8 s
2
Fault location
Figure 2.12 Setting of DTOC relays for OC protection of a feeder.
--
2.7 Application of Inverse Definite Minimum T h e Relay
on a Distribution Feeder
Consider a radial feeder with two buses A and B where IDMT OC relays are to be used
(Figure 2.13). It should be noted that:
Three-phase line
Source
0E
Load l ~ , ~
= 80 A
Bus A Bus B
Bus A Bus B Bus C
2s CB- 'R,A
v m -
If m,n = 3500 A IF,mln = 2000 A I,, ,,, = 1000 A
I,, mx= 4000 A 4mx = 3000 A %,, = 1500 A
Figure 2.13 Setting of IDMT OC relays.
-IR,B
.r
7 .
M -
Load I,,,"
= 160 A
-

Over-current Proteciion of Transmission iznes 39
The purpose of relay RB is to prov~deprimary protection to line 3C.
r The purpose of relay RAis to provide primary protection to line 33 and back-up
to line BC.
We start the setting process from ;he tail end of the system.
(a) Deciding the CT ratios and plug settings:
(i) At relay B, the maximum load current, assuming 25% overload is:
80 A + (0.25 x 80 A) = 100 A
Assuming 1A relay to be used, the CT ratio can be selected to be 100 : 1. The plug
setting PS can be done at loo%, i.e. PS = 1.0 A.
(ii) At relay A the maximum load current, assuming 25% overload is:
Assuming 1A relay to be used, the CT ratio can be selected to be 300 : 1. The plug
1) setting can be done at loo%, i.e. PS = 1.0 A.
(b) Deciding the time-multiplier settings: Starting from the most remote relay RB
(i) Since RB does not have to maintain selectivity with any other relay, it can be
made to operate the fastest. Thus the TMS of RB can be selected as 0.1.
(ii) Now, to maintain selectivity between RAand RB,the folloulng constraint must
be met:
fault at B
The operating time of RB for maximum fault just beyond bus B can be found from
For maximum fault at B, fault current = 3000 A on primary side which becomes
(30001100) = 30 A secondary. Since plug setting is done at 1.0 A,
30PSM = ---- = - = 30
PS 1
The TMS of RB has already been set at 0.1. Substituting these values, we get
Let TCB,B= 0.5 S. Then,
TR,B+ TCB,B= 0.7 s
This value of 0.7 s is the desired operating time of RA.Assuming overshoot time of RA
to be 10% of 0.7 s, i.e. TOS.*= 0.07 8.
Thus, we get the required operating time of RA for maximum fault at bus B:
TR,AmaxfaultatB= 0.2 + 0.5 + 0.07 = 0.77 s

40 Fltrldarnentals of Power Svstern Protectiorl
The TMS of RAcan be found from the following expression for the operating time of RA:
0.77 =
0.14(TMS)
PSM~."- 1
We have, for RA,for the above condition, PSM = I,,,,lPS = (3000/300)/1 = 10
Hence. for Ra
TMS = 0.77
!1o0.O2 - 1)
= 0.26
0.14
This finishes the setting of both the relays.
We can verify that the selectivity for minimum fault at bus B is automatically
maintained.
Minimum fault current for fault at bus B = 2000 A.Relay B current corresponding
to this is 20001100 = 20 A.Since plug setting is 1A, this translates into a PSM of 20.
For relay Rg, TMS = 0.1. Thus, operating time of RBfor minimum fault at bus B will be:
a0.14(0.1)
= o,226TR,B,minfault at B = T ~ , ~= 200.02 -
and
TCB,s= 0.5 s
Expected operating time of RA for this fault should be greater than
0.226 + 0.5 + O.l(O.226 + 0.5) = 0.726 + 0.0726 = 0.7986 = 0.8 s (approx.)
NOW,let us find out the actual operating time of RAfor minimum fault at bus 3:
Minimum fault current = 2000 A ..
Relay RAcurrent corresponding to this is: 20001300 = 6.66 A
Since plug setting is 1 A, this translates into a PSM of 6.66. For relay RAT
TMS = 0.26. Thus the operating time of RA for minimum fault at bus B will be:
This value of 0.94 s is greater than the minimum operating time of 0.8 s, required for
maintaining selectivity between RA and RE.
The results can be listed as follows:
Relay CT ratio Plug setting TMS
RB 100 : 1 1A 0.1
RA 300 : 1 1 A 0 26
The sketch of fault clearing time as a function of fault location for IDMT relays is shown
in Figure 2.14.
We can deduce the following general rules from the above setting exercise:
Start the setting from the relay at the tail end of the system.
Plug setting should be such that: IL,max < P S < If,,in at the end ornertsRtion i.e. for
plug setting consider minimum fault current at the end of the next section.

* TMS should be decided such that the selectivity with the next relay downstream
is maintained for maximum fault current at the beginning of the next section.
Three-phase iine
R,,eA !
Fault location
Figure 2.14 Variation of fault current against fault location for IDMT relays under
maximum fault condition.
These rules are shown in Figure 2.15 for a simple system consisting of two buses. The
same principle can be extended to an n bus system. In fact, a computer algorithm can be
developed to automate this task in case of a large system.
Three-phase line
Bus A Bus B Bus CSource
Zs cB-1~. -IR B
r m -
E
Load / Load ;
0
/ L A I IL,B I
b 4
C,min, B
4wx. B
Plug sett~ngof Re should be such that:
1If,,,,, > PS of RB > (IL, + Overload)
TMS of R0 can be set at the smallest value of 0.1.1
Plug setting of R, should be such that
(I, ,,,,c > PS of RA > [(IL + IL C) + ~verloadli
TMS of RA should be such that:
, for If,,,,
operating time time of R,
Figure 2.15 Rules for setting IDMT OC relays,

42 Fundamentals of Power System Protection
2.7.1 Choice Beiween IDMT and DTOC Relays
It can be seen that IDMT relays offer significant improvement in fault clearing times over
DTOC relays. A question that naturally arises is: if this is so, there should be no need
to use DTOC relays. However, there are situations where IDMT relays do not offer
significant advantages over DTOC relays. For example, consider a system where
Zs >> ZL. Since the fault current as a function of fault location is proportional to
I -
E Ecs -
f - Z " + z Zc ,it would remain more or less constant throughout the length of the
- L z " -feeder, therefore, the inverseness of the IDMT characteristics cannot be exploited. In such
situations, DTOC relays being cheaper may be preferred. Such feeders are also described
as electrically short in length, irrespective of their physical length. Thus we can say that
DTOC relays are suitable for lines which are short in length.
zsIt is a practice to recommend DTOC relays when -2 2 . See Figure 2.16.
ZL
I >
Fault location
A
Figure 2.16 Choice between DTOC and IDMT relays.
E
2.8 Protection of a Three-phase Feeder a
Short line
Zs ..ZL
Up to this point we have shown three-phase feeders with the help of a single-line diagram.
The single-line diagram hides the complexity of the three-phase system. The three-phase
system is subject to phase faults as well as ground faults. For providing complete
protection to a three-phase feeder, we can begin with three relays connected to three CTs
as shown in Figure 2.17. As can be seen from Table 2.2, all the 11 numbers of shunt faults
are catered for by the three relays.
The relays at bus A will be coordinated with those at bus B using the procedure
illustrated in Section 2.7.
It may be pointed out here, that fault current for a single line to ground fault,
depends upon the system grounding as well as the tower footing resistance. Therefore, it
may happen that the fault current for a single line to ground fault, may be less than the
load current. In such cases, it will not be possible to cater to such faults if we use the
d,
2 -z $
I
PL
=U I E, -
=3
m
2s + ZL

Ovrr-cxrrenr Proreerio~~of Transmission L111rs 43
<----------- ,jne*-B ------------>
Phase a m
CT ratio n : 1
Figure 2.17 OC protection of a three-phase feeder.
Table 2.2 Protection of a three-phase feeder
Fault
Relays which will operate
Three-phasefault Two-phase fault + one ground
relays of ~ i ~ u r e2.17 fa& relay of Figure 2.18
a-R R, R,, RE
b-g
c-g
a-b
b-c
c-a
a-6-g
b-c-g
c-a-g
a-6-c
a-6-c-g
scheme shown in Figure 2.17. A little thought will show that if we connect an OC relay
In the residual current path as shown in Figure 2.18, it will be blind to the load current
(which is balanced three-phase current) and see only the ground fault currents. The
current in this path will be zero or near zero during normal balanced load conditions as

44 Fl~?zdnn~entalsof Power Systen~Protection
well as during a three-phase fault. Thus, the setting of this relay, which is in the residual .
current path, can be made independent of load current and can indeed be much smaller
than the load current.
Further, as illustrated in Figure 2.18, it is not necessary to use all the three relays -
for detection and protection against phase faults. We can get rid of any one phase fault
relay without affecting the performance of the scheme. In Figure 2.18, the relay in the
phase b has been removed.
Tr~pcolt
R, Rg R'
Trlp battery Ground fault
OC relay R,
contacts
Figure 2.18 Two-phase fault relays and one ground fault relay for OC protection i
of a three-phase feeder.
@ i
.i
Table 2.2 shows the operation of relays for all the 11shunt faults for OC schemes of :it
Figure 2.17 and Figure 2.18, which shows that all the 11shunt faults are catered for by . I
2
these schemes. 1
I. !
I
2.9 Directional Over-current Relay ,i,
B
Figure 2.19 shows a double-end-fed power system. The zones to be generated by the relays Ii
Fare also shown. Consider that we have only over-current relays at our disposal. Will it be .i
possible to implement the desired zones using simple over-current relays? In order to
answer this question, let us focus on OC relays at bus C. Note that OC relays operate on
i
the magnitude of fault current and cannot sense the direction of the fault.
Consider fault F,. As per the desired zones, only CBs 4 and 5 should trip. However, j
t
it can be easily seen that if plain OC relays are used, CBs 3, 4, 5, and 6 will all trip as ?
$
'1
- - . -- -- ~ - ~ ~~~ ~~..,---..T.--- i.~, +,- -'

Over-current Protecrion of T~ans~?~issionLines 45
the fault will be seen by OC reiays at these !ocations. Thus, the desired zones are not
generated. The desired relay response is shown in Tabie 2.3 with respect to faults Fa
and F,.
Figure 2.19 Need for directional relay.
Table 2.3 Response of OC relays to generate desired zones of protection
Direction of Desired Direction of Desired
Fault fault power response fault power response of
flow at bus C of OC relay flow at bus C OC relay
as seen from 5 at 5 as seen from 6 at 6
Fo Away Trip Towards Restrain
from bus C bus C
Fb Towards Restrain Away Trip
bus C from bus C
Thus it can be seen from Table 2.3, that whenever the fault power flows away from
the bus, it is desired that the OC relay should trip. It should restrain if it sees the fault
power flowing towards the bus.
2.9.1 Other Situations Where Directional OC Relays are Necessary
There are other situations where it becomes necessary to use directional relays to
supervise OC relays. One such situation is a single-end-fed system of parallel feeders,
shown in Figure 2.20, where a fault on any of the parallel lines is fed not only from the
faulted line but from the healthy line as well.
If directional relays are not provided, in conjunctio~with OC relays, then the desired
zones will not be generated. This will result in both lines being tripped out for any fault
on any one of the lines.
It may be noted that directional relays with tripping direction away from the bus will
be required at locations '2' and '3' in Figure 2.20. However, at locations '1' and '4',
non-directional over-current relays will suffice. Since directional relay units cost more
and aiso need the provision of PTs, they should be used only when absolutely necessary.

46 Fu~rda,ne~lralsof Power Svsre171Prorecnorr
(a)Parallel feeders, singleend-fed system 4~oad
++ +,T"pping direction
1_------.-.--------------------------2_-
--
E : ::
*
--_................................ --n--'
4 - a _ - - - - - - - - ---.------------------3
,_-- ----.
4+ 'j;
?
(b) Desired zones and tripping direction of OC relays !
Figure 2.20 Single-end-fedparallel feeder needs directional OC protect~on.
Consider the ring main feeder system shown in Figure 2.21. This is another situation
where directional supervision of OC relays is called for. It is well known that the ring
main feeder allows supply to be maintained to all the loads in spite of fault on any section
of the feeder. A fault in any section causes only the CBs associated with that section to
trip out, and because of the ring topology, power flows from the alternate path.
Load$ - /
I
Load
Figure 2.21 Protection of ring feeder using directional OC relays

Characteristics of directional relay
4 directional relay can be compared to a contact making wattmeter. A wattmeter develops
maximum positive torque when the current and voltage supplied to the current coil and
the pressure coil are in phase. If we define the maximum torque angle (MTA) as the angle
between the voltage and current at which the relay develops maximum torque, then a
wattmeter can be called a directional relay with MTA of zero degree.
The phasor diagram for a directional relay is depicted in Figure 2.23.
!
From CT
,.Position of lCcfor ..~i
,,' maximum torque
i '
I
I.j
1 ;
j.. , ,
$ 8
!
Operating torque = K, @pC @CC cos (8 - 7)
= K2 ipc ICc cos ( 9 - T) '1i
.'I t' b
I
i
Figure 2.23 Phasor diagram for a directional relay based on induction principle. i1
i
Vpc is the voltage applied to the pressure coil. The current drawn by the pressure coil :/.,
IPClags the voltage by a large angle BPc -11 ,
As the fault moves from the forward to the reverse direction, the current undergoes ,i
a large change in its phase whereas the phase of the voltage does not change substantially. ,I
Thus, voltage signal is the reference against which the phase angle of the current is .i;
measured. t.
8Now, in a relay based on induction principle, the two fluxes responsible for torque
1
production, and $cc should be shifted in phase by 90°,for them to produce maximum i
torque. The torque becomes zero when the current phasor is 290"away from the MTA i
;

Ove,--cu~.r-e~zrProtecrion af Transmission Llnes 49--
position. Thls eves the direction of the current phasor for max~mumtorque, the
maximum torque angle T, and the boundary between tripping and restraining regions on
the phasor d~agram.
The operating torque of the directional relay can be expressed as:
Operating torque To,,,t,,, x @PC @CC sin (0 + 6pC)
From phasor diagram it can be seen that:
OpC + = 90'
:. Toperatinga $pCkcsin (8 + 90" - 7)
Q $pc @cCsin [(0 - T) + 90°]
= Kl Spc $CCcos (8 - d
Since $pc a VPc and @cCQ Ice
Toperating= K2 VPCICCcos (0 - 7)
From the phasor diagram, it can be easily seen that the maximum torque angle T is
given by
T = 90" - 6?pC
Since the pressure coil is highly inductive, the value of 6pCis of the order of 70" to 80".
This gives MTA of 20" to 10". However, 0pc and hence T can be adjusted to any desired
value if an external resistance or capacitance is introduced into the pressure coil circuit.
2.9.3 Application of Directional Relay to a Three-phase feeder
In case of application of directional relays to a three-phase feeder, phase faults need to be
considered separately from ground faults. There are various possibilities of energizing
these relays; hence the various alternatives need to be carefully considered. The
directional relay must meet the following requirements:
1. The relay must operate for forward faults.
2. The relay must restrain during reverse faults.
3. The relay must not operate during faults other than for which it has been
provided, i.e. the relay must not maloperate.
Directional phase fault protection
Consider a directional relay for protection against all phase faults involving phase a,
i.e. a-b, a-b-g, a-c, a-c-g, a-b-c, and a-b-c-g faults. Let us consider an a-b fault. It is logical
to choose current I, to energize the current coil. However, the choice of voltage to be
applied to the pressure coil is not immediately apparent. Figures 2.24 and 2.25 explore
the possibility of using voltage Vd and V,, for the pressure coil of the directional relay
catering to phase faults involving phase a. From Figure 2.24, it can be seen that the
voltage Vabtends to collapse duringa-b fault. Further, the angle between V,b and I, during

50 F~~~~do~rrenrrilsof Power System Protection
fault i s substantially large. F o r t h e iMTA angle shown, t h e relay does n o t develop positive
torque during f o r w a r d fault. F r o m these figures, it can b e easily seen that b o t h these
voltages are n o t suitable, as they do n o t meet the requirement set o u t in Section 2.9.3.
Phase
sequence
Restrain
vt vbt vb
(a) Phasor diagram during a-b fault
0
0
relay Trip
Reverse fault
(c) Phasor relationships during UPF load, forward and
(b) Exploring the possibility of energizing the reverse fault for phase a directional relay
phase a directional relay with V,, energized by I, and 'J,b
Figure 2.24 Exploring the possibility o f energizing the pressure coil o f phase a
directional relay with voltage VOb.
, .
..
sequence
l a "a, f
vca, 1 vab. f
UPF position
Of I,
Forward fault
v c v,, v,
0
0
0
0
1a.t
relay Trip Reverse fault
MTA line
(b) Exploring the possibility of energizing the reverse fault for phase a directional relay
phase a directional relay with V,, energized by I, and V,,.
Figure 2.25 Exploring the possibility of energizing pressure coil o f phase a directional
relay w i t h voltage V,,.

Over-cr;r!-elir Protecrio~lof Tro~~sr~~lssio!lLiner 51
Figure 2.26 shows that the voltage Vb,happens to be the correct choice. Since the unity
power factor !UPF> position of I, leads Vbcby 90°, chis connection is known as the 90"
connection.
Phase
sequence
la -Directional
relay Trip
Vbc MTA = r
UPF position
of I,
Trip '8. f
MTA line Folward
Restrain
0
0
,0
k 0
I ,f
Reverse fault
(b) Correct energization of phase a directional relay reverse fault for phase a directional relay
with I, and V,, resulting in the 90" connection energized by I, and Vbc(the 90" connection).
Figure 2.26 Correct energization of directional relay: 90" connection
The 30" and the 60" connections
As already pointed out there are other possibilities for energizing the voltage coils of
directional relays. However, all the possible voltages may not meet the requirement of no
,maloperations. Hence, the choice has been narrowed down to three. The other two
possible voltages, for phase a directional relay, are V,,and (V,,+ V,,).These are known
as the 30" and the 60' connections because of the angular relationship between the unity
power factor (UPn position of & and these voltages during the pre-fault condition.
Table 2.4 summarizes various combinations of voltages and currents to be fed to
directional phase fault relays catering to phase faults involving the three phases, for the
90°, 30" and 60" connections.
Table 2.4 Summary of phase fault relay excitation
Type of Phase faults Phase faults Phase faults
connection inuoluing phase, a inuoluzng phase, b involving phase, c
Current Voltage Current Voltage Current Voltage
90" 10 Vbc Ib Vca Ic Vmb
30" I, Vm Ib Vb, 1, V C ~
60" I, Vm + Vbe .- Ib Vhn + vc,~ Ic x b f Vnb

52 Frr~rdarne~zmlsof Power System Protectro~r
Directional ground fault protection
The directional ground fault relay develops correct tripping tendency when fed by the
residual current I. and residual voltage Vo.This is shown in Figure 2.27.
Phase
sequence
'8
= Ea - IaZs
4 = 31, I. ,
i
i
I
I
i
E, = V, E, = V,
(a) Phasor dlagram for a-g fault
i
h . . Restrain
MTA line
(b) Phasor relationships between actuat~ngquant~tiesduring foward and reverse faults L
/
Ground fault
-(V, + Vb + V,) = 3V0-1 Directional
relay Trip
(I, + lb + f C ) = 310
-w(c) Directional ground fault relay energized by residual voltage and current i
Figure 2.27 Directional ground fault relay energization. 1I
I
2.9.4 Directional O C Protection of a Three-phase Feeder i
Figure 2.28 shows a three-phase feeder protected by directional relays supervised by OC
relays. i
$

Ground fault OC
Figure 2.28 Complete scheme for directional OC protection of a three-phase feeder
2.9.5 Directional Protection Under Non-fault Conditions (Reverse
Power Relay)
There are situations where directional relays have to be used under non-fault conditions.
Such an application of directional relay exists in reverse power protection of a turbo-
alternator. To distinguish between the two, let us call these directional relays as power
directional relay.
These situations are different from those where directional relays are applied during
fault conditions in the manner that, in case of the power relays, there is no collapse of
system voltage. Directional relays for short circuit protection are so connected that they
develop maximum operating torque under fault conditions. However, directional power
relays are so connected that they develop maximum torque when direction of power flow
reverses.

54 F~~~z~l~~iize~~ruisof Power J~sronProrccnon
Consider a power relay with an MTA of 30" Figure (2.29). In order to be used as a
power relay it can be fed with I, and Vc,.
It can he seen that I, leads Vc,by 30" during reverse power flow, thus developing
maximum tripping torque.
Forward
power No trip
Reverse
power Trip
Power directional relay
I
Figure 2.29 Connections of a power directional relay with MTA of 30".
' 8 -
2.10 Drawbacks of Over-current Relays
Directional relay
MTA = 30"
The reach and operating time of the over-current relay depend upon the magnitude of
fault current. The fault current that would result in case of a fault at a particular location
depends upon:
1. The type of fault, i.e. whether it is a ground fault or a phase fault
2. The source impedance as shown in Flgure 2.30.
ZS+ Large
T Uinversp +;-a
Fault L-L-G
Zs + Small OC relay L-L-G
L-G fault T ree-phase fault
x
1 Fault location
Figure 2.30 Fault current and reach is a function of fault type and source impedance.

Since neither the type of fault nor the source impedance is predictable, the reach of
the over-current relay keeps on changing depending upon the source conditions and the
type of fault. Thus, even though the relays are set with gieat care, since their reach is
subject to variations, they are likely to suffer from loss of selectivity Such a loss of
selectivity can be tolerated to some extent in the low-voltage distribution systems, where
the only objective to be met is the continuity of supply to the consumer. However in EHV
interconnected system (grid), loss of selectivity can lead to danger to the stability of the
power system, in addition to large disruptions to loads. Therefore, over-current relays
cannot be relied upon as a primary means of protection in EHV systems.
Another principle of relaying, known as distance measurement, offers a much more
accurate reach, which is independent of source conditions and type of fault. This is
discussed in Chapter 6.
Review Questions
1. What are the necessary conditions for two alternating fluxes acting on a common
rotor (a) to produce some torque and (b) to produce maximum torque?
2. What are the situations where DTOC relays are preferred over IDMT relays?
3. What is the difference between plug setting and pick-up value of an OC relay?
4. What are the drawbacks of using DTOC relays for the protection of long feeders?
5. Why does the fault current vary between a minimum and a maximum at any
location?
6. The generator impedance does not affect the fault current to a great extent in the
low-voltage distribution system. Explain.
7. Explain the overshoot time of a relay and its significance.
8. What do you mean by loss of selectivity between two OC relays in adjoining line
sections? What are its causes?
9. While setting the pick-up value, the minimum fault current at the end of the
adjoining feeder needs to be considered; but while setting the TMS the maximum
fault current at the beginning of the next section needs to be considered. Explain.
10. What do you mean by an OC relay, supervised by a directional element?
11. What is the meaning of the term 'directional' vis a vis directional relaying?-
12. What is meant by maximum torque angle vis a vis a directional relay?
13. How will you adjust the MTA of a directional relay?
14. What is the difference between the reverse power relay and the directional relay?
15. Why polarizing voltage from a healthy phase is used in three-phase directional
relays?
16. While different connections like 90",30°,and 60" exist in case of directional phase
fault relays, why is it that no such connections exist for directional ground fault
relays?
17. What are the situations where there is no need to use directional OC relays and
the situations where directional relays must be used?
18. Give the procedure for time setting of relays on a ring main feeder system.

56 F~lr~dan~enralsof Porver Systern Prorecriorz
Problems
1. The pressure coil of a directional relay has an impedance of (100 +j 274.74) ohms.
What is the MTA for this relay? What change will have to be made to the pressure
circuit so as to change this angle to (a) 30" and (b) 15"?
2. For the system shown below, design the complete OC protection using the IDMT
relays. Thus, decide the CT ratios, the plug settings and the TMS at all locations.
Losd 115 A 80 A 100 A 77 AT
Minimum fault current 1500 A 1000 A 780 A 585 A 390 A
Maximum fault current 6000 A 5000 A 3000 A 2000 A 1000 A

3.1 Introduction
Differential protection is based on the fact that any fault within an electrical equipment
would cause the current entering it, to be different, from that leaving it. Thus, we can
compare the two currents either in magnitude or in phase or both and issue a trip output
if the difference exceeds a predetermined set value. This method of detecting faults is very
attractive when both ends of the apparatus are physically located near each other. A
typical situation, where this is true, is in the case of a transformer, a generator or a
busbar. In the case of transmission lines, the ends are too far apart for conventional
differential relaying to be directly applied.
3.2 Dot Markings
Differential protection utilizes CTs at each terminal of the equipment under protection.
Careful attention needs to be paid to the 'dot markings' (also known as 'polarity marks')
on these'c~s.We, therefore, briefly review the concept of dot markings.
Consider a set of three mutually coupled coils A, B, and C with terminals A1-A2,
B,-BZand CI-CZas shown in Figure 3.1. The question is: how shall we put dot marks on
the terminals of these coils?
To answer this question, let us energize coil A as shown in Figure 3.2 so that the
terminal Al becomes positive with respect to terminal A2. Now, this will cause an
alternating current to flow through coil A, and thus set up an alternating flux q~ in the
direction shown, at the instant of time under consideration. This flux also links both coils
B and C. Voltages will be induced in these coils. Now if a load were to be connected
between terminals B1and B2,a current'will be established. According to Lenz's law, this
current would flow in such a direction so as to oppose the very cause (flux #A)that was
responsible for its (current in coil B) production. Therefore, the direction of current
through coil B will be such that the flux ($B) due to it opposes the flux $A. Thus, current
will flow out of terminal B2, making B2 instantaneously positive with respect to B1.

Figure 3.1 Dot marking.
Induced
current
Induced
current
9c
Figure 3.2 Dot marks: induced currents and flux.
Therefore, B2will have the same polarity as that of A,. Thus, dot marks can be put on
Al and B2as shown in Figure. 3.3 to signify that these two terminals will be similarly
phased.

Similar arguments show that current must leave terminal C1 at the instant under
consideration. Thus, C1 will be similarly phased as Al. We, therefore, put dot marks on
terminals Al, B2, and C1.
A little thought will convince the reader that we can instead put dot marks on
terminals .42, B,, and C,, as shown in Figure 3.3.
Dot mark
A2
Dot mark
Figure 3.3 Dot marks: symbolic method of representation.
From the above discussion, we can generalize the following properties of dot
markings:
When current enters the dot mark on the primary side of a C r the current must leave the
similarly marked dot mark on the secondary side.
If currents are made to enter dot marked terminals on two or more coupled coils then the
fluxes produced by these currents are such that they add up.
3.3 Simple Differential Protection
3.3.1 Simple Differential ~rotection:Behaviour During Load
Figure 3.4 shows a simple differential relaying scheme (also known as Merz-Price
scheme). The currents entering and leaving the equipment to be protected are stepped
down with the help of CTs on either side. Careful attention must be paid to the dot marks
placed on the CTs.

I < I.
Figure 3i4 Simple differential protection.
CT
n :I
The following rule can be applied in order to trace the currents in the circuit:
When current enters the dot mark on the primary side of the Cq the current must lea.
the similarly marked dot mark on the secondary side.
.-- U
Instantaneous OC relay
Spill current = 0 Plug setting = I,,
For the operating condition of normal load flow shown in Figure 3.4, the currents
transformed by the two CTs, being equal in magnitude as well as in phase, just circulate
on the secondary side. There is no tendency for the current to spill into the over-current
relay. The over-current relay connected in the spill path is wired to trip the two circuit
breakers on either side of the equipment being protected.
Assuming that the protected equipment is either a 1: 1 ratio transformer or say a
generator winding or a busbar, the two currents on the primary side will be equal. Hence
the ratios of the two protective CTs will also be identical. The CT secondary circuits are
so connected that in case the conditions are normal, the secondary currents simply
circulate through the 'pilot' leads connecting the two secondary windings. For the
operating condition of normal load flow, there is no current through the 'spill path' where
an over-current relay is located. Hence, the OC relay will not trip the two CBs. Thus, the
simple differential relay meets the first and foremost requirement that it remains stable
during normal operating conditions.
3.3.2 Simple Differential Protection: Behaviour During Externa
Fault
t
Next, the differential relaying scheme should also remain stable for any fault which is
outside its protective zone. Such faults are called external faults or through faults.
Figure 3.5 shows that during external faults too, the current leaving the protected zone
is the same as that entering it. Assuming that the CTs transform the two currents with
the same fidelity, there will be no current in the spill path and the scheme remains stable.
.-
O
,,11
'L
3.3.3 Simple Differential Protection: Behaviour During Internal
Fault
-
n
Figure 3.6 shows an internal fault of magnitude If,,,,. The current leaving the protected
zone is now I2 whereas that entering it is 11,such that, I, = I2 + Ic ,,,. As can be seen
L
0
a
d

Figure 3.5 Simple differential scheme remains stable on external faults.
from the figure, current in the spill path is now (If,i,,ln), where n is the CT ratio.
Assuming that the spill current is more than the pick-up value of the over-current relay,
both the circuit breakers will be tripped out. Thus, the scheme meets the basic
requirement of clearing internal faults.
Figure 3.6 Simple differential scheme trips on internal faults
Internal fault
1
The minimum internal fault current that will cause the tripping, is given by
If,min= (CT ratio) (Plug setting of the OC relay) = nIp,
i
3.3.4 Simple Differential Protection, Double-end-fed: Behaviour
During Internal Fault*I- .+
In the preceding analysis, we have assumed a single-end-fed system. How does the
differential scheme behave in case of a double-end-fed system?
A double-end-fed system is shown in Figure 3.7, the internal fault is now fed from
both sides. The internal fault current, If,,nt, is now equal to (I,+ Iz)Again, we see that
the spill current is equal to (IC,,,In).

a- rn Equipment under I, rn -U -protection
41
,' 2, -
n
,,
Internal fault
Figure 3.7 Simple differential scheme in a double-end-fedsystem operates for
interrial fault.
Assuming that the splll current is greater than I,,, the plug setting of the OC relay,
the relay will operate and trip out the circuit breakers on either side of the protected
equipment.
3.4 Zone of Protection of the Differential Relay
The differential scheme generates a well-defined and closed zone of prote&tion.This zone
encompasses everything between the two CTs as shown in Figure 3.8. Thus, we talk of
any fault between the two CTs as an 'internal fault'. To the differential scheme, all other
faults are 'external faults' or 'through faults'. Ideally, therefore, a differential scheme is
supposed to respond only t3 internal faults, and restrain from tri~pinaon exter~al- * .- -
through faults.
Zone of differential
Equipment uqder
External fault
I 1 External fault
Figure 3.8 The zone of differential protection,

Thus, an ideal differentla1 scheme should he able to respond to the smailes~~ n t e r n d
fault but restrain from tripping on the iargest external fault This ided is difficult to
achieve, especially for very h e a y ~'through faults' because of the non-icieal nature of the
various components of the protective system. This is discussed in the following sect~ons
3.5 Actual Behaviour of a Simpie Differential Scheme
In our discussion so far we have tacitly assumed that the CTs are ideal. owever, in
practice, CTs are subject to ratio and phase angle errors. Both these errors depend upon
the burden on the CTs, which in turn depends on the lead lengths and the impedance of
the relay coil. The errors, in general, increase as the primary current increases, as in the
case of external faults. Figure 3.9 shows the primary and the secondary current phasors
during an external fault.
Ideally, for 'through faults', secondary currents of both the CTs would be equal in
.
magnitude and in phase vlth each other, and thus the spill current would be zero.
However, as shown in Figure 3.9, CT, has an actual ratio of n,and pirzse-angle error of
while CT, has an actual ratio of nz and phase angle error of 8,. The difference between
these two currents, therefore, ends up as spill current, as shown in Figure 3.9. Since both
the ratio and phase angle errors aggravate as primary current increases, the spill current
builds up as the 'through fault' current goes on increasing.
n, and n, = actual CT ratios
/P = lr,eil - Ip = If, ex1
!
Ideal positions of I,, and Is2
n : 1
'P
Primary current
current
Figure 3.9 Spill current because of CT errors
.
Spill current
External
fault
.? ? 11, ext
n = nominal CT ratio
Equipment under
protection
n :I
,,A .- - - 7
U -

64 F~lndarnentalsof Powe~Systenz Protectron
--
3.5.7 Through Fault Stability and Stability Ratio
As the 'through fault' current goes on increasing, various imperfections of the CTs get
magnified. This causes the spill current to build up. Therefore, as the 'through fault'
current goes on increasing, as shown in Figure 3.10, there comes a stage when the spill
current, due to the difference between the secondary currents of the two CTs, exceeds the
pick-up value of the over-current relay in the spill path. This causes the relay to operate,
disconnecting the equipment under protection from rest of the system. This is clearly a
case of maloperation, since the relay has tripped on external fault. In such instances, the
differential scheme is said to have lost stability. To signify the ability of the differential
scheme to restrain from tripping on external faults, we define 'through fault stability . .
limit' as the maximum 'through fault' current beyond which the scheme loses stability.
I
In Figure 3.10, 'through fault stability limit' is shown as Istab . >
External fault
characteristics
So
E
1/ Trip f' , /'
Pick-up value of OC
relay in spill path
/
<
1- Through fault current -2
Through fault stability /rob
L
Figure 3.10 Characteristics of simple differential relay.
Compare this with the situation of an internal fault. The minimum internal fault
current required for the scheme to operate, correctly in this case, is decided by pick-up
value of the over-current relay in the spill path. To signify the spread between the
minimum internal fault current at which the scheme operates and the maximum 'through
faat' current beyond which the scheme (mal)operates, we define a term called stability
ratio as:
maximum 'through fault' current beyond which scheme (ma1)operatesStability ratio =
minimum internal fault cur;ent required for tripping
The higher the stability ratio, the better is the ability of the system to discriminate
between external and internal faults. The stability ratio can be improved by improving
the match between the two CTs.

3.5.2 Equivalent Circuit of CT
F i g r e 3.11 shows the equivalent circuit of the CT as referred to the secondary side.
Burden
H
'h ( b- Excitation characteristic of CT
b
I
>
Magnetizing current. I,
(C)
Figure 3.11 Equivalent circuit of CT.
I

RLri and LLriarc the resistance and the leakage inductance of the prlmary windir,g as '
referred to. the secondary side. R,,,,, and Lmugform the shunt magnetizing branch. The
magnetizing inductancc is highly nonlinear. R,,, and I,,,, are the resistance and leakage
inductance of the secondary winding. The impedance Zhlllilenincludes the resistance and
the inductance of the relay coils and rcsistance of the pilot wire (leads). Also shown in
Figure 3.11(c) is a sketch of the magnetization characteristic of the CT (also known as
open-circuit characteristic).
Out of the current Ipln transformed by the ideal CT, the magnetizing branch draws
the magnetization current I,. It is to be noted that the magnetizing current is a nonlinear
function of the excitation voltage V,,,. During normal operating conditions, when V,, is
small, the current I, can be safely neglected. However, at higher values of primary
current, (and therefore secondary current), as in case of 'through faults', the secondary
voltage, Vse,,which is equal to I,(Z,,, + Zburden)increases and causes I, to become an
appreciable fraction of the current transformed by the ideal CT. Thus, we can no longer
ignore I,.
,:j
-1
Differential scheme considering CT equivalent circuit
Figure 3.12 shows the simple differential scheme in which CT equivalent circuit has been
explicitly included. The various currents shown in Figure 3.12 are those that result

during an external fault condition. Assuming that both CTs have the same nominal ratio
of transformation n, we see that a spill current equal to the difference of the two
magnetizing currents results. Since the magnetizing currents of the two CTs will
generally vary widely, there is a substantial spill current during 'through fault'
conditions. This results into loss of stability and maloperation of the simple differential
scheme. Thus, the simple differential scheme, which looks attractively simple, cannot be
used in practice without further modifications.
This is especially true in case of transformer protection. The CTs on the two sides of
the transformer have to work at different primary system voltage. Because the currents
on the two sides of the transformer are, in general, different, the ratios of transformation
of the CTs are also different. Their designs are therefore different, making it impossible
.d
to get a close match between their characteristics. This explains why the spill current
goes on increasing as the 'through fault' current increases.
In case of busbar protection, the primary voltages of the two CTs are the same, and
the CT ratios are also the same. However, busbars are subjected to very heavy 'through
fault' currents, which tend to magnify the differences between the characteristics of the
two CTs. Thus, for busbar protection too, the simple differential scheme needs to be
further modified.
Both these aspects have been dealt with in detail in subsequent chapters.
3.6 Percentage Differential Relay
The simple differential relay can be made more stable, if somehow, a restraining torque
proportional to the 'through fault' current could be developed-the operating torque still
being proportional to the spill current.
This idea has been implemented in the percentage differential relay shown in
Figure 3.13. This relay has a restraining coil which is tapped at the centre, thus forming
two sections with equal number of turns, NJ2. The restraining coil is connected in the
circulating current path, thus receiving the 'through fault' current. The operating coil,
having No number of turns, is connected in the spill path. Let us work out the torque
equation for this relay.
Nr
Ampere-turns acting on the left-hand section of the restraining coil = I,
N,
Ampere-turns acting on the right-hand section of the restraining coil = I2
N ,
Total ampere-turns acting on the restraining coil = -(I, + I z )2
Noting that torque in an electromagnetic relay is proportional to the square of the
flux, . ,
[ (4;"'I'Torque produced by the restraining coil = M N,
where M is a constant of proportionality.
Restraining torque produced by control spring = Tspring

68 Fundamentals oj Power Sysrem Prorecriott
CT
ir 1
Armature
SpringT
Restraining coil '&
rid output
CB n : ~ 1,
, rn -n : l CB'P
*->
12
Balanced beam structure
Figure 3.13 Percentage differential relay
Equipment under
Total restraining torque = M + Tspring
I / Trip
Similarly,
protection
Operating torque = M[N,(Il- 1211"
?
The relay trips if the operating torque is greater than the restraining torque. The relay
will be on the verge of operation when the operating torque just balances out the
restraining torque, i.e. when:
M[N,,(I, - 1,)]2 = M (neglecting the restraining torque due to spring)
T
Trip,

Dzflerenrial Prctection 69
which can be written as
(I?+I,)
I , - i , = K ) 'I
where X = N,IN,,.
However, if we take into account the effect of control spring, the above equation can
be written as
Il - I2 = K
where KOaccounts for the effect of spring.
Thus, the operating characteristics of this relay will be a straight line with a slope of
(N,IN,) and an intercept KOon the y-axis. All points above the straight line will represent
the condition where the operating torque is greater than the restraining torque and hence
will fall in the trip region of the relay. All points below the straight line belong to the
restraining region. The operating characteristics of the percentage differential relay are
shown in Figure 3.14.
Internal fault
:.. ,.. characteristic External fault
200% slope characteristic
I '
' I I Minlrnurn Internal Through fault current. -
-? ,+ fault current, IF,,,,,, (";")I !
,
!
Maximum through fault current, I,,,,,.,,I -I
I
Figure 3.14 Operating characteristics of percentae differential relay.
Thus, the spill current must be greater than a definite percentage of the 'through
fault' current for the relay to operate. Hence, the name percentage differential relay. The
slope of the relay is customarily expqessed as a percentage. Thus, a slope of 0.4 is
expressed as 40% slope.
The percentage differential relay does not have a fixed pick-up value. The relay
automatically adapts its pick-up value to the 'through fault' current. As the 'through fault'
current goes on increasing, we are in effect asking the relay to take it easy, by introducing
a restraining torque proportional to the circulatillg current. It can be seen from
Figure 3.14,that the 'through fault' stability and the stability ratio of the percentage

70 F~lrrdar~~etitnlsof Power Svsterrr Prutecriun
-- --
differential relay is substantially better than that of the simple differential relay. The
.
restraining winding is also known as the biasing winding because we bias the relay
towards restraint. The slope of the characteristic is also known as percentage bias.
The characteristic of the percentage differential relay, superimposed on the 'through
fault' characteristic, and the internal fault characteristic are shown in Figure 3.14. The
slope of the internal fault characteristic can be found as follows:
Consider an internal fault in the case of a single-end-fed system. Since CT2 will not
contribute any current, i.e., I2 = 0, the spill current, (I, - I;), will be equal to II. The
circulating current which is [(I1 + 12)121 will be equal to (1,121. ~ h u s ,the following
currents will exist during an internal fault:
Spill current Il - I2 = II
11+ I, - 11Circulating current T -- -A
'5 I
Thus, during internal faults the spill current will be two times the circul'ating current, a ,'
giving a slope of 2, which is expressed as 200%. ':5
The minimum internal fault current below which the scheme will not respond is seen . ,
to be Ir,,in,int and the maximum 'through fault' current above which the scheme will . ,
maloperate is seen to be If,,,,,,,, as shown in Figure 3.14.Thus, the stability ratio is given ,.-.
by
1 Stability ratio =
%max,ext
If,mm,lnt 1
The percentage differential relay can be made more immune to maloperation on
'through fault' by increasing the slope of the characteristic.
3.6.1 Block Diagram of Percentage Differential Relay 11
Figure 3.15 shows the block diagram of the percentage differential relay. The relay has
two settings. the slope setting and the minimum pick-up setting. The slope is adjusted by
changing the tapping on the restraining coil. It may be noted that both halves of the
restraining coil need to be symmetrically tapped. The m~nimumpick-up is adjusted by .~
changing the tension of the restraining spring.
$Adjust rnlntrnurn plck-up
Restra~n~ngcod
N.12 N.12
0 0
--- Adjust slope
1 + 20% slope
2 30% slope I
3 + 40% slope
1;-
Figure 3.15 Block diagram of percentage differential relay showing its settings.

3.7 Elarfh leakage ProSecfion
Many times because of insulatior~failure the chassis of the equipment becomes live. This
causes a leakage of current to earth from the chassis as the chassis is always connected
to earth. However, the leakage current may be too small for an over-current relay to
operate. This poses danger to the personnel who come in contact with the chassis. A
special type of differential relay known as the earth leakage relay or current balance relay
can easily detect such faults.
In case the chassis of the equipment is not earthed, the relay will not trip because of
leakage. However, as soon a person whose body is in contact with earth, touches the
chassis, a path to earth becomes available, and assuming that the leakage current is of
suficient magnitude, the OC relay trips. The person will, of course, receive an electric
shock before the circuit is tripped out.
3.7.1 Earth Leakage Protection for Single-phase Load
Figure 3.16 shows the earth leakage relay for a single-phase load.
Figure 3.16 Earth leakage protect~onfor single-phase load
The relay consists of a toroidal corson which two identical windings A and B, each
having N number of turns are wound in close proximity. A third coil C, known as the pick-
up coil,is also wound and connected across an OC relay as shown in Figure 3.16. The
phase and neutral leads are connected to these windings as shown in the figure so that
windings A and B carry the currents in the phase wire and the neutral wire, respectively.
t Under normal operating conditions, the current through the phase wire (and coil A)
is exactly the same as that through the neutral wire (and coil B). Thus, there is no net

72 F~~i~da~~ierltols01-Power S v ~ r r ~ r ~Protect~orr
magnetomotive force (mmf) acting on the toroidal core. The flux linked with the pick-up
coll is therefore zero, and thus no voltage is induced in the pick-up coil and the OC relay
remains unenergzed.
Now consider the situation of earth leakage as shown in Figure 3.16. The current in
the phase wire is now greater than that in the neutral wire, as part of the current returns
to the supply vla the earth. The mmf acting on the toroid is now equal to [N(Iyh- I,)]
or equal to [N(Il,,)]. This rnmf sets up flux in the core causing a voltage to be Induced
by the pick-up coil. The OC relay connected to the pick-up coil, therefore, gets energized,
and trips the circuit.
I
3.7.2 Earth Leakage Protection for Three-phase Loads
Figure 3.17 shows earth leakage protection for a three-phase load. The three-phase leads
are threaded through a CT core on which a pick-up winding is provided as in the case of
single-phase earth leakage protection. •
Three-phase load
la + lb + k '/leak
Iron core
Figure 3.17 Earth leakage protection for three-phase loads.
During the normal balanced operating condition, the phasor sum of the three-phase
currents is zero. Therefore, there is no net mmf acting on the core and the OC relay
remains unenergized.
However, during the earth leakage situation s h w n in Figure 3.17, the net mmf acting
on the core is (Ileak)ampere-turns. This causes a flux to be produced. A voltage is induced
in the pick-up winding causing the OC relay connected across it to operate.

Review Questions
1. Fiow will :iou check the polarity marks on a protection CT with the help of a
1.5 volt battery and a centre-zero voltmeter?
2. What do you mean by CT saturation?
3. Explain the following terms with respect to the simple differential scheme:
Circulating current, spill current, internal fault, external fault, through fault,
'through fault' stability limit and stability ratio.
4. What are the drawbacks of the simple differential scheme?
5. What is the effect of the resistance of the pilot (lead) wires on the CT errors?
6. As the burden on a CT secondary goes on increasing, what happens to the
magnitude and waveform of current delivered to the burden?
7. Explain how the percentage differential relay overcomes the drawbacks of the
simple differential relay.
8. Prove that the slope of the internal fault characteristics for a single-end-fed
system is 200%.
9. How do you adjust the slope of the percentage differential relay?
10. Show that the slope of the simple differential relay characteristics is zero.
11. Prove that the slope of the internal fault characteristics for a double-end-fed
system is greater than 200%.
12. Higher slopes are required in cases where there is a lot of mismatch between the
CTs at various terminals. Explain.
13. Which elements of the power system are ideal candidates for applying differential
protection?
14. What problems, if any, do you anticipate in applying conventional differential
protection to a transmission line?
Problems
1. For a 5 A CT, the total impedance of the secondary winding and leads is 0.01ohm.
Determine the VA capacity of the CT secondary at (a) the rated secondary current
and (b) the maximum fault current of 20 times the rated CT secondary current.
2. In a simple differential scheme, the two CTs have a nominal ratio of 100 : 1.The
CT errors for a 'through fault' current of 1000 A are as follows:
CTI CT2
..-Ratio error 5% +6%
Phase angle error 2% -4%
Determine the pick up of the OC relay in the spill path so that the scheme
remains stable.

4.1 Types of Transformers
Transformers come in all shapes and sizes from the tiny balun transformers that You can
place on the palm of your hand Lo the mammoth EHV power transformers that weigh
several metric tonnes and occupy large areas. Various types of transformers used in the
industry are listed below:
Generator transformer
Power transformer
Distribution transformer
Pole-mounted lighting transformer
Grounding transformer
Regulating transformer
Welding transformer
Converter transformer
Instrument transformers (CT and PT)
Some of the above transformers could be autotransformers.
However, in this textbook, we restrict ourselves to protection of power and
distribution transformers. A transformer will be provided with as much protection as is
commensurate with its voltage and power rating and the importance of its application.
For example, over-current protection in the form of fuses may be the only protection
provided to a small 100 kVA, 11kVi440 V distribution. transformer.
A 250 MVA, 15 kVl400 k y generator-transformer in a large thermal power station,
on the other hand, may be provided with very elaborate protection. This may consist of
percentage differential protection (with harmonic restraint), a protection against
incipient faults and a protection against over-fluxing as primary protection. These will be
backed up by the over-current protection.
Since the terminals of a transformer are physically close together, it is an ideal
candidate for application of the principle of differential protection.
74

4.2 Phasor Diagram for a Three-phase Transformer
There are four basic types of connections of a three-phase transformer, namely Y-Y,
Y-A, A-Y and A-A.
The Y-A and the A-Y transformers introduce certain phase shifts between the
voltages and currents on the primary and the secondary side. These phase shifts have to
be carefully considered while applying differential protection. While connecting the CT
secondary windings, we can choose such connections that nullify the phase shift.
Further, because of transformation ratio between the primary and the secondary sides
of the power transformer, the primary currents for the CTs on the two sides will be
different. The CTs must, therefore, have such ratio of transformation that currents in the
relay pilot wires, coming from the CTs on the two sides are equal. Thus, ratios of
transformation of the CTs on the primary and secondary side of the transformer, will in
general, be different. This will ensure that during normal load flow as well as during
external fault conditions, the differential scheme remains stable.
Figure 4.1 shows a three-phase transformer. It can be seen that the windings on the
star-connected side carry the line currents I* IB,IC,while the windings on the delta side
carry the phase currents whose magnitudes are
Primary Secondary
Core

A
Figure 4.1 Construction of a three-phase transformer.

$ 1
76 Furldarnerltuls of Power Svstern Ptotectiorl
as shown in the phasor diagram in Figure 4.2. Each line current on the delta side is the
phasor sum of two of the phase currents. Hence, there is a phase shift of 30" between the '
line currents on the two sides of the star-delta transformer. Figure 4.2 shows the
schematic representation of the transformer connection with all voltages and currents.
Figure 4.2 (a) Schematic representation of Y-A transformer; (b) phasor diagram showing the
30" phase shift between line currents on the two sides of a Y-A transformer.

Transfonner-PI-utecrio17 77
Since we are Interested in currents on :he two sides, for the sake of differential
protecrion, only the current phasors are shown. It can be seen that chere is a phase shift
of 30" between the line currents on the two sides of the star-delta transformer.
4.3 Equivalent Circuit of Transformer
Figure 4.3(a) shows the schematic representation of a single-phase transformer. The
circuit can be reduced to the equivalent form shown in part (b) of the figure. It can be
seen that the shunt branch, which represents the magnetization and accounts for the core
loss, has a much larger impedance compared to the series branch which represents the
winding resistance and the leakage reactance. Hence, in the event of short circuits, it is
the series branch which essentially decides the short-circuit current. As shown in
Figure 4.3(c), if the series impedance is 8% (i.e. 0.08 p.u.1 then the short-circuit current
for a fault on the secondary terminals will be (1.010.08) = 12.5 p.u.
C) I I n
N1 N2 "
I
(a)
Primary Secondary
Winding Leakage Ideal Wind~ng Leakage
resistance inductance transformer resistance inductance
Equivalent series impedance
-0.08 p.u. Fault on secondary
terminals
Figure 4.3 Single-phase transformer: (a) schematic diagram; (b) equivalent circult;
(c) model for finding short-circuit current.

78 Fiirrda~~~rriralso f Power Svstenl Protection
I
4.4 Types of Faults in Transformers
Transformers are subject to a variety of faults. The most common being the winding to
core faults because of weakening of insulation. Phase faults inside the transformer are
rare. However, such faults may take place outside the transformer, on the transformer
terminals, which fall within the transformer protection zone.
The variation of fault current with respect to fault location within the transformer
depends upon the type of transformer connection, the method of grounding the
transformer neutral and whether the current is being referred to the primary or the
i
secondary side of the transformer. The interested reader may refer to Power System
Protection (Vol. 3: Application) published by the Institution of Electrical Engineers, UK.
Figure 4.4 shows the variation of fault current with respect to fault location for a
winding (phase) to ground fault for a resistance-grounded delta-star transformer, as seen I
from the primary and the secondary sides.
lc
=~PrA-Y Transformer REIc
..
.--------
A
1.0-
0.8 -
0.6 -
20 40 60 80 100%
Distance x of fault from neutral
10 -
8 -
6 -
20 40 60 80 100%
Distance x of fault from neutral
Figure 4.4 Variation of fault current with location for the A-Y transformer.

As shown in Figure 4.4 for a resistance-earthed star-connected winding, a winding-
to-earth fauit will give rise to a current dependent on the value of the earthing resistor
and the distance of the fault from the neutral end of the winding. The effective ratio of
transformation between the primary winding and the short-circuited portion of the
secondary winding varies with the fault position. The current flowing through the
transformer terminals is, therefore, for all practical purposes, proportional to the square
of the percentage of the short-circuited winding.
For a solidly-earthed star winding, the fault current bears no simple relationship to
the distance of the fault from the neutral end since the effective reactance of the fault
path changes with the fault position. As shown in Figure 4.4, the minimum value of fault
current occurs for a fault at 30%to 40%of the distance of end of winding from the neutral
end.
For a delta-connected winding, the minimum voltage on the delta winding is at the
centre of one phase and is 50%of the normal phase-to-earth voltage. The range of values
of fault current is less than that of the star-connected winding. The value of the fault
current depends upon the system earthing arrangements, and the curves of Figure 4.5
show that the minimum value of fault current occurs for a fault at the centre of one phase
winding.
Y-A Transformer
L
w -
[I
m
LL .
0 50% 100%
Distance x of faultfrom end of winding
Figure 4.5 Variation of fault current with location for the Y-A transformer.

I "nc' allu ul-ru.u .ill ..--err*r ---,r-r.. --- ----.-----r -----0---0
(OLTC) gear This is another major source of faults.
All large transformers are of the oil-immersed type. There is a possibility of low level
of oil due to leakage. In such cases, an alarm must be raised and the transformer may
eventually have to be shut down.
Another peculiarity of transformers is that they experience large inrush currents at
the time of switching if they happen to be unloaded. This is neither an abnormal
condition nor a fault as far as the transformer is concerned. Inrush current needs special
attention while designing the protection for a transformer.
A transformer may develop inter-turn faults giving rise to hot-spots within the
winding. Seen from the terminals, such inter-turn faults may not cause appreciable
currents. Hence, inter-turn faults are difficult to detect by 'electrical means. These are
best detected by non-electrical methods.
Transformers may suffer from over-fluxing (also called over-excitation) due to under-
frequency operation at rated voltage. Over-fluxing may also be caused when the
transformer is subjected to over-voltage at the rated frequency. Since large transformers
usually operate at their design limits, over-fluxing can be dangerous and needs immediate
protection.
All these faults, abnormal operating conditions and peculiar operating conditions are
dealt with in the following sections.
4.5 Over-current Protection
Figure 4.6 shows two numbers of phase-fault over-current relays and one ground-fault
over-current relay for providing over-current protection to the star-delta transformer.
Such a scheme may serve the purpose of providing either the primary protection for
smaller transformers or the back-up protection for bigger transformers.
Two numbers of phase-fault
over-current relays
POne number of grou"d-fault
over-current relay
Figure 4.6 Over-current protection of a transformer.

The pick-up value of the phase-fault over-current units is set such that they do not
pick up on maxir.um permissible overload, but are sensitive enough to pick up on the
smalles~phase fault. The pick-up of the earth fault relay, on the other hand, is
independent of the ioading of the transformer. The neutral current under load conditions
is quite small. The neutral current is essentially because of load unbalance. It is
interesting to note that the third harmonic currents, in particular and triple-n harmonics
(harmonics of order 3, 6, 9, ...I in general, which arise due to distortions introduced by
electronic loads, also end up as zero sequence currents and flow through the neutral.
4.6 Percentage Differential Protection of Transformers
4.6.1 Development of Connections
Figure 4.7 shows a delta-star transformer. Assume a turns ratio of 1: 1. Note that the
@ star point is grounded.
Delta-star transformer
with neutral grounded
Figure 4.7 Development of CT connections for differential protection of three-phase
transformer.
B
E *l .I
In order to devise the CT connections, we follow the following sequence of steps:9
! 1. Determine the instantaneous directions of currents I,, Ib and I, through the
t
secondary windings (see Figure 4.7).
f 2. The primary winding currents IA, IB and Ic are then determined. Note that
because of the turns ratio of 1: 1, IA = I,, IB = Ib, IC = Ic (see Figure 4.8).
?

82 Fundamentals of Power Sysrenr Prorecnon
--
-
3. Line currents on the star side are determined. These are same as phase currents
I
,
I,, Ib and I,.
4. Line currents on the delta side are then determined. These are (Ic - IA),(IA- IB)
and (Ig - IC) as shown in Figure 4.8.
~ , , t ~ :(rc - zA),etc. are all phasor differences.
Delta-star transformer
with neutral grounded
Figure 4.8
A7
Determination of the line currents on the two sides of the transformer.
I
5. Therefore, if we connect the secondary windings of the CTs on both the sides in i
star, then the currents would not match up and a spill current would result. We
observe, however, that if the secondary windings of CTs on the star side are
i
i
connected in delta, then the line currents would exactly match with the secondary
currents of CTs on the delta side, provided that these are connected in star. This
is shown in Figure 4.9.
4.6.2 Phase c-to-Ground (c-g) External Fault II
Consider phase c-to-ground (c-g) external fault as shown in Figure 4.10. i
It can be seen that due to fault on phase c, there is an over-current in phase c. This
current is supplied through two of the lines on the delta side. Similarly, due to the delta . .
connections of CT secondary windings on the star side, two of the pilot wires carry the i
fault current, with the result that the current circulates in two of the percentage
,r '!
i

! ; Zero
i I
?
.,, . 8 . .
, _ _ _ _ _ _ _ _ - - _ _ _ _ _ A
Percentage differential relay
1
. I . _Figure 4.9 Final connections of percentage differential relay under normal load flow or
external balanced fault.
differential units and there is no current in the spill path. Thus, the scheme remains
stable on c-g external fault.

In - I I
c-g exerna faull
Figure 4.10 Phase c-to-ground (c-g) external fault.
4.6.3 Phase c-to-Ground (c-g) Internal Fault
A c-g internal fault is shown in Figure 4.11. The currents on the delta side are exactly
the same as those in the case of c-g external fault. However, since the fault 1s internal.

Transjorn~erProrecrion 35
there is no fault current through the primaries of the CTs on the scar side. The path of
the fault current 1s shown in bold lines. It can be seen from the figure that the fault
current flows through the spill path in two of the percentage differential units causlng
them to operate, thus tripping out the transformer.
,_.__________---.
Figure 4.11 Phase c-to-ground (c-g) internal fault.

86 Funda~nenralsof' Power- System Pr-orecriorz
4.7 inrush Phenomenon
Figure 4.12 shows an unloaded transformer being switched on to an ac supply.
AC supply
V, sin (at +
Switch-on Flux
Figure 4.12 Inrush phenomenon: switching on an unloaded transformer.
ILet the flux in the transformer be written as
@ = @msin ot
?'he induced voltage can then be written as
= N@mocos ot
= N@mosin (ot+ 90") (4.21
The applied voltage is exactly equal to the induced voltage. Thus, the flux in a
transformer lags the applied voltage by 90"in the steady state as shown in Figure 4.13.

Therefor., when voltage is passing through zero and becoming positive the flux
should be at its negative maxima and increasing as shcwn in Figure 4.13. In a time equal
to T!2 (half cycle), the flux changes from -$, to +6, as shown in Figure 4.14. The
change in flux is therefore 2q, in TI2 seconds. This is the steady-state picture.
I Transient flux
4
Time
flux
I
I
: Excitation characteristics of core
I H(AT1rn)
,
Figure 4.14 Inmsh phenomenon.
Steady-state
magnetizing current
i 10 : 810
I
4 Inrush current I
-

88 Fundamentals of Powel System Protection -
The variable 8 in the above expression controls the switching instant.
Let @ b ethe instantaneous value of the flux. Then we can write:
Let us assume that the transformer is switched on at positive zero crossing of the
voltage waveform as shown in Figure 4.14. Further, assume that the residual flux is zero.
Thus, the initial value of flux is zero but subsequently the flux must have the same rate I
of change and same waveform as it has in the steady-state. Thus, the flux must reach a
-
!
peak value of +29, in half a cycle. Since power transformers operate near the knee of the
saturation curve, a flux demand of 29, drives the transformer core deep into saturation,
causing it to draw a very large magnetizing current with a peaky non-sinusoidal
waveform. The magnetizing current is, therefore, very high, of the order of
8 to 30 times the full-load current. This current is known as inrush current. The time
I
constant of this transient component of current could be of the order of a few seconds at
.I,i,
d @= - sin (wt + 8) dt
(21
worst.
The inrush phenomenon can be explained mathematically as follows: ,
Let the voltage be represented as
v = Vm sin ( w t + 8) (4.3) a."
,
1where K is the constant of integration.
The value of K can be found out from the initial condition, i.e. when t = 0,
@ = @R = residual flux. Substituting this initial condition in Eq. (4.4),we get
@, = -(&)coso + K (4.5)
which gives K as
'VmK = 9, + (x;-)cos8
-
1
I

Thus the expression for flux in the transformer in the initial moments Just after
'
switching can be written as
'v,",= ,+ (t)cos~- (xjcos(Wt + e)
We can write (VmINw)as p,, the peak value of the flux, giving
Thus, the flux in the transformer is a function of the following three factors:
1. Residual flux gR
2. Instant of switching e
! 3. Magnetic properties of core, i.e. the amount of magnetizing current required to
produce a given amount of flux.
Thus, we see that for 0 = 0 and qR = +gm, the flux attains an amplitude of 34, at
OJ t = n radians. To satisfy a flux demand of 34,, the transformer primary draws a very
large magnetizing current with a peaky non-sinusoidal waveform.
Inrush is also experienced whenever there are sudden changes in the system voltage
such as sudden recovery of system voltage on clearing of a fault, somewhere in the
8 system.
! While an unloaded transformer, which is being switched on, experiences an inrush,
; an adjacent transformer, which is in service, may also experience a smaller degree of
inrush. This is known as sympathetic inrush.
Further, as such a high current flows only on one side of the transformer (on the side
which is being connected to the supply), it looks like an internal fault to the differential
scheme and ends up as spill current.
As seen in Section 4.3, a short circuit at the terminals of a transformer causes similar
. magnitudes of currents to flow. Hence, the percentage differential relay is likely to
1 maloperate on magnetizing inrush.
I
4.7.1 Percentage Differential Relay with Harmonic Restraint
i
$ We have seen that the percentage differential scheme tends to maloperate due to
j magnetizing inrush. One way to combat this problem is to desensitize the relay for a brief
i period of time, just after switching on. However, this is not desirable, since the probability
[ of insulation failure just after switching on is quite high, and a desensitized relay would
1 be blind to faults taking place at that crucial time.
1 A solution to this problem suggests itself, when we compare the waveforms of
I internal fault current with that of the inrush current. The inrush waveform is rich in
/ harmonics whereas the internal fault current consists of only of the fundamental.
b
' Thus, we can develop additional restraint based on harmonic content of the inrushi
i current. This additional restraint comes into picture only during the inrush condition and
t is ineffective during faults. Table 4.1 gives the harmonic content of a typical inrush
waveform.
j

90 Fltt~~/n~rrc.~tinl,rqf Pob~!erSj'stettr Protecrio~l
Table 4.1 Harmonic content of inrush waveform
-
Frequency MagnitudeP
Fundamental 100%
DC 40-60% i
Second harmonic 30-70s 1
Third harmonic 10-30% j
i
Fourth harmonic Less than 5% I
Fifth harmonic Less than 5%
Sixth harmonic Less than 5 6
I:
Seventh harmonic Less than 5%
1.IJ
I CT secondaw 1
Figure 4.15 shows the conceptual scheme of a harmonic restraint differential relay.
The fundamental component of spill current is segregated with the help of a filter and is @.
used to develop the tripping torque. The non-fundamental component of the spill current
(17 - 12)
I currents I,, 1;
j.,
aids the unfiltered circulating current in developing the restraining torque. This makes
the relay stable on inrush while at the same time not affecting its operation in case of
genuine internal faults. . .
Filter
I Unfiltered /
, .
1 Fundamental ( All harmon~w
I I Fundamental +
component all harmonics
i
Operating
torque -Relay
> '
Figure 4.15 Conceptual representation of harmonic restraint percentage differential relay. . .
A harmonic restraint percentage aifferential relay which implements the conceptual
scheme shown in Figure 4.15 is illustrated in Figure 4.16.
- . -
------' :

- Transf~7rmerProrecrron 91
CT
Transformer 1 ::
Fundamental + Harmonics All harmonics
.Fundamental
circulating current spill current spill current
Figure 4.16 Percentage biased differential relay with harmonic restraint.
4.8 High Resistance Ground Faults in Transformers
A percentage differential relay has a certain minimum value of pick-up for internal faults.
Faults with fault current below this value are not detected by the percentage differential
relay. Winding-to-core faults, which are of the single phase-to-ground type, involving h ~ g h
resistance, fall in this category Therefore, we must have a more sensitive relaying scheme
to cater for high resistance ground faults. Further, the reach of such a protection must
be restricted to the winding of the transformer; otherwise it may operate for any ground
fault, anywhere in the system, beyond the transformer. Hence, such ~rotectionis known
as restricted earth fault protection.
4.8.1 High Resistance Ground Faults on the Delta Side
Figure 4.17 shows the earth fault protection for the delta side of a delta-star transformer.
If there is a fault on the star side then the currents flow in the lines connected to the
delta side in such a way that there is no spill current through the relay on the CT
secondary side, thus the reach is automatically restricted to the delta side.

92 Frrndu~ner~talsof Power Sysrern Protection
Transformer
I

Reach of restricted
earth fault protection
OC relay
- !
Figure 4.17 Earth fault protection for the delta side of delta-star transformer. I.,_',, ,,
.,. ,<,
1 , ,
Since this is a current balance scheme, it is independent of the load current and hence
can be made as sensitive as desired.
i
I '
4.8-2 High Resistance Ground Faults on the Star Side
I
Figure 4.18 shows the restricted earth fault protection whose reach is limited to the star
side of the transformer. Ground faults beyond the star side CTs, anywhere in the system,
do cause current to flow on the secondary of the CTs. However, the currents circulate
through the CT in the neutral path and the CT in faulted phase. Thus, no spill current
flows and the scheme remains stable on external faults.
Transformer
earth fault relay
Figure 4.18 Restricted earth fault protection for star side of delta-star transformer.

Transformer Profection 93
The operation of the scheme for internal faults, restricted to the star side, can be
easily verified and is left as an exercise to the reader.
4.9 inter-turn Faults in Transformers
Inter-turn faults cause heavy current to flow within the shorted turns. However, seen
from the transformer terminals, the reflected current can be quite small. This can be seen
from the simplified analysis of Figure 4.19.
d
Figure 4.19 Calculation of terminal current for an inter-turn fault.
Power dissipated = 1: Rf= (5 x 103)'(1 x lo3) = 25 kW
Equating primary and secondary VA
-kV (I,) = (5 V)(5000 A)
E I
The current that circulates within the short-circuited turns is 5000 A whereas at the
400 kV terminals the current is only of the order of 0.11 A. Thus, inter-turn faults are
difficult to detect using over-current or differential principles of relaying. However, they
can cause severe hot spots resulting in deterioration of insulation.
This has led to the development of Buchholz relay which makes use of the heat
generated and the consequent decomposition of oil to sense the fault by purely non-
electrical means.
4.10 Incipient Faults in Transformers
Faults which are not significant in the beginning but which slowly develop into serious
faults are known as incipient faults. Buchholz relay provides protection against such
incipient faults.
4.10.1 Buchholz Relay
Figure 4.20 shows the position of the Buchholz relay with respect to the transformer tank
and the conservator.

94 Fundaineittals of Power Svstern Protection --
/ HV bushing
Figure 4.20 Plac
The conceptual diagram of the inner working of the Buchholz relay is shown in
Figure 4.21. When an incipient fault such as a winding-to-core fault or an inter-turn fault
occurs on the transformer winding, there is severe heating of the oil. This causes gases
to be liberated from the oil around 350°C.There is a build-up of oil pressure causing oil
to rush into the conservator. A vane is placed in the path of surge of oil between the
transformer and the conservator. A set of contacts, operated by this vane, is used as trip
contacts of the Buchholz relay This output of Buchholz relay may be used to trip the
transformer.
,.:t.
>. .
To consewator
tank
JBuchhalz trip
Figure 4.21 Construction of the Buchholz relay.
The Buchholz relay also has another set of contacts operated by a float. These
contacts stay open when the transformer tank is filled with oil. However, in case of
leakage of oil or decomposition of oil, the float sinks causing the contacts to close. Loss
of oil will no doubt cause the transformer temperature to rise but does not warrant
immediate tripping. Hence, normally these contacts are wired to an alarm which alerts
the operator.

Transjornler Protection 95
4.10.2 Analysis of Tmpped Gases
The trapped gases in the conservator can give valuable clue to the type of damage that
takes place inside the transformer. This is because the insulation between the winding
turns, the insulation between the stampings of the core and the oil, all liberate specific
gases when they get heated up due to a fault. The presence of these gases can be used
as a signature of a particular type of damage that may have taken place inside the
transformer. Table 4.2 lists this information.
Table 4.2 Analysis of trapped gases
Type of gas Diagnosis
Hz and C2Hz
Hz, CzHz and C%
Arcing in oil between constructional parts
Arcing with some deterioration of phenolic insulation,
e.g. fault in tap changer
Hot spot in core joints
HZ, CH4, COz and CsHB Hot spot in a winding
4.1 1 Phenomenon of Over-fluxing in Transformers
4.1 1.1 Protection Against Over-fluxing
The flux and the applied voltage in a transformer are related through the following
expression
v = 4.44 4, fN
where
V is the rms value of the voltage
f is the frequency
N is the number of turns in the winding.
Thus, we can write the flux as
Whenever there is an over-voltage (frequency remaining constant), the transformer
core is subjected to a higher value of flux in order to be able to support the higher applied
voltage. By design, power transformers operate at the knee of the saturation curve at
normal voltage. Hence, any increase in applied voltage, and the consequent increase in
flux density, drives the transformer deeper into saturation. The transformer, therefore,
draws an excessive magnetization current. Hence, this condition is described as ouer-
excitation. This, considerably, increases the core losses giving rise to overheating of the
transformer. Further, saturation of the core causes the flux to flow into adjacent
structures, causing high eddy current losses in the core and adjacent conducting
materials. Such an operating condition cannot be allowed to continue for long and the
transformer should be tripped if there is a prolonged over-excitation. Figure 4.22 shows
a typical allowable over-excitation limit curve.
It can be easily seen that over-excitation can also occur in case of low-frequency
operation of the transformer at rated voltage.

96 Fundame~zmlsof Power Sysrern Prorecriorl
,Prohibited operating region
I
I I I-
0.01 0.1. 1.o 10 100 1000
Time (minutes)
Figure 4.22 A typical transformer over-fluxing limit curve.
Therefore, to keep the working flux within the ~emissibledesign limits, the Vlf ratio
must not exceed the permissible limit. For elrample, a transformer designed for a per unit
voltage limit of 1.25 per unit (125%) at rated frequency will experience over-fluxing
whenever the per unit volts/hertz exceeds 1.25 (125%), i.e. whenever the voltage exceeds
125% at rated frequency or the frequency falls below approximately 80% (below
approximately 40 Hz on 50 Hz basis) at rated voltage. Thus over-excigtion can be
detected by measuring the V/f ratio by a so-called volts/hertz relay.
Microprocessor-based volt/hertz relays have been developed and are in uSe. We refrain
from further discussion of these relays in this textbook. The interested reader may
consult manufacturers, literature for details.
4.12 Transformer Protection Application Chart
Transformers are used for a very wide variety of applications. The type of protection that 1
will be provided for a transformer depends upon its kVA rating and its importance. The 1
only protection that will possibly be provided to a small lighting transformer may be in
the form of fuses while a transformer connected to a generator in a thermal power station I
may have very elaborate protection. Tables 4.3 and 4.4 summarize the transformer
I
protection scenario and application of various protection schemes.
Table 4.3 Internal and external faults affecting transformers I I
Internal faults External faults
Phase faults System phase faults
Ground faults System bound faults
Inter-turn faults Overloads
Tap-changer failure Over-fluxing
Leakage of oil from tank-

Tranz,forr?~er?:.oiecrron 97
--
Table 4.4 Application of protective schemes
Proredion scheme
Fault Priman, Back-up
Phase faults Percentage diiiorential relay Over-current/distance
Ground faults Percentage differential relay Over-current/distance
Inter-turn faults Buchholz relay
Oil leaks Buchholz relay
Overloads OC relay with thermal image of protected unit
Over-fluxing Over-fluxingrelay which measures (Vlf)ratio
4.1 3 An Illustrative Numerical Problem
Problem For a 45 MVA, 11 kVi66 kv star-delta transformer, design the percentage
differential scheme. What is the minimum recommended percentage bias?
Solution As shown in the worksheet of Table 4.5, we find that the pilot wire currents
are 6.817 A from the star side CTs while they are 3.936 A from the delta side CTs. Thus,
we need intermediate CTs to correct this mismatch as shown in Figure 4.23. Such CTs
are known as interposing CTs and are usually autotransformer types. The turns ratio of
the interposing CTs is, therefore, found out to be 6,81713,936 = 1.731 : 1.
Table 4.5 Worksheet for % differential relay calculations
Step 11kV star side 66 kV delta stde
1 Full-load line
CUTnn+ r-.
2 To allow for 25% 2361.88 x 1.25 A 393.64 x 1.25 A
overload, choosing = 2952.35 A = 492.05 A
(IF,,x 1.25) as
primary current
3 CT ratios Choosing a CT of 3000 : 5 Choosing a CT of 500 :5
(5A relay) i.e. CT ratio = 600 i.e. CT ratio = 100
4 CT secondary CT secondary current CT secondary current
currents
5 Pilot wire currents (CT secondaries are in A) (CT secondaries are in Y)
Current in the pilot wires Current in the pilot wires
= fi x 3.936 A = 6.817 A = 3.936 A
6 Turns ratio of the Current after the
interposing CT interposing CT
Current in the pilot wires
= 3.936 A

98 Fundolne~mlsof Power Sysrrm Protection
Figure 4.23 Numerical problem on percentage differential protection of transformer.
Assuming a slope of 40%, spill current required for tripping is
Actual spill current = 3.938- 3.936 = 0.002 A. Therefore, the scheme remains stable on
full load or external fault.
- ~
.~
-.. - .

Review Questions
1. What factors cause spill current on external fault in case of transformer
differential protection?
2. While connecting CT secondaries for differential protection of three-phase
transformers, the CTs on the star side have to be connected in delta and vice
versa. Explain.
3. The CT ratios of CTs on t h ~two sides of a transformer will, in general, be
different. Explain.
4. What is the effect of tap changing on the percentage bias setting of differential
relay?
5. For a three-phase delta-star transformer, show that a line-to-ground fault
a
(external as well as internal) on the star side appears like a line-to-line fault from
the delta side.
I
6. Investigate the differential units which operate on a-g external and internal
faults.
7. Repeat the above for line-to-line external and internal faults.
8. Explain the phenomenon of inrush. What are the factors on which the magnitude
of inrush current depends?
9. Consider the following switching instants for a transformer:
(a) Voltage wave passing through zero from negative side, residual flux equal to
positive peak value of steady-state flux.
(b) Voltage wave at its peak and decreasing, residual flux equal to negative peak
value of steady-state flux.
(c) Voltage wave passing through zero from positive side, residual flux equal to
zero.
Sketch the waveforms of voltage, flux and magnetization current for the above
cases.
10. Which harmonic is the most dominant in the inrush waveform?
11. Explain the principle of percentage biased differential relay with harmonic
restraint.
12. Why does the percentage differential reIay fail to detect 'high resistance winding'.
to-'core' faults? , "
13. What type of protection is used for the fault condition in Question 12?
14. Prove that the restricted earth fault relay does not operate for faults beyond the
star connected winding of a three-phase delta-star transformer.

100 F~r~~da~ne~ltalsof Power Sysre~nPmtectiort
15. Prove that the restricted earth fault relay does operate for faults within the star
connected winding of a three-phase delta-star transformer.
16. What do you mean by over-fluxing or over-excitation? What is the significance of
the (Vlf) ratio?
17. Why is over-fluxing harmful for the transformer?
18. What is the principle of over-fluxing protection?
Problems
1. Consider a single-phase 11kVI11 k y 1.1MVA transformer protected by percent-
age differential protection. CTs with 5 A secondaries are used. It is known that
the magnetizing currents of the two CTs, for maximum external fault current,
differ by 0.5 A. Assuming no other source of error and a minimum pick-up of
0.01 A, find the minimum percentage bias setting so that the scheme remains
stable on maximum external fault current.
(Ans.9.8%)
2. Design the differential protection for a three-phase, 50 Hz transformer with the
following nameplate ratings: MVA 250, 15.75 kVl400 k y 50 Hz, delta-star. . .

5.1 Introduction
The word bus is derived from the Latin word omnibus which means common for all.
Busbars are the nerve-centres of the power system where various circuits are connected
together. These are the nodes of the electrical circuit. Figure 5.1 shows a busbar having
an N,number of incoming lines and an N2 number of outgoing lines. The protective zone,
to be generated by the protective relays, is also shown. It may be noted that under the
normal power flow condition the sum of incoming currents is equal to the sum of
outgoing currents, i.e
Figure 5.1 Introduction to busbars.
101

102 F~~rzdarnentolsof Power Sysrenl Pmtecrion
_2_-
. .
Thus, there is a large concentration of short-circuit capacity at the busbars. A fault
0" the busbar, though rare, causes enormous damage. When protective relays operate .
to isolate the busbar from the system, there is a large disruption to- the loads.
Busbars are located in switchyards, substations, and supply kiosks. The switchyards
are well shielded from direct lightening strokes but because of their outdoor nature,
are subject to the vagaries of weather. The substations are well protected in all
respects and fault probability is indeed very low. Similarly, supply kiosks are totally
enclosed and sealed.
The causes of faults experienced on busbars are: weakening of insulation because of
ageing, corrosion beccause of salty water, breakdown of insulation because of over-
voltages, foreign objects, and so on. For example, rodents, lizards and snakes are known
to have caused busbar faults in remote unmanned substations.
Because of the low probability of busbar faults, for many years, it was considered
unnecessary to provide explicit protection to busbars. It was felt at that time that
maloperations of the busbar ~rotectionsystems will be problematic by themselves and of
little help in sensing genuine faults. It should be noted that busbars fall in the overlap
between ~rotectivezones on either side, so they do get back-up protection. Hence,
Protection engineers hesitated from providing exclusive busbar protection.
However, as the system voltage went on increasing and short-circuit capacities went
on building up, it was no. longer advisable to leave busbars unprotected on a primary
basis.
What form of protection is best suited for busbars? A little reflection will convince
the reader that differential protection will suit this situation best because the
ends (terminals) of the system are physically near to each other. Thus, by installing
CTs o n the two sides, we can simply compare the current entering thebusbar with
that leaving it. Any discrepancy between the two will immediately signaf an internal
fault.
In Section 5.2, we have explained the protection of busbars by the differential
Protection scheme.
5.2 Differential Protection of Busbars
I 5-2.1 Selection of CT Ratios in Case of Busbar Protection: Wrong
Method
Figure 5.2 shows a busbar, having two incoming feeders and one outgoing feeder,
being protected by a simple differential protection scheme. The currents shown are
for normal load flow. Let us decide the CT ratios on the basis of maximum primary
load current seen by each CT. Thus, the CTs on the incoming feeder will have
CT ratios of 100011 A and 200011 A, respectively. The CT on the outgoing feeder will
have a CT ratio of 300011 A. However, with this choice of CT ratios, it can be seen from
the diagram that there is a spill current even during the healthy condition. Thus, the
method of selecting CT ratio on the basis of maximum primary current seen by the
feeder is not correct.

Plug setting 4 R OC relay
'"1 =...A Q A
Trip coils of CB,. CBB, CBc
m
NO = Normally open r mOC relav out~ut Trip battery
Figure 5.2 Wrong method of selection of CT ratios for differential protection of busbars.
5.2.2 Selection of CT Ratios in Case of Busbar Protection: Correct
Method
I
Figure 5.3 shows the correct method of setting the CT ratios for the busbar differential
i protection. It can be seen that the CT ratios of all the CTs are equal and are based on
! the primary current of that feeder which carries the maximum current. Thus, all the CT
i
Figure 5.3
P I U ~setting -+ R OC relay
'"1 =...A 9Zero ampere
1 i - 1 A
Correct method of selection of CT ratios for differential protection of busbars.

'Ii
,cl:
.,,.,,
21: 104 F~rndanlrntalsof Power System Protectiotz
5.3 External and Internal Fault
~ : l
ratios are 3000/1 A. Therefore, as can be seen from the figure, there is no spill current
.,.,,,
through the OC relay connected in the spill path and the scheme remains stable.
s :.
. ,
We draw an important rule for the selection of CT ratios for all the CTs in a busbar
.,. differential protection, namely:
In the preceding discussion, we have assumed that the CTs are ideal. When the CT
primary current, or the burden on it, is within its design limits, the CT can indeed be
assumed to be more or less ideal. However, as the primary current exceeds the design
value or the CT burden (output of CT in VA) becomes excessive, the CT no longer behaves
in an ideal fashion.'~henon-ideal behaviour of the CT has very serious implications for , ,
the protective schemes.
Figure 5.4 shows currents during an external fault beyond CTc. It can be seen that
CTc, the CT on the faulted feeder, has to carry the sum of all currents fed into the fault
by various feeders. Therefore, CTc sees a substantially larger primary current than either . .
CTAor CTB.In all likelihood, CTc will therefore become saturated. We can, therefore, no
longer assume that CTc will faithfully transform the fault current. For the sake of ...
illustration, we have assumed that the secondary current of CTc is only 4 A instead of
10 A. It can be seen from Figure 5.4 that this results into a spill current of 6 A, causing
the scheme to maloperate, i.e. lose stability on external fault. ".
>, :,
b .
i.
.!i;
1; CT, and CT. are unsaturated
Maximum out of all the feeder currents
CT ratio for all CTs in bus differential scheme =
1 A or 5 A
J 4 A I External fault
+ .
Plug setting -+ R OC relay
l o = A %A
1iiiii.:
I . 1 .. - ? I
10A 4 A
Figure 5.4 Behaviour of busbar differential scheme on external fault.
In the worst case scenario, CTAand CTBcontinue to transform faithfully as per their
nameplate CT ratio but CTc, which carries the total fault current, gets completely
saturated. This clearly indicates the occurrence of an imbalance in transformed secondary
currents, resulting in substantial spill current. This situation most likely will cause the
scheme to operate. Operation of a differential scheme under external faults is, therefore,
clearly a case of maloperation.

Interestingly, as the fault shifts by a small distance to the left and becomes an
internal fault, still drawing the same current, the situation dramatically changes as far
as CTc is concerned. This is depicted in Figure 5.5, wherein it can be seen that CTc now
does not carry any fault current (assuming a single-end-fed system with source on left-
hand side). Since CTA and CTB are not carrying excessive primary currents, they
transform the current without too much error. There is thus a spill current in the spill
path and the scheme operates as expected.
No source
10A Zero
Figure 5.5 Behaviour of busbar differential scheme on internal fault.
The maloperation of the busbar differential scheme on external faults is caused due
to non-ideal behaviour of a CT carrying excessive primary current. It will, therefore, be
pertinent, at this point to take a closer look at the actual behaviour of protective current
transformers.
5.4 Actual Behaviour of a Protective CT
Figure 5.6 shows the equivalent circuit of a current transformer referred to the secondary
side. R b and 4 are the primary winding resistance and leakage reactance, respectively,
referred to the secondary side. R,and X, are the resistance and leakage reactance of the
secondary winding, respectively. The excitation is modelled by X; and core loss by Rb in
the equivalent circuit (referred to secondary).
At low values of primary current Iprand therefore I,, voltage E, to be induced by the
secondary winding, which is approximately equal to (ZburdenIs), is quite low. The working
flux in the CT, which is equal to (E,/4.44fN) is also very low. The magnetizing current
requirement is, therefore, correspondingly low. Thus, the secondary current I, is
substantially equal to I,/N.
If the primary current increases, initially, the secondary current also increases
proportionately. This causes the secondary induced voltage to increase as well. Increased
secondary voltage can only be met with an increase in the working flux of the CT. AS the
flux increases, the transformer needs to draw a higher magnetizing current. However,
because of the nonlinear nature of the B-H curve for the CT, as the knee of the excitation

106 F~rnda~tlentaisof Power Svste~nProtection
Figure 5.6 Equivalent circuit of CT.
characteristics is passed, any further increase in flux demand causes a disproportionately
large increase in the magnetizing current requirement of the CT. This is illustrated in
Figure 5.7. It may also be noted that I, is no longer sinusoidal and its waveform has a
prominent peak.
4 Flux @
i' Magnetizing current '10
Time 4
Figure 5.7 Operation of the CT beyond the knee point of the B-H curve.

-4s ~ h eprimary current goes on increasing, a stage comes when the magnetizing
current requirement is so large that almost all the transformed current is taken up by
the CT for the sole purpose of magnetization, with the result that there is hardly any
current available for the burden. When this occurs, we say that the CT is completely
saturated. The secondary induced voltage and burden current waveforms of a CT,
operating in saturation, are highly distorted. They, in fact, consist only of sharp pulses
near the zero-crossings of the primary current. This is shown in Figure 5.8, where it can
be seen that in order to reach the peak of the sinusoidal flux waveform, the CT is driven
deep into saturation. Due to flatness of the excitation curve in this region, a very large
amount of exciting current is demanded by the CT The waveform of the exciting current
becomes distorted and is, in fact, very peaky in nature.
I
U
Figure 5.8 CT saturation due to excessive primary current

-
r'1
i
:i
108 Fundr~n~etralsof Power Sysrenl Prorrcrion
i
5.5 Circuit Model of Saturated CT
::
In the light of the preceding discussion, the saturated CT is modelled as shown in
Figure 5.9, where it can be seen that the magnetizing branch is replaced with a short I .
circuit to signify the fact that the magnetizing branch is taking up all the secondary I
current and none is available to the burden.
XbIplN Rb RS Xs I, = zero
>Ii:--
1s
lo = /,IN Burden f
ru"
CT ratio = N : l
.
c
),lo = Ip/N Burden $
ru" .%-....
.,.~
-.- ..".
Figure 5.9 Circuit model of a saturated CT. -
Thus, the circuit model consists of a current source of value (IplN)feeding into a
short circuit through R; and q.The connections to the outside world are available
through R, and X,.
5.6 External Fault with One CT Saturated: Need for High
Impedance Busbar Protection
Now, consider the external fault of 30,000 A, on the busbar shown in Figure 5.4.
Assuming that CTc gets completely saturated while CTA and CTB continue to operate
normally, Figure 5.10 shows the equivalent circuit as seen from the CT secondaries. Note
that for simplicity, all leakage reactances have been neglected.
It can be seen from Figure 5.10 that currents [(IAIN) - I,,] and [(IB/N) - IoB]
sum up and the resultant current has two parallel paths available. One path is through
the over-current relay and the other is through (R,+ RL)via the short representing the
saturated CT magnetizing branch. Thus, the part of fault current will flow through the
over-current relay, causing it to trip, even though the fault is external. Hence, the OC
~-~

relay needs to be restrained from tripping on external faults (with one GT completeiy
saturated). We can easily accomplish this by connecting a high resistance (kaown as the
stabilizing reszstance) in series with the OC relay. The stabilizing resistance should be of
such a value that under the worst case of maximum external fault and full saturation of
- one CT, the current through the OC relay is less than its pick-up value. Such schemes are
known as high impedance busbar differential schemes.
Figure
CTc
I
I
Saturated CT I
I
Rb
I
I
Rb
I Short circuit I
I - - - - - - - - - - - _ _ _ _ _ _ _ - - - - .
OC relay
5.10 Secondary equivalent circuit with one CT fully saturated during external fault,
I:
i To find the value of the stabilizing resistance, let the pick-up value of the OC relay
be I,, and the value of the resistance associated with the saturated CT be (R,+ RL).The
impedance of the secondary circuit of the saturated CT be represented by Z,, where
Z, = (R, + RL).
The procedure is as follows: First consider that the 0 C relay is not connected and find
1 out the voltage that will be developed across it, let it be V,,,. Now, the stabilizing
)
resistance should be of such a value that with the relay connected, the current through
k
the relay should be less than the pick-up value of the relay
i Therefore, we have the following relationship:
I Voltage across the over current relay in series with the stabilizing resistor
In order that under this condition, the current through the relay be less than or equali
to its pick-up value Ipu,we have

110 Fundantentols of Fower Sysrenl Ptotection
Assuming n feeders and further assuming that the magnetizing current of each
unsaturated CT is same and equal to I,,, and noting that the transformation ratio of all
the CTs is same and equal to N, we get the general expression:
where the subscript k varies from 1 to n - 1, n being the total number of feeders
terminating on the bus. Note that Elk is the maximum external fault current,
[:I:1If,,xt,,,, up to which the differential scheme remains stable. Therefore, neglecting
magnetizing currents, we can write I
I
The preceding equation gives the value of maximum external fault current up to which 4
d
the differential relaying scheme remains stable as: I
i
5.7 Minimum Internal Fault That Can Be Detected by the !
High Impedance Busbar Differential Scheme 1I
It will be worthwhile to investigate the minimum internal fault current If,,,ternal,prlmary
I
that can be detected by the high impedance busbar differential scheme. The equivalent
CT secondary circuit during internal fault is shown in Figure 5 11.It is assumed that
none of the CTs is saturated. The high impedance scheme has a pick-up of I,,, a
stabilizing resistance of Rstaband, therefore, needs a minimum voltage of Vaet to be@
developed across the series combination of the stabilizing resistance and the OC relay
Thus, the minimum fault current on the CT secondary side, that can develop the required
voltage V,,,, will be given by
But
Therefore,
Vset = If,min,see Rstab
Vset
If,min, sec =
&tab
V"'= I,,
Rstab
If,min, see = Ipu

Figure 5.11 shows that during internal fault, all the CT secondaries feed into the spill
path. Therefore, the current for a minimum internal fault in the high i~~pedancespiii
path will be
plug setting = I,,,
CTA 1,
- -
, 1,
10.4 4 CTc
'c- - IOC Rs + RL Po
- . - .
Rb
-
CTB
Q
OC relay
p~ck-up
Figure 5.11 Minimum internal fault current that can be detected by high impedance busbar
differential scheme.

112 F~indamentalsof Power System Pmtecnon i
Assuming I,,*= I,, = ZOC= I, (i.e. all the CT magnetizing currents to be equal) and
multiplying both sides by N, we get
N I p u = If, lnt, mm, pri - 3 N I o
or
Zr,nt,m,,,pr, = I + I (with 3 feeders terminating on the bus)
For the general case of n feeders terminating on the busbar, the minimum internal fault
current that can be detected by the high impedance busbar differential scheme will be
given by
5.8 Stability Ratio of High Impedance Busbar Differential
Scheme
The stability ratio S of the high impedance busbar differential scheme is defined as the
ratio of maximum external fault current for which the scheme remains stgble to the
minimum internal fault current for which it operates. iIf,external, maximum
%internal, minimum
The stability ratio is a dimensionless quantity. The higher the value of stability ratio
S, the better is the quality of differential protection. Stability ratios of a few tens are
common in EHV busbar differential schemes.
5.9 Supervisory Relay 1.
In the busbar differential scheme, it may, at times, happen that a particular CT secondary
gets o m circuited. At other times there may be a break in the pilot wire coming from
a particular CT secondary winding. Thus, even though there may be no internal fault on
the busbar, an imbalance is created on the secondary side, causing a spill current which
is equal to the current that was being contributed by the particular CT before its
secondary got open circuited.
Such types of events are, no doubt, dangerous. The current contribution of an
individual CT would be much less than the pick-up value of the OC relay and the scheme
will remain insensitive to such CT open-circuit faults. All the same, we need to develop
a mechanism to detect such faults so as to raise an alarm to alert the operating personnel.

The highest spill current, in case of lcss of one CT secondary current, will be caused
in case of the CT which carries the maximum load current, lload,max.
Figure 5.12 shows the normal load being supplied by the feeders. There is a break in
the pilot wire coming from secondary of CTc. This will cause a spill current equal to the
current that was being contributed by CTc before the break occurred, as shown in
Figure 5.12. Thus, the spill current = Ic/N. This spill current will develop a voltage
across the series combination of the stabilizing resistance and OC relay, which can be
sensed by a sensitive over-voltage relay known as superuisory relay.
I Zero
/A ,(
F + W
t Pick-up
R
setting Over-voltage
relay
-
I Zero Supervisory relay
S ~ I I Icurrent = + Is =
N N N
TCCBA
Differential Alarm Supervisw
relay (NO) relay (NO)
T
Trip battery
TCCBc
- . -
NO = Normally open, NC = Normally closed, TCCB = Trip coil of CB
Highest feeder
CBc CTc current
/A CBA
-
Figure 5.12 Supervisory relay to prevent against maloperation due to loss of a CT
secondary current.
r -
! The supervisory relay is set to pick-up at:
A
r ~ .
- Iload,rnax
Yupervisory - N (Rstabilizing + %C relay
II The above discussion neglects the magnetizing currents of the CTs.
The setting of the supervisory relay V,u~N,,,, will be much less than the setting of
the high impedance differential relay V,,,.

114 F~r~zdnrrrenmlsof Power Sysrrrn Protect~o~l
5.10 Protection of Three-phase Busbars
All high voltage busbars are three-phase, however we showed single-phase busbars so as
to keep the diagrams uncluttered. Figure 5.13 shows a three-phase busbar with two
incoming and three outgoing lines.
"-
.-
-~ .~~-- --
- . . ---- .- -. ~
~ ..,. -- ~.

5.1 1 Numerical Example on Design of High Impedance
Busbar Differential Scheme
A 132 kV busbar consists of two incoming lines and four outgoing lines. The system is
soiidly earthed and the switchgear capacity is 3500 LMVAat 132 kV The parameters are:
Maximum full-load current in one line = 500 A
R, = CT secondary resistance = 0.7 R
R ~ ~ dwire = 2.0 R
Relay load (1A relay is used) = 1.0 R
CT magnetizing current up to 120 V = 0.28 mAiV (assumed linear)
CT saturation voltage Vk,, > 120 V
1. If the over-current relay in the spill path is set at 1.0 A and the voltage setting
V,,, is 100 V, find
(a) the maximum 'through fault' current up to which the scheme will remain
stable.
(b) whether the answer in part (a) is commensurate with the switchgear capacity.
(c) the minimum internal fault current which will be detected by the scheme.
(d) the setting for detecting minimum internal fault current of 500 A?
(e) the value of the stabilizing resistance.
2. It is required that a break in the pilot wire from a CT carrying a current of
25 A and more should be detected by the supervisory relay. Calculate the setting
of the supervisory relay?
Solution
l(a). Let us choose 1A CTs. Therefore, as explained in the text:
CT ratio for all CTs = Maximum of all the feeder currents : 1
= 500 : 1
I
l(b). From the given data, the maximum 'through fault' current that can be
handled by the switchgear is:

116 Fundamentals of Power Systern Prorecrion
The scheme remains stable up to 'through fault' current of 18518.51 A.
However, the switchgear is designed to handle only 15,300 A. Therefore, wi?
need to fine tune the setting to:
l(c). Minimum internal fault current (for V,,, = 100 V and I,, = 1.0 A) is given
by
- NUpu+ do)If,int,min,pri -
N = 500, Ipu= 1.0 A and n = 6
I, is given as 0.28 mA per volt, therefore, for a voltage of 82.62 V;
I, = (0.28 mA/V)(82.62 V) mA = 0.02313 A
Thus,
,
If,int,rnin,pri = 500 11 + (6)(0.0231)1 = 569.39 A
4.
l(d). For minimum internal fault current of 500 A, the pick-up value should be: '
Rstabilizing + ROCrelay = --
0.861A
ROCrelay = 1*
Rstabllizing = 94.93 *
2. Setting of supervisory relay
Neglecting magnetizing currents of the CTs, we get
'load, lost, CT
vsupervisory = N (Rstabilising + Roc

B~tsbarProtection 117
Review Questions
1. Describe the unique features of a busbar, from the point of view of application of
its protection.
2. Maloperation of busbar protection causes large disturbances to the system.
Explain.
3. The CT ratio for all the CTs in the busbar differential scheme has to be same and
I is decided by the feeder carrying maximum current. Explain.
I 4. Discuss the behaviour of a CT in deep saturation. What are its implications for
1 the busbar differential protection?
5. Why does a busbar differential scheme have a tendency to operate for external
! faults.
C 6. How is the value of stabilizing resistance and its wattage decided?
7. In the case of high impedance busbar differential scheme, how will you find out
I the minimum internal fault current for which the scheme will operate?
I
I
8. Define stability ratio and discuss its significance. What is the typical range of
i values of stability ratio for a high impedance busbar differential scheme?
i 9. While normal load is being supplied, an open circuit takes place in one of the pilot
wires. What will be the consequences as far as the busbar differential relay is
concerned?
I
I
i
10. Suggest an add-on to the differential relay, to avert a possible maloperation in the
b above scenario.
! 11. Sketch the high impedance busbar differential protection for a three-phase busbar
having three incoming and two outgoing feeders.
I
II
i

6 ~jstance~rotectionof
Tvawnission Lines 1
I
6.1 Drawbacks of Over-current Protection /Over-current protection is very appealing and attractive because of its inherent simplicity.
It is used as a primary protection for low voltage (LV) distribution lines. However, it has
some major drawbacks which causes it to maloperate. In LV systems, however,
maloperation of relays can be tolerated. The only consideration in LV systems is the
continuity of supply to the consumers. However, in EHV systems maloperations cannot
be tolerated. This is because EHV lines are part of an interconnected grid. Any
maloperation on these systems jeopardizes the stability of the electric grid.
The reach of over-current relay depends on the type of fault as well as on the source
impedance as shown in Figures 6.1 and 6.2.
ZS= constant PlPUpick UP /
of OC relav!
Fault current
T
w ; Distance from
Reach for L-L-G faults relay locationr------------_---------------
Reach for three-phase faults1 I
r - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Figure 6.1 Effect of type of fault on reach of over-current relay.
, 118
, ,
L--

Distartce Protecrion of Trarlsnlirsion Lines 119
I
It can be seen from Figure 6.1 that if the OC relay pick-up setting equal to ipugives
( . a reach up to bus B for L-L-G faults, then the reach for L-G faults is only up to point
3,whereas the reach for three-phase faults is up to point Bz. Thus, the relay may under-
reach or over-reach depending upon the type of fault. This is clearly not a desirable trait.
Figure 6.2 shows that if the OC relay pick-up setting equal to Ipugives a reach up to
I bus B, assuming a source impedance of Zszthen it under-reaches to point B1if the source
I impedance increases to Zsl, and over-reaches to point Bz if the source impedance
!i decreases to Zsz (assuming that the fault type is the same in all the three cases). This,
!
i
again, is not a desirable feature.
Three-phase
61 I fault 62
! A !
IpUpick-up I
of OC relay; !
I Fault of I
: same type I
I
I
I
I
i Reach for Zs3
L---------------- 4 ..
I Distance from
Reach for Zs2 I relay location
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - 9
I Reach for Zs,? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
21
Figure 6 2 Effect of source impedance on reach of over-current relay.
i
I Thus, we see that the fault current is a function of fault type as well as the source
t
impedance, both of which are variable. We must, therefore, look for a relay whose reach
1 does not depend upon the actual magnitude of the fault current. Search for such a
i relaying principle has led to distance relays, whose reach is not dependent on the actual
t
! magnitude of the fault current but on the ratio of voltage at relay location and the fault
I current. This is discussed in Section 6.2.
i
1 6.2 Introduction to Distance Protection
ib
i Consider a transmission line AB as shown in Figure 6.3(a). Let us assume that there is
i
source only at end A. We wish to generate a zone of protection which extends from A to
r

130 Fl117dfl1nenmlsof Power Systrn~Prorectrorr
B. Assume that the proposed relay is located at end A, where the local current and voltage
are available through a CT and a PT, whose ratios have been assumed as 1: 1for the sake .
of simplicity. The reach of the distance relay is thus made equal to Z,,,. The line is I.
modelled as a series R-L circuit for the purpose of relaying without much loss of accuracy,
as shown in Figure 6.3(b). t
A Reach point fault
Reach = Z,,, -)
.l PT Internal fault 1 External fault
Trip;
Consider three faults: an internal fault Fl, an external fault F3, and a fault at reach
point fault F2.Now, let us compare the relay voltage VR with the product of relay current
IRand Z,,, as shown in Table 6.1 for all the three faults.
'R 4
' t -
Table 6.1 Introduction to distance relays f
E
Current Voltage Compare Desired
Fault at relay at relay 1v ~ l : ~ ' ~ R ~ ' ~ ~ ~ ~ L ~response of
location,'IR location, VR relay
F3,External 183 VR, IV831 > lI~31IZsetI Restrain
F,, Reach point IRZ VRZ I VRZ1 = II*, I I Zoet1 Verge of operation
I
F,, Internal
i IRI v ~ l 1 V~~1 < IIRII lZset1 Trip
r,
RL XL
rv
VR
1
Thus, we can see from Table 6.1 that the trip law that emerges is;
iI
1
i
1
I
;
nm i(b)
Figure 6.3 Introduction to distance relaying.

Distarlce Protection of Tra~~s~nissionLines 131
This can be written as:
1 else restrain
However, the ratio (VR1/I IRI is the magnitude of the apparent impedance lZRl as seen
by the relay, therefore, the trip law can be written as:
If IZRI <: IZ,,,I then trip;
The relay, therefore, somehow, has to compute the impedance as seen from its location
and compare it with set value to take the trip decision. Because of the simple series model
of the faulted line, the line impedance is directly proportional to the distance to fault.
Hence the name distance relay. Such a relay is called under-impedance relay. In practice,
however, the word under is dropped and the relay is simply called impedance relay. It is
possible to synthesize several more complicated distance relays. To distinguish this relay
from the other distance relays, we will call it simple impedance relay.
It may be noted that we need not actually perform a division of (VR(by JIRIto
compute IZRI.We can get around the computation by performing a comparison instead!
The readers would appreciate that an arithmetic division is a much more complicated
operation than a straight comparison. In fact, till microprocessors became available, it
was not possible at all to do any arithmetic computation in a relay. This is indeed one of
those engineering solutions, which is very ingenious.
The characteristic of a distance relay on the V-I plane is shown in Figure 6.4.
However, it is more instructive to represent this characteristic on the R-X plane. The R
(resistance) axis represents the real part of the (V/n ratio whereas the X (reactance) axis
Relay current. IR
Figure 6.4 Characteristic of simple impedance relay on V-I plane.
represents the imaginary part of the (V/I?;both V and I being phasors. This is shown in
Figure 6.5 wherein the fault characteristic of the faulted line, for metallic faults, is also
superimposed. (Metallic faults are those faults which do not involve appreciable fault
resistance.) This is a straight line with a slope equal to the line characteristic angle
tan-'(wL/R), where L is the inductance per unit length of the line and R is the resistance
per unit length of the line. Thus, a fault anywhere on the transmission line can be

122 F~rndarne~~talsof Power System Pmtecrion
mapped on to this straight line. It is obvious that the tripping characterist~cof the
distance relay to protect the entire length of the transmission line should actually be a
small area on the R-X plane, which snugly encompasses the fault characteristics of the
transmission line. Unfortunately, the tripping characteristic of the simple impedance
relay encompasses too large an area on the R-X plane than that ideally required. This is
an undesirable trait because it gives rise to maloperations of the relay. This is discussed
in greater detail in subsequent sections.
A Reach ~ointfault
-Reach = Z,,,
4 Internal fault )B External fault
Trip i F3
Model of the faulted transmission line
Fault characteristic
X = lm(VI1)
of the line
Restrain
-R
Trip R = Re(VI1)
Restram Operating characteristic
of the relay
1 wL= tan- -
R
Figure 6.5 Characteristics of simple impedance relay on R-X plane with fault characteristic
of the line superimposed.

Disrance Prorfcrion of Tronnnission Lines 113
--
Further, most of the faults involve an arc. The arc is resistive in nature. The arc
resistance is a function of the sparkover distance S in feet. the wind veiocity u in mph
and time t in seconds and the current I in amperes, as already pointed out in Chapter 1.
The arc resistance is given by the well-known Warnn@on formula:
-
When we consider the arc resistance, the fault characteristic of the transmission line
gets modified from the straight line with a slope of tan-'(AIR) to an area as shown in
Figure 6.6.
Fault characteristic of the
line with arc resistance
-R
Figure 6.6 Fault characteristic of transmission line with fault resistance.
6.3 Simple Impedance Relay
6.3.1 Trip Law for Simple Impedance Relay Using Universal
Torque Equation
It is possible to synthesize many types of relays using the electromechanical structures.
We can write a generic torque equation for such a structure where there are torques
produced within the relay structure by
current at relay location
voltage at relay location
interaction between the above volCage and current (directional unit).
Individual torques may be made to act in such a way as to close the trip contact or
to oppose the closing of the trip contact. The torque which tends to close the trip contact,
is called the operating torqw, and the torque which tends to oppose the closing of the trip
contact, is called the restraining torque.

-
Consider the generic torque equation
T s k1llRl2 + k21VR2+ k31VRl[ I ECOS ( 8 - d + 41
where
T is the net torque on the actuating structure of the relay
klJIR12is the torque due to current fed to the relay current coil
k2(VR(Zis the torque due to voltage applied to the relay pressure coil
kSIVR(IIRJcos (0- Z) is the torque due to the directional unit
8 is the angle between voltage and current fed to the relay
z is the maximum torque angle for the directional unit '.:
k, is the torque due to spring, which can be neglected compared to the operating
torque when the relay is on the verge of operation
Let k, be positive, kzbe negative and kgbe equal to zero. Therefore, the relay will tri8 ;
if
k2IVRl2< kllI~Z
Further manipulation leads to
Now,
where JZ,,,J is the magnitude of the impedance seen by the relay.
Further, let = (Z,,,(be the impedance setting.
Thus, we can write
If Z 1 < Z then trip; else restrain
This is the trip law for the so-called simple tmpedance relay. We can, therefore, describe
the simple impedance relay as an over-current relay with voltage restraint.
6-3.2 Implementation of Simple Impedance Relay Using Balanced
Beam Structure
The simple impedance relay can be easily implemented using a balanced beam structure
as shown in Figure 6.7. It can be seen from the figure that the current coil exerts a torque

Dis:cnce Protection of Tra~:r~nirsionLiries 125
on the soft iron armature in 3uch a way that it :ends to close the rip contacts. The
voltage coil, on the other hand, tends to keep the trip contacts open, thus providing the
restraining torque. The controI spring keeps the contacts open when the relay is in
unenergized condition.
simple Qimpedance
relay
IR
Trip output
aa Softiron
armature
Restraining *torque * 2Spring-Operatingtorque
0--1 r-+--o
Restraining Voltage
quantity VR coil coil quantity
I
Figure 6.7 Balanced beam construction of simple impedance relay.
The operating torque is proportional to ( 1 ~ 1 ~and the restraining torque is propor-
tional to IVR1'. Thus, the relay operates if
hllIR1 > kz1VRI', where k1 and kz are proportionality constants.
Thus, the balanced beam structure implements the simple impedance relay.

126 F~~ndatne~~tnlsof Power System Protection
6.3.3 Performance of Simple Impedance Relay During Normal
Load Flow
A distance relay is fed with current and voltage at the relay location. Thus, it keeps on
monitoring the transmission llne all the time, whlch Includes the normal operating
conditions when load is being supplied. What is the Impedance seen by the relay under
such conditions? Does the relay tend to (mal)operate during such normal operating
conditions? These are some of the questions whlch need to be addressed.
The impedance seen by the relay during normal load flow will be as shown in
Figure 6.8 for the double-end-fed system. Fortunately, the impedance seen by the relay
under such a condition is quite large and falls outside the trip area of the relay operating
characteristics. Thus, the simple impedance relay is stable during normal operating
conditions.
load
Figure 6.8 Performance of simple impedance relay during normal load flow. 9 j
i
6.3.4 Effect of Arc Resistance on Reach of Simple Impedance Relay
:,
Consider an arcing fault, with a fault resistance of R,, at point C in the single line , i:
diagram of Figure 6.9. The impedance seen by the relay, lies on the boundary between the 5
.;trip and restraining regions, thus any arcing fault just beyond point C will not be
detected. , 4d
Therefore, the simple impedance relay under-reaches because of an arcing fault. The E
3
percentage under-reach is defined as the ratio of the distance by which the relay under- .,i:.A
reaches, to the reach se'tfing of the relay. With reference to Figure 6.9, the percentage ..?
under-reach can be seen to be 3
i

Distance Protection of Transmission Lines 127---
C,A .
I
Slrnpie impedance
relay
Arc~ngfault
X
Line fault characteristic
I BC
Percentage under-reach = -x 100%
A 6
Figure 6.9 Effect of fault resistance on reach of simple impedance relay
6.3.5 Directional Properly Exhibited by Simple lmpedance Relay
The reach of the simple impedance relay is independent of the phase angle between
L . voltage and current at the relay location. Thus, the relay does not possess directional
property. Its reach would extend equally in the forward as well as the reverse direction.
@ As shown in Figure 6.10,the first quadrant of the R-Xplane represents the forward faults
whereas the third quadrant represents the reverse faults.
Therefore, the simple impedance relay, by itself, will not be useful in situations where
selectivity between the forward and reverse faults has to be maintained. We can, however,
t
- i supervise it with the help of a directional element and get the desired selectivity.
6.3.6 Performance of Simple lmpedance Relay During Power Swing
When a power system is operating in steady state, all the rotor or machine angles are
i constant. Whenever there are sudden and large changes of power in the system, (say due
to outage of a major tie-line), the rotor angles undergo oscillations till the system reaches
a new stable state. This phenomenon is known as power swing. The frequency of
oscillations of the rotor angle during power swing is quite low, of the order of a few hertz,
' due to large inertias of the rotating masses involved.

128 Fundamentals of Power System Protect~on
Reverse t Forward
I I
Simple impedance
relay
Forward faults (First quadrant)
I
f > R
111
;r
.-u.
IV
r ~
Reverse faults (Third quadrant)
:.3:
V
Figure 6.10 Directional property of simple impedance relay
The impedance seen by the distance relay during power swing is of special interest
to the relaying engineer. It can be shown that, during power swing, the locus of the tip
of impedance seen by the relay passes, rather slowly, through the electrical centre of the
transmission system consisting of the series combination of the source impedance behind
the relay location, the transmission line impedance and the impedance of the source at
the remote end. This is shown in Figure 6.11.
Thus, at some point during the power swing, the apparent impedance enters the trip
region of the relay operating characteristic. Further, when it passes through the electrical
centre, it looks as if there is a metallic fault at the electrical centre of the transmission
system. This causes the relay to trip, putting the line out of service, adding to the
disturbance already present in the system. Therefore, tripping because of power swing
has to be more often blocked than unblocked.

Disrance Protecrion of Tror!smission Lines 129
C = Electrical centre
Figure 6.11 Effect of power swing on simple impedance relay.
It may be mentioned here that the larger the area occupied by the relay on the R.X
diagram, the more prone it is to maloperation due to power swing. Since the simple
impedance relay occupies substantial area in all the four quadrants of the R-X plane, it
is very much vulnerable to maloperation on power swing.
6.4 Reactance Relay
6.4.1 Trip Law for Reactance Relay Using Universal Torque
Equation
Again consider the universal torque equation:
If we set k2 equal to zero, make kl positive (i.e. cause the current to provide tripping
torque) and make k3negative (i.e. cause the directional torque to oppose tripping), noting
that k4 can be neglected when the relay is on the verge of operation, we get the following
-trip law:
1If kllIRl > k3(VR(I R1 cos (8- 7) then trip; else restrain 1
which can be written as:
k31vRl1 1 ~ 1 cos (8- 7) < k111~12

130 Frrrida~~re~~talsof Power Sysren~Prorecriorr
--
and can be simplified as:
However, 1 VR//(IRI = IZ,,,,I, the apparent impedance seen by the relay.
Therefore,
hIZ,,nJCOS ce - T) < -
K3
If we set the MTA of the directional element to be 90°, and let (kl/k,) = X,,, we get ,., ~.,
IZ,,,/ cos (6'- 90") < Xn
Since JZ,,,,I cos (9 - 90") = JZ,,,,I sin 0 = JX,,,, 1, which is the reactive part of the
impedance seen by the relay, we finally get the trip law as:
If X 1 < X 1 then trip; else restrain
The relay is thus sensitive only to the reactive part of the impedance seen, and trips if
the reactive part is less than a particular set value X,,.Hence, such a relay is called a :14
reactance relay. The operating characteristic of the relay on the R-X plane is a:~traight i
line with intercept of X, on the reactance axis. The entire area below this straight line :.'4
represents the trip region. Thus, the area occupied is too large. This is shown in " r;
Figure 6.12. ~~
, i
,
t
." 4
1I
1
-4
characteristic
Restrain
/ / / / / / / / / , / / / / / / / /,,/,
X"
< t R
1Trip Trip
Figure 6.12 Characteristic of reactance relay.
.-~
~ ~ - -- -- - .~

Distante Prorecrio~~07Tra~rsrn~ssionLbres 121
6.4.2 lmplernenta?ionof Reactance Relay Using the induction Cup
Structure
The implementation of the reactance relay using the four-pole induction cup structure is
Trio
Polarizing
current coil
Restra~ning
Pressure mil phase
Figure 6.13 Implementation of reactance relay using the four-poleinduction cup structure.
The current through one of the coils is shifted in phase so that the torque
proportional to I2is produced by the interaction of the fluxes created by the two currents.
The current through the pressure coiI is made to flow nearly in phase with the pressure
coil voltage by connecting a resistance whose value is much large compared to the
pressure coil inductance. This makes the phase angle of pressure coil nearly equal to zero,
making the maximum torque angle r equal to 90" (since MTA = 90" - phase angle of
pressure coil).
The four-pole induction cup structure has a high torque to weight ratio and is,
therefore, a very sensitive measuring unit.
I
, 6.4.3 Performance of Reactance Relay During Normal Load Flow
i
The reactance relay occupies all the area below the straight lineX = X, on the R-X plane.
The impedance seen by the relay during normal load flow conditions (double-end-fed
system) unfortunately falls in the trip region of the reactance relay operating
l 1

132 Fundarnenrals of Power Sysrem Prorecrion
characteristic as shown in Figure 6.14.Thus, a reactance relay will operate during normal .
load flow. This is clearly unacceptable. Therefore, the reactance relay cannot be used by
itself for protection of the transmission line but needs to be supewised from another relay
to prevent its operation on load. A question may arise in the readers' mind at this stage.
Why to bother about a relay which cannot even restrain on load? The answer lies in the
superior performance of the relay in the face of fault resistance. This is discussed in
Section 6.4.4.
Figure 6.14 Reactance relay operates during normal load flow.
i
6.4.4 Effect of Arc Resistance on Reach of Reactance Relay 4
a
Figure 6.15 shows a line section A-B being protected using a reactance relay. Let there
be a fault at the end of the protected line section, at point B, with a resistance equal to
Ii1
B-C. It can be seen that the tip of the impedance seen phasor AC, still remains within
the trip region. Thus, the reach of the reactance relay remains unaffected in spite of the I
presence of arc resistance. This is only to be expected, as the relay measures only the
reactive part of the ratio of phasors V and I. 1i
..
Restrain
7 > 1 1 , , 1 1 ,
Setting = X,, f Reactance seen
<
A
Trip
Impedance seen
Trip
V
Figure 6.15 Effect of arc resistance on reach of reactance relay.

Distance Prorection of Transmission Lines 133
The aoliity of the reactance relay io respond correctly in the presence of fault
resistance is a very useful trait and accounts for the popularity of the reiay, in spite of
the fact that it undesirabiy trips during normal load flow. The reactance relay finds wide
applications in fault locators where the exact location of the fault can be found out in the
presence o f fault resistance.
6.4.5 Directional Property Exhibited by Reactance Relay
As mentioned previously, the first quadrant represents the forward faults whereas the
third quadrant represents the reverse faults. Since the trip characteristic of the reactance
relay occupies areas in both these quadrants, it does not exhibit any directional property
Thus a reactance relay which is set to protect the line section AB, as shown in
Figure 6.16, in the forward direction also responds in the reverse direction for an
unlimited distance. This again, is not a desirable feature. Therefore, we should use the
reactance relay in conjunction with a directional relay or another distance relay having
the directional feature like the h010 relay.
Reverse c -4Forward
Restrain Restrain
? / / / / / / / I I I I I / J / / / f / / ' / /
I/ Forward faults
(First quadrant)
Reverse**" faults (Third quadrant)
(Reverse)
Trip Trip
Figure 6.16 Directional property o f reactance relay.

134 Fur~darnenrulsof Power System Protection -
6.4.6 Performance of Reactance Relay During Power Swing
The reactance relay occupies such a large area on the R-X plane that it operates even
during normal load flow. As shown in Figure 6.17, during power swing, the tip of the
impedance-seen phasor approaches the electrical centre of the system. Even before this
happens, it is already in the trip region of the reactance relay characteristic. Therefore,
the reactance relay operates on power swing as well. Again,this is not a desirable trait.
A
Restrain
C = Electrical centre
Locus of power
swing
Figure 6.17 Performance of reactance relay during power swing. :i
, .
i
6.5 Mho Relay
1
6.5.1 Trip Law for Mho Relay Using Universal Torque Equation I
Once again, consider the universal torque equation:
T = k,l1~1~+ + k31VRlJI~lcos ( 0 - 7) + k4
If we set k, = 0,make k2 negative (i.e. make the voltage provide restraining torque) and
make k3 positive (i.e. make the directional element produce tripping torque), since k4 is
negligible compared to the operating and restraining torques, the relay will trip if
~SIVRI(IR(COS (0 - 7) > k21v~7R)~
The relay can thus be described as directional relay with voltage restraint. The torque
equation can be manipulated as
.I
~ Z ~ V R I ~< ~ ~ ( V R IIIRI ( 0 - 7) . - iI
.i
-- .~ - ~ ~
.~-. ~ ~~.~

Dfssnce Protection of i'ransrnission Lines 135
Here IVRl/lIEJis the impedance seen by the relay Z 1 and we can set the ratio
kl/kz = Z,,the setting impedance. Now, the trip law can be written as
1If IZ,,,, J i12, / cos (8 - z) then trip; else restrain 1
where 9 is the phase angle between the voltage and current fed to the relay. The relay
characteristic is as shown in Figure 6.18.
X
if 2, < 2, cos (0 -c) then trip: else restrain
I Figure 6.18 Mho relay characteristic.
a 6.5.2 implementation of Mho Relay Using induction Cup Structure
Figure 6.19 shows a four-pole induction cup structure. The flux due to operating voltage
coil interacts with the induced current due to the current coil to produce the operating
torque proportional to cos (9 - z). The restraining torque is produced because of the
fluxes created by the operating and polarizing voltage coils. The resistor R and capacitor
C in the voltage coil circuit enable adjustment of MTA to any desired value.
The advantage of the four-pole induction cup structure is its increased sensitivity due
to high torque to weight ratio, over the simple induction disc structure.
?.
6.5.3 Performance of Mho Relay During Normal Load Flow
It can be seen from Figure 6.20 that the impedance seen by the relay during normal
load (double-end-fed system) is well outside the trip region of the characteristic. Thus, the
relay is stable during load conditions.

136 F~olda~~~enralsof Power Svsrrnt Prurecrion
Trip
A I R
C. .
Polarizng
voltage coli
IR
Ld/Induction cup
XL
Polarizing
voltage coil
Figure 6.19 Implementation of mho relay using the four-pole induction cup structure.
, if 2, < 2, cos (0 - T) then trip:
Restrain
on = Z"
08 = 2,
else restrain
I '.'.Normal load
Figure 6.20 Performance of mho relay on load.
6.5.4 Effect of Arc Resistance on Mho Relay Reach
Cons~deran arcing fault at point B towards the end of the protected line section OA as
shown in Figure 6.21. Let the fault resistance be BC. The impedance seen by the relay
considering the fault resistance just lies on the verge of the trip region. Any fault beyond
point B will cause the relay to restrain. Thus, effectively, the reach of the relay has come
down from OA to OB. The absolute under-reach is AB. The percentage under-reach is
(ABIOA) x 100%.

Distance Protecrio!~of Tra~umissionLirlrs 137
X I
Under-reach = AB
Percentage under-reach
<
Figure 6.21 Effect of arc resistance on reach of mho relay.
Recall that the simple impedance relay also suffers from under-reach due to fault
resistance. If we compare the under-reach of the two relays for the same fault resistance
then we find that the percentage under-reach of the mho relay is slightly more than that
of the simple impedance relay.
6.5.5 Directional Property Exhibited by Mho Relay
Figure 6.22 shows the characteristic of a directional relay on the R-X plane. It is seen to
be a straight line at right angle to the MTA line. The straight line can be considered as
a circle with infinite radius. A mho relay is a directional relay with voltage restraint. The
addition of voltage restraint to directional relay causes the radius to take a finite value
and collapse intothe mho circle with diameter equal to 2, as shown in Figure 6.23. Thus,
the mho relay very much possesses the directional property which makes it so useful.
X
, I
!
Figure 6.22 Characteristic of directional relay on the R-Xplane.

138 F~rndarnenmlso f Power Svrrem Protection
?I,'I Figure 6.23 Directional property of rnho relay. w .,' !
,,d, .:
1::;
i
kl
., ,:i
;'. It 6.5.6 Performance of Mho Relav Durina Power Swina ., ,.j. - - !
1
The mho relay bccupies a much smaller area on the R-X plane. To that extent, it is less 1
1
immune to power swing. However, when the swing is very large, the impedance seen
4 enters the mho circle and the relay trips, as shown in Figure 6.24. Special relays known
as blinders can be used to prevent operation on power swing.
Blocking and tripping schemes are discussed in Appendix B. *v-"
i
on = z, 1
AB = Zs,
OD ZSA iiC = Electrical centre 1
Restrain
+Figure 6 - - ~
I Locus of power swing
-24 Performance of mho relay during power swing.

Df~tanceProtec!lorl of Transrnrss~o~~Lines 139
6.6 Comparison Behveen Disfunee Relays
It is instructive to compare the three distance relays as shown in Table 6.2.
Table 6.2 Comparison of distance relays
Simple impedance Reactance relay Mho relay
relay (5'.T.R.)
Operating Current Current Directional element,
quantity MTA = .r
Restraining Voltage Directional element, Voltage
quantity MTA = 90"
Directional No No Yes
property
Performance Restrains Trips Restrains
on load
Effect of fault Under-reaches Reach unaffected Under-reaches
resistance more than S.I.R.
Area occupied on Moderate Vefy large Smallest
the R-X plane
Effectofpower Maloperates Maloperates Maloperates, though
swing effect is less than S.1.R
We can see from Table 6.2 that it is not possible to use the reactance relay for
transmission line protection on a standalone basis. It has to be used in conjunction with
a directional or a mho element. The mho relay is much better on most of the counts. One
remarkable property of reactance relay is its immunity to fault resistance. However, it
lacks stability on load and does not have directional property. Considering pros and cons,
the mho relay is found to be a much better fit for long lines which are likely to be
subjected to frequent power swings, whereas the reactance relay (in conjunction with
mho) is preferred for short lines.
6.7 Distance Protection of a Three-phase Line
Up till now we have been tacitly assuming the transmission line to be a single-phase line.
However, in practice, transmission lines are always three-phase in nature. A three-phase
line is subject to phase faults as well as ground faults. The questions that naturally arise
are:
1. How are we going to provide protection against all the ten shunt faults?
2. In what way the CT currents and PT voltage will have to be processed?
3. Can a single distance measurement unit look after all the phase faults as well as
ground faults? If no, how many aistance measurement units will be required for
catering to all the ten shunt faults?
4. What will be the setting of the distance measuring units?
5. Whether to measure positive sequence impedance or negative sequence impedance
or zero sequence impedance? See Figure 6.25.

140 Furldatrte,ztals of Power Svstertz Pmtrcrior~
How to combine?
I U 1
How many un~tsrequired?
SeNng = ?
i
14
,?
. ,,
, ,~
, ,, ,
Figure 6.25 The problem of providing distance protection to a three-phase line.
t
..
It turns out that we have to provide separate protection for phase faults and ground
faults. Phase faults associated with one pair of phases are catered to by a singledistance-
measuring unit. Thus, three numbers of phase fault-measuring units can cater for all the . ,
sevendphase faults, namely, a-b, a-b-g, b c , b-c-g, c-a, c-a-g, a-b-C. ..~
Each of the three ground faults are catered to by a separate ground fault-measuring
distance unit. Thus, three numbers of ground fault-measuring units can cater for all the
three ground faults.
Therefore, a total of six numbers of measuring units are required for protection
against all the ten shunt faults.
Table 6.3 lists the presence of sequence components, in voltage and current, during
various faults wherein it can be seen that positive sequence component is the only
component which is present during all faults. Thus, it would be prudent to measure
positive sequence impedance between the relay location and the fault so as to cater for
every fault.
Table 6.3 Presence of sequence components in various faults
p~
---Fault Positive sequence Negative sequence Zero sequence
-
L-G Yes Yes Yes
L-L Yes Yes No
L-L-G Yes Yes Yes
L-L-L Yes No No

Distance Protection of Transmission Lines 141
5.7.1 Phase Faults
Let us consider a phase b to phase c fault as shown in Figure 6.26. What combination of
voltage and current when fed to a distance-neasuring unit will measure the positive
sequence impedance between the relay location and the fault point?
This question can be answered if we analyze the problem with the help of symmetrical
components. A phase-to-phase fault can be represented by a parallel combination of the
positive and negative sequence networks at the fault point. The zero-sequence network
remains open circuited as shown in Figure 6.26.
CB
---I I
I rn Va
Three-phase line 1.P . " ?
I I
la
1
I I
I'! !I" 1:
I I I I
I I
I I metallic fault8 I
I rn VC .r t
Positive sequence
network
Negative
seauence network
Zero sequence
1 network
z, = Zi
.. n
+ Relay location Fault location
Vaz
I
Figure 6.26 Phase a sequence network connection for b-c phase fault.

7i'I
il, 1
!/ !
:,
142 Fiazdarnentals of Power System Protection
t! ,Y
!I ,'
Writing KVL around the loop in Figure 6.26, we get
Val - I a ~ z l+ Ia&l - Va2 = 0
, ,
or Val.-Va2 = (Id - Ia2)21
Thus, the ratio of difference of positive and negative sequence voltages and currents gives
the desired value of positive sequence impedance between the relay location and the fault
point. However, the sequence components of voltage and current are not readily available
at the relay location. Instead, the line voltages and currents are readily available. Let us
see if we can manipulate the line voltages and currents to get the desired sequence
components.
We have
...
,.:. .
from which we get ,
" ,,:',
,:: ,!
Vb- Vc = (aZ- a)Val . . .(a?-a2)Vnz
--'i-= (a2- a)V,, - (a - a)V.z
= (a2- a)(V,, - Va2)
Therefore, . .
v, - v c
... .i.
V,,-V.z= 2 :!a - a ..... ,'.1Similarly it can be proved that 1
~*,
.I
1.1 - 1.2 =
1
Therefore,
Thus, a distance measuring unit with voltage of (Vb- V, = Vbe)and current of (Ib-I,)
will measure positive sequence impedance up to fault point Z , , in.case of phase b-to*
faults. Similarly, we shall need two more units with inputs of Vab,(Ia - Ib) and V,,
(I, - I,) to cater for phase. a-to-b and phase c-to-&.faults. The distance measuring units
which cater for phase a-b, b-c and c-a faults are called phase fault units.
i
6.7.2 Ground Faults
A ground fault is represented by series connection of the positive, negative and the zero
sequence equivalent circuit. See Figure 6.27.
Applying KVL around the loop formed by the series connection of the three sequence
networks, we get
V.0 + Val + Vaz = Ialzl + Ia2Z1 + IaoZo

Distance Protection of' Transmission Lines 1-13
-
Positive sequence
nehvork
r "
Negative
sequence network
Zero sequence
nehvork
+ I
v,, Relay Fault locatlon
location
+ I Relay
Vaz location
I 1
. .
Figure 6.27 Phase a sequence network connections for a-g fault.
-~ .,.. ....
However, noting that Vao+ Val+ Vaz= V, and adding and subtracting (ZaoZ1)on the
right-hand side, we get
v, = Za1Z1+ ZazZ1 + I,oZ1 - IaOZ1 + zaozo
= (Ia1+ IaZ + Iao)Z1 + (ZO- Z1)Ia0
= I,Z1 + (20- Zl)laO
or

144 Fundamentals of Power System Protecrion
However,
L o = 'a + I b3 + Ic . Let us also write: I, + Ib + I, = I,,,
Therefore, we have
Hence.
Ire,
I,, = -
3
, where I,, is the residual current.
Finally, we get the desired impedance as the ratio of:
..
In the above equation Z1 appears on both sides and the expression appears a bit mixed ~::,
!
up. However, in actual practice, there is a definite relationship between Zo and Z1. For .I,, j~
three-phase transmission lines Z, is 2.5 to 3 times Z1. The exact relationship depends , :
upon the geometry of the phase conductors and the placement of earth conductors. Let .:i
us assume that Zo= 3Z1. Then, the above equation simplifies to:
-- v a
; where K =
zo - Zl
Ia + KIres 321
4Thus, the phase current has to be compensated with a fraction of the residual cu'rrent , :
I,,. The factor K is known as the residual current compensation factor or zero-sequence - ' ?:
current compensation factor.
Therefore, three numbers of distance measuring units with inputs of
I,.t".i
[va,(1, + KIres)l,[Vb,(Ia + KIr,)I, and [V,, (I, + KIre,)]
will be needed for catering to all the three single line to ground faults. These units will
be called ground fault units.
j
5
1
6.7.3 Complete Protection of a Three-phase Line /
Further it can be shown that the phase fault units also cater for corresponding double
line-to-ground faults (L-L-Gfaults). In the case of a balanced three-phase fault, again, all
the phase fault units respond. The proof of this is left to the reader. i!
Thus, in all, six distance measuring units each set at Z,, the positive-sequence
impedance of the line section, are sufficient for complete protection against all the ten
shunt faults, as shown in Figure 6.28. 1i

6.8 Reasons for Inaccuracy of Distance Relay Reach
Di.rrii~rce?ro:ecrion of Tin~ra~iir.ri~,~z l d j
Trip
f3-
Setting = Z1 ' b c v a ~
-vm-
Setting = Zl
V b C
[b -/c
Ideally we would have liked to set the reach of the distance relay to 100% of the line
section. However, it is not possible to get the exact reach of 100% in practice. There is
=--
OR gate
Setting = Z,
*< z v c ,
C / , - I ,
Setting = Z1
*< Z v,
C (8 + Klres
Setting = Z,
C
v b
4 C lb + Klrer
Setting = Z,
* v c
4 C I, + KI,,
Figure 6.28 Complete protection of a three-phase line.

146 F~riidai?~entalsof Power System P~oteciion
always certain amount of uncertainty and ambiguity about the actual reach. Various
contributing factors for this ambiguity in reach are:
Inaccuracy in CT and PT ratios.
.Ambiguity about line parameters (line parameters are seldom measured, they are
calculated from line data).
Variation of line parameters with atmospheric conditions.
DC offset in fault current.
Transient response of capacitive voltage transformers (CVT).
Out of these factors DC offset and CVT transient response cause over-reach. Other
factors may cause error on either side. Thus, there is always a possibility of over-reach.
If the reach of distance relay is adjusted to 100% then over-reach will cause loss of
selectivity with the distance protection of the next section. This cannot be tolerated in the
case of EHV lines. Thus, it is a usual practice to set the reach of distance protectio
about 80 to 90% of the line section. This leaves 20% to 10% of line without prim%protection. Therefore, a comprehensive scheme of distance protection has evolved,
providing primary protection to the line section under consideration as well as back-up
to the next line section. This is discussed in Section 6.9.
6.9 Three-stepped Distance Protection
6.9.1 First Step
As discussed in Section 6.8, it is not advisable to set the reach of distance protection to
100%. The first step of distance protection is, therefore, set to reach up to 80 to 90% of
the length of the line section. This is an instantaneous protection, i.e. there is no
intentional time delay.
6.9.2 Second Step
The second step is required in order to provide primary protection to the remaining
to 10% of the line, which is left out of the first step. In addition, it is set to cover up to
50% of the next line section. The motivation behind this extended reach is: (i) it should
provide some back-up to the next line section including the bus; (ii) in the event of
maximum under-reach it should still be able to cover the bus faults at the bus between
the two lines. The operating time of this step has to be delayed so as to be selective with
step I. Thus:
Operating time of step I1 = Operating time of step I + Selective time interval
where
Selective time interval = CB operating time + Relay over-travel time
When there are more than one adjoining lines, the second step should extend up to
50% into the shortest adjoining line. If it is set to reach up to 50% of longest adjoining
line, as shown in Figure 6.29(d), then there is a loss of selectivity with second step of

Disla~~ceProtecrrurr of T,ur~sn~isslo~~Lines 117
shortest adjoining line. In Figure 6.29(d) faults in the region becween points Dl and D2
are in the second step of prlmary protection at bus B, provided by relay RB, as well as
in the second step of re!ay RA at bus A. Therefore, there is loss of selectivity between
second steps of distance relays RA and RB.Hence the second step of the distance relay is
set to reach up to 50% into the shortest adjoining line.
6.9.3 Third Step
The third step is provided with an intention to give full back-up to the adjoining line
section. It covers the line section under consideration, 100%of the next line section and
reaches further into the system. The motivation behind the extended reach of this step
is to give full back-up to the next line section in spite of the maximum under-reach of the
third step.
The three-stepped distance protection is shown in Figures 6.29(a), (b), (c), and (d).
Note that in Figure 6.29(c), there is an additional distance measuring unit whose
reach is beyond the third zone reach. The operating time of this unit is instantaneous.
This unit is known as a fault detector or starter unit.
Tl 'Operat~ngtime I
I
4 J
I I
I
" M - I I !f i
instantaneous I B C :
I Adjoining line
1 (next line)
consideration I
(0.8 to ~ . ~ ) Z A BZas + 0.5Z~c ZAB+ 1.2Z~c
Figure 6.29(a) Three-stepped distance protection.
Figure 6.29(b) Three-stepped distance protection simplified representation.

"1.. 1qu runaarnenrars OJ rower bysfem ~rorecfron
qi, -
-.
$1
5. Zt Zz Z3 FD
I , , ,
L F
A h
if!,, D------'-------.--.L---.--------->--------.----
Instantaneous B
) j
C
I ! 1 fiLin! under Adjoining line
I Yconsideration (next line)
-R
of;
I'
,'.
Figure 6.29(c) Three-stepped distance protection using rnho relays.
. '
B y-?Dl ,,D2
AB-Line under consideration RB
BC-Longest adjoining line
B-hortest adjoining line
Figure 699(d) Loss of selectivity of second zone of RA with second zone of R ~ .
I
J. 1 # I
IT1"IL 9
T lnstantaneous
IB , J. I i, 5
I ,
I I
8 I .l.
Ic

Distance Prorecrion of Transmission Liner 149
!5
3a,!.
3
0
Table 6.3 summarizes the philosophy of three-stepped distance protection.
Table 6.3 Philosophy of the three-stepped distance protection
Purpose Reach Operating time Remarks
First Primary 80 to 90% Instantaneous, Avoids loss of selectivity
step protection of line section i.e. no intentional with protection of next
time delay zone in case of maximum
3'instantaneoua
Second Primary 100%of line under Tinstantaneouai
step protection of consideration Selective time
remaining + 50% of shortest interval= TI
20 to 10% adjoining line
Third Back-up 100% of line under T, + Selective
step protection consideration time interval= T2
+ 100% of longest
adjoining line + 10
to 20% extra
over-reach
Provides primary
protection to part of line
left out of first step and
provides some back-up to
the bus and the next line.
Shortest adjoining line
is to be considered.
If the longest adjoining
line is considered, then it
causes loss of selectivity.
Idea is to provide full
back-up to the adjoining
line, even in case of
maximum under-reach.
Longest adjoining line
has to be considered. If
shortest adjoining line is
considered then the longer
adjoining line will not get
back-up protection.
6.10 Trip Contact Configuration for the Three-stepped
Distance Protection
The trip contact circuit which implements the three-stepped distance protection scheme
is shown in Figure 6.30. The fault detector initiates the timer in case it detects a fault
I==z1
7-
CB Timer
Trip cn~l T,,
3
Trip battery
Fo = NO contact of fault detector, Z, = NO contact of step I measuring unit, Z2 = NO contact of Step II
measuring unit, T, = NO contact closed by timer after time T, after closure of Fo, Z3= NO contact of step Ill.
T2 = NO contact closed by timer after time T2 after dosure of Fo
Figure 6.30 Trip contact circuit of the three-stepped distance scheme.

150 F[iiz~lame~~talsof Power Systenz Pmtection
within its reach setting. The timer issues two outputs after it gets energized. The first
output is after an elapse of time T1and the second after time Tz. Both these outputs are
in the form of closure of a normally open (NO) contact.
In case the fault is within the first step of distance protection, the trip coil gets
energized through the Z, and FD contacts. Depending upon whether the fault is within
the second or the third step, the trip coil gets energized through the series combination
of either Zz,Tl or Z3, T2. I
6.11 Three-stepped Protection of Three-phase Line i
Against A~I-Ten Shunt Faults
We have already seen that three numbers of phase fault measuring units, which are fed i
with delta voltages and delta currents, and three numbers of ground fault measuring
units, which are fed with phase voltages and phase currents compensated with residual
current, are required for complete protection of a three-phase line against all the ten
shunt faults. Thus in all six measuring units are required.
The setting of each measuring unit is based on the positive sequence impedance of the
line.
Now, in order to generate three zones, 3 x 6 = 18, measuring units will be required.
This is a rather costly affair! Therefore, schemes, which save upon the number of
measuring units, have been devised.
One popular idea, known as the switched distance scheme uses only three measuring
units, but switches the inputs to them with the help of a fault detector. This brings down
the number of measuring units from 18 to 3 x 3 or 9. The interested reader should look
up literature on protective relaying to learn more about these schemes. ",.
1
1
1
6.12 Impedance Seen from Relay Side
Up till now we have assumed that the CT ratio as well as the PT ratio is 1:1. In practice,
however, the CT ratio as well as the PT ratio are far from unity. In such a situation, what
is the impedance seen from the relay side, i.e. from the CT and PT secondary sides?
It can be seen from Figure 6.31 that:
8 I
VLv, = -PTR
I' . where PTR = PT ratio, CTR = CT ratioand IR = -CTR '
VLbut -= Z, = actual line side impedance
1'
Therefore, .
F:zqq
where Zr is the fault impedance as seen from the line side.

Disrance Protection of i ransmisslon Lines 151-
Reach = Z,., Y
Internal fault j B
I
I
I
Model of the faulted tmnsrnission line
Figure 6.31 Impedance seen from the relay side.
6.13 Three-stepped Protection of Double-End-Fed Lines
Figure 6.32 shows a double-end-fed line AB. There are sources at both the ends.
Therefore, there is an in-feed of fault power from both sides. Hence, circuit breakers and
three-stepped distance schemes will have to be provided at both the ends.
Zl z2
$. 4
I I
I I ' I
+20% It-- 60% 420% y I
I
I
, I J. tInstantaneous
,
I I T2 ,
i I ,,1 I # ' ! r1 I :& A . tI D t A
I? 0 C
Instantaneous
Line under
I cons~demtion
I +
v + Zl
4 z2
Figure 6.32 Only 60% of the line gets high speed distance protection.

152 Fundamentals of Power Systenr Protection
The time versus reach characteristics for three-stepped distance schemes at both the
ends are shown in Figure 6 32. It can be easily seen that only 60% of the line gets h~gh
speed distance protection. The remainder 40% of the line length falls in the step I1 which
is a delayed one. This is clearly not a happy situation. We need to improve upon the
operating time for rest of the 40% of the line.
A fault in the end 20% of the line falls within the first zone of the distance relays
installed at the nearest end and there is no ambiguity about its location. The same fault
when seen from the far end because of the uncertainties involved could well be beyond
the bus. Thus, if we could, somehow convey the information that the fault is within the
protected zone to the far end, and then the tripping from the remote end need not wait
till time TIof the second step.
This principle is made use of in the carrier-aided distance schemes discussed in
Chapter 7.
Review Questions
1. What are the drawbacks, if any, of over-current relays?
2. Why are over-current relays not used for primary protection of EHV lines in spite rof the fact that instantaneous over-current relays exist?
i
3. How is the transmission line modelled for the sake of distance relaying? !
4. Arc resistance is a function of spark-over distance, wind velocity and time. I
Explain. +'"2 1
5. What do you mean by a metallic fault? .+
6. How is it different from an arcing fault? +
7. What is the effect of fault resistance on the reach of various distance relays?
Which relay is the most affected and which the least affected?
.=
8. What do you mean by power swing?
4
9. Will an over-current relay be affected by power swing?
10. How do different distance relays perform with respect to their behaviour on load,
effect of arc resistance on the reach and response to power swing?
11. Prove that a-6 distance measuring unit fed with (V,- Vb)and (I,- Ib) responds
a II
1
correctly to a-6-g faults as well as a-6-c faults. i
12. Why is residual current compensation required in case of ground fault distance
measuring unit?
i3
1
13. Explain the need for a three-stepped distance protection of a transmission line.
14. How many distance measuring units will be required for the complete three-
stepped protection of a transmission line section in case of (i) a singly-fed-
systems and (ii) a double-end-fed system?
15. The impedance seen from the relay side in a distance relay is 10 ohms. Given that
the CT ratio is 1000:1 and the PT ratio is 100,000 :110, determine the actual
impedance. Given that the llne has a resistance of 1 milliohm per km and a
reactance of 20 milliohm per km, find the distance to fault. Assume single-phase
line.

7.1 Need for Carrier-aided Protection
The main aim of the electrical power system is to maintain uninterrupted supply of
electricity to consumers. Electrical faults, however, cause interruption to the supply
When a fault takes place it is detected by protective relays and the fault current is
interrupted by the circuit breaker. The maintenance personnel must then rush to the
fault location, rectify the fault, and restore the supply This applies to permanent faults.
However, there is statistical evidence, as shown in Table 7.1, that about 80% of faults
are not permanent but are transient. These faults are caused by breakdown of air
surrounding the insulator. These faults can disappear by themselves, if the supply is
briefly interrupted and the arc-path is allowed to de-ionize.
Table 7.1 Fault statistics
Type of fault Pmbabclity
Transient 80%
Semi-permanent 10%
Permanent 10%
Thus, whenever a fault takes place, we can tentatively assume that a transient fault has
interrupted the supply We then wait for a short while before switchingon the circuitbreaker.
This is known as reclosure. The reclosure can be carried out manually or automatically
If the fault was indeed a transient one and the interruption was of a duration greater
than the de-ionization time, then the reclosure would be successful, that is, there would
be no recurrence of the fault. The typical de-ionization times for various system voltages
are listed in Table 7.2.
Table 7.2 Typical de-ionization times
System voltage Typical de-ionization trme
66 kV 0.10 s
132 kV 0.17 s
220 kV 0.28 s
400 k V 0.50 s

154 F~ittdut~let~talsof Power Systenz Protection
If the fault is a permanent one, reclosure will be unsuccessful, i.e. the protective relay
would immediately cause the circuit breaker to trip. Thus, in case of a transient fault,
reclosure helps in keeping the downtime to a minimum and in increasing the availability :
of supply. Reclosure has different implications for low/medium voltage (LV/MV)and high
or extra high voltage (HVIEHV) systems.
In low and medium voltage systems, a maximum of three consecutive reclosures are
allowed. If the fault persists even after the third reclosure, i.e even when the third
reclosure fails, then the circuit breaker is locked out and no more reclosures are allowed.
The multiple reclosures in LV and MV systems help in burning out the object responsible
for the fault, say, a tree branch, and thus in clearing out the fault.
Only one reclosure is allowed in HV/EHV systems because reclosure imposes arduous
duty on the circuit breakers and other elements of the power system as the fault MVA
is very large.
In HV/EHV systems, reclosure, if done sufficiently fast, helps in improving the
, ,-stability of the system. This is so because as soon as there is an interruption in thei: ,
: system, the rotor angles of various generators start drifting apart and if they drift apart
', beyond a critical angle, the system loses stability. If, however, the supply'isrestored before
i, .this critical time elapses, the system can pull together and remain stable.
Since HVIEHV lines are generally tie lines, there is presence of source at both the
ends. Thus, in order for the transient fault arc to be quickly quenched, the line must be
instantaneously and simultaneously tripped from both ends, before a reclosure can be
attempted.
,.-.
The three-stepped distance protection for the entire line length does not meet the
requirement of instantaneous and simultaneous tripping from both ends. Only about 60%
of the length in the middle of the line gets high speed protection from 60th ends. For
X
i
about 20% of line length, near each end of the line, i.e. a total of 40% of i n e length, the
!!
protection is instantaneous from the local end but is delayed from the rekote end. This
is shown in Figure 7.1. Thus, in order to be able to implement auto-recl~sure,we need
to augment the distance protection so that instantaneous tripping from' both ends for
100% of the line length becomes possible.
Carrier-based schemes help us in achieving this objective.
Figure 7.1 Only 60% of line length in the middle gets high speed protection from both ends.
Delayed z2
A protection from
end A
+'20% *60% __j: 20% :$-I I
I
J t
I Tz
I
I Tl
I i,.
B
t C
Line under
v
consideration

Carrier-alded Protect~onof Transrn~ss~onLznes 155
7.2 Vari~usOptions for a Carrier
Protective relays process information contained in the voltage and current at the local
end. The relay, only indirectly infers about the conditions at the remote end through these
signals. As the fault distance increases, the picture becomes more and more fuzzy. Hence,
there is always an ambiguity about the exact location of a remote fault. It becomes
impossible to distinguish between a fault just beyond the remote bus and one just ahead
of it. However, there is no ambiguity about the same fault from the end nearest to the
fault because as the fault moves from just beyond the bus to just ahead of it, there is an
almost 180 degrees change in the phase of current at the nearest end. Thus, the nearest
end has the clear-cut informat~onwhich is so difficult to extract using power, frequency,
current and voltage at the remote end. If we could, somehow pass on this small amount
of information from one end to the other, it would enhance the quality of decision making
at both the ends. We, therefore, need some carrier to carry this information. Various
attributes of an ideal carrier channel can be listed as follows:
, .
i'
: Delay involved in the communication should be small compared to the time period
i *
of the system frequency. At 50 Hz, the delay should be much less than
, ,. 20 milliseconds.
Since only a small amount of information is to be passed, the carrier channel need
not have very high bandwidth for protection purposes.
Faults on the power system should not adversely affect the functioning of the
carrier channel.
I Carrier channel should be under full control of the utility company.
I
t
The carrier equipment, such as carrier transmitter and receiver, should be
protected from the high potential of the EHV line.
I
I The carrier channel should be economical.
1 Various available options for a carrier signal are listed, along with their salient
features, in Table 7.3.
I 7.3 Coupling and Trapping the Carrier into the Desired
i Line Section
The power transmission line operates at very high voltage levels of the order of hundreds
of kilovolts. The carrier signalling equipment, viz. the carrier current transmitter and the
carrier current receiver, operate at a much lower voltage. Therefore, we need a method
of coupling the two so that neither the high voltage line gets shorted through the carrier
equipment nor does the signalling equipment get damaged due to the extra-high voltages
of the power line. Figure 7.2 shows one such arrangement for coupling the carrier on a
line-to-ground basis. Line traps which confine the carrier signal to the desired line section-
are also shown.

156 F~inda~?le~~tolsof Power System Prorecrion
..
Table 7.3 Various possible carriers of information for relaying purposes
Leased telephone line rrom Running cost is very high. Maintenance is a problem and
the telephone service guarantee of quality of service may be difficult to obtain.
Terrestrial microwave Frequency range is between 3 and 30 GHz. The range of
communication channel communication is line of sight. A large number of antenna
(either owned by the towers are required. Therefore, initial investment and main-
utility or leased) tenance cost are both very high. Provides very large bandwidth,
which may be shared with other data co~unicationservices.
Satellite communication Frequency range is between 3 and 30 GHz. Propagation
using VSAT terminals delays involved are of the order of (2)(36000)kmi(3)(10)~krru's
using geostationary = 240 ms i.e. 12cycles (50Hz basis) and this is not permissible,
satellite at 36,000 km for real-time power system protection. Large bandwidth is
available.
Power line carrier Most economical, since power line conductor doubles as the,
communication physical medium for carrying the carrier signal. The carrier
signal is a signal of much higher frequency, compared to power
frequency, which is coupled to the EHV line. Frequency band
allocated to this service is 50-200 kHz.Thus, the camer signal
frequency is just above the audible frequency range and just
below the medium wave radio broadcast band. Due to
moderately low frequency of the carrier, a small bandwidth is
available. However, protective relaying does not need a large
bandwidth. What is important is the delay involved, which is
' '
very small in case of power line carrier, for example,a LOO0 kms.
line will cause a delay of 0.33 milliseconds. ., .
The impedance of the coupling capacitor is very large at 50 Hz compared to that of
the parallel tuned circuit (which is tuned to carrier frequency) consisting of Lp a d Cp
Therefore, the coupling capacitor drops most of the 50 Hz voltage so that a veG'smal1
50 HZvoltage appears across the signalling equipment. The series circuit consisting of CS
and Ls, as shown in Figure 7.2, is designed to'resonate at the carrier frequency. Since the
impedance of a series resonant L-C circuit is ideally zero, it provides very good coupling
at the carrier frequency.
The parallel circuit consisting of Lp and Cp is tuned to resonance at the carrier
frequency. Since the impedance of a parallel resonant circuit is ideally infinite a t the
resonant frequency, it develops maximum voltage at carrier frequency, thus helping to
extract the maximum carrier signal.
The series and parallel L-C tuned circuits, therefore, help in efficiently coupling the
carrier into the EHV line. The carrier signal, however, needs to be confined to the desired
line section. The two line traps, which are parallel tuned L-C circuits, resonant at the
carrier frequency, prevent the carrier signal from spreading into rest of the transmission
system by virtue of their extremely high impedance at the carrier frequency. The line
traps have to be so designed, however, that they do not offer any significant impedance
at 50 Hz (power frequency). The line ends are thus clearly demarcated as far as the
carrier signal is concerned. This clear-cut demarcation helps in establishing a well-
defined zone whose boundaries are crisply defined.

Cnrrier-aided Protectior~of Transnr~ssionLines 157
Lir;e trap :or carrler blocking Line trap for carrier blocking
B
EHV -ine
Start carrier-+ CStart carrier
Ls. Cs: Series ckt. tuned to carrier frequency
(Lp, Cp), (Ltmp, Gmp):Parallel ckt. tuned b carrier frequency
Tx: Carrier transmitter
Rx: Carrier receiver
CRR: Carrier receipt relay at A and B.
Figure 7 2 Coupling a carrier and trapping it into the desired line section (single line-to-
ground coupling).
7.3.1 Single Line-to-ground Coupling
In Figure 7.2we have shown carrier coupling on a single line-to-ground basis. Is this type
of coupling, a wise choice?
Recall that, statistically, majority of faults are of the line-to-ground type. Further, in
power line carrier communication, the information has to be passed over the power line
itself Therefore, during faults, when the carrier is needed the most, the carrier will have
to be passed across the line-to-ground fault. This is bound to cause severe attenuation of
the carrier signal, rendering it unusable at the remote end. Thus, line-to-ground coupling
is not a very sound choice as far as carrier coupling is concerned.
7.3.2 Line-to-line Coupling
Figure 7.3 shows carrier coupling on the line-to-line basis. The carrier signals propagate
through air between the line conductors, therefore, the attenuation is much less. This
mode of transmission, known as the aerial mode, results in a much better performance
during single line-to-ground faults.

158 Fundamentals of Power Sysrem Pmrecrion --
A
Three-phase EHV line Phase a"
Line trap for blocking carrier
A LV~P
Phase b
Coupling capacitor
Figure 7.3 Line-to-line coupling.
7.4 Unit Type Carrier-aided Directional Comparison
Relaying
Line trap
A Ltrap
This protection takes advantage of the fad that as the fault location changes from just
ahead of the bus to just beyond the bus, the nearest directional relay sees a sharp change
in the fault direction whereas the remote relay does not see any change in the direction
of the fault. The remote relay cannot tell whether the fault is yithin the line zone or
outside it whereas the nearest end relay has no difficulty at all in discriminating between
the same. The information about the fault direction, as seen from each end, is conveyed
over the power-line carrier to the other end. At each end, simply ANDing the contact of
the local relay with the status of the contact of the remote relay gives rise to a unit type
of directional protection.
Cs.L, series circuit tuned to carrier frequency
Phase c
. --J
Coupling capacitor
Ls
Cp,Lp: Parallel circuit tuned
-i
*.
Start carrier

Currier-aided Prorecrion of Trartsrnission Lines 159
F i g ~ r e7.4(a) shows an internal fault for wh~chAND gates at both the ends become
enabled and instantaneously trip the associated circuit breakers. This generates a well-
defined zone of protection consisting of the line length between buses A and B.
Figure 7 4(b) shows an external fault. Since one input for each of the AND gates is
low, both zhe AND gates are disabled, thus the unit scheme restrains on external faults.
Figure 7.4(a) Unit type carrier-aided directional comparison relaying: internal fault.
Carder
External
fault
Figure 7.4(b) Unit type carrier-aided directional comparison relaying: external fault.
There is absolute selectivity as far as the ends of the zone are concerned, giving rise
to a well-defined protective zone, hence this scheme is classified as a unit type of
protection. Both the relays use the directional principle, hence it is called unit type
directional protection.

160 Fu~zdamenralsof Power Sysre~nProrecrion
7.5 Carrier-aided Distance Schemes for Acceleration of
Zone 11
7.5.1 Transfer Trip or inter-trip
As mentioned earlier, the faults in the end 40% (20% on each side) of the transmission
line fall in the second step of distance protection. It is, therefore, a delayed protection.
Thus, only about 60% of the mid-length of the line, gets high-speed distance protection.
For faults in the end 40%, the nearest distance protection trips instantaneously but the
remote end protection is a delayed one. How to speed up the remote end distance .:I
protection? - 1
Consider a fault in the second zone of distance protection, but not beyond end B, as - !
seen from end A. We can make use of the first zone, Zicontact of the local relay at end ,
:.)
B, to initiate a carrier and thus remotely operate a contact to close the trip circuit of the . . :1
remote circuit breaker at end A. The logic of this scheme is shown in Figure 7.5. The log* :'{
can be i?nderstoodby following the Roman numerals written in parentheses as follows: . . '1,"
,
pp, Trip contact circuit at end A
-T @
CB
trip
coil
Trip
Trip contact circuit at end B 1 i
trip
coil
Timer
Trip
battely
Figure 7.5 Acceleration of zone I1 o f distance relay using carrier. I
(I) Z1 contact of the local relay at end B operates (NO + CLOSES).
(11) This contact closure is used to switch on the carrier transmitter at end B, marked
as Tx in the figure.
(111) The carrier transmitter injects the carrier into the line.

Carrier-aided Prorectioll o/ Trarts~nlsaio~tLines 161
-
The carrier signal arrives at the remote end A at approximately the speed of light,
after a very short delay, and is rece~vedby the carrier current receiver, marked
as Rx.
(V) The output of the receiver (Carrier Receipt Relay, at end A, designated as CRRa4)
is in the form of closure of the contact CRRA.
Now, the CRRAcontact can be used to energize the trip coil of the circuit breaker at
remote end A in several alternative ways.
If we bypass the fault detector FDcontact by connecting point P with PI, then the
scheme is known as transfer trip or inter-trip.
In this scheme, the carrier signal is required for tripping purposes. Therefore, in case
of either the failure of carrier equipment or severe attenuation of the carrier signal due
to fault, the operation of the scheme is jeopardized. Thus a tripping carrier scheme lacks
robustness. Ideally, the carrier-based scheme should be such that in case of failure of
carrier, it should automatically revert back to the three-stepped distance scheme. The
logic can be built in such a way that the carrier signal is not required for tripping but
is required for blocking the tripping. Such schemes are obviously more robust and are
known as blocking carrier schemes.
7.5.2 Permissive Inter-trip-
At times, noise may cause false tripping in the scheme described in Section 7.5.1.
Therefore, we can take advantage of the fault detector output. Hence if point El in
Figure 7.5 is connected to point P2 then the scheme is known as permissive inter-trip.
7.5.3 Acceleration of Zone II
Alternatively we can simply bypass the zone I1 timer contact T2,in Figure 7.5, with
I CRRA,in which case the scheme is known as acceleration of zone II.
1 7.5.4 Pre-acceleration of Zone III
In this scheme, the zone II timing is accelerated from T1 to a much smaller value. This
is done by shorting out the Ti contact of the timer (which controls Z2 timing), with the
normally closed output of carrier receipt relay at end A, CRR,, as shown in Figure 7.6.
In case the fault is beyond the bus, the directional relay sees the fault and initiates a
carrier. The carrier is now sent over a line section which is healthy (on which there is no
s fault). On receipt of the carrier at end A, the carrier receipt relay changes state from
i CLOSE to OPEN. Thus Ti contact now comes into picture and decides the operating time
t of zone 11. The sequence of events can be easily understood, if one follows the Roman
1 numerals written in parentheses in Figure 7.6.
1I (I) Fault takes place beyond the bus, in zone 11, as seen' from end A.
i (11) Directional relay at end B senses the fault and instantaneously issues the trip
I output.!
i (111) The trip output of directional relay is used to start the carrier transmitter at
1 end B.
I (IV) The carrier transmitter at end B sends the carrier over the healthy power line.
E

162 F~ir~darn~nrolso f Power Systcrn Protection -~
(V) The carrier is received at end A, after a brief propagation delay, by the carrier
receiver
(VI) Carrier receiver issues an output, CRRA,in the form of a changeover of contact
from CLOSE to OPEN.
(VII) This output is used in parallel with the TIcontact to de-accelerate the zone I1
time wh~chwas pre-accelerated with the help of NC contact of CRRA.
I zone el----------
Tnp contact c~rcu~tat end A
7
Pre-acceleration
ofZ2 by NC*
contact of CRRn
'See text
Trip battery
Figure 7.6 Pre-acceleration of zone 11.
This has been a rather idealistic discussion of the operation of the system. In actual
practice, Z2operation should not be made instantaneous. If Z2is made instantaneous then
it will not give chance to the directional relay to operate and de-accelerate the Z2 time,
in case, the fault is beyond the bus. We have to allow for the following delays:
1. Operating time of directional relay Tdir
2. Propagation time of carrier over the length of the line Tprop
3. Operating time of the carrier receiver TCRRA
Thus, zone I1 should be pre-accelerated to an operating time of:
Tpre-aceelerated 2 Tdir + Tprop + TCRR*
1
This is, however, not shown in the figure.
It can be seen that the carrier is required for blocking the instantaneous operation :
of the pre-accelerated zone. This is an example of a blocking currier. i
1

Carrier-aided Protection of Transmissiur~Lines 163
7.6 Phase Comparison Relaying (Unif Scheme)
In this type of relaying, we exploit the phase shift undergone by the current at the end
which is nearest to the fault, as the fault changes from internal to external. The end,
which is far from the fault, cannot discern any change in the phase of the fault current
as the fault changes from internal to external but the end which is closer to the fault sees
a sharp, almost 180" change in the phase of current.
The local and remote end currents can be arranged to be out of phase for external
fault or load condition as shown in Figure 7.7(a). This can be achieved by selecting the
appropriate end of the CT winding as the reference. The phase shift will, however, not be
exactly 18O0,but may lag or lead this position by a small angle f6representing the load
bemg carried over the 11ne.
As the fault changes from an external fault to an internal one, the current at the
nearest end will undergo an approximately 180" change in its phase and will now be more
or less in phase with the remote end current as shown in Figure 7.7(b). Thus, if we
measure the phase shift between the currents at the two ends, then we can easlly decide
whether the fault is internal or external.
External fault (Ideal)
C.P. = 2.22 rns la,erl
C.P. = Zero 10,,t < *h.-r
External fault (Actual)
C.P. = 2.22 ms 10,
A -b +" a . .-- /A, ex1 l~rexl
Figure 7.7(a) Phase comparison relaying (currents shown on the CT secondary slde)
O
,
C.mt-tInternal fault b.mr
!I
I I0.lnt Coincidence
;ln temalfaultA,IA.I period = 10 ms
/A. ext IBerl External fault
Co~ncidence
period = zero
/B. exr + I + [A, ex1
Figure 7.7(b) Phase comparison relaying.

164 F~t~rda~ne~ltal~of Porver Svstefn Prorecrro~l
Assuming 6 to be, say, 20" then any phase shift between 0 and 1160" will indicate an
internal fault, as shown in Figure 7.7(c). A phase shift of k6 gives rise to a coincidence
period C.E of
I for phase shift of k160".I
C.P.r 2.22
C.P. = Zero
C.P. = 2.22rns
Figure 7.7(c) Phase comparison relaying.
- 3
1
-
Figures 7.7(d), (e), and (f) show a method for physical implementation of the above
mentioned concept.
Figure 7.7(d) shows an internal fault. As shown in the figure, each end
periodically sends carrier only during the positive-half of the time period of the
power frequency ac wave. This results in generation of a modulated carrier wave.
This modulation can be easily recovered back by demodulation to get a square
waveform at the output. For an internal fault, the figure shows that the
demodulated square waves are exactly coincidental. The coincidence period, thus, is 10 ms
(on a 50 Hz basis).
Figure 7.7(e) shows an external fault. Again the two ends generate carrier only during
the positive-half of the power frequency wave, generating similar modulated waves.
However, because of the phase shift, now, the demodulated square waves do not have any
coincidence at all or the coincidence period is nearly zero. . ,,,:;j~
The coincidence period can be easily found by ANDing the two demodulated waves.
To see if the coincidence period is greater than a certain threshold, we can either use any
digital method or follow the simple expedient of integrating the square wave and
comparing it with a preset dc value which represents the desired threshold, as shown in
Figure 7.7(e).

Carrirr-aidedProiecrio~!of Transmission Littrs 165
Dir A 3ir 8
A + 4- 3
r n - /A. ~nt
- 13,,,,I
1"
m 1
I - I"<(' I
'A, In! Internal fault h,PI
I: End A current for Internal as well
as external fault.
II: Modulated carrier sent by end A
for internal as wall as external
faults.
Ill: Demodulated end A carder.
IV: End B current for internal fault.
V: Modulated carrier sent from end
B and received at end A for
internal fault.
VI: Demodulated end B carrier
available at end A.
Vll: Coincidence period pulse
10ms /t- obtalned by ANDlng Ill and VI
Figure 7.7(d) Phase comparison relaying (internal fault).
--

166 Fu~ldun~e~ttulsof Power Svsrem Protectiorl
Dir A
C B ~
-b /A. ex,
r n - . 10, ex! CBS
/. rn n
O
A , B
, I
/A. ext Is,BXI External fault
I: End A current for internal
as well as external faults.
I
I
I
11: Modulated carrier sent by
end Afor internal as well
as external faults.
'5
-.-~
Ill: Demodatation of end A
nent for external
V: Modulated carrier sent by
end B during external
VI: Demodulation of end B
carrier received at end A
No coincidence VII: Pulse corresponding to
coincidence period
No output obtained by ANDing of ill
and VI.
Figure 7.7(e) Phase comparison relaying (external fault).
~ ~
-, ~. ~~ ~ ~.

Carrier-aided Prorection o f Transn~issionLines 167
Set threshold level
$?
Puise corresponding
10 coincidence period
Ground d
Figure 7.7(0 Hardware to measure coincidence period.
Trip CB,
Review Questions
Integrator
+ vcc -
1. What do you mean by reclosure?
2. What is the motivation for using reclosure?
3. Differentiate between reclosure in case of low-voltage systems and high-voltage
systems.
4. What is meant by single-shot reclosure and multi-shot reclosure?
5. What is the motivation for using a carrier?
6. What are the various options for implementing the carrier communication
channel?
7. What are the advantages of power line carrier?
8. What frequency band is normally used for power line carrier signalling?
9. What is the frequency band used for microwave communication?
10. What is the motivation for coupling the carrier between two of the lines rather
than between a line and ground? Which method results in more reliable carrier
communication?
11. Explain why only middle 60% of the double-end-fed line gets instantaneous
distance protection from both ends in a three-stepped distance scheme.
12. How does the carrier help in overcoming the limitation of the three-stepped
distance protection?
13. Explain the difference between transfer trip and permissive inter-trip schemes.
Which scheme is more robust?
14. How does the carrier-based acceleration of zone I1 differ from the transfer trip
and permissive inter-trip schemes?
15. Why does sending the carrier over a faulty line need to be avoided?
16. What do you mean by tripping carrier and blocking carrier? Which one is more
robust?
17. What do you mean by pre-acceleration of zone II?
18. In practice, the zone I1 cannot be pre-accelerated to an instantaneous operation.
Explain.
19. Explain the operation of the unit type of carrier-based directional protection.
20. Explain the principle of carrier-based phase comparison scheme.

8.1 Introduction
~, .
A generator could be pert of: >:, .
water turbine based hydropower station
gas turbine based power station
steam turbine based thermal power station
nuclear power station
In all the above installations, the protection of the generator pre.5ents a very
challenging problem because of its system connections on three different sides as shown
in Figure 8.1. On the one side, it is connected to the prime mover and on the other side,
it has to run in synchronism with the grid because of its connection to the &wer system.
On yet another (third) side, it is connected to the source of DC excitation. It is thus
obvious that generator protection is very complex compared to protection for other
elements of the power system.
(Turbo-alternator)
DC excitation system
Figure 8.1 Complexities of generator protection.
168
- ~
-- . ~. . . ~~ . . . ~

this book, we will restrict ourselves to various aspects of protection of a large
mv or higher) steam turbine based turbo-alternator,
case of a fault on a turbo-alternator, it is not enough to open the main circuit
r connecting it to the power grid. For example, when a turbo-alternator driven by
team turbine is tripped, the following must be done:
.Steam supply to the turbine is stopped or bypassed.
Firing of the boiler is stopped.
Coal mills are stopped.
Coal supply to the coal mills is stopped.
Field circuit of the alternator is interrupted.
Field coils are connected across a resistor to dissipate the stored energy.
Alternator is kept running at a slow speed (fewrpm) with the help of barring gear
till it cools down uniformly, so as to avoid uneven expansions.
Putting back the alternator on line is rather a slow process because all the parameters
(temperatures and pressures) have to be progressively built up to avoid thermal shock
resulting in uneven expansions which might cause unacceptable vibrations. Therefore,
unscheduled outage of a thermal power station is avoided as far as possible.
We have to keep in mind that a modern large turbo-alternator is a huge mass rotating
at a very high speed (3000 rpm) in a very small air-gap. Thus, apart from the large
electrical energies involved, there is tremendous amount of mechanical energy in the form
of moment of inertia of the rotating mass and resultant forces on the shaft, the rotor body
and the stator structure.
Thus, any slight increase in temperature or uneven heating of the rotor may cause
eccentricity, which gets accentuated because of the high speed of rotation and small air-
gap. The entire system has, therefore, to be run in a narrow range of various parameters
like temperatures and pressures, displacements, flows, voltages, currents, power factor,
and so forth. The operation outside the specified parameter range may cause a substantial
decrease in the life of the equipment.
Since the power station equipment represents a very high investment of money, the
operation of the power plant is very closely monitored and controlled.
Figure 8.2 illustrates the complexities of a turbo-alternator in a more detailed
manner.
It is said that running a large power station is like flying a supersonic jet aircraft
! without any forced landings or crashes!
I
I
I 8.2 Electrical Circuit of the GeneratorI
I
I
The electrical circuit of the generator is very simple in spite of the complexity of the
overall system. This is shown in Figures 8.3(a), 8.3(b) and 8.3(c). It is to be noted
that the generator is nwer solidly grounded. If it were solidly grounded, the single
line-to-ground fault current would be dangerously high Apart from thdhigh value of fault
current, the resulting asymmetry in the rotating magnetic field inside the generator

~ I ~ L U U ~ I Iu IeblbbauLe. 111 U I U ~ I bu g e ~a ~ L U L ~ I L U U I ~v a u e UL L I L ~~ I U U I I U I I I ~1eblbbu1, ~b
connected through a step-down transformer, known as grounding transformer.

The power plant has a sizeable auxiliary electrical load of its own, of .;he order of 10%
of the power rating of the generator, w'nich is supplied through the unit armillan
transformer (UAT).It is to be noted that these auxiliaries require power even before the
generator can be started, run up to speed and synchronized with the grid. Hence, there
is the switching facility to energize the UAT directly from the grid.
Generator
transformer Main CB EHV bus
&="-&
- -.- :s$# *To grid
Unit auxiliary
transformer
il) station auxiliaries
. .
Figure 8.3(a) Alternator unit auxiliary transformer and main CB.
+Phase
eiiGrounding . ~
tra,isformer ?:
(Step-down :I"
transformer) 8
I
I
Figure 8,3(b) Alternator and neutral grounding transformer.
I The rotor of the generator houses the field winding. A separate dc generator, which
is mounted on the turbo-alternator shaft, feeds the field. The dc system is kept floating
with respect to the ac ground, i.e. neither the +ve nor the -ve terminal is grounded. The
field interrupter and the arrangement for field suppression is also shown in Figure 8.3(c).

172 Fundan~enralsof Power Systeln Pmtectiolr
Field interruptor
Field current . . .,
I h
Excitation control
; -. Field---4 4Field winding
system of generator
DC system is isolated
alternator shaft from ac ground
Figure 8.3(c) Electrical circuit of the exciter of the generator.
a8.3 Various Faults and Abnormal Operating Conditions
In addition various electrical faults, a generator goes through many abnormal operating
conditions, which need to be understood. Figure 8.4(a) and Figure 8.4(b) show the
hierarchy of the electrical faults and abnormal operating conditions.
r Phase fault
Stator e
-
lnter-turn fault on the
samelphase
Electrical-
faults - Ground faults
Rotor
Field winding Short circuit to ground
Figure 8.4(a) Various electrical faults on a turbo-alternator.
Stator
Electrical Unbalanced ioadlng
Abnormal
operating
conditions
Rotor
Field winding Loss of excitation
Mechanical Loss of
prime mover
Over-speeding
Figure 8.4(b) Various abnormal operating conditions of a turbo-alternator.

8.3.1 Stater Faults
The chree-phase armature winding on the stator can develop phase as well as ground
faults. Another possibility is inter-turn faults between turns of the same phase.
8.3.2 Stator Phase and Ground Faults
Phase and ground faults on the stator armature winding can be easily detected by a
conventional percentage differential protection scheme as shown in Figure 8.5.This type
of scheme is also known as longitudinal differential scheme in order to differentiate it
from another differential scheme, known as transverse differential scheme which is used
to detect inter-turn faults.
Generator Prorectron 173
I Figure 8.5 LongitudinalIpercentage differential protection.

It may be noted that there are differences between the differential protection of a
power transformer and that of a generator as shown in Table 8.1. As a result of these

174 F~rrtdarireriralsof Power Sysrenl Pmrecriort
differences, the percentage bias setting for the generator differential relay is quite small
compared to that for the power transformer.
Table 8.1 Difference between transformer and generator differential protection
Power transformer Generator
Primary and secondary voltages Same voltage for CTs on two sides of the generator
are in general different winding
Turns-ratio of the CTs are different Turns-ratio of CTs on the two sides of the generator
because of ratlo of transformation winding is same
of the transformer
Tap changer may be present No such device is present
This gives rise to a larger spill current, during normal load and external faults, in
case of the transformer differential protection than in case of the generator differential
protection. Normally, the percentage bias setting of 5-10% is adequate for longitudinal
differential protection of the generator stator winding whereas a setting of 20-40% may
*be required in case of power transformers.
The longitudinal differential scheme caters for phase as well as ground faults on the
stator winding. However, it is unable to detect the inter-turn faults between the turns of
the same phase. This is discussed in the following Section 8.3.3. ,..
8.3.3 Transverse Differential Protection
I? order to apply this type of protection, a special type of split winding is reeuired as . .
shown in Figure 8.6. Current in each parallel section is now compared with that in the
other section. If there is an inter-turn fault in one section then the currents will differ
and flow as spill current through the OC relay, as shown in Figure 8.6. ..
Figure 8.6 Transverse protection of generator winding
In Figure 8.6, only the winding with the inter-turn fault is shown in detail. The half
of the winding in which there is an inter-turn fault is shown to carry 3000 A whereas the

Generaror Protection 175
healthy half carries 3500 A. 4 s seen from the figure, the current entering the phase c
winding, as a whole, is 6500 A which is the same as that leaving it. Therefore, a
longitudinal differential relay would be incapable of detecting such faults.
However, because of the splitting of the winding and transverse connection of the
CTs, there is a spill current of 0.72 A in the transverse differential relay Thus, a setting
of, say, 0.5 A will be enough to detect such an inter-turn fault.
8.4 Rotor Faults
The rotor carries the field winding which is kept isolated from the ground. Neither the
positive nor the negative terminal of the dc supply is grounded. Thus, any ground fault
on the rotor field winding does not affect the working of the alternator. However, a
subsequent fault would cause a section of the rotor winding to be short circuited, giving
rise to a secondary flux which opposes the main flux in the proximity of the shorted turns,
causing distortion in the distribution of main flux. The flux will get concentrated on one
pole but dispersed over the other and intervening surfaces. The resulting asymmetry in
the electromagnetic forces will cause severe vibrations of the rotor. In a modern turbo-
alternator, the inertia of rotation is very large and the rotor-to-stator clearances are very
small, therefore, there is a likelihood of permanent damage to the turbo-alternator.
Instances have been reported where, during rotor faults, because of severe mechanical
stresses structural damage was caused.
In the light of the above, the very first fault on the field winding must be detected
and the set tripped in a controlled manner. An arrangement for rotor earth fault detection
and protection is shown in Figure 8.7, wherein an external voltage source is superimposed
Field winding Sllp ring
of generator Generator shaft
Exciter
Rotor earth
fault
Time
I Plug
L-L&.J Alarm
OC relay
setting Trip
setting Trip circuit of main
CB of generator
fiIsolation transformer
Figure 8.7 Protection against rotor faults.

$jj;
jli;; :8 p-
176 Fundamentals of Power Svstefn Protection
;rli -
:I I
' I
),
on the rotor circuit. This external voltage source is grounded so that the very first rotor
.,r<,
.f,! earth fault causes a dc fault current to flow which is easily detected by an OC relay
~!
f!, 8;
, ,
,,
1 8.5 Abnormal Operating Conditions
:!I!.,
As pointed out earlier, a generator cannot be considered in isolation because of a very
large number of other equipment connected to it. Even though there is no electrical fault
in the generator, if one of its associated equipment develops a fault, then it has serious
implications for the generator. Every auxiliary equipment connected to the generator is
a likely source of trouble. There are a large number of possible faults, as well as
combinations of faults, on these equipment, that threaten the operation of the generator.
Instances where there is no direct electrical fault in the generator but one or more of its
associated equipment develop a fault or an abnormality, may lead to an abnormal
operating condition, which may or may not be serious. However, all abnormal operating
conditions need to be detected as quickly and as sensitively as possible so that the
corrective action can be taken and a possible shutdown averted or anticipated.
In the following sections, we consider some prominent abnormal operating conditions
that need to be carefully considered while providing protection to the generator.
8.5.1 Unbalanced Loading
If there is an unbalanced loading of the generator then the stator currents have a
negative sequence component. The stator field due to these negative sequence currents,
rotates at synchronous speed but in a direction opposite to the direction of the field
structure on the rotor. Thus, the negative sequence stator armature mmf rotates at a
speed -Ns while the rotor field speed is +Ns.Therefore, there is a relative velocity of
between the two. This causes double frequency currents, of large amplitude, to be induced
in the rotor conductors and iron. Recall that the eddy current loss component of iron loss
in the rotor is proportional to f2(Bm,)' while the hysteresis loss is proportional to
f (B,,)" where n = 16 to 2 depending upon the core material. Therefore, both the eddy
current as well as the hysteresis losses increase due to these double frequency induced
currents in the rotor. This is shown in Figure 8.8.
Thus, if the stator carries unbalanced currents, then it is the rotor, which is
overheated. How long the generator can be allowed to run under unbalanced loading,
depends upon the thermal withstand capacity of the machine, which in turn depends upon
the type of cooling system adopted. The rate of heat generation is proportional to I ~ R
while the heat energy is proportional to IiRt, where t is the time and I, is negative
sequence current. Since the capacity of a particular machine, to safely dissipate energy,
is limited to a certain value k, we can write
I ; R ~= k
Assuming R to be a constant, and K = klR, we get the thermal characteristics of the
machine as
1;t = K
In other words, the time t for which the offending current I can be allowed to flow should
be less than or equal to ~11;.

steady state
Unbalanced loading?
eYes
Negative sequence component in stator
current
Relative speed between rotor and the field due
to negative sequence currents = 2Ns
!
Double frequency currents of frequency
2Nsp/120 induced in rotor core and winding
Stator armature MMF due to negative
sequence currents rotates at -Ns (rpm) F~eldwlnd~ngrotating at Ns (rpm)
Additional heat generated
Figure 8.8 Unbalanced loading of stator causes the rotor to overheat.
Thus, the current-time characteristic can be written as
The readers will recall that this characteristic is similar to that of the inverse time over-
current relay. Thus an inverse type of over-current relay, which is fed with the negative
sequence component of stator current, gives protection against unbalanced loading of the
generator.
The preceding discussion suggests that if we could, somehow, extract the negative
sequence component of the stator current then the protection against unbalanced loading
1 I.
can be implemented by applying the inverse-time OC relay as shown in Figure 8.9.

178 F~alclanrenralsof Powrr Sysrem Protection
Stator currents
12 Negative sequence current (rms)
8
I Over-current relay with inverse
characteristic To, = MI:
I--Set K for the machine
Trip main CB of generator
Figure 8.9 Logic of the protection against unbalanced loading.
Consider that a turbo-alternator is supplying its rated real electrical power P, to the grid.
Its mechanical input Pmis nearly equal to P, (except for the losses) and the machine runs
at constant synchronous speed Ns.
Now, consider that due to some fault the generator is tripped and disconnected from
the grid. Thus, P, becomes zero. However, the mechanical power input Pm cannot be
suddenly reduced to zero. Therefore, we land up in a situation where the generator has
full input mechanical power but no output electrical power. This would cause the machine
to accelerate to dangerously high speeds, if the mechanical input is notpquickly reduced
by the speed-governing mechanism.
The protection against such an eventuality can be provided by sensing the over-
speeding and taking steps such as operating the steam valve so as to stop steam input to
the turbine. The speed-governing mechanism or the speed governor gf the turbine is
basically responsible for detecting this condition. The over-speeding can also be detected
either by an over-frequency relay or by monitoring the output of the tachogenerator
mounted on the generator shaft. The logic of protection against over-speeding is shown
in Figure 8.10.
0
Tachogenerator Over-frequency
output relav
.C Yes
Stop steam supply
to turbine
J.
Start shutdown of
generator
Figure 8.10 Protection against over-speeding.

Generator Protec!ion 179
8.5.3 Loss of Excitation
There are several possible causes due to which field excitation may be lost, namely:
Loss of field to main exciter
Accidental tripping of the field breaker
Short circuit in the field winding
Poor brush contact in the exciter
Field circuit breaker latch failure
Loss of ac supply to excitation system
The generator delivers both real as well as reactive power to the grid. The real power
comes from the turbine while the reactive power is due to the field excitation. Consider
I
a generator delivering the complex power, S = P, +jQ,,to the grid.
r Corresponding to real power P,, there is the shaft mechanical power input P,,, and
corresponding to reactive power Q,,there is the field current If as shown in
Figure 8.11(a) and (b).
Now, consider that the field excitation is lost while the mechanical input remains
intact. Since the generator is already synchronized with the grid, it would attempt to
remain synchronized by running as an rnduction generator. As an induction generator, the
machine speeds up slightly above the synchronous speed and draws its excitation from the
grid. This is shown in Figure 8.11(b). Operation as an induction generator necessitates
I the flow of slip frequency current in the rotor, the current flowing in the damper winding
I
I
and also in the slot wedges and the surface of the solid rotor body.
Voltage = V L ~ E
pe d
Generator Grid
input
Mechanics?Speed > NS
-~ Q L O E
f * . oQLOE1"
!
Voltage = vmled Q~
i
Field cume"t If = zero
(Loss of excitation)
M e c h a n i c a y
~nput
(b) After loss of excitation
Figure 8.11 Loss of excitation.
Speed = Ns
tField cumnt I f LpGenerator
(a)Before loss of excitation
Generator
pe - Grid
jQe--+

180 Fundor71erzrolr of Power System Prnrecrrorl
Now, there are two possibilities. Either the grid is able to meet this reactive power
demand fully or meet it partially. If the grid is able to fully satisfy this demand for reactive
power, the machine continues to deliver active power of P,MW but draws reactive power
of QLOEMVA and there is no risk of instability. However, the generator is not designed
as an induction machine, so abnormal heating of the rotor and overloading of the stator
winding will take place.
If the grid were able to meet the reactive power demand only partially then this would
be reflected by a fall of the generator terminal voltage. The generator would be under
excited. There are certain limits on the degree to which a generator can be operated
within the under-excited mode. Therefore, the operation in case of loss of excitation must
be quickly detected and checked to avert any shutdown of the generator.
The simplest method by which loss of excitation can be detected is to momtor the field
current of the generator. If the field current falls below a threshold, a loss of field signal
can be raised. A complicating factor in this protection is the slip frequency current
induced in the event of loss of excitation and running as an induction generator.
The quantity which changes most when a generator loses field excitation is t h e
impedance measured at the stator terminals. On loss of excitation, the terminal voltage
begins to decrease and the current begins to increase, resulting in a decrease of
impedance and also a change of power factor.
Thus, loss of excitation can be unambiguously detected by a mho relay located at the
generator terminals as shown in the following Section 8.5.4.
8.5.4 Protection Against Loss of Excitation Using Offset Mbo Relay
During normal steady-state operation, the impedance seen from the stator terminals, i.e.
the apparent impedance lies in quadrant I, of the R-Xplane as shown in Figure 8.12.
X
Medium initial I
Low initial output
Figure 8-12 Protection against loss of excitation.

After the loss of excitation, the apparent impedance enters quadrant I!? Tlle exact
locus of the apparent impedance and the rate at which it is traced out depends upon the
initial complex power that was being delivered by the generator. If the initial power
output was high then the locus is traced out quickiy. However, if the initial power output
was low then the locus is traced out rather slowly [taking up to a few seconds).
In order to keep the generator online as long as it is safe, the generator may not be
instantaneously tripped in case of loss of excitation. As soon as loss of excitation is
detected by the relay, an alarm may be sounded and an attempt may be made to see if
excitation can be restored.
A mho type distance relay with offset characteristic may be used for protection
against loss of excitation. The offset is by an amount equal to Xh/2.The impedance setting
of the relay is IXd1 at an angle of -90" as shown in Figure 8.12. In order to give time for
change over to the standby exciter by the control circuitry, the relay operation can be
delayed by about 0.5-3 s.
8.5.5 Loss of Prime Mover
In case of loss of prime mover, i.e. loss of mechanical input, the machine continues to
remain synchronized with the grid, running as a synchronous motor. The machine, now,
draws a small amount of active power (compared to its rating) from the grid in order to
drive the turbine and meet the losses taking place in the machine. At the same time, the
machine supplies reactive power to the grid since its excitation is intact. This is depicted
in Figure 8.13(a) and (b). Running in this mode is not harmful to the generator, but is
definitely harmful to a prime mover like a steam turbine.
Field current 1, excitation
(a) Before loss of prime mover
Runnlng as motor
mover
Field currh /,excitation
(b) After loss of prime mover
Figure 8.13 Loss of prime mover.

182 F~rndarnettralsof Power System Pmrection
Normally, loss of steam supply to the turbine causes loss of prime mover. When the
machine runs as a motor, there is a churning of trapped steam m the turbine causing
objectionable temperature rise and damage to the blades. Therefore, the loss of prime
mover needs quick detection followed by tripping of generator.
When the prime mover is lost, the generator starts drawing real power from the gnd,
supplying the reactive power to the grid as before. The real power drawn from the grid
is quite small compared with the generator rating. The generator draws real power which
is just enough to meet the losses and the load put on it by the turbine. Hence, the
magnitude of stator current is smaller than when it was generating, but the stator
current undergoes 180" phase shift as shown in Figure 8.14.
This suggests that if we use a directional relay with an MTA of 180" (using generator
phase angle conventions) as shown then it would detect the loss of prime mover as the
current phasor would reverse and enter the trip reson. However,,the magnitude of this
reversed current phasor is quite small compared to the forward current as the generator
draws just enough real power to meet the losses and drive the turbine. Hence, the
directional relay for detecting the loss of prime mover needs to have a high degree ofasensitivity compared to directional relays used for crver-current application.
c Active pol
Loss of prirne
mover
Trip
D~rect~onal-va
relay -' a
Loss of prirne
mover
" I, Generating (unity PF)
Directional relay . .
MTA 180'
Restr-'n
Trip
Y
Setting: MTA = 180"
'a
(Motoring)'
Figure 8.14 Duectional relay for protection against loss of prime mover.
I

Gerrerator Protecrioiz 153
Review Questions
1. Discuss the scenario that the turbo-alternator presents to the protection engineer.
2. Tripping the main circuit breaker is not enough protection for a generator.
Explain.
3. What are the various faults to which a turbo-alternator is likely to be subjected?
4. Differentiate between longitudinal and transverse differential protection.
1
! 5. Why conventional differential protection cannot detect inter-turn faults on the
I
I same phase?
!
I
6. What are the typical values of % bias used for generator protection? How does this
setting compare with that of similar protection for transformer?
7. What special type of winding construction is required in case of transverse
differential protection?
i
8. What are the various abnormal operating conditions to which a modern turbo-
alternator is likely to be subjected?
9. Why the first ground fault on the rotor does not cause any damage while a second
fault can be catastrophic?
10. What do you mean by loss of excitation (LOE) (in the context of generator
I
protection)?
I 11. Why does a generator need to be tripped in case of loss of excitation?
I 12. Why is loss of excitation difficult to detect by monitoring the field current?
1 13. How does a LOE distance relay work?
14. What causes over-speeding? Explains the remedial action that needs to be taken
to prevent over-speeding.
15. What causes loss of prime mover?
16. Can a generator be allowed to run with its prime mover lost? If not, why?
17. How is loss of prime mover detected? What are the problems encountered in
implementing this protection?

9.1 Introduction
A stupendous number of induction motors are being used in the industry. The induction
motor is truly thg workhorse of the modern age. Even though the speed control of
induction motor is not simple and efficient, the reason for the motor's popularity is its
ruggedness and simplicity. However, with the introduction of power eledronlc controllers,
the case of speedltorque control of the induction motor is now comparable with that of
the dc motor. 5
Induction motors come in a wide range of ratings, from fractionalPorsepower motors
used in tools and domestic appliances to motors of megawatt rating .used for boiler feed
pump in thermal power stations. A broad classification is presentedjn Table 9.1.
Table 9.1 Broad classification of induction motofs
Small Medium Big
FHP > 50 HP > 1500 HP
c 1kW > 40 k W > 1000 kW
It is not possible to make any general statements about the protection of induction :
motor, since the protection scheme depends on the size (horsepower/kW rating) of the !
motor and its importance in the system. This is the reason why induction motor .i
protection has not been standardized to the extent that other protection schemes have 1been.
However, regardless of what protection we may provide, all motors, big or small, are
subjected to similar faults and abnormal operating conditions. 3
1
9.2 Various Faults and Abnormal Operating Conditions
The induction motor cannot be considered in isolation. On the one side, it is connecte
to the supply, possibly through some kind of power electronic controller and on the 0th
side, it is mechanically coupled to the load. Therefore, the induction motor is subjecte
to a large number of faults and abnormal operating conditions as depicted in Figure 9.
184

'orLoad
Power
Trip electron~c
controller
3Bearing Bearing
supply Motor Load
1. Fault on motor terminals 1. Phase faults 1. Failure of bearing
II 2. Unbalanced supply voltage 2. Ground faults 2. Prolonged overloadI 3. Single phasing 3. Inter-turn faults 3. Rotor jam
4. Reduced supply voltage
L, 5. Reversal of phases -
t Figure 9.1 Abnormal operating conditions and faults experienced on induction motors.
I 9.3 Starting Current
I
An induction motor draws a very large starting current, of the order of 6 to 8 times the
full-load current if started direct-on-line. The amplitude of the starting current may be
I
comparable to fault current. Therefore, the over-current protection provided to the motor
1 must be able to discriminate between a genuine fault and an over-current due to starting
of the motor. Hence, coordination between the starting characteristic of the motor and the
over-current relay is required Figure 9.2 shows the starting current superimposed on the
1 thermal capab~litycurve of the motor, and the characteristic of an over-current relay,
which mlght be used for protection of the motor. It can be seen from Figure 9.2 that the
i
OC relay characteristic must be above the starting characteristics but below the thermal
j
characteristics of the motor. This will ensure that the protective relay does not operate
1 during starting phase the motor but will positively operate when the load exceeds the
I motor's thermal capability.
Over-current relay
characteristic
Thermal capability
I
,
I
I
.
!characteristic
i 1 2 3 4 5 6 7
I IFL Current +Istan ' '+T-
~ ~ l l - l ~ ~ d(multiples of Starting 'oh-rault
current hflload) current
:d I Figure 9.2 Starting and thermal characteristics of induction motor.
1 t

186 F~o~ria~i~eniuLrof Power S?~srenrProrection . .
9.4 Electrical Fauljs
9.4.1 Fault on Motor Terminals
The phase-fault current at the terminals of a motor is considerably larger than any .
normal current such as starting current or any internal-fault current. Hence, a high set I
instantaneous over-current relay is recommended for fast, reliable, inexpensive and 1
simple protection.
9.4.2 Phase Faults Inside the Motor 1Protection against phase faults as well as ground faults can be provided using either fuses
,
or over-current relays depending upon the voltage rating and size of the motor. Most
motors will be protected by HRC fuses (Flgure 9.3). The fusing current should be gre
than the starting current of the motor. The fuse operating time should be less than
permissible locked rotor time of the motor. The locked rotor tlme is the time for whic
the rotor can be safely stalled with full supply voltage applied to the stator.
Induction motor
f i n i -
-.
Figure 9.3 HRC fuses for protection of induction motor.
Big motors, which are high voltage. motors, will need to be ~rovidedwith an
over-current protection for increased accuracy of protection as shown in Figure 9.4. The
thermal capability characteristic of the motor should be kept in mind while applying
over-current protection. The OC relay characteristic should be below the thermal
capability characteristic as shown in Figure 9.2.
In case of high impedance ground faults inside the motor, the fault current may
happen to be less than the full-load current. Such faults are difficult to detect using
over-current approach. A current balance type of protection caters for such faults as
explained in Section 9.4.3.
In case of big motors whose kVA rating is more than half of the supply transformer
kVA rating, the current for a three-phase fault may be less than five times the current
for locked rotor condition. In such cases, it is recommended to use percentage differential
protection as shown in Figure 9.6. If the motor kVA rating is less than half of the supply
transformer kVA rating, over-current relays can be relied upon. The logic for this
criterion can be explained as follows:
Assume a motor is connected to a supply transformer with 8% impedance. The
maximum fault currerit at the transformer secondary with an infinite source is:

Inducrion !Woror Prorecrion 187
TS
Ground
fault relay
phaserelaysfault PSTTS
1 Figure 9.4 Phase fault and ground fault protection of HV induction motor.
,Trip
coil
Induction motor
i Figure 9.5 Percentage differential relay for protection of induction motor
i

188 Fundamenrals of Power System Prorecrion
1
I ~ - ~ ~= (108 = 12.5 per unit on transformer base
The maximum motor starting current in this case is
where XM is the motor impedance. In order that (13.ph/ILR)> 5, XMmust be greater than
0.32 per unit on the transformer kVA base.
If the motor has a full-voltage starting current of six times the full load, then
XM = 116 = 0.167 on the motor rated kVA base. With a motor kVA of half of the
transformer kVA, an XM of 0.167 would be 0.333 on the transformer base, which is
greater than 0.32. Clearly, this rule of thumb should only be applied when there is no
appreciable deviation from the parameters assumed above.
9.4.3 Ground Faults Inside the Motor @
Figure 9.6 shows an arrangement for detecting high impedance ground faults. The three-
phase line conductors carrying current to the motor form the primary of a transformer.
The secondary consists of a pick-up coil wound on the core.
Figure 9.6 Earth fault protection for induction motor
When the motor is running normally, the instantaneous sum of all the three line
currents is zero. Thus, there is no net flux in the core. Hence, the ~ick-upcoil does not
have any voltage induced in it.
Now, consider a ground fault as shown. The three line currents do not sum up to zero.
Thus, there is a net primary mmf proportional to the fault current If, returning to the
supply neutral through the fault path. There is, thus, a flux in the CT core. The pick-up
coil has a voltage induced which can be sensed by an electronic circuitry or the pick-up
coil can be made to drive the operating coil of a sensitive relay.
If an electronic circuit is used to sense the voltage developed by the pick-up coil, the
current balance relay described above can be made extremely sensitive and can detect
earth fault currents down to a few tens of milliamperes. Very high sensitivity, however,
is likely to cause some nuisance tripping.

9.4.4 Infer-turn Faults
IInter-turn faults on the same phase are difficult to detect because they do not cause
appreciable change in the current drawn by the motor. However, such faults cause hot
spots to develop, leading to deterioration of insulation.
No specific protection against inter-turn faults is needed for most motors except very
big motors. Embedded temperature detectors may be relied upon to provide protection
against inter-turn faults.
9.5 Abnormal Operating Conditions from Supply Side
An induction motor is subject to many abnormal operating conditions as far as the
electric supply side is concerned. In some cases, quick disconnection of the motor may be
needed and, in others, only an alarm may be sounded for an operator to take corrective
action or be ready for shutdown.
9.5.1 Unbalanced Supply Voltage
Large induction motors are very sensitive to unbalances in supply voltage. The negative
sequence component, which comes into picture because of the unbalance in the supply, is
particularly troublesome. This is because the motor offers very small impedance to the
negative sequence currents. In fact, the negative sequence impedance is less than the
positive sequence standstill-impedance as shown in Figure 9.7. Thus, a 4% negative
sequence supply voltage causes more than 24% negative sequence current to be drawn by
the motor, if the starting current of the motor is six times the full-load current. This
causes increased heating of the stator.
Rs
At start (s= 1)
xr
Z.1." -)
Rm Xm
Z,,, = Rs + R, + ~(XS+ X,)
(a)Equivalent circuit while starting
At rated speed
1.99
z2 < zstall
0 I(b) Equivalent circuit for negative sequence
Figure 9.7 Equivalent circuit of induction motor.
I

190 Fundamentals of Power System Pmtection
Further, the magnetic field due to negative sequence rotates at synchronous speed Ns
in a direction opposite to that of the rotor which is rotating at a speed equal to (sNs),
which is slightly less than the synchronous speed, where s is the slip of the motor. This
causes currents of lf(2 - s)] frequency, i.e. almost double the supply frequency, to be
induced in the rotor circuit. Because of skin effect, the rotor offers five to ten times its
normal resistance to these double frequency currents, thus, causing excessive heating of
the rotor.
Therefore, for large motors any unbalance in the supply voltage needs to be quickly
detected and corrective action taken. A scheme for detecting unbalanced supply voltage
is shown in Figure 9.8.
$5
Figure 9.8 Negative sequence voltage relay for protection against unbalance in supply
voltage.
There are certain situations where the negative sequence relay does not operate ~,.'{
correctly. For example, if there is an open circuit fault between the supply and theYelay I
:jthen the relay measures the negative sequence voltage across the motor, which is
substantial and, therefore, the relay operates
Open
CB Motor
Negative sequence relay
Figure 9.9 Negative sequence voltage relay correctly detects an open circuit between supply
and relay.

However, if the open circuit is between zhe relay and the motor then the negative
sequence relay ends up measuring ihe negative sequence component of the supply voltage,
which is very small and does not cause the relay to pick up as shown in Figure 9.10,
Equivalent sequence
network connection
Open circuit CB M~~~~
Val 'V z1m
hCz+ f
R Vzs Zzm V2,
: Negative
sequence relay
Time setting ''2s << v2m
Figure 9.10 Negative sequence voltage relay fails to detect an open circuit between relay
~ and motor.
I
1 For positive detection of such faults, we need to detect the negative sequence
!
component in the line currents. This is described in Section 9.5.2.
9.5.2 Single Phasing
I
1 Single phasing can occur because of a non-closure of one pole of a three-phase contactor
1 or circuit breaker, a fuse failure or similar causes.
Single phasing causes negative sequence current to flow. The motor has a limited
ability to carry negative sequence currents, because of thermal limitations.
I
i
Single phasing causes the motor to develop insufficient torque, leading to stalling,
i
making the motor to draw excessive current and finally leads to burn out unless the
motor is tripped.
i
Thus, there is a thermal limit on the amount of the negative sequence current that
can be safely carried by the motor. The quantity 1; t represents the energy liberated as
I heat due to negative sequence current 12.
t 1; t = 40 is conventionally used as the thermal capability of motor to carry negative
I sequence current.
1 Figure 9.11 shows the characteristic of a relay for detecting imbalance in the line
I currents. The relay consists of two units. One unit balances I, against Ib while the other
I balances Ib against I,. When the currents become sufficiently unbalanced, torque is
developed in one or both units causing the relay to trip The relay can be set to pick up
! when negative sequence current I2 = 5-30% of the full-load current.
I
I
- - - - -

192 Fl~ndamenralsof Power Sysrenr Prorection
1 A Val --)
Figure 9.11 Negative sequence current relay to detect aingle phasing.
9.5.3 Reduction in Supply Voltage
The torque developed by an induction motor is proportional to the square of the applied
voltage, therefore, any small reduction in iroltage has a marked effect on the developed
torque. The reduced torque may cause the motors to lose speed and draw more current.
Large motors should be disconnected when a severe low voltage condition persists for
more than a few seconds.
Under-voltage relays may be used for protection against reduced supply voltage.
9.5.4 Reversal of Phases *
When there is a reversal of phase sequence, possibly due to reversal of phases, the motor
rotates in a direction opposite to its normal direction of rotation. In several applications,
such as hoists and elevators, this is a serious hazard. In such situations, a phase sequence
detector, which is generally a part of under-voltageiover-voltage, or a negative phase
sequence protection scheme, can be used to instantaneously trip the motor.
9.6 Abnormal Operating Conditions from MechanicalSide
9.6.1 Failure of Bearing and Rotor Jam
i
Bearing failure or rotor jam causes excessive load torque on the motor. This is reflected
in the increase in stator current. In order to discriminate between rotor jam and other .$
*operating conditions that can also cause over-current, the high current is not recognized I,$,>
as a jam condition unless the motor has reached its rated speed and the current is in ..,-
excess of 20% of full load persisting for at least twice the locked rotor time setting. .<
<,{
9.6.2 Overload 8
,$
.TThermal overload relays offer good protection against short, medium, and long duration
1
overloads but may not provide protection against heavy overloads shown in Figure 9.12.
q1
..
~ ~ .-. - - i ', -.-- --, -
I

!nd~rcrionMotor Protection 193
The long time induction over-current relays provide good protection against heavy
overloads but over-protection agalnst light and medium overloads, as shown in
Figure 9.13. Therefore, a combination of both the relays provides adequate protection as
Thermai overload
Inadequate
protection
protection
I Starting time
, ,
I 4 i >
Motor current
Figure 9.12 Thermal overload relays offer good protection against short, medium, and long
duration overloads.
Thermai capability
Long time induction
.'OC relay
Good
Over- protection
protection
rotor time
I Starting time
I
1 t
Motor current
8 Figure 9.13 Long time induction OC relays offer good protection against heavy overloads.
A Thermal capab~lity
Long time induction
OC relay
Thermal capability
rotor time
- Starting tlme
J. t
Motor current
Figure 9.14 Combination of thermal overload relays and OC relays provides complete
thermal protection.

194 F~oldo~lre~lralsof Porver Svsrem Prorecrioll
Resistance temperature detector relays (RTDs)
These relays operate from one or more RTDs that monitor the temperature of the
machine winding, motor or load bearings or load case. They are usually applied to large
motors of 1500 HP and above.
Figure 9.15 shows an RTD which is embedded in the machine connected to a
Wheatstone bridge. The arms of the bridge are adjusted so that the bridge is balanced at
normal temperature. A sensitive relay in the form of a contact making dc galvanometer
may be connected as a detector.
~ r n b e d min
machine winding
Figure 9.16 RTD embedded in the machine connected to a bridge'
.,..
The RTD is an excellent indicator of average winding temperature, however, it is
influenced by ambient temperature, ventilation conditions and recent loading history.
Several types of RTDs are available for use in temperature monitoring, namely
10 0 copper, 100 R nickel, 120 R nickel, 120 R platinum.
Thermal replica relays
Replica type relays are designed to replicate, within the relay operating unit, the heating
characteristics of the machine. Thus, when current from the CT secondary passes
through the relay, its time over-current characteristic approximately parallels that of the
machine capability curve at moderate overload.
The thermal replica relays are recommended when the embedded temperature
detectors are not available, otherwise the RTD input type relays may be used.
Replica relays are typically temperature compensated and operate in a fixed time at
a given current regardless of relay ambient variations. Although this characteristic is
desirable for the stated condition, it produces under-protection for high motor ambient
and over-protection for low motor ambient.

I~tiucrion,kloror Protection 195
9.7 Dafa Required for Designing Motor Prokd*onSchemes
The following data is required for designing the various motor protection schemes:
H P rating
Supply voltage
Full-load current
r Permissible continuous allowable temperature rise
Locked rotor current
w Permissible maximum time with locked rotor
w Accelerating time
Starting voltage
Review Questions
1. What are the various abnormal operating conditions from supply side to which an
induction motor is likely to be subjected?
2. What are the various abnormal operating conditions from the load (mechanical)
side to which an induction motor is likely to be subjected?
3. Why is an induction motor very sensitive to unbalance in supply voltage?
4. What are the consequences of running an induction motor on unbalanced supply
voltage?
5. What are the effects of running an induction motor at reduced supply voltage?
6. Why is protection of an induction motor against reversal of phase sequence
required?
7. What kind of protection is provided to an induction motor against overload?
8. How is the thermal replica relay used to protect the induction motor?
9. What are the effects of single phasing on the induction motor?
10. What is the effect of blocked rotor on the motor? What protection is provided
against blocked rotor?
11. Why a negative sequence voltage relay cannot detect single phasing between relay
and motor but can detect single phasing between the supply and the relay?
12. What data is required for designing a scheme for motor protection?

10.1 Comparison vs Computation
An over-current relay compares the magnitude of the current in its current coil with a
set value and operates if the current is more than the set value. A directional relay
compares phase angle of the measured quantity (i.e. current) with a reference c has or (1.e.
voltage) and operates if this phase angle exceeds a redetermined threshold. A simple
impedance relay compares the torque generated by the current (operating torque) with
the torque generated by the voltage (restrainingtorque) at the relay location and operates
if the operating torque is greater than the restraining torque. All the relays perfom some
or the other kind of comparison. Thus, at the heart of any relay, is always a comparator.
Historically, these comparators were implemented using electromechanical technology.
But eventually the electromechanical relays gave way to the solid-state relays.
An alternative strategy to comparison is to perform dlrect numerical computation.
Rowever, in the p a t , when electromechan~calrelays were being wldely used it was not
possible to perform the numerical computation in a relay. The comparators helped in
avoiding direct numerical computation. The relays based on comparators were found to
be quite simple and robust. This gave rise to the technology of protective relays built
around comparators,
The metaphor of the comparator-based relay was so powerful that long after
numerical computation became easily possible in protect~verelays, the engineers
continued to implement the comparator-based relays in their relaying algorithms.
The comparator-based relays are very attractive because of their inherent simplicity
and low cost. However, they suffer from the drawback that (since a comparator-based
relay essentially gives a go-no-go type of decision) the fault cannot be precisely located.
I The comparators can be classified into two types; those based on comparison of
amplitude and those based on comparison of phase angle.
10.2 Amplitude Comparator
1
The amplitude comparator has two inputs, Soand S, and a trip output. Both the inputs
1%

Static Compnrnrors as Relays 197
--- - --- -
are phasors. The input phasor So is called the operating quantity and the input phasor
S, is called the restraining quantity. The amplitude comparator follows the simple law
(Figure 10.1)
If 1S o > 1S then trip; else restrain
Amplitude comparator
s-rr~Tsr - (;ip,Figure 10.1 Amplitude comparator.
Some specific instances where the amplitude comparator gives the trip output are
shown in Figure 10.2(a), which emphasize the fact that the amplitude comparator
responds only to amplitude and is blind to the phase angle between the inputs.
I
,,
,
I
------------so s, ---------.--
/-''
,
so
IS,[ > ISrl :. Trap S o > IS, :. Trap
Figure 10.2(a) Inputs to amplitude comparator resulting in trip output.

198 Fu~tdamentalsof Power Systen~Protection
Figure 10.2(b) shows some specific instances where the amplitude comparator is Caused
to restrain. It again emphasizes the fact that amplitude comparator responds only to
amplitude and is blind to the phase angle between the inputs.
,,
,I
I
S, ------------
I
II,II
/ r s r
I /Sol< IS,I :. Restrain
so
II (Sol< (S,I :. Restraln
I
I I
I
I I
I 1
, ,?
I
------------ ------------p so sr
a,.j
T'sr
IIIII . , '1j
I
I So I
I
I
,I
1:
[Sol4 lSll :. Restrain lSol < /Srl :. Restraln , '7
4
FigurelO.Z(b) Inputs to amplitude comparator causing it to restrain. 3
4
Further, some specific instances where the amplitude comparator is on the verge or
threshold of tripping, are shown in Figure 10.2(c),which again emphasizes the f&dthat . .!
amplitude comparator responds only to amplitude and is blind to the phase angle between
.nthe inputs.
G :
I I
I ISol = IS,! .: Threshold I
I (Sol= ISr/ .: Threshold
Figure 10.2(c) Inputs to amplitude comparator causing it to be on the threshold.

raric Comparators as Relays 199
7 0.3 Phase Comparator
Phase comparators are of two types: the cosine type and the aine type.
.:10.3.1 The Cosine-type Phase Comparator
The cosine-type phase comparator has two phasors Spand 9, at its input and has a trip
output. The input-phasor, designated as Spris the polarizing or reference input. The
input-phasor, designated as S,, is called the measured input. The cosine-type phase
comparator follows the trip law:
If -90" < Arg (S,/Sp) < +90° then trip; else restrain
This is shown in Figure 10.3.
+goo
* Srn
Sm- Cosine-type phaseF l T r l pcomparator Restrain F*sReference
SP-
Figure 10.3 Cosine-type phase comparator.
Some specific instances where the cosine-type phase comparator gives the trip output
are shown in Figure 10.4(a), which emphasize the fact that phase comparator responds
only to phase angle and is blind to the relative amplitudes of the two inputs.
1Arg (SdS,) = zero :. Trip
: ,
.---------
, .
,---------
..
, .
f m ,. ' k s p
s m
Arg (S,,,'Sp) c 90' :. Trip Arg (SdS,) > -90' :. Trip
Figure 10.4(a) Inputs to cosine-type phase comparator resulting in trip output.

200 Furnlarire~italsof Power Systern Protection
---
Some specific instances, where the cosine-type phase comparator is caused to restrain
are shown in Figure 10.4(b),which further emphasize the fact that the phase comparator
responds only to phase angle and is blind to the relative amplitudes of the two inputs.
Arg (SJS,) = 180" :. Restrain Arg (SJS,) = 180" :. Restrain
Arg (sJS,) r 90' :. Restrain Arg (SJS,) > -90" :. Restrain
Figure 10.4(b) Inputs to cosine-type phase comparator causing it to restran
.
Further, some specific instances where the cosine-type phase comparator remains on the i
threshold of operation are shown in Figure 10.4(c), again emphasizing the fact that the '
phase comparator responds only to phase angle and is blind to the relative amplitudes of !
the two inputs.
Arg (SJS,) = +90" :. Threshold Arg (SJS,) = -90' Threshold
Figure 10.4(c) Inputs to cosine-type comparator causing it to be on threshold.
10.3.2 The Sine-type Phase Comparator
The sine-type phase comparator has two phasors Spand S, at its input and has a trip
output. The input phasor, designated as S,, is thepolarizing or reference input. The input
phasor, designated as S,, is called the measured input. The sine-type phase comparator
follows the trip law:
If 0" < Arg (S,/Sp) < 180" then trip; else restrain

Sruric Compuraturs as Relays 201
Figure 10.5shows the various cases of input so the s l n e - t ~ ephase comparator, which
result in trip, restrain, or threshold output. It emphasizes the fact that, ideally, the phase
comparator is sensitive only to the phase of the signals and ignores their magnitudes.
Sine-typephase
comparator
0'
Restrain SP
Restrain
Threshold Threshold
I
I I
8
8
I
I smI r
I
,I
I
I I
Figure 10.5 Sine-type phase comparator: hip, restrain and threshold conditions.
10.4 Duality Between Amplitude and Phase Comparators
There is a relationship of duality between the amplitude and phase comparators. If the
inputs of an amplitude comparator are modified according to the theorem of duality then
they become suitable as inputs for a phase comparator and vice versa. In the discussionI
that follows, unless otherwise explicitly specified, we mean cosine comparator when we
I mention phase comparator. Let S, and S, be the original inputs to an amplitude
comparator. If we derive S, and Spfrom Soand S, such that
i
I S, = (So+ S,) and Sp= (So- S,),
and feed these to a phase comparator, then the output of the phase comparator would be
I exactly the same as that of the original amplitude comparator (see Figure 10.6).
I
I

202 Fundamenrals of Power System Pmfection
..........................................
So + S, = s,
so
comparator comparator
S,
I So- S, = SP
'---------------------------------------->
Figure 10.6 Duality between amplitude and phase comparators.
Similarly, let S, and S, be the original inputs to a phase comparator, then if we derive
Soand S, from S, and S, such that
So= (S, + S,) and S, = (S, - S,)
and feed these to an amplitude comparator, then the output of the amplitude comparat
Thus, we can generalize the duality theorem as follows:
"Cwould be exactly the same as that of the original phase comparator (see Figure 10.7)
..........................................
Sp + S, = So
Sm
SP
Sp- S, = S,
..........................................
Figure 10.7 Duality between phase and amplitude comparaf$rs. .,
. ., ,
The two signal, obtained by adding and subtracting tge inputs to a
comparator, are the inputs suitable for its dual. If such signals are fed to the
dual, the output would remain unchanged.
The duality theorem can be easily and elegantly proved with the help of graphi*
construction as shown in Figure 10.8.
By theorem of duality
S, = So + S,
s, Sp = So- S,
IS01 < ISrI
AmplitudesOjpbs, comparator Restrain i
- i
, .:
Arg (SdS,) > 90' g
>
Phase , , :
comparator Restrain . j

-
Statrc Con~pararorsas Relays 203
In Figure 10.8, we can see that IS,( < IS,/. Therefore, an amplitude comparator
would restrain. The geometrical construction shows, how the S, and Spare synthesized,
by addition and subtraction of /Sol and IS,/. It can also be easily seen that since
Xrg [(So+ S,)/(S, - S,)] > 9O0,the dual-phase comparator would also restrain if fed with
such signals.
In Figure 10.9, we can see that ( SoI > J S, I. Therefore, an amplitude comparator would
operate (trip). The geometrical construction shows, how S, and Sp are synthesized,
by addition and subtraction of So and S,. It can also be easily seen that since
arg [(So+S,)/(S,- S,)] i90°, the dual-phase comparator would also operate (trip)if fed with
such signals.
e By theorem of dual~ty
S, = So + S,
Sp = So - S,
Is01'Is,[ Arg (SJS,) < 90"
Amplitudes"l[Ts, comparator Tnp C) comparatorPhase
Figure 10.9 Duality between amplitude and phase comparators for So > S,.
In Figure 10.10, we can see that arg (Sm/Sp) > 90". Therefore, a phase-type
comparator (cosine-type) would restrain. The geometrical construction shows that the
signals Soand S, can be synthesized by addition and subtraction of S, and Sp.It can also
be easily seen that since ISo( < ( S, I, the dual-amplitude comparator would also restrain
if fed with such signals.
I
Arg (SJSp) > 90"
SP
By theorem of duality *
So = Sp + Sm
S, = Sp - S,
Amplitude
I Figure 10.10 Duality between phase comparator and amplitude comparator for
arg (S,/Sp) > 90".

204 F~o~n'nnre~,mlsof Power Systein Protectiorz
-
In Figure 10.11, we can see that arg (S,/S,) < 90". Therefore, a phase comparator
would operate (trip).The geometrical const~uctionshows, how the signals Soand S, are
synthesized by the addition and subtraction of S, and Sp.It can also be easily seen that
since JS,1 3 IS,), the dual-phase comparator would also operate (trlp) if fed with such
signals.
S,4
Arg (SJS,) < 90'
Phase
comparator Trip
By Theorem of duality
So = Sp + S,
S, = S, - S,
ISOI 'ISrI
Amplitude
comparator
Figure 10.11 Duality between phase comparator and amplitude comparator for
arg (S,/S,) -= 90".
Similarly, it can be shown that the duality holds good when the comparator is on
threshold of operation. Thus, if the original inputs to an amplitude comparator cause it
to remain on the threshold of operation then the modified inputs to its dual-phase
comparator would also cause it to remain on the threshold of operation.
10.5 Synthesis of Various Distance Relays Using Statiy
Comparators
It is possible to synthesize a variety of relays using static comparators. We develop here,
a purely geometric method for deriving inputs suitable for the synthesis of various
distance relays. The method consists of locating two phasors, involving Z, the impedance
seen by the relay and Z,, the setting of the relay, such that the phase angle between them
crosses +90" as the impedance seen by the relay moves from the trip to the restrain
region. These two phasors, in principle, are suitable for driving a phase comparator
(cosine-type). Next, we convert these two phasors into two voltages suitable for feeding
a practical electronic c~rcuit.
10.5.1 Synthesis of Mho Relay Using Static Phase Comparator
Figure 10.12 shows the synthesis of a mho relay using a phase comparator. The mho relay
to be synthesized has a setting of (Z,ILB,. The characteristic to be synthesized is thus

a circle with diameter as phasor Z,. Now, let the impedance seen by the relay be Zrl
represented by point =1 in Figure 10.12. Since the impedance phasor lies within the trip
region, the relay must issue the irip output. It can be easily seen from the figure that the
phasor (Z, - Zrl), represented by line AE: !eads the phasor Zrl by an angle which is
definitely less than 90". The figure shows that as the impedance seen by the relay moves
towards the boundary between the trip and restrain regions, the angle between (Z, - Z,)
and Z, moves towards 90". When the phasor representing the impedance seen by the relay,
lies on the boundary, this angle is exactly 90" (for example, the angle between PB and
OB = 90"). For all impedances lying outside the trip region, i.e. in the restraining region,
the angle between (Z, - Z,) and Z, is always greater than 90" (for example, the angle
between CP and CD).
I OA = IZ,,l + Trip AP = (2, - Z,,l
I
1 OB = lZr21+ Threshold BP = 12, - Z,zl
I
1, OC = lZr31+ Restrain CP = 12, - Zr31
I 2" - 1 I _ < 90"
Arg I Zr1I
I) Trip
IZn -"" = LCBP = 90" I) Threshold
Arg 12,21
I
I IZn = LDCP > 90' I) Restram
12~31
Trip law:
If Arg lZn go", then tr~p
IZrI
I Figure 10.12 Synthesis of mho relay using cosine-type phase comparator.
I
Similar analysis shows that even if the impedance seen by the relay is on the other
i side of Z, as shown in Figure 10.13, as long as it is in the trip region, the angle between
(Z, - Z,) and Z, is always greater than -90". The angle hits 90" for boundary conditions

206 Fundamentals of Power System Pmrect~on
and becomes less than -90" as the impedance seen by the relay moves into the restraining
region.
OA = IZril + Trip
OB = IZ,ZI -P Threshold
OC = (Zr31+ Restrain
Arg IZn -Zr7 I = LPAB > -90" I) ~~i~
1
Izril i~.
IZn -Zf21 = LPBC = 90' I) Threshold
Arg 1zr21
I
i i .
I_/ !
Arg IZn -Zr31 = LPCD < -90" ~ e s t ~ i n
-.> $ i
Izr3I 5 : ! I. j
-.,. i .
Trim law: . A . j l...r
If Arg I '"-Zr I > -90"; then trip
I Z,I
Figure 10.13 Synthesis of mho relay using phase comparator.
*; /
Thus, the phasors (Z, - &) and Z, obey the law of cosine-type phase comparison.
Therefore, if (Z,- Z,) and Z, are used as inputs to a cosine comparator, the resulting
entity would behave exactly like a mho relay.
However, there is a practical problem here. The problem is that the electronic circuit
of the comparator accepts only voltage signals at its input. We, therefore, need to convert
these two impedance phasors into voltage signals.
If we multiply both (Z, - Z,) and Z, by the current at the relay location I,, then we
get (I,& - I,Z,) and Z,I, .Note that Z,I, is nothing but the voltage at the relay location
V,. The two modified signals therefore are:
I - V and V,
Thus, we find that (I,Z, - V,) and V, are the two voltage signals which can be fed . -
to a cosine-type comparator for synthesis of a mho relay with a setting of Z,.

3tatic Comparators as Relay: 207
Mho relay----------------------------, X
! Cosine-type phase comparator
"I Trip
s p = ? t Trip I
I
I
I
I R
Mho relayr _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ - - - - - - - - -
' Cosine-type phase comparator
j!
Trip
S p = Vr I
Trip
I
I
I RI I
Figure 10.14 Deriving practical signals for mho relay synthesis.
At the relay location, we have the signals V, and I, readily available. In order to form
Spand S, inputs suitable for synthesis of mho relay, we will have to mix them using
suitable hardware to get the required signals.
The circuit arrangement for mixing the relay voltage and current signals is shown in
Figure 10.15.
Trip
Figure 10.15 Mho relay synthesis using cosine-type phase comparator.

208 F~trtda~~te~~ralsof Power Sysrenl Prorecrio~l --
10.5.2 Synthesis of Reactance Relay Using Cosine-type Phase
Comparator
Figure 10.16 shows the synthesis of a reactance relay using a phase comparator. The
reactance relay to be synthesized has a setting ofjX,,. The characteristic to be synthesized
is thus a straight line parallel to the R-axis (abscissa), with an intercept of IX,( on the
X-axis (ordinate). Let the impedance seen by the relay be ql,which lies within the trip
region at point A. Let us construct the phasor (X,- Zrl) represented by line AE! It can
be easily seen that (X,- Zrl) leads Xn by an angle which is definitely less than 90". Now,
as the impedance seen by the relay moves towards the boundary of the trip region, the
angle between (Xn - Zrl) and Xn approaches 90". When the impedance lies on the
boundary, the angle becomes exactly equal to 90". For all points lying in the restraining
region, the angle becomes greater than 90".
X
- ":
Restrain ,
".
"t""""""""'"' / 1 1 / 1 , 1 / 1 , 1 1 , / 1 /
Trip
!
X"
I
..
V >R
0
OP = IX,I = Setting
OA = IZ,,I + Trip AP = IXn -Z,,I
OB = IZr21-+ Threshold BP = [X, - Zr21
OC = IZ,,/ -+ Restra~n CP = IX, - Z,,I
Arg I n - 2 = LOPB .1 1 1 = 90"
IXnI
1) Threshold
IXn -Zr3' = LOPC = LIII > 90" 1) Restrain
Arg I X"I
Trip law:
If Arg --Xn - Zr < go", then trip
X"
Figure 10.16 Deriving inputs for synthesis of reactance relay
I

Sraric Cornparators as Relays 209
Similar analysis shows thac if the impedance seen by the relay lies to the left of the
JX, phasor, the angle between (Xn - Zrl) and &, is greacer than -go', as long as the
impedance falls within the trip region. It is exactly equal to 90" for impedance lying on
the boundary and is less chan -90" for all impedances lying in the restraining region to
the left of the jXn phasor. This is shown in Figure 10.17.
OP = /X,I = Setting
OA = IZ,,( + Trip AP = JX, -Z,,l
08 = (Zr2(+ Threshold BP = IX, - Zr2)
OC = /Zr31-+ Restrain CP = IX, - &$I
IXn -Zr21 = LOPB = LII = 90" + Threshold
Arg IX"I
I Xn -Zr3' = LOPC = Lill < -90" Restrain
Arg IXnI
Trip law:
If -90" < Arg I Xn then trip
IXnl
Figure 10.17 Deriving inputs for synthesis of reactance relay.
Thus (X, - Z,,) and X, seem to be suitable for feeding to a cosine-type phase
comparator for synthesizing the reactance relay.
As discussed earlier, electronic circuits, which are used to implement the cosine-type
comparator, need voltage signals. Therefore, we can get voltage signals from these two
inputs by multiplying each of them by I,, the current at the relay location. The modified
signals that we thus get are (X,I, - Zrl I,) and XnI,. This is shown in F i e r e 10.18.
Note that Zrl I, is nothing but the voltage at the relay location, i.e. V,. Thus, the final
inputs to the cosine comparator for synthesis of reactance relay are:
S,=X,,I, and S,=(X,I,-V,)

210 Funda~nenralsof Power Systenz Protection
Reactance relayr _ _ _ _ _ _ _ _ _ - _ - _ _ - - - - - - - - - - - - - ,
R
X,I, = S,
(X" - Z,)I, = X,I, - v, = S,
Reactance relayr_________---_---__---------, X
S, = X,I, ATbTflp,,,,1,,,,,,,,,,,, ,
0
w
S, = X,I, - V, , Trip x,
R
Figure 10.18 Deriving practical signals for reactance relay synthesis
10.5.3 Synthesis of Simple Impedance Relay Using Ahrplitude
Comparator .:
The simple impedance relay is inherently based on an amplitude compabator. If the
magnitude of the impedance seen by the relay IZ,( is less than the setting";of the relay
(Z, 1, then the relay issues a trip output. Thus, the simple impedance relay can be most
easily synthesized by an amplitude comparator with the following signals.
Operating Signal So = Z,
Restraining Signal S, = Z,
In order to make the inputs suitable for driving an electronic amplitude comparator
circuit, we multiply each of them by I, to get the modified signals:
S , = Z , I , and S , = Z , I , = V ,
10.6 Development of an Electronic Circuit for Implementing
a Cosine-type Phase Comparator
There are various ways in which a cosine-type phase comparator might be implemented
using an electronic circuit. The approach described here is based on measuring the
coincidence period between the two waveforms whose phase difference is to be measured.
One can measure either the positive or the negative coincidence period.
h -

Simple impedance reisy............................
I
Amplitude
wmparator Trip, , r R
If IS,I > S,I then trip
I
4
L - - - - - - - - - - - - - - - - - - - - - - - - - - - ,
Simple impedance relay,____--___-____-___----------
i Amplitude
wmparator
Trip
R
i S, = V, If (Sol > IS,( then trip
i ,
k I I
i
L _ _ _ _ - _ _ _ _ - _ _ _ - _ _ _ _ - - - - - - - - - ,
r Figure 10.19 Synthesis of simple impedance relay using amplitude comparator.
The positive coincidence period is defined as that tlme during whlch both the waves
are of positive polarity. The negative coincidence period is defined on similar lines.
In the case of two pure sine waves, the positive and the negative coincidence periods
are equal.
By measuring the coincidence period, we have essentially converted the problem of
phase angle measurement into that of time period measurement. Observation of the
waveforms of Figure 10.20 shows that, considering 50 Hz power frequency, the
Phase shift between S, and S, = Zero
Figure 10.20 Coincidence
----20 ms- ---4
S, lags S, by 90'
period for phase shift of 0" and 90" lag.

I 212 Fu~~da~?ienmlsof Power System protect lot^
- -
coincidence period is always greater than 5 ms (or Ti4 s where T iu the time period of the
power frequency) if the S , wave is within +9O0of the S pwave or within the trip region
of the phase comparator. Thus, implementing a cosine-type comparator boils down to
generating a pulse whose width is proportional to the phase difference between the two
input waves. Next, we should have an arrangement to measure the width ofthis pulse.
If the pulse width is greater than 5 ms (or T/4 s) then a trip output should be issued. If
the width of the coincidence period pulse is less than 5 ms then output should be
restrained.
Figure 10.20 shows that the coincidence period pulse is of 10 ms duration when the
two inputs are in phase. As S , starts lagging Sp,the coincidence period decreases. When
S, lags S , by 90°, the coincidence period falls exactly to 5 ms.
Figure 10.21shows that the coincidence period pulse is of zero duration when the two
inputs are out of phase by 180".As S, starts leading S,, the coincidence period increases.
When S,,, leads S, by 90°,the coincidence period builds upto exactly 5 ms.
---- 20 ",s -----
4
S, leads S, by 90" Phase shlft between S, and S, = 180'
Figure 10.21 Coincidence period for phase shift of 90" lead. fs
The variation of coincidence period with the phase shift between the two signals S,
and S,, with S, as the reference phasor, is shown in Figure 10.22.
It can thus be seen that for tripping condition, the coincidence period is always
greater than 5 ms. For restraining condition, the coincidence period is always less than
5 ms. For boundary of tripping or verge condition, the coincidence period is exactly equal
to 5 ms.
The above analysis clearly suggests that if we can devise a circuit which is able to
generate a pulse whose width is equal to the actual coincidence period between the two
signals, and check whether the pulse width is greater than 5 ms, then we can easily
implement a cosine-type phase comparator. Thus, we need not measure the absolute value
of pulse width but should only be able to compare it with a 5 ms time period. This has

the advantage of avoiding actual measurement. We thus circumvent the measurement
problem by using a comparator.
Smleads Spby 90'
ColP = 5 ms Sm
ColP c 5 ms ,* CoiP > 5 ms
am
ColP = 5 ms
S, lags Spby 90"
Restraining
reglon
s m
ColP = Zero <
Smout of phase Restraining
with Spby 180"
region
CoiP c 5 ms
1 Figure 10.22 Variation of coincidence period with phase shift (superimposed on cosine-type
1 phase comparator characteristic).
I
Trip
,, region
SP
* CoiP = 10 ms
;'-, Trip Smin phase with Sp
I ,
, region,
,
' '. ColP > 5 rns
Figure 10.23 shows the block diagram of a cosine comparator based on comparison of
1
positive coincidence period. The input signals are first rectified to remove the negative
excursions. The resulting waves are converted to blocks by passing them through a
zero-crossing detector. We thus get two square waves whose high time is equal to the time
1 for which the oriplnal waves were positive. The coincidence period is detected by logical
i ANDing of these two signals. The width of the resulting pulse is equal to the positive
V '4
- s m
I
Sm+ negative
half
Squaring Comparator
s~ negative circuit
E
i
A
i
Figure 10.23 Block diagram of static cosine-type phase comparator based on coincidence
principle.

214 Fundatne~ltalsof Power System Pmtectian
coincidence period between the two signals. This pulse is then integrated and the output
of the integrator is compared with the expected output for a pulse of 5 ms duration. This
expected output is pre-calculated and set up on the potentiometer as Vref.
If the coincidence period is more than 5 ms then the output of the integrator is more
than Vrefand the comparator is triggered into high output state. The output of the
comparator can be treated as the trip output.
If the coincidence period is less than 5 ms, the output of the integrator never reaches
the level of Vref,thus the comparator output remains low.
The waveforms at various points are briefly shown in Figure 10.23and in more detail
in Figure 10.24.
".
Integrator I j a
?
r Time
I
I I
!
Time
Monostable outout~,
Tme
Figure 10.24 Waveforms for cosine-type phase comparator based on comparison of
,,$
coincidence period.
i(

Srar~cCon~poroiorsas Relovs 315
Figure 10.24 shows that the inputs s3',and Spto the cosine-type phase comparator
are in phase. The coincidence period is, therefore, 10 ms. The integator output,
therefore, exceeds the reference voltage Vref and the comparator is triggered into a high
output state, thus issuing a trip output. This low-to-high transition of the comparator is
latched by a re-triggerable monostable so that it remains continuously high.
Figure 10.25 shows an implementation of cosine comparator which is built around the
quad comparator integrated circuit (IC) LLM339. The comparator IC works on a single
(unipolar) dc supply.
Figure 10.25 An integrated circuit comparator-based circuit for cosine-type phase comparator
based on coincidence principle.
The input signals are clipped to safe values before feeding to the IC input. The first
two comparators work as zero-crossing detectors producing a square wave during the
positive excursion of their respective inputs. The output of LM 339 IC is of pen-collector
The comparator IC follows the following law:I If Vp> V ,then the output point floats.
If Vp< V, then the output point is effectively connected to ground.
This is shown with the help of a switch inside the IC in Figure 10.25.
I The outputs of the two zero-crossing detectors are wire-ANDed by physically
a connecting them together. Thus, the output is high if and only if both the zero-crossing
detector outputs are hlgh. Thus, in effect, we get the coincidence period pulse at the
wire-ANDing point. Further, since both the outputs float during the coincidence period,
the C,,,, can charge through Rlntg,for a time equal to the coincidence period. The voltage
across the integrator capacitor is thus proportional to the coincidence period. This voltage

216 filndarnenra/s of power System Protection
-
is compared with a preset value obtained with the help of the potentiometer. The preset
value is same as the value that the integrator capacitor would reach for a coincidence
period of 5 ms, corresponding to phase difference of 90" (either 90" lag or lead). Thus, if
the coincidence period is more than 5 ms, the integrator develops a higher voltage than
the reference voltage and we get a trip output. In order to latch the output to a steady
high value, a re-triggerable monostable circuit is used.
10.7 An Electronic Circuit for implementing a Sine-type
Phase Comparator
Recall that a sine comparator issues a trip output if Sm leads Spby any angle between
0" and 180". In order to develop an electronic circuit for implementing a sine-type phase
comparator, refer to Figure 10.26, where S, is shown to lag S,. This is the phase
relationship for which the sine comparator should restrain.
9 r;For this condition, it is seen that there is no coincidence between the spike and t e
block. In fact, for any angle of lag of S, with respect to S,, it can be seen that there is .
no coincidence between the spike and the block.
Trip
output
I Trip
Restrain l
Figure 10.26 Relationship between spike and block for S, lagging S,.

Static Comparators ns Re1a.y~ 217
Firare 10.27 shows that if S, leads Spthen there is always a coincidence between the
spike and the block, whatever be the angle of lead. This is the pnase relationship for
which we want the sine comparator to trip.
Figure 10.27 Relationship between block and spike for S, leading S,.
The above relationship between the spike and the block can be utilized to implement
the sine-type phase comparator as shown in the block diagram of Figure 10.28.
I I
Bypass
negative-half
Bypass CMOS
negative-half switch
I -Shunt 1
/ / / I / / / ,
Restrain s~
Figure 10.28 Block diagram of sine-type phase comparator based on coincidence between
b
1 spike and block.
i

218 F~rndamenrolsof Power Systenl Protecrion
The shunt switch is operated by the control voltage. If the control voltage is high, the
shunt switch is ON, thus bypassing the spike to ground.
It can be seen from the figure that when S, lags Sp,the block is low when the spike
appears. However, the invertor makes the control voltage high, thus the switch is closed,
bypassing the spike to ground. This is the restrmning region of the relay.
However, when S, leads S,, there is a coincidence between the spike and the block.
The block remains high when the spike appears. The invertor, however, makes the control
voltage low. Thus, the shunt switch remains open and the spike is allowed to hit the
output terminal. This is the trip region of the sine-type phase comparator.
This is one of the many possible ways in which a sine-type phase comparator can be
implemented.
10.8 Synthesis of Quadrilateral Distance Relay
@ :The fault characteristic of a transmission line is a quadrilateral because of the arcin , ,,?
fault resistance. All the conventional distance relays, such as simple impedance, reactance ,..:
and mho, encompass much more area on the R-Xdiagram than this quadrilateral. An 3
ideal distance relay should have a characteristic which snugly fits around the ,:{
quadrilateral. Such a relay, called a quadrilateral relay, whose characteristic is shown ,!
- 9
in Figure 10.29, is very stable on power swing because it encompasses minimum area on :
the R-Xplane. Note that the quadrilateral is shown slightly enlarged so as to positively i
encompass the fault area.
Line impedance phasor
X = lrn(Vl1)
Trip
R =
I A
Figure 10.29 Characteristic of quadrilateral distance relay.
: I
Such a characteristic can be synthesized by AND compounding the trip outputs of
four different two-input relays shown in Figure 10.30.We need to synthesize the following
characteristics:
Characteristic 1: Reactance relay with setting of X,,
Characteristic 2: Angle-impedance relay with setting of Zn2
Characteristic 3: Directional relay with MTA of -8,
Characteristic 4: Directional relay with MTA of 8,

Static Comparators as Rriays 219
Characteristic 3 Characteristic 2
Figure 10.30 The four characteristics to be synthesized.
I We can synthesize all the four characteristics by using a +90° cosine-type phase
comparator.
Characterzstic Polarizing qty. Measured qty.
Reactance IXn, - V Ixn1
Angle impedance IZn, - V I z n 2
Directional with MTA = el V L -0, I
Directional with MTA = -B2 v L 82 I
Figure 10.31 shows the synthesis of the reactance and angle-impedance
characteristics using cosine comparator.
X = lm(VI1) Line ~mpedancephasor
Charactenstic 2
>
R = Re(V1r)
Characteristic 1
IX,, - V +90" cosine-type
Trip
phase comparator
IXn1
Characterishc 2
I&2 - v k90' cos~ne-type
phase comparator
IZnz
Figure 10.31 Synthesis of reactance and angle-impedance characteristics.

220 Fu'u,ldunzenralsof Power Sysrem Protection -
Figure 10.32 shows the synthesis of directional characteristic with MTA of B2,
x = lm (~11) MTA line
i1 Characteristic 4
t90' cosine-type
' Trip
phase comparator
I
Figure 10.32 Synthesis of directional characteristic with MTA of e2.
Figure 10.33 shows the synthesis of directional characteristic with MTA of el.
Characteristic 3
+90" cosine-type
phase comparator
Trip
C ' .
Figure 10.33 Synthesis of directional characteristic with MTA of el.
Figure 10.34 shows the ANDing of the four characteristics to synthesize thidesired..quadrilateral characteristics.
Line impedance phasor
Characteristic 1
/Xnl - V* A90' cosine-type
IX,, +,phase comparator
Characteristic 2 _
IZn2- V* *90" cosine-type
Z P
IZ,, ,,phase comparator
Characteristic 3
Characteristic 4
*90" cosine-type
phase comparator
10-34 ANDing of the four characteristics to synthesize the
characteristic.

Review Questions
1. List the advantages of static relays.
2. Describe how comparison can circumvent direct computation in protective relays.
3. What is the price to be paid for not implementing direct numerical computation?
4. Define the characteristics of amplitude comparator.
5. Define the characteristics of cosine- and sine-type phase comparators.
6. What is the theorem of duality?
7. Give graphical proof of the theorem of duality.
!
8. Suggest different methods to implement static comparators, than those given in
the text.
i
0,.
9. How will you synthesize a mho relay using an amplitude comparator?
10. How will you synthesize a reactance relay using an amplitude comparator?
!
11. How will you synthesize a directional relay with an MTA of 7 using a cosine-type
! '1 phase comparator?
I!
1 .
12. When the input signal to the cosine-type phase comparator contains a dc offset,
i how does the performance of the relay get affected?
!
.I 13. What is the remedy for the above problem?
i 14. What is the effect of noise and harmonics on the performance of the cosine and
1 sine type phase comparators described in the text?
i 15. Suggest a method to make the static comparators immune, to a large extent, to
all non-fundamental components.
16. A generalized phase comparator can have a phase angle margin of +a,-P. The
cosine-type phase comparator is a special case where a = P = 90". How will the
mho relay characteristic appear if the phase angle margin is changed to ?45"?
!

11.I Introduction
Protective relays, which started out as meters with contacts, have undergone tremendous
evolution over the years. They were soon replaced by electromechanical relays which were
sensitive and accurate. When vacuum tubes were in vogue, protection engineers
implemented relays using vacuum tubes. Within a year of invention of the transistor, its
use in protective relays was reported. With the development of large-scale integrated
circuits, these were extensively used in the protective relays. The microprocessor that was
invented around 1971 revolutionized the electronics scene in its entirety and the
development of a microprocessor-based relay followed soon thereafter. However, a subtle
shift in the paradigm takes place when we move on to the microprocessor-based relay,
which works on numbers representing instantaneous values of the signals. Hence, the
name numerical relay. Other popular nomenclatures for such relays are digital relay,
computer-basedrelay or microprocessor-basedrelay.
In numerical relays, there is an addit~onalentity, the software, which runs in t e
background and which actually runs the relay. With the advent of numerical relays, dbemphasis has shifted from hardware to software. Hardware is more or less the same
between any two numerical relays. What distinguishes one numerical relay from the other
is the software.
The conventional non-numerical relays are go-no-go devices. They perform
comparison rather than straight numerical computation. In fact, the convent~onalrelay
cleverly bypasses the problem of computation by performing comparison. The numerical
relay does not have any such limitation because of its ability to perform real-time
computation. Thus, the relay engineer need not merely implement the old relaying
concepts but can devise entirely new computation-based concepts.
The modern numerical relay has thus evolved from a torque balanczng device to a
programmable znformation processor.
We can implement an existlng relaying concept using the numerical technique.
However, the possibilities of developing a new numerical relay are almost endless and
there is very little standardization. The process of development of a new numerical relay
is shown in the flowchart of Figure 11.1
222

State the relaying problem
I
Mathematically mod
Write algorithm
Write program simulation
(High-level language)
T Data
WL<>algorithm
bench
i
Analogue
Test with test inouts I
inpuk from
CT and PT
existing relay t
period of 2-3 years
Figure 11.1 Development cycle of a new numerical relay
11.2 Block Diagram of* Numerical Relay
Figure 11.2 shows the block diagram of a numerical relay. The signals from the CTs and
PTs cannot be sampled directly and converted to the digital form. This is to make sure
that the signal does not contain frequency components having a frequency greater than
one half of the sampling frequency. This limit is enforced by the Shannon's sampling
theorem.

224 F1r1rdo1~re11ru1.yof Pon'er S!JSIPI~IPvo[e~fioll -
/
Trip
/. -Select .-
Start conversion t
'Ommand command i,
I'
Analogue Anti-
signals aliasing +Multiplexer 1,Sample
and holdfrom CT filters
and PT (Analogue) Circuits
I-
*
Figure 11.2 Block diagram of numerical relay.
Therefore, the signals are first passed through a low-pass filter, which has to be an
analogue type of filter, because digital processing can only take place after the frequency
spectrum of the signal is properly shaped.
Next, the analogue signal is sampled and held constant during the time the value is
converted to digital form. The sample and hold circuit is an absolute must. The range of
frequencies that can be handled by the analogue-to-digital converter AD^) without the
sample and hold (S/H) circuit is extremely low as shown in Table 11.1.
-7.
..A
Table 11.1 Comparison of maximum allowable frequency with and without S/H
Without SIH circuit With SIH circuit-
dv
1. -= VI~IIscale d i ~
1. -= Vfui~scale
dtmm ~ " T A D C ~ ~ ~ T ~ / ~ a p e r t u T e
where TADc,, is the conversion where Tsm aperture is the acquisition
time of the ADC. time of the S B circuit.
1 7-
- 1 .4
2. fm, = 2. fmax= Ii
2 n 2 n T . ~ w 2x2" T s ~aperture ;a,..;I
n = ADC word length = 16 bits n = ADC word length = 16 bits .' j
:..<
Tmc,,, = 10 ,US (~ypick) T s i ~aperture = 250 ps (Typical) .?'<1
Vm = VU ..A. Vm = "full acale ;; ..
Gives: Gives: ,;{:*:
f,, = 0.24 Hz f,, = 9.7 kHz .$
;.,?
Thus, without S B , the ADC can handle With S B , the same ADC can now handle .:i
only extremely low frequencies. much higher frequencies. 4..>,
. ..
.:I

The sampled and held value is passed on to the ADC through a multiplexer so as to
accommodate a large number of input signals The sample and hold circuit and the ADC
work under the control of the microprocessor and communicate with it wlth the help of
control slgnals such as the end-ofconverszon signal issued by the ADC. The ADC passes
on the digital representation of the ~nstantaneousvalue of the signal to the
microprocessor via an input port. The output of the ADC may be 4, 8, 12, 16, or 32 bits
wide or even wider. The wider the output of the ADC, the greater its resolution.
The incomlng digital values from the ADC are stored in the RAM of the
microprocessor and processed by the relay software in accordance with an underlying
relaying algorithm. The microprocessor issues the trip signal on one of the bits of its
output port which is then suitably processed so as to make it compatible with the trip coil
of the CB. The microprocessor can also be used to communicate with other relays or
another supervisory computer, if so desired. The relaying program or the relay software,
which resides in the EPROM, can only be upgraded or modified by authorized personnel.
Thus, new features and functionalities can be added to an existing relay by upgrading its
software.
A numerical relay can be made to run a program which periodically performs a self-
diagnostic test and issues an alarm signal if any discrepancy is noticed. Other features
like a watch-dog timer can also be implemented, which issues an alarm if the
microprocessor does not reset it, periodically, within a stipulated time of a few
milliseconds. This gives an increased user confidence and improves the reliability of the
relay.
11.3 Sampling Theorem
The sampling theorem states that in order to preserve the information contained in a
signal of frequency C O , , ~ ~ ,it must be sampled at a frequency at least equal to or greater
than twice the signal frequency. Thus, we must have
(11.1)1msamging, min 2 2msigna1
The lower limit on sampling frequency, equal to ~OJ,,,,~, is known as the Nyquist
limit. If the signal is sampled below the Nyquist limit, it gives rise to the phenomenon
of aliasing. Aliaszng is the phenomenon of the given signal being lost in the process of
digitzzation, and its place being taken by a different lorver frequency waue.
The above signal refers to a pure sinusoid, which contains only one frequency
component OJ,,,,~. However, when the signal is distorted, as most real-life signals are,
then the Nyquist frequency is equal to 2mslgnel, mar, where m,,,,l, ,,is the highest
frequency component contained in the signal. Thus, the allowable sampling frequencies
are those equal to or greater than 20,,~~,~,max Therefore, we have
1 Wssmp~mg,mm 2 2mslgna1, m u 1 (11.2)
The proof of the sampling theorem can be seen from Figure 11.3.

226 F~tndamentalsof Power Systern Protectiorz
Time domain
Time
Spectrum of sampling impulses
Time
o, = Sampling frequency us- om us+ W,
om= Maximum frequency content of signal
Figure 11.3 Proof of sampling theorem.
The signal has a frequency spectrum which extends up to %.The sampling impulses,
which appear at a frequency of o,, have a repetitive frequency spectrum which repeats at
a spacing of o,. In the process of sampling, the sampling frequency gets modulated by'the
signal. The spectrum of the sampled signal has peaks around 0,f o,, + 2 4 , f30s, and so
on. In order that the envelope of modulation remains distinct, the envelopes should kot
overlap. This will be so provided if
n.
& - % ' %
or
Therefore, we have
%mnpling, min '2usigna1,mru
If the samples of signal, which is sampled below the Nyquist rate, are fed to a digital
to analogue converter (DAC),then the DAC does not reproduce the original analogue
signal, instead it recreates a different low frequency signal as shown in Figure 11.4. The
infomiation contained in the original waveform is thus lost.
Figure 11.4 Phenomenon of aliasing.

Numerical Prorertron 237
--
Protective relaylng signals contain dc offset, a number of harmonics and random
noise. whose spectrum extends from dc to several megahertz. Thus, in order to preserve
information in such signals, we will need an impract~cablyhigh sampling frequency. In
order to get around this problem, the signal is first passed through a low-pass filter t o
shape its frequency spectrum, i.e. remove all frequencies above the cut-off frequency, so
that the minimum (Nyquist) sampling rate comes down to a manageable value as shown
in Figure 11.5. The cut-off frequency is decided so that frequencies of interest are
retained in the sampled version of the signal.
//,//////////,////.
Allowable sampling frequencies
C ,,/,/,,,,,,,,/,,/,,
0 0, 0, = 2 0 ,
Figure 11.5 Minimum sampling frequency.
The above discussion would be applicable, however, if an ideal low-pass filter, which
totally rejects all signals above the cut-off frequency, were available. Such filters do not
exist! What we get is a finite roll-off in the stop band. Thus, the Nyquist sampling rate
has to be pushed further away and a much higher minimum sampling frequency has to
be used in practice as shown in Figure 11.6.
Anti-aliasing low-pass Sample and hold
i%Time + jFkqsSample
(Samplingfrequency)
Actual
Ideal Ideal
{,,,,,,,,,,,,,,,,,,,,,,,,,------------------
Y
Allowable sampling frequencies
Y
Y
/ / / , , 1 / / / / / , / / / / / J / ~ J / I f f / ' / / ' ' / ,
0 w, = 2wk
Figure 11.6 Practical limit on minimum sampling frequency.

ZZS Filndamentals of Power System Protection
-
11.4 Correlation with a Reference Wave
The mathematical operation of correlating a given signal waveform with a set of
orthogonal reference waveforms is the basis of a large family of very useful
transformations. Fourier analysis is a special case of such transformations wherein the
orthogonal reference waves are sine and cosine waves. When the reference wave is the !
square wave with amplitude of unity, the analysis is known as Walsh analysis. ?I
When the analysis is done with respect to the scale and position of the reference
(non-sinusoidal) wave, the analysis is known as wavelet analysis. Haar analysis is the 1I
simplest type of wavelet analysis. I
Expansion of a given function in various orthogonal sets of functions plays an
important role in the processing of signals. It will be pertinent here to briefly review the
I2
concept of orthogonal sets of functions. An infinite set of real functions &(t), I
&(t),..., @,,(t)is called orthogonal in an interval [a, b] if
b 1
a I
Assuming that
b
J@;(t)dt= K # 0
i.e. none of the functions of the set are identically equal to zero. It is known from
mathematics that if functions @,,(t)are continuous, an arbitrary piecewise-continuous
function f(t) satisfying the condition
i
may be expressed as the sum of the series
f(t)= C&(t) + C I @ I ( ~ )+ ...+ cn@,,(t) (11.6)
Let us multiply both sides of Eq. (11.6) by $,,(t)and integrate between a and b. All
b
the terms of the form ~ , , , @ ~ ( t ) @ ~ ( t ) d tare zero if m # n, because of the orthogonality
J0
of the functions @m(t)and @,,(t).The only term remaining on the right-hand side of this
equation will be
where

from which we get an important expression
IQ I
The series of Eq. (11.6)with coefficients c, defined by Eq. (11.9)is called the generalized
Fourier series in a given set of $,(t).
The generalized Fourier series has the following important property:
For a given set of functions $,,(t) and with a certain definite number of terms in the series
given by Eq. (11.9),it gives the best approximation ( i.e. with a minimum mean squared
error) of the given function f(t). This means that the mean squared error:
is minimal when a, = c,,
11.4.1 Fourier Analysis of Analogue Signals
When expanding a periodic oscillation f(t)in terms of trigonometric functions, if we take
the following orthogonal set
1, COB w, t, sin q t, cos 2wl t, sin 2 q t,...,cos nul t, sin n q t (11.11)
which can be more compactly written in the complex form as
e - ~ 2 W l t -jwlt 1 ejcult, ,j2w,t
,e , , (11.12)
then the interval of orthogonality coincides with the fundamental period T = 2 a I q of the
function f (t).
Thus, using Fourier complex series, we can write
f(t) = ...+ C-2 e - j 2 w ~ L+ c-l e-j~lL+ Co + Cl eja"t + C2 ej21u't + ...
0,
= zC,eJnalt (11.12a)
,=-m
The trigonometric representation of the Fourier series is
f(t) = a. + al COB q t + a2 cos 2wl t + ... + a, COB n q t + ... (11.13)
+ b, sin q t + b2 sin 2 q t + ... + b, sin wlt
The series of Eqs. (11.12a) and (11.13) are known as Fourier complex series and
Fourier trigonometric series, respectively.
f(t) = Fo +* Fl + F2 + ... + F,
where Fo is the dc component and the other components are: I
F1 = a, cos qt +jb, sin qt, F2 = a2 cos 2wl t +jb2 sin 2 q t , and so on.
Given a signal f(t), Fourier analysis is the process of finding the values of the Fourier
coefficients, ao, al,..., a, and bl, b2,..., b,, which represent the amplitudes and phase

230 F~mda~nentalsof Power Systen~Protectron
- -.
angles of various frequency components contained in the signal. It is to be noted that the
frequency of the fundamental (hence its time period) is known apriori.
Thus, the amplitude of the nth harmonic is
and its phase angle is
The Fourier coefficients can be easily found by using Eq. (11:9) and using the , , ,I
following trigonometric identities: ;i1
and
T
Isin(mo,t)dt = 0, all m (11.16)
0
T
Icos(nw,t)dt = 0, a l l n t O (11.17)
0
Since the average value of a sinusoid over m or n complete cycles in the period T is -1
zero, the following three cross-product terms are also zero for the stated relationship of i
m and n: 1
T ,IIsin(mo,t) cos(nw,t) dt = 0, all m, n (13.18)
?
0 . - j
Non-zero values for the integrals result when m and n are equal; thus
T
Isin2(mo,t)dt = -2 ' all m (11.21)
0
1
T
Icos2(no,t) dt = -, all n
2
(11.22)
0
Thus, the coefficients ao,a,, and b, are

Nu~ner.lcslProtection 231
/-
Figure 11.7 shows the input and the output of a Fourier analysis.
r,t,f Signal
Fundamental cosine
I +a. -
6
analysis 0, = tan-'(b, la,)
wTime - . .. .I' . .Fundamental sine
F" F"
Lbn d 0, = tan-'(b, la,) t- 0.
Figure 11.7 Input output of Fourier analysis
Fourier analysis of discrete signals
The above Fourier analysis assumes that the signal being processed is continuous and
extends from t = - a to t = a.However, for practical reasons, we can analyze the signal
over only a finlte duration. The Fourier analysis of finite-duration continuous (analogue)
signals is known as Fourier Transform and its counterpart in the discrete digital domain
is known as Discrete Fourier Transform (DFT).
Numerical relays work with the digitized version of the analogue signal. Therefore,
the Fourier analysis described for analogue signals has to be suitably modified. The
modification consists in replacing the respective entities with their discrete counterparts,
as shown in Table 11.2.
Table 11.2 Analog vs discrete domain
Analog domain Digital or discrete domain
Continuous signal fit), Discrete signal f(k At),
where t can take any value and, therefore, where k is the sample number which is a
f(t) can take any value from an infinite positive integer and At is the sampling
set of numbers. interval, i.e. the time period between two
consecutive samples.
Continuous time t Integer sample number k
Integration Summation Z
Time period T Number of samples per cycle N
Integration between infinite limits Summation of finite samples

232 Fundamentals of Power System Pmtectlon
The time At is the time period corresponding to the sampling frequency, hence
At =
1
= Tsamp~ing
fsampiing
since there are N samples per cycle of fundamental, we get
2n
NTSampling= NAt = TI= -0 1
Noting that k is the sample number and N is the number of samples per cycle, the 3
expressior.~for evaluating the Fourier coefficients in the discrete domain can be obtained
from those for the continuous domain by making substitutions shown in Table 11.2. 1i:
Table 11.3 lists the expressions for evaluating discrete Fourier coefficients alongside :
those of continuous Fourier coefficients so that the readers can easily associate the i
discrete expressions with the more familiar continuous expressions. !
a
Table 11.3 Discrete Fourier transform coefficients ,a,,','.I
Discrete
, . iContinuous i
In order to process a signal, we consider the signal over a finite duration, known as a
window.The implicit assumption is that the signal samples are zero uniformly outside the
window. The process of windowing and finding the discrete Fourier transform isbshown
in Figure 11.8.Since we are applying the Fourier transform only to samples which occur
within a window of 1cycle, this is known as a full cycle window.
*-Continuous slgnal
I Window i
Sampling
1
.M.M.fvm +Time
W~ndowedand
sampled slgnal
+Time
Figure 11.8 Windowing and sampling of a continuous signal.

Numerical Protec:ion 233
Windowing is a mathematical operation, in iime domain, of multiplying all samples
outside the window by zero and those within the window by unity Every operation in the
time domain has its repercussions in the frequency domain. It is, therefore, only natural
that windowing affects the frequency domain picture, and may depict some frequencies
which were not present in the original signal! In order to faithfully preserve the
information content, windowing should be done in a manner, as unobtrusive as possible.
Fortunately, windows can be shaped in such a way that the effect in frequency domain
is minimal. Various early researchers have proposed window shapes to meet a variety of
criteria. Interested readers may refer to any standard text on Digital Signal Processing
for more information on this very interesting topic.
Figure 11.9 shows the process of computing the Fourier transform. Samples of the
signal denoted by f(k 4t)are stored in the memory of the computer. The samples of the
fundamental sine and cosine waves, known as weights,are precalculated and also stored
in the memory. The Fourier transform is the process of multiplying the sample with the
corresponding weight and accumulating the sum. When the process is complete we get
one estimate of the magnitude of the desired frequency component and its phase angle.
In protective relaying application, the process continues in an infinite loop. The time
window is continuously kept sliding forward. In the meanwhile, the results of the Fourier
transform are passed on to a relaying program which may further perform over-current,
directional, differential or any other type of relaying function. Thus, the process is similar
to a machine which keeps on running.
Samples of signal
I I
Fundamental sine weights Fundamental cosine weights
Accumulate Accumulate
Figure 11.9 The discrete Fourier machine for eight samples/cycle.

234 Fundamenrals of Power Systern Protection
The same process has been depicted in the flowchart of Figure 11.10. If we wish to
extract other frequency components then the corresponding weights need to be
precalculated and stored.
For example, to extract the second harmonic, the weights will be the samples of
second harmonic sine and cosine waves W2,,,,(n) and W2eos,ne(n).
I Read sampling rate N; therefore
samples per cycle = N
I Compute samples of fundamental sine and cosine waves and store as
weights, w1,dl) to Wlsin(N) and Wlc,(l) to Wlcm(N) I
I Initialization I
4
Read the nth sam
I
J. Yes
a, = A,IN: DC offset <
a, = (2N) A,
bl = (ZN)Bl .?
I FI = dm:peak magnitude of fundamental I-9, = tan-'(blial): phase angle of fundamental
I
.4.
Pass values to relaying algorithm
<*,Figure 11.10 Flow chart for the computation of Discrete Fourier Transform.

-
Numenciil Protection 235
Walsh analysis
In Walsh analysis, the reference correlating functions are square waves of unit amplitude
as shown in Figure 11.11.In terms of Walsh functions, a periodic function f(t) can be
expanded over the interval (tl, tl + T)as follows:
m
f(t) = whWal(k,tiT)
h=O
WaI(2. UT)
-1
WaI(6. UT)
-1
Wal(7. UT)
-1
I Figure 11.11 First eight Walsh functions.

236 Fui~damet~ralsof Power System Protection
where the Walsh coefficients Wh are given by
Note that the weights, Wal(k, t/T),are all, either +1 or -1; thus making the Wdsh
transform computationally very efficient as multiplication by floating po~ntnumbers is
avoided and only additions and subtractions of the samples are required to be done.
Walsh transform gained popularity during the initial years of numerical relaying
because at that time the microprocessors were not able to perform floating point
arithmetic However, the modem microprocessors and the digital signal processors (DSP)
can routinely perform high speed, high precision, floating point arithmetic, hence Walsh
approach seems to have taken a back seat.
Another factor limiting the proliferation of Walsh analysis is that the electrical circuit
theory is deeply rooted in the sine waves. Thus, in order to relate to concepts such as*
impedance, we have to come back to Fourier domain. This involves another
transformation from the Walsh to the Fourier domain, which is computationally
intensive. Thus, the initial advantage of Walsh analysis, being computationally easy, is to
some extent lost. ,.
All the same, Walsh analysis opens up a fresh viewpoint and leads to many new
interesting possibilities. The interested reader may refer to standard texts on digital
signal processing.
I1:" ,
.7 a Wavelet analysis
When we perform conventional Fourier analysis, we get the information about the
frequencies that are present in the signal. However, all clues about the time, a6which
these frequencies appear, are lost.
Thus, if we were to perform Fourier analysis of an orchestra, we would name with
confidence, all musical instruments which were being played, but not the respective times
at which these were be~ngplayed!
Conventional Fourier analysis does not preserve any information about time but gives (I)
very detailed information about frequency.
Discrete Fourier transform, on the other hand, preserves some information about
time since the location of the time-window is known. However, the time-window size is
fured. In order to increase the precision of information about time, the time-window needs
to be made smaller. However, as we make the time-window small, the information about
the low frequencies loses its precision.
Continuous Wavelet analysis attempts to remove this lacuna of Fourier analysis and
gives information about the frequencies and the times at which they appear. This is
achieved by using a family of correlating functions which have well marked attributes of
position and scale. The position attr~buteis analogous to the time domain of Fourier
analysis while the scale attribute 1s analogous to the frequency domain.
Discrete Wavelet analysis is a discrete implementation of the continuous wavelet
transform.
Wavelet analysis is very useful for analyzing signals generated by a non-stationary
phenomenon whereas Fourier analysis is suitable for stationary phenomenon.

~V~irnerlcalProrecrror! 237
During the immediate post-fault conditions or other disturbed conditions like power
swings, the power system gves rise to non-stationary signals. In the steady state (both
pre-fauIt and post-fault), the signals are ~tationary.
Recently researchers have started reporting a number of Wavelet based approaches
for data compression and recognition of certain fault signatures like high impedance
faults or magnetizing current inrush. However, the applications are still in their infancy
and are being investigated.
Interested readers may refer to advanced texts on image processing for more detailed
information on the theory of Wavelets.
11.5 Least Error Squared (LES) Technique
As pointed out in Section 11.4, the least error squared technique is directly related to the
Fourier technique. If a given function were to be synthesized by using a dc component,
a sine wave of fundamental frequency and harmonics of this fundamental, then the
amplitudes of various components given by the Fourier analysis are the ones which give
the least squared error.
We can directly find out the amplitudes of the components by using the LES
technique. To illustrate the LES technique, let us assume that the fault current consists
of:
;
I . .V ' ,. A dc offset
1 A fundamental component
i
i Other harmonic components of higher order
11
The LES technique helps us in estimating the values of these components.
t
The assumed signal is:
1 N
i(t) = ~ ~ e - ' "+ K2, sin(nolt + 8,) (11.26)
+ n = l
For the sake of illustration, assuming that the current consists of a dc offset, the
I
fundamental and a third harmonic component, we can write
i
I We can represent e-'/' as a sum of an infinite series, i.e.
1
/ Assuming that truncating the series for e-'/: to the first three terms, gives adequate
I accuracy, we get
Kl K,?i(t) = K, - -t1 + -+ Kzl cos 81 sin olt + Kz1 sin 81 cos q t
T 2!T2
+ KZ3cos Q3 sin 3u1t + KZ3sin 83 cos 3 q t (11.29)

Amplitude of fundamental, ' 2 2
F: = i x 2 +z3 8~11.36)
Phase angle of fundamental, = Lan-'(3) (11.37)
Xzi
The same technique can be applied to the samples of the voltage waveform to extract
the fundamental and other higher frequency components of voltage.
Once equipped with the above information, we can perform a variety of relaying
functions such as over-current relaying, differential relaying, detecting magnetizing
in-rush by extracting the second harmonic component, estimating impedance up to fault
location, i.e. performing distance relaying or fault location.
11.6 Digital Filtering
Filtering is a very important and the most frequently needed operation in numerical
relaying. We are familiar with the analogue filters consisting of R-L-C circuits and active
filters using operational amplifiers. However, there are certain drawbacks associated with
analogue and active analogue filters, namely:
They are bulky, specially inductors require a large space.
High precision components are needed, making them expensive.
Their characteristics drift with respect to time and temperature.
Filters for very low frequencies need impracticably high component values.
Their characteristics are limited to the certain well known conventional
characteristics.
They are not adaptable, i.e. they cannot change their characteristics in response
to the input signal.
They are not programmable.
Digital filters offer advantages with respect to all of the above points. The most
important advantage of digital filters is that they do not require high precision and high
quality R-L-C components. All types of digital filters require the same basic hardware
consisting of anti-aliasing filters, sample and hold circuits and analogue-to-digital
converters. The underlying software decides the filtering action. Thus, the digital filter
exists in software. This has several advantages, for example, it is easy to change the
characteristics of the filter by simply using another program. Digital filters do not need
any tuning and maintenance. There is no ageing and no drift caused by time or
temperature.
11.6.1 Simple Low-pass Filter
If we form the output by simply taking the running average of last two samples then the
simple mathematical operation has the effect of performing a low-pass filtering operation.
The filter can be expressed mathematically as

-
340 F~mdamentalsof Power System Protecrio!~
Consider a signal as shown in Figure 11.12. ,4t sample number 3, there is a large
noise signal of positive polarity. At sample number 4, there is a noise signal of equal
magnitude but of opposite polarity. Thus, we have a high frequency noise signal riding
over the low frequency information-carrying-signal. Now, since the output signal is
formed by taking a running average, the effect of a positive spike followed by a negative
spike, is totally cancelled out and we get a smoother signal as shown in Figure 11.12.
Thus, we have got rid of the high frequency signal, allowing only low frequencies to
pass. This amounts to low-pass filtering.
I' lnput
ll,Il 21,,1,14 q=k 7e;iitr
x, + X" ., output
Figure 11.12 A simple mnning average filter works as a low-pass filter.
11.6.2 Simple High-pass Filter
If the output sequence is formed by taking a running difference of the samples of the
input sequence then it has the effect of high-pass filtering as shown in Figure 11.13. The
filter can be expressed mathematically as
T Input
Running difference
-Input Output
Output
1
Figure 11.13 A simple running difference filter works as a high-pass filter.
The high-pass filtering takes place when any sudden changes of sign of the samples get
amplified as a result of taking the difference. Slowly varying samples of signal almost
cancel out each other in the output. Thus, only the high frequency component appears
at the output.

iV~r/ilrricalProtection 241
7 1.6.3 Finite Impulse Response (FIR] Filters
Digital filters are linear systems. The impulse response completeiy characterizes any
linear system. If the impulse response has a finite number of terms then the filter is
known as the finite impulse response filter. Figure 11.14 shows the block diagram of a
digital filter with finite impulse response.
Time
Present output
y , = a o x , + a , x , ~ , + a z x , ~ 2 +...+ a,x,-,
Figure 11.14 Block diagram of FIR digital filter (canonical).
The filter generates the output samples by forming a weighted sum of the input
sample and a limited number of previous input samples. The weights are nothing but the
samples of impulse response of the filter. Thus, the output of an FIR filter of length m
is given by performing the convolution of the incoming sequence of samples with the
t impulse response of the filter. The nth output will be given by
Note that the above filter will need memory to store m samples and (m + 1)number of
coefficients.
The frequency response of the above filter is given by
",
Thus, the frequency response depends upon the frequency w of the input signal, the
sampling interval A t and the set of coefficients a,. The following important points are
worth noting:

242 F~crldarnenralsof Power Sysrer?l Prorecriorz
1. The frequency response of a digital filter is a periodic function with a period equal
to 2 d A t
2. The frequen~yresponse, given by the function f(jo),is the Fourier transform of
the impulse response (ao,..., a,) of the digital filter.
The transfer function of the filter in the z-domain is given by
Y(z) - aozm+ a1zm-' + azzm-' + ...+ a,- - (11.42)
X(z) zm
11.6.4 Infinite Impulse Response (IIR) Filter
This filter is characterized by the fact that the nth sample of the output is formed by
using the previous values of both inputs and outputs. The coefficients ao,...,a, are similar
to those of the FIR filter. The coefficients bo,...,bh form the recursive part of the fi~teQ
Figure 11.15 shows a canonical implementation of the digital filter with infinite impulse
response (IIR). There are, however, many alternative ways in which these filters can be
implemented.
k---- m number of past inputs ----4
Present output
k-----k number of past outputs
y, = aoxn+ a,x,-, + a2x,_, + ... + a,x,_,
+ biyn-i + b2~o-2+... + bky0-k
Figure 11.15 Block diagram of IIR digital filter (canonical).
The output at the nth sampling instant is given by
yn = sox, + alx,_l + ... + a,x,-,
+ b1 yn-I + b2 yn-2 + ... + bk ~ n - A (11.43)
~~~.~
,

Note that the output at any sampling instant is a function of 13 number of past inputs
iI
and k number of past outputs. Thus this type of filter has feedback, hence the filter is
! also known as recursive (which literally means running backwards).
i
I
The transfer function of the filter in the -7-domain is given by
I A recursive digital filter is stable if the output of the filter is a non-increasing
1 sequence, i.e. for n tending to infinity yn should not exceed some positive number M,
I '
I
irrespective of the choice of initial conditions.
i
11.6.5 Comparison Between FIR and IIR Filters
The following table lists several important issues concerning the FIR and IIR filters.
. . ~ .
FIR Filter IIR Filter'- ~
Output is a function of past m inputs. Output is a function ofpast m inputs
Therefore, non-recursive. as well a s k past outputs. Therefore ,
recursive.
Finite impulse response. Infinite impulse response.
I Always stable since there is no Because of feedback, possibility of
feedback. instability exists.
Has less number of coefficients. Has more number of coefficients.
Transfer function has only the numerator Transfer function has both the numerator
terms. and denominator terms.
Higher-order filter required for a given Lower-order filter required for a given
s frequency response. frequency response.
1
Has linear phase response. Has nonlinear phase response.
y, = a,%, + alxn-l + ...+ a,x,_, yn = aOxn + alxn- + ... +
+ blyn-1 + b2yn-2 + ...+ bk~n-k
i m-1
Y(z) n,zm + a,t + a2zm-2+...+ am Y(z) a, + alz-' + a2z-' +...+ a,.z-,
I - = - =
! * X(z) zm X(z) 1 - hz-' -...-bkZ-k
1 Very simple to implement. Not as simple as the FIR filter.
I
/ 11.7 Numerical Over-current Protection
Numerical over-current protection is a straightforward application of the numerical relay.
Here we describe a possible method of implementing a numerical over-current relay.
The algorithm first reads all the settings such as the type of characteristics to be
implemented, the pick-up value Ip,, the time multiplier setting in case of inverse time
over-current relay or the time delay in case of DTOC relay.
The algorithm of a numerical over-current relay will first extract the fundamental
component of the fault current Im,, from the post-fault samples of current and establish
its rms value. Full cycle window Fourier transform may be used for this purpose as it

effectively filters out the dc offset. It will then compare this fundamental component I,,,
with the pick-up setting and compute the plug setting multiplier, given by (IrmsiIpu)at
which the relay will be operating.
Equipped with the PSM value, the relay will either compute or look up the required
time delay depending upon the type of over-current characteristic that is being
implemented. The algorithm will then cause the relay to go into a wait state for a time
equal to the operating time.
At the end of this time delay, the relay will once again evaluate the rms value of the
fundamental to find if the fault has already been cleared by some other relay. If the fault
current still persists then the relay will issue a trip output. This signal will be suitably
processed to make it compatible with the trip coil of the circuit breaker. The algorithm
of a typical over-current relay is shown in Figure 11.16.
< start >i
Read type of OC relay characteristic, for example. DTOC, IDMT inverse.
extremely inverse or any custom characteristic
Read plug setting
jRead time setting in case of DTOC I
3.
Read time multiplier settlng in case of inverse time OC relays
C
+
Find the rms value of fundamental I , using full cycle window
discrete Fourier transform
C
I Com~uteor look-UDtime delay T,. 1
Figure 11.16 Flowchart for a numerical over-current relay algorithm.

7 7.8 Numerical Transformer Differential Protection
Figure 11.17 shows the conceptual block diagram for numerical protection of a
transformer. The idea is to estimate the phasor value of the current on both sides of the
transformer and find the phasor difference between the two. If the magnitude of this
difference is substantial, an internal fault is indicated and the trip signal should be
issued. The above is a description of the simple differential scheme. All the reasons that
prompt us to go in for the percentage differential relay exist here as well. Therefore, the
numerical relay algorithm should be made to implement the percentage differential relay.
Transformer
. V
,,
IP 1s
current to 7fI voltage V,
a
Current to converter
voltage converter Vq a 'P I -+
% B~asB
Min pick-up I,,
T~mesetting
Tap setting
Figure 11.17 Block diagram of numerical protection
Trip
Restrain
of transformer
Algorithm for percentage differential relay will consist of the following steps:
Read percentage bias B and minimum pick-up Ipu.
Read i, samples -t Estimate phasor I, using any technique.
Read is samples + Estimate phasor I, using any technique.
Compute spill current Ispill= I, - Is.
Compute circulating current Icirfulating= (1, + Is)/2.
If Ispill> (BIcirculating+ Ipu)then trip, else restrain.
11.9 Numerical Distance Protection of Transmission Line
11.9.1 Mann and Morrison Method
Let voltage at the relay location be described by
v = V,,, sin(ot + 8,)

246 Fui~damentalsof Power Sysreni Pmrection
and the current by
i = I, sin(wt + Bi)
It may be noted that voltage and current are assumed to be pure sinusoids.
Let u' and i' represent the derivatives of voltage and current, respectively. Then we
can write
and
or
Combining expressions for u and (ul/o), we get
Similarly
Further, the phase angles can be found as follows: a
-1 O U
eu = tan (a)
The phase angle between the relay voltage and relay current will be given by
e = e, - e, (11.53)(I,
Note that this analysis refers to continuous signals. However, the same can be adapted
for numerical relaying by substituting sample values instead of instantaneous values and
numerically computed derivatives instead of continuous derivatives. The numerical
derivatives at the nth sampling instant, u; and i h can be written as
Similarly
Substituting Eqs. (11.54) and (1155) in the expressions for V, and I,, we get

N~inler~calProrecrron 247
Thus, using a window of three samples, we can estimate the peak and hence the rms
values of voltage and current at the relay location as well as the phase angle between
I them. In other words, the phasors for voltage and current can be estimated.
t We can keep on sliding the window to make a running estimate of rms value of
current, rms value of voltage, phase angle between voltage and current and, hence
compute the apparent impedance seen from the relay location.
The algorithms appear to be very attractive because of their simplicity. However,
closer examination reveals that the Mann and Morrison method is based on the following
assumption:
I Waveforms of both the voltage and current consist of undistorted sine waues of
fundamental frequency which is accurately known and is constant.
Obviously, the above assumption will be seldom, if ever, true in a power system
relaylng scenario Thus, the method will introduce significant errors if the assumption is
not true. How then can we use the method in practice?
We can use the method in practice, provided we operate as close to the assumption
as possible. This can be achieved by heavily filtering the voltage and the current
waveforms so as to remove all traces of dc offsets, harmonics and noise. Thus, the price
for the simplicity of the method has to be paid in terms of complex preprocessing of the
voltage and current signals.
In order to make a robust relay based on the above algorithm, we will have to employ
additional methods to make sure that stray noise signals do not cause false tripping. One
such method is to increment a counter every tlme the estimated value is such that
tripping is called for The actual tnp output is issued only if this counter reaches a
predetermined threshold. If the counter does not reach the threshold, it is reset to zero
after a predetermined time-out. The counter threshold depends upon the expected level
of noise at the particular location and has to be determined empirically.
11.9.2 Differential Equation Method
In this method, the faulted line is modelled as a lumped series R-L circuit. The distributed
nature of the line parameters as well as the shunt capacitance are neglected. Thus, we
can relate the voltage and current at the relay location and the resistance and inductance
up to the fault location with the help of the differential equation:

where
i, is the current in the faulted phase
i, is the function of ail the three-phase currents
R and L are the functions of resistance and inductance of the transmission line up
to the fault location.
In order to keep things simple while developing the concept, we first consider a
single-phase transmission line.
Application to single-phase transmission line
Consider a single-phase transmission line fed from one end. Let us assume a ground fault
at a certain distance x from the sending end. The transmission line can be modelled as
a series R-L circuit. This is shown in Fimre 11.18.
Fault
1
Figure 11.18 Faulted transmission line modelled by lumped series R-L circuit.
The voltage and current at the relay location are v and i, respectively. For the looil)
formed by the equivalent circuit of the faulted line, using KVL, we can write
Though Eq. (11.62) is a differential equation, the numerical values of u and i are known
and the numerical value of diidt can be computed, the equation, in fact, is a linear
algebraic equation in two unknowns, R and L. We, therefore, need one more equation in
u and i to solve for the two unknowns. Writing Eq. (11.62) for two different sampling
instants n and n + 1as shown in Figure 11.19, we get

I
I t t t t t t t . l t t t t T T T T I t t t t ,.,,I
Sampling Instants
I Figure 11.19 Numbering of samples of voltage and current for differential equation algorithm.
I
From Figure 11.19, we can easily see that the numerical derivative of the current at
instants n and n + 1is
) w h r e d l is the sampling interval.
I Expressing the simultaneous algebraic Eqs. (11.63) and (11.64) in matrix notation
and solving for the unknowns R and L, we get

250 Funda~nenralsof Power S)'stem Protection
-
where
From which we get
A window of four samples is seen to be adequate for computing one estimate of the
values of R and L. In order to make the method more robust, the window can be shifted
further and another estimate can be made. If the fault is a metallic fault, the estimated
values will converge on to a stable value.
Application to three-phase transmission line
The above discussion referred to a single-phase transmission line. However, in practice,
the power transmission lines are always three-phase in nature. It will be $ertinent,
therefore, to see how we can apply the differential equation approach to a three-phase
transmission line. Consider the model of the three-phase transmission line%hown in
Figure 11.20. The elemental length dx of any phase is assumed to have a resistance, an
inductance and a mutual inductance parameter associated with it The shunt apacitan'ce
is neglected.
Self inductance
Mutual
inductance
Figure 11.20 Model of three-phase lme.

Nunzerical Protecr~o~l251
The voltage drop across the infinitesimal length dz,of phase a can be written as
Similarly the voltage and current relationships for phases b and c can be written as
, , (11.75)
: If the line is assumed to be ideally transposed, we have
La = Lb = LC= L, (11.77)
L, = La, = Lbo = Lbc= Leo= Lcb= Lm (11.78)
where
Rs, Ls are the series resistance and self-inductance per unit length of each phase
LMis the mutual inductance per unit length between any two phases.
By substituting Eqs. (11.76) to(11.78) into Eqs. (11.73) to (11.751, we obtain
Now, the self- and mutual-parameters are related to the zero and positive sequence
parameters as follows:
Lo = Ls + 2LM (11.82)
R1= Rs (11.83)
L1 = Ls - LM (11.84)
and
I
i, +ib+ L,
io = (11.85)
3

252 F~iii~la,r~ei~ralsof Pu~verSysreifi Prurecrron -
where
R1, L1 are positive sequence resistance and inductance, respectively
Lo is the zero sequence inductance
i, is the zero sequence current.
By combining Eqs. (11.79) to (11.81) and Eqs. (11.82) to (11.851, we obtain
Equations (11.72)to (11.75) can be used to compute the voltage drop between the relay
location and the fault point for different types of faults as shown next.
Single-phase to ground fault. Assume a metallic single-phase to ground fault on phase
a at a distance r from the relay location. The instantaneous value of voltage u, at the relay
location can be calculated using Eqs. (11.72) and (11.73) for untransposed lines and
Eqs. (11.79) to (11.81) for ideally transposed lines.
Using the instantaneous values of the voltages, currents and the rate of&hange of
currents, the voltage u, can be obtained by using Eqs. (11.72) to (11.73) as shogn below:
= xRaia+ xLo
dt
(11.89)
La
or
di,u, = xR,i, + rL,-
d t
(11.90)
where
1, = I., (11.91
and
9
1Y = ia + [%)ib + (4). (11.92)
Equations relating to the transposed lines can be expressed in the same way and in
this case Eqs. (11.79) to (11.81) can be used to obtain the following relationship:
where
and

N~rrnericnlProtection '753
Phase-to-phase and three-phase faults. When the fault involves two or three phases, the
voltage between the faulted phases, say a and b, can be found as follows:
Equation (11.96) can be reduced to the more compact form as
diY
u, - ub = xR,i, + x (La-Lab)-
dt
(11.97)
where
and
When the line is assumed ideally transposed, Eq. (11.93) can be written in terms of
the difference between the currents on each faulted phase, giving
The above analysis shows that the behaviour of the transmission line under fault
conditions is governed by a differential equation having the general form of
The measured values of the currents and the voltages are taken in the form of
samples and the measurement is usually done simultaneously on all the three phases.
In Eq. (11.102), all the terms except R and L, are either the measured samples or the
quantities easily computed from the samples. The values of R and L can be found by
solving the simultaneous equations involving R and L. One of the methods, which
involves computing the numerical derivatives has already been described in
Section 11.9.2.
We can convert the differential equation into an integral equation by integrating both
sides, in which case the numerical integration rather than differentiation will have to be
performed. Integration, being an inherently low-pass operation, yields better results in
the presence of higher frequency components present in the voltage and current
waveforms.
11.I 0 Algorithms and Assumptions
We may easily get bogged down by the sheer number of algorithms for digital protection
which have been proposed in the literature. However, algorithms can be broadly classified
into time-domain algorithms and frequency-domain algorithms. For example, the solution

254 Fundanaentals of Power Svsteln Protection
of a differential equation is in time domain whereas the Fourier algorithm is in frequency
domain.
We must bear in mind that there is no algorithm which can offer a panacea.
Underlying every algorithm, is a set of assumptions. The algorithm is good only within
the constraints imposed by the assumptions. The effectiveness of an algorithm depends
on how far, in practice, the assumptions on which it is basrd, are close to reality.
For example, if we assume that the signals are undistorted sine waves then we can
use very simple algorithms such as those of Mann and Morrison's.
Review Questions
1. Trace the evolution of protective relays.
2. What are the advantages of numerical relays over conventional relays?
3. What paradigm shift can be seen with the development of numerical relays?
4. Draw the block diagram of the numerical relay
5. What do you mean by aliasing?
6. State and explain Shannon's sampling theorem.
7. What happens if the sampling frequency is less than the Nyquist limit?
8. What are the drawbacks of a very high sampling frequency?
9. Is sample and hold circuit an absolute must?
10. A 12-bit ADC has conversion time of 10 microseconds. What is the maximum
frequency that can be acquired without using a sample and hold unit?
11. If a sample and hold circuit of 100 picoseconds is available, how will the &ximum
frequency found out in Question 10 be affected?
12. Explain the statement that all numerical relays have the same hardwarebut what
distinguishes the relay is the underlying software.
13. Explain the sample and derivative methods of estimating the rms value and phase
angle of a signal. Clearly state the underlying assumptions.
14. What do you mean by Fourier analysis? Explain.
15. How does Fourier transform differ from conventional Fourier analysis?
0
16. What do you mean by a full cycle window?
17. What are the advantages and disadvantages of a half cycle window?
18. What do you mean by a digital filter? Explain.
19. Draw the block diagram of an FIR and an IIR filter.
20. Compare the FIR and IIR filters.
21. Develop the differential equation algorithm for distance protection of a
transmission line.
22. For numerical relaying purpose the differential equation gets converted into a
linear algebraic equation. Explain.
23. Discuss the methods to find numerical differentiation and numerical integration.
24. How can certain frequencies be filtered out in solving the differential equation by
integration?

Appendix A
CT anb PT Errors
A.1 Introduction
CTs and PTs are the eyes and ears of the protective system. They extract information
from the power system and form an important link between the high-voltage high-current
power system and the low-voltage low-current protective system. CTs and PTs have two
important roles to play, namely:
i (.. .i.>,, . Electrically isolate the protective relays from the high-voltage power system for,
3 , . the purpose of safety of the operating personnel.
. , ,
Step down the current and voltage to standard values of 1A, 5 A, 110 V so that
. :
I( .- the design of relays can be standardized irrespective of the actual primary voltage
I ,
i. :,',
and current.
. . ,
!
I;-'
I ',
3
1
1
A.2 CT Construction
CTs can be constructed as two-winding transformers with independent primary and
secondary windings. We can, however, get rid of the primary winding and use the primary
conductor itself as a one-turn primary winding, known as bar-primary, when the
magnitude of the primary current is sufficiently high. In such CTs, the secondary winding
can be conveniently put inside the high voltage bushings. The auto-transformer type CTs
may also be used in conjunction with two-winding CTs for the purpose of fine tuning the
ratio of transformation.
A.3 Measurement CT and Protective CT
L
CTs are also used for measurement purposes. However, the desired response from
measurement CTs under short-circuit conditions (when the primary current is high) is
quite different. A protection CT is required to faithfully transform the primary current
throughout its entire range from normal load current to short-circuit current. A
255

256 Appendix A-CT and PT Errors
measurement CT, on the other hand, is designed to saturate at currents more than
around 1.2 times the full-load current, and thus save the measuring instruments from
possible damage.
By suitable design, the operating point of the measurement CT is kept near the knee
of the excitation characteristic. The knee point is defined as that point on the excitation
characteristic at which 10% increase in excztation voltage results in a 50% increase in the
ezcitation current (see Figure A.1).
Knee point
I
t
I
1
,I
I
;P = Operating point of
IM = Operating point of
I
I
4
I
I
,
1k"ee 1.5lk",
>
Magnetizing current
protective CT
measurement
Protective CT
Poutput
LL
2 1 Slope = IICT ratio
Metering CT output
-1 Full &-
I ~ I ~ I ~ I ~ I ~ I ~ I S I ~ I ~ , ~ I ~ I ~ ly
I load l Primary current (rms)
;current
, Maximum fault current = 20 to
30 times the full-load wrrent
Figure A.l Difference in the response of a measurement CT and protective CT.
A protective CT is designed to operate much below the knee point so that it maintains
its transformation ratio during high magnitude short-circuit currents.
!
A.4 Steady State Ratio and Phase Angle Errors I
A.4.1 Current Transformer
Figure A.2(a) shows the connections of a CT and a PT to supply, load, and relay. The
equivalent circuit of the CT is shown in Figure A.2(b). The corresponding phasor diagram
is shown in Figure A.2(c).
-

.,,c Appendi,~A-CT and PT Errors 255
I CC: Currenl
PC: Pressu~,-,, tr,ar
: mil of relay
.a ,-nil ,.f --,-,,
,,~~
' ..
,.:.,-
Figure k 2 ( a ) Connections of a CT and a PT to supply, load and relay.
.:,
I
I
I
Burden
j I I
I
I
I I
I I
I I
I I I
I
Ideal CT I

258 Appertdix A-C7 and PT Errors
8'
h The ratio error which is defined as
Actual ratio - Ideal ratio
Ratio error = Ideal ratio
is approximately given by
-1
/ Ratio error s 2 1nz, I
as shown in Figure A.3.
I I
Primary current, lp = nls t le
R = n t Actual ratio
1,
a
Figure A.3 Approximate method of expressing ratio error.
F
Ei The phase angle error is defined as the angular difference between the secondary
+i
1 current phasor reversed and the primary current phasor. If the reversed current phasor
leads the primary current phasor then the phase angle error is
otherwise it is taken as negative. As shown in Figure A.4, the phase
approximately by
I, 1Phase angle error = 7
I3 Assuming I. = 0
Since 0 is very small
tans = e 31 h~n1s
defint
angle
positive
is given

- F Flux (#)
b
15
Figure A.4 Approximate method of expressing phase angle error.

A.4.2 Potential Transformer
Aooendix A-CT ~ n dPT Errors 239
Fotential zransformers are mucn like power transformers operating on very light load.
Two types of potential transformers are used in protective systems:
1. Conventional two-winding, electromagnetic iype
2. Capacitive voltage divider type, known as capacitive voltage transformer
Electromagnetic potential transformer
We will first consider the conventional electromagnetic type two-winding voltage
transformer whose equivalent circuit and phasor diagram are shown in Figures A.5(a)
and A.5(b), respectively.
Burden
I I
I I
I
Figure A.5(a) Equivalent circuit of electromagnetic type PT.
y = Phase angle error
,I 6 = Phase angle of burden
n = Turns ratio
, I, = Magnetizing component
, I, = Iron loss component
1, = Excitation
I, = Prtmary current
I, = Secondary current
Ep= Primary induced voltage
V, = Primary terminal voltage
+ Flux (0) E, = Secondary induced voltage
Vs = Secondary terminal voltage
Figure A.5(b) Phasor diagram of electromagnetic PT.

260 Append~sA-CT and PT Errors
Figure A.5(c) illustrates the ratio and phase angle errors of a PT.
OA = Pnmary voltage
OB = Secondary voltage (Ideal)
OC = Secondary voltage (Actual)
Ratio error -- O8 - Oc w. 100%
OB
Phase angle error = -y
Figure A.5(c) Ratio and phase angle errors of electromagnetic PT.
Capacitive voltage transformer (CVT)
Capacitive voltage transformer consists of a capacitive voltage divider as shown in
Figure A.6(a). However, a simple capacitor divider cannot be used as a CVT because the
output voltage will depend on the current drawn by the burden. Hence, a tuning coil is
used so that it resonates with the equivalent capacitance seen looking into the capacitor
potential divider. This makes the output voltage, a constant fraction of line voltage and
independent of the current drawn. -.-
Z
Figure A.6(a) Capacitive voltage transformer.
The thevenin's impedance seen from the primary of electromagnetic PT, into the CVT
is shown in Figure A.6(b) and is equal to the LC series circuit, where C is the parallel
combination of C, and Cz.Thus, if L is chosen to resonate with C at the system frequency

Appertdix A-CT and PT Errors 261.:,
(50 Hz or 60 Hz), there - d l be no voltage drop across che LC circuit. Thus, the output
of CVT will become independent of the current drawn by the burden.
cz>> C1
XL is designed such that:
Since Xm << Xc,
lXLl IXczl
Figure A.6(b) Tuning of the CVT to make output voltage independent of burden.
A.5 Transient Errors in CT
The fault current on the primary side of the CT can, in general, be described as
* EP
[sin(wt + fl - a ) + sin(a - fl)e
-(RIL)r 1
where
E, is the peak system voltage
R, L are system resistance and inductance, respectively.
The peak value of the ac component of the fault current is given by
w
where
fl is the phase angle representing instant of switching
a is the characteristic angle of the system [= t a n - ' ( ~ ~ ) I

262 Appr1rdi.r A-CT or~dPT Errors - - ---
Thus, the fault current consists of a steady state ac component and a tr~nsientdecaying
dc offset. The maximum dc offset takes place when sin(cr-p) = 1 or when
( a-p) = n!2, Since we wish to perform the worst case analysis assuming ( a- = n/2,
i.e. (p- a)= -n/2, we get
where T = LIR with L and R as the inductance and resistance of the power system,
respectively
Assuming that this primary current is being correctly reproduced at the
the secondary excitation voltage will be
or
where
e,, = ImRt sin - - = -I,& cos(wt) [This is shown in Figure A.7(c)]
[
.edc = ImRte-'IT [This is shown in Figure A.7(a)]
a
where Rt is the resistance of the CT secondary plus the resistances of the burden
The mutual magnetic flux of the CT is given by
drpe, = N,-
d t
or the flux ql is given by
1
@ =-le,dt
e
N8 C
Let us find the flux variation to support the dc component of the voltage across the
CT secondary. As we know
Solving the above integral, we have
[ - T e - 6 / ~ ] '
ddc = -- 0
--
InRtT [1 - e-6'T
Ns ] [This is depicted in Figure ~ : i ( b ) ]
- -~. ~
- - . -,-

,.,.,....,, ,.-.h. '
Appendix A-CT and PT Errors 263
..
, ,, ,
.At t = 9. .., ,,
Pdc = 0
.,.
-,..
. ,
,. .. Thus, the decaying dc offset requires flux t o increase exponentially a n d t h e n remain
constant a t t h e maximum value...
3iiTime
(a) Voltage required to force dc component through secondary resistance
I, RlL
G
(b) Flux variation to induce voltage wave of (a)
J.Time
I
(c) Voltage required to force ac component through secondary resistance
Time
(d) Flux variation to induce voltage of (c)
I (e) Total flux vanation
Figure A.7 Transient response of CT.

264 Appendir A-CT and PT Errors
N ~ ~ ,let us find the flux variation necessary to support the steady-state ac component
of the CT secondary voltage. From
1
$ = -Je,dt
Ns
I R
(-sin ot) [This is shown in Figure A.7(d)l
Peak value of ac flux,
%,-
@dc,max -- ImRtL ON, ----OL XL--
@ae,max N,R ImRt R - R
If it is desired to reproduce the ac component at the secondary of the CTJhen the core
must be of a suficiently large size so as not to saturate on totd flux of + $ae,max
Thus, the core size has to be increased by (XdR) times than that required to
reproduce only the ac flux. Since (XdR) ratio is typically of the order of 20 to 30, the core
size will be substantially large, if designed to reproduce the fully offset current.
Even if the core is not designed to continuously reproduce the fully offset current,
still it can reproduce the fault current faithfully till such time as the transient flux
reaches saturation. This fits in well with the scenario of high speed protection because
we are interested in faithful reproduction of the fault current only for the first few cycles
aRer the fault. There is no harm if the CT introduces large errors after that. This saves
us from the expense of over-sized CTs.
A.6 Transient Errors in CVT
Ideally, the low voltage applied to the protective relays should be an exact replica of the
primary system voltage. The CVTs lose some fidelity in reproducing transient voltage

Appe~ldixA-CT and PT E.rrors 365
variations because of inductive, capacitive, and nonlinear elements in the device.
Electromagnetic voitage transformers perform better than CVTs with respect to transient
response but cost more at high voltages. A subsidence transient occurs following a fault
and as a result of a fault.
It should be noted that the transient response of a CT refers to the ability of the CT
to reproduce an offset current wave but the transient response of a CVT refers to its
ability to control the tendency to create extraneous frequencies in the output.
A subsidence transient is an error voltage appearing at the output terminals of a CVT
resulting from a sudden significant drop in the primary voltage, typically produced by a
nearby phase to ground fault. This produces a transient voltage in the secondary that may
be damped oscillatory or decaying unidirectional depending upon the design of the CVT,
the connected burden and the incidence point on the voltage wave. The apparent
impedance to a relay may include errors in both magnitude and phase angle.
Figure A.8 shows the manner in which the secondary voltage may collapse in
response to a sudden reduction to zero in primaxy voltage.
Prefault secondary voltage
Oscillation at
frequency < 50 Hz
Unidirectional
Figure A.8 Transient response of CVT.
A.7 Saturation of CT
Figure A.9 shows the equivalent circuit of CT referred to secondary. As the primary
current goes on increasing, the secondary current tends to increase proportionately. The
secondary voltage, therefore, increases. This necessitates the establishment of a
proportionately large magnitude of flux given by
where f is the frequency and N the number of turns.
As the operating point is near the knee of the excitation characteristic, as shown in
Figure A.l, the magnetizing current requirement becomes disproportionately large.
Further, since the voltage waveform is sinusoidal, the flux waveform is also sinusoidal.
However, because of the nonlinear characteristics the magnetizing current becomes vexy
large with peaky waveform.

266 Appendi,~A-CT oitd PT Errors
CT ratio
= l : N
Figure A.9 Equivalent circuit of CT.
--
1
As the primary current increases, a stage comes where almost all the transformed
I
secondary current (IpfN)is used up in exciting the CT core. Thus, the CT cannot deliver
any current to the load. However, large voltage spikes are generated around zero-crossing
1
of the fluxwaveform. The drop in rms value of secondary current as a function of primary
current is also shown in Figure A.1.
1 The actual output waveform of saturated CT is shown in Chapter 5 on busbar
protection.
Similar saturation of the CT takes place at normal values of primary current if the
burden impedance is increased beyond the design value. The extreme case of increase in
burden impedance happens if the burden gets open circuited while the primary is carrying
current. Such CT open circuits lead to dangerously high values of secondary voltage,
resulting in spark-over and causing the CT to go deep into saturation. The increased iron
f
Current /,, = IpIN
source
--

-- Appendix A-CT and ?T Errors 267
loss in this state can also thermally damage the CT A CT subjected io open circuit can
have a large value of remnant fluxill it and will therefore give excessive raiio and phase
angle errors.
A.8 CT Accuracy Classification
The following table lists the CT accuracy classification.
Class Ratio error Phase angle error

6.1 Introduction
e
In an interconnected power system, Under steady state conditions, all the generators run
in synchronism. There is a balance between the load and the generation. This state is
characterized by constant rotor angles, However, when there is a disturbance in the
system, say, shedding of a large chunk of load or tripping of a line, the system has to
adjust to the new operating conditions. 1, order to balance the generation with the load,
the rotors need to take on new angular positions. Because of the inertia of_the rotating
system and their dynamics, the rotors slowly reach their new angular positions in an
oscillatory manner. This Process of rotor angles reaching their new positions, in a rather
slow oscillatow manner. subsequent to some large disturbance is known asdower swing.
The'time constants involved in these oscillations are of the order of a few seconds.
B.2 Stable and Unstable Power Swing
Figure B.l(a) shows a simple transmission system. There are two parallel lina
let One the parallel lines be lost, say, because of a fault on the line as shown
in Figwe B.l(b) and (c). Since the Power input to the generator remains the same
(assuming no by the Weed governor), the system settles to a new rotor angle &,
which is given by the intersection of the power transfer curve a d the input power line
as shown in Figure B.2(b). This is a case of stable power swing,
The Of with respect time is also sketched in Figure B.2(c).Next assume
a different and higher initial power transfer Piniti,,,,with initid rotor angle at end A to
be 63. Since thereis no intersection between the power transfercurve with one line out
and the power input line, the rotor angle 6 keeps increasing without bounds. This is a
case of unstable power swing as shown in ~i~~~~ ~ , z ( b ) ,
268

Figure B.?(c) shows the variation of 6 m t h respect to time for stable and unstable power
swing
?re-iault
p")
pfinal= = L+LXI sin 4
/
XI1 = X,,llX,,
E2 sin 6,8niriar = -
XI1
(a)
V
/
/
A A
(b)
(C)
Figure B.l Power transfer on a parallel line-pre-fault and post-fault.
El 1a,
I, '
I ',
, .
7 With both lines
Post-fault
V

xi = XL,
Rotor angle
Figure B.2(a) Situation leading to stable power swing

7
'1
270 Appendix B-Power Swing .A
..,-.
With both lines
I 4 Rotor angle
Figure B.2(b) Situation leading to unstable power swing.
$/ Unstable pavier shng
c
m
z A Stable power swing
I F
Time
Figure B.2(c) Variation of 6 with respect to time for stable and unstable pswer swing.
Unstable power swing is an indication that the generators are getting out-of-step.
8.3 Impedance Seen by Relay During Power Swing
Figure B.3(a) shows a simple interconnected system for detailed analysis of the power
swing phenomenon. Generators A and B are connected through a transmission line.
Generator A is exporting power, hence its rotor angle 6 is positive. Generator B is
importing power, its rotor angle is taken as the reference zero.
Voltage and current at the relay location can be written as
where ZT= ZSA+ ZL+ ZsB

Figure B.3(a) Impedance seen by relay on power swing.
We can rearrange the preceding equations in terms of impedances alone, by dividing by
I,, i.e.
EBLO E A L 6
2, + - = 0
1, 1,
and
f (.: Impedance seen by the relay is given by 2, = V,/Zr)
These equations give us a graphical method, wh~chis more insightful than the analytical
method, for constructing impedance triangles and locating 2, as a function of the rotor
angle 6, as shown in Figure B.3(b).
"T
Locus of power swing as 6
Increases for lEAl= lEBl
I Figure B.3(b) Power swing locus construction.
!
1 When 6 becomes equal to 180",the apparent impedance is at the electrical centre of

the system, causing the relay to believe that there is a three-phase short circuit there.
I In the above analysis, it was assumed that (EA( = (EB( for simplicity. However, in
practice, the two voltages will be different. Figure B.3(c) shows that when
IEAI/IEB1= n, the locus of power swing is a c~rclewith distance from point B to centre
given by

Figure B.3(c) Locus of power swing when IEAl/lEBI = n.
The radius of power swing circle is given by
nz,
n 2 - 1
Thus, it can be seen that the impedance seen by the relay is a function of the &tor
angle 6. As the rotor angle 6 goes on increasing, the apparent Impedance approaches the
electrical centre of the system. As it does so, it may enter into the relay &rip
characteristics causing the relay to trip the circuit, thus, adding another shock to the
system and causing further instability. Therefore, the protective relay should not trip on
stable power swings This type of scheme is known as out-of-step blocking scheme.
For a large external disturbance, the power swing is unstable and the two machines
must be separated. The point of split in a large interconnected system should be decided ein advance through system stability studies so that the separated systems have the
balance between generation and load. Thus, at the predecided split point, we need a
deliberate out-of-step tripping scheme.
B.4 Out-of-step Blocking Scheme
As already pointed out, an out-of-stepblocking relay is required where the zone I distance
relay is likely to operate but we wish to block the distance scheme at this location so that
the system is disconnected elsewhere at the most appropriate point.
Further, the location of the locus of power swing depends upon the source and line
impedances (perpendicular bisector of ZT= ZSA+ZL+ ZSB).Although the line impedance
is constant, the source impedances are likely to vary over a period of time due to either
decrease or increase in the number of generating units or line trippings behind the relay
location. Thus, the location of power swing cannot be precisely predetermined.

The power swi~lgis assumed to be in the trip region of zone I, thereby causing the
, ,
t, relay to crip and possibIy split the system at the wrong place. To avoid tfils: an
? . out-of-stepblocking relay is used as shown in Figure B.4(a). The out-of-stepblocking relay!
has a circular characteristic which is concentric with zone I. Let the power swing enter
the blocking relay at t = 0. At t = T,, the power swing enters zone I. The whole distance
scheme is blocked by the blocking scheme in a time less than T,. Thus, Tblocklng< Te.The
trip contact circuit of the three-stepped distance scheme along with the contacts of the
blocking relay are shown in Figure B.4(b).
At A, power swing enters the blocking relay at t = 0
At B, the distance scheme 1s completely blocked (t < T,)
At C, power swing enters zone I (t = T,)
Figure B.4(a) Out-of-stepblocking arrangement
To 3-stepped
distance scheme
Timer with contact T,
Figure B.4(b) Out-of-stepblocking logic.
Since the blocking relay prevents the distance scheme from operating, it is desirable
to prove that the blocking relay does not interfere with the distance scheme for genuine
internal faults.
Consider an internal line fault. Durlng this fault, the impedance seen by the relay
abruptly changes from Zloadto ZraLllt.The blocking relay does see this change in impedance

274 Append~xB-Power Swing
s
but by the time it blocks the distance scheme, the distance scheme has already operated.
Thus, we take advantage of speed with which impedance change takes place. The power 1
swing is a pretty slow phenomenon compared to short-circuit faults.
I
I
8.5 Out-of-step Tripping Scheme 1
As already pointed, we must isolate the system at certain points in case of out-of-step
conditions. This deliberate tripping does not depend upon whether the distance scheme
operates or not. For this reason, the power swing whose location is variable, is assumed
to be outside zone I as shown in Figure B.5.
The out-of-step tripping scheme consists of two blinder relays B1 and B2 havlng
straight line characteristics parallel to the line impedance phasor. The hatching indicates
the trip region. The blinders split the R-X diagram into three distinct areas Al, A2, and
As. In case of power swing, the locus enters the three areas in the following sequence:
Direction of Sequence of Sequence of contact Sequence of contact 5
power swing traversal of areas Bl status B2 status
Right to left Al +A, + Ag closed + open + open closed + closed + open
Left to right A3 + A2 + Al open + open + closed open + closed + closed 43
We can verify that the out-of-step tripping scheme does not mal-operate for external
faults. When there is an external fault, the impedance phasor crosses only one blinder and
the sequencing required for tripping is never completed. The only time when the
impedance crosses both the blinders is in the case of power swing. 4
X = lrn(W1) .,
Three-input, one-output
seauential circuit
if sequence is:
P, -+ P, -+ P3
P, = El B, Tr~p
PI = B, .Bz PJ +P2 -+ pl
then trip
1; if blinder trips
0;if blinder restrains
Mot~onof power swing
Area A1 -+ A, + A3 : Trip circuit breaker
Area A3 -+ A, -+ A, : Trip circuit breaker
Area A, -+ A, : External fault
Area A3 -+ A, : External fault

Protection of Largest
Appendix C
an3 ~bortest~ines
Distance relays have certain drawbacks which need to be carefully considered while
applying them in practical situations. We had not considered the effect of source
impedance or source impedance ratio Zs/ZLon the performance of distance relays. In this
appendix, we will therefore study the effect of source impedance ratio on the performance
of distance relays.
1 C.2 Longest Line That Can Be Protected
The longest line that a relay can protect depends on the relay's performance during stable
power swing. If the protected line is subjected to a stable power swing (i.e. it can recover
by itself from the swing and maintain synchronization) and the distance relay mal-
operates, the relay is Incapable of accommodating maximum swing angle &,.
It is well known that a long line is less stable than a short line. Figure C.l(a) shows
the power angle diagram for long and short llnes. The short line has higher P,, than
that of long line. For a given mechanical input P,, the quiescent operating angle for a
long line is more than that of a short line, i.e.
&,long > &,short
f Therefore, for a disturbance that does not cause instability, the longer line goes through
a larger swing angle than does a shorter line. Hence, a long line is more unstable than
a short line, i.e.
&ax,lang > &ax,shart
The longer the line, the greater is &,. It is of interest to note that &,, on a stable power
swing, can be accommodated by the relay without malfunctioning.
Lines are defined as short or long on the basis of system impedance ratio Zs/Z~,
rather than on the basis of 'heir physical length. Zs is the source impedance or the
impedance behind the relay location and ZLis the line impedance. This is summarized as
follows:
275

Long or short Simnplifiing assumption
long line + ZCIZT= small ZS = 0
diI Figures C.l(b) and (c) show these two cases with mho relay adjusted to reach 100%
- -.
short line + Zs/ZL = large Zs = finite
of the line length for simplicity. It can be easily seen that the &, that the mho relay can
accommodate without maloperation. is about 90" for a long line but meater than 90" for
C L U
- -
a short line. This is exactly opposite of what is needed. A long line goes through a larger
value of 6,, and the relay must accommodate it. Hence, there is a limitation to the
longest line a relay can protect without maloperation on a stable power swing.
&,long line '&,shot line
.{,
&.anon line _
Figure C.l(a) Quiescent operating points for long and short lines.
I Power swing
Figure C.l(b) Power angle accommodation in long line.

Append1.r C-Pr0rec:ion of Longesr and Sliortast Lines 777
*--------------700%
ZL...................................... = L O
/
I
r y
RA ZSB
(finite) (finite)
X
4
I Figure C.l(c) Power angle accommodation in short line.
I C.3 Shortest Line That Can Be Protected
! Figure C.Z(a) shows a single line diagram of a transmission line with CT and PT at the
relay location, the impedance behind the relay location being Zs. The distance relay is
energized by Vrand I,.Assume that the distance relay is of the mho type and is set to
I reach Z, along the line. If the fault takes place at the reach point, the relay voltage drops
I
to a value which is a function of Zs/Z,,. (Note that Z, = 0.8ZL.)
The larger the value of Zs/&, the shorter the line. Thus, the shorter the line, the
I smaller is the voltage Vrfed to the relay. An ideal distance relay is supposed to measure
the ratio VII,irrespective of the individual magnitudes of either V or I. However, in
practice, it is not true.
Zone I
A
Figure Cd(a) Shortest line that a mho relay can protect.
2" ----------------,
B
I
Fault

To find the effect of voltage on the rnho relay's reach, consider the torque equation
for a rnho relay:
If /ZnI I Vl (I1 cos (8, - 8,) > I V1 then trip; else restrain
Considering the restraining spring, the equation is
If 12, I 1VI 111 cos (8, - 8,) > I VI + T,p,,ng then trip; else restrain
Dividing both sides by I VI 111, we have
Tspring
lZnlc0s(Gn- 8,) > IZI +-
IVI III
Substituting 11)= I VlIlZI, we get
To find the reach along the diameter, i.e. with 8, = Or, we get
IZI <
l z n l
Tspring
I + -
I vI2
Thus, the actual reach, considering the effect of the restraining spring, is a function
of the voltage fed to the relay V.
Figure C.2(b) shows the reach versus voltage characteristic of the rnho relay. Similar
proofs can be developed for other distance relays.
Figure C.2(b) Reach versus relay voltage characteristic.
2"
under-reach
2"
Rated voltage
= 110 v,
,I
A
'v,
I
I+ Relay operating range 4

The rench versus relay yoltage characteristic is not very convenie~tto use. since the
reach Znis required to be changed depending on the length of'~heline. To make the actual
reach inciependent of IZ,I: we divide it by Z and define the accuracy of the distance
relay as
Actual reach
Accuracy = z =
Zn
To eliminate voltage, for a fault at the reach point, we calculate
Dividing the numerator and the denominator by Z,,we have
Vr = E
1+ SIR
Thus, instead of plotting reach versus relay voltage, we plot accuracy versus range.
Note that for a small system impedance ratio (SIR) or range, the relay voltage V, tends
to be equal to the rated voltage E. For a large system impedance ratio or range,
V, << E.
Figure C.2(c) shows the graph of Figure C.2(b) drawn in terms of accuracy versus
range. It can be seen that higher the source impedance or shorter the line, the lower is
the actual reach or the accuracy of the relay.
If one stipulates a limit that the accuracy should not be less than 0.9 (i.e. the actual
reach not less than 90% of reach setting) then there is limit to the shortest line that a
distance relay can protect.
Accuracy = ZmaCh/Z,
A
1.o
Operating range in
-terms of SIR (z~z,)-
SIR = 0 'SIR = Maximum
Z, = O Z, = Finite
vr = E = Vrated V, = E = Vr,Mn
Figure C.Z(c) Accuracy versus range graph

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Harmonic restraint percentage differential
relay, 90
High resistance ground faults, 91, 92
Induction generator, 179
Inrush
current, 89
harmonic content of, 90
magnetizing, 89
phenomenon, 86
sympathetic, 89
Least Error Squared (LES) technique, 237
Loss of prime mover, 181
Mann and Morrison method, 245, 247
Negative coincidence period, 210
Neutral grounding transformer, 171
Parallel line, 269
Permanent faults, 153
Phase fault units, 142
Phasor diagrams, 5, 7, 47
of a three-phase transformer, 75, 76
Positive coincidence period, 210
Power line carrier, 156
Power swing, 127, 268
effect on simple impedance relay, 129
impedance seen by relay, 270
locus construction, 271
performance of mho relay, 138
stable, 268, 269
unstable, 268, 269, 270
Protection
against earth leakage
single-phase load, 71
three-phase load, 72
against loss of excitation, 180
against loss of prime mover, 182
against over-fluxing, 95
against over-speeding, 177, 178
back-up, 20, 21, 36
carrier-aided of transmission lines, 153
differential, 23, 49, 57
simple relaying scheme, 59, 60, 63, 66
characteristics of, 64
double-end-fed system, 61
directional ground fault, 51
distance, 118
of a three-phase line, 139, 140, 145
of transmission lines. 13. 118
three-stepped, 146, 147; 148, 149, 150,
151, 154
of generator, 168
longitudinal percentage differential, 173
of longest line, 275
rotor faults, 175
of shortest line, 277
stator faults, 175
transverse differential, 174
induction motor, 184
earth fault, 188
negative sequence voltage relay, 190
percentage differential relay for, 187
single phasing, 191
thermal protection, 193
unbalanced supply voltage, 189
non-directional over-current, 26
primary, 20, 21, 36
principles of, 23, 24
restricted earth fault, 91, 92
zone of, 17, 18, 19, 45, 62
Protection system
dependability, 14
deregulated, 12
dynamic entity, 11
elements, 5, 23
evolution of, 9
interconnected, 10
isolated, 10
negative synergy of, 10, 11
reliability, 14
selectivity, 14, 22
sensitivity, 14
speed, 14
various states of, 11, 12
Protective relays, 9
Reclosure, 1, 153, 154
Relay(s)
bimetallic, 28
Buchholz, 93
computer-based, 222
d i ~ t a l ,222
directional, 23, 47, 49, 50, 51, 52, 53
phasor diagram, 48
distance, 23, 119, 120
earth leakage (or current balance), 71
induction disc type, 32, 33
mho, 134
directional property of, 137
implementation of, 135
performance of, 135
reach of, 136
synthesis of, 205, 206, 207
trip law, 134

Acceleration (of carrier), 159, 160, 161 Deionization times, 153
Accuracy vs range graph, 280 Digital filter, 239. 241, 242
Algorithms for digital protection, 253 recursive, 243
Arc resistance, 3 Discrete Fourier machine, 233
Auto-reclosure, 154 Discrete Fourier Transform, 231. 234
Distance measuring units, 142, 144
Balanced beam structure, 124 Duality between comparators, 201
Blinders, 138
Blocking Excitation
arrangement, out of step, 273 loss of, 179
carrier, 162 Excitation characteristic of CT, 256
logic, out-of-step, 273
scheme, out-of-step, 272 Fault(s1, 1
Busbars external, 18, 60
differential protection of, 102, 112 forward and reverse, 47
high impedance scheme, 112, 114, 115 ground, 5, 6, 42, 142
external and internal faults, 104, 108, 110 incipient, 93
internal, 18
Carrier signal, 155 metallic, 3, 6
acceleration, 160, 161 phase, 5, 6, 42, 151
coupling probability of, 5
line-to-line, 157, 158 resistance, 3
single line-to-ground, 157 series, 7
distance relaying, 159, 160 short-circuit, 8
preacceleration, 161, 162 single line-to-ground, 2
protection, 153 statistics, 5
for relaying, 156, 157 through, 18, 60, 63, 64, 67, 69
directional protection, 157, 158, 159 stability, 64
unit schemes, 162 stability ratio, 64, 70
Circuit breaker, 17 in transformers, 78, 91, 93
trip circuit, 17, 18 internal and external, 96
Coincidence Fault detector unit, 147
period, 164, 165, 167, 210 Flashover, 2, 3
principle, 213, 215 Fourier analysis, 229, 231, 236
Comparator Fuse, 26
amplitude, 196, 198, 201, 210, 211 characteristics of, 27
phase, 199, 201, 206
cosine-type 199, 200, 205, 206, 208, 210, Ground fault units, 144
212, 213 Grounding resistance, 171
sine-type, 200, 216, 217, 218 Grounding transformer, 170, 171
285

numencal, 222 directional, i9
block diagram, 223 distance, 23, 55, 120
development cycle, 223 over-current, 23
differential equation algorithm, 249 phase comparison, 162, 163, 164, 165
distance protection of transmission line, Xotor angle, 4
245
over-current protection, 243
algorithm, 244
transformer differential protection, 245
operating time, 36, 37
out-of-step blocking, 272
over-current, 28, 29, 34
definite time, 30, 35, 36, 42, 47
directional, 44, 46
drawbacks, 54
instantaneous, 29
inverse definite minimum time (IDMT),
31, 37, 38, 39, 40, 41, 42
inverse time, 30, 31
percentage differential, 67, 68, 89, 245
block diagram, 70
characteristics of, 69, 70
harmonic restraint, 90
restraining regon, 69
t r ~ pregion, 69
pick-up value, 35, 37
quadrilateral distance
synthes~sof, 218
reach, 18, 118, 119, 145
reactance, 129, 130
directional property of, 133
t implementation of, 131
performance of, 131, 134
reach of, 132
synthesis of, 208
trip law, 129
replica type, 194
resistance temperature detector, 194
reverse power, 52
selective t ~ m einterval, 37
simple impedance, 121, 122, 123, 124, 125,
126, 127
balance beam construction, 125
directional property of, 127, 128, 129
performance of, 126
reach setting of ,126
synthesis of, 210, 211
trip law, 123, 124
supervisory, 112, 113
thermal, 27
voltshertz
Relaying
differential, 19
Merz-Price scheme, 59
Sample and hold, 224
Sampling theorem, 225
Short circuit, 1
Spill current, 63, 67, 70
Synchronous
alternator, 10
impedance, 3
Tie lines, 10
Transformers
current, 14, 15
accuracy, 267
circuit model, 108
construction, 255
equivalent cirwit, 65, 105, 257, 266
magnetizat~oncharacteristic, 66
measurement, 16, 255
phase angle error, 15, 256, 257, 258
protective, 16, 105, 255
ratio error, 15, 258
saturation, 107, 265
transient errors, 261
transient response, 263
equivalent circuit, 77
over-current prothction, 80
over-fluxing in, 95
percentage differential protection, 81
potential, 259
capacitive, 259, 260
electromagnetic, 259
phase angle error, 260
ratio error, 260
transient errors, 264
transient response, 265
types of, 74
voltage, 14, 16
capacitive, 17
errors, 16
Tripping scheme, out-of-step, 274
Unbalanced loading, 176, 178
Walsh analysis, 228, 235
Warrington, 3
formula, 123
Wavelet analysis, 228, 236

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