Transmission and Distribution Electrical Engineering PDF

Transmission and Distribution Electrical Engineering This Page Intentionally Left Blank Transmission and Distribution Electrical Engineering Second edition Dr C. R. Bayliss CEng FIEE Newnes An imprint of Elsevier Linacre House, Jordan Hill, Oxford OX2 8DP 200 Wheeler Road, Burlington, MA 01803 First published 1996 Second edition 1999 Reprinted 2001, 2002, 2003 Copyright © 1996, 1999, C. R. Bayliss. All rights reserved The right of C.R. Bayliss to be identiﬁed as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1T 4LP. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (;44) 1865 843830, fax: (;44) 1865 853333, e-mail: permissions/elsevier.co.uk. You may also complete your request on-line via the Elsevier homepage (http://www.elsevier.com), by selecting ‘Customer Support’ and then ‘Obtaining Permissions’ British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress ISBN 0 7506 4059 6 For information on all Newnes publications visit our website at www.newnespress.com Typeset by Vision Typesetting, Manchester Printed and bound in Great Britain by MPG Books Ltd, Bodmin Contents About the author xx List of Contributors xxi Preface xxiii 1 System Studies 1 1.1 Introduction 1 1.2 Load ﬂow 1 1.2.1 Purpose 1 1.2.2 Sample study 2 1.3 System stability 8 1.3.1 Introduction 8 1.3.2 Analytical aspects 10 1.3.3 Steady state stability 14 1.3.4 Transient stability 17 1.3.5 Dynamic stability 28 1.3.6 Eﬀect of induction motors 28 1.3.7 Data requirements and interpretation of transient stability studies 29 1.3.8 Case studies 34 1.4 Short circuit analysis 42 1.4.1 Purpose 42 1.4.2 Sample study 42 2 Drawings and Diagrams 50 2.1 Introduction 50 2.2 Block diagrams 50 2.3 Schematic diagrams 51 2.3.1 Method of representation 51 2.3.2 Main circuits 55 v vi Contents 2.3.3 Control, signalling and monitoring circuits 55 2.4 Manufacturers’ drawings 55 2.4.1 Combined wiring/cabling diagrams 55 2.4.2 British practice 61 2.4.3 European practice 63 2.4.4 Other systems 68 2.5 Computer aided design (CAD) 68 2.6 Case study 69 2.7 Graphical symbols 70 Appendix A—Relay identiﬁcation—numerical codes 72 Appendix B—Comparison between German, British, US/Canadian and international symbols 82 B1 General circuit elements 83 B2 Operating mechanisms 86 B3 Switchgear 89 3 Substation Layouts 92 3.1 Introduction 92 3.2 Substation design considerations 92 3.2.1 Security of supply 92 3.2.2 Extendibility 93 3.2.3 Maintainability 93 3.2.4 Operational ﬂexibility 94 3.2.5 Protection arrangements 94 3.2.6 Short circuit limitations 94 3.2.7 Land area 94 3.2.8 Cost 95 3.3 Alternative layouts 95 3.3.1 Single busbar 95 3.3.2 Transformer feeder 97 3.3.3 Mesh 101 3.3.4 Ring 103 3.3.5 Double busbar 104 3.3.6 1 Circuit breaker 106 3.4 Space requirements 106 3.4.1 Introduction 106 3.4.2 Safety clearances 108 3.4.3 Phase-phase and phase-earth clearances 109 4 Substation Auxiliary Power Supplies 115 4.1 Introduction 115 4.2 DC supplies 115 4.2.1 Battery/battery charger conﬁgurations 115 4.2.2 Battery charger components 118 Contents vii 4.2.3 Installation requirements 121 4.2.4 Typical enquiry data—DC switchboard 124 4.3 Batteries 125 4.3.1 Introduction 125 4.3.2 Battery capacity 125 4.3.3 Characteristics of batteries 128 4.3.4 Battery sizing calculations 129 4.3.5 Typical enquiry data 132 4.4 AC supplies 134 4.4.1 Power sources 134 4.4.2 LVAC switchboard fault level 134 4.4.3 Auxiliary transformer LV connections 134 4.4.4 Allowance for future extension 136 4.4.5 Typical enquiry data 138 4.4.6 Earthing transformer selection 139 4.4.7 Uninterruptible power supplies 143 5 Current and Voltage Transformers 147 5.1 Introduction 147 5.2 Current transformers 147 5.2.1 Introduction 147 5.2.2 Protection CT classiﬁcations 147 5.2.3 Metering CTs 151 5.2.4 Design and construction considerations 152 5.2.5 Terminal markings 154 5.2.6 Speciﬁcations 155 5.3 Voltage transformers 155 5.3.1 Introduction 155 5.3.2 Electromagnetic VTs 155 5.3.3 Capacitor VTs 156 5.3.4 Speciﬁcations 157 6 Insulators 160 6.1 Introduction 160 6.2 Insulator materials 160 6.2.1 Polymeric and resin materials 160 6.2.2 Glass and porcelain 161 6.3 Insulator types 161 6.3.1 Post insulators 161 6.3.2 Cap and pin insulators 165 6.3.3 Long rod 166 6.4 Pollution control 167 6.4.1 Environment/creepage distances 167 6.4.2 Remedial measures 169 viii Contents 6.4.3 Calculation of speciﬁc creepage path 170 6.5 Insulator speciﬁcation 171 6.5.1 Standards 171 6.5.2 Design characteristics 175 6.6 Tests 176 6.6.1 Sample and routine tests 176 6.6.2 Technical particulars 177 7 Substation Building Services 179 7.1 Introduction 179 7.2 Lighting 179 7.2.1 Terminology 179 7.2.2 Internal lighting 185 7.2.3 External lighting 187 7.2.4 Control 195 7.3 Distribution characterization 196 7.4 Heating, ventilation and air conditioning 199 7.4.1 Air circulation 199 7.4.2 Air conditioning 201 7.4.3 Heating 206 7.5 Fire detection and suppression 206 7.5.1 Introduction 206 7.5.2 Fire extinguishers 207 7.5.3 Access, ﬁrst aid and safety 207 7.5.4 Fire detection 208 7.5.5 Fire suppression 211 7.5.6 Cables, control panels and power supplies 212 8 Earthing and Bonding 214 8.1 Introduction 214 8.2 Design criteria 215 8.2.1 Time/current zones of eﬀects of AC currents on persons 215 8.2.2 Touch and step voltages 215 8.2.3 Comparison of touch and step potential design criteria 217 8.3 Substation earthing calculation methodology 220 8.3.1 Boundary conditions 220 8.3.2 Earthing materials 222 8.3.3 Earthing impedance and earthing voltage 225 8.3.4 Hazard voltage tolerable limits 226 8.4 Computer generated results 228 8.4.1 Introduction 228 8.4.2 Case study 231 References 232 Contents ix 9 Insulation Co-ordination 234 9.1 Introduction 234 9.2 System voltages 234 9.2.1 Power frequency voltages 234 9.2.2 Overvoltages 235 9.3 Clearances 245 9.3.1 Air 245 9.3.2 SF 246 9.4 Procedures for co-ordination 247 9.4.1 Statistical approach 247 9.4.2 Non-statistical approach 248 9.5 Surge protection 248 9.5.1 Rod or spark gaps 248 9.5.2 Surge arresters 250 References 265 10 Relay Protection 266 10.1 Introduction 266 10.2 System conﬁgurations 267 10.2.1 Faults 267 10.2.2 Unearthed systems 267 10.2.3 Impedance earthed systems 267 10.2.4 Solidly earthed systems 268 10.2.5 Network arrangements 268 10.3 Power system protection principles 271 10.3.1 Discrimination by time 271 10.3.2 Discrimination by current magnitude 272 10.3.3 Discrimination by time and fault direction 272 10.3.4 Unit protection 272 10.3.5 Signalling channel assistance 273 10.4 Current relays 274 10.4.1 Introduction 274 10.4.2 Inverse deﬁnite minimum time lag (IDMTL) relays 274 10.4.3 Alternative characteristic curves 277 10.4.4 Plotting relay curves on log/log graph paper 277 10.4.5 Current relay application examples 278 10.5 Diﬀerential protection schemes 289 10.5.1 Biased diﬀerential protection 289 10.5.2 High impedance protection 292 10.5.3 Transformer protection application examples 293 10.5.4 Pilot wire unit protection 297 10.5.5 Busbar protection 300 10.6 Distance relays 303 10.6.1 Introduction 303 x Contents 10.6.2 Basic principles 304 10.6.3 Relay characteristics 305 10.6.4 Zones of protection 309 10.6.5 Switched relays 311 10.6.6 Typical overhead transmission line protection schemes 312 10.7 Auxiliary relays 316 10.7.1 Tripping and auxiliary 316 10.7.2 AC auxiliary relays 321 10.7.3 Timers 321 10.7.4 Undervoltage 321 10.7.5 Underfrequency 322 10.8 Computer assisted grading exercise 325 10.8.1 Basic input data 325 10.8.2 Network fault levels 325 10.8.3 CT ratios and protection devices 326 10.8.4 Relay settings 326 10.9 Practical distribution network case study 326 10.9.1 Introduction 326 10.9.2 Main substation protection 328 10.9.3 Traction system protection 328 10.9.4 21 kV distribution system and protection philosophy 331 10.9.5 21 kV pilot wire unit protection 332 10.9.6 21 kV system backup protection 333 10.9.7 Use of earth fault indicators 335 10.9.8 Summary 335 11 Fuses and Miniature Circuit Breakers 336 11.1 Introduction 336 11.2 Fuses 336 11.2.1 Types and standards 336 11.2.2 Deﬁnitions and terminology 339 11.2.3 HRC fuses 339 11.2.4 High voltage fuses 344 11.2.5 Cartridge fuse construction 349 11.3 Fuse operation 350 11.3.1 High speed operation 350 11.3.2 Discrimination 351 11.3.3 Cable protection 354 11.3.4 Motor protection 355 11.3.5 Semiconductor protection 357 11.4 Miniature circuit breakers 359 11.4.1 Operation 359 11.4.2 Standards 360 11.4.3 Application 361 Contents xi References 367 12 Cables 368 12.1 Introduction 368 12.2 Codes and standards 368 12.3 Types of cables and materials 371 12.3.1 General design criteria 371 12.3.2 Cable construction 371 12.3.3 Submarine cables 382 12.3.4 Terminations 382 12.4 Cable sizing 383 12.4.1 Introduction 383 12.4.2 Cables laid in air 383 12.4.3 Cables laid direct in ground 385 12.4.4 Cables laid in ducts 386 12.4.5 Earthing and bonding 387 12.4.6 Short circuit ratings 390 12.4.7 Calculation examples 392 12.5 Calculation of losses in cables 403 12.5.1 Dielectric losses 403 12.5.2 Screen or sheath losses 403 12.6 Fire properties of cables 404 12.6.1 Toxic and corrosive gases 404 12.6.2 Smoke emission 405 12.6.3 Oxygen index and temperature index 405 12.6.4 Flame retardance/ﬂammability 406 12.6.5 Fire resistance 406 12.6.6 Mechanical properties 407 12.7 Control and communication cables 407 12.7.1 Low voltage and multicore control cables 407 12.7.2 Telephone cables 408 12.7.3 Fibre optic cables 410 12.8 Cable management systems 416 12.8.1 Standard cable laying arrangements 416 12.8.2 Computer aided cable installation systems 419 12.8.3 Interface deﬁnition 425 References 428 13 Switchgear 429 13.1 Introduction 429 13.2 Terminology and standards 429 13.3 Switching 431 13.3.1 Basic principles 431 13.3.2 Special switching cases 443 xii Contents 13.3.3 Switches and disconnectors 446 13.3.4 Contactors 447 13.4 Arc quenching media 453 13.4.1 Introduction 453 13.4.2 Sulphur hexaﬂuoride (SF ) 454 13.4.3 Vacuum 460 13.4.4 Oil 461 13.4.5 Air 463 13.5 Operating mechanisms 465 13.5.1 Closing and opening 465 13.5.2 Interlocking 469 13.5.3 Integral earthing 471 13.6 Equipment speciﬁcations 471 13.6.1 12 kV metal-clad indoor switchboard example 471 13.6.2 Open terminal 145 kV switchgear examples 475 13.6.3 Distribution system switchgear example 481 13.6.4 Distribution ring main unit 485 14 Power Transformers 490 14.1 Introduction 490 14.2 Standards and principles 490 14.2.1 Basic transformer action 490 14.2.2 Transformer equivalent circuit 492 14.2.3 Voltage and current distribution 494 14.2.4 Transformer impedance representation 494 14.2.5 Tap changers 497 14.2.6 Useful standards 507 14.3 Voltage, impedance and power rating 508 14.3.1 General 508 14.3.2 Voltage drop 509 14.3.3 Impedance 509 14.3.4 Voltage ratio and tappings — general 510 14.3.5 Voltage ratio with oﬀ-circuit tappings 510 14.3.6 Voltage ratio and on-load tappings 511 14.3.7 Basic insulation levels (BIL) 511 14.3.8 Vector groups and neutral earthing 511 14.3.9 Calculation example to determine impedance and tap range 514 14.4 Thermal design 522 14.4.1 General 522 14.4.2 Temperature rise 523 14.4.3 Loss of life expectancy with temperature 524 14.4.4 Ambient temperature 525 14.4.5 Solar heating 526 Contents xiii 14.4.6 Transformer cooling classiﬁcations 526 14.4.7 Selection of cooling classiﬁcation 529 14.4.8 Change of cooling classiﬁcation in the ﬁeld 530 14.4.9 Capitalization of losses 531 14.5 Constructional aspects 532 14.5.1 Cores 532 14.5.2 Windings 533 14.5.3 Tanks and enclosures 535 14.5.4 Cooling plant 537 14.5.5 Low ﬁre risk types 538 14.5.6 Neutral earthing transformers 540 14.5.7 Reactors 541 14.6 Accessories 543 14.6.1 General 543 14.6.2 Buchholz relay 543 14.6.3 Sudden pressure relay and gas analyser relay 544 14.6.4 Pressure relief devices 544 14.6.5 Temperature monitoring 544 14.6.6 Breathers 545 14.6.7 Miscellaneous 545 14.6.8 Transformer ordering details 547 References 553 15 Substation and Overhead Line Foundations 555 15.1 Introduction 555 15.2 Soil investigations 555 15.3 Foundation types 556 15.4 Foundation design 565 15.5 Site works 565 15.5.1 Setting out 565 15.5.2 Excavation 565 15.5.3 Piling 566 15.5.4 Earthworks 567 15.5.5 Concrete 568 15.5.6 Steelwork ﬁxings 573 16 Overhead Line Routing 575 16.1 Introduction 575 16.2 Routing objectives 575 16.3 Preliminary routing 577 16.3.1 Survey equipment requirements 577 16.3.2 Aerial survey 577 16.3.3 Ground survey 577 16.3.4 Ground soil conditions 577 xiv Contents 16.3.5 Wayleave, access and terrain 577 16.3.6 Optimization 579 16.4 Detailed line survey and proﬁle 581 16.4.1 Accuracy requirements 581 16.4.2 Proﬁle requirements 582 16.4.3 Computer aided techniques 584 17 Structures, Towers and Poles 586 17.1 Introduction 586 17.2 Environmental conditions 587 17.2.1 Typical parameters 587 17.2.2 Eﬀect on tower or support design 588 17.2.3 Conductor loads 592 17.2.4 Substation gantry combined loading example 598 17.3 Structure design 599 17.3.1 Lattice steel tower design considerations 599 17.3.2 Tower testing 611 17.4 Pole and tower types 611 17.4.1 Pole structures 611 17.4.2 Tower structures 613 References 618 18 Overhead Line Conductor and Technical Speciﬁcations 619 18.1 Introduction 619 18.2 Environmental conditions 619 18.3 Conductor selection 620 18.3.1 General 620 18.3.2 Types of conductor 621 18.3.3 Aerial bundled conductor 624 18.3.4 Conductor breaking strengths 625 18.3.5 Bi-metal connectors 626 18.3.6 Corrosion 626 18.4 Calculated electrical ratings 628 18.4.1 Heat balance equation 628 18.4.2 Power carrying capacity 629 18.4.3 Corona discharge 632 18.4.4 Overhead line calculation example 636 18.5 Design spans, clearances and loadings 639 18.5.1 Design spans 639 18.5.2 Conductor and earth wire spacing and clearances 650 18.5.3 Broken wire conditions 661 18.5.4 Conductor tests/inspections 661 18.6 Overhead line ﬁttings 661 18.6.1 Fittings related to aerodynamic phenomena 661 Contents xv 18.6.2 Suspension clamps 665 18.6.3 Sag adjusters 665 18.6.4 Miscellaneous ﬁttings 665 18.7 Overhead line impedance 665 18.7.1 Inductive reactance 665 18.7.2 Capacitive reactance 667 18.7.3 Resistance 668 18.8 Substation busbar selection—case study 668 18.8.1 Introduction 668 18.8.2 Conductor diameter/current carrying capacity 668 18.8.3 Conductor selection of weight basis 669 18.8.4 Conductor short circuit current capability 672 18.8.5 Conductor support arrangements 673 References 677 19 Testing and Commissioning 680 19.1 Introduction 680 19.2 Quality assurance 680 19.2.1 Introduction 680 19.2.2 Inspection release notice 682 19.2.3 Partial acceptance testing 682 19.2.4 System acceptance testing 682 19.2.5 Documentation and record systems 683 19.3 Works inspections and testing 685 19.3.1 Objectives 685 19.3.2 Speciﬁcations and responsibilities 685 19.3.3 Type tests 685 19.3.4 Routine tests 686 19.4 Site inspection and testing 686 19.4.1 Pre-commissioning and testing 686 19.4.2 Maintenance inspection 687 19.4.3 On-line inspection and testing 687 19.5 Testing and commissioning methods 691 19.5.1 Switchgear 691 19.5.2 Transformers 701 19.5.3 Cables 704 19.5.4 Protection 707 Appendix A Commissioning test procedure requirements 723 Appendix B Drawings, diagrams and manuals 724 20 Electromagnetic Compatibility 726 20.1 Introduction 726 20.2 Standards 726 20.3 Testing 727 xvi Contents 20.3.1 Magnetic ﬁeld radiated emission measurements 728 20.3.2 Electric ﬁeld radiated emission measurements 730 20.3.3 Conducted emission measurements 732 20.3.4 Immunity testing 732 20.4 Screening 734 20.4.1 The use of screen wire 734 20.4.2 The use of screen boxes and Faraday enclosures 734 20.4.3 The use of screen ﬂoors in rooms 738 20.5 Typical useful formulae 739 20.5.1 Decibel reference levels 740 20.5.2 Field strength calculations 740 20.5.3 Mutual inductance between two long parallel pairs of wires 741 20.5.4 Attenuation factors 741 20.6 Case studies 742 20.6.1 Screening power cables 742 20.6.2 Measurement of ﬁeld strengths 745 References 747 21 System Control and Data Acquisition 748 21.1 Introduction 748 21.2 Programmable logic controllers (PLCs) 748 21.2.1 Functions 748 21.2.2 PLC selection 750 21.2.3 Application example 753 21.3 Power line carrier communication links 758 21.3.1 Introduction 758 21.3.2 Power line carrier communication principles 761 21.4 Supervisory control and data acquisition (SCADA) 766 21.4.1 Introduction 766 21.4.2 Typical characteristics 767 21.4.3 Design issues 769 21.4.4 Example (Channel Tunnel) 770 21.5 Software management 772 21.5.1 Software—a special case 773 21.5.2 Software life cycle 774 21.5.3 Software implementation practice 778 21.5.4 Software project management 780 References 783 22 Project Management 784 22.1 Introduction 784 22.2 Project evaluation 784 22.2.1 Introduction 784 Contents xvii 22.2.2 Financial assessment 785 22.2.3 Economic assessment 792 22.3 Financing 796 22.3.1 Responsibilities for funding 796 22.3.2 Cash ﬂow 796 22.3.3 Sources of ﬁnance 797 22.3.4 Export credit agencies 798 22.3.5 Funding risk reduction 798 22.4 Project phases 800 22.4.1 The project life cycle 800 22.4.2 Cash ﬂow 803 22.4.3 Bonds 804 22.4.4 Advance payments and retentions 806 22.4.5 Insurances 806 22.4.6 Project closeout 806 22.5 Terms and conditions of contract 807 22.5.1 Time, cost and quality 807 22.5.2 Basic types of contract 808 22.5.3 Standard terms and conditions of contract 810 22.5.4 Key clauses 812 22.6 Tendering 815 22.6.1 Choosing the contractor 815 22.6.2 Estimating 816 22.6.3 Tender evaluation 817 22.7 Model forms of contract—exercise 819 Appendix A Project deﬁnition/questionnaire 821 Appendix B Bidding checklist 845 23 Distribution Planning 849 23.1 Introduction 849 23.2 Deﬁnitions 851 23.2.1 Demand or average demand 851 23.2.2 Maximum demand (MD) 851 23.2.3 Demand factor 852 23.2.4 Utilization factor (UF) 852 23.2.5 Load factor (LDF) 853 23.2.6 Diversity factor (DF) 853 23.2.7 Coincident factor (CF) 855 23.2.8 Load diversity 855 23.2.9 Loss factor (LSF) 856 23.2.10 Load duration 860 23.2.11 Loss equivalent hours 861 23.2.12 Peak responsibility factor (PRF) 862 23.3 Load forecasting 863 xviii Contents 23.3.1 Users of load forecasts 863 23.3.2 The preparation of load forecasts 864 23.3.2 The micro load forecast 865 23.3.4 The macro load forecast 867 23.3.5 Nature of the load forecast 868 23.4 System parameters 870 23.4.1 Distribution feeder arrangements 870 23.4.2 Voltage drop calculations 871 23.4.3 Positive sequence resistance 873 23.4.4 Inductive reactance 874 23.4.5 Economic loading of distribution feeders and transformers 875 23.4.6 System losses 876 23.5 System reliability 877 23.5.1 Introduction 877 23.5.2 Reliability functions 880 23.5.3 Predictability analysis 882 23.6 Drawings and materials take oﬀ 886 24 Harmonics in Power Systems 888 24.1 Introduction 888 24.2 The nature of harmonics 888 24.2.1 Introduction 888 24.2.2 Three phase harmonics 889 24.3 The generation of harmonics 889 24.3.1 Transformers 890 24.3.2 Converters 890 24.3.3 The thyristor bridge 892 24.3.4 AC railway traction systems 894 24.3.5 Static VAr compensators and balancers 894 24.4 The eﬀects of harmonics 894 24.4.1 Heating eﬀects of harmonics 894 24.4.2 Overvoltages 896 24.4.3 Resonances 897 24.4.4 Interference 898 24.5 The limitation of harmonics 900 24.5.1 Harmonic ﬁlters 900 24.5.2 Capacitor detuning 902 24.6 Ferroresonance and subharmonics 903 24.6.1 Introduction 903 24.6.2 A physical description of ferroresonance 905 24.6.3 Subharmonics 906 24.7 References 906 Contents xix 25 Fundamentals 908 25.1 Introduction 908 25.2 Symbols and nomenclature 908 25.2.1 Symbols 909 25.2.2 Units and conversion tables 914 25.3 Alternating quantities 917 25.4 Vector representation 922 25.5 Vector algebra 922 25.5.1 The j operator 924 25.5.2 Exponential vector format 925 25.5.3 Polar co-ordinate vector format 925 25.5.4 Algebraic operations on vectors 925 25.5.5 The h operator 925 25.6 Sequence components 926 25.6.1 Theoretical background 926 25.6.2 Calculation methodology and approximations 927 25.6.3 Interpretation 928 25.7 Network fault analysis 932 25.7.1 Introduction 932 25.7.2 Fundamental formulae 933 25.7.3 Simpliﬁed network reduction example 938 25.8 Design optimization 944 25.8.1 Introduction 944 25.8.2 Technical problems 945 25.8.3 Loss reduction 949 25.8.4 Communication link gain or attenuation 958 25.8.5 Reactive compensation 958 25.8.6 Power factor correction calculation procedures 962 References 966 Index 969 About the author Colin Bayliss gained a ﬁrst class honurs degree in Electrical and Electronic Engineering at Nottingham University and went on to receive a PhD in Materials Science. He has worked on major power projects both at home in the UK and throughout the world with client, contractor and consultancy organizations. He was appointed Engineering Director by the Channel Tunnel main contractors (Transmache Link — TML) during the last two years of that project’s construction, having been involved previously in the earlier design stages. He is currently Planning, Performance and Engineering Director of the United Kingdom Atomic Energy Authority (UKAEA). xx Contributors The preparation of a book covering such a wide range of topics would not have been possible without contributions and advice from major manufacturers, electrical supply utilities, contractors, academics and consulting engineers. Indeed, encouragement for the preparation of this book has come from the Institution of Electrical Engineers (IEE) Transmission and Distribution Professional Group, P7, under the chairmanship of David Rigden (Hawker Siddeley Switchgear) and John Lewis (Scottish Power). The names of the major contributors are listed below. D. Auckland Professor of Electrical Engineering, University of Manchester A. Baker Principal Geotechnical Engineer, Balfour Beatty Projects and Engineering R. H. Barnes Associate Director and Principal Systems Analyst, Engineering and Power Development Consultants (EPDC) P. Bennett Director, Centre for Software Engineering N. Bird Director, Balfour Beatty Cruickshank Ltd K. Blackmore Senior Engineer, Interference Technology International L. Blake Yorkshire Electricity Group S. A. Bleazard Reyrolle Limited, Tyne and Wear D. Boulu Principal Engineer, Tractabel, Belgium D. Brady General Manager, Optimal Software Ltd D. Brown Director, BICC, Wrexham J. Finn Principal Engineer, Reyrolle Projects (formerly Power Systems Project Manager, TML) H. Grant Deputy Chief Design Engineer, Parsons Peebles Transformers, Edinburgh G. Harris Livingstone Hire M. R. Hill Marketing Director, Bowthorpe EMP Ltd P. Hindle Principal Engineer, GEC-Alsthom T&D Protection & Control I. Johnston Senior Software Engineer, Centre for Software Engineering xxi xxii Contributors C. Lau Senior Data Transmission and Control Engineer, TML F. J. Liptrot Technical Director, Allied Insulators G. Little Balfour Kilpatrick, Hackbridge, London I. E. Massey Senior Civil Engineer, Balfour Beatty Projects and Engineering T. Mennell Head of Engineering, EMMCO, Merlin Gerin E. Meyer Control Engineer, Technip, Paris A. Monro Design Engineer, Peebles Power Transformers, Edinburgh R. Monk Senior Applications Engineer, GEC-Alsthom T&D Protection & Control D. Moore Principal Engineer, National Grid Company (formerly Ewbank Preece Consulting Engineers) P. G. Newbery Technical Director, Cooper Bussmann (formerly Hawker Fusegear) G. Orawski Consultant Engineer, Balfour Beatty Power S. D. Pugh Senior SCADA Engineer, Centre for Software Development D. Rigden Director, Hawker Siddeley Switchgear A. Smith Design Draughtsman, EPDC M. Swinscale Principal Technical Engineer, Furze, Nottingham M. Tearall Senior Building Services Engineer, Wimpey Major Projects M. Teliani Senior Systems Engineer, Engineering and Power Develop- ment Consultants Ltd (EPDC) A. Thomas Senior Communications Engineer, Ewbank Preece Consulting Engineers Preface This book covers the major topics likely to be encountered by the transmission and distribution power systems engineer engaged upon international project works. Each chapter is self-contained and gives a useful practical introduction to each topic covered. The book is intended for graduate or technician level engineers and bridges the gap between learned university theoretical textbooks and detailed single topic references. It therefore provides a practical grounding in a wide range of transmission and distribution subjects. The aim of the book is to assist the project engineer in correctly specifying equipment and systems for his particular application. In this way manufacturers and contractors should receive clear and unambiguous transmission and distribution equipment or project enquiries for work and enable competitive and comparative tenders to be received. Of particular interest are the chapters on project, system and software management since these subjects are of increasing importance to power systems engineers. In particular the book should help the reader to understand the reasoning behind the diﬀerent speciﬁcations and methods used by diﬀerent electrical supply utilities and organizations throughout the world to achieve their speciﬁc transmission and distribution power system requirements. The second edition includes updates and corrections, together with the addition of two extra major chapters covering distribution planning and power system harmonics. C. R. Bayliss xxiii This Page Intentionally Left Blank 1 System Studies 1.1 INTRODUCTION This chapter describes the three main areas of transmission and distribution network analysis; namely load ﬂow, system stability and short circuit analysis. Such system studies necessitate a thorough understanding of network parameters and generating plant characteristics for the correct input of system data and interpretation of results. A background to generator characteristics is therefore included in Section 1.3. The analysis work, for all but the simplest schemes, is carried out using tried and proven computer programs. The application of these computer methods and the speciﬁc principles involved are described by the examination of some small distribution schemes in suﬃcient detail to be applicable for use with a wide range of commercially available computer software. The more general theoretical principles involved in load ﬂow and fault analysis data collection are explained in Chapter 25. 1.2 LOAD FLOW 1.2.1 Purpose A load ﬂow analysis allows identiﬁcation of real and reactive power ﬂows, voltage proﬁles, power factor and any overloads in the network. Once the network parameters have been entered into the computer database the analysis allows the engineer to investigate the performance of the network under a variety of outage conditions. The eﬀect of system losses and power factor correction, the need for any system reinforcement and conﬁrmation of economic transmission can then follow. 1 2 System Studies 1.2.2 Sample study 1.2.2.1 Network single line diagram Figure 1.1 shows a simple ﬁve busbar 6 kV generation and 33 kV distribution network for study. Table 1.1 details the busbar and branch system input data associated with the network. Input parameters are given here in a per unit (pu) format on a 100 MVA base. Diﬀerent programs may accept input data in diﬀerent formats, for example % impedance, ohmic notation, etc. Please refer to Chapter 25, for the derivation of system impedance data in diﬀerent formats from manufacturers’ literature. The network here is kept small in order to allow the ﬁrst-time user to become rapidly familiar with the procedures for load ﬂows. Larger networks involve a repetition of these procedures. 1.2.2.2 Busbar input database The busbars are ﬁrst set up in the program by name and number and in some cases by zone. Bus parameters are then entered according to type. A ‘slack bus’ is a busbar where the generation values, P(real power in MW) and Q (reactive power in MVAr), are unknown. Therefore busbar AO in the example is entered as a slack bus with a base voltage of 6.0 kV, a generator terminal voltage of 6.3 kV (1.05 pu) and a phase angle of 0.0 degrees (a default value). All load values on busbar AO are taken as zero (again a default value) due to unknown load distribution and system losses. A ‘P,Q generator bus’ is one where P and Q are speciﬁed to have deﬁnite values. If, for example, P is made equal to zero we have deﬁned the constant Q mode of operation for a synchronous generator. Parameters for busbar BO in the example may be speciﬁed with base voltage 6.0 kV, desired voltage 6.3 kV and default values for phase angle (0.0 degrees), load power (0.0 MW), load reactive power (0.0 MVAr), shunt reactance (0.0 MVAr) and shunt capacitance (0.0 pu). Alternatively, most programs accept generator busbar data by specifying real generator power and voltage. The program may ask for reactive power limits to be speciﬁed instead of voltage since in a largely reactive power network you cannot ‘ﬁx’ both voltage and reactive power — something has to ‘give way’ under heavy load conditions. Therefore busbar BO may be speciﬁed with generator power 9.0 MW, maximum and minimum reactive power as 4.3 MVAr and transient or subtransient reactance in per unit values. These reactance values are not used in the actual load ﬂow but are entered in anticipation of the need for subsequent fault studies. For the calculation of oil circuit breaker breaking currents or for electromechanical protection relay operating currents it is more usual to take the generator transient reactance values. This is because the subtransient reactance eﬀects will generally disappear within the ﬁrst few cycles and before the circuit breaker or System Studies 3 Figure 1.1 Load ﬂow sample study single line diagram Table 1.1 Load ﬂow sample study busbar and branch input data Bus data Voltage Gen Load Shunt Bus Bus Bus L or C Name Number Type pu Angle MW MVAR MW MVAR pu Slack AO 1 1 1.05 0.0 0 0 0 0 0 A 2 2 1.0 0.0 0 0 0 0 0 BO 3 3 1.0 0.0 9 4.3 0 0 0 B 4 4 1.0 0.0 0 0 0 0 0 C 5 5 1.0 0.0 0 0 25 9 0 Branch data Rpu Xpu Bpu Circ 100MVA 100MVA 100MVA Tap Bus Bus base base base ratio 1 2 — 0.5 — 1.02 2 4 0.8 1.73 — 0.0 2 5 0.2 1.15 — 0.0 3 4 — 0.8 — 1.02 4 5 0.08 0.46 — 0.0 4 System Studies protection has operated. Theoretically, when calculating maximum circuit breaker making currents subtransient generator reactance values should be used. Likewise for modern, fast (say 2 cycle) circuit breakers, generator breakers and with solid state fast-relay protection where accuracy may be important, it is worth checking the eﬀect of entering subtransient reactances into the database. In reality, the diﬀerence between transient and subtransient reactance values will be small compared to other system parameters (transformers, cables, etc.) for all but faults close up to the generator terminals. A ‘load bus’ has ﬂoating values for its voltage and phase angle. Busbar A in the example has a base voltage of 33 kV entered and an unknown actual value which will depend upon the load ﬂow conditions. 1.2.2.3 Branch input data base Branch data is next added for the network plant (transformers, cables, overhead lines, etc.) between the already speciﬁed busbars. Therefore from busbar A to busbar B the 30 km, 33 kV overhead line data is entered with resistance 0.8 pu, reactance 1.73 pu and susceptance 0.0 pu (unknown in this example and 0.0 entered as a default value). Similarly for a transformer branch such as from busbar AO to A data is entered as resistance 0.0 pu, reactance 0.5 pu (10% on 20 MVA base rating : 50% on 100 MVA base or 0.5 pu), susceptance 0.0 pu (unknown but very small compared to inductive reactance), load limit 20 MVA, from bus AO voltage 6 kV to bus A voltage 33.66 kV (1.02 pu taking into account transformer < 5% taps). Tap ranges and short-term overloads can be entered in more detail depending upon the exact program being used. 1.2.2.4 Saving data When working at the computer it is always best regularly to save your ﬁles both during data-base compilation as well as at the end of the procedure when you are satisﬁed that all the data has been entered correctly. Save data onto the hard disk and make ﬂoppy disk backups for safe keeping. Figure 1.2 gives a typical computer printout for the bus and branch data ﬁles associated with this example. 1.2.2.5 Solutions Diﬀerent programs use a variety of diﬀerent mathematical methods to solve the load ﬂow equations associated with the network. Some programs ask the user to specify what method they wish to use from a menu of choices (Newton—Raphson, Gauss—Seidel, Fast decoupled with adjustments, etc.). A System Studies 5 Figure 1.2 Load ﬂow sample study busbar and branch computer input data ﬁles 6 System Studies Figure 1.3 Load ﬂow sample study base case busbar and branch report System Studies 7 Figure 1.4 Load ﬂow sample study. Base case load ﬂow results superimposed upon single line diagram. full understanding of these numerical methods is beyond the scope of this book. It is worth noting, however, that these methods start with an initial approximation and then follow a series of iterations or steps in order to eliminate the unknowns and ‘home in’ on the solutions. The procedure may converge satisfactorily in which case the computer continues to iterate until the diﬀerence between successive iterates is suﬃciently small. Alternatively, the procedure may not converge or may only converge extremely slowly. In these cases it is necessary to re-examine the input data or alter the iteration in some way or, if desired, stop the iteration altogether. The accuracy of the solution and the ability to control round-oﬀ errors will depend, in part, upon the way in which the numbers are handled in the computer. For accurate ﬂoating-point arithmetic, where the numbers are represented with a ﬁxed number of signiﬁcant ﬁgures, a microcomputer with separate maths coprocessor integrated circuit or a central processing unit (CPU) with in-built maths coprocessor (for example the Intel 80486DX integrated circuit) will be required. It is a most important principle in numerical work that all sources of error (round-oﬀ, mistakes, nature of 8 System Studies formulae used, approximate physical input data) must be constantly borne in mind if the ‘junk in equals junk out’ syndrome is to be avoided. Some customers ask their engineering consultants or contractors to prove their software by a Quality Assurance Audit which assesses the performance of one software package with another for a single trial network. Figure 1.3 gives typical busbar and branch reports resulting from a load ﬂow computation. It is normal to present such results by superimposing them in the correct positions on the single line diagram as shown in Fig. 1.4. Such a pictorial representation may be achieved directly with the more sophisticated system analysis programs. The network single line diagram is prepared using a computer graphics program (Autocad, Autosketch, GDS, etc.) and the load ﬂow results transferred using data exchange ﬁles into data blocks on the diagram. 1.2.2.6 Further studies The network already analysed may be modiﬁed as required, changing loads, generation, adding lines or branches (reinforcement) or removing lines (simulating outages). Consider, for example, removing or switching oﬀ either of the overhead line branches running from busbars A to C or from B to C. Non-convergence of the load ﬂow numerical analysis occurs because of a collapse of voltage at busbar C. If, however, some reactive compensation is added at busbar C — for example a 33 kV, 6 MVAr (0.06 pu) capacitor bank — not only is the normal load ﬂow improved, but the outage of line BC can be sustained. An example of a computer generated single-line diagram describing this situation is given in Fig. 1.5. This is an example of the beauty of computer aided system analysis. Once the network is set up in the database the engineer can investigate the performance of the network under a variety of conditions. Refer to Chapter 25 ‘Fundamentals’, Section 8.5 regarding Reactive Compensation principles. 1.3 SYSTEM STABILITY 1.3.1 Introduction The problem of stability in a network concerns energy balance and the ability to generate suﬃcient restoring forces to counter system disturbances. Minor disturbances to the system result in a mutual interchange of power between the machines in the system acting to keep them in step with each other and to maintain a single universal frequency. A state of equilibrium is retained between the total mechanical power/energy input and the electrical power/energy output by natural adjustment of system voltage levels and the common system frequency. There are three regimes of stability. System Studies 9 Figure 1.5 Load ﬂow sample study. Computer generated results superimposed on single-line diagram-reactive compensation added. Steady state stability describes the ability of the system to remain in synchronism during minor disturbances or slowly developing system changes such as a gradual increase in load as the 24-hour maximum demand is approached. Transient stability is concerned with system behaviour following an abrupt change in loading conditions as could occur as a result of a fault, the sudden loss of generation or an interconnecting line, or the sudden connection of additional load. The duration of the transient period is in the order of a second. System behaviour in this interval is crucial in the design of power systems. Dynamic stability is a term used to describe the behaviour of the system in the interval between transient behaviour and the steady state region. For example, dynamic stability studies could include the behaviour of turbine governors, steam/fuel ﬂows, load shedding and the recovery of motor loads, etc. The response of induction motors to system disturbances and motor starting is also thought of as a stability problem. It does not relate speciﬁcally to the ability of the system to remain in synchronism. This description is divided into two parts: the ﬁrst deals with the analytical nature of synchronous machine behaviour and the diﬀerent types of stability; the second deals with the more practical aspects of data collection and interpretation of transient stability study results with case studies to illustrate 10 System Studies the main points and issues. The complexity of such analysis demands the use of mini- or microcomputing techniques and considerable data collection. 1.3.2 Analytical aspects 1.3.2.1 Vector diagrams and load angle Figure 1.6a shows the synchronous generator most simply represented on a per phase basis by an internally generated voltage (E) and an internal reactance (X). The internal voltage arises from the induction in the stator by the rotating magnetic ﬂux of the rotor. The magnitude of this voltage is determined by the excitation of the ﬁeld winding. The reactance is the synchronous reactance of the machine for steady state representation and the transient and subtransient reactance for the representation of rapid changes in operating conditions. The generator terminals are assumed to be connected to an ‘inﬁnite’ busbar which has the properties of constant voltage and frequency with inﬁnite inertia such that it can absorb any output supplied by the generator. In practice, such an inﬁnite busbar is never obtained. However, in a highly interconnected system with several generators the system voltage and frequency are relatively insensitive to changes in the operating conditions of one machine. The generator is synchronised to the inﬁnite busbar and the bus voltage (U) is unaﬀected by any changes in the generator parameters (E) and (X). The vector diagrams associated with this generator arrangement supplying current (I) with a lagging power factor (cos ) are shown in Figs 1.6b to 1.6e for low electrical output, high electrical output, high excitation operation and low excitation operation respectively. The electrical power output is UI cos per phase. The angle between the voltage vectors E and U is the load angle of the machine. The load angle has a physical signiﬁcance determined by the electrical and mechanical characteristics of the generator and its prime mover. A stroboscope tuned to the supply frequency of the inﬁnite busbar would show the machine rotor to appear stationary. A change in electrical loading conditions such as that from Figs 1.6b to 1.6c would be seen as a shift of the rotor to a new position. For a generator the load angle corresponds to a shift in relative rotor position in the direction in which the prime mover is driving the machine. The increased electrical output of the generator from Figs 1.6b to 1.6c is more correctly seen as a consequence of an increased mechanical output of the prime mover. Initially this acts to accelerate the rotor and thus to increase the load angle. A new state of equilibrium is then reached where electrical power output matches prime mover input to the generator. Figures 1.6d and 1.6e show the eﬀect of changing the ﬁeld excitation of the generator rotor at constant electrical power output and also with no change in electrical power output from the Fig. 1.6b condition — that is UI cos is unchanged. An increase in (E) in Fig. 1.6d results in a larger current (I) but a more lagging power factor. Similarly, in Fig. 1.6e the reduction in (E) results in System Studies 11 Figure 1.6 Vector diagrams and load angle a change in power factor towards the leading quadrant. The principle eﬀect of a variation in generator internal voltage is therefore to change the power factor of the machine with the larger values of (E) resulting in lagging power factors and the smaller values for (E) tending towards leading power factors. A secondary eﬀect, which is important in stability studies, is also the change in load angle. The increased value of (E) shown in Fig. 1.6d (high excitation operation) has a smaller load angle compared to Fig. 1.6e (low excitation 12 System Studies operation) for the same electrical power. Figures 1.6f and 1.6g show approximately zero lag and lead power factor operation where there is no electrical power output and the load angle is zero. 1.3.2.2 The power/load angle characteristic Figure 1.6b represents the vector diagram for a low electrical power output: P : UI cos (per phase) also for the vector triangles it is true that: E sin : IX cos substitute for I: U cos ; E sin UE sin P: : X cos X The electrical power output is therefore directly proportional to the generator internal voltage (E) and the system voltage (U) but inversely proportional to the machine reactance (X). With (U), (E) and (X) held constant the power output is only a function of the load angle . Figure 1.7 shows a family of curves for power output vs load angle representing this. As a prime mover power increases a load angle of 90 degrees is eventually reached. Beyond this point further increases in mechanical input power cause the electrical power output to decrease. The surplus input power acts to further accelerate the machine and it is said to become unstable. The almost inevitable consequence is that synchronism with the remainder of the system is lost. Fast-acting modern automatic regulators (AVRs) can now actually enable a machine to operate at a load angle greater than 90 degrees. If the AVR can increase (E) faster than the load angle (): dE d dt dt then stability can be maintained up to a theoretical maximum of about 130 degrees. This loss of synchronism is serious because the synchronous machine may enter phases of alternatively acting as a generator and then as a motor. Power surges in and out of the machine, which could be several times the machine rating, would place huge electrical and mechanical stresses on the machine. Generator overcurrent relay protection will eventually detect out-of-synchronism conditions and isolate the generator from the system. Before this happens other parts of the network may also trip out due to the power surging and the whole system may collapse. The object of system stability studies is therefore to ensure appropriate design and operational measures are taken in order to System Studies 13 Figure 1.7 Power/load angle relationship retain synchronism for all likely modes of system operation, disturbances and outages. 1.3.2.3 The synchronous motor Operation of the synchronous motor may be envisaged in a similar way to the synchronous generator described in Section 1.3.2.2 above. In this case, however, the power ﬂow is into the machine and, relative to the generator, the motor load angle is negative. An increase in load angle is in the opposite direction to shaft rotation and results in greater electrical power consumption. A leading power factor corresponds to high excitation and a lagging power factor low excitation. 1.3.2.4 Practical machines In reality practical machine characteristics depart from the behaviour of the simple representations described above. However, in most cases the eﬀects are 14 System Studies small and they do not invalidate the main principles. The principle diﬀerences are due to saturation, saliency and stator resistance. Saturation describes the non-linear behaviour of magnetic ﬂuxes in iron and air paths produced by currents in the machine stator and rotor windings. Saturation eﬀects vary with machine loading. Saliency describes the eﬀect of the diﬀering sizes of air gap around the circumference of the rotor. This is important with salient pole rotors and the eﬀect varies the apparent internal reactance of the machine depending upon the relative position of rotor and stator. Saliency tends to make the machine ‘stiﬀer’. That is, for a given load the load angle is smaller with a salient pole machine than would be the case with a cylindrical rotor machine. Salient pole machines are in this respect inherently more stable. The eﬀect of stator resistance is to produce some internal power dissipation in the machine itself. Obviously the electrical power output is less than the mechanical power input and the diﬀerence is greatest at high stator currents. 1.3.3 Steady state stability 1.3.3.1 Pull out power Steady state stability deals with the ability of a system to perform satisfactorily under constant load or gradual load-changing conditions. In the single machine case shown in Fig. 1.7 the maximum electrical power output from the generator occurs when the load angle is 90 degrees. The value of peak power or ‘pull out power’ is given as: EU P : (from Section 1.3.2.2) +6 X With (U) ﬁxed by the inﬁnite bus and (X) a ﬁxed parameter for a given machine, the pull out power is a direct function of (E). Figure 1.7 shows a family of generator power/load angle curves for diﬀerent values of (E). For a generator operating at an output power P , the ability to accommodate an increase in loading is seen to be greater for operation at high values of (E) — increased ﬁeld excitation. From Section 1.3.2 and Figs 1.6d and 1.6e, operation at high values of (E) corresponds with supplying a lagging power factor and low values of (E) with a leading power factor. A generator operating at a leading power factor is therefore generally closer to its steady state stability limit than one operating at a lagging power factor. The value of (X), used in the expression for pull out power for an ideal machine, would be the synchronous reactance. In a practical machine the saturation of the iron paths modiﬁes the assumption of a constant value of synchronous reactance for all loading conditions. The eﬀect of saturation is to give a higher pull out power in practice than would be expected from a System Studies 15 Figure 1.8 Typical generator operation chart calculation using synchronous reactance. Additionally, in practical machines saliency and stator resistance, as explained in Section 1.3.2.4, would modify the expression for pull out power. Saliency tends to increase pull out power and reduces to slightly below 90 degrees the load angle at which pull out power occurs. Stator resistance slightly reduces both the value of pull out power and the load angle at which it occurs. 1.3.3.2 Generator operating chart An example of the eﬀect of maximum stable power output of a generator is given in the generator operating chart of Fig. 1.8. This is basically derived as an extension of the vector diagrams of Fig. 1.6 where the value of internal voltage (E) and load angle is plotted for any loading condition of MW or MVAr. In the operating chart, the circles represent constant values of (E) and load angle is shown for an assumed operating point. The operating points for which the load angle is 90 degrees are shown as the theoretical stability limit. Operation 16 System Studies in the area beyond the theoretical stability limit corresponds with load angles in excess of 90 degrees and is not permissible. The theoretical stability limit is one of the boundaries within which the operating point must lie. Other boundaries are formed by: 1. The maximum allowable stator current, shown on the chart as an arc of maximum MVA loading. 2. The maximum allowable ﬁeld excitation current shown on the chart as an arc at the corresponding maximum internal voltage (E). 3. A vertical line of maximum power may exist and this represents the power limit of the prime mover. Whichever of the above limitations applies ﬁrst describes the boundaries of the diﬀerent areas of operation of the generator. In a practical situation, operation at any point along the theoretical stability limit line would be most undesirable. At a load angle of 90 degrees, the generator cannot respond to a demand for more power output without becoming unstable. A practical stability limit is usually constructed on the operating chart such that, for operation at any point on this line, an increased power output of up to a certain percentage of rated power can always be accommodated without stability being lost. The practical stability limit in Fig. 1.8 is shown for a power increase of 10% of rated power output. The dotted line beyond the theoretical stability limit with a load angle 90 degrees shows the stabilizing eﬀect of the AVR. 1.3.3.3 Automatic voltage regulators (AVRs) The AVR generally operates to maintain a constant generator terminal voltage for all conditions of electrical output. This is achieved in practice by varying the excitation of the machine, and thus (E), in response to any terminal voltage variations. In the simple system of one generator supplying an inﬁnite busbar, the terminal voltage is held constant by the inﬁnite bus. In this case changes in excitation produce changes in the reactive power MVAr loading of the machine. In more practical systems the generator terminal voltage is at least to some degree aﬀected by the output of the machine. An increase in electrical load would reduce the terminal voltage and the corrective action of the AVR would boost the internal voltage (E). Referring to the generator operating chart of Fig. 1.8, an increase in power output from the initial point A would result in a new operating point B on the circle of constant internal voltage (E) in the absence of any manual or automatic adjustment of (E). Such an increase in power output takes the operating point nearer to the stability limit. If, at the same time as the power increase, there is a corresponding increase in (E) due to AVR action the new operating point would be at C. The operation of the AVR is therefore to hold System Studies 17 the operating point well away from the stability limit and the AVR can be regarded as acting to preserve steady state stability. 1.3.3.4 Steady state stability in industrial plants From Section 1.3.3.3 it can be seen that the steady state stability limits for generators are approached when they supply capacitive loads. Since industrial plants normally operate at lagging power factors the problem of steady state stability is unlikely to occur. Where power factor compensation is used or where synchronous motors are involved the possibility of a leading power factor condition is relevant and must be examined. Consider the Channel Tunnel 21 kV distribution scheme shown in Fig. 1.9. This consists of long 50 km lengths of 21 kV XLPE cable stretching under the Channel between England and France. Standby generation has been designed to feed essential services in the very unlikely case of simultaneous loss of both UK and French National Grid supplies. The 3 MVAr reactor shown on the single line diagram is used to compensate for the capacitive eﬀect of the 21 kV cable system. The failed Grid supplies are ﬁrst isolated from the system. The generators are then run up and initially loaded into the reactor before switching in the cable network. The Channel Tunnel essential loads (ventilation, drainage pumping, lighting, control and communications plant) are then energized by remote control from the Channel Tunnel control centre. 1.3.4 Transient stability 1.3.4.1 A physical explanation and analogy Transient stability describes the ability of all the elements in the network to remain in synchronism following an abrupt change in operating conditions. The most onerous abrupt change is usually the three phase fault, but sudden applications of electrical system load or mechanical drive power to the generator and network switching can all produce system instability. This instability can usually be thought of as an energy balance problem within the system. The analogy of the loaded spring is a useful aid to help visualize the situation. The general energy equation is as follows: Kinetic energy Mechanical energy : Electrical energy < ; Losses (Energy of motion) Under steady state conditions when changes are slow the system kinetic energy remains unchanged. However, if the disturbance to the machine is sudden (fault or load change) the machine cannot supply the energy from its prime mover or absorb energy from the electrical supply instantaneously. 18 System Studies Figure 1.9 Channel Tunnel 21 kV simpliﬁed distribution network with standby generation System Studies 19 Figure 1.10 Loaded spring machine stability analogy The excess or deﬁcit or energy must go to or come from the machine’s kinetic energy and the speed changes. As an example, if a motor is suddenly asked to supply more mechanical load it will supply it from the kinetic energy of its rotor and slow down. The slowing down process will go too far (overshoot) and will be followed by an increase in speed so that the new load condition is approached in an oscillatory manner just like the loaded spring (see Fig. 1.10). If a spring of stiﬀness S is gradually loaded with a mass M it will extend by a distance x until the stiﬀness force Sx : Mg, the weight of the mass. The kinetic energy of the system will not be disturbed. The spring is analogous to the machine and the extension of the spring x is analogous to the machine load angle . Loading the spring beyond its elastic limit is analogous to steady state instability of a loaded machine. A machine cannot be unstable by itself, it can only be unstable with respect to some reference (another machine or inﬁnite busbar to which it is connected) with which it can exchange a restoring force and energy. In the analogy the spring can only be loaded against a restraining mass (its attachment): an unattached spring cannot be extended. Consider the spring analogy case with the spring being suddenly loaded by a mass M to represent the transient condition. The kinetic energy of the system is now disturbed and the weight will stretch the spring beyond its normal extension x to x where x x (see Fig. 1.11). The mass M moves past x to x until the initial kinetic energy of the mass is converted into strain energy in the spring according to: MV : S(x 9 x) When the weight momentarily comes to rest at x the kinetic energy of the weight has now been absorbed into the strain energy in the spring and the spring now accelerates the mass upwards beyond x so there is an overshoot. The mass eventually settles down to its steady position in an oscillatory manner. It should be noted that the spring could support a weight which, if it were dropped on the spring, would cause its elastic limit to be exceeded before the downward motion of the weight was stopped. This is analogous to transient instability. 20 System Studies Figure 1.11 Loaded spring machine stability analogy–overshoot It can be seen how close the above analogy is by examining the equations of motion of the loaded spring and the synchronous machine as follows. For the spring: dx dx M ; K ; Sx : Force dt dt where M is the applied mass, x is the extension, dx/dt is the acceleration or deceleration of mass M, Kdx/dt is the velocity damping and Sx is the restoring force. For the synchronous machine: d d M ; K ; Pe sin P mechanical power dt dt where M is the angular momentum and Pe sin is the electrical power. For small , sin tends to d d M ; K ; Pe P dt dt and if we change power into torque by dividing by the synchronous speed, the analogy is exact: d d J ; K ; Te T the mechanical torque dt dt 1.3.4.2 Load angle oscillations The power/load angle curve shown in Fig. 1.12 can be used to show graphically the eﬀect of a sudden change in machine load. The response shown System Studies 21 Figure 1.12 Basic transient stability assessment can apply to either a synchronous generator or a synchronous motor, but the sudden loading of a motor is easier to visualize. Suppose we consider a synchronous motor initially operating with a mechanical power P and with a load angle at a point ‘a’ on its characteristic operating curve. This curve is deﬁned by the function: EU Power P sin xd 22 System Studies where xd is the machine transient reactance. Operation at ‘a’ represents an equilibrium state in which the mechanical power P equals the electrical power P , neglecting losses. The machine is operating at synchronous speed. Suppose now that there is a sudden change in mechanical load of the synchronous motor. The mechanical power demand increases to P. This sudden energy demand cannot be immediately supplied from the electrical system so it must be supplied from the motor’s stored rotational energy and the motor slows down. As the motor slows down its load angle increases allowing more power to be drawn from the electrical supply and the motor moves to point ‘c’ on its power/load angle curve where it is supplying the new power demand P. However, at ‘c’ the motor is going too slowly and therefore its load angle continues to increase. Beyond ‘c’ the electrical power supplied to the motor exceeds the new mechanical demand P and the motor is accelerated. The motor overswings to ‘d’, where the machine is again running at synchronous speed. Here, since the electrical power is still greater than the mechanical power, the motor continues to accelerate above synchronous speed and hence starts to reduce its load angle. Back at point ‘c’, the electrical power is again equal to the mechanical power but the machine is operating above synchronous speed so it backswings towards ‘a’. The machine will be prevented from reaching ‘a’ by damping; nevertheless it oscillates about ‘c’ until it ﬁnally stops at ‘c’ because of the damping eﬀects. 1.3.4.3 The equal area criterion The shaded areas ‘a’-‘b’-‘c’ and ‘c’-‘d’-‘e’ in Fig. 1.12 respectively represent the loss and gain of kinetic energy and for stability these two areas should balance. This is the basis of the equal area criterion of stability. Three distinct alternative consequences occur for a sudden load change from P to P. 1. If area ‘c’-‘d’-‘e’ can equal area ‘a’-‘b’-‘c’ at load angle the machine is stable. 2. If the disturbance is such as to make the motor swing to , area ‘c’-‘d’-‘e’ just equals area ‘a’-‘b’-‘c’ and the motor is critically stable. 3. If area ‘c’-‘d’-‘e’ cannot equal area ‘a’-‘b’-‘c’ before angle the motor is unstable. This is because, if the motor has not reaccelerated to synchronous speed at , where the electrical power equals the mechanical power P , it slows down beyond . For angles greater than the mechanical power is greater than the electrical power and the motor continues to slow down. For angles greater than 180° the motor starts to pole slip (it becomes unstable) towards a stall. In reality, the motor protection would operate and disconnect the motor from the busbar. System Studies 23 From this explanation it can be seen that, unlike the steady state case, the machine can swing beyond 90° and recover. Note that a similar explanation could be applied to the generator case. Here the generator would accelerate upon a sudden fault disturbance such that the area ‘a’-‘b’-‘c’ represents a gain in kinetic energy whereas area ‘c’-‘d’-‘e’ represents a loss of kinetic energy. 1.3.4.4 Swing curves The swing curve is generally a plot of load angle with time. The connection between the power/load angle characteristic and the dimension of time is the mechanical inertia. Actual inertias vary widely depending upon machine capacity and speed but when expressed in terms of the machine electrical rating, a narrow band of values is obtained. This gives the inertia (or stored energy) constant, H, and is deﬁned as: stored energy in Megajoules or kilojoules H: MVA or kVA rating J ; 10\ : kVA where : 2f for a two pole machine or generally : 2n, where n is the machine speed in revolutions per second. 2 ; 10\ Jn H: kVA J is the moment of inertia in kg m and the dimensions of the stored energy constant, H are kW sec/ kVA or seconds. From Section 1.3.4.1 it will be remembered that the swing equation of motion takes the form: d d M ; K ; Pe sin : P mechanical power dt dt where M is the angular momentum of the machine. Like the inertia the angular momentum of various machines diﬀers widely. We can replace M by H in the above equation according to: H ; kVA : M : M2n so H ; kVA M: n Typical values of the stored energy constant, H, for various machines are listed below: 24 System Studies Machine description H (kW sec/ kVA) Full condensing steam turbine generators 4—10 Non-condensing steam turbine generators 3—5 Gas turbine generators 2—5 Diesel generators 1—3 (low speed) 4—5 (with ﬂywheel) Synchronous motor with load 1—5 Induction motor with load 0.03—1.4 (100 kW—2000 kW but depends on speed) The load angle swing curves shown in Fig. 1.12 are obtained by solving the equation of motion of the machine or by solving the equations of motion of several machines in a group. Since the equations are non-linear numerical iterative methods computed with short time intervals (0.01 seconds or less) must be used for the solutions. Since the number of steps is enormous this is a job for computer analysis. 1.3.4.5 Transient stability during faults In Fig. 1.13 a generator is shown feeding a load via a twin circuit transmission line. Under normal operation the load and voltage (U) are assumed to remain constant and the generator internal voltage (E) is also held constant. The power/load angle diagram for the whole system is shown in curve 1 with: EU P: sin (per phase) X where X is the total system transfer reactance with both lines in service. A fault is now assumed at point (S). During the fault there will be a reduced possibility of power transfer from generator to load as indicated in Fig. 1.13 by curve 2 where the electrical power is given by: EU P: sin X where X is the transfer reactance under the fault conditions. The fault is assumed to be cleared in time (t) by the circuit breakers isolating the faulty line. Post fault conditions are now shown by curve 3 with: EU P: sin (per phase) X where X is greater than X due to the loss of the parallel overhead line section. Throughout the period under consideration the driving power to the System Studies 25 Figure 1.13 Transient stability to faults—power/load angle curve under fault conditions generator is assumed constant at P. Prior to the fault a state of equilibrium exists with the electrical power matching the mechanical power at load angle . During the fault the driving power considerably exceeds the transmittable electrical power (shown by curve 2) and the rotor system accelerates. At the time taken to reach the fault is assumed to be cleared and the power/load angle characteristic changes to curve 3. At the transmitted power exceeds the driving power and the rotor decelerates. By the equal area criterion, the 26 System Studies maximum swing angle is determined by the area ‘a’-‘b’-‘c’-‘d’ equal to area ‘d’-‘e’-‘f’-‘g’. The eventual new equilibrium angle can be seen to be where P intercepts curve 3. In this instance the swing curve shows the system to be stable. The following points should, however, be noted: 1. Had the angle reached during the fault been larger, for example with a slower circuit breaker and protection, the system could have become unstable. 2. The value of is determined both by the inertia constant H and the time duration of the fault. The load angle will be larger for smaller values of H and longer fault durations. 3. The decelerating power after the fault is related to the size of the post fault power/load angle curve. The larger the post fault reactance the lower the decelerating power and consequently the greater the possibility of instability. 1.3.4.6 Transient stability for close-up faults on generator terminals The worst case fault conditions for the generator are with a three phase fault applied close to its terminals. The terminal voltage reduces to zero and the electrical power output must also reduce to zero. The whole of the prefault mechanical driving power is then expended in accelerating the generator rotor because no power can be transferred across this close-up fault. The maximum permissible fault duration to avoid instability under these conditions is a useful guide to the correct protection settings and selection of circuit breaker characteristics used in the vicinity of generators. The maximum permissible fault duration is referred to in technical literature as the critical switching time. The maximum (critical) fault duration is relatively insensitive to machine rating and any variation from one machine to another would largely be due to diﬀerences in inertia constant H. The two examples for critical fault duration given below are for identical machines with diﬀerent inertia constants and give the order of fault durations for typical machines. Drive source Inertia constant (H) Max. fault duration 1. Hydro or low speed diesel 1.0 MJ/MVA approx. 0.14 seconds 2. Steam turbine 10 MJ/MVA approx. 0.50 seconds (Figures are for generators with 25% transient reactance, no AVR action and feeding into an inﬁnite busbar.) 1.3.4.7 Auto-reclosing and single pole switching Section 1.3.4.6 shows that if the fault is of a transient nature it is advantageous (from a stability point of view) to rapidly put the system back into service by use of auto-reclosing circuit breakers once the fault has cleared. If the fault persists the generator will be subjected to a second fault impact upon reclosing System Studies 27 the circuit breaker and a stable situation may be rendered unstable. Great care is therefore necessary when considering auto-reclosing. Applicable cases for overhead lines might be where historical records show that the majority of faults are of a transient nature due to lightning or perhaps high impedance earth faults due to bush ﬁres. Over 90% of overhead line faults are single phase to earth faults. As an aid to stability auto-reclose single pole circuit breaker switching is often employed. A typical transmission system strategy is to employ single shot auto-reclose facilities only for single phase to earth faults. If the fault persists then three phase switching takes over to disconnect the circuit. Typical delay times between circuit breaker auto-reclose shots are of the order of 0.4 to 0.5 seconds allowing for a 0.3 second arc deionization time. The single pole auto-reclose technique is well established for transmission line voltages below 220 kV and stability is aided because during the fault clearance process power can be transferred across the healthy phases. It should be noted, however, that fault arc deionization takes longer with single pole switching because the fault is fed capacitively from the healthy phases. In addition the system cannot be run for more than a few seconds with one open circuit phase or serious overheating of the rotating plant may take place. Distribution systems employ three phase autoreclose breakers and sectionalisers to isolate the fault if it persists. See Chapter 13, ‘Switchgear’. 1.3.4.8 Hunting of synchronous machines The load angle of a stable machine oscillates about a point of equilibrium if momentarily displaced. The machine has a characteristic natural frequency associated with this period of oscillation which is inﬂuenced by its loading and inertia constant. In order to avoid large angle swings, the possibility of mechanical damage to the shaft and couplings and loss of synchronism, the natural frequency should not coincide with the frequency of pulsating loads or prime mover torque. Hunting of this type may be detected from pulsating electrical measurements seen on machine meters and excessive throbbing machine noise. Damping windings on the machine and the power system load itself assist in reduction of hunting eﬀects. In both these cases damping arises from induced currents in the damper windings caused by rotor oscillation. The damping torques decrease with increasing resistance in the paths of the induced currents. Machines operating at the ends of long, high resistance supply lines or having high resistance damper windings can be particularly susceptible to hunting. The possibility of hunting can be seen from the equations in Section 1.3.4.1 if the mechanical torque takes the form T sin t. The second order diﬀerential equation of motion has oscillatory solutions exhibiting a natural frequency . A resonance condition will arise if the mechanical driving torque frequency approaches the machine natural frequency . 28 System Studies 1.3.5 Dynamic stability Although a system may not lose synchronism in the transient interval following a disturbance, the ability to adapt in the longer term to a signiﬁcantly new set of operating conditions is the subject of dynamic stability studies. In the transient period of perhaps a second or two following a disturbance, many of the slower reacting power system components can be assumed constant. Their eﬀect on the preservation or otherwise of transient stability is negligible. In the seco

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