Protection

Relay hardware is becoming even more standardised, to the point atwhich versions of a relay may differ only by the software they contain.

This accurate prediction in the preface to the Third Edition of the ProtectiveRelay Application Guide (PRAG), 1987, has been followed by the rapiddevelopment of integrated protection and control devices. The change intechnology, together with significant changes in Utility, Industrial andCommercial organisations, has resulted in new emphasis on Secondary SystemsEngineering.

In addition to the traditional role of protection & control, secondary systemsare now required to provide true added value to organisations.

When utilised to its maximum, not only can the integration of protection &control functionality deliver the required reduction in life-time cost of capital,but the advanced features available (Quality of Supply, disturbance recordingand plant monitoring) enable system and plant performance to be improved,increasing system availability.

The evolution of all secondary connected devices to form digital controlsystems continues to greatly increase access to all information available withinthe substation, resulting in new methodologies for asset management.

In order to provide the modern practising substation engineer with referencematerial, the Network Protection & Automation Guide provides a substantiallyrevised and expanded edition of PRAG incorporating new chapters on all levelsof network automation. The first part of the book deals with the fundamentals,basic technology, fault calculations and the models of power system plant,including the transient response and saturation problems that affectinstrument transformers.

The typical data provided on power system plant has been updated andsignificantly expanded following research that showed its popularity.

The book then provides detailed analysis on the application of protectionsystems. This includes a new Chapter on the protection of a.c. electrifiedrailways. Existing chapters on distance, busbar and generator protection havebeen completely revised to take account of new developments, includingimprovements due to numerical protection techniques and the applicationproblems of embedded generation. The Chapter on relay testing andcommissioning has been completely updated to reflect modern techniques.Finally, new Chapters covering the fields of power system measurements,power quality, and substation and distribution automation are found, to reflectthe importance of these fields for the modern Power System Engineer.

The intention is to make NPAG the standard reference work in its subject area- while still helping the student and young engineer new to the field. We trustthat you find this book invaluable and assure you that any comments will becarefully noted ready for the next edition.

1 Int roduct ion

N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 3

Chapt1-2-3 18/06/02 17:34 Page 3

Introduction 2.1

Protection equipment 2.2

Zones of protection 2.3

Reliability 2.4

Selectivity 2.5

Stability 2.6

Speed 2.7

Sensitivity 2.8

Primary and back-up protection 2.9

Relay output devices 2.10

Relay tripping circuits 2.11

Trip circuit supervision 2.12

2 F u n d a m e n t a l so f P r o t e c t i o n P r a c t i c e

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2.1 INTRODUCTION

The purpose of an electrical power system is to generateand supply electrical energy to consumers. The systemshould be designed and managed to deliver this energyto the utilisation points with both reliability andeconomy. Severe disruption to the normal routine ofmodern society is likely if power outages are frequent orprolonged, placing an increasing emphasis on reliabilityand security of supply. As the requirements of reliabilityand economy are largely opposed, power system designis inevitably a compromise.

A power system comprises many diverse items ofequipment. Figure 2.2 shows a hypothetical powersystem; this and Figure 2.1 illustrates the diversity ofequipment that is found.

2 Fundamentalso f P ro te c t i o n P ra c t i c e

Figure 2.1: Modern power station

Chap2-4-15 21/06/02 10:42 Page 5

N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e

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Figur

e 2.Figure 2.2: Example power system

R1 R2

G1 G2

T1 T2T

R3 R4

G3 G4

T10 T11

T14

T16 T17

T15

T12 T13

R5 R6

G5 G6

T7 T8T

R7

G7

T9T

T5T T6T T3T T4T

L2

L3 L4

L1A

L7A

L5

L6

L8

L7B

L1B

A380kV

380kV380kV

110kV

Hydro power station

BC

B'33kVC'

380kV

CCGT power station

ED220kV

Steam power station

Gridsubstation

F

33kV D' 110kV

380kV

G'

G

Grid380kV F'

Chap2-4-15 21/06/02 10:42 Page 6


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Many items of equipment are very expensive, and so thecomplete power system represents a very large capitalinvestment. To maximise the return on this outlay, thesystem must be utilised as much as possible within theapplicable constraints of security and reliability ofsupply. More fundamental, however, is that the powersystem should operate in a safe manner at all times. Nomatter how well designed, faults will always occur on apower system, and these faults may represent a risk tolife and/or property. Figure 2.3 shows the onset of a faulton an overhead line. The destructive power of a fault arccarrying a high current is very great; it can burn throughcopper conductors or weld together core laminations ina transformer or machine in a very short time sometens or hundreds of milliseconds. Even away from thefault arc itself, heavy fault currents can cause damage toplant if they continue for more than a few seconds. Theprovision of adequate protection to detect anddisconnect elements of the power system in the event offault is therefore an integral part of power systemdesign. Only by so doing can the objectives of the powersystem be met and the investment protected. Figure 2.4provides an illustration of the consequences of failure toprovide appropriate protection.

This is the measure of the importance of protectionsystems as applied in power system practice and of theresponsibility vested in the Protection Engineer.

2.2 PROTECTION EQUIPMENT

The definitions that follow are generally used in relationto power system protection:

a. Protection System: a complete arrangement ofprotection equipment and other devices required toachieve a specified function based on a protectionprincipal (IEC 60255-20)

b. Protection Equipment: a collection of protectiondevices (relays, fuses, etc.). Excluded are devicessuch as CTs, CBs, Contactors, etc.

c. Protection Scheme: a collection of protectionequipment providing a defined function andincluding all equipment required to make thescheme work (i.e. relays, CTs, CBs, batteries, etc.)

In order to fulfil the requirements of protection with theoptimum speed for the many different configurations,operating conditions and construction features of powersystems, it has been necessary to develop many types ofrelay that respond to various functions of the powersystem quantities. For example, observation simply ofthe magnitude of the fault current suffices in some casesbut measurement of power or impedance may benecessary in others. Relays frequently measure complexfunctions of the system quantities, which are only readilyexpressible by mathematical or graphical means.

Relays may be classified according to the technologyused:

a. electromechanical

b. static

c. digital

d. numerical

The different types have somewhat different capabilities,due to the limitations of the technology used. They aredescribed in more detail in Chapter 7.

Figure 2.3: Onset of an overhead line fault

Figure 2.4: Possible consequence of inadequate protection

Chap2-4-15 21/06/02 10:42 Page 7


In many cases, it is not feasible to protect against allhazards with a relay that responds to a single powersystem quantity. An arrangement using severalquantities may be required. In this case, either severalrelays, each responding to a single quantity, or, morecommonly, a single relay containing several elements,each responding independently to a different quantitymay be used.

The terminology used in describing protection systemsand relays is given in Appendix 1. Different symbols fordescribing relay functions in diagrams of protectionschemes are used, the two most common methods (IECand IEEE/ANSI) are provided in Appendix 2.

2.3 ZONES OF PROTECTION

To limit the extent of the power system that isdisconnected when a fault occurs, protection is arrangedin zones. The principle is shown in Figure 2.5. Ideally, thezones of protection should overlap, so that no part of thepower system is left unprotected. This is shown in Figure2.6(a), the circuit breaker being included in both zones.

Figure 2.52.6

For practical physical and economic reasons, this ideal isnot always achieved, accommodation for currenttransformers being in some cases available only on oneside of the circuit breakers, as in Figure 2.6(b). Thisleaves a section between the current transformers and

the circuit breaker A that is not completely protectedagainst faults. In Figure 2.6(b) a fault at F would causethe busbar protection to operate and open the circuitbreaker but the fault may continue to be fed through thefeeder. The feeder protection, if of the unit type (seesection 2.5.2), would not operate, since the fault isoutside its zone. This problem is dealt with byintertripping or some form of zone extension, to ensurethat the remote end of the feeder is tripped also.

The point of connection of the protection with the powersystem usually defines the zone and corresponds to thelocation of the current transformers. Unit typeprotection will result in the boundary being a clearlydefined closed loop. Figure 2.7 illustrates a typicalarrangement of overlapping zones.

Figure 2.7

Alternatively, the zone may be unrestricted; the start willbe defined but the extent (or reach) will depend onmeasurement of the system quantities and will thereforebe subject to variation, owing to changes in systemconditions and measurement errors.

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Figure 2.7: Overlapping zonesof protection systems

~

~Figure 2.5: Division of power system

into protection zones

Feeder 2Feeder 1 Feeder 3Zone 6

Zone 5 Zone 7

Zone 4

Zone 3

Zone 2

Zone 1

AA

FF

Feederedprotection

Feederedprotection

Busbarprotectionec

Busbarprotectione

(a) CT's on both sides of circuit breaker

(b) CT's on circuit side of circuit breaker

Figure 2.6: CT Locations

Chap2-4-15 21/06/02 10:42 Page 8


2.4 RELIABIL ITY

The need for a high degree of reliability is discussed inSection 2.1. Incorrect operation can be attributed to oneof the following classifications:

a. incorrect design/settings

b. incorrect installation/testing

c. deterioration in service

2.4.1 Design

The design of a protection scheme is of paramountimportance. This is to ensure that the system willoperate under all required conditions, and (equallyimportant) refrain from operating when so required(including, where appropriate, being restrained fromoperating for faults external to the zone beingprotected). Due consideration must be given to thenature, frequency and duration of faults likely to beexperienced, all relevant parameters of the power system(including the characteristics of the supply source, andmethods of operation) and the type of protectionequipment used. Of course, no amount of effort at thisstage can make up for the use of protection equipmentthat has not itself been subject to proper design.

2.4.2 Settings

It is essential to ensure that settings are chosen forprotection relays and systems which take into accountthe parameters of the primary system, including faultand load levels, and dynamic performance requirementsetc. The characteristics of power systems change withtime, due to changes in loads, location, type and amountof generation, etc. Therefore, setting values of relaysmay need to be checked at suitable intervals to ensurethat they are still appropriate. Otherwise, unwantedoperation or failure to operate when required may occur.

2.4.3 Installation

The need for correct installation of protection systems isobvious, but the complexity of the interconnections ofmany systems and their relationship to the remainder ofthe installation may make checking difficult. Site testingis therefore necessary; since it will be difficult toreproduce all fault conditions correctly, these tests mustbe directed to proving the installation. The tests shouldbe limited to such simple and direct tests as will provethe correctness of the connections, relay settings, andfreedom from damage of the equipment. No attemptshould be made to 'type test' the equipment or toestablish complex aspects of its technical performance.

2.4.4 Testing

Comprehensive testing is just as important, and thistesting should cover all aspects of the protectionscheme, as well as reproducing operational andenvironmental conditions as closely as possible. Typetesting of protection equipment to recognised standardsfulfils many of these requirements, but it may still benecessary to test the complete protection scheme (relays,current transformers and other ancillary items) and thetests must simulate fault conditions realistically.

2.4.5 Deterioration in Service

Subsequent to installation in perfect condition,deterioration of equipment will take place and mayeventually interfere with correct functioning. Forexample, contacts may become rough or burnt owing tofrequent operation, or tarnished owing to atmosphericcontamination; coils and other circuits may becomeopen-circuited, electronic components and auxiliarydevices may fail, and mechanical parts may seize up.

The time between operations of protection relays may beyears rather than days. During this period defects mayhave developed unnoticed until revealed by the failure ofthe protection to respond to a power system fault. Forthis reason, relays should be regularly tested in order tocheck for correct functioning.

Testing should preferably be carried out withoutdisturbing permanent connections. This can be achievedby the provision of test blocks or switches.

The quality of testing personnel is an essential featurewhen assessing reliability and considering means forimprovement. Staff must be technically competent andadequately trained, as well as self-disciplined to proceedin a systematic manner to achieve final acceptance.

Important circuits that are especially vulnerable can beprovided with continuous electrical supervision; sucharrangements are commonly applied to circuit breakertrip circuits and to pilot circuits. Modern digital andnumerical relays usually incorporate self-testing/diagnostic facilities to assist in the detection offailures. With these types of relay, it may be possible toarrange for such failures to be automatically reported bycommunications link to a remote operations centre, sothat appropriate action may be taken to ensurecontinued safe operation of that part of the powersystem and arrangements put in hand for investigationand correction of the fault.

2.4.6 Protection Performance

Protection system performance is frequently assessedstatistically. For this purpose each system fault is classed

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as an incident and only those that are cleared by thetripping of the correct circuit breakers are classed as'correct'. The percentage of correct clearances can thenbe determined.

This principle of assessment gives an accurate evaluationof the protection of the system as a whole, but it issevere in its judgement of relay performance. Manyrelays are called into operation for each system fault,and all must behave correctly for a correct clearance tobe recorded.

Complete reliability is unlikely ever to be achieved byfurther improvements in construction. If the level ofreliability achieved by a single device is not acceptable,improvement can be achieved through redundancy, e.g.duplication of equipment. Two complete, independent,main protection systems are provided, and arranged sothat either by itself can carry out the required function.If the probability of each equipment failing is x/unit, theresultant probability of both equipments failingsimultaneously, allowing for redundancy, is x2. Where xis small the resultant risk (x2) may be negligible.

Where multiple protection systems are used, the trippingsignal can be provided in a number of different ways.The two most common methods are:

a. all protection systems must operate for a trippingoperation to occur (e.g. two-out-of-twoarrangement)

b. only one protection system need operate to causea trip (e.g. one-out-of two arrangement)

The former method guards against maloperation whilethe latter guards against failure to operate due to anunrevealed fault in a protection system. Rarely, threemain protection systems are provided, configured in atwo-out-of three tripping arrangement, to provide bothreliability of tripping, and security against unwantedtripping.

It has long been the practice to apply duplicateprotection systems to busbars, both being required tooperate to complete a tripping operation. Loss of abusbar may cause widespread loss of supply, which isclearly undesirable. In other cases, important circuits areprovided with duplicate main protection systems, eitherbeing able to trip independently. On critical circuits, usemay also be made of a digital fault simulator to modelthe relevant section of the power system and check theperformance of the relays used.

2.5 SELECTIVITY

When a fault occurs, the protection scheme is requiredto trip only those circuit breakers whose operation isrequired to isolate the fault. This property of selectivetripping is also called 'discrimination' and is achieved bytwo general methods.

2.5.1 Time Grading

Protection systems in successive zones are arranged tooperate in times that are graded through the sequence ofequipments so that upon the occurrence of a fault,although a number of protection equipments respond,only those relevant to the faulty zone complete thetripping function. The others make incompleteoperations and then reset. The speed of response willoften depend on the severity of the fault, and willgenerally be slower than for a unit system.

2.5.2 Unit Systems

It is possible to design protection systems that respondonly to fault conditions occurring within a clearlydefined zone. This type of protection system is known as'unit protection'. Certain types of unit protection areknown by specific names, e.g. restricted earth fault anddifferential protection. Unit protection can be appliedthroughout a power system and, since it does not involvetime grading, is relatively fast in operation. The speed ofresponse is substantially independent of fault severity.

Unit protection usually involves comparison of quantitiesat the boundaries of the protected zone as defined by thelocations of the current transformers. This comparisonmay be achieved by direct hard-wired connections ormay be achieved via a communications link. Howevercertain protection systems derive their 'restricted'property from the configuration of the power system andmay be classed as unit protection, e.g. earth faultprotection applied to the high voltage delta winding of apower transformer. Whichever method is used, it mustbe kept in mind that selectivity is not merely a matter ofrelay design. It also depends on the correct co-ordination of current transformers and relays with asuitable choice of relay settings, taking into account thepossible range of such variables as fault currents,maximum load current, system impedances and otherrelated factors, where appropriate.

2.6 STABIL ITY

The term stability is usually associated with unitprotection schemes and refers to the ability of theprotection system to remain unaffected by conditionsexternal to the protected zone, for example through loadcurrent and external fault conditions.

2.7 SPEED

The function of protection systems is to isolate faults onthe power system as rapidly as possible. The mainobjective is to safeguard continuity of supply byremoving each disturbance before it leads to widespreadloss of synchronism and consequent collapse of thepower system.

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N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 1 1

As the loading on a power system increases, the phaseshift between voltages at different busbars on thesystem also increases, and therefore so does theprobability that synchronism will be lost when thesystem is disturbed by a fault. The shorter the time afault is allowed to remain in the system, the greater canbe the loading of the system. Figure 2.8 shows typicalrelations between system loading and fault clearancetimes for various types of fault. It will be noted thatphase faults have a more marked effect on the stabilityof the system than a simple earth fault and thereforerequire faster clearance.

Figure 2.8

System stability is not, however, the only consideration.Rapid operation of protection ensures that fault damageis minimised, as energy liberated during a fault isproportional to the square of the fault current times theduration of the fault. Protection must thus operate asquickly as possible but speed of operation must beweighed against economy. Distribution circuits, whichdo not normally require a fast fault clearance, are usuallyprotected by time-graded systems. Generating plant andEHV systems require protection gear of the highestattainable speed; the only limiting factor will be thenecessity for correct operation, and therefore unitsystems are normal practice.

2.8 SENSIT IV ITY

Sensitivity is a term frequently used when referring tothe minimum operating level (current, voltage, poweretc.) of relays or complete protection schemes. The relayor scheme is said to be sensitive if the primary operatingparameter(s) is low.

With older electromechanical relays, sensitivity wasconsidered in terms of the sensitivity of the measuringmovement and was measured in terms of its volt-ampereconsumption to cause operation. With modern digitaland numerical relays the achievable sensitivity is seldomlimited by the device design but by its application andCT/VT parameters.

2.9 PRIMARY AND BACK-UP PROTECTION

The reliability of a power system has been discussedearlier, including the use of more than one primary (ormain) protection system operating in parallel. In theevent of failure or non-availability of the primaryprotection some other means of ensuring that the faultis isolated must be provided. These secondary systemsare referred to as back-up protection.

Back-up protection may be considered as either beinglocal or remote. Local back-up protection is achievedby protection which detects an un-cleared primarysystem fault at its own location and which then trips itsown circuit breakers, e.g. time graded overcurrent relays.Remote back-up protection is provided by protectionthat detects an un-cleared primary system fault at aremote location and then issues a local trip command,e.g. the second or third zones of a distance relay. In bothcases the main and back-up protection systems detect afault simultaneously, operation of the back-upprotection being delayed to ensure that the primaryprotection clears the fault if possible. Normally beingunit protection, operation of the primary protection willbe fast and will result in the minimum amount of thepower system being disconnected. Operation of theback-up protection will be, of necessity, slower and willresult in a greater proportion of the primary systembeing lost.

The extent and type of back-up protection applied willnaturally be related to the failure risks and relativeeconomic importance of the system. For distributionsystems where fault clearance times are not critical, timedelayed remote back-up protection may be adequate.For EHV systems, where system stability is at risk unlessa fault is cleared quickly, multiple primary protectionsystems, operating in parallel and possibly of differenttypes (e.g. distance and unit protection), will be used toensure fast and reliable tripping. Back-up overcurrentprotection may then optionally be applied to ensure thattwo separate protection systems are available duringmaintenance of one of the primary protection systems.

Back-up protection systems should, ideally, becompletely separate from the primary systems. Forexample a circuit protected by a current differential relaymay also have time graded overcurrent and earth faultrelays added to provide circuit breaker tripping in theevent of failure of the main primary unit protection. Tomaintain complete separation and thus integrity, currenttransformers, voltage transformers, relays, circuit breakertrip coils and d.c. supplies would be duplicated. Thisideal is rarely attained in practice. The followingcompromises are typical:

a. separate current transformers (cores and secondarywindings only) are provided. This involves little extracost or accommodation compared with the use of

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Figure 2.8: Typical power/time relationshipfor various fault types

Time

Load

pow

er

Phase-earth

Phase-phase

Three-phase

Phase-phase-earth

Chap2-4-15 21/06/02 10:45 Page 11


common current transformers that would have to belarger because of the combined burden. This practiceis becoming less common when digital or numericalrelays are used, because of the extremely low inputburden of these relay types

b. voltage transformers are not duplicated because ofcost and space considerations. Each protection relaysupply is separately protected (fuse or MCB) andcontinuously supervised to ensure security of the VToutput. An alarm is given on failure of the supply and,where appropriate, prevent an unwanted operation ofthe protection

c. trip supplies to the two protections should beseparately protected (fuse or MCB). Duplication oftripping batteries and of circuit breaker tripping coilsmay be provided. Trip circuits should be continuouslysupervised

d. it is desirable that the main and back-up protections (orduplicate main protections) should operate on differentprinciples, so that unusual events that may causefailure of the one will be less likely to affect the other

Digital and numerical relays may incorporate suitableback-up protection functions (e.g. a distance relay mayalso incorporate time-delayed overcurrent protectionelements as well). A reduction in the hardware required toprovide back-up protection is obtained, but at the risk thata common relay element failure (e.g. the power supply)will result in simultaneous loss of both main and back-upprotection. The acceptability of this situation must beevaluated on a case-by-case basis.

2.10 RELAY OUTPUT DEVICES

In order to perform their intended function, relays must befitted with some means of providing the various outputsignals required. Contacts of various types usually fulfilthis function.

2.10.1 Contact Systems

Relays may be fitted with a variety of contact systemsfor providing electrical outputs for tripping and remoteindication purposes. The most common typesencountered are as follows:

a. Self-resetThe contacts remain in the operated condition onlywhile the controlling quantity is applied, returningto their original condition when it is removed

b. Hand or electrical resetThese contacts remain in the operated conditionafter the controlling quantity is removed. They canbe reset either by hand or by an auxiliaryelectromagnetic element

The majority of protection relay elements have self-resetcontact systems, which, if so desired, can be modified toprovide hand reset output contacts by the use ofauxiliary elements. Hand or electrically reset relays areused when it is necessary to maintain a signal or lockoutcondition. Contacts are shown on diagrams in theposition corresponding to the un-operated or de-energised condition, regardless of the continuous servicecondition of the equipment. For example, anundervoltage relay, which is continually energised innormal circumstances, would still be shown in the de-energised condition.

A 'make' contact is one that closes when the relay picksup, whereas a 'break' contact is one that is closed whenthe relay is de-energised and opens when the relay picksup. Examples of these conventions and variations areshown in Figure 2.9.

A protection relay is usually required to trip a circuitbreaker, the tripping mechanism of which may be asolenoid with a plunger acting directly on themechanism latch or an electrically operated valve. Thepower required by the trip coil of the circuit breaker mayrange from up to 50 watts for a small 'distribution'circuit breaker, to 3000 watts for a large, extra-high-voltage circuit breaker.

The relay may therefore energise the tripping coildirectly, or, according to the coil rating and the numberof circuits to be energised, may do so through theagency of another multi-contact auxiliary relay.

The basic trip circuit is simple, being made up of a hand-trip control switch and the contacts of the protectionrelays in parallel to energise the trip coil from a battery,through a normally open auxiliary switch operated bythe circuit breaker. This auxiliary switch is needed toopen the trip circuit when the circuit breaker openssince the protection relay contacts will usually be quiteincapable of performing the interrupting duty. Theauxiliary switch will be adjusted to close as early aspossible in the closing stroke, to make the protectioneffective in case the breaker is being closed on to a fault.

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Figure 2.9: Contact types

Self reset

Hand reset

`make' contacts(normally open)

`break' contacts(normally open)

Time delay onpick up

Time delay ondrop-off

Chap2-4-15 21/06/02 10:45 Page 12


Where multiple output contacts, or contacts withappreciable current-carrying capacity are required,interposing, contactor type elements will normally be used.

In general, static and microprocessor relays have discretemeasuring and tripping circuits, or modules. Thefunctioning of the measuring modules is independent ofoperation of the tripping modules. Such a relay isequivalent to a sensitive electromechanical relay with atripping contactor, so that the number or rating ofoutputs has no more significance than the fact that theyhave been provided.

For larger switchgear installations the tripping powerrequirement of each circuit breaker is considerable, andfurther, two or more breakers may have to be tripped byone protection system. There may also be remotesignalling requirements, interlocking with otherfunctions (for example auto-reclosing arrangements),and other control functions to be performed. Thesevarious operations may then be carried out by multi-contact tripping relays, which are energised by theprotection relays and provide the necessary number ofadequately rated output contacts.

2.10.2 Operation Indicators

Protection systems are invariably provided withindicating devices, called 'flags', or 'targets', as a guidefor operations personnel. Not every relay will have one,as indicators are arranged to operate only if a tripoperation is initiated. Indicators, with very fewexceptions, are bi-stable devices, and may be eithermechanical or electrical. A mechanical indicator consistsof a small shutter that is released by the protection relaymovement to expose the indicator pattern.

Electrical indicators may be simple attracted armatureelements, where operation of the armature releases ashutter to expose an indicator as above, or indicatorlights (usually light emitting diodes). For the latter, somekind of memory circuit is provided to ensure that theindicator remains lit after the initiating event has passed.

With the advent of digital and numerical relays, theoperation indicator has almost become redundant.Relays will be provided with one or two simple indicatorsthat indicate that the relay is powered up and whetheran operation has occurred. The remainder of theinformation previously presented via indicators isavailable by interrogating the relay locally via a man-machine interface (e.g. a keypad and liquid crystaldisplay screen), or remotely via a communication system.

2.11 TRIPPING CIRCUITS

There are three main circuits in use for circuit breakertripping:

a. series sealing

b. shunt reinforcing

c. shunt reinforcement with sealing

These are illustrated in Figure 2.10.

For electromechanical relays, electrically operatedindicators, actuated after the main contacts have closed,avoid imposing an additional friction load on themeasuring element, which would be a serious handicapfor certain types. Care must be taken with directlyoperated indicators to line up their operation with theclosure of the main contacts. The indicator must haveoperated by the time the contacts make, but must nothave done so more than marginally earlier. This is to stopindication occurring when the tripping operation has notbeen completed.

With modern digital and numerical relays, the use ofvarious alternative methods of providing trip circuitfunctions is largely obsolete. Auxiliary miniaturecontactors are provided within the relay to provideoutput contact functions and the operation of thesecontactors is independent of the measuring system, asmentioned previously. The making current of the relayoutput contacts and the need to avoid these contactsbreaking the trip coil current largely dictates circuitbreaker trip coil arrangements. Comments on thevarious means of providing tripping arrangements are,however, included below as a historical referenceapplicable to earlier electromechanical relay designs.

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Figure 2.10: Typical relay tripping circuits

(a) Series sealing

PR TC

PR TC

PR TC

52a

(b) Shunt reinforcing

52a

(c) Shunt reinforcing with series sealing

52a

Chap2-4-15 21/06/02 10:45 Page 13


2.11.1 Series sealing

The coil of the series contactor carries the trip currentinitiated by the protection relay, and the contactor closesa contact in parallel with the protection relay contact.This closure relieves the protection relay contact of furtherduty and keeps the tripping circuit securely closed, even ifchatter occurs at the main contact. The total tripping timeis not affected, and the indicator does not operate untilcurrent is actually flowing through the trip coil.

The main disadvantage of this method is that such serieselements must have their coils matched with the tripcircuit with which they are associated.

The coil of these contacts must be of low impedance,with about 5% of the trip supply voltage being droppedacross them.

When used in association with high-speed trip relays,which usually interrupt their own coil current, theauxiliary elements must be fast enough to operate andrelease the flag before their coil current is cut off. Thismay pose a problem in design if a variable number ofauxiliary elements (for different phases and so on) maybe required to operate in parallel to energise a commontripping relay.

2.11.2 Shunt reinforcing

Here the sensitive contacts are arranged to trip thecircuit breaker and simultaneously to energise theauxiliary unit, which then reinforces the contact that isenergising the trip coil.

Two contacts are required on the protection relay, sinceit is not permissible to energise the trip coil and thereinforcing contactor in parallel. If this were done, andmore than one protection relay were connected to tripthe same circuit breaker, all the auxiliary relays would beenergised in parallel for each relay operation and theindication would be confused.

The duplicate main contacts are frequently provided as athree-point arrangement to reduce the number ofcontact fingers.

2.11.3 Shunt reinforcement with sealing

This is a development of the shunt reinforcing circuit tomake it applicable to situations where there is apossibility of contact bounce for any reason.

Using the shunt reinforcing system under thesecircumstances would result in chattering on the auxiliaryunit, and the possible burning out of the contacts, notonly of the sensitive element but also of the auxiliaryunit. The chattering would end only when the circuitbreaker had finally tripped. The effect of contact bounce

is countered by means of a further contact on theauxiliary unit connected as a retaining contact.

This means that provision must be made for releasing thesealing circuit when tripping is complete; this is adisadvantage, because it is sometimes inconvenient tofind a suitable contact to use for this purpose.

2.12 TRIP C IRCUIT SUPERVIS ION

The trip circuit includes the protection relay and othercomponents, such as fuses, links, relay contacts, auxiliaryswitch contacts, etc., and in some cases through aconsiderable amount of circuit wiring with intermediateterminal boards. These interconnections, coupled withthe importance of the circuit, result in a requirement inmany cases to monitor the integrity of the circuit. Thisis known as trip circuit supervision. The simplestarrangement contains a healthy trip lamp, as shown inFigure 2.11(a).

The resistance in series with the lamp prevents thebreaker being tripped by an internal short circuit causedby failure of the lamp. This provides supervision whilethe circuit breaker is closed; a simple extension givespre-closing supervision.

Figure 2.11(b) shows how, the addition of a normallyclosed auxiliary switch and a resistance unit can providesupervision while the breaker is both open and closed.

2

Fun

dam

enta

ls o

fP

rote

ctio

n P

ract

ice

1 4

Figure 2.11: Trip circuit supervision circuits.

PR TC52a

PR TC

PR TC

52a

52b

(c) Supervision with circuit breaker open or closed with remote alarm (scheme H7)

52a

A

Alarm

52a

52b

TCCircuit breaker

Trip

Trip

(d) Implementation of H5 scheme in numerical relay

(a) Supervision while circuit breaker is closed (scheme H4)

(b) Supervision while circuit breaker is open or closed (scheme H5)

C

B

Chap2-4-15 21/06/02 10:45 Page 14


In either case, the addition of a normally open push-button contact in series with the lamp will make thesupervision indication available only when required.

Schemes using a lamp to indicate continuity are suitablefor locally controlled installations, but when control isexercised from a distance it is necessary to use a relaysystem. Figure 2.11(c) illustrates such a scheme, which isapplicable wherever a remote signal is required.

With the circuit healthy, either or both of relays A and Bare operated and energise relay C. Both A and B mustreset to allow C to drop-off. Relays A, B and C are timedelayed to prevent spurious alarms during tripping orclosing operations. The resistors are mounted separatelyfrom the relays and their values are chosen such that ifany one component is inadvertently short-circuited,tripping will not take place.

The alarm supply should be independent of the trippingsupply so that indication will be obtained in case offailure of the tripping supply.

The above schemes are commonly known as the H4, H5and H7 schemes, arising from the diagram references ofthe Utility specification in which they originallyappeared. Figure 2.11(d) shows implementation ofscheme H5 using the facilities of a modern numericalrelay. Remote indication is achieved through use ofprogrammable logic and additional auxiliary outputsavailable in the protection relay.

2 F

unda

men

tals

of

Pro

tect

ion

Pra

ctic

e

Chap2-4-15 21/06/02 10:45 Page 15

Introduction 4.1

Three phase fault calculations 4.2

Symmetrical component analysis 4.3of a three-phase network

Equations and network connections 4.4for various types of faults

Current and voltage distribution 4.5in a system due to a fault

Effect of system earthing 4.6on zero sequence quantities

References 4.7

4 F a u l t C a l c u l a t i o n s

Chap4-30-45 21/06/02 9:57 Page 30


4.1 INTRODUCTION

A power system is normally treated as a balancedsymmetrical three-phase network. When a fault occurs,the symmetry is normally upset, resulting in unbalancedcurrents and voltages appearing in the network. The onlyexception is the three-phase fault, which, because itinvolves all three phases equally at the same location, isdescribed as a symmetrical fault. By using symmetricalcomponent analysis and replacing the normal systemsources by a source at the fault location, it is possible toanalyse these fault conditions.

For the correct application of protection equipment, it isessential to know the fault current distributionthroughout the system and the voltages in differentparts of the system due to the fault. Further, boundaryvalues of current at any relaying point must be known ifthe fault is to be cleared with discrimination. Theinformation normally required for each kind of fault ateach relaying point is:

i. maximum fault current

ii. minimum fault current

iii. maximum through fault current

To obtain the above information, the limits of stablegeneration and possible operating conditions, includingthe method of system earthing, must be known. Faultsare always assumed to be through zero fault impedance.

4.2 THREE-PHASE FAULT CALCULATIONS

Three-phase faults are unique in that they are balanced,that is, symmetrical in the three phases, and can becalculated from the single-phase impedance diagramand the operating conditions existing prior to the fault.

A fault condition is a sudden abnormal alteration to thenormal circuit arrangement. The circuit quantities,current and voltage, will alter, and the circuit will passthrough a transient state to a steady state. In thetransient state, the initial magnitude of the fault currentwill depend upon the point on the voltage wave at whichthe fault occurs. The decay of the transient condition,until it merges into steady state, is a function of theparameters of the circuit elements. The transient currentmay be regarded as a d.c. exponential current

4 Fault Calculat ions

Chap4-30-45 21/06/02 9:57 Page 31


4

Fau

lt C

alcu

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ons

3 2

superimposed on the symmetrical steady state faultcurrent. In a.c. machines, owing to armature reaction,the machine reactances pass through 'sub transient' and'transient' stages before reaching their steady statesynchronous values. For this reason, the resultant faultcurrent during the transient period, from fault inceptionto steady state also depends on the location of the faultin the network relative to that of the rotating plant.

In a system containing many voltage sources, or havinga complex network arrangement, it is tedious to use thenormal system voltage sources to evaluate the faultcurrent in the faulty branch or to calculate the faultcurrent distribution in the system. A more practicalmethod [4.1] is to replace the system voltages by a singledriving voltage at the fault point. This driving voltage isthe voltage existing at the fault point before the faultoccurs.

Consider the circuit given in Figure 4.1 where the drivingvoltages are

E and

E , the impedances on either side of

fault point F are Z1 and

Z1 , and the current through

point F before the fault occurs is I .

Figure 4.1:

The voltageV at F before fault inception is:

V =

E -

I

Z =

E +

I

Z

After the fault the voltageV is zero. Hence, the change

in voltage is -V . Because of the fault, the change in the

current flowing into the network from F is:

and, since no current was flowing into the network fromF prior to the fault, the fault current flowing from thenetwork into the fault is:

By applying the principle of superposition, the loadcurrents circulating in the system prior to the fault may

I f I VZ Z

Z Z= =

+( ) 1 1

1 1

' ''

' ' '

I VZ

VZ Z

Z Z= =

+( )1

1 1

1 1

' ''

' ' '

be added to the currents circulating in the system due tothe fault, to give the total current in any branch of thesystem at the time of fault inception. However, in mostproblems, the load current is small in comparison to thefault current and is usually ignored.

In a practical power system, the system regulation issuch that the load voltage at any point in the system iswithin 10% of the declared open-circuit voltage at thatpoint. For this reason, it is usual to regard the pre-faultvoltage at the fault as being the open-circuit voltage,and this assumption is also made in a number of thestandards dealing with fault level calculations.

For an example of practical three-phase faultcalculations, consider a fault at A in Figure 3.9. With thenetwork reduced as shown in Figure 4.2, the load voltageat A before the fault occurs is:

Figure 4.2:

V = 0.97

E - 1.55

I

For practical working conditions,E 1.55

I and

E 1.207

I . Hence

E E V.

Replacing the driving voltages E and

E by the load

voltageV between A and N modifies the circuit as shown

in Figure 4.3(a).

The node A is the junction of three branches. In practice,the node would be a busbar, and the branches arefeeders radiating from the bus via circuit breakers, asshown in Figure 4.3(b). There are two possible locationsfor a fault at A; the busbar side of the breakers or theline side of the breakers. In this example, it is assumedthat the fault is at X, and it is required to calculate thecurrent flowing from the bus to X.

The network viewed from AN has a driving pointimpedance |Z1| = 0.68 ohms.

The current in the fault is.

VZ1

V E I= + +

+

0 99 1 2 2 52 5 1 2

0 39. . .. .

.' '

Figure 4.1: Network with fault at F

N

FZ '1 Z ''1

I

VE' E'' Figure 4.2: Reduction of typicalpower system network

N

1.55 A B

2.5

1.2

0.39

0.99E ''0.97E '

Chap4-30-45 21/06/02 9:57 Page 32


4 F

ault

Cal

cula

tion

s

Let this current be 1.0 per unit. It is now necessary tofind the fault current distribution in the various branchesof the network and in particular the current flowing fromA to X on the assumption that a relay at X is to detectthe fault condition. The equivalent impedances viewedfrom either side of the fault are shown in Figure 4.4(a).

Figure 4.3

Figure 4.4

The currents from Figure 4.4(a) are as follows:

From the right:

From the left:

There is a parallel branch to the right of A

1 212 76

0 437..

.= p.u.

1 552 76

0 563..

.= p.u.

Therefore, current in 2.5 ohm branch

and the current in 1.2 ohm branch

Total current entering X from the left, that is, from A toX, is 0.437 + 0.183 = 0.62 p.u. and from B to X is0.38p.u. The equivalent network as viewed from therelay is as shown in Figure 4.4(b). The impedances oneither side are:

0.68/0.62 = 1.1 ohmsand

0.68/0.38 = 1.79 ohms

The circuit of Figure 4.4 (b) has been included becausethe Protection Engineer is interested in these equivalentparameters when applying certain types of protectionrelay.

4.3 SYMMETRICAL COMPONENT ANALYSIS OF A THREE-PHASE NETWORK

The Protection Engineer is interested in a wider variety offaults than just a three-phase fault. The most commonfault is a single-phase to earth fault, which, in LVsystems, can produce a higher fault current than a three-phase fault. Similarly, because protection is expected tooperate correctly for all types of fault, it may benecessary to consider the fault currents due to manydifferent types of fault. Since the three-phase fault isunique in being a balanced fault, a method of analysisthat is applicable to unbalanced faults is required. It canbe shown [4.2] that, by applying the 'Principle ofSuperposition', any general three-phase system ofvectors may be replaced by three sets of balanced(symmetrical) vectors; two sets are three-phase buthaving opposite phase rotation and one set is co-phasal.These vector sets are described as the positive, negativeand zero sequence sets respectively.

The equations between phase and sequence voltages aregiven below:

Equation 4.1

E E E E

E a E aE E

E aE a E E

a

b

c

= + +

= + +

= + +

1 2 0

21 2 0

12

2 0

= =2 5 0 5633 7

0 38. ..

. p.u.

= =1 2 0 5633 7

0 183. ..

. p.u.

Figure 4.3: Network with fault at node A

N

A

V

B

A

X

(b) Typical physical arrangement of node A with a fault shown at X

(a) Three - phase fault diagram for a fault at node A

BusbarCircuit breaker

1.55

1.2

2.5

0.39

Figure 4.4: Impedances viewed from fault

N

V

A

N

V

X

1.55 1.21

1.791.1

(a) Impedance viewed from node A

(b) Equivalent impedances viewed from node X

Chap4-30-45 21/06/02 9:57 Page 33


Equation 4.2

where all quantities are referred to the reference phaseA. A similar set of equations can be written for phaseand sequence currents. Figure 4.5 illustrates theresolution of a system of unbalanced vectors.

Figure 4.5

When a fault occurs in a power system, the phaseimpedances are no longer identical (except in the case ofthree-phase faults) and the resulting currents andvoltages are unbalanced, the point of greatest unbalancebeing at the fault point. It has been shown in Chapter 3that the fault may be studied by short-circuiting allnormal driving voltages in the system and replacing thefault connection by a source whose driving voltage isequal to the pre-fault voltage at the fault point. Hence,the system impedances remain symmetrical, viewed fromthe fault, and the fault point may now be regarded as thepoint of injection of unbalanced voltages and currentsinto the system.

This is a most important approach in defining the faultconditions since it allows the system to be representedby sequence networks [4.3] using the method ofsymmetrical components.

4.3.1 Positive Sequence Network

During normal balanced system conditions, only positivesequence currents and voltages can exist in the system,and therefore the normal system impedance network is apositive sequence network.

When a fault occurs in a power system, the current in the

E E aE a E

E E a E aE

E E E E

a b c

a b c

a b c

12

22

0

13

13

13

= + +( )= + +( )= + +( )

fault branch changes from 0 to I and the positive

sequence voltage across the branch changes from V to

V1 ;

replacing the fault branch by a source equal to the changein voltage and short-circuiting all normal driving voltagesin the system results in a current I flowing into thesystem, and:

Equation 4.3

where Z1 is the positive sequence impedance of the

system viewed from the fault. As before the fault nocurrent was flowing from the fault into the system, itfollows that

I1 , the fault current flowing from the

system into the fault must equal - I . Therefore:V1 =

V -

I1

Z1 Equation 4.4

is the relationship between positive sequence currentsand voltages in the fault branch during a fault.

In Figure 4.6, which represents a simple system, thevoltage drops

I1

Z1 and

I1

Z1 are equal to (

V -

V1 )

where the currents I1 and

I1 enter the fault from the

left and right respectively and impedancesZ1 and

Z1

are the total system impedances viewed from either sideof the fault branch. The voltage

V is equal to the open-

circuit voltage in the system, and it has been shown thatV E E (see Section 3.7). So the positive sequencevoltages in the system due to the fault are greatest at thesource, as shown in the gradient diagram, Figure 4.6(b).

Figure 4.6

4.3.2 Negative Sequence Network

If only positive sequence quantities appear in a powersystem under normal conditions, then negative sequencequantities can only exist during an unbalanced fault.

If no negative sequence quantities are present in the

IV V

Z=

)( 11

4

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lt C

alcu

lati

ons

3 4

Figure 4.6: Fault at F:Positive sequence diagrams

(a) System diagramN

F

X

N

X

F

N '(b) Gradient diagram

ZS1 Z '1

Z '1

Z '1

Z ''1

I '1

I '1

I '1

I1

V1

V1V '1 +I '1 Z '1

V

I ''1

E ' E '

Figure 4.5: Resolution of a systemof unbalanced vectors

a2E2

a2E1

aE1

aE2

Eo

Eo

Eo

E1

E2 Ea

Eb

Ec

Chap4-30-45 21/06/02 9:57 Page 34


fault branch prior to the fault, then, when a fault occurs,the change in voltage is

V2 , and the resulting current

I2

flowing from the network into the fault is:

Equation 4.5

The impedances in the negative sequence network aregenerally the same as those in the positive sequencenetwork. In machines

Z1

Z2 , but the difference is

generally ignored, particularly in large networks.

The negative sequence diagrams, shown in Figure 4.7, aresimilar to the positive sequence diagrams, with twoimportant differences; no driving voltages exist beforethe fault and the negative sequence voltage

V2 is

greatest at the fault point.

Figure 4.7

4.3.3 Zero Sequence Network

The zero sequence current and voltage relationshipsduring a fault condition are the same as those in thenegative sequence network. Hence:

V0 = -

I0

Z0 Equation 4.6

Also, the zero sequence diagram is that of Figure 4.7,substituting

I0 for

I2 , and so on.

The currents and voltages in the zero sequence networkare co-phasal, that is, all the same phase. For zerosequence currents to flow in a system there must be areturn connection through either a neutral conductor orthe general mass of earth. Note must be taken of thisfact when determining zero sequence equivalent circuits.Further, in general

Z1

Z0 and the value of

Z0 varies

according to the type of plant, the winding arrangementand the method of earthing.

IVZ

22

2=

4.4 EQUATIONS AND NETWORK CONNECTIONS FOR VARIOUS TYPES OF FAULTS

The most important types of faults are as follows:

a. single-phase to earth

b. phase to phase

c. phase-phase-earthd. three-phase (with or without earth)

The above faults are described as single shunt faultsbecause they occur at one location and involve aconnection between one phase and another or to earth.

In addition, the Protection Engineer often studies twoother types of fault:

e. single-phase open circuitf. cross-country fault

By determining the currents and voltages at the faultpoint, it is possible to define the fault and connect thesequence networks to represent the fault condition.From the initial equations and the network diagram, thenature of the fault currents and voltages in differentbranches of the system can be determined.

For shunt faults of zero impedance, and neglecting loadcurrent, the equations defining each fault (using phase-neutral values) can be written down as follows:

a. Single-phase-earth (A-E)

Equation 4.7

b. Phase-phase (B-C)

Equation 4.8

c. Phase-phase-earth (B-C-E)

Equation 4.9

d. Three-phase (A-B-C or A-B-C-E)

Equation 4.10

It should be noted from the above that for any type offault there are three equations that define the faultconditions.

I I I

V V

V V

a b c

a b

b c

+ + =

=

=

0

I

V

V

a

b

c

=

=

=

0

0

0

I

I I

V V

a

b c

b c

=

=

=

0

I

I

V

b

c

a

=

=

=

0

0

0

4 F

ault

Cal

cula

tion

s

Figure 4.7: Fault at F:Negative sequence diagram

(a) Negative sequence networkN

F

X

F

X

N

(b) Gradient diagram

ZS1 Z '1

Z '1

Z ''1I '2

I2

V2

V2

V2 + I '2Z '1

I ''2

Chap4-30-45 21/06/02 9:57 Page 35


When there is a fault impedance, this must be taken intoaccount when writing down the equations. For example,with a single-phase-earth fault through fault impedanceZf , Equations 4.7 are re-written:

Equation 4.11

Figure 4.8

4.4.1 Single-phase-earth Fault (A-E)

Consider a fault defined by Equations 4.7 and by Figure4.8(a). Converting Equations 4.7 into sequencequantities by using Equations 4.1 and 4.2, then:

Equation 4.12V1 = - (

V2 +

V0 ) Equation 4.13

Substituting for V1 ,

V2 and

V0 in Equation 4.13 from

Equations 4.4, 4.5 and 4.6:V -

I1

Z1 =

I2

Z2 +

I0

Z0

but, from Equation 4.12, I1 =

I2 =

I0 , therefore:

V =

I1 (

Z1 +

Z2 +

Z3 ) Equation 4.14

The constraints imposed by Equations 4.12 and 4.14indicate that the equivalent circuit for the fault isobtained by connecting the sequence networks in series,as shown in Figure 4.8(b).

4.4.2 Phase-phase Fault (B-C)

From Equation 4.8 and using Equations 4.1 and 4.2:I1 = -

I2 Equation 4.15

I0 = 0V1 =

V2 Equation 4.16

From network Equations 4.4 and 4.5, Equation 4.16 canbe re-written:

V -

I1

Z1 =

I2

Z2 +

I0

Z0

I I I Io a1 213

= = =

I

I

V I Z

b

c

a a f

=

=

=

0

0

V -

I1

Z1 =

I2

Z2

and substituting for I2 from Equation 4.15:

V =

I1 (

Z1 +

Z2 ) Equation 4.17

The constraints imposed by Equations 4.15 and 4.17indicate that there is no zero sequence networkconnection in the equivalent circuit and that the positiveand negative sequence networks are connected inparallel. Figure 4.9 shows the defining and equivalentcircuits satisfying the above equations.

Figure 4.9

4.4.3 Phase-phase-earth Fault (B-C-E)

Again, from Equation 4.9 and Equations 4.1 and 4.2:I1 = -(

I2 +

Io ) Equation 4.18

andV1 =

V2 =

V0 Equation 4.19

Substituting for V2 and

V0 using network Equations 4.5

and 4.6:I2

Z2 =

I0

Z0

thus, using Equation 4.18:

Equation 4.20

Equation 4.21

Now equating V1 and

V2 and using Equation 4.4 gives:

V -

I1

Z1 = -

I2

Z2

orV =

I1

Z1 -

I2

Z2

Substituting for I2 from Equation 4.21:

or

Equation 4.22I V

Z Z

Z Z Z Z Z Z1

0 2

1 0 1 2 0 2=

+ )(+ +

V ZZ Z

Z ZI= +

+

1

0 2

0 21

IZ I

Z Z2

0 1

0 2=

+

IZ I

Z Z0

2 1

0 2=

+

4

Fau

lt C

alcu

lati

ons

3 6

Figure 4.8: Single-phase-earth fault at F

(a) Definition of fault

F

C

B

A

(b) Equivalent circuit

Ia

Ib

Va F1

N1

N2 N0

F2 F0Vb

VcIc

Ib =0Ic =0Va=0

V

Z1 Z2 Z0

Figure 4.9: Phase-Phase fault at F


F

C

B

A


Ia

Ia =0Ib =-IcVb=-Vc

IbIc

F1

N1

N2 N0

F2 F0Vb

Va

Vc

V

Z1 Z2 Z0

Chap4-30-45 21/06/02 9:57 Page 36


From the above equations it follows that connecting thethree sequence networks in parallel as shown in Figure4.10(b) may represent a phase-phase-earth fault.

Figure 4.10 Phase-phase-earth fault

4.4.4 Three-phase Fault (A-B-C or A-B-C-E)

Assuming that the fault includes earth, then, fromEquations 4.10 and 4.1, 4.2, it follows that:

Equation 4.23

andI0 = 0 Equation 4.24

Substituting V2 = 0 in Equation 4.5 gives:

I2 = 0 Equation 4.25

and substituting V1 = 0 in Equation 4.4:

0 =V1 -

I1

Z1

orV =

I1

Z1 Equation 4.26

Further, since from Equation 4.24 Io = 0 , it follows from

Equation 4.6 that Vo is zero when

Zo is finite. The

equivalent sequence connections for a three-phase faultare shown in Figure 4.11.

Figure 4.11

4.4.5 Single-phase Open Circuit Fault

The single-phase open circuit fault is showndiagrammatically in Figure 4.12(a). At the fault point,the boundary conditions are:

Equation 4.27

I

V V

a

b c

=

= =

0

0

V V

V V

a0

1 2 0

=

= =

Hence, from Equations 4.2,

V0 = 1/3 VaV1 = 1/3 VaV2 = 1/3 Va

and therefore:

Equation 4.28

From Equations 4.28, it can be concluded that thesequence networks are connected in parallel, as shown inFigure 4.12(b).

4.4.6 Cross-country Faults

A cross-country fault is one where there are two faultsaffecting the same circuit, but in different locations andpossibly involving different phases. Figure 4.13(a)illustrates this.

The constraints expressed in terms of sequencequantities are as follows:

a) At point F

Equation 4.29

Therefore:

Equation 4.30

b) At point F

Equation 4.31

and therefore:

I b1 = I b2 = I b0 Equation 4.32

To solve, it is necessary to convert the currents andvoltages at point F to the sequence currents in thesame phase as those at point F. From Equation 4.32,

I I

V

' '

'

a c

b

= =

=

0

0

I I I

V V V

a a a

a a a

1 2 0

1 2 0 0

= =

+ + =

I I

V

b c

a

+ =

=

0

0

V V V V

I I I I

a

a

1 2 0

1 2 0

1 3

0

= = =

= + + =

4 F

ault

Cal

cula

tion

s

Figure 4.10: Phase-phase-earth fault at F


F

C

B

A


F1 F2 F0

N0N2N1

Va

Vb

Vc

Ib

Ic

Ia

Ia=0Vb=0Vc=0

Z1 Z2 Z0

V

Figure 4.11: Three-phase-earth fault at F

(a) Definition of fault (b) Equivalent circuit

F

C

B

A F1 F2 F0

N0N2N1Ia

Ia+Ib+Ic=0

Ic Ib

Vb

Vc

Va

Va+Vb+Vc=0

Z0Z2Z1

V

Figure 4.12: Open circuit on phase A

Va Va'a

bc

1

Ib

IcVc

N1 N2 N0I1 P1

Q1

2

I2 P2

Q2

0

I0 P0

Q0

Vb'Vc'

P Q

(a) Circuit diagram


+veSequenceNetwork

-veSequenceNetwork

ZeroSequenceNetwork

Chap4-30-45 21/06/02 9:57 Page 37


4

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3 8

(a) `A' phase to ground at F and `B' phase to ground at F'

a-e b-e


F 'F

Ia1F1 F '1

N1 N '1

I 'a1

V 'a1Va1

Ia2F2 F '2

N2 N '2

I 'a2

V 'a2Va2

Ia0F0 F '0

N0 N '0

I 'a0

V 'a0aV 'a0

aI 'a0

a2V 'a2

a2I 'a2

1a2

1a

Va0

Figure 4.13: Cross - country fault - phase A to phase B

a2 I a1 = aI a2 = I a0 orI a1 = a2I a2 = aI a0 Equation 4.33

and, for the voltages

V b1 + V b2 +V b0 = 0

Converting:

a2V a1 + aV a2 +V a0 = 0

or

V a1 + a2V a2 + aV a0 = 0 Equation 4.34

The fault constraints involve phase shifted sequencequantities. To construct the appropriate sequencenetworks, it is necessary to introduce phase-shiftingtransformers to couple the sequence networks. Thisis shown in Figure 4.13(b).

4.5 CURRENT AND VOLTAGE DISTRIBUTION IN A SYSTEM DUE TO A FAULT

Practical fault calculations involve the examination ofthe effect of a fault in branches of network other thanthe faulted branch, so that protection can be appliedcorrectly to isolate the section of the system directlyinvolved in the fault. It is therefore not enough tocalculate the fault current in the fault itself; the faultcurrent distribution must also be established. Further,abnormal voltage stresses may appear in a systembecause of a fault, and these may affect the operation ofthe protection. Knowledge of current and voltagedistribution in a network due to a fault is essential forthe application of protection.

The approach to network fault studies for assessing theapplication of protection equipment may be summarised asfollows:

Chap4-30-45 21/06/02 10:00 Page 38


a. from the network diagram and accompanying data,assess the limits of stable generation and possibleoperating conditions for the system

NOTE: When full information is not availableassumptions may have to be made

b. with faults assumed to occur at each relaying pointin turn, maximum and minimum fault currents arecalculated for each type of fault

NOTE: The fault is assumed to be through zeroimpedance

c. by calculating the current distribution in thenetwork for faults applied at different points in thenetwork (from (b) above) the maximum throughfault currents at each relaying point areestablished for each type of fault

d. at this stage more or less definite ideas on the typeof protection to be applied are formed. Furthercalculations for establishing voltage variation atthe relaying point, or the stability limit of thesystem with a fault on it, are now carried out inorder to determine the class of protectionnecessary, such as high or low speed, unit or non-unit, etc.

4.5.1 Current Distribution

The phase current in any branch of a network isdetermined from the sequence current distribution in theequivalent circuit of the fault. The sequence currents areexpressed in per unit terms of the sequence current inthe fault branch.

In power system calculations, the positive and negativesequence impedances are normally equal. Thus, thedivision of sequence currents in the two networks willalso be identical.

The impedance values and configuration of the zerosequence network are usually different from those of thepositive and negative sequence networks, so the zerosequence current distribution is calculated separately.

If Co and C1 are described as the zero and positivesequence distribution factors then the actual current ina sequence branch is given by multiplying the actualcurrent in the sequence fault branch by the appropriatedistribution factor. For this reason, if

I1 ,

I2 and

I0 are

sequence currents in an arbitrary branch of a networkdue to a fault at some point in the network, then thephase currents in that branch may be expressed in termsof the distribution constants and the sequence currentsin the fault. These are given below for the variouscommon shunt faults, using Equation 4.1 and theappropriate fault equations:

a. single-phase-earth (A-E)

Equation 4.35

b. phase-phase (B-C)

Equation 4.36

c. phase-phase-earth (B-C-E)

Equation 4.37

d. three-phase (A-B-C or A-B-C-E)

Equation 4.38

As an example of current distribution technique, considerthe system in Figure 4.14(a). The equivalent sequencenetworks are given in Figures 4.14(b) and (c), togetherwith typical values of impedances. A fault is assumed atA and it is desired to find the currents in branch OB dueto the fault. In each network, the distribution factors aregiven for each branch, with the current in the faultbranch taken as 1.0p.u. From the diagram, the zerosequence distribution factor Co in branch OB is 0.112and the positive sequence factor C1 is 0.373. For anearth fault at A the phase currents in branch OB fromEquation 4.35 are:

Ia = (0.746 + 0.112)

I0

= 0.858I0

andI b =

I c = -(0.373 + 0.112)

I0

= -0.261I0

By using network reduction methods and assuming thatall impedances are reactive, it can be shown thatZ1 =

Z0 = j0.68 ohms.

Therefore, from Equation 4.14, the current in fault

branch IV

a = 0 68.

I C I

I a C I

I aC I

'

'

'

a

b

c

=

=

=

1 1

21 1

1 1

I C C I

I a a CZZ

a C C I

I a a CZZ

aC C I

'

'

'

a

b

c

= ( )

= ( )

= ( ) +

1 0 0

21

0

1

21 0 0

21

0

11 0 0

I

I a a C I

I a a C I

'

'

'

a

b

c

=

= ( )= ( )

0

21 1

21 1

I C C I

I C C I

I C C I

'

'

'

a

b

c

= +( )= ( )= ( )

2 1 0 0

1 0 0

1 0 0

4 F

ault

Cal

cula

tion

s

Chap4-30-45 21/06/02 10:00 Page 39


Assuming that |V | = 63.5 volts, then:

If V is taken as the reference vector, then:

I a = 26.8 -90 AI b = I c =8.15 -90 A

The vector diagram for the above fault condition isshown in Figure 4.15.

Figure 4.15

I Ix

Aa0 1363 5

3 0 6831 2= = =.

..

4.5.2 Voltage DistributionThe voltage distribution in any branch of a network isdetermined from the sequence voltage distribution. Asshown by Equations 4.4, 4.5 and 4.6 and the gradientdiagrams, Figures 4.6(b) and 4.7(b), the positivesequence voltage is a minimum at the fault, whereas thezero and negative sequence voltages are a maximum.Thus, the sequence voltages in any part of the systemmay be given generally as:

Equation 4.39

Using the above equation, the fault voltages at bus B inthe previous example can be found.

From the positive sequence distribution diagram Figure4.8(c):

From the zero sequence distribution diagram Figure4.8(b):

For earth faults, at the fault I1 =

I2 =

I0 = j31.2A, when

|V | = 63.5 volts and is taken as the reference vector.Further,

Z1 =

Z0 = j0.68 ohms.

Hence:V1 = 63.5 - (0.216 x 31.2)

= 56.76 0 voltsV2 = 6.74 180 voltsV0 = 2.25 180 volts

and, using Equations 4.1:Va =

V1 +

V2 +

V0

= 56.76 -(6.74 + 2.25) Va = 47.8 0Vb = a2

V1 + a

V2 +

V0

= 56.76a2 -(6.74a + 2.25) Vb = 61.5 -116.4 volts

= [ ]I Z j0 0 0 608.V I Z j' 0 = ( ) + ( ){ }[ ]0 0 0 165 2 6 0 112 1 6. . . .

V V I Z j' 2 = [ ]1 1 0 464 .V V I Z j'1 = ( ) + ( ){ }[1 1 0 395 0 75 0 373 0 45 . . . .

V V I Z C Z

V I Z C Z

V I Z C Z

n

n

n

n

n

n

n

n

n

1 1 1 11

1

2 2 1 11

1

0 0 0 01

0

' =

=

=

'

'

4

Fau

lt C

alcu

lati

ons

4 0

Figure 4.15: Vector diagram: Fault currentsand voltages in branch OB due to P-E fault at bus A

V ' c =61.5-116.4

V ' a =47.8-0

V ' b =61.5-116.4

V=63.5-0

I ' b =I ' c =8.15-90

I ' a =26.8-90

A

Power system

B

Fault

Load

O

(a) Single line diagram

A0

B

0.165 0.112

0.08

0.053

0.755 0.1921.0

(b) Zero sequence network

j7.5j0.4

j0.4

j0.9j2.6 j1.6

j1.6j0.75 j0.45

j4.8

j2.5

j18.850.3731.0 0.395

(c) Positive and negative sequence networks

0.422

0.022

0.556

A0

0.183

B

Figure 4.14: Typical power system

Chap4-30-45 21/06/02 10:00 Page 40


Vc = a

V1 + a2

V2 +

V0

= 56.75a -(6.74a2 + 2.25) Vc = 61.5 116.4 volts

These voltages are shown on the vector diagram, Figure4.15.

4.6 EFFECT OF SYSTEM EARTHINGON ZERO SEQUENCE QUANTIT IES

It has been shown previously that zero sequence currentsflow in the earth path during earth faults, and it followsthat the nature of these currents will be influenced bythe method of earthing. Because these quantities areunique in their association with earth faults they can beutilised in protection, provided their measurement andcharacter are understood for all practical systemconditions.

4.6.1 Residual Current and Voltage

Residual currents and voltages depend for their existenceon two factors:

a. a system connection to earth at two or more points

b. a potential difference between the earthed pointsresulting in a current flow in the earth paths

Under normal system operation there is a capacitancebetween the phases and between phase and earth; thesecapacitances may be regarded as being symmetrical anddistributed uniformly through the system. So even when(a) above is satisfied, if the driving voltages aresymmetrical the vector sum of the currents will equateto zero and no current will flow between any two earthpoints in the system. When a fault to earth occurs in asystem an unbalance results in condition (b) beingsatisfied. From the definitions given above it followsthat residual currents and voltages are the vector sum ofphase currents and phase voltages respectively.

Hence:

Equation 4.40

Also, from Equations 4.2:

Equation 4.41

It should be further noted that:

Equation 4.42

V V V

V V V

V V V

ae an ne

be bn ne

ce cn ne

= +

= +

= +

I I

V V

R

R

=

=

3

3

0

0

I I I I

V V V V

R a b c

R ae be ce

= + +

= + +

and

and since Vbn = a2

Van ,

Vcn =a

Van then:

VR = 3

Vne Equation 4.43

where Vcn - neutral displacement voltage.

Measurements of residual quantities are made usingcurrent and voltage transformer connections as shown inFigure 4.16. If relays are connected into the circuits inplace of the ammeter and voltmeter, it follows that earthfaults in the system can be detected.

4.6.2 SystemZ0 /

Z1 Ratio

The system Z0 /

Z1 ratio is defined as the ratio of zero

sequence and positive sequence impedances viewed fromthe fault; it is a variable ratio, dependent upon themethod of earthing, fault position and system operatingarrangement.

When assessing the distribution of residual quantitiesthrough a system, it is convenient to use the fault pointas the reference as it is the point of injection ofunbalanced quantities into the system. The residualvoltage is measured in relation to the normal phase-neutral system voltage and the residual current iscompared with the three-phase fault current at the faultpoint. It can be shown [4.4/4.5] that the character ofthese quantities can be expressed in terms of the systemZ0 /

Z1 ratio.

The positive sequence impedance of a system is mainlyreactive, whereas the zero sequence impedance beingaffected by the method of earthing may contain bothresistive and reactive components of comparablemagnitude. Thus the express of the

Z0 /

Z1 ratio

approximates to:

Equation 4.44

Expressing the residual current in terms of the three-phase current and

Z0 /

Z1 ratio:

ZZ

XX

jRX

0

1

0

1

0

1=

4 F

ault

Cal

cula

tion

s

(a) Residual current

C

B

A

(b) Residual voltage

Vae

Ia

Ib

Ic

VceVbe

A

V

Figure 4.16: Measurement of residual quantities

Chap4-30-45 21/06/02 10:00 Page 41


a. Single-phase-earth (A-E)

where K =

Z0 /

Z1

Thus:

Equation 4.45

b. Phase-phase-earth (B-C-E)

Hence:

Therefore:

Equation 4.46

Similarly, the residual voltages are found by multiplyingEquations 4.45 and 4.46 by -

K

V .

a. Single-phase-each (A-E)

Equation 4.47

b. Phase-phase-earth (B-C-E)

Equation 4.48

The curves in Figure 4.17 illustrate the variation of theabove residual quantities with the

Z0 /

Z1 ratio. The

residual current in any part of the system can beobtained by multiplying the current from the curve bythe appropriate zero sequence distribution factor.Similarly, the residual voltage is calculated bysubtracting from the voltage curve three times the zerosequence voltage drop between the measuring point inthe system and the fault.

V K

KVR =

+( )3

2 1

V K

KVR =

+( )3

2

II K

R

3

32 1

= +( )

IV Z

Z Z Z K

VZ

R = +

= +( )

3

2

3

2 11

1 0 12

1

IV Z Z

Z Z Z1

1 0

1 0 122

=+( )+

I IZ

Z ZIR = = +

33

01

1 01

II K

R

3

3

2=

+( )

I VZ

31

=

I VZ Z K

VZ

R = +=

+( )3

23

21 0 1

4.6.3 Variation of Residual Quantities

The variation of residual quantities in a system due todifferent earth arrangements can be most readilyunderstood by using vector diagrams. Three exampleshave been chosen, namely solid fault-isolated neutral,solid fault-resistance neutral, and resistance fault-solidneutral. These are illustrated in Figures 4.18, 4.19 and4.20 respectively.

4

Fau

lt C

alcu

lati

ons

4 2

Figure 4.17: Variation of residual quantities at fault point

Residual voltage forSingle-Phase-Earth fault

Residual current forDouble-Phase-Earth fault

1 2 3 4 5

0.5

0

1.0

1.5

2.0

2.5

3.0

= Z0Z1

K

Residual voltage forDouble-Phase-Earth fault

Residual current forDouble-Phase-Earth fault

VR

and

I R a

s m

ultip

les

of V

and

I3

(a) Circuit diagram

C

B

A

(c) Residual voltage diagram

X

N

F

b

n

c

a(F)

(b) Vector diagram

Iab+Iac

Iab+Iac

-VcF=Eac

-VbF=Eab VR

VcFVbF

Iab

Iab

Iab

Iac

Iac

Iac

Figure 4.18: Solid fault-isolated neutral

Chap4-30-45 21/06/02 10:00 Page 42


4.6.3.1 Solid fault-isolated neutral

From Figure 4.18 it can be seen that the capacitance toearth of the faulted phase is short circuited by the faultand the resulting unbalance causes capacitance currentsto flow into the fault, returning via sound phasesthrough sound phase capacitances to earth.

At the fault point:

VaF = 0and

VR =VbF +

VcF

= -3 Ean

At source:VR = 3

Vne = -3

Ean

sinceEan +

Ebn +

Ecn = 0

Thus, with an isolated neutral system, the residualvoltage is three times the normal phase-neutral voltageof the faulted phase and there is no variation betweenVR at source and

VR at fault.

In practice, there is some leakage impedance betweenneutral and earth and a small residual current would bedetected at X if a very sensitive relay were employed.

4.6.3.2 Solid fault-resistance neutral

Figure 4.19 shows that the capacitance of the faultedphase is short-circuited by the fault and the neutralcurrent combines with the sound phase capacitivecurrents to give

Ia in the faulted phase.

With a relay at X, residually connected as shown inFigure 4.16, the residual current will be

Ian , that is, the

neutral earth loop current.Figure 4.19

At the fault point:VR =

VbF +

VcF since

VFe = 0

At source:VR =

VaX +

VbX +

VcX

From the residual voltage diagram it is clear that there islittle variation in the residual voltages at source and fault,as most residual voltage is dropped across the neutralresistor. The degree of variation in residual quantities istherefore dependent on the neutral resistor value.

4.6.3.3 Resistance fault-solid neutral

Capacitance can be neglected because, since thecapacitance of the faulted phase is not short-circuited,the circulating capacitance currents will be negligible.

At the fault point:VR =

VFn +

Vbn +

Vcn

At relaying point X:VR =

VXn +

Vbn +

Vcn

4 F

ault

Cal

cula

tion

s

Figure 4.19: Solid fault-resistance neutral

(a) Circuit diagram

C

B

AX F

b

n

c

a(F)

X

(b) Vector diagram

(at source)

(at fault)

(c) Residual voltage diagram

Ia

Ia

Iab

Iab Iab

Iac

Iac

Ian

ZL

-Vcf

-Vbf

Vbf

VcX VcF

VbX

VR

VR

VaX

-VbX

-VcX

-VXn

Iab

Ia

IabIan

Iac-IaZL

(a) Circuit diagram

CBA

X

b

n

c

a

X

(b) Vector diagram

(c) Residual voltage at fault

F

F

(d) Residual voltage at relaying point

IF

IF

IF-IFZL

-IFZS

IF

ZS ZL

Vcn

Vcn

VR VR

Vcn

Vbn

Vbn Vbn

VbF

VFn

VFn

VXn

VXn

Van

VcF

Figure 4.20: Resistance fault-solid neutral

Chap4-30-45 21/06/02 10:00 Page 43


From the residual voltage diagrams shown in Figure 4.20,it is apparent that the residual voltage is greatest at thefault and reduces towards the source. If the faultresistance approaches zero, that is, the fault becomessolid, then

VFn approaches zero and the voltage drops in

ZS and ZL become greater. The ultimate value of

VFn

will depend on the effectiveness of the earthing, and thisis a function of the system

Z0 /

Z1 ratio.

4.7 REFERENCES

4.1 Circuit Analysis of A.C. Power Systems, Volume I.Edith Clarke. John Wiley & Sons.

4.2 Method of Symmetrical Co-ordinates Applied tothe Solution of Polyphase Networks. C.L.Fortescue. Trans. A.I.E.E.,Vol. 37, Part II, 1918, pp1027-40.

4.3 Power System Analysis. J.R. Mortlock and M.W.Humphrey Davies. Chapman and Hall.

4.4 Neutral Groundings. R Willheim and M. Waters,Elsevier.

4.5 Fault Calculations. F.H.W. Lackey, Oliver & Boyd.

4

Fau

lt C

alcu

lati

ons

4 4

Chap4-30-45 21/06/02 10:00 Page 44

Introduction 5.1Synchronous machines 5.2

Armature reaction 5.3Steady state theory 5.4

Salient pole rotor 5.5Transient analysis 5.6

Asymmetry 5.7Machine reactances 5.8

Negative sequence reactance 5.9Zero sequence reactance 5.10

Direct and quadrature axis values 5.11Effect of saturation on machine reactances 5.12

Transformers 5.13Transformer positive sequence equivalent circuits 5.14

Transformer zero sequence equivalent circuits 5.15Auto-transformers 5.16

Transformer impedances 5.17Overhead lines and cables 5.18

Calculation of series impedance 5.19Calculation of shunt impedance 5.20

Overhead line circuits with or without earth wires 5.21OHL equivalent circuits 5.22

Cable circuits 5.23Overhead line and cable data 5.24

References 5.25

5 E q u i v a l e n t C i r c u i t s a n d P a r a m e t e r s o f P o w e r S y s t e m P l a n t

Chapt 5-46-77 21/06/02 9:31 Page 46


5.1 INTRODUCTION

Knowledge of the behaviour of the principal electricalsystem plant items under normal and fault conditions isa prerequisite for the proper application of protection.This chapter summarises basic synchronous machine,transformer and transmission line theory and givesequivalent circuits and parameters so that a fault studycan be successfully completed before the selection andapplication of the protection systems described in laterchapters. Only what might be referred to as 'traditional'synchronous machine theory is covered, as that

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