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Rs
...
00
FUNDAMENTALS OF POWER SYSTEM PROTECTION
Y
...
Paithankar and S
...
Bhide
O 2003 by Prentice-Hall of lndia Private Limited, New Delhi
...
No part of this book
may be reproduced in any form, by mimeograph or any other means, without permission in writing
from the publisher
...
Published by Asoke K
...
M-97, Connaught Circus,
New Oelhi-110001 and Printed by Meenakshi Printers, Delhi-110006
...
Formerly Professor and Head
Electrical Engineering Department
Visvesvaraya National Institute of Technolorn
Nagpur
S
...
Bhide
Assistant Professor
Electrical Engineering Department
Visvesvaraya National Institute of Technology
Nagpur
-
-
...
I --IL
-,f India
Saeed Book Bank
hc Delhi - 1 1
2003
Dependence of Modern Society on Electric Supply I
Faults and Abnormal Operating Conditions I
1
...
1 Shunt Faults (Short Circuits) 1
1
...
2 Causes of Shunt Faults 3
1
...
3 Effects of Shunt Faults 3
1
...
3
...
3
...
3
...
4
...
4
...
3 What are Protective Relays Supposed to Do? 9
volution of Power Systems 9
1
...
1 Isolated Power System 10
1
...
2 Interconnected Power System 10
1
...
3 Negative Synergy of a n Interconnected System 10
ates of Operation of a Power System 11
...
5 From Natural Monopoly to the Deregulated Power System 12
Protection System and Its Attributes 13
...
1 Sensitivity 14
...
2 Selectivity 14
?-
...
4 Reliability and Dependability 14
ystem Transducers 14
...
1 Current Transformer 15
nsforrner 16
iii
1
...
3 Circuit Breaker 1 7
1
...
4 Trip Circuit of a CB 1 7
17 5 Organization of Protection 1 7
1
...
7 Primary and Back-up Protection 2 0
1
...
8 Maloperations 22
1
...
9 Various Principles of Power System Protection 23
Reuiew Questions 24
Problems
25
2 OVER-CURRENT PROTECTION OF TRANSMISSION LINES
26-56
2
...
3 Thermal Relays 27
2
...
4
...
4
...
4
...
5 Implementation of Over-current Relay Using Induction Disk 32
2
...
7 Application of Inverse Definite Minimum Time Relay on a
Distnbution Feeder 3 7
2
...
1 Choice Between IDMT and DTOC Relays 42
2
...
9 Directional Over-current Relay 44
2
...
9
...
9
...
9
...
9
...
10 Drawbacks of Over-current Relays 54
Reuzew Questions 55
Problems
56
3 DIFFERENTIAL PROTECTION
57-73
3
...
2 Dot Markings 57
3
...
3
...
3
...
3
...
3
...
5
...
6 Percentage Differential Relay 67
3
...
1 Block Diagram of Percentage Differential Relay 70
3
...
7
...
7
...
4
35
4 TRANSFORMER PROTECTION
*
74-100
4
...
2 Phasor Diagram for a Three-phase Transformer 75
4
...
4 Types of Faults in Transformers 78
4 5 Over-current Protection 80
4
...
6 1 Development of Connections 81
4
...
2 Phase c-to-Ground (c-g) External Fault 82
4
...
3 Phase c-to-Ground (c-g) Internal Fault 84
4
...
7
...
8 High Resistance Ground Faults in Transformers 91
4
...
2 High Resistance Ground Faults on the Star Side 92
4
...
10
...
10
...
11 Phenomenon of Over-fluxing in Transformers 95
4
...
1 Protection Against Over-fluxing 95
4
...
13 An Illustrative Numerical Problem 97
Reuzew Questions 99
Problems
100
5 BUSBAR PROTECTION
...
1 Introduction 101
5
...
2
...
2
...
5 Circuit Model of Saturated CT 108
5
...
7
Impedance Busbar Differential Scheme 110
5
...
9 Supervisory Relay 112
5
...
11 Numerical Example on Design of High Impedance Busbar Differential
Scheme 115
Review Questions 117
53
...
4
6 DISTANCE PROTECTION OF TRANSMISSION LINES
118-152
6
...
2 Introduction to Distance Protection 119
6
...
3
...
3
...
3
...
3 4 Effect of Arc Resistance on Reach of Simple Impedance Relay 126
6
...
5 Directional Property Exhibited by Simple Impedance Relay 127
6
...
6 Performance of Simple Impedance Relay During Power Swing 127
6
...
4
...
4
...
4
...
4
...
4
...
4
...
5 Mho Relay 134
6
...
1 Trip Law for Mho Relay Using Universal Torque Equation 134
6
...
2 Implementation of Mho Relay Using Induction Cup Structure 135
6
...
3 Performance of Mho Relay During Normal Load Flow 135
6
...
4 Effect of Arc Resistance on Mho Relay Reach 136
6
...
5 Directional Property Exhibited by Mho Relay 137
6
...
6 Performance of Mho Relay During Power Swing 138
6
...
7 Distance Protection of a Three-phase Line 139
6
...
1 Phase Faults 141
6
...
2 Ground Faults 142
6
...
3 Complete Protection of a Three-phase Line 144
...
1 Introduction 184
9
...
3 Starting Current 185
9
...
4 1 Fault on Motor Terminals 186
9
...
2 Phase Faults Inside the Motor 186
9
...
3 Ground Faults Inside the Motor 188
9
...
4 Inter-turn Faults 189
9
...
5
...
5
...
5
...
5
...
6 Abnormal Operating Conditions from Mechanical Side 192
9
...
1 Failure of Bearing and Rotor J a m 192
9
...
2 Overload 192
9
...
1 Comparison vs Computation 196
10
...
3 Phase comparator 199
10
...
1 The Cosine-type Phase Comparator 199
10
...
2 The Sine-type Phase Comparator 200
10
...
5 Synthesis of Various Distance Relays Using Static Comparators 204
10
...
1 Synthesis of Mho Relay Using Static Phase Comparator 204
10
...
2 Synthesis of Reactance Relay Using Cosine-type Phase Comparator 208
10
...
3 Synthesis of Simple Impedance Relay Using Amplitude Comparator 210
10
...
7 An Electronic Circuit for Implementing a Sine-type Phase Comparator 216
10
...
1
11
...
3
11
...
4
...
5 Least Error Squared (LES) Technique 237
e
...
9
...
9
...
9
...
10 Trip Contact Configuration for the Three-stepped Distance
Protection 149
6
...
12 Impedance Seen from Relay Side 150
6
...
8
6
...
1
7
...
3
Need for Carrier-aided Protection 153
Various Options for a Carrier 155
Coupling and Trapping the Carrier into the Desired Line Section 155
7
...
1 Single Line-to-ground Coupllng 157
7
...
2 Line-to-line Coupling 157
7
...
5 Carrier-aided Distance Schemes for Acceleration of Zone I1 160
7
...
1 Transfer Trip or Inter-trip 160
7
...
2 Permissive Inter-trip 161
7
...
3 Acceleration of Zone I1 161
7
...
4 Pre-acceleration of Zone I1 161
7
...
1 Introduction 168
8
...
3 Various Faults and Abnormal Operating Conditions 172
8
...
1 Stator Faults 173
8
...
2 Stator Phase and Ground Faults 173
8
...
3 Transverse Differential Protection 174
8
...
5 Abnormal Operating Conditions 176
8
...
1 Unbalanced Loading 176
8
...
2 Over-speeding 178
8
...
3 Loss of Excltation 179
8
...
4 Protection Against Loss of Excitation Using Offset Mho Relay 180
8
...
5 Loss of Prime Mover 181
Revzew Questions 183
...
6 Digital Filtering 239
11
...
1 Simple Low-pass Filter 239
11
...
2 Simple High-pass PLlter 240
11
...
3 Finite Impulse Response ( X R ) Filters 241
11
...
4 Infinite Impulse Response (IIR) Filter 242
11
...
5 Comparison Between FIR and IIR Filters 243
11
...
8 Kumerical Transformer Differential Protection 245
11
...
9
...
9
...
10 Algorithms and Assumptions 253
Review Questions 254
@
1
0
...
...
l Introduction 255
A
...
3 Measurement CT and Protective CT 255
A
...
4
...
4
...
5 Transient Errors in CT 261
A
...
7 Saturation of CT 265
A
...
l Introduction 268
B
...
3 Impedance Seen by Relay During Power Swing 270
B
...
5 Out-of-step Tripping Scheme 274
268-274
Appendix C P R O T E C T I O N OF LONGESTAND SHORTEST LINES
275-279
C
...
2
C
...
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
...
One should also be knowledgeable about the
tripping characteristics of various protective relays
...
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
...
Whenever a tripping takes place it has all the elements of intrigue, drama, and
suspense
...
It needs to be established why the relay has tripped
...
What and where was the fault? These are some of the questions
required to be answered
...
I t is always in a state of flux
...
New loads are added all the time
...
In view of such possible
consequences, a protective system with surgical accuracy is the only insurance against
potentially large losses due to electrical 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
...
This is possibly an area where
protection tends to become an art
...
xi
xii
Prefncc
The book is focused on teaching the fundamental concepts and the related design aspects of protective relay schemes
...
The text contains a wealth of figures, block diagrams, and tables to illustrate the
concepts discussed
...
The students are urged to
spend some time to read the annotations on the figures, so that learning becomes easy
and concepts are reinforced
...
The authors will gratefully receive
suggestions and comments from the readers for improvement of the book
...
PAITHANKAR
S
...
BHIDE
0
Dependence of Modern Society on Electric Supply
1
...
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
...
Thus, the importance of maintaining continuous supply of
electricity round the clock cannot be overemphasized
...
So, one has
to live with the failures
...
There is no negative connotation to the word fault in this context
...
minimized by q",ck!y
...
element from
...
...
faults
...
...
~
...
~
...
limiting the disturbance footprint to as~
...
small an ~qeea_
-
~
~
-
1
...
2
...
The insulation can break down for a variety of
reasons, some of which are listed in Section 1
...
2
...
1shows a single line-to-ground
fault on a transmission line due to flashover of spark gap across the string insulator
...
e
...
This p r o ~ ~ ~ f
...
In low-voltage systems up
...
...
<< ?
7 ' 3
' : c:<
...
1 Single line-to-ground fault due to flashover of insulator string
...
recl~~re_s_-ar_eattem~ted~
...
e r locked out
...
~~ is,
...
The reclosure may also be done automatically In EHV systems,
,,-
...
At times the short circuit may be total (sometimes called a dead short circuit), or it
may be a partial short circuit
...
A metallic fault presents a very low, practically zero, fault
resistance
...
Most of the times, the fault resistance
is nothing but the resistance of the arc that is formed as a result of the flashover
...
Early researchers have developed models of
the arc resistance
...
S~u~&
...
basicall~~,~due_~to~fajl
...
re
of insulation
...
The weakening of insulation may
be due to one or more of the following factors:
_
-
Ageing
Temperature
Rain, hail, snow
Chemical pollution
Foreign objects
Other causes
'"
...
'
The overvoltage may be either internal (due to switching) or external (due to lightening)
...
2
...
Consider a n isolated
turboalternator with a three-phase short circuit on its terminals as shown in Figure 1
...
Assuming the internal voltage to be 1 p
...
and a value of synchronous impedance,
Xd = 2 p
...
, the steady-state short-circuit current would only be 0
...
u
...
However considering subtransient impedance, X = 0
...
u
...
...
Faults, thus, cause heavy currents to flow
...
Over-currents, in general, cause overheating and attendant danger of fire
...
Not SO
apparent is the mechanical damage due to excessive mechanlcal forces developed during
over-current
...
This is due to the fact that any two current-carrying conductors
experience a force
...
Further, in an interconnected system, there is another dimension to the effect of
faults
...
The electrical power output from an alternator near the fault drops
sharply
...
This causes the alternator to accelerate
...
Thus, the alternators start swinging with respect to each other
...
Thus, in an interconnected power
system, the system stability is a t stake
...
3
Clussificafi~nof Shunf Fslulfs
1
...
1
Phase Faults and Ground Faults
Those faults, which involve only one of the phase conductors and ground, are called
ground faults
...
Power systems have been in operation for over a hundred years now
...
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-phase fault (L-L-L), is the least likely
...
1
Table 1
...
The transmission lines which are exposed to the vagaries of the atmosphere are
the most likely to be subjected to faults
...
The fault statistics is shown in Table 1
...
Table 1
...
In the power system, the three-phase
fault is the most severe whereas the single line-to-ground fault is the least severe
...
3
...
At the same time there
of
6 Fu~~da~,rentaLsPower Systen~Protectio~l
is a fall in voltage throughout the power system
...
The voltage at the terminals of the generator will also drop,
though not drastically
...
Normally the relay is away from the fault location
...
Figure 1
...
-
a
(b) L-L fault
(a) L-Gfault
( d ) L-L-L fault
(c) L-L-G fault
a
I
iI
i
I,;
1
!
(e) L-L-L-G fault
13
...
-
~
~
...
,
...
4 depicts a radial power system with a fault near the remote end of the
transmission line
...
In order not to clutter the diagram, only phase a voltage is
shown
...
5, the distortion in voltages during all the 11 shunt faults are
considered
...
/
Source
'b
lc
Three-phase line
Three-phase fault
I
Relay
E
a
-
la =
Zs + ZL
'b
C=-
e
I, =
Eb
zs + ZL
Ec
-
zs
+
ZL
Va=E,-IZ
8 S
Vb = Eb - lbZS
Vc = E, - I$s
Figure 1
...
1
...
3
Series Faults
Series faults are nothing but a break in the path of current
...
- -
Grounded
neutral
- - -
...
_____
N
va
--
...
--
...
',
,
---_-----
...
___-__-
...
V C f l- - - - -
...
5 Voltages at the relay location during various faults
...
It is observed in practice that most of the open conductor faults
sooner or later develop into some or the other short-circuit fault
...
1
...
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
...
1
...
1
Should Protective Relays Trip During Abnormal
Operating Conditions?
How the protective system should respond to the abnormal operating conditions needs
careful consideration
...
Some examples of abnormal operating conditions are starting
currents of motors, inrush currents of transformers and stable power swings
...
...
Thus, the w t e c t i v e system m u s t be able to discriminate between the normal
--- -~
...
conditions, abnormal operating condi&io
...
...
...
',
,
~
~~
1
...
2
~
...
To
a certain extent, faults can be prevented by using the properly designed and maintained
equipment
...
1
...
3 What are Protective Relays Supposed to Do?
a
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
tripping an appropriate number of circuit breakers
...
I n a power system, faults are not an everyday
occurrence
...
I t must, therefore, be ready all the time in anticipation of a fault
...
1
...
The evolution has progressed
from low-voltage systems to high-voltage systems and low-power handling capacities to
high-power handling capncities
...
1
...
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
...
As shown
in Section 1
...
3, the steady-state fault current in a single machine power system may even
be less than the full-load current
...
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
...
5
...
An interconnected power system
also makes it possible to implement an economic load dispatch
...
6 shows a simple interconnected power system
...
At the receiving end, the voltage is stepped
down to the distribution level, which is further stepped down before it reaches the
consumers
...
1
...
3
a
Negative Synergy of an Interconnected System
There are other undesirable effects of interconnection
...
Disturbances quickly propagate
throughout the system endangering the integrity of the whole system
...
In addition to the angle
stability problem, a n interconnected system also suffers from the voltage stability
problem
...
Also, there is the possibility of cyber-attacks and
acts of malicious hacking, which have a greater footprint in the case of an interconnected
()
I
BusA
Load A
A
Load 3
A
Bus B
Generating
statlon A
Generating
me
0
-
...
6 Single-line diagram of a simple interconnected power system
power system
...
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
...
5
...
Its state is likely to drift from one state to the other
as shown in Figure 1
...
When the power system is operating in steady state, it is said to
be in the normal operating state
...
This state is also characterized by reactive power balance
between generation and load
...
The above is almost a theoretical proposition and a real power
system rarely finds itself in this state
...
7 Various states of the power system
...
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
...
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
...
This is
indeed the nightmare and the system controllers at the load dispatch centres try their
best to avoid it
...
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
...
The relay engineers want their protective system to be as simple as possible
...
Thus the relay engineers follow the KISS philosophy; Keep I t Simple, Stupid!
1
...
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
...
In
this scenario, big electric utility companies are no longer monopolizing the generation of
electric power
...
The customers have a choice to buy
electricity from the cheapest bidder (albeit through the distribution company)
...
The relaying engineer cannot remain unaffected by this change which IS sweeping
through the power industry
...
•
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
...
(In non-directional over-current protection, as
well as in differential protection, the PT will not be required
...
7
...
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
...
The relay has another user settable input which is the setting of
the relay
...
The conceptual diagram of
a generalized relay is shown in Figure 1
...
Setting
I
Current from CT 4
Current from PT
4
1 1
I
Relay d Trip signal to CB
T
t
Setting
Figure 1
...
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
...
7 -6
...
The
smaller the fault current it can detect, the more sensitive it is
...
6
...
-
,
,
,
Selectivity
In detecting the fault and isolating the faulty element, the protective system must be very
selective
...
1
...
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
...
Therefore, the speed of the~protectionis very important
...
This is for the simple reason that the highspeed system has lesser amount of information at its disposal than a slow-speed system
...
!
...
6
...
There are many ways in which
reliability can be built into the system
...
In general, it is found that simple
systems are more reliable
...
However, in spite of best efforts to make the system reliable, we cannot rule
out the possibility of failure of the (primary) protection system
...
1
...
These transducers basically extract the
information regarding current and voltage from the power system undcr protection and
pass it on to the protective relays
...
e
1
...
1
Current Transformer
The current transformer has two jobs to do
...
The standard secondary current ratings used in practice are 5 A and 1 A
...
Secondly, it isolates the relay
circuitry from the high voltage of the EHV system
...
10
...
I n practice, there is always some
error
...
These errors are known
as raho error and phase angle error
...
Bus
j
i/
Pr~mary
/
*i
7
Secondary
...
10 Current transformer
...
However, there is a very important difference between a metering CT and a
protection CT
...
The operating po~nts, the excitation charactenstics, for the
on
two types of CTs are shown in Figure 1
...
Further treatment of CT errors is given in
Appendix 1
I,
i
16
F ~ ~ n c i a ~ ~ ~ e i l t Power
of o l s
Svsre~nProrection
A
-
-
"
E
Measurement CT
operating point
m
5
-5
c
m
51
Protective CT
operating point
--f
Excitation, H(AT/m)
Protective CT
output
s
1
Slope =
...
11 Protective CT vs measurement CT
...
7
...
The standard
secondary voltage on line-to-line basis is 110 V
...
-A PT primary is connected in parallel a t 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
...
12
...
Further treatment of VT errors can b e found in
Appendix 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
...
1
...
3
Circuit Breaker
The circuit breaker is an electrically operated switch, which is capable of safely making,
as well as breaking, short-circuit currents
...
When the circuit breaker is in the closed condition, its contacts
are held closed by the tension of the closing spring
...
1
...
4
Trip Circuit of a C
B
The circuit breaker contacts are in a closed position by the force of a spring
...
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 relay
output contact is wired in series with the trip-battery and the trip-coil
...
The mechanical arrangement is quite complicated and only its essence is
depicted in Figure 1
...
1
...
5
Organization of Protection
The protection is organized in a very logical fashion
...
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 is depicted in Figure 1
...
Without going into the detailed
working of the differential relaying scheme, we can make the following statements:
lf r o l s
18 F ~
...
13 Trip circuit of a circuit breaker
...
14 Zone of protection, external and internal faults
...
External faults are also known as through faults
...
It should restrain from operating for external faults
...
The distance
between the relay location and
...
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
...
In general, it can be said that the differential relaying gives a
much more crisply carved out zone than over-current or distance relaying
...
1
...
5
Zones of Protection
Various zones, for a typical power system, are shown in Figure 1
...
It can be seen that
the adjacent zones overlap, otherwise there could be some portion which is left out and
Generator zone
Transformerzone
Transmiss~on zone
line
Transformer zone
Generator zone
Figure 1
...
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
...
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
...
7
...
This could
be due to failure of the CTIVT or relay, or failure of the circuit breaker
...
We must have a second line of defence in such a situation
...
A little thought
will convince the reader that the back-up protection should not have anything in common
with the primary protection
...
Further, the back-up protection must wait for the
primary protection to operate, before issuing the trip command to its associated circuit
breakers
...
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
...
16
...
Relay A with circuit
breaker CBA provides back-up protection to the section B-C
...
16
...
i n 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
...
The sequence of events in such a case is depicted in Figure 1
...
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
...
Fault
instant
Primary relay RB
operates
P-
Primary
Primary relay CBB
interrupts
the fault current
Primary CB
operating time
Pr~mary
fault clearing time
3
Back-up relaying time > Primary fault clearing time
T A > TB + CBB
e
Primary protection provided by RB starts operating
I)
\
Back-up protection prov~ded RA starts operating
by
/
Primary protection issues trip command to primary circuit breaker CBB
'
Primary circuit breaker starts operating
/
Primary circuit breaker CBB trips
...
17 Primary and back-up protection: sequence o f events: normal operation
i
I
22
i
1
...
8 Maloperations
i
!
v
{
I,
1
1
1
1
F~~ncla~nenralsPower Sysrem Prorection
of
There should be proper coordination between the operating time of primary and back-up
protection
...
18 shows an instance of loss of selectivity between the primary and
...
It can be seen that the back-up protection in this case issues trip
command to its breaker without waiting for the primary protection to do its job
...
It is said that with every additional relay used,
there is an increase in the probability of maloperation
...
Primary fault clearing time
6
Back-up relaying operating time c Primary fault clearing time
TA-= TB+CBB
Fault instant
Primary protection provided by RB starts operating
Back-up protection provided by RA starts operating
/ Primary protection issues command to primary CB(RB + CBB)
'
Primary CB, CBs, starts operating
,
Back-up protection issues command to back-up CB(RA + CBA)
'
Back-up CB
...
18 Primary and back-up protection: sequence of events: loss of selectivity
*
1
...
Each of these entities needs
protection
...
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
...
Thus each apparatus needs a different kind of protective system
targeted to its unique set of anticipated faults and abnormal operating conditions
...
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
...
1
...
Thus, over-current relaying
is the most natural principle of relaying
...
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
...
This has led relay engineers to think of other principles of protection
...
I t is based on the premise
that the current entering a protected section must be equal to that leaving it
...
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
...
This, in effect, measures the impedance between the relay location and the
fault point
...
In case of a double-end feed system, or parallel lines, or a ring main system, a fault
gets fed from both sides
...
The relays which exhibit such property are termed
directional relays
...
3
...
3 The gamut of power system protection
1
1
Principle
Alternator
Busbar
Transformer
Transmission Line
Large Induction
Motor
Won-directional
- ouer-current
Primary
Protection
Primary
Protection
Primary
Protection
Primary
Protection
Primary
Protection
Directional
ouer-current
Differential
Distance
J
I
Apparatus
J
J
I
J
J
J
J
J
J
J
The cells of the Table 1
...
In chapters to come, we will try to fill up these cells or try
to understand why some of the cells remain vacant!
Review Questions
Power systems are moving towards increasing complexity and demand equally
complex protection
...
Compare an isolated power system and an interconnected power system
...
Discuss
...
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
...
Problems
1
...
2
...
16, T B = 0
...
If the circuit breaker operating time
is 0
...
3
...
16, the operating time of relay RB = 0
...
6 s
...
5 s
...
4
...
The short-circuit current for the smallest
fault is 1000 A
...
(a) Suggest a suitable CT ratio
...
1
Introduction
As already pointed out, the most obvious effect of a shunt fault is a sudden build up of
current
...
I t is no wonder, therefore, that the over-current
protection is the most widely used form of protection
...
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
...
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 a t the
relay location
...
A little thought will convince the readers that a directional over-current
protection affords greater selectivity than a non-directional over-current protection
...
Then, it needs to
be implemented
...
We can thus imagine a non
directional over-current relay, which provides the non-directional over-current protection
and so on
...
We will, therefore, take a brief look a t fuses in the next section
...
2
Fuse
Fuses are the oldest protective devices that have survived from the dawn of the age of
electricity to the present times
...
time
...
Figure Z
...
The current
26
versus time characteristic of a fuse is shown in Figure Z
...
The waveform of che shortcircuit current interrupted by a fuse is shown in Figure 2
...
where it can be seen that
the fuse interrupts the current even before it attains its peak value
...
1 High rupturing capacity (HRC) fuse
...
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~dainirrerirnlsf Power Svsrerrr Prvtecrion
o
passage of the fault current
...
2(a) shows a bimetallic relay consisting of strips AB
...
Both the strips get heated up by the same amount but
are deformed by diqering amounts
...
2(b) shows the rclay operation
...
with higher coefficient of expansion is a t the outer surface of the curve while that with
lower coefficient is at the inner surface
...
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
...
very q u i c-k m a t i o n
...
is not d e d f ~A
...
The thermal overload relay thus let; the motor supply
overload for a preset amount of time before tripping it off
...
4
~
Over-current Relay
An over-current (OC) relay has a single input in the form of ac current
...
The relay has two settings
...
The
time setting decides the operating time of the relay while the plug setting decides the
current required for the relay to pick up
...
In these relays, we have io ~ n s e r a shorting ?lug in
t
J
...
The same terminologlv continues to be used in the modern
relays
...
3
...
3 Block diagram of an over-current relay
...
The value of PSM tells us about the severity of the current as seen by the relay
A PSM less than 1 means that normal load current is flowing
...
Higher values of PSM indicate how serious the fault is
...
0 A relay (i
...
a relay with current coil designed t o
carry 1
...
5 A, i
...
at 50%
...
0 A
...
0/0
...
@
2
...
1
Instantaneous OC Relay
It is to be noted that the word instantaneous has a different connotation in the field of
power system protection
...
Howsoever fast we want the relay to operate; it needs a certain minimum amount of time
...
Such
a relay has only the pick-up setting and does not have any time setting
...
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 is a positive feedback action which
results in the armature moving quickly in an instantaneous snap action
...
30
F ~ ~ ~ r c l r ~ r r ~ e ~ ~ t a l s Sj~sreti7P,vr?crior~
o f Po~ver
-
:
:
C
0
a
,
0
...
-
E
-
E
...
4 Instantaneous over-current relay characteristic
...
4
...
Thus, it has a time-setting adjustment and
a pick-up adjustment
...
9
...
Time setting
m
Current
Plug setting
m
E
...
-
@'
Trip output
Plug setting
t
t
j
...
...
----- r - - Current
+
f
Figure 2
...
2
...
3
:'
,,
!I
I:,
r:
,I
Inverse Time Over-current Relay
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
...
With the advent of microprocessor-based relays, it is
now possible to generate any imaginable time-current characteristic
...
, have beer,
standardized
...
The characteristic is inverse in the
initial part, which tends to a definite minimum operating time as the current becomes
very high
...
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
...
Thus, the operating time is directly proportional to the TMS and inversely
proportional to the PSM
...
6
...
6 Inverse definite minimum time relay characteristics (TMS = 1
...
-
32 Funda~nenmlso j Power Sysrern Prorectioi~
Very inverse time over-current relay
The inverseness of this characteristic is higher than that of the IDMT characteristic
...
6
...
The mathematical relation between the current and the operating time of
such a characteristic can he written as
I ,
t ;
80
...
(PSM)~ 1
-
The characteristic of the relay is shown in Figure 2
...
2
...
Figure 2
...
Induced flux
f
hernating fluxes
Ed<-
...
7 Operating principle of induction disc type relay
...
7, 4 interacts with i to produce force Fl
...
Assuming w to be constant, we have
@
sin wt cos ( w t
F1 = $liCz a
F2 =
+ 8)
hi,,a &,&, sin ( w t + 8) cos wt
The net force (F2 - F l ) is thus, given by
3'2 -
FI a
[sin ( w t
+
8) cos ot - cos ( w t
+
8) sin wt ]
which simplifies to
I F2 - F1
sin 81,
The following important conclusions can be drawn from the above expression for
torque:
$m1&2
Two alternating fluxes with a phase shift are needed for torque production,
i
...
a single alternating flux would not produce torque
...
The resultant torque is steady, i
...
it is not a function of time, as time t is not
involved in the expression for torque
...
The above principle has been used in the induction disc type over-current relay whose
construction is shown in Figure 2
...
Herein two fluxes shifted in time phase are obtained
from the input current, by using a shading coil
...
The torque thus produced by the interaction of the two fluxes, neglecting saturation,
is proportional to I 2 since each of the flux is proportional to I
...
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
...
crioll
f~
ThlS adjustment dial
Movable contact
0
...
8
Constmction of an induction disc relay
...
,
...
All these constants depend upon the design of the relay
...
e
...
Now,
At
At
t = 0;
6=
i
6,,,t,,1
t = top; 6 = 0
We can find the operating time by finding the value of time t for which 6 becomes
zero
...
i
I
The exact analysis of the dynamics of induction disc is quite involved
...
2
...
9, with two
line sections AB and BC
...
There are
loads at all the three buses
...
9 Application of DTOC relays for feeder protection
...
The first step in designing the over-current protection is to select the ratios for all
the CTs
...
The CT primary current is decided by the maximum load current to be carried by
the CT primary
...
It may be noted that setting of the
relay, where the DTOC relays are involved, means:
1
...
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
...
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
...
rlmlsof Power S
...
At the same time, the relay
should be sensitive enough to respond to the smallest fault
...
Therefore, we can write the foliowing rule,
as far as setting the pick-up value of the OC relay is concerned:
1 IL,
m a
< Ipu<
Permissible ,
I
overload
Minimum fault current --+
%
Ic,
mln
1
-
I
I
I
I
I
Maximum fault current
Figure 2
...
Only if the primary protection does'not clear the
fault, the back-up protection should initiate tripping
...
~ a t u r a l l j ! primary
protectioil is the first to operate, its operating time being less than that of the back-up
relay
...
11 shows the relationship between the operating time of the primary relay
and that of the back-up relay
...
Overshoot time
Overshoot
If fault i cleared beyond this porn1
s
the relay RA does not reset
Relay R, operating time
...
v
4
+
I
Fault instant
f
<
-Time
I Reiay RA
I trips
I
Relay Re operating
time, T,,,
-
Circuit breaker B
perating time
...
B Tca
...
1
+
+
TOSA
-,
,
4
,
The time setting of DTOC relays
...
vnission
Lines
37
is defined as the time for which the relay mechanism continues to move, even after the
operating coil has been de-energized
...
i n the light of the above discussion, the correct procedure would be to start
the setting from the tail end of the feeder system
...
In the given example of Figure 2
...
1 6
...
1 s plus, a time equal to the
plus overshoot time of relay A (ToS,*)
...
1 s (fastest)
Assuming CB operating time = 0
...
2 s, we have
TR,, = 0
...
5 + 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
...
The worksheet for the settings of the relays
thus can be written as shown in Table 2
...
Table 2
...
1 s
TR,A= TRB+ TCB,B TOS,A
+
= 0
...
5 + 0
...
8 s
Note that the setting process has to be started from the relay which is at the tail end
of the system
...
All other upstream relay settings are tied up with their downstream neighbours
...
12
...
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
...
I t 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
...
8 s
w
n
ST1 = 0
...
8 s
0
m
X
2
Fault location
Figure 2
...
--
2
...
13)
...
r
7
...
13 Setting of IDMT OC relays
...
The purpose of relay RA is to provide primary protection to line 33 and back-up
to line BC
...
(a) Deciding the CT ratios and plug settings:
(i) At relay B, the maximum load current, assuming 25% overload is:
80 A + (0
...
The plug
setting PS can be done at loo%, i
...
PS = 1
...
(ii) At relay A the maximum load current, assuming 25% overload is:
1)
Assuming 1 A relay to be used, the CT ratio can be selected to be 300 : 1
...
e
...
0 A
...
Thus the TMS of RB can be selected as 0
...
(ii) Now, to maintain selectivity between RA and 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
...
0 A,
PSM =
---- =
PS
30
1
= 30
The TMS of RB has already been set at 0
...
Substituting these values, we get
=
Let TCB,B 0
...
Then,
TR,B + TCB,B 0
...
7 s is the desired operating time of RA
...
7 s, i
...
TOS
...
07 8
...
2
a B
+ 0
...
07
= 0
...
77
=
0
...
" 1
-
We have, for RA, for the above condition, PSM = I,,,,lPS
= (3000/300)/1 = 10
Hence
...
O2 - 1)
= 0
...
77
0
...
We can verify that the selectivity for minimum fault at bus B is automatically
maintained
...
Relay B current corresponding
to this is 20001100 = 20 A
...
For relay Rg, TMS = 0
...
Thus, operating time of RB for minimum fault at bus B will be:
TR,B,min fault at B
0
...
1)
= T ~ =, 200
...
5 s
Expected operating time of RA for this fault should be greater than
0
...
5 + O
...
226 + 0
...
726
+ 0
...
7986 = 0
...
)
NOW,let us find out the actual operating time of RA for minimum fault at bus 3:
...
66 A
Since plug setting is 1 A, this translates into a PSM of 6
...
For relay RAT
TMS = 0
...
Thus the operating time of RA for minimum fault at bus B will be:
This value of 0
...
8 s, required for
maintaining selectivity between RA and RE
...
1
0 26
The sketch of fault clearing time as a function of fault location for IDMT relays is shown
in Figure 2
...
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
...
e
...
a
* 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
...
14 Variation of fault current against fault location for IDMT relays under
maximum fault condition
...
15 for a simple system consisting of two buses
...
In fact, a computer algorithm can be
developed to automate this task in case of a large system
...
m
Zs
Bus B
-
Bus C
IR B
r
E
Load /
Load ;
I
IL,B I
/LA
0
b
4
C,min, B
4 wx
...
1
...
15 Rules for setting IDMT OC relays,
time of R
,
42 Fundamentals of Power System Protection
2
...
1
Choice Beiween IDMT and DTOC Relays
It can be seen that IDMT relays offer significant improvement in fault clearing times over
DTOC relays
...
However, there are situations where IDMT relays do not offer
significant advantages over DTOC relays
...
Since the fault current as a function of fault location is proportional to
E
I f-Z"+z
"
-Lz
cs
E
-, it would remain more or less constant throughout the length of the
Zc
-
feeder, therefore, the inverseness of the IDMT characteristics cannot be exploited
...
Such feeders are also described
as electrically short in length, irrespective of their physical length
...
It is a practice to recommend DTOC relays when
A
2
P
2
...
16
...
Short line
Zs
E
z
s
-2
ZL
ZL
$
-z
=
L
I
I, - E
U
=
3
2 s + ZL
m
I
>
Fault location
Figure 2
...
2
...
The single-line diagram hides the complexity of the three-phase system
...
For providing complete
protection to a three-phase feeder, we can begin with three relays connected to three CTs
as shown in Figure 2
...
As can be seen from Table 2
...
The relays a t bus A will be coordinated with those a t bus B using the procedure
illustrated in Section 2
...
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
...
In such cases, it will not be possible to cater to such faults if we use the
a
Ovrr-cxrrenr Proreerio~~ Transmission L111rs 43
of
<----------- ,jne*-B ------------>
Phase a
m
CT ratio n : 1
Figure 2
...
Table 2
...
17
re
fa& relay of Figure 2
...
17
...
18, it will be blind to the load current
(which is balanced three-phase current) and see only the ground fault currents
...
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
...
18, it is not necessary to use all the three relays
for detection and protection against phase faults
...
In Figure 2
...
...
18 Two-phase fault relays and one ground fault relay for OC protection
i
of a three-phase feeder
...
2 shows the operation of relays for all the 1 shunt faults for OC schemes of
1
Figure 2
...
18, which shows that all the 11 shunt faults are catered for by
these schemes
...
i
t
2
...
!
2
...
19 shows a double-end-fed power system
...
Consider that we have only over-current relays a t our disposal
...
Note that OC relays operate on
the magnitude of fault current and cannot sense the direction of the fault
...
As per the desired zones, only CBs 4 and 5 should trip
...
i
i
j
t
?
$
--
...
T
...
~,
+
,
i
-'
Over-current Protecrion o f T~ans~?~ission
Lines
45
the fault will be seen by OC reiays at these !ocations
...
The desired relay response is shown in Tabie 2
...
Figure 2
...
Table 2
...
3, that whenever the fault power flows away from
the bus, it is desired that the OC relay should trip
...
2
...
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
...
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
...
This will result in both lines being tripped out for any fault
on any one of the lines
...
20
...
Since directional relay units cost more
and aiso need the provision of PTs, they should be used only when absolutely necessary
...
--------------------------2_-
E
:---_
...
-----------------3
--- -
...
20 Single-end-fed parallel feeder needs directional OC protect~on
...
21
...
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
...
I
Load
$
\
-
/
Load
Figure 2
...
A wattmeter develops
maximum positive torque when the current and voltage supplied to the current coil and
the pressure coil are in phase
...
The phasor diagram for a directional relay is depicted in Figure 2
...
!
From CT
...
Position of lCc for
maximum torque
,'
,
i
I
'
I
...
Operating torque = K ,
@pC @CC
cos ( 8 -
j
$
, ,
!
7)
= K2 \ipc ICc cos ( 9 - T)
I'
...
23 Phasor diagram for a directional relay based on induction principle
...
The current drawn by the pressure coil
IPC the voltage by a large angle BPc
lags
As the fault moves from the forward to the reverse direction, the current undergoes
a large change in its phase whereas the phase of the voltage does not change substantially
...
Now, in a relay based on induction principle, the two fluxes responsible for torque
production,
for
and $cc should be shifted in phase by 90°, them to produce maximum
torque
...
,
-1,
1
,i
,I
...
8
1
i
i
;
8
Ove,--cu~
...
Thls e v e s the direction of the current phasor for max~mum torque, the
maximum torque angle T, and the boundary between tripping and restraining regions on
the phasor d~agram
...
+
= 90'
Toperating $pC kc sin (8 + 90" a
Q
$pc @cC [(0 sin
T)
= Kl Spc $CCcos (8 -
Since $pc a VPc and @cC
Q
7)
+ 90°]
d
Ice
Toperating=
K2
VPCICC ( 0 cos
7)
From the phasor diagram, it can be easily seen that the maximum torque angle
given by
T = 90" - 6?pC
T
is
Since the pressure coil is highly inductive, the value of 6pC is of the order of 70" to 80"
...
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
...
9
...
There are various possibilities of energizing
these relays; hence the various alternatives need to be carefully considered
...
The relay must operate for forward faults
...
The relay must restrain during reverse faults
...
The relay must not operate during faults other than for which it has been
provided, i
...
the relay must not maloperate
...
e
...
Let us consider an a-b fault
...
However, the choice of voltage to be
applied to the pressure coil is not immediately apparent
...
24 and 2
...
From Figure 2
...
Further, the angle between V,b and I, during
50 F~~~~do~rrenrrils
of Power System Protection
fault i s s u b s t a n t i a l l y large
...
F r o m these figures, it c a n b e easily seen that b o t h these
voltages a r e n o t suitable, as t h e y d o n o t m e e t t h e r e q u i r e m e n t set o u t in S e c t i o n 2
...
3
...
24 E x p l o r i n g t h e possibility o f energizing the pressure coil o f phase a
directional relay w i t h voltage
VOb
...
sequence
la
vca, 1
...
f
UPF position
O I
f ,
Forward fault
vc
v,,
v,
(a) Phasor diagram during a-b fault
0
0
0
0
1a
...
,
Figure 2
...
Over-cr;r!-elir Protecrio~lof Tro~~sr~~lssio!l
Liner
51
Figure 2
...
Since the unity
power factor !UPF> position of I, leads Vbc by 90°, chis connection is known as the 90"
connection
...
f
MTA line Folward
Restrain
(a) Phasor
la
diagram during a-b fault
-
Vbc
0
,
0
0
k 0
Directional
relay
MTA = r
I ,f
Trip
Reverse fault
energization of phase a directional relay
with I, and V,, resulting in the 90" connection
(b) Correct
(c) Phasor relationships during UPF load, forward and
reverse fault for phase a directional relay
energized by I, and Vbc(the 90" connection)
...
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
...
Hence, the choice has been narrowed down to three
...
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
...
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
...
4
Type o f
connection
Summary of phase fault relay excitation
Phase faults
inuoluing phase, a
90"
30"
Current
10
I,
60"
I,
Phase faults
inuoluzng phase, b
Voltage
Vbc
Vm
Vm +
Vbe
Current
Ib
Ib
...
and residual voltage Vo
...
27
...
,
i
i
I
I
i
E, = V,
E, = V,
i
(a) Phasor dlagram for a-g fault
h
...
27 Directional ground fault relay energization
...
9
...
28 shows a three-phase feeder protected by directional relays supervised by OC
relays
...
28 Complete scheme for directional OC protection of a three-phase feeder
2
...
5
Directional Protection Under Non-fault Conditions (Reverse
Power Relay)
There are situations where directional relays have to be used under non-fault conditions
...
To distinguish between the two, let u s call these directional relays as power
directional relay
...
Directional relays for short circuit protection are so connected that they
develop maximum operating torque under fault conditions
...
54
F~~~z~l~~iize~~ruis J~sron
of Power
Prorccnon
Consider a power relay with an MTA of 30" Figure (2
...
In order to be used as a
power relay it can be fed with I, and Vc,
...
Forward
power
Power directional relay
No trip
Reverse
power
I
Trip
'8
-
Directional relay
MTA = 30"
Figure 2
...
2
...
The fault current that would result in case of a fault at a particular location
depends upon:
1
...
e
...
The source impedance as shown in Flgure 2
...
ZS+ Large
Zs + Small
T U
Fault
inversp +;-a
OC relay
x
L-G fault
1
L-L-G
L-L-G
T
ree-phase fault
Fault location
Figure 2
...
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
...
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
...
Another principle of relaying, known as distance measurement, offers a much more
accurate reach, which is independent of source conditions and type of fault
...
Review Questions
1
...
3
...
5
...
7
...
9
...
11
...
13
...
15
...
17
...
rotor (a) to produce some torque and (b) to produce maximum torque?
What are the situations where DTOC relays are preferred over IDMT relays?
What is the difference between plug setting and pick-up value of an OC relay?
What are the drawbacks of using DTOC relays for the protection of long feeders?
Why does the fault current vary between a minimum and a maximum at any
location?
The generator impedance does not affect the fault current to a great extent in the
low-voltage distribution system
...
Explain the overshoot time of a relay and its significance
...
Explain
...
56
F~lr~dan~enralsPorver Systern Prorecriorz
of
Problems
1
...
74) ohms
...
For the system shown below, design the complete OC protection using the IDMT
relays
...
Losd
Minimum fault current
Maximum fault current
115 A
1500 A
6000 A
80 A
1000 A
5000 A
100 A
780 A
3000 A
A
T
77
585 A
2000 A
390 A
1000 A
3
...
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
...
A
typical situation, where this is true, is in the case of a transformer, a generator or a
busbar
...
3
...
Careful attention needs to be paid to the 'dot markings' (also known as 'polarity marks')
on t h e s e ' c ~ s
...
Consider a set of three mutually coupled coils A, B, and C with terminals A1-A2,
B,-BZ and CI-CZas shown in Figure 3
...
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
...
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
...
Voltages will be induced in these coils
...
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
...
Thus, current
will flow out of terminal B2, making B2 instantaneously positive with respect to B1
...
1 Dot marking
...
2 Dot marks: induced currents and flux
...
Thus, dot marks can be put on
Al and B2 as shown in Figure
...
3 to signify that these two terminals will be similarly
phased
...
Thus, C1 will be similarly phased as Al
...
A little thought will convince the reader that we can instead put dot marks on
terminals
...
3
...
3 Dot marks: symbolic method of representation
...
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
...
1
Simple Differential Protection
Simple Differential ~rotection:
Behaviour During Load
Figure 3
...
The currents entering and leaving the equipment to be protected are stepped
down with the help of CTs on either side
...
CT
n :I
...
O
,,11
n
'L
L
0
a
Instantaneous OC relay
Spill current = 0
I
d
Plug setting = I,
,
...
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 C q the current must la
e
...
For the operating condition of normal load flow shown in Figure 3
...
There is no tendency for the current to spill into the over-current
relay
...
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
...
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
...
Hence, the OC relay will not trip the two CBs
...
332
...
Such faults are called external faults or through faults
...
5 shows that during external faults too, the current leaving the protected zone
is the same as that entering it
...
333
...
Figure 3
...
As can be seen
,
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
...
Thus, the scheme meets the basic
requirement of clearing internal faults
...
The minimum internal fault current that will cause the tripping, is given by
If,min(CT ratio) (Plug setting of the OC relay) = nIp,
=
3
...
4 Simple Differential Protection, Double-end-fed: Behaviour
...
How does the
differential scheme behave in case of a double-end-fed system?
A double-end-fed system is shown in Figure 3
...
The internal fault current, If, is now equal to (I, + I z )Again, we see that
the spill current is equal to (IC
,,,In)
...
interrial fault
...
3
...
This zone
encompasses everything between the two CTs as shown in Figure 3
...
Thus, we talk of
any fault between the two CTs as an 'internal fault'
...
Ideally, therefore, a differential scheme is
supposed to respond only t3 internal faults, and restrain from t r i
...
Zone of differential
Equipment uqder
External fault
I
1 External fault
Figure 3
...
This is discussed in the following sect~ons
3
...
in
practice, CTs are subject to ratio and phase angle errors
...
The errors, in general, increase as the primary current increases, as in the
case of external faults
...
9 shows the primary and the secondary current phasors
during an external fault
...
However, as shown in Figure 3
...
The difference between
z
these two currents, therefore, ends up as spill current, as shown in Figure 3
...
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
...
/P
= lr, eil
n:1
-
Equipment under
protection
,,
A
...
Spill current
\
?
External
fault
11, ext
...
9 Spill c u r r e n t
because of CT errors
'P
64
- F~lndarnentalsof P o w e ~Systenz Protectron
-
3
...
7
Through Fault Stability and Stability Ratio
As the 'through fault' current goes on increasing, various imperfections of the CTs get
magnified
...
Therefore, as the 'through fault'
current goes on increasing, as shown in Figure 3
...
This causes the relay to operate,
disconnecting the equipment under protection from rest of the system
...
In such instances, the
differential scheme is said to have lost stability
...
In Figure 3
...
I
...
10 Characteristics of simple differential relay
...
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
...
The stability ratio can be improved by improving
the match between the two CTs
...
5
...
11 shows the equivalent circuit of the CT as referred to the secondary side
...
I,
(C)
Figure 3
...
I
RLri and LLri arc the resistance and the leakage inductance of the prlmary windir,g as
referred to
...
R,,,,, and Lmug
form the shunt magnetizing branch
...
R,,, and I,,,, are the resistance and leakage
inductance of the secondary winding
...
Also shown in
Figure 3
...
Out of the current Ipln transformed by the ideal CT, the magnetizing branch draws
the magnetization current I,
...
During normal operating conditions, when V,, is
small, the current I, can be safely neglected
...
Thus, we can no longer
ignore I,
...
12 shows the simple differential scheme in which CT equivalent circuit has been
explicitly included
...
12 are those that result
-1
during an external fault condition
...
Since the magnetizing currents of the two CTs will
generally vary widely, there is a substantial spill current during 'through fault'
conditions
...
Thus, the simple differential scheme, which looks attractively simple, cannot be
used in practice without further modifications
...
The CTs on the two sides of
the transformer have to work at different primary system voltage
...
Their designs are therefore different, making it impossible
...
This explains why the spill current
goes on increasing as the 'through fault' current increases
...
However, busbars are subjected to very heavy 'through
fault' currents, which tend to magnify the differences between the characteristics of the
two CTs
...
Both these aspects have been dealt with in detail in subsequent chapters
...
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
...
13
...
The restraining coil is connected in the
circulating current path, thus receiving the 'through fault' current
...
Let us work out the torque
equation for this relay
...
,
flux,
[
Torque produced by the restraining coil = M N ,
where M is a constant of proportionality
...
13 Percentage differential relay
Total restraining torque = M
+ Tspring
Similarly,
Operating torque = M [ N , ( I l - 1211"
The relay trips if the operating torque is greater than the restraining torque
...
e
...
However, if we take into account the effect of control spring, the above equation can
be written as
Il - I2
=
K
where KO accounts for the effect of spring
...
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
...
The operating characteristics of the percentage differential relay are
shown in Figure 3
...
:
...
External fault
characteristic
I
Minlrnurn Internal
-? , fault current, IF ,,,,,,
+
I
I
I
!
I
I
I
Figure 3
...
-
(";")
,
!
Maximum through fault current, I,,,,,
...
Thus, the spill current must be greater than a definite percentage of the 'through
fault' current for the relay to operate
...
The
slope of the relay is customarily expqessed as a percentage
...
4 is
expressed as 40% slope
...
The relay
automatically adapts its pick-up value to the 'through fault' current
...
I t can be seen from
Figure 3
...
The
restraining winding is also known as the biasing winding because we bias the relay
towards restraint
...
The characteristic of the percentage differential relay, superimposed on the 'through
fault' characteristic, and the internal fault characteristic are shown in Figure 3
...
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
...
e
...
The
circulating current which is [ ( I 1 12)121 will be equal to (1,121
...
+
Spill current I l
-
I2 = I I
11 + I,
Circulating current T
5
'
- 11
-A
- I
Thus, during internal faults the spill current will be two times the circul'ating current,
giving a slope of 2, which is expressed as 200%
...
14
...
,
...
,
...
3
...
1
Block Diagram of Percentage Differential Relay
Figure 3
...
The relay has
two settings
...
The slope is adjusted by
changing the tapping on the restraining coil
...
The m~nimumpick-up is adjusted by
changing the tension of the restraining spring
...
~
$Adjust rnlntrnurn plck-up
Restra~n~ng
cod
N
...
12
0
Adjust slope
1
2
3
+ 20% slope
30% slope
+ 40% slope
;
-
Figure 3
...
I
1
3
...
This
causes a leakage of current to earth from the chassis as the chassis is always connected
t o earth
...
This poses danger to the personnel who come in contact with the chassis
...
In case the chassis of the equipment is not earthed, the relay will not trip because of
leakage
...
The person will, of course, receive an electric
shock before the circuit is tripped out
...
7
...
16 shows the earth leakage relay for a single-phase load
...
16 Earth leakage protect~onfor single-phase load
t
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
...
16
...
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)
...
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
...
16
...
The mmf acting on the toroid is now equal to [N(Iyh I,)]
or equal to [N(Il,,)]
...
The OC relay connected to the pick-up coil, therefore, gets energized,
and trips the circuit
...
7
...
17 shows earth leakage protection for a three-phase load
...
Three-phase load
la
+
lb
+
k '/leak
Iron core
Figure 3
...
During the normal balanced operating condition, the phasor sum of the three-phase
currents is zero
...
However, during the earth leakage situation s h w n in Figure 3
...
This causes a flux to be produced
...
•
Review Questions
1
...
5 volt battery and a centre-zero voltmeter?
2
...
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
...
What are the drawbacks of the simple differential scheme?
5
...
As the burden on a CT secondary goes on increasing, what happens to the
magnitude and waveform of current delivered to the burden?
7
...
8
...
9
...
Show that the slope of the simple differential relay characteristics is zero
...
Prove that the slope of the internal fault characteristics for a double-end-fed
system is greater than 200%
...
Higher slopes are required in cases where there is a lot of mismatch between the
CTs at various terminals
...
13
...
What problems, if any, do you anticipate in applying conventional differential
protection to a transmission line?
Problems
1
...
01 ohm
...
2
...
The
CT errors for a 'through fault' current of 1000 A are as follows:
Ratio error
Phase angle error
...
4
...
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
...
A transformer will be provided with as much protection as is
commensurate with its voltage and power rating and the importance of its application
...
transformer
...
This may consist of
percentage differential protection (with harmonic restraint), a protection against
incipient faults and a protection against over-fluxing as primary protection
...
Since the terminals of a transformer are physically close together, it is an ideal
candidate for application of the principle of differential protection
...
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
...
These phase shifts have to
be carefully considered while applying differential protection
...
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
...
Thus, ratios of
transformation of the CTs on the primary and secondary side of the transformer, will in
general, be different
...
Figure 4
...
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
76
Furldarnerltuls of Power Svstern Ptotectiorl
as shown in the phasor diagram in Figure 4
...
Each line current on the delta side is the
phasor sum of two of the phase currents
...
Figure 4
...
(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
...
2
'
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
...
4
...
3(a) shows the schematic representation of a single-phase transformer
...
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
...
As shown in
Figure 4
...
e
...
08 p
...
1 then the short-circuit current
for a fault on the secondary terminals will be (1
...
08) = 12
...
u
...
08 p
...
Fault on secondary
terminals
Figure 4
...
78
Fiirrda~~~rrirals Power Svstenl Protection
of
I
4
...
The most common being the winding to
core faults because of weakening of insulation
...
However, such faults may take place outside the transformer, on the transformer
terminals, which fall within the transformer protection zone
...
The interested reader may refer to Power System
Protection (Vol
...
Figure 4
...
=~Pr
lc
A-Y
Transformer
RE
Ic
...
- - - - - - - A
1
...
8 -
8
0
...
4
100%
-
20
40
60
80
100%
Distance x o fault from neutral
f
Variation of fault current with location for the A-Y transformer
...
4 for a resistance-earthed star-connected winding, a windingto-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 current flowing through the
transformer terminals is, therefore, for all practical purposes, proportional to the square
of the percentage of the short-circuited winding
...
As shown in Figure 4
...
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 value of the fault
current depends upon the system earthing arrangements, and the curves of Figure 4
...
Y-A
L
w
-
m
Transformer
...
5 Variation of fault current with location for the Y-A transformer
...
u
...
--
err*r
---,
...
--- -
...
All large transformers are of the oil-immersed type
...
In such cases, an alarm must be raised and the transformer may
eventually have to be shut down
...
This is neither an abnormal
condition nor a fault as far as the transformer is concerned
...
A transformer may develop inter-turn faults giving rise to hot-spots within the
winding
...
Hence, inter-turn faults are difficult to detect by 'electrical means
...
Transformers may suffer from over-fluxing (also called over-excitation) due to underfrequency operation a t rated voltage
...
Since large transformers
usually operate at their design limits, over-fluxing can be dangerous and needs immediate
protection
...
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
...
Two numbers of phase-fault
over-current relays
P
One number o grou"d-fault
f
over-current relay
Figure 4
...
The pick-up value of the phase-fault over-current units is set such that they do not
pick up on maxir
...
The pick-up of the earth fault relay, on the other hand, is
independent of the ioading of the transformer
...
The neutral current is essentially because of load unbalance
...
I in general, which arise due to distortions introduced by
electronic loads, also end up as zero sequence currents and flow through the neutral
...
6
4
...
1
@
Percentage Differential Protection of Transformers
Development of Connections
Figure 4
...
Assume a turns ratio of 1: 1
...
Delta-star transformer
neutral grounded
with
B
E
9
!
t
f
?
Figure 4
...
*l
...
Determine the instantaneous directions of currents I,, Ib and I, through the
secondary windings (see Figure 4
...
2
...
Note that
because of the turns ratio of 1: 1, IA = I,, IB = Ib, IC = Ic (see Figure 4
...
82
Fundamentals of Power Sysrenr Prorecnon
-
-
I
3
...
These are same as phase currents
I,, Ib and I,
...
Line currents on the delta side are then determined
...
8
...
are all phasor differences
...
8 Determination of the line currents on the two sides of the transformer
...
Therefore, if we connect the secondary windings of the CTs on both the sides in
star, then the currents would not match up and a spill current would result
...
This
is shown in Figure 4
...
4
...
2
i
i
i
I
Phase c-to-Ground (c-g) External Fault
I
Consider phase c-to-ground (c-g) external fault as shown in Figure 4
...
I t can be seen that due to fault on phase c, there is an over-current in phase c
...
Similarly, due to the delta
connections of CT secondary windings on the star side, two of the pilot wires carry the
fault current, with the result that the current circulates in two of the percentage
i
\
...
i
,
r! '
i
; Zero
!
i
I
,
?
...
...
I
...
9 Final connections of percentage differential relay under normal load flow or
external balanced fault
...
Thus, the scheme remains
stable on c-g external fault
...
10 Phase c-to-ground (c-g) external fault
...
A c-g internal fault is shown in Figure 4
...
The currents on the delta side are exactly
the same as those in the case of c-g external fault
...
Transjorn~er
Prorecrion
35
there is no fault current through the primaries of the CTs on the scar side
...
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
...
_ _ _ _ _ _ _ _ _ _ ---
...
11 Phase c-to-ground (c-g) internal fault
...
Figure 4
...
Switch-on
Flux
AC supply
V, sin (at +
Figure 4
...
Let the flux in the transformer be written as
@ = @m sin o
t
?'he induced voltage can then be written as
= N@mo
cos ot
= N@mo
sin (ot
+ 90")
(4
...
Thus, the flux in a
transformer lags the applied voltage by 90" in the steady state as shown in Figure 4
...
I
Therefor
...
13
...
14
...
This is the steady-state picture
...
14
Inmsh phenomenon
...
14
...
Thus, the initial value of flux is zero but subsequently the flux must have the same rate
of change and same waveform as it has in the steady-state
...
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
...
This current is known as inrush current
...
The inrush phenomenon can be explained mathematically as follows:
Let the voltage be represented as
v = Vm sin ( w t
+
8)
(4
...
i,I ,
,
,
a
...
Let @ b ethe instantaneous value of the flux
...
The value of K can be found out from the initial condition, i
...
when t = 0,
@ = @R = residual flux
...
(4
...
5)
which gives K as
'
V
m
K = 9, + (x;-)cos8
-
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
...
Instant of switching
e
3
...
e
...
!
OJ t
8
!
;
...
To satisfy a flux demand of 34,, the transformer primary draws a very
large magnetizing current with a peaky non-sinusoidal waveform
...
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
...
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
...
3, a short circuit at the terminals of a transformer causes similar
magnitudes of currents to flow
...
I
4
...
1
i
$
j
i
[
1
1
I
/
'
b
i
i
t
j
Percentage Differential Relay with Harmonic Restraint
We have seen that the percentage differential scheme tends to maloperate due to
magnetizing inrush
...
However, this is not desirable, since the probability
of insulation failure just after switching on is quite high, and a desensitized relay would
be blind to faults taking place at that crucial time
...
The inrush waveform is rich in
harmonics whereas the internal fault current consists of only of the fundamental
...
This additional restraint comes into picture only during the inrush condition and
is ineffective during faults
...
1 gives the harmonic content of a typical inrush
waveform
...
~tinl,r
qf Pob~!er
Sj'stettr Protecrio~l
Table 4
...
I
56
5%
J
Figure 4
...
The fundamental component of spill current is segregated with the help of a filter and is @
...
The non-fundamental component of the spill current
aids the unfiltered circulating current in developing the restraining torque
...
...
\,
I
CT secondaw
currents I,, 1;
Filter
Unfiltered
(
All harmon~w
I I
/
Fundamental +
all harmonics
i
> '
Operating
torque
-Relay
Figure 4
...
...
A harmonic restraint percentage aifferential relay which implements the conceptual
scheme shown in Figure 4
...
16
...
-
------'
:
Transf~7rmer
Prorecrron
-
Transformer
Fundamental + Harmonics
circulating current
harmonics
spill current
All
1 :
91
CT
...
16 Percentage biased differential relay with harmonic restraint
...
8
High Resistance Ground Faults in Transformers
A percentage differential relay has a certain minimum value of pick-up for internal faults
...
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
...
Hence, such ~rotection known
is
as restricted earth fault protection
...
8
...
17 shows the earth fault protection for the delta side of a delta-star transformer
...
92
Frrndu~ner~tals Power Sysrern Protection
of
Transformer
I
\
OC relay
Reach of restricted
earth fault protection
Figure 4
...
Since this is a current balance scheme, it is independent of the load current and hence
can be made as sensitive as desired
...
8-2 High Resistance Ground Faults on the Star Side
Figure 4
...
Ground faults beyond the star side CTs, anywhere in the system,
do cause current to flow on the secondary of the CTs
...
Thus, no spill current
flows and the scheme remains stable on external faults
...
18 Restricted earth fault protection for star side of delta-star transformer
...
,, ',
_ ,,
...
4
...
However, seen
from the transformer terminals, the reflected current can be quite small
...
19
...
19 Calculation of terminal current for an inter-turn fault
...
11 A
...
However, they
can cause severe hot spots resulting in deterioration of insulation
...
4
...
Buchholz relay provides protection against such
incipient faults
...
1 0
...
20 shows the position of the Buchholz relay with respect to the transformer tank
and the conservator
...
20 Plac
The conceptual diagram of the inner working of the Buchholz relay is shown in
Figure 4
...
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
...
There is a build-up of oil pressure causing oil
to rush into 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
...
...
21 Construction of the Buchholz relay
...
These
contacts stay open when the transformer tank is filled with oil
...
Loss
of oil will no doubt cause the transformer temperature to rise but does not warrant
immediate tripping
...
Transjornler Protection 95
4 1 0
...
The trapped gases in the conservator can give valuable clue to the type of damage that
takes place inside the transformer
...
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
...
2 lists this information
...
2 Analysis of trapped gases
Type of gas
Hz and C2Hz
Hz, CzHz and C%
HZ, CH4, C O z and CsHB
Diagnosis
Arcing in oil between constructional parts
Arcing with some deterioration of phenolic insulation,
e
...
fault in tap changer
Hot spot in core joints
Hot spot in a winding
4
...
1 1
...
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
...
By design, power transformers operate a t the knee of the saturation curve at
normal voltage
...
The transformer, therefore,
draws a n excessive magnetization current
...
This, considerably, increases the core losses giving rise to overheating of the
transformer
...
Such an operating condition cannot be allowed to continue for long and the
transformer should be tripped if there is a prolonged over-excitation
...
22 shows
a typical allowable over-excitation limit curve
...
96 Fundame~zmlsof Power Sysrern Prorecriorl
,Prohibited operating region
I
I
0
...
o
I-
I
0
...
10
Time (minutes)
100
1000
Figure 4
...
Therefore, to keep the working flux within the ~ e m i s s i b l e
design limits, the Vlf ratio
must not exceed the permissible limit
...
25 per unit (125%) at rated frequency will experience over-fluxing
whenever the per unit volts/hertz exceeds 1
...
e
...
Thus over-excigtion can be
detected by measuring the V/f ratio by a so-called volts/hertz relay
...
We refrain
from further discussion of these relays in this textbook
...
4
...
The type of protection that
will be provided for a transformer depends upon its kVA rating and its importance
...
Tables 4
...
4 summarize the transformer
protection scenario and application of various protection schemes
...
3
Internal and external faults affecting transformers
Internal faults
Phase faults
Ground faults
Inter-turn faults
Tap-changer failure
Leakage of oil from tank
-
External faults
System phase faults
System bound faults
Overloads
Over-fluxing
1
1
I
I
II
Tranz,forr?~er
?:
...
4
Fault
Phase faults
Ground faults
Inter-turn faults
Oil leaks
Overloads
Over-fluxing
97
--
Application of protective schemes
Proredion scheme
Priman,
Back-up
Percentage diiiorential relay
Over-current/distance
Percentage differential relay
Over-current/distance
Buchholz relay
Buchholz relay
OC relay with thermal image of protected unit
ratio
Over-fluxing relay which measures (Vlf)
4
...
What is t h e minimum recommended percentage bias?
Solution As shown in the worksheet of Table 4
...
817 A from the star side CTs while they are 3
...
Thus,
we need intermediate CTs to correct this mismatch as shown in Figure 4
...
Such CTs
are known as interposing CTs and are usually autotransformer types
...
731 : 1
...
5 Worksheet for % differential relay calculations
11 kV star side
Step
66 kV delta stde
1 Full-load line
CUTnn+
r-
...
25) as
primary current
2361
...
25 A
= 2952
...
64 x 1
...
05 A
3
CT ratios
(5 A relay)
Choosing a CT of 3000 : 5
i
...
CT ratio = 600
Choosing a CT of 500 : 5
i
...
CT ratio = 100
4
CT secondary
currents
CT secondary current
CT secondary current
5
Pilot wire currents
(CT secondaries are in A)
Current in the pilot wires
=
x 3
...
817 A
(CT secondaries are in Y)
Current in the pilot wires
Current after the
interposing CT
Current in the pilot wires
= 3
...
936 A
98
Fundolne~mlsof Power Sysrrm Protection
Figure 4
...
Assuming a slope of 40%, spill current required for tripping is
Actual spill current = 3
...
936 = 0
...
Therefore, the scheme remains stable on
full load or external fault
...
~
-
...
-
...
differential protection?
2
...
Explain
...
The CT ratios of CTs on t h ~
two sides of a transformer will, in general, be
different
...
4
...
For a three-phase delta-star transformer, show that a line-to-ground fault
(external a s well as internal) on the star side appears like a line-to-line fault from
the delta side
...
Investigate the differential units which operate on a-g external and internal
faults
...
Repeat the above for line-to-line external and internal faults
...
Explain the phenomenon of inrush
...
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
...
(c) Voltage wave passing through zero from positive side, residual flux equal to
zero
...
10
...
Explain the principle of percentage biased differential relay with harmonic
restraint
...
Why does the percentage differential reIay fail to detect 'high resistance winding'
...
What type of protection is used for the fault condition in Question 12?
14
...
100 F ~ r ~ ~ d a ~ n e of l t a l s Sysre~nPmtectiort
~ Power
15
...
16
...
Why is over-fluxing harmful for the transformer?
18
...
Consider a single-phase 11 kVI11 k y 1
...
CTs with 5 A secondaries are used
...
5 A
...
01 A, find the minimum percentage bias setting so that the scheme remains
stable on maximum external fault current
...
9
...
Design the differential protection for a three-phase, 50 Hz transformer with the
following nameplate ratings: MVA 250, 15
...
...
5
...
Busbars are the nerve-centres of the power system where various circuits are connected
together
...
Figure 5
...
The protective zone,
to be generated by the protective relays, is also shown
...
e
Figure 5
...
101
102 F~~rzdarnentols Power Sysrenl Pmtecrion
o
f
...
A fault
the busbar, though rare, causes enormous damage
...
Busbars are located in switchyards, substations, and supply kiosks
...
The substations are well protected in all
respects and fault probability is indeed very low
...
T h e causes of faults experienced on busbars are: weakening of insulation because of
ageing, corrosion beccause of salty water, breakdown of insulation because of overvoltages, foreign objects, and so on
...
Because of the low probability of busbar faults, for many years, it was considered
unnecessary to provide explicit protection to busbars
...
It should be noted that busbars fall in the overlap
between ~ r o t e c t i v ezones on either side, so they do get back-up protection
...
However, as the system voltage went on increasing and short-circuit capacities went
on building up, it was no
...
W h a t form of protection is best suited for busbars? A little reflection will convince
the r e a d e r that differential protection will suit this situation best because the
ends (terminals) of the system are physically near to each other
...
Any discrepancy between the two will immediately signaf an internal
fault
...
2, we have explained the protection of busbars by t h e differential
Protection scheme
...
2
I
5-2
...
2 shows a busbar, having two incoming feeders and one outgoing feeder,
being protected by a simple differential protection scheme
...
Let us decide the CT ratios on the basis of maximum primary
load c u r r e n t seen by each CT
...
The CT on the outgoing feeder will
have a CT ratio of 300011 A
...
Thus, the
m e t h o d of selecting CT ratio on the basis of maximum primary current seen by the
feeder is not correct
...
'"1
Plug setting 4 R OC relay
QA
=
...
B
,
CBB, CBc
m
NO = Normally open
r m
OC
relav o u t ~ u t
Trip battery
Figure 5
...
5
...
2
Selection of CT Ratios in Case of Busbar Protection: Correct
Method
I
i
!
i
Figure 5
...
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
...
A
1 i
-
1A
Figure 5
...
'Ii
,cl:
...
21:
~ : l
...
s :
...
,
...
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
...
...
i
...
3
=
Maximum out of all the feeder currents
1 A or 5 A
External and Internal Fault
In the preceding discussion, we have assumed that the CTs are 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
non-ideal behaviour of the CT has very serious implications for
in a n ideal fashion
...
Figure 5
...
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
...
In all likelihood, CTc will therefore become saturated
...
For the sake of
illustration, we have assumed that the secondary current of CTc is only 4 A instead of
10 A
...
4 that this results into a spill current of 6 A, causing
the scheme to maloperate, i
...
lose stability on external fault
...
1;
CT, and C
...
...
?
I
External fault
1iiiii
...
4 Behaviour of busbar differential scheme on external fault
...
This clearly indicates the occurrence of an imbalance in transformed secondary
currents, resulting in substantial spill current
...
Operation of a differential scheme under external faults is, therefore,
clearly a case of maloperation
...
...
This is depicted in Figure 5
...
Since CTA and CTB are not carrying excessive primary currents, they
transform the current without too much error
...
N source
o
10A
Zero
Figure 5
...
The maloperation of the busbar differential scheme on external faults is caused due
to non-ideal behaviour of a CT carrying excessive primary current
...
5
...
6 shows the equivalent circuit of a current transformer referred to the secondary
side
...
R, and X, are the resistance and leakage reactance of the
secondary winding, respectively
...
At low values of primary current Ipr and therefore I,, voltage E, to be induced by the
secondary winding, which is approximately equal to (Zburden is quite low
...
44 fN) is also very low
...
Thus, the secondary current I, is
substantially equal to I,/N
...
This causes the secondary induced voltage to increase as well
...
AS the
flux increases, the transformer needs to draw a higher magnetizing current
...
...
This is illustrated in
Figure 5
...
It may also be noted that I, is no longer sinusoidal and its waveform has a
prominent peak
...
7 Operation of the CT beyond the knee point of the B-H curve
...
When this occurs, we say that the CT is completely
saturated
...
They, in fact, consist only of sharp pulses
near the zero-crossings of the primary current
...
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
...
U
Figure 5
...
5
Circuit Model of Saturated CT
:
In the light of the preceding discussion, the saturated CT is modelled as shown in
Figure 5
...
IplN
Rb
>Ii:
Xb
RS
I, =
Xs
I
...
c
),
lo
= Ip/N
Burden
$
ru"
...
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
...
5
...
4
...
10 shows the equivalent circuit as seen from the CT secondaries
...
It can be seen from Figure 5
...
One path is through
the over-current relay and the other is through (R, RL) via the short representing the
+
saturated CT magnetizing branch
...
Hence, the OC
~~
-
relay needs to be restrained from tripping on external faults (with one GT completeiy
saturated)
...
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
...
I
CTc
Saturated CT
Rb
I
I
I
I
I
Rb
I Short circuit
I-----------_______----
...
10 Secondary equivalent circuit with one CT fully saturated during external fault,
I
:
i
1
)
k
i
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 procedure is as follows: First consider that the 0 C relay is not connected and find
out the voltage that will be developed across it, let it be V,,,
...
Note that
up to which the differential scheme remains stable
...
7 Minimum Internal Fault That Can Be Detected by the
High Impedance Busbar Differential Scheme
It will be worthwhile to investigate the minimum internal fault current If,,,ternal,prlmary
that can be detected by the high impedance busbar differential scheme
...
It is assumed that
none of the CTs is saturated
...
11 shows that during internal fault, all t h e CT secondaries feed into the spill
path
...
4
1,
, - - 1,
4
'c
--
CTc
IOC
-
...
P
o
CTB
Q
OC relay
p~ck-up
Figure 5
...
i
112 F~indamentalsof Power System Pmtecnon
Assuming I,,* = I,, = ZOC = I, (i
...
all the CT magnetizing currents to be equal) and
multiplying both sides by N, we get
N I p u = I f , lnt, mm, pri
- 3NIo
or
(with 3 feeders terminating on the bus)
I
+I
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
Zr,nt,m,,,pr,
=
5
...
i
If,external, maximum
%internal, minimum
The stability ratio is a dimensionless quantity
...
Stability ratios of a few tens are
common in EHV busbar differential schemes
...
9
Supervisory Relay
In the busbar differential scheme, it may, at times, happen that a particular CT secondary
gets o m circuited
...
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
...
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
...
1
...
in case of the CT which carries the maximum load current, lload,
Figure 5
...
There is a break in
the pilot wire coming from secondary of CTc
...
12
...
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
/A
F+W
Highest feeder
current
Zero
,(
R
t Pick-up
setting
S ~ Icurrent =
II
N
+
Over-voltage
relay
Supervisory relay
Zero
Is = IN
N
TCCBA
Differential
relay (NO)
Alarm
TCCBc
-
T
Supervisw
relay (NO)
Trip battery
...
12 Supervisory relay to prevent against maloperation due to loss of a CT
secondary current
...
The setting of the supervisory relay V,u~N,,,, will be much less than the setting of
the high impedance differential relay V,,,
...
1 0
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
...
13 shows a three-phase busbar with two
incoming and three outgoing lines
...
-
"-
-~
...
...
~
~
...
5
...
The system is
soiidly earthed and the switchgear capacity is 3500 LMVAat 132 kV The parameters are:
Maximum full-load current in one line
R, = CT secondary resistance
R
= 500 A
= 0
...
0 R
~ wire d
~
Relay load (1 A relay is used)
= 1
...
28 mAiV (assumed linear)
CT saturation voltage
V,
k,
> 120 V
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
...
(c) the minimum internal fault current which will be detected by the scheme
...
2
...
Calculate the setting
of the supervisory relay?
Solution
l(a)
...
Therefore, as explained in the text:
CT ratio for all CTs = Maximum of all the feeder currents : 1
= 500 : 1
I
l(b)
...
51 A
...
Therefore, wi?
need to fine tune the setting to:
l(c)
...
0 A) is given
by
If,int,min,pri
- NUpu + do)
N = 500, Ipu 1
...
28 mA per volt, therefore, for a voltage of 82
...
28 mA/V)(82
...
02313 A
,
Thus,
If,int,rnin,pri
= 500
11 + (6)(0
...
39 A
l(d)
...
861 A
ROCrelay = 1
*
Rstabllizing = 94
...
Setting of supervisory relay
Neglecting magnetizing currents of the CTs, we get
vsupervisory
=
'load,
lost, CT
N
(Rstabilising
+ Roc
4
...
Describe the unique features of a busbar, from the point of view of application of
its protection
...
Maloperation of busbar protection causes large disturbances to the system
...
3
...
Explain
...
Discuss the behaviour of a CT in deep saturation
...
!
C
6
...
I
I
Ii
i
I
I
i
b
!
I
II
i
8
...
10
...
How is the value of stabilizing resistance and its wattage decided?
In the case of high impedance busbar differential scheme, how will you find out
the minimum internal fault current for which the scheme will operate?
Define stability ratio and discuss its significance
...
What will be the consequences as far as the busbar differential relay is
concerned?
Suggest an add-on to the differential relay, to avert a possible maloperation in the
above scenario
...
Sketch the high impedance busbar differential protection for a three-phase busbar
having three incoming and two outgoing feeders
...
1
~jstance~rotectionof
Tvawnission Lines
Drawbacks of Over-current Protection
Over-current protection is very appealing and attractive because of its inherent simplicity
...
However, it has
some major drawbacks which causes it to maloperate
...
The only consideration in LV systems is the
continuity of supply to the consumers
...
This is because EHV lines are part of an interconnected 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
...
2
...
1 Effect of type of fault on reach of over-current relay
...
(
I
I
!
i
!
i
It can be seen from Figure 6
...
Thus, the relay may underreach or over-reach depending upon the type of fault
...
Figure 6
...
This,
again, is not a desirable feature
...
...
i
I
t
1
i
t
!
I
Thus, we see that the fault current is a function of fault type as well as the source
impedance, both of which are variable
...
Search for such a
relaying principle has led to distance relays, whose reach is not dependent on the actual
magnitude of the fault current but on the ratio of voltage at relay location and the fault
current
...
2
...
2
i
Consider a transmission line AB as shown in Figure 6
...
Let us assume that there is
source only a t end A
...
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: 1 for the sake
of simplicity
...
The line is
modelled as a series R-L circuit for the purpose of relaying without much loss of accuracy,
as shown in Figure 6
...
A
Reach point fault
Reach = Z, ) ,,
Internal fault
1 External fault
...
I
...
3 Introduction to distance relaying
...
Now, let us compare the relay voltage VR with the product of relay current
IRand Z as shown in Table 6
...
,
f
Table 6 1 Introduction to distance relays
...
1 that the trip law that emerges is;
i
I
1
i
1
I
;
Distarlce Protection of T r a ~ ~ s ~ n i s sLines
ion
131
This can be written as:
1
else restrain
1 I
However, the ratio (VR/ I IR 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
...
Hence the name distance relay
...
In practice,
however, the word under is dropped and the relay is simply called impedance relay
...
To distinguish this relay
from the other distance relays, we will call it simple impedance relay
...
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
...
This is indeed one of
those engineering solutions, which is very ingenious
...
4
...
The R
(resistance) axis represents the real part of the (V/n ratio whereas the X (reactance) axis
Relay current
...
4 Characteristic of simple impedance relay on V-I plane
...
This is shown in
Figure 6
...
(Metallic faults are those faults which do not involve appreciable fault
resistance
...
Thus, a fault anywhere on the transmission line can be
122 F~rndarne~~talsPower System Pmtecrion
of
mapped on to this straight 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 discussed
in greater detail in subsequent sections
...
5 Characteristics of simple impedance relay on R-X plane with fault characteristic
of the line superimposed
...
The arc is resistive in nature
...
the wind veiocity u in mph
and time t in seconds and the current I in amperes, as already pointed out in Chapter 1
...
6
...
6 Fault characteristic of transmission line with fault resistance
...
3
6
...
1
Simple Impedance Relay
Trip Law for Simple Impedance Relay Using Universal
Torque Equation
It is possible to synthesize many types of relays using the electromechanical structures
...
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
...
-
124 Fundamentals of Power System Protection
Consider the generic torque equation
T
s
k1llRl2 + k21VR2 k31VRl[ I E COS ( 8 - d
+
+4
1
where
T is the net torque on the actuating structure of the relay
klJIR12 the torque due to current fed to the relay current coil
is
k2(VR(Zthe torque due to voltage applied to the relay pressure coil
is
kS I VR(IRJ cos (0 - Z) is the torque due to the directional unit
I
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
'
...
Therefore, the relay will tri
if
which can be written as
k2IVRl2 < k l l I ~ \ Z
Further manipulation leads to
Now,
JZ,,,J is the magnitude of the impedance seen by the relay
...
be
where
Thus, we can write
If Z
1
<
Z
then trip; else restrain
This is the trip law for the so-called simple tmpedance relay
...
6-3
...
7
...
The
voltage coil, on the other hand, tends to keep the trip contacts open, thus providing the
restraining torque
...
Q
simple
impedance
relay
I
R
aa
Trip output
Restraining
torque
*
0 - 1
Restraining
quantity
I
VR
Soft iron
armature
2
Spring
Voltage
coil
*
Operating
torque
r-+--o
coil
quantity
Figure 6
...
The operating torque is proportional to
tional to VR1 '
...
Thus, the balanced beam structure implements the simple impedance relay
...
Performance of Simple Impedance Relay During Normal
Load Flow
A distance relay is fed with current and voltage a t the relay location
...
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
...
8 for the double-end-fed system
...
Thus, the simple impedance relay is stable during normal operating
conditions
...
8 Performance of simple impedance relay during normal load flow
...
3
...
9
...
Therefore, the simple impedance relay under-reaches because of an arcing fault
...
With reference to Figure 6
...
;
4
d
5
,
E
3
...
A
...
C
,
A
I
Slrnpie impedance
relay
Arc~ngfault
X
I
Line fault characteristic
BC
Percentage under-reach = - x 100%
A6
Figure 6
...
3
...
@
-
t
i
The reach of the simple impedance relay is independent of the phase angle between
voltage and current a t the relay location
...
Its reach would extend equally in the forward as well as the reverse direction
...
10,the first quadrant of the R-Xplane represents the forward faults
whereas the third quadrant represents the reverse faults
...
We can, however,
supervise it with the help of a directional element and get the desired selectivity
...
3
...
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
...
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
...
u
IV
Reverse faults (Third quadrant)
r
~
:3:
...
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
...
This is shown in Figure 6
...
Thus, at some point during the power swing, the apparent impedance enters the trip
region of the relay operating characteristic
...
This causes the relay to trip, putting the line out of service, adding to the
disturbance already present in the system
...
Disrance Protecrion of Tror!smission Lines 129
C = Electrical centre
Figure 6
...
It may be mentioned here that the larger the area occupied by the relay on the R
...
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
...
4
Reactance Relay
6
...
1
Trip Law for Reactance Relay Using Universal Torque
Equation
Again consider the universal torque equation:
If we set k2 equal to zero, make k l positive (i
...
cause the current to provide tripping
torque) and make k3 negative (i
...
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(R 1 cos (8 I
7)
then trip; else restrain
which can be written as:
k31vRl 1 1 ~ 1 cos ( 8 -
7) <
k111~12
1
of Power Sysren~Prorecriorr
130 Frrrida~~re~~tals
--
and can be simplified as:
I
I
However, 1 VR//(IR= Z,,I, the apparent impedance seen by the relay
...
...
Hence, such a relay is called a
reactance relay
...
The entire area below this straight line
represents the trip region
...
This is shown in
Figure 6
...
~~
41
:
i
r;
:
...
"
4
1
I
1
-4
characteristic
Restrain
/,,/,
/////////,///////
X"
<
t R
1
Trip
Trip
Figure 6
...
...
~
Distante Prorecrio~~ Tra~rsrn~ssion
07
Lbres
121
6 4 2 lmplernenta?ionof Reactance Relay Using the induction Cup
...
13
...
13 Implementation of reactance relay using the four-pole induction cup structure
...
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
...
The four-pole induction cup structure has a high torque to weight ratio and is,
therefore, a very sensitive measuring unit
...
4
...
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
1
Performance of Reactance Relay During Normal Load Flow
132 Fundarnenrals of Power Sysrem Prorecrion
characteristic as shown in Figure 6
...
Thus, a reactance relay will operate during normal
...
This is clearly unacceptable
...
A question may arise in the readers' mind at this stage
...
This is discussed in
Section 6
...
4
...
14 Reactance relay operates during normal load flow
...
4
...
15 shows a line section A-B being protected using a reactance relay
...
It can be seen that the tip of the impedance seen phasor AC, still remains within
the trip region
...
This is only to be expected, as the relay measures only the
reactive part of the ratio of phasors V and I
...
Line fault characteristic
Restrain
7 > 1 1 , , 1 1 ,
Setting = X,,
<
f
Reactance seen
A
Impedance seen
Trip
Trip
V
Figure 6 1 Effect of arc resistance on reach of reactance relay
...
5
i
4
Ii
1
I
1
i
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
...
6
...
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
...
16, in the forward direction also responds in the reverse direction for a n
unlimited distance
...
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
...
16
Trip
Trip
Directional property o f reactance relay
...
4
...
As shown in Figure 6
...
Even before this
happens, it is already in the trip region of the reactance relay characteristic
...
Again, this is not a desirable trait
...
17 Performance of reactance relay during power swing
...
i
6
...
5
...
e
...
e
...
The torque
equation can be manipulated as
~ Z ~ V< ~I~~ V R I
R
( IIRI
--
...
I
...
-I i
...
~
~~
...
Now, the trip law can be written as
1 If IZ,
J
i 1,
2
/
cos ( 8 - z) then trip; else restrain
1
where 9 is the phase angle between the voltage and current fed to the relay
...
18
...
18 Mho relay characteristic
...
5
...
19 shows a four-pole induction cup structure
...
The restraining torque is produced because of the
fluxes created by the operating and polarizing voltage coils
...
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
...
3
Performance of Mho Relay During Normal Load Flow
It can be seen from Figure 6
...
Thus, the
relay is stable during load conditions
...
C
...
19 Implementation of mho relay using the four-pole induction cup structure
...
'
...
20 Performance of mho relay on load
...
5
...
21
...
The impedance seen by the relay
considering the fault resistance just lies on the verge of the trip region
...
Thus, effectively, the reach of the relay has come
down from OA to OB
...
The percentage under-reach is
(ABIOA) x 100%
...
21 Effect of arc resistance on reach of mho relay
...
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
...
5
...
22 shows the characteristic of a directional relay on the R-X plane
...
The straight line can be considered as
a circle with infinite radius
...
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
...
Thus,
the mho relay very much possesses the directional property which makes it so useful
...
22 Characteristic of directional relay on the R-X plane
...
'; It
4
w
Figure 6
...
?I,'
I
,,d,
...
5
...
-
...
, ,:i
-
Performance of Mho Relav Durina Power Swina
...
To that extent, it is less
immune to power swing
...
24
...
Blocking and tripping schemes are discussed in Appendix B
...
j
!
1
1
1
-
*v
"
+
on = z,
AB
= Zs,
OD
C=
ZSA
Electrical centre
Restrain
I
Locus of power swing
Figure 6 -24 Performance of mho relay during power swing
...
6 Comparison Behveen Disfunee Relays
It is instructive to compare the three distance relays as shown in Table 6
...
Table 6
...
T
...
)
Reactance relay
Current
Current
Voltage
No
Directional element,
MTA = 90"
No
Yes
Restrains
Trips
Restrains
Under-reaches
Reach unaffected
Moderate
Vefy large
Under-reaches
more than S
...
R
...
r
Voltage
Maloperates, though
effect is less than S
...
R
We can see from Table 6
...
It has to be used in conjunction with
a directional or a mho element
...
One
remarkable property of reactance relay is its immunity to fault resistance
...
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
...
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
...
A three-phase
line is subject to phase faults as well as ground faults
...
How are we going to provide protection against all the ten shunt faults?
2
...
Can a single distance measurement unit look after all the phase faults as well a s
ground faults? If no, how many aistance measurement units will be required for
catering to all the ten shunt faults?
4
...
Whether to measure positive sequence impedance or negative sequence impedance
or zero sequence impedance? See Figure 6
...
140 Furldatrte,ztals of Power Svstertz Pmtrcrior~
I
H w to combine?
o
U
1
i
1
4
Hw many un~tsrequired?
o
SeNng = ?
,?
...
25 The problem of providing distance protection to a three-phase line
...
...
Phase faults associated with one pair of phases are catered to by a singledistancemeasuring unit
...
...
Thus, three numbers of ground fault-measuring units can cater for all the
three ground faults
...
Table 6
...
Thus, it would be prudent to measure
positive sequence impedance between the relay location and the fault so as to cater for
every fault
...
3 Presence of sequence components in various faults
p~
Fault
Positive sequence
L-G
L-L
L-L-G
L-L-L
Yes
Yes
Yes
Yes
-
Negative sequence
Yes
Yes
Yes
No
- sequence
Zero
Yes
No
Yes
No
...
7
...
26
...
A phase-to-phase fault can be represented by a parallel combination of the
positive and negative sequence networks at the fault point
...
26
...
I
'!
I
I
I
!
I
I
I
I
8
1:
...
VC
r
Positive sequence
network
1
1
Zero sequence
network
Negative
seauence network
...
26 Phase a sequence network connection for b-c phase fault
...
26, we get
Val - I a ~ z l+ Ia&l - Va2 = 0
,
,
Val
...
However, the sequence components of voltage and current are not readily available
at the relay location
...
Let us
see if we can manipulate the line voltages and currents to get the desired sequence
components
...
...
" ,,:',
,::
,!
Vb - Vc = (aZ- a)Val
...
z
= (a2 - a)(V,, - Va2)
Therefore,
...
z=
Similarly it can be proved that
v,2 - v c
a - a
...
i
...
...
1
1
...
1 - 1
...
case of phase b-to*
faults
...
a-to-b and phase c-to-&
...
The distance measuring units
which cater for phase a-b, b-c and c-a faults are called phase fault units
...
7
...
See Figure 6
...
Applying KVL around the loop formed by the series connection of the three sequence
networks, we get
V
...
Figure 6
...
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
or
+
(20- Zl)laO
144 Fundamentals of Power System Protecrion
However,
Lo
=
a
'
+
I3
b
+
Ic
...
3
Hence
...
In the above equation Z1 appears on both sides and the expression appears a bit mixed
up
...
For
three-phase transmission lines Z, is 2
...
The exact relationship depends
upon the geometry of the phase conductors and the placement of earth conductors
...
Then, the above equation simplifies to:
-
va
; where K =
~::
,
...
: i
z - Zl
o
Ia + KIres
32
1
4
Thus, the phase current has to be compensated with a fraction of the residual cu'rrent
:
- ?
:
I,,
...
I ,
...
i
[va, + KIres)l, [Vb, (Ia + KIr,)I,
(1,
and [V,, (I,
+ KIre,)]
will be needed for catering to all the three single line to ground faults
...
j
5
1
6
...
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-G faults)
...
The proof of this is left to the reader
...
28
...
rrii~rce
?ro:ecrion o Tin~ra~iir
...
28 Complete protection of a three-phase line
...
8
Reasons for Inaccuracy of Distance Relay Reach
Ideally we would have liked to set the reach of the distance relay to 100% of the line
section
...
There is
of
146 F~riidai?~entals Power System P~oteciion
always certain amount of uncertainty and ambiguity about the actual reach
...
Inaccuracy in CT and PT ratios
...
Variation of line parameters with atmospheric conditions
...
Transient response of capacitive voltage transformers (CVT)
...
Other
factors may cause error on either side
...
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
...
Thus, it is a usual practice to set the reach of distance protectio
about 80 to 90% of the line section
...
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
...
9
...
9
6
...
1
Three-stepped Distance Protection
First Step
As discussed in Section 6
...
The first step of distance protection is, therefore, set to reach up to 80 to 90% of
the length of the line section
...
e
...
6
...
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
...
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 a t the bus between
the two lines
...
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
...
29(d), then there is a loss of selectivity with second step of
Disla~~ce
Protecrrurr o f T , u r ~ s n ~ i s s l o ~ ~
Lines
117
shortest adjoining line
...
29(d) faults in the region becween points Dl and D2
are in the second step of prlmary protection a t bus B, provided by relay RB, as well as
in the second step of re!ay RA at bus A
...
Hence the second step of the distance relay is
set to reach up to 50% into the shortest adjoining line
...
9
...
It covers the line section under consideration, 100% of the next line section and
reaches further into the system
...
The three-stepped distance protection is shown in Figures 6
...
Note that in Figure 6
...
The operating time of this unit is instantaneous
...
Tl
I
'
4 J
f i
Operat~ngtime I
" M -
instantaneous I
I
I
I
B
I
!
C
I
:
I Adjoining line
(next line)
1
consideration
I
(0
...
~ ) Z A Zas
B
+
0
...
2Z~c
Figure 6
...
Figure 6
...
I
1"
...
-
$1
5
...
L - - -
...
Figure 6
...
...
IT1"IL
T
1
#I
I
I
...
I
B
y?
Dl
I i
Ic
,
,
D2
RB
Figure 6 9 9 ( d ) Loss of selectivity of second zone o f RA w i t h second zone of R ~
...
3 summarizes the philosophy of three-stepped distance protection
...
3 Philosophy of t h e three-stepped distance protection
Purpose
First
step
Primary
protection
Reach
Operating time
80 to 90%
of line section
Remarks
Instantaneous,
i
...
no intentional
time delay
3'instantaneoua
Second Primary
100% of line under
protection of consideration
step
+ 50% of shortest
remaining
20 to 10%
adjoining line
!5
3
...
Shortest adjoining line
is to be considered
...
Idea is to provide full
back-up to the adjoining
line, even in case of
maximum under-reach
...
If
shortest adjoining line is
considered then the longer
adjoining line will not get
back-up protection
...
1 0 Trip Contact Configuration for the Three-stepped
Distance Protection
The trip contact circuit which implements t h e three-stepped distance protection scheme
is shown in Figure 6
...
T h e fault detector initiates the timer in case i t detects a fault
I
==
Trip battery
z
1
7
-
CB
Trip cn~l T
,,
Timer
3
Fo = NO contact o fault detector, Z, = NO contact of step I measuring unit, Z2 = NO contact of Step II
f
measuring unit, T, = NO contact closed by timer after time T, after closure of Fo, Z3= NO contact of step Ill
...
30 Trip contact circuit of the three-stepped distance scheme
...
The timer issues two outputs after it gets energized
...
Both these outputs are
in the form of closure of a normally open (NO) contact
...
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, T l or Z3, T2
...
1 1 Three-stepped Protection of Three-phase Line
Against A ~ ITen Shunt Faults
We have already seen that three numbers of phase fault measuring units, which are fed
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
...
The setting of each measuring unit is based on the positive sequence impedance of the
line
...
This is a rather costly affair! Therefore, schemes, which save upon the number of
measuring units, have been devised
...
This brings down
the number of measuring units from 18 to 3 x 3 or 9
...
"
,
...
12
I
i
i
1
1
1
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 such a situation, what
is the impedance seen from the relay side, i
...
from the CT and P T secondary sides?
It can be seen from Figure 6
...
CTR
=
PT ratio, CTR = CT ratio
V
L
but - = Z, = actual line side impedance
'
1
Therefore,
...
8 I
Disrance Protection of
-
i
ransmisslon Lines
Reach = Z
,
...
31 Impedance seen from the relay side
...
1 3 Three-stepped Protection of Double-End-Fed Lines
Figure 6
...
There are sources at both the ends
...
Hence, circuit breakers and
three-stepped distance schemes will have to be provided at both the ends
...
z
2
4
I
I
+ 20%
I
,
'
I
I
I
I
I
D
t
I
I
v
4
+
Instantaneous
I
I\#
1
'
A
!
?
i
&
A
I
I ,,
...
r
1
t
t
,
,
T
2
I
C
Line under
cons~demtion
Z
l
z
2
Figure 6
...
:
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
...
The remainder 40% of the line length falls in the step I1 which
is a delayed one
...
We need to improve upon the
operating time for rest of the 40% of the line
...
The same fault
when seen from the far end because of the uncertainties involved could well be beyond
the bus
...
This principle is made use of in the carrier-aided distance schemes discussed in
Chapter 7
...
What are the drawbacks, if any, of over-current relays?
2
...
How is the transmission line modelled for the sake of distance relaying?
4
...
Explain
...
What do you mean by a metallic fault?
...
How is it different from an arcing fault?
+
7
...
=
8
...
Will an over-current relay be affected by power swing?
10
...
Prove that a-6 distance measuring unit fed with (V,- Vb) and (I, - Ib) responds
correctly to a-6-g faults as well as a-6-c faults
...
Why is residual current compensation required in case of ground fault distance
measuring unit?
13
...
14
...
The impedance seen from the relay side in a distance relay is 10 ohms
...
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
...
2
"
'
r
i
!
I
1+
4
aI
I
1
i
i
3
1
7
...
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
...
However, there is statistical evidence, as shown in Table 7
...
These faults are caused by breakdown of air
surrounding the insulator
...
Table 7
...
This is known as reclosure
...
The typical de-ionization times for various system voltages
are listed in Table 7
...
Table 7
...
10 s
132 k V
220 k V
400 k V
0
...
28 s
0
...
e
...
Thus, in case of a transient fault,
reclosure helps in keeping the downtime to a minimum and in increasing the availability
of supply
...
In low and medium voltage systems, a maximum of three consecutive reclosures are
allowed
...
e even when the third
reclosure fails, then the circuit breaker is locked out and no more reclosures are allowed
...
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
...
This is so because as soon as there is an interruption in the
:
system, the rotor angles of various generators start drifting apart and if they drift apart
', beyond a critical angle, the system loses stability
...
this critical time elapses, the system can pull together and remain stable
...
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
...
For
about 20% of line length, near each end of the line, i
...
a total of 40% of i n e length, the
protection is instantaneous from the local end but is delayed from the rekote end
...
1
...
Carrier-based schemes help us in achieving this objective
...
I
B
v
t
J
Tl
t
I
I
Tz
I
i
C
Line under
consideration
Figure 7
...
X
i
!!
Carrier-alded Protect~onof Transrn~ss~on
Lznes
155
7
...
The relay, only indirectly infers about the conditions at the remote end through these
signals
...
Hence,
there is always an ambiguity about the exact location of a remote fault
...
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
...
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
...
Various
attributes of an ideal carrier channel can be listed as follows:
...
Delay involved in the communication should be small compared to the time period
of the system frequency
...
Since only a small amount of information is to be passed, the carrier channel need
not have very high bandwidth for protection purposes
...
I
I
tI
I
1
I
i
Carrier channel should be under full control of the utility company
...
The carrier channel should be economical
...
3
...
3 Coupling and Trapping the Carrier into the Desired
Line Section
The power transmission line operates at very high voltage levels of the order of hundreds
of kilovolts
...
the carrier current transmitter and the
carrier current receiver, operate a t a much lower voltage
...
Figure 7
...
Line traps which confine the carrier signal to the desired line section
are also shown
...
F~inda~?le~~tols
of Power System Prorecrion
Table 7
...
Maintenance is a problem and
guarantee of quality of service may be difficult to obtain
...
The range of
communication is line of sight
...
Therefore, initial investment and maintenance cost are both very high
...
Frequency range is between 3 and 30 GHz
...
e
...
Large bandwidth is
available
...
The carrier
signal is a signal of much higher frequency, compared to power
frequency, which is coupled to the EHV line
...
Thus, the camer signal
frequency is just above the audible frequency range and just
below the medium wave radio broadcast band
...
However, protective relaying does not need a large
bandwidth
...
0 k m
O
sO
line will cause a delay of 0
...
...
The series circuit consisting of CS
and Ls, as shown in Figure 7
...
Since the
impedance of a series resonant L-C circuit is ideally zero, it provides very good coupling
a t the carrier frequency
...
Since the impedance of a parallel resonant circuit is ideally infinite a t the
resonant frequency, it develops maximum voltage a t carrier frequency, thus helping to
extract the maximum carrier signal
...
The carrier signal, however, needs to be confined to the desired
line section
...
The line
traps have t be so designed, however, that they do not offer any significant impedance
o
a t 50 Hz (power frequency)
...
This clear-cut demarcation helps in establishing a welldefined zone whose boundaries are crisply defined
...
Cs: Series ckt
...
tuned b carrier frequency
Tx: Carrier transmitter
Rx: Carrier receiver
CRR: Carrier receipt relay at A and B
...
7
...
1
Single Line-to-ground Coupling
In Figure 7
...
Is this type
of coupling, a wise choice?
Recall that, statistically, majority of faults are of the line-to-ground type
...
This is bound to cause severe attenuation of
the carrier signal, rendering it unusable a t the remote end
...
7
...
2
Line-to-line Coupling
Figure 7
...
The carrier signals propagate
through air between the line conductors, therefore, the attenuation is much less
...
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
A
Line trap
Cs
...
J
Coupling capacitor
Ls
Cp,Lp: Parallel
circuit tuned
-i
*
...
3 Line-to-line coupling
...
4 Unit Type Carrier-aided Directional Comparison
Relaying
This protection takes advantage of the f a d 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 information about the fault direction, as seen from each end, is conveyed
over the power-line carrier to the other end
...
Currier-aided Prorecrion o f Trartsrnission Lines
159
Fig~re
7
...
This generates a welldefined zone of protection consisting of the line length between buses A and B
...
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
...
4(a) Unit type carrier-aided directional comparison relaying: internal fault
...
4(b) Unit type carrier-aided directional comparison relaying: external fault
...
Both the relays use the directional principle, hence it is called unit type
directional protection
...
5
Carrier-aided Distance Schemes for Acceleration of
Zone 11
7
...
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
...
Thus, only about 60% of the mid-length of the line, gets high-speed distance protection
...
How to speed up the remote end distance
protection?
Consider a fault in the second zone of distance protection, but not beyond end B, as
seen from end A
...
The logic of this scheme is shown in Figure 7
...
The log*
can be i?nderstood by following the Roman numerals written in parentheses as follows:
Trip contact circuit at end B
p p , Trip contact circuit at end A
T
1
Timer
-1
!
:
...
...
,
,"
i
@
Trip
...
5 Acceleration of zone I1 o f distance relay using carrier
...
(11) This contact closure is used to switch on the carrier transmitter at end B, marked
as Tx in the figure
...
I
-
Carrier-aided Prorectioll o/ Trarts~nlsaio~t
Lines
161
The carrier signal arrives at the remote end A at approximately the speed of light,
after a very short delay, and is rece~ved the carrier current receiver, marked
by
as Rx
...
Now, the CRRA contact can be used to energize the trip coil of the circuit breaker at
remote end A in several alternative ways
...
In this scheme, the carrier signal is required for tripping purposes
...
Thus a tripping carrier scheme lacks
robustness
...
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
...
-
7
...
2 Permissive Inter-trip
At times, noise may cause false tripping in the scheme described in Section 7
...
1
...
Hence if point El in
Figure 7
...
7
...
3
I
1
I
s
i
t
1
1
I
iI
!
i
1
IE
Acceleration of Zone II
Alternatively we can simply bypass the zone I1 timer contact T2, Figure 7
...
7
...
4
Pre-acceleration of Zone II
In this scheme, the zone II timing is accelerated from T1 to a much smaller value
...
6
...
The carrier is now sent over a line section which is healthy (on which there is no
fault)
...
Thus Ti contact now comes into picture and decides the operating time
of zone 11
...
6
...
(11) Directional relay at end B senses the fault and instantaneously issues the trip
output
...
(IV) The carrier transmitter at end B sends the carrier over the healthy power line
...
(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
...
...
In actual
practice, Z2 operation should not be made instantaneous
...
We have to allow for the following delays:
1
...
Propagation time of carrier over the length of the line Tprop
3
...
It can be seen that the carrier is required for blocking the instantaneous operation
of the pre-accelerated zone
...
1
:
i
1
Carrier-aided Protection of Transmissiur~Lines
7
...
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
...
7(a)
...
The phase shift will, however, not be
exactly 18O0, but may lag or lead this position by a small angle f 6 representing the load
bemg carried over the 11ne
...
7(b)
...
-b
A
a
O
...
/A, ex1
l~rexl
,
!I
/A
...
exr
10,,t
IB
erl
Co~ncidence
period = zero
+
External fault
+ [A, ex1
I
External fault (Ideal)
C
...
= 2
...
P
...
-r
<
External fault (Actual)
C
...
= 2
...
7(a) Phase comparison relaying (currents shown on the CT secondary slde)
C
...
mr
I
n
l
I0
...
fu,I
lI
Figure 7
...
Coincidence
period = 10 ms
of Porver
164 F~t~rda~ne~ltal~ 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
...
A phase shift of k6 gives rise to a coincidence
period C
...
C
...
r 2
...
P
...
P
...
22rns
Figure 7
...
-
3
-
Figures 7
...
Figure 7
...
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 modulation can be easily recovered back by demodulation to get a square
waveform at the output
...
The coincidence period, thus, is 10 ms
(on a 50 Hz basis)
...
7(e) shows an external fault
...
However, because of the phase shift, now, the demodulated square waves do not have any
coincidence a t all or the coincidence period is nearly zero
...
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
...
1
...
~ n t
13,,,,I
-
"
I
1
' I
h,PI
Internal fault
'A, In!
I"<(
m
3
I: End A current for Internal as well
as external fault
...
Ill: Demodulated end A carder
...
V: Modulated carrier sent from end
B and received at end A for
internal fault
...
10ms
Vll: Coincidence period pulse
obtalned by ANDlng Ill and VI
/t-
Figure 7
...
of
166 Fu~ldun~e~ttulsPower Svsrem Protectiorl
Dir A
C B ~
-b
...
ex,
10, ex!
r n -
...
ext
I: End A current for internal
as well as external faults
...
'5
-~
-
...
No output
Figure 7
...
~
~
-,
~
...
Carrier-aided Prorection o f Transn~ission
Lines
Puise corresponding
10
coincidence period
Integrator
+
vcc
-$?
167
Trip CB,
Set threshold level
Ground
d
Figure 7
...
Review Questions
1 What do you mean by reclosure?
...
3 Differentiate between reclosure in case of low-voltage systems and high-voltage
...
4 What is meant by single-shot reclosure and multi-shot reclosure?
...
6 What are the various options for implementing the carrier communication
...
8 What frequency band is normally used for power line carrier signalling?
...
10
...
Explain why only middle 60% of the double-end-fed line gets instantaneous
distance protection from both ends in a three-stepped distance scheme
...
How does the carrier help in overcoming the limitation of the three-stepped
distance protection?
13
...
Which scheme is more robust?
14
...
Why does sending the carrier over a faulty line need to be avoided?
16
...
What do you mean by pre-acceleration of zone II?
7
18
...
Explain
...
Explain the operation of the unit type of carrier-based directional protection
...
Explain the principle of carrier-based phase comparison scheme
...
1
Introduction
...
,
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
...
1
...
On yet another (third) side, it is connected to the source of DC excitation
...
(Turbo-alternator)
DC excitation system
Figure 8
...
168
-
~
--
...
~~
...
For example, when a turbo-alternator driven by
team turbine is tripped, the following must be done:
mv
...
Firing of the boiler is stopped
...
Coal supply to the coal mills is stopped
...
Field coils are connected across a resistor to dissipate the stored energy
...
!
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
...
We have to keep in mind that a modern large turbo-alternator is a huge mass rotating
a t a very high speed (3000 rpm) in a very small air-gap
...
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 airgap
...
The operation outside the specified parameter range may cause a substantial
decrease in the life of the equipment
...
Figure 8
...
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
I
I
I
8
...
This is shown in Figures 8
...
3(b) and 8
...
It is to be noted
that the generator is n w e r solidly grounded
...
111 U I U ~ I bu
I I
g e a
~
~ L U L ~ I L U v a u e UL L I L ~~ I U U I I U I I I 1eblbbu1, ~b
U I ~
~
connected through a step-down transformer, known as grounding transformer
...
;he order of 10%
of the power rating of the generator, w'nich is supplied through the unit armillan
transformer (UAT)
...
Hence, there
is the switching facility to energize the UAT directly from the grid
...
*To grid
Unit auxiliary
transformer
il)
...
Figure 8
...
+
Phase
Grounding
e
i
i
tra,isformer ?:
(Step-down :I"
transformer)
...
The rotor of the generator houses the field winding
...
The dc system is kept floating
with respect to the ac ground, i
...
neither the +ve nor the -ve terminal is grounded
...
3(c)
...
I
...
Field---
;
44
Field winding
of generator
DC system is isolated
from ac ground
alternator shaft
Figure 8
...
a
8
...
Figure 8
...
4(b) show the
hierarchy of the electrical faults and abnormal operating conditions
...
4(a) Various electrical faults on a turbo-alternator
...
4 ( b ) Various abnormal operating conditions of a turbo-alternator
...
3
...
Another possibility is inter-turn faults between turns of the same phase
...
3
...
5
...
I
Figure 8
...
\
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
...
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
...
1 Difference between transformer and generator differential protection
Power transformer
Primary and secondary voltages
are in general different
Turns-ratio of the CTs are different
because of ratlo of transformation
of the transformer
Tap changer may be present
Generator
Same voltage for CTs on two sides of the generator
winding
Turns-ratio of CTs on the two sides of the generator
winding is same
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
...
The longitudinal differential scheme caters for phase as well as ground faults on the
stator winding
...
This is discussed in the following Section 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
...
Current in each parallel section is now compared with that in the
other section
...
and flow as spill current through the OC relay, as shown in Figure 8
...
Figure 8
...
6, only the winding with the inter-turn fault is shown in detail
...
Generaror Protection
175
healthy half carries 3500 A
...
Therefore, a
longitudinal differential relay would be incapable of detecting such faults
...
72 A in the transverse differential relay Thus, a setting
of, say, 0
...
8
...
Neither the
positive nor the negative terminal of the dc supply is grounded
...
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 resulting asymmetry in
the electromagnetic forces will cause severe vibrations of the rotor
...
Instances have been reported where, during rotor faults, because of severe mechanical
stresses structural damage was caused
...
An arrangement for rotor earth fault detection
and protection is shown in Figure 8
...
J
Alarm
OC relay
I
Time setting
Plug setting
Trip
Trip circuit of main
CB of generator
fiIsolation transformer
Figure 8
...
$j;
jli;; :
p;rli
8
I:
I
'
I
),
...
f,!
~!
1
f!,
,
,,
:!I!
...
This external voltage source is grounded so that the very first rotor
earth fault causes a dc fault current to flow which is easily detected by an OC relay
8;
,
8
...
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
...
There are a large number of possible faults, as well as
combinations of faults, on these equipment, that threaten the operation of the generator
...
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
...
8
...
1
Unbalanced Loading
If there is a n unbalanced loading of the generator then the stator currents have a
negative sequence component
...
Thus, the negative sequence stator armature mmf rotates a t a
speed -Ns while the rotor field speed is +Ns
...
This causes double frequency currents, of large amplitude, to be induced
in the rotor conductors and iron
...
Therefore, both the eddy
current as well as the hysteresis losses increase due to these double frequency induced
currents in the rotor
...
8
...
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
...
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 ~ 1 1 ;
...
8 Unbalanced loading of stator causes the rotor to overheat
...
The readers will recall that this characteristic is similar to that of the inverse time overcurrent relay
...
The preceding discussion suggests that if we could, somehow, extract the negative
sequence component of the stator current then the protection against unbalanced loading
can be implemented by applying the inverse-time OC relay as shown in Figure 8
...
178 F~alclanrenralsof Powrr Sysrem Protection
Stator currents
12
I
Negative sequence current (rms)
I--
8
Over-current relay with inverse
characteristic To, = MI:
Set K for the machine
Trip main CB o generator
f
Figure 8
...
Consider that a turbo-alternator is supplying its rated real electrical power P, to the grid
...
Now, consider that due to some fault the generator is tripped and disconnected from
the grid
...
However, the mechanical power input Pm cannot be
suddenly reduced to zero
...
This would cause the machine
to accelerate to dangerously high speeds, if the mechanical input is notpquickly reduced
by the speed-governing mechanism
...
The speed-governing mechanism or the speed governor gf the turbine is
basically responsible for detecting this condition
...
The logic of protection against over-speeding is shown
in Figure 8
...
0
Tachogenerator
Over-frequency
relav
output
...
Start shutdown of
generator
Figure 8
...
Generator Protec!ion
179
Loss of Excitation
8
...
3
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
r
I
I
I
I!
i
The generator delivers both real as well as reactive power to the grid
...
Consider
a generator delivering the complex power, S = P, + jQ,,to the grid
...
11(a) and (b)
...
Since the generator is already synchronized with the grid, it would attempt to
remain synchronized by running as an rnduction generator
...
This is shown in Figure 8
...
Operation as an induction generator necessitates
the flow of slip frequency current in the rotor, the current flowing in the damper winding
and also in the slot wedges and the surface of the solid rotor body
...
Field cume"t If = zero
(Loss o excitation)
f
(b) After loss o excitation
f
Figure 8
...
QLOE
180 Fundor71erzrolr of Power System Prnrecrrorl
Now, there are two possibilities
...
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
...
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
...
There are certain limits on the degree to which a generator can be operated
within the under-excited mode
...
The simplest method by which loss of excitation can be detected is to momtor the field
current of the generator
...
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
...
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
...
5
...
8
...
4
Protection Against Loss of Excitation Using Offset Mbo Relay
During normal steady-state operation, the impedance seen from the stator terminals, i
...
the apparent impedance lies in quadrant I, of the R-X plane as shown in Figure 8
...
X
Medium initial
I
L w initial output
o
Figure 8-12 Protection against loss of excitation
...
If the initial power
output was high then the locus is traced out quickiy
...
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
...
A mho type distance relay with offset characteristic may be used for protection
against loss of excitation
...
The impedance setting
of the relay is IXd1 a t an angle of -90" as shown in Figure 8
...
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
...
8
...
5
Loss of Prime Mover
In case of loss of prime mover, i
...
loss of mechanical input, the machine continues to
remain synchronized with the grid, running as a synchronous motor
...
At the same time, the
machine supplies reactive power to the grid since its excitation is intact
...
13(a) and (b)
...
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
...
182 F~rndarnettralsof Power System Pmrection
Normally, loss of steam supply to the turbine causes loss of prime mover
...
Therefore, the loss of prime
mover needs quick detection followed by tripping of generator
...
The real power drawn from the grid
is quite small compared with the generator rating
...
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
...
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
...
Hence, the
directional relay for detecting the loss of prime mover needs to have a high degree of
sensitivity compared to directional relays used for crver-current application
...
...
14 Duectional relay for protection against loss of prime mover
...
Discuss the scenario that the turbo-alternator presents to the protection engineer
...
Tripping the main circuit breaker is not enough protection for a generator
...
3
...
Differentiate between longitudinal and transverse differential protection
...
Why conventional differential protection cannot detect inter-turn faults on the
same phase?
6
...
What special type of winding construction is required in case of transverse
differential protection?
8
...
Why the first ground fault on the rotor does not cause any damage while a second
fault can be catastrophic?
10
...
Why does a generator need to be tripped in case of loss of excitation?
12
...
How does a LOE distance relay work?
14
...
15
...
Can a generator be allowed to run with its prime mover lost? If not, why?
17
...
1
Introduction
A stupendous number of induction motors are being used in the industry
...
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
...
5
Induction motors come in a wide range of ratings, from fractionalPorsepower motors
used in tools and domestic appliances to motors of megawatt rating
...
A broad classification is presentedjn Table 9
...
Table 9
...
This is the reason why induction motor
...
However, regardless of what protection we may provide, all motors, big or small, are
3
subjected to similar faults and abnormal operating conditions
...
2
Various Faults and Abnormal Operating Conditions
The induction motor cannot be considered in isolation
...
Therefore, the induction motor is subjecte
to a large number of faults and abnormal operating conditions as depicted in Figure 9
...
Unbalanced supply voltage
3
...
Fault on
I
I
I
L,
t
I
1
...
Ground faults
3
...
2
...
Rotor jam
4
...
Reversal of phases
-
Figure 9
...
9
...
The amplitude of the starting current may be
comparable to fault current
...
Hence, coordination between the starting characteristic of the motor and the
over-current relay is required Figure 9
...
It can be seen from Figure 9
...
This will ensure that the protective relay does not operate
during starting phase the motor but will positively operate when the load exceeds the
motor's thermal capability
...
I
I
! characteristic
i1 2 3 4
I
:d
1
I
t
5
6 7
IFL
Current
~ ~ l l - l ~ (multiples o
~ d
f
current
hflload)
+Istan '
'+T-
Starting
'oh-rault
current
Figure 9
...
...
4
9
...
1
Electrical Fauljs
Fault on Motor Terminals
The phase-fault current a t the terminals of a motor is considerably larger than any
normal current such as starting current or any internal-fault current
...
9
...
2
...
I
1
1
Phase Faults Inside the Motor
,
Protection 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
...
3)
...
The fuse operating time should be less than
permissible locked rotor time of the motor
...
Induction motor
fin
Figure 9
...
i
-
...
motors, will need to be ~rovidedwith an
over-current protection for increased accuracy of protection as shown in Figure 9
...
The
thermal capability characteristic of the motor should be kept in mind while applying
over-current protection
...
2
...
Such faults are difficult to detect using
over-current approach
...
4
...
I n 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
...
6
...
The logic for this
criterion can be explained as follows:
Assume a motor is connected to a supply transformer with 8% impedance
...
...
5 Percentage differential relay for protection of induction motor
187
188 Fundamenrals of Power System Prorecrion
I
~ = -( 1~ = 12
...
In order that (13
...
32 per unit on the transformer kVA base
...
167 on the motor rated kVA base
...
167 would be 0
...
32
...
9
...
3
Ground Faults Inside the Motor
Figure 9
...
The threephase line conductors carrying current to the motor form the primary of a transformer
...
Figure 9
...
Thus, there is no net flux in the core
...
Now, consider a ground fault as shown
...
Thus, there is a net primary mmf proportional to the fault current If, returning to the
supply neutral through the fault path
...
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
...
Very high sensitivity, however,
is likely to cause some nuisance tripping
...
Inter-turn faults on the same phase are difficult to detect because they do not cause
appreciable change in the current drawn by the motor
...
No specific protection against inter-turn faults is needed for most motors except very
big motors
...
I
9
...
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
...
5
...
The negative
sequence component, which comes into picture because of the unbalance in the supply, is
particularly troublesome
...
In fact, the negative sequence impedance is less than the
positive sequence standstill-impedance as shown in Figure 9
...
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
...
Rs
x
r
)
Z
...
"
Rm
= Rs
Z,,,
+
R,
+
At start (s = 1)
Xm
~ ( X S X,)
+
(a) Equivalent circuit while starting
At rated speed
1
...
7 Equivalent circuit of induction motor
...
This
causes currents of lf(2 - s] frequency, i
...
almost double the supply frequency, to be
)
induced in the rotor circuit
...
Therefore, for large motors any unbalance in the supply voltage needs to be quickly
detected and corrective action taken
...
8
...
8 Negative sequence voltage relay for protection against unbalance in supply
voltage
...
For example, if there is an open circuit fault between the supply and theYelay
then 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
...
~,
...
10,
Equivalent sequence
network connection
Open circuit CB
M~~~~
Val 'V
z m
1
h
Cz +
R Vzs
Zzm
f
V,
2
Negative
sequence relay
:
Time setting
2
's
<<
v2m
~
Figure 9
...
1!
For positive detection of such faults, we need to detect the negative sequence
component in the line currents
...
5
...
I
9
...
2
Single Phasing
I
1
1
I
i
i
i
I
t
I
1I
I!
Single phasing can occur because of a non-closure of one pole of a three-phase contactor
or circuit breaker, a fuse failure or similar causes
...
The motor has a limited
ability to carry negative sequence currents, because of thermal limitations
...
Thus, there is a thermal limit on the amount of the negative sequence current that
can be safely carried by the motor
...
1; t = 40 is conventionally used as the thermal capability of motor to carry negative
sequence current
...
11 shows the characteristic of a relay for detecting imbalance in the line
currents
...
One unit balances I, against Ib while the other
balances Ib against I,
...
I
I
--
--
-
192 Fl~ndamenralsof Power Sysrenr Prorection
1A
Val
- )
-
Figure 9
...
9
...
3
Reduction in Supply Voltage
The torque developed by an induction motor is proportional to t h e square of the applied
voltage, therefore, any small reduction in iroltage has a marked effect on the developed
torque
...
Large motors should be disconnected when a severe low voltage condition persists for
more than a few seconds
...
9
...
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
...
I n 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
...
6 Abnormal Operating Conditions from Mechanical Side
9
...
1
Failure of Bearing and Rotor Jam
i
Bearing failure or rotor jam causes excessive load torque on the motor
...
In order to discriminate between rotor jam and other
operating conditions that can also cause over-current, the high current is not recognized
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 a t least twice the locked rotor time setting
...
6
...
$
*
I,$,
>
...
T
Thermal overload relays offer good protection against short, medium, and long duration
overloads but may not provide protection against heavy overloads shown in Figure 9
...
1
q
1
...
-
-
-
,
-
...
13
...
14
...
12 Thermal overload relays offer good protection against short, medium, and long
duration overloads
...
'
Good
protection
Overprotection
rotor time
I
I
Starting time
1
t
Motor current
8
Figure 9
...
A
Thermal capab~lity
Long time induction
OC relay
Thermal capability
rotor time
-
Starting tlme
J
...
14 Combination of thermal overload relays and OC relays provides complete
thermal protection
...
They are usually applied to large
motors of 1500 HP and above
...
15 shows an RTD which is embedded in the machine connected to a
Wheatstone bridge
...
A sensitive relay in the form of a contact making dc galvanometer
may be connected as a detector
...
16 RTD embedded in the machine connected to a bridge'
...
,
...
Several types of RTDs are available for use in temperature monitoring, namely
10 0 copper, 100 R nickel, 120 R nickel, 120 R platinum
...
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
...
Replica relays are typically temperature compensated and operate in a fixed time at
a given current regardless of relay ambient variations
...
I~tiucrion,kloror Protection
9
...
What are the various abnormal operating conditions from supply side to which an
induction motor is likely to be subjected?
2
...
Why is an induction motor very sensitive to unbalance in supply voltage?
4
...
What are the effects of running an induction motor a t reduced supply voltage?
6
...
What kind of protection is provided to an induction motor against overload?
8
...
What are the effects of single phasing on the induction motor?
10
...
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
...
1
I
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
...
e
...
e
...
A simple
impedance relay compares the torque generated by the current (operating torque) with
the torque generated by the voltage (restraining torque) at the relay location and operates
if the operating torque is greater than the restraining torque
...
Thus, a t the heart of any relay, is always a comparator
...
But eventually the electromechanical relays gave way to the solid-state relays
...
Rowever, in the p a t , when electromechan~cal
relays were being wldely used it was not
possible to perform the numerical computation in a relay
...
The relays based on comparators were found to
be quite simple and robust
...
The comparator-based relays are very attractive because of their inherent simplicity
and low cost
...
The comparators can be classified into two types; those based on comparison of
amplitude and those based on comparison of phase angle
...
2 Amplitude Comparator
1
The amplitude comparator has two inputs, Soand S , and a trip output
...
The input phasor So is called the operating quantity and the input phasor
S , is called the restraining quantity
...
1)
If 1 S o > 1 S
then trip; else restrain
s-rr~T
(i
;p
sr
Amplitude comparator
,
Figure 10
...
Some specific instances where the amplitude comparator gives the trip output are
shown in Figure 10
...
I
,,
,
/-'
I
-so\- - - - - - - - - -
s,
---------
...
Trap
S o > IS,
:
...
2(a) Inputs to amplitude comparator resulting in trip output
...
2(b) shows some specific instances where the amplitude comparator is Caused
to restrain
...
,,
,
I
S,
I
------------
I
,
I
I
/Sol < IS,I
:
...
: Restraln
I
I
I
,
------------
r
I
I
(Sol < (S,I
I
\ '
T
I
I
I
p
...
j
...
'1
j
1
I
,
:
'7
4
FigurelO
...
3
4
Further, some specific instances where the amplitude comparator is on the verge or
threshold of tripping, are shown in Figure 10
...
n
the inputs
...
2(c)
ISol = IS,!
I
...
:
Threshold
Inputs to amplitude comparator causing it to be on the threshold
...
...
Phase comparators are of two types: the cosine type and the aine type
...
: Cosine-type Phase Comparator
The
10
...
1
The cosine-type phase comparator has two phasors Spand 9 at its input and has a trip
,
output
...
The
input-phasor, designated as S,, is called the measured input
...
3
...
3 Cosine-type phase comparator
...
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
...
Trip
:,
,
...
,
,
- - - - -- ---
f m
...
sm
,
Arg (S,S
,' p)
c 90'
:
...
p
Trip
Figure 10
...
200
Furnlarire~itals Power Systern Protection
of
- -
Some specific instances, where the cosine-type phase comparator is caused to restrain
are shown in Figure 10
...
Arg (SJS,) = 180"
Arg (sJS,) r 90'
: Restrain
...
: Restrain
...
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
Figure 10
...
10
...
2
The Sine-type Phase Comparator
The sine-type phase comparator has two phasors Sp and S, a t its input and has a trip
output
...
The input
phasor, designated as S,, is called the measured input
...
'
i
!
Sruric Compuraturs as Relays
201
Figure 10
...
It emphasizes the fact that, ideally, the phase
comparator is sensitive only to the phase of the signals and ignores their magnitudes
...
5 Sine-type phase comparator: hip, restrain and threshold conditions
...
4
I
I
i
,
I
I
I
I
Duality Between Amplitude and Phase Comparators
There is a relationship of duality between the amplitude and phase comparators
...
In the discussion
that follows, unless otherwise explicitly specified, we mean cosine comparator when we
mention phase comparator
...
If we derive S, and Spfrom So and S, such that
S, = (So+ S,)
and Sp = (So- S,)
and feed these to a phase comparator, then the output of the phase comparator would be
exactly the same as that of the original amplitude comparator (see Figure 10
...
f
202 Fundamenrals o Power System Pmfection
...
6 Duality between amplitude and phase comparators
...
7)
Thus, we can generalize the duality theorem as follows:
"C
...
...
7 Duality between phase and amplitude comparaf$rs
...
...
If such signals are fed to the
dual, the output would remain unchanged
...
8
...
:
g
>
Phase
comparator
,:
,
Restrain
...
8, we can see that IS,( < IS,/
...
The geometrical construction shows, how the S and Spare synthesized,
by addition and subtraction of /Sol and IS,/
...
In Figure 10
...
Therefore, an amplitude comparator would
operate (trip)
...
It can also be easily seen that since
arg [(So+ S,)/(S,- S,)] i
90°, the dual-phase comparator would also operate (trip) if fed with
such signals
...
Duality between amplitude and phase comparators for So > S,
...
10, we can see that arg (Sm/Sp) > 90"
...
The geometrical construction shows that the
signals Soand S, can be synthesized by addition and subtraction of S, and Sp
...
Arg (SJSp) > 90"
SP
By
comparator
I
theorem o duality
f
So = Sp + Sm
S, = Sp - S,
*
Amplitude
comparator
Figure 1
...
204
-
F~o~n'nnre~,mls Power Systein Protectiorz
of
In Figure 10
...
Therefore, a phase comparator
would operate (trip)
...
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
...
11 Duality between phase comparator and amplitude comparator for
arg (S,/S,)
-= 90"
...
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
...
5 Synthesis of Various Distance Relays Using S t a t i y
Comparators
It is possible to synthesize a variety of relays using static comparators
...
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
...
Next, we convert these two phasors into two voltages suitable for feeding
a practical electronic c~rcuit
...
5
...
12 shows the synthesis of a mho relay using a phase comparator
...
The characteristic to be synthesized is thus
a circle with diameter as phasor Z,
...
12
...
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"
...
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")
...
e
...
+ Trip
OB = lZr21+ Threshold
OC = lZr31+ Restrain
OA = IZ,,l
I
I
1
I
1,
I 2" - 1 I
I Zr1I
_
AP = (2,
- Z,,l
BP = 12, - Z,zl
CP = 12,
- Zr31
Arg
I
I
< 90"
I)
Trip
IZn -"" = LCBP = 90"
I)
Threshold
IZn
Arg
I
)
Restram
12,21
= LDCP > 90'
12~31
Trip law:
If
I
Arg
lZn
IZrI
go",
then t r ~ p
Figure 10
...
I
i
Similar analysis shows that even if the impedance seen by the relay is on the other
side of Z, as shown in Figure 10
...
The angle hits 90" for boundary conditions
206 Fundamentals o Power System Pmrect~on
f
and becomes less than -90" as the impedance seen by the relay moves into the restraining
region
...
-
i
I Z n -Zr31
= LPCD < -90"
~est~in
Izr3I
Arg
I
'" I > -90";
- Zr
I Z,I
then trip
Figure 10
...
:
...
jl
...
Therefore, if ( , Z,) and Z, are used as inputs to a cosine comparator, the resulting
Z
entity would behave exactly like a mho relay
...
The problem is that the electronic circuit
of the comparator accepts only voltage signals a t its input
...
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,
...
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,
...
,
Trim law:
...
>
...
...
14
...
14 Deriving practical signals for mho relay synthesis
...
In order to form
Sp and S , inputs suitable for synthesis of mho relay, we will have to mix them using
suitable hardware to get the required signals
...
15
...
15 Mho relay synthesis using cosine-type phase comparator
...
5
...
16 shows the synthesis of a reactance relay using a phase comparator
...
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 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"
...
When the impedance lies on the
boundary, the angle becomes exactly equal to 90"
...
X
-
Restrain
":
,
"
...
I
>R
V
0
OP = IX,I = Setting
OA = IZ,,I + Trip
A P = IXn -Z,,I
OB = IZr21 -+ Threshold
BP
-+ Restra~n
OC = IZ,,/
Arg
Arg
I n
-
IXn
-Zr3'
I XnI
I X"I
CP = IX,
- Z,,I
...
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
J X , phasor, the angle between (Xn - Zrl) and &, is greacer than -go', as long as the
impedance falls within the trip region
...
This is shown in Figure 10
...
OP = /X,I = Setting
- Z,,l
OA = IZ,,( + Trip
AP = JX,
0 8 = (Zr2(+
BP = IX, - Zr2)
Threshold
OC = /Zr31-+ Restrain
Arg
Arg
IXn - Z r 2 1 = LOPB =
I X"I
CP = IX,
LII = 90"
- &$I
+
I Xn - Z r 3 ' = LOPC = Lill < -90"
IXnI
Threshold
Restrain
Trip law:
I Xn
then trip
I Xnl
Figure 10
...
If
-90" < Arg
Thus (X, - Z,,) and X, seem to be suitable for feeding to a cosine-type phase
comparator for synthesizing the reactance relay
...
Therefore, we can get voltage signals from these two
inputs by multiplying each of them by I,, the current at the relay location
...
This is shown in F i e r e 10
...
Note that Zrl I, is nothing but the voltage a t the relay location, i
...
V,
...
18 Deriving practical signals for reactance relay synthesis
10
...
3
Synthesis of Simple Impedance Relay Using Ahrplitude
Comparator
...
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
...
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,
This is shown in Figure 10
...
10
...
The approach described here is based on measuring the
coincidence period between the two waveforms whose phase difference is to be measured
...
h
-
...
impedance
...
...
19 Synthesis of simple impedance relay using amplitude comparator
...
The negative coincidence period is defined on similar lines
...
By measuring the coincidence period, we have essentially converted the problem of
phase angle measurement into that of time period measurement
...
20 shows that, considering 50 Hz power frequency, the
----20
Phase shift between
S
,
and S, = Zero
ms-
---4
S,
lags
S by 90'
,
Figure 10
...
I
212
-
Fu~~da~?ienmls
of Power System
-
protect lot^
coincidence period is always greater than 5 ms (or Ti4 s where T i u the time period of the
power frequency) if the S , wave is within +9O0 of the S p wave or within the trip region
of the phase comparator
...
Next, we should have an arrangement to measure the width ofthis pulse
...
If
the width of the coincidence period pulse is less than 5 ms then output should be
restrained
...
20 shows that the coincidence period pulse is of 10 ms duration when the
two inputs are in phase
...
When
S , lags S , by 90°, the coincidence period falls exactly to 5 ms
...
21 shows that the coincidence period pulse is of zero duration when the two
inputs are out of phase by 180"
...
When S,,, leads S , by 90°,the coincidence period builds upto exactly 5 ms
...
21 Coincidence period for phase shift of 90" lead
...
22
...
For restraining condition, the coincidence period is always less than
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
...
This has
fs
the advantage of avoiding actual measurement
...
Smleads Sp by 90'
ColP = 5 ms
ColP c 5 ms
Restraining
reglon
,,
;
'-,
Trip
,
,
region
region
CoiP c 5 m s
I
,
'
V
-
I
1
1
i
Trip
region
\
,
a
m
ColP = 5 ms
S, lags Spb y 90"
11
,* CoiP > 5 ms
Restraining
sm
ColP = Zero <
Smout ofyphase
with Sp b 180"
Sm
'
...
2 Variation of coincidence period with phase shift (superimposed on cosine-type
02
phase comparator characteristic)
...
23 shows the block diagram of a cosine comparator based on comparison of
positive coincidence period
...
The resulting waves are converted to blocks by passing them through a
zero-crossing detector
...
The coincidence period is detected by logical
ANDing of these two signals
...
23 Block diagram of static cosine-type phase comparator based on coincidence
principle
...
This pulse is then integrated and the output
of the integrator is compared with the expected output for a pulse of 5 ms duration
...
If the coincidence period is more than 5 ms then the output of the integrator is more
than Vref
and the comparator is triggered into high output state
...
If the coincidence period is less than 5 ms, the output of the integrator never reaches
the level of Vref, the comparator output remains low
...
23 and in more detail
in Figure 10
...
"
...
24 Waveforms for cosine-type phase comparator based on comparison of
coincidence period
...
24 shows that the inputs s3', S p to the cosine-type phase comparator
and
are in phase
...
The integator output,
therefore, exceeds the reference voltage Vref and the comparator is triggered into a high
output state, thus issuing a trip output
...
Figure 10
...
The comparator IC works on a single
(unipolar) dc supply
...
25 An integrated circuit comparator-based circuit for cosine-type phase comparator
based on coincidence principle
...
The first
two comparators work as zero-crossing detectors producing a square wave during the
positive excursion of their respective inputs
...
If V p < V, then the output point is effectively connected to ground
...
25
...
Thus, the output is high if and only if both the zero-crossing
detector outputs are hlgh
...
Further, since both the outputs float during the coincidence period,
the C,,,, can charge through Rlntg, a time equal to the coincidence period
...
This voltage
216
-
filndarnenra/s o power System Protection
f
is compared with a preset value obtained with the help of the potentiometer
...
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
...
10
...
In order to develop an electronic circuit for implementing a sine-type phase
comparator, refer to Figure 10
...
This is the phase
relationship for which the sine comparator should restrain
...
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
...
26 Relationship between spike and block for S, lagging S,
...
Static Comparators ns Re1a
...
27 shows that if S , leads Sp then there is always a coincidence between the
spike and the block, whatever be the angle of lead
...
Figure 10
...
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
...
I
I
Bypass
negative-half
Bypass
negative-half
CMOS
switch
I
///
i
1
I///,
Restrain
b
1
Shunt
s~
Figure 10
...
of
218 F~rndamenrols Power Systenl Protecrion
The shunt switch is operated by the control voltage
...
It can be seen from the figure that when S, lags Sp,the block is low when the spike
appears
...
This is the restrmning region of the relay
...
The block remains high when the spike appears
...
Thus, the shunt switch remains open and the spike is allowed to hit the
output terminal
...
This is one of the many possible ways in which a sine-type phase comparator can be
implemented
...
8 Synthesis of Quadrilateral Distance Relay
@
The fault characteristic of a transmission line is a quadrilateral because of the arcin
fault resistance
...
An
ideal distance relay should have a characteristic which snugly fits around the
quadrilateral
...
29, is very stable on power swing because it encompasses minimum area on
the R-Xplane
...
X = lrn(Vl1)
:
,?
,
,
...
29 Characteristic of quadrilateral distance relay
...
30
...
30
I
219
Characteristic 2
The four characteristics to be synthesized
...
Characterzstic
Reactance
Angle impedance
Directional with MTA = el
Directional with MTA = -B2
Polarizing qty
...
I n1
x
Izn2
I
I
Figure 10
...
X = lm(VI1)
Line ~mpedance
phasor
Characteristic 1
IX,,
-
V
IXn1
+90" cosine-type
phase comparator
Characterishc 2
Charactenstic 2
I&2
-v
IZnz
k90' cos~ne-type
phase comparator
>
R=
Re(V1r)
Figure 10
...
Trip
220
Fu'u,ldunzenralsof Power Sysrem Protection
-
Figure 10
...
32 Synthesis of directional characteristic with MTA of
e2
...
33 shows the synthesis of directional characteristic with MTA of
el
...
33 Synthesis of directional characteristic with MTA of
el
...
Figure 10
...
quadrilateral characteristics
...
Review Questions
List the advantages of static relays
...
What is the price to be paid for not implementing direct numerical computation?
Define the characteristics of amplitude comparator
...
...
What is the theorem of duality?
7
...
8
...
9
...
How will you synthesize a reactance relay using an amplitude comparator?
11
...
When the input signal to the cosine-type phase comparator contains a dc offset,
how does the performance of the relay get affected?
13
...
What is the effect of noise and harmonics on the performance of the cosine and
sine type phase comparators described in the text?
15
...
16
...
The
cosine-type phase comparator is a special case where a = P = 90"
...
2
...
4
...
!
!I
!
1
i
!
...
1 1
...
They were soon replaced by electromechanical relays which were
sensitive and accurate
...
Within a year of invention of the transistor, its
use in protective relays was reported
...
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
...
Hence, the
name numerical relay
...
In numerical relays, there is an addit~onalentity, the software, which runs in t e
background and which actually runs the relay
...
Hardware is more or less the same
between any two numerical relays
...
The conventional non-numerical relays are go-no-go devices
...
In fact, the convent~onalrelay
cleverly bypasses the problem of computation by performing comparison
...
Thus, the relay engineer need not merely implement the old relaying
concepts but can devise entirely new computation-based concepts
...
We can implement an existlng relaying concept using the numerical technique
...
The process of development of a new numerical relay
is shown in the flowchart of Figure 11
...
1 Development cycle of a new numerical relay
11
...
2 shows the block diagram of a numerical relay
...
This is to make sure
that the signal does not contain frequency components having a frequency greater than
one half of the sampling frequency
...
224
F1r1rdo1~re11ru1
...
-
/
Select
'Ommand
Analogue
signals
Start
...
2 Block diagram of numerical relay
...
Next, the analogue signal is sampled and held constant during the time the value is
converted to digital form
...
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
...
-7
...
A
Table 11
...
With SIH circuit
dv
-=
VI~II
scale
dtmm
~"TADC~~~
where TADc,, is the conversion
time of the ADC
...
fm,
=
1
-
2n2nT
...
A
Gives:
f,
,
= 0
...
1
...
2
...
4
1
I
i
;a
,
...
<
...
?
'<1
...
$
;
...
:i
= 9
...
4
...
...
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 output of the ADC may be 4, 8, 12, 16, or 32 bits
wide or even wider
...
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 can also be used to communicate with other relays or
another supervisory computer, if so desired
...
Thus, new features and functionalities can be added to an existing relay by upgrading its
software
...
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
...
11
...
Thus, we must have
1 msamging,
min
(11
...
If the signal is sampled below the Nyquist limit, it gives rise to the phenomenon
of aliasing
...
The above signal refers to a pure sinusoid, which contains only one frequency
component OJ,,,,~
...
Thus, the allowable sampling frequencies
are those equal to or greater than 2 0 , , ~ ~ ,max Therefore, we have
~,
1
Wssmp~mg,
mm
2 2mslgna1, m u
1
The proof of the sampling theorem can be seen from Figure 11
...
(11
...
3 Proof of sampling theorem
...
The sampling impulses,
which appear at a frequency of o,, have a repetitive frequency spectrum which repeats at
a spacing of o,
...
The spectrum of the sampled signal has peaks around 0,f o,, + 2 4 , f 3 0 s , and so
on
...
overlap
...
4
...
Figure 11
...
Numerical Prorertron
-
237
Protective relaylng signals contain dc offset, a number of harmonics and random
noise
...
Thus, in order to preserve
information in such signals, we will need an impract~cablyhigh sampling frequency
...
e
...
5
...
//,//////////,////
...
5 Minimum sampling frequency
...
Such filters do not
exist! What we get is a finite roll-off in the stop band
...
6
...
6 Practical limit on minimum sampling frequency
...
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
...
When the reference wave is the
square wave with amplitude of unity, the analysis is known as Walsh analysis
...
Haar analysis is the
simplest type of wavelet analysis
...
It will be pertinent here to briefly review the
concept of orthogonal sets of functions
...
,
is
b
?I
1
I
I
I
2
I
1
a
!
I
Assuming that
b
J @ ; ( t ) d t= K
#
0
i
...
none of the functions of the set are identically equal to zero
...
+ cn@,,(t)
)
(11
...
(11
...
All
b
the terms of the form
J
~ , , , @ ~ ( t ) @ ~are d t if m
( t ) zero
#
n, because of the orthogonality
0
of the functions @m(t) @,,(t)
...
(11
...
(11
...
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
...
9),it gives the best approximation ( i
...
with a minimum mean squared
error) of the given function f(t)
...
4
...
, cos nul t , sin n q t
which can be more compactly written in the complex form as
(11
...
12)
then the interval of orthogonality coincides with the fundamental period T = 2 a I q of the
function f (t)
...
+ C-2
z
e - j 2 w ~ L+
c-l
e - j ~ l L + Co + Cl
eja"t + C 2 ej21u't +
...
12a)
,=-m
The trigonometric representation of the Fourier series is
f ( t ) = a
...
+ a, COB n q t
+ b, sin q t + b2 sin 2 q t +
...
(11
...
(11
...
13) are known as Fourier c o m p l e x series and
Fourier trigonometric series, respectively
...
+ F,
*
I
where Fo is the dc component and the other components are:
F1 = a, cos q t
+ jb,
sin q t ,
F2 = a2 cos 2wl t
+ jb2
sin 2 q t , and so on
...
, a, and bl, b2,
...
-
angles of various frequency components contained in the signal
...
Thus, the amplitude of the nth harmonic is
and its phase angle is
The Fourier coefficients can be easily found by using Eq
...
16)
allntO
(11
...
18)
...
21)
all n
(11
...
lcslProtection
231
/
-
Figure 11
...
Fundamental cosine
r,t,f Signal
+a
...
...
...
0, = tan-'(b, la,)
I'
Fundamental sine
Lbn
d
F"
0, = tan-'(b, la,)
t-
F"
0
...
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
...
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)
...
Therefore,
the Fourier analysis described for analogue signals has to be suitably modified
...
2
...
2 Analog vs discrete domain
Analog domain
Continuous signal fit),
where t can take any value and, therefore,
f(t) can take any value from an infinite
set of numbers
...
e
...
Integer sample number k
Summation Z
Number of samples per cycle N
Summation of finite samples
232 Fundamentals of Power System Pmtectlon
The time A t is the time period corresponding to the sampling frequency, hence
1
At =
fsampiing
=
Tsamp~ing
since there are N samples per cycle of fundamental, we get
2n
NTSamplingNAt = TI= =
01
Noting that k is the sample number and N is the number of samples per cycle, the
expressior
...
2
...
3 lists the expressions for evaluating discrete Fourier coefficients alongside
those of continuous Fourier coefficients so that the readers can easily associate the
discrete expressions with the more familiar continuous expressions
...
3 Discrete Fourier transform coefficients
Continuous slgnal
Window
Sampling
i
1
...
M
...
I
a
...
The implicit assumption is that the signal samples are zero uniformly outside the
window
...
8
...
I
1
i:
:
,
Discrete
Continuous
3
+Time
W~ndowedand
sampled slgnal
+Time
Figure 11
...
*
-
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
...
Fortunately, windows can be shaped in such a way that the effect in frequency domain
is minimal
...
Interested readers may refer to any standard text on Digital Signal Processing
for more information on this very interesting topic
...
9 shows the process of computing the Fourier transform
...
The samples of the
t
fundamental sine and cosine waves, known as weights,are precalculated and also stored
in the memory
...
When the process is complete we get
one estimate of the magnitude of the desired frequency component and its phase angle
...
The time
window is continuously kept sliding forward
...
Thus, the process is similar
to a machine which keeps on running
...
9 The discrete Fourier machine for eight samples/cycle
...
10
...
For example, to extract the second harmonic, the weights will be the samples of
second harmonic sine and cosine waves W 2
,,,,(n) and W2eos,ne(n)
...
Yes
<
a, = A,IN: DC offset
a, = ( 2 N ) A,
I
bl =
...
4
...
10 Flow chart for the computation of Discrete Fourier Transform
...
11
...
U T )
-1
WaI(6
...
U T )
-1
I
Figure 1
...
11
236 Fui~damet~rals Power System Protection
o
f
where the Walsh coefficients Wh are given by
I 1:
"
...
Walsh transform gained popularity during the initial years of numerical relaying
because a t 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
...
Thus, i n order to relate t concepts such as*
impedance, we have to come back to Fourier domain
...
Thus, the initial advantage of Walsh analysis, being computationally easy, is to
...
All the same, Walsh analysis opens up a fresh viewpoint and leads to many new
interesting possibilities
...
,
Wavelet analysis
When we perform conventional Fourier analysis, we get the information about the
frequencies that are present in the signal
...
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
played!
a t which these were b e ~ n g
Conventional Fourier analysis does not preserve any information about time but gives
very detailed information about frequency
...
However, the time-window size is
fured
...
However, as we make the time-window small, the information about
the low frequencies loses its precision
...
This is
achieved by using a family of correlating functions which have well marked attributes of
position and scale
...
Discrete Wavelet analysis is a discrete implementation of the continuous wavelet
transform
...
(I)
~V~irnerlcal
Prorecrror! 237
During the immediate post-fault conditions or other disturbed conditions like power
swings, the power system gves rise to non-stationary signals
...
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
...
Interested readers may refer to advanced texts on image processing for more detailed
information on the theory of Wavelets
...
5
;
I ' ,
...
1
i
i
1
1
t
+
Least Error Squared (LES) Technique
As pointed out in Section 11
...
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
...
To illustrate the LES technique, let us assume that the fault current consists
of:
A dc offset
A fundamental component
Other harmonic components of higher order
The LES technique helps us in estimating the values of these components
...
26)
n=l
For the sake of illustration, assuming that the current consists of a dc offset, the
fundamental and a third harmonic component, we can write
We can represent e-'/' as a sum of an infinite series, i
...
Assuming that truncating the series for e-'/:
accuracy, we get
i(t) = K,
-
to the first three terms, gives adequate
Kl
K,?
-t1 + - + Kzl cos 81 sin
T
2! T 2
ol t
+ KZ3cos Q3 sin 3u1t + KZ3sin 83 cos 3 q t
+ Kz1 sin 81 cos
qt
(11
...
36)
= Lan-'(3)
(11
...
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
...
performing distance relaying or fault location
...
6
Filtering is a very important and the most frequently needed operation in numerical
relaying
...
However, there are certain drawbacks associated with
analogue and active analogue filters, namely:
They are bulky, specially inductors require a large space
...
Their characteristics drift with respect to time and temperature
...
Their characteristics are limited to the certain well known conventional
characteristics
...
e
...
They are not programmable
...
The most
important advantage of digital filters is that they do not require high precision and high
quality R-L-C components
...
The underlying software decides the filtering action
...
This has several advantages, for example, it is easy to change the
characteristics of the filter by simply using another program
...
There is no ageing and no drift caused by time or
temperature
...
6
...
The filter can be expressed mathematically as
-
340
F~mdamentalsof Power System Protecrio!~
Consider a signal as shown in Figure 11
...
,4t sample number 3, there is a large
noise signal of positive polarity
...
Thus, we have a high frequency noise signal riding
over the low frequency information-carrying-signal
...
12
...
This amounts to low-pass filtering
...
output
7e;iitr
Figure 11
...
1 1
...
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 a s shown in Figure 11
...
The
filter can be expressed mathematically as
T
Input
-
Output
Running difference
Input
Output
1
Figure 11
...
The high-pass filtering takes place when any sudden changes of sign of the samples get
amplified as a result of taking the difference
...
Thus, only the high frequency component appears
a t the output
...
241
Finite Impulse Response (FIR] Filters
Digital filters are linear systems
...
If the impulse response has a finite number of terms then the filter is
known as the finite impulse response filter
...
14 shows the block diagram of a
digital filter with finite impulse response
...
+ a,x,-,
Figure 11
...
t
The filter generates the output samples by forming a weighted sum of the input
sample and a limited number of previous input samples
...
Thus, the output of an FIR filter of length m
is given by performing the convolution of the incoming sequence of samples with the
impulse response of the filter
...
The frequency response of the above filter is given by
",
+ 1)number of
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 frequency response of a digital filter is a periodic function with a period equal
to 2 d A t
2
...
, a,) of the digital filter
...
6
...
+ a,
(11
...
The coefficients ao,
...
The coefficients bo,
...
15 shows a canonical implementation of the digital filter with infinite impulse
response (IIR)
...
k---- m number of past inputs ----4
Present output
k-----k number of past outputs
y, = aoxn + a , x , - , + a2x,_, +
...
+ bky0-k
Figure 11
...
The output at the nth sampling instant is given by
yn = sox,
+ alx,_l +
...
+ b
k
(11
...
~
,
Note that the output at any sampling instant is a function of 13 number of past inputs
and k number of past outputs
...
The transfer function of the filter in the -7-domain is given by
iI
!
i
I
I
1
I
I
'
i
A recursive digital filter is stable if the output of the filter is a non-increasing
sequence, i
...
for n tending to infinity yn should not exceed some positive number M,
irrespective of the choice of initial conditions
...
6
...
...
Therefore, non-recursive
...
Always stable since there is no
feedback
...
Transfer function has only the numerator
terms
...
Has linear phase response
...
+ a,x,_,
Y(z) n,zm + a , t m - 1 + a2zm-2+
...
-=
...
Therefore ,
recursive
...
Because of feedback, possibility of
instability exists
...
Transfer function has both the numerator
and denominator terms
...
Has nonlinear phase response
...
+
+ blyn-1 + b2yn-2 +
...
+ a,
...
- bkZ-k
X(z)
Not as simple as the FIR filter
...
7 Numerical Over-current Protection
Numerical over-current protection is a straightforward application of the numerical 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
...
Full cycle window Fourier transform may be used for this purpose as it
214 Fundamentals of Power System Protection
effectively filters out the dc offset
...
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
...
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
...
This signal will be suitably
processed to make it compatible with the trip coil of the circuit breaker
...
16
...
DTOC, IDMT inverse
...
I
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~ute look-UD time delay T,
or
...
16 Flowchart for a numerical over-current relay algorithm
...
8 Numerical Transformer Differential Protection
Figure 11
...
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
...
The above is a description of the simple differential scheme
...
Therefore, the
numerical relay algorithm should be made to implement the percentage differential relay
...
Transformer
,
,
V
IP
1s
current to
voltage
converter
I
Current to
voltage converter
Vq
a
'P
7f
V,
-+
a
I
Trip
% B~asB
Min pick-up I,,
Restrain
T~me
setting
Tap
setting
Figure 11
...
Read i, samples -t Estimate phasor I, using any technique
...
Compute spill current Ispill I, - Is
...
= (1,
If Ispill (BIcirculating Ipu)
>
+
then trip, else restrain
...
9
11
...
1
Numerical Distance Protection of Transmission Line
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
...
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:
eu =
tan
-1
a
(a)
O U
The phase angle between the relay voltage and relay current will be given by
e = e,
(,
I
- e,
(11
...
However, t h e same can be adapted
for numerical relaying by substituting sample values instead of instantaneous values and
numerically computed derivatives instead of continuous derivatives
...
(11
...
In other words, the phasors for voltage and current can be estimated
...
The algorithms appear to be very attractive because of their simplicity
...
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
...
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
...
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
...
If the counter does not reach the threshold, it is reset to zero
after a predetermined time-out
...
11
...
2
Differential Equation Method
In this method, the faulted line is modelled as a lumped series R-L circuit
...
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
...
Application to single-phase transmission line
Consider a single-phase transmission line fed from one end
...
The transmission line can be modelled as
a series R-L circuit
...
18
...
18 Faulted transmission line modelled by lumped series R-L circuit
...
For the looil)
formed by the equivalent circuit of the faulted line, using KVL, we can write
Though Eq
...
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
...
Writing Eq
...
62) for two different sampling
instants n and n + 1 as shown in Figure 11
...
l t Sampling T T T T I t t t t
t t t Instants
,
...
19 Numbering of samples of voltage and current for differential equation algorithm
...
19, we can easily see that the numerical derivative of the current at
instants n and n + 1 is
)
I
w h r e d l is the sampling interval
...
(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
...
If the fault is a metallic fault, the estimated
values will converge on to a stable value
...
However, in practice,
the power transmission lines are always three-phase in nature
...
Consider the model of the three-phase transmission line%hown in
Figure 11
...
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
...
20 Model of three-phase lme
...
75)
, ,
:
If the line is assumed to be ideally transposed, we have
La = Lb = LC = L,
(11
...
78)
where
Rs, Ls are the series resistance and self-inductance per unit length of each phase
LM is the mutual inductance per unit length between any two phases
...
(11
...
78) into Eqs
...
73) to (11
...
82)
Lo = Ls + 2LM
R1 = Rs
(11
...
84)
and
I
io =
i, + ib +
3
L,
(11
...
By combining Eqs
...
79) to (11
...
(11
...
851, we obtain
Equations (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
...
Assume a metallic single-phase to ground fault on phase
a at a distance r from the relay location
...
(11
...
73) for untransposed lines and
Eqs
...
79) to (11
...
Using the instantaneous values of the voltages, currents and the rate of&hange of
currents, the voltage u, can be obtained by using Eqs
...
72) to (11
...
89)
or
u, =
where
xR,i, + rL,- di,
dt
=
1Y
=
ia + [%)ib
+
9
I
...
90)
(11
...
(11
...
(11
...
81) can be used to obtain the following relationship:
where
and
N~rrnericnl
Protection
'753
Phase-to-phase a n d three-phase faults
...
96) can be reduced to the more compact form as
u,
-
ub = xR,i,
diY
+ x (La-Lab)-
where
dt
(11
...
(11
...
In Eq
...
102), all the terms except R and L, are either the measured samples or the
quantities easily computed from the samples
...
One of the methods, which
involves computing the numerical derivatives has already been described in
Section 11
...
2
...
Integration, being an inherently low-pass operation, yields better results in
the presence of higher frequency components present in the voltage and current
waveforms
...
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
...
For example, the solution
f
254 Fundanaentals o Power Svsteln Protection
of a differential equation is in time domain whereas the Fourier algorithm is in frequency
domain
...
Underlying every algorithm, is a set of assumptions
...
The effectiveness of an algorithm depends
on how far, in practice, the assumptions on which it is basrd, are close to reality
...
Review Questions
1 Trace the evolution of protective relays
...
2
...
What paradigm shift can be seen with the development of numerical relays?
4
...
What do you mean by aliasing?
6
...
7 What happens if the sampling frequency is less than the Nyquist limit?
...
9 Is sample and hold circuit an absolute must?
...
A 12-bit ADC has conversion time of 10 microseconds
...
If a sample and hold circuit of 100 picoseconds is available, how will the & x i m u m
frequency found out in Question 10 be affected?
12
...
1
...
Clearly state the underlying assumptions
...
What do you mean by Fourier analysis? Explain
...
How does Fourier transform differ from conventional Fourier analysis?
5
16
...
What are the advantages and disadvantages of a half cycle window?
7
1
...
8
1
...
9
2
...
0
2
...
22
...
Explain
...
Discuss the methods to find numerical differentiation and numerical integration
...
How can certain frequencies be filtered out in solving the differential equation by
4
integration?
0
Appendix A
A
...
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
...
(
...
>,
...
Step down the current and voltage to standard values of 1A, 5 A, 110 V so that
the design of relays can be standardized irrespective of the actual primary voltage
and current
...
I
(
I
i
...
!
,
...
,
:,' ,
...
2
C Construction
T
1
CTs can be constructed as two-winding transformers with independent primary and
secondary windings
...
I n such CTs, the secondary winding
can be conveniently put inside the high voltage bushings
...
A
...
However, the desired response from
measurement CTs under short-circuit conditions (when the primary current is high) is
quite different
...
A
255
256
and PT Errors
Appendix A-CT
measurement CT, on the other hand, is designed to saturate at currents more than
around 1
...
By suitable design, the operating point of the measurement CT is kept near the knee
of the excitation characteristic
...
1)
...
5lk",
1k"ee
Magnetizing current
P
Protective CT output
LL
2
1
Slope = IICT ratio
Metering CT output
-1
I
~
Full
I load l
;current
,
I
~
&-
I
~
I
~
I
~
I
~
I
S
I
y
~
I
~
,
~
I
~
I
~
l
Primary current (rms)
Maximum fault current = 20 to
30 times the full-load wrrent
Figure A
...
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
...
4
A
...
1
Steady State Ratio and Phase Angle Errors
Current Transformer
Figure A
...
The
equivalent circuit of the CT is shown in Figure A
...
The corresponding phasor diagram
is shown in Figure A
...
-
!
I
CC: Currenl: mil of relay
...
tr,ar
I
'
,,~
...
,
...
,,c
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
Ideal CT
I
I
I
I
I
I
I
I
I
I
I
255
258
8'
h
Appertdix A-C7
and PT Errors
The ratio error which is defined as
Ratio error =
is approximately given by
/
Actual ratio - Ideal ratio
Ideal ratio
-
Ratio error
I
as shown in Figure A
...
1
s 2
nz,
1
I
I
Primary current, lp = nls
t le
R =n t
1,
Actual ratio
a
Figure A
...
F
E
i
+
i
1
The phase angle error is defined as the angular difference between the secondary
current phasor reversed and the primary current phasor
...
As shown in Figure A
...
\
h~
n1s
=0
F Flux (#)
b
15
Figure A 4 Approximate method of expressing phase angle error
...
Aooendix A-CT
A
...
2
~ n PT Errors
d
239
Potential Transformer
Fotential zransformers are mucn like power transformers operating on very light load
...
Conventional two-winding, electromagnetic iype
2
...
5(a)
and A
...
Burden
I
I
I
I
I
Figure A
...
I
y = Phase angle error
6 = Phase angle of burden
n = Turns ratio
I, = Magnetizing component
I, = Iron loss component
,
,
,
1,
= Excitation
= Prtmary current
Secondary current
Primary induced voltage
Primary terminal voltage
Secondary induced voltage
Vs = Secondary terminal voltage
I,
+ Flux
(0)
I, =
Ep =
V =
,
E =
,
Figure A
...
260 Append~sA-CT
and PT Errors
Figure A
...
OA =
OB =
OC =
Pnmary voltage
Secondary voltage (Ideal)
Secondary voltage (Actual)
-
Ratio error
O8
- Oc
OB
w
...
5(c) Ratio and phase angle errors of electromagnetic PT
...
6(a)
...
Hence, a tuning coil is
used so that it resonates with the equivalent capacitance seen looking into the capacitor
potential divider
...
-
...
6(a) Capacitive voltage transformer
...
6(b) and is equal to the LC series circuit, where C is the parallel
combination of C, and Cz
...
and PT Errors
261
(50 Hz or 60 Hz), there - d l be no voltage drop across che LC circuit
...
cz >> C1
XL is designed such that:
Since Xm << Xc,
lXLl
IXczl
Figure A
...
A
...
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
...
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
...
(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 a t the
the secondary excitation voltage will be
or
where
e,, = ImRt sin
[
...
7(c)]
[This is shown in Figure A
...
As we know
Solving the above integral, we have
ddc
=
-
- [-Te-6/~]'
InRtT
Ns
-
[1 -
0
e-6'T
]
[This is depicted in Figure ~ : i ( b ) ]
-~
...
-,-
,
...
,
...
Appendix A-CT
'
h
...
, ,,
...
...
-,
...
,
,
...
...
i
i
3
Time
(a) Voltage required to force dc component through secondary resistance
I, Rl L
G
J
...
7 Transient response of CT
...
From
1
Ns
$ = -Je,dt
I R
(-sin ot)
[This is shown in Figure A
...
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
...
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
...
This saves
us from the expense of over-sized CTs
...
6
Transient Errors in CVT
Ideally, the low voltage applied to the protective relays should be an exact replica of the
primary system voltage
...
rrors 365
variations because of inductive, capacitive, and nonlinear elements in the device
...
A subsidence transient occurs following a fault
and as a result of a fault
...
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
...
The apparent
impedance to a relay may include errors in both magnitude and phase angle
...
8 shows the manner in which the secondary voltage may collapse in
response to a sudden reduction to zero in primaxy voltage
...
8 Transient response of CVT
...
7
Saturation of CT
Figure A
...
As the primary
current goes on increasing, the secondary current tends to increase proportionately
...
This necessitates the establishment of a
proportionately large magnitude of flux given by
where f is the frequency and N the number of turns
...
l, the magnetizing current requirement becomes disproportionately large
...
However, because of the nonlinear characteristics the magnetizing current becomes vexy
large with peaky waveform
...
9 Equivalent circuit of CT
...
Thus, the CT cannot deliver
any current to the load
...
The drop in rms value of secondary current as a function of primary
current is also shown in Figure A
...
The actual output waveform of saturated CT is shown in Chapter 5 on busbar
protection
...
The extreme case of increase in
burden impedance happens if the burden gets open circuited while the primary is carrying
current
...
The increased iron
--
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 flux ill it and will therefore give excessive raiio and phase
angle errors
...
8
CT Accuracy Classification
The following table lists the CT accuracy classification
...
1
e
Introduction
In an interconnected power system, Under steady state conditions, all the generators run
in synchronism
...
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
...
Because of the inertia of_the rotating
system and their dynamics, the rotors slowly reach their new angular positions in an
oscillatory manner
...
subsequent to some large disturbance is known as dower swing
...
B
...
l(a) shows a simple transmission system
...
l(b) and ( ) Since the Power input to the generator remains the same
c
...
2(b)
...
2(c)
...
Since there is no intersection between the power transfer curve with one line out
and the power input line, the rotor angle 6 keeps increasing without bounds
...
?(c) shows the variation of 6 m t h respect to time for stable and unstable power
swing
?re-iault
p")
/\
X
I
1
= XlX
, ,
8niriar =
E2
-sin 6,
XI1
(a)
V
/\
\/
A
A
(b)
I,'
I
,
'
,
Post-fault
V
El 1 a,
\
...
l Power transfer on a parallel line-pre-fault
7
and post-fault
...
2(a) Situation leading to stable power swing
7
'1
270 Appendix B-Power
Swing
-
...
A
...
2(b) Situation leading to unstable power swing
...
2(c) Variation of 6 with respect to time for stable and unstable pswer swing
...
8 3 Impedance Seen by Relay During Power Swing
...
3(a) shows a simple interconnected system for detailed analysis of the power
swing phenomenon
...
Generator A is exporting power, hence its rotor angle 6 is positive
...
Voltage and current at the relay location can be written as
where
ZT= ZSA + ZL+ Z B
s
Figure B
...
We can rearrange the preceding equations in terms of impedances alone, by dividing by
I,, i
...
EBLO - E A L 6
=0
2, +
1,
1,
and
f
(
...
3(b)
...
3(b) Power swing locus construction
...
In the above analysis, it was assumed that ( E A = ( E B for simplicity
...
Figure B
...
3(c) Locus of power swing when IEA l/lEBI = n
...
As the rotor angle 6 goes on increasing, the apparent Impedance approaches the
electrical centre of the system
...
Therefore, the protective relay should not trip on
stable power swings This type of scheme is known as out-of-step blocking scheme
...
The point of split in a large interconnected system should be decided
in advance through system stability studies so that the separated systems have the
balance between generation and load
...
B
...
Further, the location of the locus of power swing depends upon the source and line
+
Although the line impedance
impedances (perpendicular bisector of ZT = ZSA ZL+ ZSB)
...
Thus, the location of power swing cannot be precisely predetermined
...
!
,
The power swi~lg assumed to be in the trip region of zone I, thereby causing the
is
relay to crip and possibIy split the system at the wrong place
...
4(a)
...
Let the power swing enter
the blocking relay at t = 0
...
The whole distance
< Te
...
Thus, Tblocklng The
trip contact circuit of the three-stepped distance scheme along with the contacts of the
blocking relay are shown in Figure B
...
At A,
At B,
At C,
power swing enters the blocking relay at t = 0
the distance scheme 1 completely blocked ( t < T,)
s
power swing enters zone I ( t = T,)
Figure B
...
4(b) Out-of-step blocking logic
...
Consider an internal line fault
...
blocking relay does see this change in impedance
to
The
274
Append~x B-Power
s
Swing
but by the time it blocks the distance scheme, the distance scheme has already operated
...
The power
swing is a pretty slow phenomenon compared to short-circuit faults
...
5
1
I
I
Out-of-step Tripping Scheme
As already pointed, we must isolate the system at certain points in case of out-of-step
conditions
...
For this reason, the power swing whose location is variable, is assumed
to be outside zone I as shown in Figure B
...
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 blinders split the R-X diagram into three distinct areas Al, A2, and
As
...
When there is an external fault, the impedance phasor crosses only one blinder and
the sequencing required for tripping is never completed
...
...
Bz
PJ
+ P2 -+ pl
Tr~p
then trip
1; if blinder trips
0; if blinder restrains
Mot~on power swing
of
Area
Area
Area
Area
A1
A3
A,
A
3
-+ A
,
-+ A
,
-+ A
,
-+ A
,
+ A3 : Trip circuit breaker
-+ A, : Trip circuit breaker
: External fault
: External fault
5
4
3
Appendix C
1
Protection of Largest
an3 ~bortest i n e s
~
Distance relays have certain drawbacks which need to be carefully considered while
applying them in practical situations
...
In this
appendix, we will therefore study the effect of source impedance ratio on the performance
of distance relays
...
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
...
e
...
,
It is well known that a long line is less stable than a short line
...
l(a) shows
the power angle diagram for long and short llnes
...
For a given mechanical input P,, the quiescent operating angle for a
long line is more than that of a short line, i
...
&,long
f
>
&,short
Therefore, for a disturbance that does not cause instability, the longer line goes through
a larger swing angle than does a shorter line
...
e
...
,
,
,
swing, can be accommodated by the relay without malfunctioning
...
Zs is the source impedance or the
impedance behind the relay location and ZL is the line impedance
...
short line + Zs/ZL = large
-
dI
i
Simnplifiing assumption
ZS = 0
Zs = finite
Figures C
...
I t can be easily seen that the & that the mho relay can
accommodate without maloperation
...
This is exactly opposite of what is needed
...
Hence, there is a limitation to the
longest line a relay can protect without maloperation on a stable power swing
...
anon line
' &,shot
...
l(a) Quiescent operating points for long and short lines
...
l(b) Power angle accommodation in long line
...
r C-Pr0rec:ion
of Longesr and Sliortast Lines
777
*-------------700%
ZL
...
...
3
Shortest Line That Can Be Protected
Figure C
...
The distance relay is
energized by Vrand I,
...
If the fault takes place a t the reach point, the relay voltage drops
to a value which is a function of Zs/Z,,
...
8ZL
...
Thus, the shorter the line, the
smaller is the voltage Vrfed to the relay
...
However, in
practice, it is not true
...
To find the effect of voltage on the rnho relay's reach, consider the torque equation
for a rnho relay:
If
/ Zn I I Vl ( I1
cos (8,
-
8,) > I V
1
then trip; else restrain
Considering the restraining spring, the equation is
If
1 , I 1 VI 1 cos (8, - 8,) > I VI
2
1
1
+
T,p,,ng then trip; else restrain
Dividing both sides by I VI 111, we have
lZnlc0s(Gn- 8,) > IZI
+- Tspring
IVI II
I
Substituting 1 ) = I VlIlZI, we get
1
To find the reach along the diameter, i
...
with 8, = Or, we get
which can be written as
IZI <
lznl
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
...
2(b) shows the reach versus voltage characteristic of the rnho relay
...
2"
under-reach
A
2"
Rated voltage
,
= 110 v
'v,
I , \
I
I+ Relay operating range 4
Figure C
...
The rench versus relay yoltage characteristic is not very convenie~t use
...
To make the actual
e
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
Vr =
1 + SIR
Z , have
, we
E
Thus, instead of plotting reach versus relay voltage, we plot accuracy versus range
...
For a large system impedance ratio or range,
V, < < E
...
2(c) shows the graph of Figure C
...
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
...
9 (i
...
the actual
reach not less than 90% of reach setting) then there is limit to the shortest line that a
distance relay can protect
...
o
-terms
Operating range in
of SIR (z~z,)-
SIR = 0
Z, = O
v =E=
r
'SIR = Maximum
Z, = Finite
Vrated
Figure C
...
N
...
I
!
Electricity Training Association, Power System Protection, Vol
...
F IEE,
(
Elmore, WA
...
,
New York
...
!
I
I
I
'*
I
i
I
Gonowsky, I
...
, Radio Circuits and Signals, Mir Publishers, Moscow
...
, New York
...
T
...
K
...
Kimbark, E
...
11, Power Circuit Breakers and Protective
Relays, John Wiley and Sons, New York
...
, New York
...
S
...
I
1
I
1
I
!
i
!
Mason, C
...
, The Art and Science of Protective Relaying, John Wiley and Sons, New York
...
G
...
, New York
...
K
...
Choudhary, Power System Protection, Oxford and IBH
Publishing Co
...
Stanley H
...
Van C
...
R
...
I and 11,
Chapman and Hall, London
...
M
...
IEE, 117, 1970, p
...
Cordray, R
...
and A
...
Van C
...
A
...
E
...
, 63, 1944, p
...
Gilcrest, G
...
, G
...
Rockefeller and E
...
Udren, High speed distance relaying using a
digital computer part I-system description, Trans
...
1235,
Part 11-Test results, ibid, p
...
Hamilton, F
...
and J
...
Patrickson, Application of transistor techniques to relays and
protection for power systems, Proc
...
213
...
L
...
S
...
Horton, J
...
582-587
...
and M
...
Kandil, Discriminative performance of distance protection under
fault operating conditions, Proc
...
141
...
M
...
A
...
E
...
, 65, 1945, pp
...
Ingloe, VT
...
Paithankar, New technique for quadrilateral distance relay, Proc
...
464
...
and WJ
...
3358-3359
...
T
...
A
...
IEE, 125, 1978, pp
...
Khincha, H
...
Parthasarthy, B
...
Ashok Kumar, and C
...
Arun, New possibilities in
amplitude comparison techniques in distance relays, Proc
...
2133
...
and L
...
Tippett, Fundamental basis for distance relaying on three phase
systems, Trans
...
I
...
E
...
694-708
...
and C
...
W Lackey, Protection of electrical power systems-a critical review#
...
IEE, 98, Part 11, 1951, p
...
Maclaren, EG
...
IEE, 115, 1968, p
...
Maclaren, F!G
...
A
...
IEE, 122, 1975, pp
...
~ a c l & e n PG
...
A
...
IEE, 122, 1975, p
...
Macpherson, R
...
, A
...
Van C
...
J
...
A
...
E
...
, 67, Part 111, 1948, pp
...
Mann, B
...
and I
...
Morrison, Digital calculation of impedance for transmission line
protection, Trans
...
270
...
D
...
of IEEE, PAS N o
...
165
...
D
...
of IEE, 110, 1963,
p
...
McInnes, A
...
and 1
...
Eng
...
Inst
...
,
-4ustralia, 197, EE7, pp
...
Nellist, B
...
and El Mathews, The design of air cored toroids or linear couplers,
I
...
E
...
Paithankar, Y
...
, Improved version of zener diode phase detection relay, Proc
...
821
...
G
...
1703
...
G
...
U
...
IEE, 119, 1972, p
...
Paithankar, Y
...
and M
...
Deshpande, Improved pulse forming circuit for protective
relays, ibid, p
...
Parthasarthy, K
...
IEEE, 31, CP 66, 181, 1966
...
G
...
Hibika, and M
...
Ibrahim, A digital computer system for EHV
substations: analysis and field tests, IEEE Trans
...
291-301
...
A
...
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Ranjabar, A
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, 1969, PAS-88,
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, The application of the ohm and mho principles to protective
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IEE, 112, 1965, p
...
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
...
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
characteristics of, 48
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
Deionization times, 153
Digital filter, 239
...
234
Distance measuring units, 142, 144
Duality between comparators, 201
Acceleration (of carrier), 159, 160, 161
Accuracy vs range graph, 280
Algorithms for digital protection, 253
Arc resistance, 3
Auto-reclosure, 154
Balanced beam structure, 124
Blinders, 138
Blocking
arrangement, out of step, 273
carrier, 162
logic, out-of-step, 273
scheme, out-of-step, 272
Busbars
differential protection of, 102, 112
high impedance scheme, 112, 114, 115
external and internal faults, 104, 108, 110
Excitation
loss of, 179
Excitation characteristic of CT, 256
Carrier signal, 155
acceleration, 160, 161
coupling
line-to-line, 157, 158
single line-to-ground, 157
distance relaying, 159, 160
preacceleration, 161, 162
protection, 153
for relaying, 156, 157
directional protection, 157, 158, 159
unit schemes, 162
Circuit breaker, 17
trip circuit, 17, 18
Coincidence
period, 164, 165, 167, 210
principle, 213, 215
Comparator
amplitude, 196, 198, 201, 210, 211
phase, 199, 201, 206
cosine-type 199, 200, 205, 206, 208, 210,
212, 213
sine-type, 200, 216, 217, 218
Fault(s1, 1
external, 18, 60
forward and reverse, 47
ground, 5, 6, 42, 142
incipient, 93
internal, 18
metallic, 3, 6
phase, 5, 6, 42, 151
probability of, 5
resistance, 3
series, 7
short-circuit, 8
single line-to-ground, 2
statistics, 5
through, 18, 60, 63, 64, 67, 69
stability, 64
stability ratio, 64, 70
in transformers, 78, 91, 93
internal and external, 96
Fault detector unit, 147
Flashover, 2 3
,
Fourier analysis, 229, 231, 236
Fuse, 26
characteristics of, 27
Ground fault units, 144
Grounding resistance, 171
Grounding transformer, 170, 171
285
t
numencal, 222
block diagram, 223
development cycle, 223
differential equation algorithm, 249
distance protection of transmission line,
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
tr~p
region, 69
pick-up value, 35, 37
quadrilateral distance
synthes~s 218
of,
reach, 18, 118, 119, 145
reactance, 129, 130
characteristics of, 130
directional property of, 133
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
interval, 37
selective t ~ m e
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
directional, i 9
distance, 23, 55, 120
over-current, 23
phase comparison, 162, 163, 164, 165
Xotor angle, 4
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~on
characteristic, 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