Protection & Guide Network Automation

Network P rotection & Automation Guide First edition July 2002 Previously called Protective Relays Application Guide First printed Reprinted Ju ne 1966 January 1967 August 1968 November 1970 September 1971 February 1973 Janu ary 1974 March 1975 November 1977 December 1979 November 1982 October 1983 Octob er 1985 June 1987 September 1990 March 1995 Second edition First printed Reprinted Third edition First printed Reprinted All rights reserved Copyright AREVA 2005 AREVA T&D - 1, Place de la Coupole - 92084 Paris La Dfense - France. www.areva-td .com AREVA T&D Worlwide Contact Centre: http://www.areva-td.com/contactcentre/ T el.: +44 (0) 1785 250 070 ISBN : 2-9518589-0-6 Layout by Flash Espace, Montpellier, France - Printed by Cayfosa, Barcelona, Spa in

Acknowledgements This book is the result of the co-operation and teamwork of the many specialist engineers employed by AREVA T&D Automation & Information Systems. The Company wo uld like to acknowledge their assistance in producing this edition. AREVA T&D wo uld also like to acknowledge gratefully the co-operation of the following compan ies in providing material for this edition. ALSTOM Power AREVA T&D Transformers AREVA T&D Instrument Transformers AREVA T&D Distribution Switchgear AREVA T&D Ne twork Planning ALSTOM Electrical Machines ALSTOM Transport/Virgin Trains The inv aluable contributions of PB Power within the review process are also acknowledge d gratefully. Peter Rush Network Protection & Automation Guide Acknowledgements

Contents 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Appendix 1 App endix 2 Appendix 3 Index Introduction Fundamentals of Protection Practice Fundam ental Theory Fault Calculations Equivalent Circuits and Parameters of Power Syst em Plant Current and Voltage Transformers Relay Technology Protection: Signallin g and Intertripping Overcurrent Protection for Phase and Earth Faults Unit Prote ction of Feeders Distance Protection Distance Protection Schemes Protection of C omplex Transmission Circuits Auto-Reclosing Busbar Protection Transformer and Tr ansformer-Feeder Protection Generator and Generator-Transformer Protection Indus trial and Commercial Power System Protection A.C. Motor Protection Protection of A.C. Electrified Railways Relay Testing and Commissioning Power System Measurem ents Power Quality Substation Control and Automation Distribution System Automat ion Terminology ANSI/IEC Relay Symbols Application Tables .................... p2 p4 .................... ................ p16 p30 p46 p78 p98 ................. ................. ................. ................. ............... p112 p122 p152 p170 p192 p202 p218 p232 p254 p280 p316 p336 p352 p370 p398 p410 p422 p442 p454 p466 p468 p476 .............. .............. .............. .............. .............. .............. .............. .............. .............. .............. .............. ..............

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1 Introduction

1 Introduction Relay hardware is becoming even more standardised, to the point at which versions of a relay may differ only by the software they contain. This accurate predictio n in the preface to the Third Edition of the Protective Relay Application Guide (PRAG), 1987, has been followed by the rapid development of integrated protectio n and control devices. The change in technology, together with significant chang es in Utility, Industrial and Commercial organisations, has resulted in new emph asis on Secondary Systems Engineering. In addition to the traditional role of pr otection & control, secondary systems are now required to provide true added val ue to organisations. When utilised to its maximum, not only can the integration of protection & control functionality deliver the required reduction in life-tim e cost of capital, but the advanced features available (Quality of Supply, distu rbance recording and plant monitoring) enable system and plant performance to be improved, increasing system availability. The evolution of all secondary connec ted devices to form digital control systems continues to greatly increase access to all information available within the substation, resulting in new methodolog ies for asset management. In order to provide the modern practising substation e ngineer with reference material, the Network Protection & Automation Guide provi des a substantially revised and expanded edition of PRAG incorporating new chapt ers on all levels of network automation. The first part of the book deals with t he fundamentals, basic technology, fault calculations and the models of power sy stem plant, including the transient response and saturation problems that affect instrument transformers. The typical data provided on power system plant has be en updated and significantly expanded following research that showed its popular ity. The book then provides detailed analysis on the application of protection s ystems. This includes a new Chapter on the protection of a.c. electrified railwa ys. Existing chapters on distance, busbar and generator protection have been com pletely revised to take account of new developments, including improvements due to numerical protection techniques and the application problems of embedded gene ration. The Chapter on relay testing and commissioning has been completely updat ed to reflect modern techniques. Finally, new Chapters covering the fields of po wer system measurements, power quality, and substation and distribution automati on are found, to reflect the importance of these fields for the modern Power Sys tem Engineer. The intention is to make NPAG the standard reference work in its su bject area - while still helping the student and young engineer new to the field . We trust that you find this book invaluable and assure you that any comments w ill be carefully noted ready for the next edition. Network Protection & Automation Guide 3

2 Fundamentals of Protection Practice Introduction Protection equipment Zones of protection Reliability Selectivity St ability Speed Sensitivity Primary and back-up protection Relay output devices Re lay tripping circuits 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 Trip circuit supervision 2.12

2 Fundamentals of P rotection P ractice 2.1 INTRODUCTION The purpose of an electrical power system is to generate and su pply electrical energy to consumers. The system should be designed and managed t o deliver this energy to the utilisation points with both reliability and econom y. Severe disruption to the normal routine of modern society is likely if power outages are frequent or prolonged, placing an increasing emphasis on reliability and security of supply. As the requirements of reliability and economy are larg ely opposed, power system design is inevitably a compromise. A power system comp rises many diverse items of equipment. Figure 2.2 shows a hypothetical power sys tem; this and Figure 2.1 illustrates the diversity of equipment that is found. Figure 2.1: Power station Network Protection & Automation Guide 5

Hydro power station R1 G1 G2 R2 T1 T2 380kV L2 L1B A L1A Fundamentals of P rotection P ractice 380kV C L3 380kV L4 B T5 T6 T3 T4 1 10kV Steam power station R3 G3 G4 R4 C

33kV CCGT power station R5 G5 G6 B

R6 G7 R7 T9 T10 T11 T7 T8 220kV D L7A T14 380kV E

L6 2 L7B T15 T12 T13 Grid substation F 380kV L5 G T16 L8 T17 33kV D

Grid 380kV F

1 10kV G

e 2. Figur Figure 2.1: Example power system Figure 2.2: Example power system 6 Network Protection & Automation Guide

Figure 2.4: Possible consequence of inadequate protection 2 . 2 P R OT E C T I O N E Q U I P M E N T a. Protection System: a complete arrangement of protection equipment and other d evices required to achieve a specified function based on a protection principal (IEC 60255-20) b. Protection Equipment: a collection of protection devices (rela ys, fuses, etc.). Excluded are devices such as CTs, CBs, Contactors, etc. Figure 2.3: Onset of an overhead line fault Many items of equipment are very expensive, and so the complete power system rep resents a very large capital investment. To maximise the return on this outlay, the system must be utilised as much as possible within the applicable constraint s of security and reliability of supply. More fundamental, however, is that the power system should operate in a safe manner at all times. No matter how well de signed, faults will always occur on a power system, and these faults may represe nt a risk to life and/or property. Figure 2.3 shows the onset of a fault on an o verhead line. The destructive power of a fault arc carrying a high current is ve ry great; it can burn through copper conductors or weld together core lamination s in a transformer or machine in a very short time some tens or hundreds of mill iseconds. Even away from the fault arc itself, heavy fault currents can cause da mage to plant if they continue for more than a few seconds. The provision of ade quate protection to detect and disconnect elements of the power system in the ev ent of fault is therefore an integral part of power system design. Only by so do ing can the objectives of the power system be met and the investment protected. Figure 2.4 provides an illustration of the consequences of failure to provide ap propriate protection. This is the measure of the importance of protection system s as applied in power system practice and of the responsibility vested in the Pr otection Engineer. c. Protection Scheme: a collection of protection equipment providing a defined f unction and including all equipment required to make the scheme work (i.e. relay s, CTs, CBs, batteries, etc.) In order to fulfil the requirements of protection wi th the optimum speed for the many different configurations, operating conditions and construction features of power systems, it has been necessary to develop ma ny types of relay that respond to various functions of the power system quantiti es. For example, observation simply of the magnitude of the fault current suffic es in some cases but measurement of power or impedance may be necessary in other s. Relays frequently measure complex functions of the system quantities, which a re only readily expressible by mathematical or graphical means. Relays may be cl assified according to the technology used: a. electromechanical b. static c. dig ital d. numerical The different types have somewhat different capabilities, due to the limitations of the technology used. They are described in more detail in Chapter 7. Network Protection & Automation Guide 7 Fundamentals of P rotection P ractice The definitions that follow are generally used in relation to power system prote ction: 2

In many cases, it is not feasible to protect against all hazards with a relay th at responds to a single power system quantity. An arrangement using several quan tities may be required. In this case, either several relays, each responding to a single quantity, or, more commonly, a single relay containing several elements , each responding independently to a different quantity may be used. The termino logy used in describing protection systems and relays is given in Appendix 1. Di fferent symbols for describing relay functions in diagrams of protection schemes are used, the two most common methods (IEC and IEEE/ANSI) are provided in Appen dix 2. 2 . 3 Z O N E S O F P R OT E C T I O N A Busbar protection rotection Feed Feeder protection (a) CT s on both sides of circuit breaker Busbar protecti on rotection F Fundamentals of P rotection P ractice To limit the extent of the power system that is disconnected when a fault occurs , protection is arranged in zones. The principle is shown in Figure 2.5. Ideally , the zones of protection should overlap, so that no part of the power system is left unprotected. This is shown in Figure 2.6(a), the circuit breaker being inc luded in both zones. Feed Feeder protection (b) CT s on circuit side of circuit breaker Figure 2.6: C T Locations Figure 2.6: CT Locations Zone 1 the circuit breaker A that is not completely protected against faults. In Figure 2.6(b) a fault at F would cause the busbar protection to operate and open the c ircuit breaker but the fault may continue to be fed through the feeder. The feed er protection, if of the unit type (see section 2.5.2), would not operate, since the fault is outside its zone. This problem is dealt with by intertripping or s ome form of zone extension, to ensure that the remote end of the feeder is tripp ed also. The point of connection of the protection with the power system usually defines the zone and corresponds to the location of the current transformers. U nit type protection will result in the boundary being a clearly defined closed l oop. Figure 2.7 illustrates a typical arrangement of overlapping zones. Zone 2 Zone 3 2 Zone 5 Zone 4 ~ ~ Figure 2.7 Figure 2.7: Overlapping zones of protection systems Zone 7

Feeder 1 Feeder 2 Zone 6 Feeder 3 Figure 2.5: Division of power system FigureFigure 2.5: Division of power system into protection zones 2.52.6 into protection zones For practical physical and economic reasons, this ideal is not always achieved, accommodation for current transformers being in some cases available only on one side of the circuit breakers, as in Figure 2.6(b). This leaves a section betwee n the current transformers and Alternatively, the zone may be unrestricted; Figure 2.7: Overlapping zones of pr otection systems the start will be defined but the extent (or reach) will depend on measurement of the system quantities and will therefore be subject to variation, owing to chang es in system conditions and measurement errors. 8 Network Protection & Automation Guide

2.4 RELIABILITY The need for a high degree of reliability is discussed in Sectio n 2.1. Incorrect operation can be attributed to one of the following classificat ions: a. incorrect design/settings b. incorrect installation/testing c. deterior ation in service 2.4.1 Design The design of a protection scheme is of paramount importance. This is to ensure that the system will operate under all required co nditions, and (equally important) refrain from operating when so required (inclu ding, where appropriate, being restrained from operating for faults external to the zone being protected). Due consideration must be given to the nature, freque ncy and duration of faults likely to be experienced, all relevant parameters of the power system (including the characteristics of the supply source, and method s of operation) and the type of protection equipment used. Of course, no amount of effort at this stage can make up for the use of protection equipment that has not itself been subject to proper design. 2.4.2 Settings It is essential to ens ure that settings are chosen for protection relays and systems which take into a ccount the parameters of the primary system, including fault and load levels, an d dynamic performance requirements etc. The characteristics of power systems cha nge with time, due to changes in loads, location, type and amount of generation, etc. Therefore, setting values of relays may need to be checked at suitable int ervals to ensure that they are still appropriate. Otherwise, unwanted operation or failure to operate when required may occur. 2.4.3 Installation The need for c orrect installation of protection systems is obvious, but the complexity of the interconnections of many systems and their relationship to the remainder of the installation may make checking difficult. Site testing is therefore necessary; s ince it will be difficult to reproduce all fault conditions correctly, these tes ts must be directed to proving the installation. The tests should be limited to such simple and direct tests as will prove the correctness of the connections, r elay settings, and freedom from damage of the equipment. No attempt should be ma de to type test the equipment or to establish complex aspects of its technical performance. Network Protection & Automation Guide 9 2.4.4 Testing Comprehensive testing is just as important, and this testing shoul d cover all aspects of the protection scheme, as well as reproducing operational and environmental conditions as closely as possible. Type testing of protection equipment to recognised standards fulfils many of these requirements, but it ma y still be necessary to test the complete protection scheme (relays, current tra nsformers and other ancillary items) and the tests must simulate fault condition s realistically. 2.4.5 Deterioration in Service Subsequent to installation in pe rfect condition, deterioration of equipment will take place and may eventually i nterfere with correct functioning. For example, contacts may become rough or bur nt owing to frequent operation, or tarnished owing to atmospheric contamination; coils and other circuits may become open-circuited, electronic components and a uxiliary devices may fail, and mechanical parts may seize up. The time between o perations of protection relays may be years rather than days. During this period defects may have developed unnoticed until revealed by the failure of the prote ction to respond to a power system fault. For this reason, relays should be regu larly tested in order to check for correct functioning. Testing should preferabl y be carried out without disturbing permanent connections. This can be achieved by the provision of test blocks or switches. The quality of testing personnel is an essential feature when assessing reliability and considering means for impro vement. Staff must be technically competent and adequately trained, as well as s elf-disciplined to proceed in a systematic manner to achieve final acceptance. I mportant circuits that are especially vulnerable can be provided with continuous electrical supervision; such arrangements are commonly applied to circuit break er trip circuits and to pilot circuits. Modern digital and numerical relays usua lly incorporate selftesting/diagnostic facilities to assist in the detection of failures. With these types of relay, it may be possible to arrange for such fail ures to be automatically reported by communications link to a remote operations centre, so that appropriate action may be taken to ensure continued safe operati on of that part of the power system and arrangements put in hand for investigati

on and correction of the fault. 2.4.6 Protection Performance Protection system p erformance is frequently assessed statistically. For this purpose each system fa ult is classed Fundamentals of P rotection P ractice 2

as an incident and only those that are cleared by the tripping of the correct ci rcuit breakers are classed as correct . The percentage of correct clearances ca n then be determined. This principle of assessment gives an accurate evaluation of the protection of the system as a whole, but it is severe in its judgement of relay performance. Many relays are called into operation for each system fault, and all must behave correctly for a correct clearance to be recorded. Complete reliability is unlikely ever to be achieved by further improvements in construct ion. If the level of reliability achieved by a single device is not acceptable, improvement can be achieved through redundancy, e.g. duplication of equipment. T wo complete, independent, main protection systems are provided, and arranged so that either by itself can carry out the required function. If the probability of each equipment failing is x/unit, the resultant probability of both equipments failing simultaneously, allowing for redundancy, is x2. Where x is small the res ultant risk (x2) may be negligible. Where multiple protection systems are used, the tripping signal can be provided in a number of different ways. The two most common methods are: a. all protection systems must operate for a tripping operat ion to occur (e.g. two-out-of-two arrangement) b. only one protection system need operate to cause a trip (e.g. one-out-of two arrangement) The former method guards against maloperation while the latter guards against failure to operate due to an unrevealed fault in a protection system. Rarely, three main protection system s are provided, configured in a two-out-of three tripping arrangement, to provide both reliability of tripping, and security against unwanted tripping. It has lon g been the practice to apply duplicate protection systems to busbars, both being required to operate to complete a tripping operation. Loss of a busbar may caus e widespread loss of supply, which is clearly undesirable. In other cases, impor tant circuits are provided with duplicate main protection systems, either being able to trip independently. On critical circuits, use may also be made of a digi tal fault simulator to model the relevant section of the power system and check the performance of the relays used. 2.5 SELECTIVITY When a fault occurs, the pro tection scheme is required to trip only those circuit breakers whose operation i s required to isolate the fault. This property of selective tripping is also cal led discrimination and is achieved by two general methods. 10 2.5.1 Time Grading Protection systems in successive zones are arranged to operat e in times that are graded through the sequence of equipments so that upon the o ccurrence of a fault, although a number of protection equipments respond, only t hose relevant to the faulty zone complete the tripping function. The others make incomplete operations and then reset. The speed of response will often depend o n the severity of the fault, and will generally be slower than for a unit system . 2.5.2 Unit Systems It is possible to design protection systems that respond on ly to fault conditions occurring within a clearly defined zone. This type of pro tection system is known as unit protection . Certain types of unit protection a re known by specific names, e.g. restricted earth fault and differential protect ion. Unit protection can be applied throughout a power system and, since it does not involve time grading, is relatively fast in operation. The speed of respons e is substantially independent of fault severity. Unit protection usually involv es comparison of quantities at the boundaries of the protected zone as defined b y the locations of the current transformers. This comparison may be achieved by direct hard-wired connections or may be achieved via a communications link. Howe ver certain protection systems derive their restricted property from the confi guration of the power system and may be classed as unit protection, e.g. earth f ault protection applied to the high voltage delta winding of a power transformer . Whichever method is used, it must be kept in mind that selectivity is not mere ly a matter of relay design. It also depends on the correct coordination of curr ent transformers and relays with a suitable choice of relay settings, taking int o account the possible range of such variables as fault currents, maximum load c urrent, system impedances and other related factors, where appropriate. 2 . 6 S TA B I L I T Y The term stability is usually associated with unit protection schem es and refers to the ability of the protection system to remain unaffected by co

nditions external to the protected zone, for example through load current and ex ternal fault conditions. 2.7 SPEED The function of protection systems is to isol ate faults on the power system as rapidly as possible. The main objective is to safeguard continuity of supply by removing each disturbance before it leads to w idespread loss of synchronism and consequent collapse of the power system. Network Protection & Automation Guide Fundamentals of P rotection P ractice 2

As the loading on a power system increases, the phase shift between voltages at different busbars on the system also increases, and therefore so does the probab ility that synchronism will be lost when the system is disturbed by a fault. The shorter the time a fault is allowed to remain in the system, the greater can be the loading of the system. Figure 2.8 shows typical relations between system lo ading and fault clearance times for various types of fault. It will be noted tha t phase faults have a more marked effect on the stability of the system than a s imple earth fault and therefore require faster clearance. Figure 2.8 Phase-earth Load power 2 . 9 P R I M A R Y A N D B A C K - U P P R OT E C T I O N The reliability of a power system has been discussed earlier, including the use of more than one prim ary (or main) protection system operating in parallel. In the event of failure or non-availability of the primary protection some other means of ensuring that the fault is isolated must be provided. These secondary systems are referred to as b ack-up protection. Back-up protection may be considered as either being local or rem ote. Local back-up protection is achieved by protection which detects an un-clear ed primary system fault at its own location and which then trips its own circuit breakers, e.g. time graded overcurrent relays. Remote back-up protection is pro vided by protection that detects an un-cleared primary system fault at a remote location and then issues a local trip command, e.g. the second or third zones of a distance relay. In both cases the main and back-up protection systems detect a fault simultaneously, operation of the back-up protection being delayed to ens ure that the primary protection clears the fault if possible. Normally being uni t protection, operation of the primary protection will be fast and will result i n the minimum amount of the power system being disconnected. Operation of the ba ck-up protection will be, of necessity, slower and will result in a greater prop ortion of the primary system being lost. The extent and type of back-up protecti on applied will naturally be related to the failure risks and relative economic importance of the system. For distribution systems where fault clearance times a re not critical, time delayed remote back-up protection may be adequate. For EHV systems, where system stability is at risk unless a fault is cleared quickly, m ultiple primary protection systems, operating in parallel and possibly of differ ent types (e.g. distance and unit protection), will be used to ensure fast and r eliable tripping. Back-up overcurrent protection may then optionally be applied to ensure that two separate protection systems are available during maintenance of one of the primary protection systems. Back-up protection systems should, ide ally, be completely separate from the primary systems. For example a circuit pro tected by a current differential relay may also have time graded overcurrent and earth fault relays added to provide circuit breaker tripping in the event of fa ilure of the main primary unit protection. To maintain complete separation and t hus integrity, current transformers, voltage transformers, relays, circuit break er trip coils and d.c. supplies would be duplicated. This ideal is rarely attain ed in practice. The following compromises are typical: a. separate current trans formers (cores and secondary windings only) are provided. This involves little e xtra cost or accommodation compared with the use of 11 Phase-phase-earth Three-phase Time Figure 2.8: Typical power/time relationship for various fault types System stability is not, however, the only consideration. Rapid operation of pro tection ensures that fault damage is minimised, as energy liberated during a fau lt is proportional to the square of the fault current times the duration of the fault. Protection must thus operate as quickly as possible but speed of operatio n must be weighed against economy. Distribution circuits, which do not normally

require a fast fault clearance, are usually protected by time-graded systems. Ge nerating plant and EHV systems require protection gear of the highest attainable speed; the only limiting factor will be the necessity for correct operation, an d therefore unit systems are normal practice. 2.8 SENSITIVITY Sensitivity is a t erm frequently used when referring to the minimum operating level (current, volt age, power etc.) of relays or complete protection schemes. The relay or scheme i s said to be sensitive if the primary operating parameter(s) is low. With older electromechanical relays, sensitivity was considered in terms of the sensitivity of the measuring movement and was measured in terms of its volt-ampere consumpt ion to cause operation. With modern digital and numerical relays the achievable sensitivity is seldom limited by the device design but by its application and CT /VT parameters. Network Protection & Automation Guide Fundamentals of P rotection P ractice Phase-phase 2

common current transformers that would have to be larger because of the combined burden. This practice is becoming less common when digital or numerical relays are used, because of the extremely low input burden of these relay types b. volt age transformers are not duplicated because of cost and space considerations. Ea ch protection relay supply is separately protected (fuse or MCB) and continuousl y supervised to ensure security of the VT output. An alarm is given on failure o f the supply and, where appropriate, prevent an unwanted operation of the protec tion c. trip supplies to the two protections should be separately protected (fus e or MCB). Duplication of tripping batteries and of circuit breaker tripping coi ls may be provided. Trip circuits should be continuously supervised d. it is des irable that the main and back-up protections (or duplicate main protections) sho uld operate on different principles, so that unusual events that may cause failu re of the one will be less likely to affect the other Digital and numerical rela ys may incorporate suitable back-up protection functions (e.g. a distance relay may also incorporate time-delayed overcurrent protection elements as well). A re duction in the hardware required to provide back-up protection is obtained, but at the risk that a common relay element failure (e.g. the power supply) will res ult in simultaneous loss of both main and back-up protection. The acceptability of this situation must be evaluated on a case-by-case basis. 2 . 10 R E L AY O U T P U T D E V I C E S In order to perform their intended function, relays must be fitted with some means of providing the various output signals required. Cont acts of various types usually fulfil this function. 2.10.1 Contact Systems Relay s may be fitted with a variety of contact systems for providing electrical outpu ts for tripping and remote indication purposes. The most common types encountere d are as follows: a. Self-reset The contacts remain in the operated condition on ly while the controlling quantity is applied, returning to their original condit ion when it is removed b. Hand or electrical reset These contacts remain in the operated condition after the controlling quantity is removed. They can be reset either by hand or by an auxiliary electromagnetic element 12 The majority of protection relay elements have self-reset contact systems, which , if so desired, can be modified to provide hand reset output contacts by the us e of auxiliary elements. Hand or electrically reset relays are used when it is n ecessary to maintain a signal or lockout condition. Contacts are shown on diagra ms in the position corresponding to the un-operated or deenergised condition, re gardless of the continuous service condition of the equipment. For example, an u ndervoltage relay, which is continually energised in normal circumstances, would still be shown in the deenergised condition. A make contact is one that close s when the relay picks up, whereas a break contact is one that is closed when the relay is de-energised and opens when the relay picks up. Examples of these c onventions and variations are shown in Figure 2.9. Self reset Fundamentals of P rotection P ractice Hand reset make contacts (normally open) break contacts (normally open)

Time delay on pick up Time delay on drop-off Figure 2.9: Contact types Figure 2.9: Contact types 2 A protection relay is usually required to trip a circuit breaker, the tripping m

Network Protection & Automation Guide

echanism of which may be a solenoid with a plunger acting directly on the mechan ism latch or an electrically operated valve. The power required by the trip coil of the circuit breaker may range from up to 50 watts for a small distribution circuit breaker, to 3000 watts for a large, extra-highvoltage circuit breaker. The relay may therefore energise the tripping coil directly, or, according to th e coil rating and the number of circuits to be energised, may do so through the agency of another multi-contact auxiliary relay. The basic trip circuit is simpl e, being made up of a handtrip control switch and the contacts of the protection relays in parallel to energise the trip coil from a battery, through a normally open auxiliary switch operated by the circuit breaker. This auxiliary switch is needed to open the trip circuit when the circuit breaker opens since the protec tion relay contacts will usually be quite incapable of performing the interrupti ng duty. The auxiliary switch will be adjusted to close as early as possible in the closing stroke, to make the protection effective in case the breaker is bein g closed on to a fault.

Where multiple output contacts, or contacts with appreciable current-carrying ca pacity are required, interposing, contactor type elements will normally be used. In general, static and microprocessor relays have discrete measuring and trippi ng circuits, or modules. The functioning of the measuring modules is independent of operation of the tripping modules. Such a relay is equivalent to a sensitive electromechanical relay with a tripping contactor, so that the number or rating of outputs has no more significance than the fact that they have been provided. For larger switchgear installations the tripping power requirement of each circ uit breaker is considerable, and further, two or more breakers may have to be tr ipped by one protection system. There may also be remote signalling requirements , interlocking with other functions (for example auto-reclosing arrangements), a nd other control functions to be performed. These various operations may then be carried out by multicontact tripping relays, which are energised by the protect ion relays and provide the necessary number of adequately rated output contacts. 2.10.2 Operation Indicators Protection systems are invariably provided with ind icating devices, called flags , or targets , as a guide for operations personn el. Not every relay will have one, as indicators are arranged to operate only if a trip operation is initiated. Indicators, with very few exceptions, are bi-sta ble devices, and may be either mechanical or electrical. A mechanical indicator consists of a small shutter that is released by the protection relay movement to expose the indicator pattern. Electrical indicators may be simple attracted arm ature elements, where operation of the armature releases a shutter to expose an indicator as above, or indicator lights (usually light emitting diodes). For the latter, some kind of memory circuit is provided to ensure that the indicator re mains lit after the initiating event has passed. With the advent of digital and numerical relays, the operation indicator has almost become redundant. Relays wi ll be provided with one or two simple indicators that indicate that the relay is powered up and whether an operation has occurred. The remainder of the informat ion previously presented via indicators is available by interrogating the relay locally via a manmachine interface (e.g. a keypad and liquid crystal display scree n), or remotely via a communication system. 2 . 11 T R I P P I N G C I R C U I T S There are three main circuits in use for circuit breaker tripping: a. series sealing b. shunt reinforcing c. shunt reinfo rcement with sealing These are illustrated in Figure 2.10. PR 52a TC (a) Series sealing PR 52a TC (b) Shunt reinforcing PR 52a TC (c) Shunt reinforcing with series sealing Figure 2.10: Typical relay tripping circuits Figure 2.10: Typical relay tripping circuits For electromechanical relays, elect rically operated indicators, actuated after the main contacts have closed, avoid imposing an additional friction load on the measuring element, which would be a serious handicap for certain types. Care must be taken with directly operated i

ndicators to line up their operation with the closure of the main contacts. The indicator must have operated by the time the contacts make, but must not have do ne so more than marginally earlier. This is to stop indication occurring when th e tripping operation has not been completed. With modern digital and numerical relays, the use of various alternative methods of providing trip circuit functions is largely obsolete. Auxiliary miniature co ntactors are provided within the relay to provide output contact functions and t he operation of these contactors is independent of the measuring system, as ment ioned previously. The making current of the relay output contacts and the need t o avoid these contacts breaking the trip coil current largely dictates circuit b reaker trip coil arrangements. Comments on the various means of providing trippi ng arrangements are, however, included below as a historical reference applicabl e to earlier electromechanical relay designs. Network Protection & Automation Guide 13 Fundamentals of P rotection P ractice 2

2.11.1 Series sealing The coil of the series contactor carries the trip current initiated by the protection relay, and the contactor closes a contact in paralle l with the protection relay contact. This closure relieves the protection relay contact of further duty and keeps the tripping circuit securely closed, even if chatter occurs at the main contact. The total tripping time is not affected, and the indicator does not operate until current is actually flowing through the tr ip coil. The main disadvantage of this method is that such series elements must have their coils matched with the trip circuit with which they are associated. T he coil of these contacts must be of low impedance, with about 5% of the trip su pply voltage being dropped across them. is countered by means of a further contact on the auxiliary unit connected as a retaining contact. This means that provision must be made for releasing the seal ing circuit when tripping is complete; this is a disadvantage, because it is som etimes inconvenient to find a suitable contact to use for this purpose. 2.12 TRI P CIRCUIT SUPERVISION The trip circuit includes the protection relay and other c omponents, such as fuses, links, relay contacts, auxiliary switch contacts, etc. , and in some cases through a considerable amount of circuit wiring with interme diate terminal boards. These interconnections, coupled with the importance of th e circuit, result in a requirement in many cases to monitor the integrity of the circuit. This is known as trip circuit supervision. The simplest arrangement co ntains a healthy trip lamp, as shown in Figure 2.11(a). The resistance in series with the lamp prevents the breaker being tripped by an internal short circuit c aused by failure of the lamp. This provides supervision while the circuit breake r is closed; a simple extension gives pre-closing supervision. Figure 2.11(b) sh ows how, the addition of a normally closed auxiliary switch and a resistance uni t can provide supervision while the breaker is both open and closed. PR 52a TC Fundamentals of P rotection P ractice When used in association with high-speed trip relays, which usually interrupt th eir own coil current, the auxiliary elements must be fast enough to operate and release the flag before their coil current is cut off. This may pose a problem i n design if a variable number of auxiliary elements (for different phases and so on) may be required to operate in parallel to energise a common tripping relay. 2.11.2 Shunt reinforcing Here the sensitive contacts are arranged to trip the c ircuit breaker and simultaneously to energise the auxiliary unit, which then rei nforces the contact that is energising the trip coil. Two contacts are required on the protection relay, since it is not permissible to energise the trip coil a nd the reinforcing contactor in parallel. If this were done, and more than one p rotection relay were connected to trip the same circuit breaker, all the auxilia ry relays would be energised in parallel for each relay operation and the indica tion would be confused. The duplicate main contacts are frequently provided as a three-point arrangement to reduce the number of contact fingers. 2.11.3 Shunt r einforcement with sealing This is a development of the shunt reinforcing circuit to make it applicable to situations where there is a possibility of contact bou nce for any reason. Using the shunt reinforcing system under these circumstances would result in chattering on the auxiliary unit, and the possible burning out of the contacts, not only of the sensitive element but also of the auxiliary uni t. The chattering would end only when the circuit breaker had finally tripped. T he effect of contact bounce 14 (a) Supervision while circuit breaker is closed (scheme H4) PR 52a 52b (b) Super vision while circuit breaker is open or closed (scheme H5) PR A TC

2 52a B TC C Alarm (c) Supervision with circuit breaker open or closed with remote alarm (sch eme H7) Trip Trip Circuit breaker 52a TC 52b (d) Implementation of H5 scheme in numerical relay Figure 2.11: Trip circuit supervision circuits. Network Protection & Automation Guide

In either case, the addition of a normally open pushbutton contact in series wit h the lamp will make the supervision indication available only when required. Sc hemes using a lamp to indicate continuity are suitable for locally controlled in stallations, but when control is exercised from a distance it is necessary to us e a relay system. Figure 2.11(c) illustrates such a scheme, which is applicable wherever a remote signal is required. With the circuit healthy, either or both o f relays A and B are operated and energise relay C. Both A and B must reset to a llow C to drop-off. Relays A, B and C are time delayed to prevent spurious alarm s during tripping or closing operations. The resistors are mounted separately fr om the relays and their values are chosen such that if any one component is inad vertently short-circuited, tripping will not take place. The above schemes are commonly known as the H4, H5 and H7 schemes, arising from the diagram references of the Utility specification in which they originally app eared. Figure 2.11(d) shows implementation of scheme H5 using the facilities of a modern numerical relay. Remote indication is achieved through use of programma ble logic and additional auxiliary outputs available in the protection relay. Network Protection & Automation Guide 15 Fundamentals of P rotection P ractice The alarm supply should be independent of the tripping supply so that indication will be obtained in case of failure of the tripping supply. 2

3 Fundamental Theory Introduction Vector algebra 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Manipulation of complex quantities Circuit quantities and conventions Impedance notation Basic circuit laws, theorems and network reduction References

3 Fundamental Theor y 3.1 INTRODUCTION The Protection Engineer is concerned with limiting the effects of disturbances in a power system. These disturbances, if allowed to persist, ma y damage plant and interrupt the supply of electric energy. They are described a s faults (short and open circuits) or power swings, and result from natural haza rds (for instance lightning), plant failure or human error. To facilitate rapid removal of a disturbance from a power system, the system is divided into protec tion zones . Relays monitor the system quantities (current, voltage) appearing i n these zones; if a fault occurs inside a zone, the relays operate to isolate th e zone from the remainder of the power system. The operating characteristic of a relay depends on the energizing quantities fed to it such as current or voltage , or various combinations of these two quantities, and on the manner in which th e relay is designed to respond to this information. For example, a directional r elay characteristic would be obtained by designing the relay to compare the phas e angle between voltage and current at the relaying point. An impedance-measurin g characteristic, on the other hand, would be obtained by designing the relay to divide voltage by current. Many other more complex relay characteristics may be obtained by supplying various combinations of current and voltage to the relay. Relays may also be designed to respond to other system quantities such as frequ ency, power, etc. In order to apply protection relays, it is usually necessary t o know the limiting values of current and voltage, and their relative phase disp lacement at the relay location, for various types of short circuit and their pos ition in the system. This normally requires some system analysis for faults occu rring at various points in the system. The main components that make up a power system are generating sources, transmission and distribution networks, and loads . Many transmission and distribution circuits radiate from key points in the sys tem and these circuits are controlled by circuit breakers. For the purpose of an alysis, the power system is treated as a network of circuit elements contained i n branches radiating from nodes to form closed loops or meshes. The system varia bles are current and voltage, and in Network Protection & Automation Guide 17

steady state analysis, they are regarded as time varying quantities at a single and constant frequency. The network parameters are impedance and admittance; the se are assumed to be linear, bilateral (independent of current direction) and co nstant for a constant frequency. 3 . 2 V E C TO R A L G E B R A A vector represe nts a quantity in both magnitude and direction. In Figure 3.1 the vector OP has a magnitude Z at an angle with the reference axis OX. Y Figure 3.1 The representation of a vector uantity algebraically in terms of its rectangula r co-ordinates is called a 'complex uantity'. Therefore, x + jy is a complex u antity and is the rectangular form of the vector Z where: + y2 y = tan 1 x x = Z cos y = Z sin Z= 2 (x ) E uation 3.2 From E uations 3.1 and 3.2: Z = Z (cos + jsin ) P E uation 3.3 and since cos and sin may be expressed in exponential form by the identities: sin = X Z y q e j e j 2j 0 Figure 3.1: Vector OP Figure 3.1: Vector OP x Fundamental Theor y It may be resolved into two components at right angles to each other, in this ca se x and y. The magnitude or scalar value of vector Z is known as the modulus Z , and the angle is the argument, and is written as arg. Z. The conventional met hod of expressing a vector Z is to write simply Z . This form completely specifie s a vector for graphical representation or conversion into other forms. For vect ors to be useful, they must be expressed algebraically. In Figure 3.1, the vecto r Z is the resultant of vectorially adding its components x and y; algebraically this vector may be written as: Z = x + jy E uation 3.1 e j e j 2 it follows that Z may also be written as: Z = Z e j cos = E uation 3.4 Therefore, a vector uantity may also be represented trigonometrically and expon entially. 3 . 3 M A N I P U L AT I O N OF COMPLEX QUANTITIES Complex uantities may be represented in any of the four co ordinate systems given below: a. Polar b. Rectangular c. Trigonometric d. Exponential Z x + jy Z (cos + jsin ) Z e j

3 where the operator j indicates that the component y is perpendicular to componen t x. In electrical nomenclature, the axis OC is the 'real' or 'in phase' axis, a nd the vertical axis OY is called the 'imaginary' or ' uadrature' axis. The oper ator j rotates a vector anticlockwise through 90. If a vector is made to rotate a nticlockwise through 180, then the operator j has performed its function twice, a nd since the vector has reversed its sense, then: j x j or j2 = 1 whence j = 1 The modulus Z and the argument are together known as 'polar co ordinates', and x and y are described as 'cartesian co ordinates'. Conversion between coordinat e systems is easily achieved. As the operator j obeys the ordinary laws of algeb ra, complex uantities in rectangular form can be manipulated algebraically, as can be seen by the following: Z1 + Z2 = (x1+x2) + j(y1+y2) E uation 3.5 Z1 (x1 x2) + j(y1 y2) E uation 3.6 (see Figure 3.2) 18 Network Protection & Automation Guide

Z2 =

Z1Z2 = Z1 Z2

1 + 2

Z1 Z1 = 1 2

Z2 Z2

3.3.2 Complex Numbers A complex number may be defined as a constant that represe nts the real and imaginary components of a physical uantity. The impedance para meter of an electric circuit is a complex number having real and imaginary compo nents, which are described as resistance and reactance respectively. Confusion o ften arises between vectors and complex numbers. A vector, as previously defined , may be a complex number. In this context, it is simply a physical uantity of constant magnitude acting in a constant direction. A complex number, which, bein g a physical uantity relating stimulus and response in a given operation, is kn own as a 'complex operator'. In this context, it is distinguished from a vector by the fact that it has no direction of its own. Because complex numbers assume a passive role in any calculation, the form taken by the variables in the proble m determines the method of representing them. 3.3.3 Mathematical Operators Mathe matical operators are complex numbers that are used to move a vector through a g iven angle without changing the magnitude or character of the vector. An operato r is not a physical uantity; it is dimensionless. The symbol j, which has been compounded with uadrature components of complex uantities, is an operator that rotates a uantity anti clockwise through 90. Another useful operator is one whi ch moves a vector anti clockwise through 120, commonly represented by the symbol a. Operators are distinguished by one further feature; they are the roots of uni ty. Using De Moivre's theorem, the nth root of unity is given by solving the exp ression: 11/n = (cos2m + jsin2m)1/n where m is any integer. Hence: Equation 3.7 Y Z2 y2 Z1 y1 0 x1 x2 X Figure 3.2: Addition of vectors Figure 3.2: Addition of vectors 3.3.1 Complex variables Some complex quantities are variable with, for example, time; when manipulating such variables in differential equations it is expedient to write the complex quantity in exponential form. When dealing with such funct ions it is important to appreciate that the quantity contains real and imaginary components. If it is required to investigate only one component of the complex variable, separation into components must be carried out after the mathematical operation has taken place. Example: Determine the rate of change of the real com ponent of a vector Z wt with time. Z wt = Z (coswt + jsinwt) = Z e jwt The re al component of the vector is Z coswt. Differentiating Z e jwt with respect to time: d Z e jwt = jw Z e jwt dt = jw Z (coswt + jsinwt) Separating into real and imaginary components: 2 m 2 m + j sin n n where m has values 1, 2, 3, ... (n-1) 11/ n = cos From the above ex ression j is found to be the 4th root and a the 3rd root of un ity, as they have four and three distinct values res ectively. Table 3.1 gives s ome useful functions of the a o erator. d Z e jwt = Z ( w sin wt + jw cos wt ) dt Thus, the rate of change of the real c omponent of a vector Z wt is: - Z w sinwt

( ) Network Protection & Automation Guide 19 Fundamental Theor y 3

1 3 a= + j =e 2 2 4 j 1 3 =e 3 a2 = j 2 2 j0 1=1+ j0 = e 2 j 3 For exam le, the instantaneous value, e, of a voltage varying sinusoidally with time is: e=Emsin(wt+) where: Em is the maximum amplitu e of the waveform; =2f, the angular velocity, is the argument efining the am litu e of the voltage at a tim e t=0 At t=0, the actual value of the voltage is Emsin . So if Em is regar e as the mo ulus of a vector, hose argument is , then Emsin is the imaginary com onen t of the vector Em . Figure 3.3 illustrates this quantity as a vector an as a si nusoi al function of time. Figure 3.3 Y Em e Em X t Equation 3.8 1+ a + a2 = 0 1a = j 3a2 1a2 = j 3a a a2 = j 3 j= a a2 3 Table 3.1: Pro erties of the a o erator 3.4 CIRCUIT QUANTITIES AND CONVENTIONS Circuit analysis may be escribe as the stu y of the res onse of a circuit to an im ose con ition, for exam le a short circuit. The circuit variables are current an voltage. Conventionally, current flo results from the a lication of a riving voltage, but there is com lete u ality bet een the variables an either may be regar e as the cause of the other . When a circuit exists, there is an interchange of energy; a circuit may be es cribe as being ma e u of 'sources' an 'sinks' for energy. The arts of a circ uit are escribe as elements; a 'source' may be regar e as an 'active' element an a 'sink' as a ' assive' element. Some circuit elements are issi ative, tha t is, they are continuous sinks for energy, for exam le resistance. Other circui t elements may be alternately sources an sinks, for exam le ca acitance an in uctance. The elements of a circuit are connecte together to form a net ork havi ng no es (terminals or junctions) an branches (series grou s of elements) that form close loo s (meshes). In stea y state a.c. circuit theory, the ability of a circuit to acce t a current flo resulting from a given riving voltage is cal le the im e ance of the circuit. Since current an voltage are uals the im e a nce arameter must also have a ual, calle a mittance. 3.4.1 Circuit Variables As current an voltage are sinusoi al functions of time, varying at a single an constant frequency, they are regar e as rotating vectors an can be ra n as lan vectors (that is, vectors efine by t o co or inates) on a vector iagram. X' 0 Y' t=0 Fun amental Theor y Figure 3.3: Re resentation of a sinusoi al function Figure 3.3: Re resentation o f a sinusoi al function The current resulting from a lying a voltage to a circuit e en s u on the circ uit im e ance. If the voltage is a sinusoi al function at a given frequency an the im e ance is constant the current ill also vary harmonically at the same fr equency, so it can be sho n on the same vector iagram as the voltage vector, an

3 Equation 3.9 where: Z = R2 + X 2 Equation 3.10 From Equations 3.9 and 3.10 it can be seen that the angular displacement between the current and voltage vectors and the current magnitude Im = Em / Z is depe ndent upon the impedance Z . In complex form the impedance may be written Z=R+jX . The real component , R, is the circuit resistance, and the 20 Network Protection & Automation Guide 1 X = L C = tan 1 X R

is given by the equation i= Em Z sin ( t + )

imaginary component , X, is the circuit reactance. When the circuit reactance i s inductive (that is, wL>1/wC), the current lags the voltage by an angle , and when it is capacitive (that is, 1/wC>wL) it 'leads' the voltage by an angle . Whe n drawing vector diagrams, one vector is chosen as the 're erence vector' and al l other vectors are drawn relative to the re erence vector in terms o magnitude and angle. The circuit impedance Z is a complex operator and is distinguished from a vector only by the fact that it has no direction of its own. A further c onvention is that sinusoidally varying quantities are described by their effect ive or root mean square (r.m.s.) values; these are usually written using the relevant symbol without a suffix. Thus: 2 E = Em 2 Equation 3.11 The root mean square value is that value which has the same heating effect as a direct current quantity of that value in the same circu it, and this definition applies to non-sinusoidal as well as sinusoidal quantiti es. I = Im steady state terms Equation 3.12 may be written: E = I Z Equation 3.13 and this is known as the equated-voltage equation [3.1]. It is the equation most usually adopted in electrical network calculations, since it equates the drivin g voltages, which are known, to the passive voltages, which are functions of the currents to be calculated. In describing circuits and drawing vector diagrams, for formal analysis or calculations, it is necessary to adopt a notation which d efines the positive direction of assumed current flow, and establishes the direc tion in which positive voltage drops and voltage rises act. Two methods are avai lable; one, the double suffix method, is used for symbolic analysis, the other, the single suffix or diagrammatic method, is used for numerical calculations. In the double suffix method the positive direction of current flow is assumed to b e from node a to node b and the current is designated Iab . With the diagrammati c method, an arrow indicates the direction of current flow. The voltage rises ar e positive when acting in the direction of current flow. It can be seen from Fig ure 3.4 that E1 and Ean are positive voltage rises and E2 and Ebn are negative v oltage rises. In the diagrammatic method their direction of action is simply ind icated by an arrow, whereas in the double suffix method, Ean and Ebn indicate th at there is a potential rise in directions na and nb. Figure 3.4 Methods or representing a circuit 3.4.2 Sign Conventions In describing the electrical state of a circuit, it is of ten necessary to refer to the potential difference existing between two points in the circuit. Since wherever such a potential difference exists, current will flow and energy will either be transferred or absorbed, it is obviously necessa ry to define a potential difference in more exact terms. For this reason, the te rms voltage rise and voltage drop are used to define more accurately the nature of the potential difference. Voltage rise is a rise in potential measured in the direction of current flow between two points in a circuit. Voltage drop is the converse. A circuit element with a voltage rise across it acts as a source of en ergy. A circuit element with a voltage drop across it acts as a sink of energy. Voltage sources are usually active circuit elements, while sinks are usually pas sive circuit elements. The positive direction of energy flow is from sources to sinks. Kirchhoff s first law states that the sum of the driving voltages must eq ual the sum of the passive voltages in a closed loop. This is illustrated by the fundamental equation of an electric circuit: Ldi 1 iR + + idt = e Equation 3.12 dt C where the terms on the left hand side of the equation are voltage drops across the circuit elements. Expressed in Z3 Z1 E1 I Z2 E2

E1-E2=(Z1+Z2+Z3)I (a) Diagrammatic a Zan Ean Iab Zab b Zbn Ebn n Ean-Ebn=(Zan+Zab+Zbn)Iab (b) Double suffix Figure 3.4 Methods of representing a circuit Figure 3.4: Circuit representation methods Network Protection & Automation Guide 21 Fundamental Theor y 3

Voltage drops are also positive when acting in the direction of current flow. Fr om Figure 3.4(a) it can be seen that ( Z1+ Z2+ Z3) I is the total voltage drop i n the loop in the direction of current flow, and must equate to the total voltag e rise E1- E2. In Figure 3.4(b), the voltage drop between nodes a and b designat ed Vab indicates that point b is at a lower potential than a, and is positive wh en current flows from a to b. Conversely Vba is a negative voltage drop. Symboli cally: Vabab =V an V bn V = Van Vbn Vbaba =V bn V an V = Vbn Van common re erence point. 3.4.3 Power The product o the potential di erence acro ss and the current through a branch o a circuit is a measure o the rate at whi ch energy is exchanged between that branch and the remainder o the circuit. I the potential di erence is a positive voltage drop, the branch is passive and a bsorbs energy. Conversely, i the potential di erence is a positive voltage ris e, the branch is active and supplies energy. The rate at which energy is exchang ed is known as power, and by convention, the power is positive when energy is be ing absorbed and negative when being supplied. With a.c. circuits the power alte rnates, so, to obtain a rate at which energy is supplied or absorbed, it is nece ssary to take the average power over one whole cycle. I e=Emsin(wt+) an i=Imsin ( t+ ), then the power equation is: p=ei=P[1 cos2(wt+)]+Qsin2( t+) here: P= E I co s Q= E I sin From Equation 3.15 it can be seen that the quantity P varies rom 0 to 2P and quantity Q varies rom Q to +Q in one cycle, and that the wave orm is o twice the periodic requency o the current voltage wave orm. The average value o the power exchanged in one cycle is a constant, equal to quantity P, an d as this quantity is the product o the voltage and the component o current wh ich is 'in phase' with the voltage it is known as the 'real' or 'active' power. The average value o quantity Q is zero when taken over a cycle, suggesting that energy is stored in one hal cycle and returned to the circuit in the remaining hal cycle. Q is the product o voltage and the quadrature and Equation 3.15 component o current, and is known as 'reactive power'. As P and Q are constants which speci y the power exchange in a given circuit, and are products o the cu rrent and voltage vectors, then i S is the vector product E I it ollows that wi th E as the re erence vector and as the angle between E and I : S = P + jQ Equati on 3.16 The quantity S is described as the 'apparent power', and is the term use d in establishing the rating o a circuit. S has units o VA. 3.4.4 Single Phase and Polyphase Systems A system is single or polyphase depending upon whether th e sources eeding it are single or polyphase. A source is single or polyphase ac cording to whether there are one or several driving voltages associated with it. For example, a three phase source is a source containing three alternating driv ing voltages that are assumed to reach a maximum in phase order, A, B, C. Each p hase driving voltage is associated with a phase branch o the system network as shown in Figure 3.5(a). I a polyphase system has balanced voltages, that is, eq ual in magnitude and reaching a maximum at equally displaced time intervals, and the phase branch impedances are identical, it is called a 'balanced' system. It will become 'unbalanced' i any o the above conditions are not satis ied. Calc ulations using a balanced polyphase system are simpli ied, as it is only necessa ry to solve or a single phase, the solution or the remaining phases being obta ined by symmetry. The power system is normally operated as a three phase, balanc ed, system. For this reason the phase voltages are equal in magnitude and can be represented by three vectors spaced 120 or 2/3 ra ians a art, as sho n in Figure 3.5(b). A Ecn C Ean N Ebn B A' N' C' Phase branches B' Equation 3.14 Fun amental Theor y 3

(a) Three hase system Ea Direction 120 of rotation 120 Ec=aEa 120 Eb=a2Ea (b) Balance system of vectors Figure 3.5: Three hase systems Figure 3.5: Three hase systems 22 Net ork Protection & Automation Gui e

Since the voltages are symmetrical, they may be ex resse in terms of one, that is: = E E Eaa= Eaa = 2 E aE Ebb= a 2 Eaa Ec c= aEa E = Ea system im e ances may be converte to those base quantities by using the equatio ns given belo : MVAb 2 MVAb1 2 kVb1 Zb 2 = Zb1 kVb 2 Zb 2 = Zb1 Equation 3.17 here a is the vector o erator e j2/3. Further, if the hase branch im e ances ar e i entical in a balance system, it follo s that the resulting currents are als o balance . 3.5 IMPEDANCE NOTATION It can be seen by ins ection of any o er sys tem iagram that: a. several voltage levels exist in a system b. it is common r actice to refer to lant MVA in terms of er unit or ercentage values c. transm ission line an cable constants are given in ohms/km Before any system calculati ons can take lace, the system arameters must be referre to 'base quantities' an re resente as a unifie system of im e ances in either ohmic, ercentage, o r er unit values. The base quantities are o er an voltage. Normally, they are given in terms of the three hase o er in MVA an the line voltage in kV. The base im e ance resulting from the above base quantities is: ohms Equation 3.18 MV A an , rovi e the system is balance , the base im e ance may be calculate usi ng either single hase or three hase quantities. Zb Equation 3.20 here suffix b1 enotes the value to the original base an b2 enotes the value to ne base The choice of im e ance notation e en s u on the com lexity of the system, lant im e ance notation an the nature of the system calculations envis age . If the system is relatively sim le an contains mainly transmission line ata, given in ohms, then the ohmic metho can be a o te ith a vantage. Ho ever , the er unit metho of im e ance notation is the most common for general syste m stu ies since: 1. im e ances are the same referre to either si e of a transfo rmer if the ratio of base voltages on the t o si es of a transformer is equal to the transformer turns ratio 2. confusion cause by the intro uction of o ers o f 100 in ercentage calculations is avoi e 3. by a suitable choice of bases, th e magnitu es of the ata an results are ke t ithin a re ictable range, an he nce errors in ata an com utations are easier to s ot Most o er system stu ies are carrie out using soft are in er unit quantities. Irres ective of the meth o of calculation, the choice of base voltage, an unifying system im e ances to this base, shoul be a roache ith caution, as sho n in the follo ing exam le . (kV )2 = The er unit or ercentage value of any im e ance in the system is the ratio of actual to base im e ance values. Hence: 11.8kV 11.8/141kV 132kV Overhea line Wrong selection of base voltage Equation 3.19 132/11kV 11kV Distribution MVAb (kVb )2 Z (% ) = Z ( .u .) 100 here MVAb = base MVA kVb = base kV Z (

.u .) = Z (ohms )

11.8kV Right selection 11.8kV 132kV 11kV

141kV 141 x 11=11.7kV 132 Sim le trans osition of the above formulae ill refer the ohmic value of im e an ce to the er unit or ercentage values an base quantities. Having chosen base quantities of suitable magnitu e all Figure 3.6: Selection of base voltages Figure 3.6: Selection of base voltages Net ork Protection & Automation Gui e 23 Fun amental Theor y 3

From Figure 3.6 it can be seen that the base voltages in the three circuits are relate by the turns ratios of the intervening transformers. Care is require as the nominal transformation ratios of the transformers quote may be ifferent f rom the turns ratios e.g. a 110/33kV (nominal) transformer may have a turns rat io of 110/34.5kV. Therefore, the rule for han calculations is: 'to refer an im e ance in ohms from one circuit to another multi ly the given im e ance by the s quare of the turns ratio (o en circuit voltage ratio) of the intervening transfo rmer'. Where o er system simulation soft are is use , the soft are normally has calculation routines built in to a just transformer arameters to take account of ifferences bet een the nominal rimary an secon ary voltages an turns rati os. In this case, the choice of base voltages may be more conveniently ma e as t he nominal voltages of each section of the o er system. This a roach avoi s co nfusion hen er unit or ercent values are use in calculations in translating the final results into volts, am s, etc. For exam le, in Figure 3.7, generators G1 an G2 have a sub transient reactance of 26% on 66.6MVA rating at 11kV, an t ransformers T1 an T2 a voltage ratio of 11/145kV an an im e ance of 12.5% on 7 5MVA. Choosing 100MVA as base MVA an 132kV as base voltage, fin the ercentage im e ances to ne base quantities. a. Generator reactances to ne bases are: 3 . 6 B A S I C C I R C U I T L AW S , THEOREMS AND NETWORK REDUCTION Most ract ical o er system roblems are solve by using stea y state analytical metho s. The assum tions ma e are that the circuit arameters are linear an bilateral an constant for constant frequency circuit variables. In some roblems, escribe as initial value roblems, it is necessary to stu y the behaviour of a circuit in the transient state. Such roblems can be solve using o erational metho s. A gain, in other roblems, hich fortunately are fe in number, the assum tion of linear, bilateral circuit arameters is no longer vali . These roblems are solv e using a vance mathematical techniques that are beyon the sco e of this book . 3.6.1 Circuit La s In linear, bilateral circuits, three basic net ork la s a ly, regar less of the state of the circuit, at any articular instant of time. T hese la s are the branch, junction an mesh la s, ue to Ohm an Kirchhoff, an are state belo , using stea y state a.c. nomenclature. 3.6.1.1 Branch la The c urrent I in a given branch of im e ance Z is ro ortional to the otential iffe rence V a earing across the branch, that is, V = I Z . 3.6.1.2 Junction la The algebraic sum of all currents entering any junction (or no e) in a net ork is ze ro, that is: Fun amental Theor y (11) =0.27% 100 26 66.6 (132 )2 2 b. Transformer reactances to ne bases are: 100 (145 ) 12.5 = 20.1% 75 (132 )2 2 I =0 3.6.1.3 Mesh la The algebraic sum of all the riving voltages in any close at h (or mesh) in a net ork is equal to the algebraic sum of all the assive voltag es ( ro ucts of the im e ances an the currents) in the com onents branches, tha t is: 3 NOTE: The base voltages of the generator an circuits are 11kV an 145kV res ect ively, that is, the turns ratio of the transformer. The corres on ing er unit v alues can be foun by ivi ing by 100, an the ohmic value can be foun by using Equation 3.19. Figure 3.7

T1 G1 132kV overhea

E = Z I Alternatively, the total change in otential aroun a close loo is zero. 3.6.2 Circuit Theorems From the above net ork la s, many theorems have been erive f or the rationalisation of net orks, either to reach a quick, sim le, solution to a roblem or to re resent a com licate circuit by an equivalent. These theorem s are ivi e into t o classes: those concerne ith the general ro erties of n et orks an those G2 Figure 3.7: Section of a o er system Figure 3.7: Section of a o er system 24 Net ork Protection & Automation Gui e

lines T2

concerne ith net ork re uction. Of the many theorems that exist, the three mos t im ortant are given. These are: the Su er osition Theorem, Thvenin's Theorem an Kennelly's Star/Delta Theorem. 3.6.2.1 Su er osition Theorem (general net ork theorem)

The resultant current that flows in any branch of a network ue to the simultane ous action of several riving voltages is equal to the algebraic sum of the comp onent currents ue to each riving voltage acting alone with the remain er short -circuite . 3.6.2.2 Thvenin s Theorem (active network re uction theorem) Any acti ve network that may be viewe from two terminals can be replace by a single ri ving voltage acting in series with a single impe ance. The riving voltage is th e open-circuit voltage between the two terminals an the impe ance is the impe a nce of the network viewe from the terminals with all sources short-circuite . 3 .6.2.3 Kennelly s Star/Delta Theorem (passive network re uction theorem) Any thr ee-terminal network can be replace by a elta or star impe ance equivalent with out isturbing the external network. The formulae relating the replacement of a elta network by the equivalent star network is as follows (Figure 3.8): Zco = 13 Z23 / (Z12 + Z13 + Z23) an so on. a Zao O Zco Zbo b 1 Z13 Z12 2 Z23 0 N Figure 3.9: Typical power system network Figure 3.9: Typical power system netw ork Z AN = Z AO + Z NO + Z AO Z NO Z BO = 0.75 +18.85 + = 51 ohms 0.75 18.85 0.45 c (a) Star network 3 (b) Delta network Z BN = Z BO + Z NO + Figure3.8: Star-Delta network transformation Figure 3.8: Star/Delta network re u ction Figure 3.8: Star-Delta network transformation Z BO Z NO Z AO The impe ance of a elta network correspon ing to an

replacing any star network

3.6.3 Net ork Re uction The aim of net ork re uction is to re uce a system to a sim le equivalent hile retaining the i entity of that art of the system to be stu ie . For exam le, consi er the system sho n in Figure 3.9. The net ork has t o sources E an E , a line AOB shunte by an impe ance, which may be regar e the re uction of a further network connecte between A an B, an a loa connect e between O an N. The object of the re uction is to stu y the effect of openin g a breaker at A or B uring normal system operations, or of a fault at A or B. Thus the i entity of no es A an B must be retaine together with the sources, b ut the branch ON can be eliminate , simplifying the stu y. Procee ing, A, B, N, forms a star branch an can therefore be converte to an equivalent elta. Figur e 3.9 2.55 1.6 A 0.75 E 18.85 B 0.45 E 0.4

as

is: Zao Zbo Z12 = Zao + Zbo + Zco an so on. = 0.45 +18.85 + =30.6 ohms 0.45 18.85 0.75 Z AN = Z AO + Z BO + Z AO Z BO Z NO = 1.2 ohms (since ZNO>>> ZAOZBO) Figure 3.10 Network Protection & Automation Gui e 25 Fun amental Theor y 3

2.5 1.6 A E

51 1.2 B 30.6 E

Most re uction problems follow the same pattern as the example above. The rules to apply in practical network re uction are: a. eci e on the nature of the ist urbance or isturbances to be stu ie b. eci e on the information require , for example the branch currents in the network for a fault at a particular location c. re uce all passive sections of the network not irectly involve with the se ction un er examination . re uce all active meshes to a simple equivalent, that is, to a simple source in series with a single impe ance With the wi esprea av ailability of computer-base power system simulation software, it is now usual t o use such software on a routine basis for network calculations without signific ant network re uction taking place. However, the network re uction techniques gi ven above are still vali , as there will be occasions where such software is not imme iately available an a han calculation must be carrie out. In certain ci rcuits, for example parallel lines on the same towers, there is mutual coupling between branches. Correct circuit re uction must take account of this coupling. Figure 3.13 P I Ib Zbb (a) Actual circuit I Z Z -Z2 Z= aa bb ab Zaa+Zbb-2Zab (b) Equivalent when ZaaZbb P I Z= 1 (Zaa+Zbb) 2 (c) Equivalent when Zaa=Zbb Figure 3.13: Re uction of two branches Figure 3.13: Re uction of two branches wi th mutual coupling coupling with mutual N Figure 3.10: Re uction using star/ elta transform

A Fun amental Theor y B 30.6 0.4 B E

30.6 E Ia

31 N

Zaa Zab Q N (b) Re uction of right active mesh Figure 3.11: Re uction of active meshes: Thven in s Theorem Figure 3.11: Re uction of active meshes: Thvenin s Theorem 3 The network shown in Figure 3.9 is now re uce to that shown in Figure 3.12 with

The network is to the active s with an impe A E 51 51 E 2.6

now re uce as shown in Figure 3.10. By applying Thvenin s theorem loops, these can be replace by a single riving voltage in serie ance as shown in Figure 3.11. Figure 3.11 1.6 52.6 N (a) Re uction of left active mesh N 0.4 x 30.6 31 1.6 x 51 5

0.4

the no es A an B retaining their i entity. Further, the loa impe ance has bee n completely eliminate . The network shown in Figure 3.12 may now be use to stu y system isturbances, for example power swings with an without faults. Figure 3.12 2.5 1.55 A 1.2 0.97E 0.99E B 0.39 P Q Q

Three cases are of interest. These are: a. two branches connecte together at th eir no es b. two branches connecte together at one no e only c. two branches th at remain unconnecte N Figure 3.12: Re uction of typical Figure 3.12: Re uction of typical power system network power system network 26 Network Protection & Automation Gui e

Consi ering each case in turn: a. consi er the circuit shown in Figure 3.13(a). The application of a voltage V between the terminals P an Q gives: V = IaZaa + IbZab V = IaZab + IbZbb where Ia an Ib are the currents in branches a an b, re spectively an I = Ia + Ib , the total current entering at terminal P an leavin g at terminal Q. Solving for Ia an Ib : The assumption is ma e that an equivalent star network can replace the network s hown. From inspection with one terminal isolate in turn an a voltage V impress e across the remaining terminals it can be seen that: Za+Zc=Zaa Zb+Zc=Zbb Za+Zb =Zaa+Zbb-2Zab Solving these equations gives: Ia = from which (Zbb Zab )V 2 Zaa Zbb Zab Za = Zaa Zab Zb = Zbb Zab see Figure 3.14(b). Equation 3.23 Ib = and (Zaa Zab )V 2 Zaa Zbb Zab I = Ia +Ib = V (Zaa + Zbb 2 Zab ) 2 Zaa Zbb Zab c. consider the our terminal network given in Figure 3.15(a), in which the bran ches 11' and 22' are electrically separate except or a mutual link. The equatio ns de ining the network are: V1=Z11I1+Z12I2 I1=Y11V1+Y12V2 V2=Z21I1+Z22I2 I2=Y21 V1+Y22V2 where Z12=Z21 and Y12=Y21 , i the network is assumed to be reciprocal. Further, by solving the above equations it can be shown that: 2 Zaa Zbb Zab V Z= = I Zaa + Zbb 2 Zab Equation 3.21 (Figure 3.13(b)), and, i the branch impedances are equal, the usual case, then: Z= (Figure 3.13(c)). 1 (Zaa + Zab ) 2 Equation 3.22 Y11 = Z22 b. consider the circuit in Figure 3.14(a). Zaa A Zab B C Y22 = Z11 Equation 3.24 Y12 = Z12 2 = Z11Z22 Z12 Zc = Zab

Zbb (a) Actual circuit Za=Zaa Zab There are three independent coe icients, namely Z12, Z11, Z22, so the original circuit may be replaced by an equivalent mesh containing our external terminals , each terminal being connected to the other three by branch impedances as shown in Figure 3.15(b). A C Zc=Zab B Zb=Zbb Zab (b) Equivalent circuit Figure 3.14: Reduction o mutually coupled branches with a common terminal 1 Z11 Z12 1' 1 Z12 Z12 Z11 Z21 Z22 Z12 1' 2 Z22 2' 2 2' (a) Actual circuit 1 Z11 Z12 Z12 27 (b) Equivalent circuit Z11 Figure 3.15 : Equivalent circuits or 1 1' Z12 our t erminal network with mutual coupling Z12 2 Z12 Z12 (d) Equivalent circuit Z12 2' Figure 3.14: Reduction o mutually coupled branches with a common terminal Network Protection & Automation Guide C (c) Equivalent with all nodes commoned Fundamental Theor y so that the equivalent impedance o the original circuit is: 3

In order to evaluate the branches o the equivalent mesh let all points o entry o the actual circuit be commoned except node 1 o circuit 1, as shown in Figur e 3.15(c). Then all impressed voltages except V1 will be zero and: I1 = Y11V1 I2 = Y12V1 I the same conditions are applied to the equivalent mesh, then: I1 = V 1Z11 I2 = V1/Z12 = V1/Z12 These relations ollow rom the act that the branch connecting nodes 1 and 1' carries current I1 and the branches connecting nodes 1 and 2' and 1 and 2 carry current I2. This must be true since branches between pairs o commoned nodes can carry no current. By considering each node in turn w ith the remainder commoned, the ollowing relationships are ound: Z11 = 1/Y11 Z2 2 = 1/Y22 efining the equivalent mesh in Figure 3.15(b), an inserting ra ial branches ha ving impe ances equal to Z11 an Z22 in terminals 1 an 2, results in Figure 3.1 5( ). 3.7 REFERENCES 3.1 Power System Analysis. J. R. Mortlock an M. W. Humphre y Davies. Chapman & Hall. 3.2 Equivalent Circuits I. Frank M. Starr, Proc. A.I.E .E. Vol. 51. 1932, pp. 287-298. Fun amental Theor y Z12 = -1/Y12 Z12 = Z1 2 = -Z21 = -Z12 Z Z Z 2 Z ' = 11 22 2 12 Z11 11 Z11Z22-Z 12 = _______________ Z22 Z22 2 Z11Z22 Z= = Z22 22 Z11Z22-Z212 _______________ Z11 Z11 2 Z11Z -Z2Z12 Z12 12 Z11Z2222 2 Z= = _______________ ZZ12 Equation 3.25 12 A similar but equally rigorous equiv alent circuit is shown in Figure 3.15(d). This circuit [3.2] ollows rom the a ct that the sel impedance o any circuit Z11 Z11 1 1' 1' is independent o all other circuits. There ore, it need not appear in any o the mutual branches i i t Z12 Z12 Z Z Z is lumped as a radial branch at12 terminals. So the 21 12 puttin g Z11 and Z22 equal to zero in Equation 2' 3.25, 2 2' Z22 Z22 (b) Equivalent circuit 1 Z11 Z12 Z12 C (c) Equivalent with all nodes com moned except 1 2 Z11 Z12 Z12 Z12 Z12 (d) Equivalent circuit Z12 2' 1' Hence: 3 1 2 (a) Actual circuit 1 Figure 3.15: Equivalent circuits or our terminal network with mutual coupling Figure 3.15: Equivalent circuits or our terminal network with mutual coupling 28 Network Protection & Automation Guide

4

Symmetrical component analysis o a three phase network Equations and network co nnections or various types o aults Current and voltage distribution in a syst em due to a ault E ect o system earthing on zero sequence quantities Re erenc es

Fault Calculations Introduction Three phase

ault calculations 4.1 4.2 4.3 4.4 4.5 4.6 4.7

4 Fault Calculations 4.1 INTRODUCTION A power system is normally treated as a balanced symmetrical th ree phase network. When a ault occurs, the symmetry is normally upset, resultin g in unbalanced currents and voltages appearing in the network. The only excepti on is the three phase ault, which, because it involves all three phases equally at the same location, is described as a symmetrical ault. By using symmetrical component analysis and replacing the normal system sources by a source at the ault location, it is possible to analyse these ault conditions. For the correct application o protection equipment, it is essential to know the ault current distribution throughout the system and the voltages in di erent parts o the sy stem due to the ault. Further, boundary values o current at any relaying point must be known i the ault is to be cleared with discrimination. The in ormatio n normally required or each kind o ault at each relaying point is: i. maximum ault current ii. minimum ault current iii. maximum through ault current To o btain the above in ormation, the limits o stable generation and possible operat ing conditions, including the method o system earthing, must be known. Faults a re always assumed to be through zero ault impedance. 4 . 2 T H R E E P H A S E F A U LT C A L C U L AT I O N S Three phase aults are unique in that they are balanced, that is, symmetrical in the three phases, and can be calculated rom the single phase impedance diagram and the operating conditions existing prior t o the ault. A ault condition is a sudden abnormal alteration to the normal cir cuit arrangement. The circuit quantities, current and voltage, will alter, and t he circuit will pass through a transient state to a steady state. In the transie nt state, the initial magnitude o the ault current will depend upon the point on the voltage wave at which the ault occurs. The decay o the transient condit ion, until it merges into steady state, is a unction o the parameters o the c ircuit elements. The transient current may be regarded as a d.c. exponential cur rent Network Protection & Automation Guide 31

superimposed on the symmetrical steady state ault current. In a.c. machines, ow ing to armature reaction, the machine reactances pass through 'sub transient' an d 'transient' stages be ore reaching their steady state synchronous values. For this reason, the resultant ault current during the transient period, rom ault inception to steady state also depends on the location o the ault in the netw ork relative to that o the rotating plant. In a system containing many voltage sources, or having a complex network arrangement, it is tedious to use the norma l system voltage sources to evaluate the ault current in the aulty branch or t o calculate the ault current distribution in the system. A more practical metho d [4.1] is to replace the system voltages by a single driving voltage at the au lt point. This driving voltage is the voltage existing at the ault point be ore the ault occurs. Consider the circuit given in Figure 4.1 where the driving vo ltages are E and E , the impe ances on either si e of fault point F are Z1 an Z1 , an the current through point F before the fault occurs is I . Figure 4.1: Z 1 I F Z 1 be a e to the currents circulating in the system ue to the fault, to give the total current in any branch of the system at the time of fault inception. Howev er, in most problems, the loa current is small in comparison to the fault curre nt an is usually ignore . In a practical power system, the system regulation is such that the loa voltage at any point in the system is within 10% of the ecl are open-circuit voltage at that point. For this reason, it is usual to regar the pre-fault voltage at the fault as being the open-circuit voltage, an this a ssumption is also ma e in a number of the stan ar s ealing with fault level cal culations. For an example of practical three-phase fault calculations, consi er a fault at A in Figure 3.9. With the network re uce as shown in Figure 4.2, the loa voltage at A before the fault occurs is: Figure 4.2: 1.55 A 1.2 0.97E 0.99E 2.5 B 0.39 Fa u l t C a l c u l a t i o n s

V Figure 4.2: Re uction of typical power system network V = 0.97 E - 1.55 I N Figure 4.1: Network with fault at F 4

The voltage V at F before fault inception is: V = E - I Z = E + I Z Af voltage V 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: Z1 + Z1 V = V ' '' Z1 Z1 Z1 and, since no current was lowing into the netwo rk rom F prior to the ault, the ault current lowing rom the network into th e ault is:

1.2 2.5 + E 1.207 I A an N mo ifies The no e A is the

0.39 I V . Hence E the circuit junction of

= 0.99 E '' + 2.5 + 1.2 For practical working co E V. Replacing the riving voltages E an E by the as shown in Figure 4.3(a). three branches. In practice, the no e woul be a b

N E E

usbar, an the branches are fee ers ra iating from the bus via circuit breakers, as shown in Figure 4.3(b). There are two possible locations for a fault at A; t he busbar si e of the breakers or the line si e of the breakers. In this example , it is assume that the fault is at X, an it is require to calculate the curr ent flowing from the bus to X. The network viewe from AN has a riving point im pe ance Z1 = 0.68 ohms. The current in the fault is I = ( ) ' '' Z1 Z1 By applying the principle o superposition, the load currents circula ting in the system prior to the ault may

( Z1' + Z1'' ) = I = V V Z1 . 32 Network Protection & Automation Guide

I

Let this current be 1.0 per unit. It is now necessary to find the fault current distribution in the various branches of the network and in particular the curren t flowing from A to X on the assumption that a relay at X is to detect the fault condition. The equivalent impedances viewed from either side of the fault are s hown in Figure 4.4(a). Figure 4.3 Figure 4.4 2.5 1.55 A V N (a) Three - phase fault iagram for a fault at no e A Busbar Circui t breaker 1.2 B 0.39 Therefore, current in 2.5 ohm branch 1.2 0.563 = 0.183 p.u. 3.7 an the current in 1.2 ohm branch = 2.5 0.563 = 0.38 p.u. 3.7 Total current entering X from the left, that is, from A to X, is 0.437 + 0.183 = 0.62 p.u. an from B to X is 0.38p.u. The equivalent network as viewe from the relay is as shown in Figure 4.4(b). The impe ances on either si e are: = an

0.68/0.62 = 1.1 ohms 0.68/0.38 = 1.79 ohms A X The circuit of Figure 4.4 (b) has been inclu e because the Protection Engineer is intereste in these equivalent parameters when applying certain types of prot ection relay. 4 . 3 S Y M M E T R I C A L C O M P O N E N T A N A LY S I S OF A THREE-PHASE NETWORK 1.21 (b) Typical physical arrangement of no e A with a fault shown at X Figure 4.3: Network with fault at no e A 1.55 A V N (a) Impe ance viewe from no e A 1.1 X 1.79 V N (b) Equivalent impe ances viewe from no e X Figure 4.4: Impe ances viewe from fault The Protection Engineer is intereste in a wi er variety of faults than just a t hree-phase fault. The most common fault is a single-phase to earth fault, which, in LV systems, can pro uce a higher fault current than a threephase fault. Simi larly, because protection is expecte to operate correctly for all types of faul t, it may be necessary to consi er the fault currents ue to many ifferent type s of fault. Since the three-phase fault is unique in being a balance fault, a m etho of analysis that is applicable to unbalance faults is require . It can be shown [4.2] that, by applying the Principle of Superposition , any general thr ee-phase system of vectors may be replace by three sets of balance (symmetrica l) vectors; two sets are three-phase but having opposite phase rotation an one

set is co-phasal. These vector sets are escribe as the positive, negative an zero sequence sets respectively. The equations between phase an sequence voltag es are gi