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More About This Textbook
Overview
The third edition has been fully updated throughout in line with current IEC and European standards, an approach which has resulted in a thoroughly rewritten chapter on earthing and bonding and significant revisions to the chapters on EMC, insulation coordination and overhead line design. There is increased emphasis on reliability concepts and greatly expanded treatment of the subject of power quality. The resulting book is an essential guide and a hardworking reference for all engineers, technicians, managers and planners involved in the electricity supply industry, and related areas such as generation, and industrial electricity usage.
Editorial Reviews
From the Publisher
‘Surely the most comprehensive tome ever published on the subject. Transmission and Distribution Electrical Engineering should be weighing down the bookshelves of all engineers, manufacturers and contractors involved with transmission and distribution networks.’, Electrical Review‘Colin Bayliss should be applauded for producing... a book that presents a comprehensive range of subjects that would give the young engineer a good base knowledge of transmission and distribution electrical engineering and to help him or her to be a useful member of a project team.’, Power Engineering Journal
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Transmission and Distribution Electrical Engineering
By C. R. Bayliss B. J. Hardy
Newnes
Copyright © 2012 Elsevier Ltd.All right reserved.
ISBN: 9780080969138
Chapter One
System Studies1.1 INTRODUCTION
This chapter describes 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.
It is now recognized that harmonic analysis is also a major system study tool. This is discussed separately in Chapter 24. Reliability studies are considered in Chapter 23.
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 to a wide range of commercially available computer softwares. The more general theoretical principles involved in load flow and fault analysis data collection are explained in Chapter 28.
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.
1.2.2 Sample Study
1.2.2.1 Network SingleLine 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 for cables and overhead lines are given here in a per unit (pu) format on a 100 MVA base. Different programs may require input data in different formats, for example per cent impedance, ohmic notation, etc. Please refer to Chapter 28, for the derivation of system impedance data in different formats from manufacturers' literature. The network here is kept small in order to allow the firsttime 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; there will always be one such busbar in any system. 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° (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°), 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 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 fastrelay 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 Database
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 shortterm 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 to regularly save your files both during database compilation and at the end of the procedure when you are satisfied that all the data have been entered correctly. Save data onto the hard disk and make backups for safe keeping to suitable alternative media (e.g. CD, USB flash drive). 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 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 iterations is sufficiently small. Alternatively, the procedure may not converge or may only converge extremely slowly. In these cases it is necessary to reexamine 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 roundoff errors will depend, in part, upon the way in which the numbers are handled in the computer. In the past it was necessary to ensure that the computer used was capable of handling accurate floatingpoint arithmetic, where the numbers are represented with a fixed number of significant figures. Today these can be accepted as standard. It is a most important principle in numerical work that all sources of error (round off, mistakes, nature of formulae used, approximate physical input data) must be constantly borne in mind if the 'junk in equals junk out' syndrome is to be avoided. A concern that remains valid in selecting computing equipment is the need to ensure that the available memory is adequate for the size of network model under consideration.
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 singleline diagram as shown in Fig. 1.4. Such a pictorial representation may be achieved directly with the more sophisticated system analysis programs. Alternatively, the network singleline diagram may be 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 the overhead line branches running either from busbars A to C or from B to C. Nonconvergence 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 singleline 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 28 'Fundamentals', Section 28.8.5 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/energyinput and the electrical power/energyoutput by natural adjustment of system voltage levels and the common system frequency. There are three regimes of stability:
(a) 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 24hour maximum demand is approached.
(b) 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.
(c) 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.
(Continues...)
Table of Contents
About the authors xxi
Contributors xxiii
Preface xxvii
System Studies 1
Introduction 1
Load flow 1
Purpose 1
Sample study 2
System stability 8
Introduction 8
Analytical aspects 10
Steady state stability 14
Transient stability 17
Dynamic stability 28
Effect of induction motors 29
Data requirements and interpretation of transient stability studies 30
Case studies 35
Short circuit analysis
Purpose 42
Sample study 42
Drawings and Diagrams 50
Introduction 50
Block diagrams 50
Schematic diagrams 51
Method of representation 51
Main circuits 55
Control, signalling and monitoring circuits 55
Manufacturers' drawings 55
Combined wiring/cabling diagrams 55
British practice 61
European practice 64
Other systems 67
Computeraided design (CAD) 68
Case study 69
Graphical symbols 69
Relay identification  numerical codes 71
Comparison between German, British, US/Canadian and international symbols 82
General circuit elements 83
Operating mechanisms 86
Switchgear 89
Substation Layouts 92
Introduction 92
Substation design considerations 92
Security of supply 92
Extendibility 93
Maintainability 93
Operational flexibility 94
Protection arrangements 94
Short circuit limitations 94
Land area 94
Cost 95
Alternative layouts 95
Single busbar 95
Transformer feeder 97
Mesh 101
Ring 103
Double busbar 104
1 1/2 Circuit breaker 105
Space requirements 107
Introduction 107
Safety clearances 108
Phasephase and phaseearth clearances 109
Substation Auxiliary Power Supplies 115
Introduction 115
DC supplies 115
Battery and charger configurations 115
Battery charger components 118
Installation requirements 121
Typical enquiry data  DC switchboard 125
Batteries 126
Introduction 126
Battery capacity 126
Characteristics of batteries 127
Battery sizing calculations 130
Typical enquiry data 133
AC supplies 135
Power sources 135
LVAC switchboard fault level 137
Auxiliary transformer LV connections 137
Allowance for future extension 139
Typical enquiry data 139
Earthing transformer selection 140
Uninterruptible power supplies 144
Current and Voltage Transformers 149
Introduction 149
Current transformers 149
Introduction 149
Protection CT classifications 149
Metering CTs 153
Design and construction considerations 154
Terminal markings 156
Specifications 157
Voltage transformers 157
Introduction 157
Electromagnetic VTs 157
Capacitor VTs 158
Specifications 159
Future trends 159
Insulators 163
Introduction 163
Insulator materials 163
Polymeric and resin materials 163
Glass and porcelain 164
Insulator types 164
Post insulators 164
Cap and pin insulators 168
Long rod 168
Pollution control 169
Environment/creepage distances 169
Remedial measures 172
Calculation of specific creepage path 173
Insulator specification 174
Standards 174
Design characteristics 174
Tests 180
Sample and routine tests 180
Technical particulars 180
Substation Building Services 181
Introduction 181
Lighting 181
Terminology 181
Internal lighting 186
External lighting 187
Control 197
Distribution characterization 199
Heating, ventilation and airconditioning 200
Air circulation 200
Airconditioning 202
Heating 207
Fire detection and suppression 207
Introduction 207
Fire extinguishers 208
Access, first aid and safety 208
Fire detection 209
Fire suppression 212
Cables, control panels and power supplies 213
Earthing and Bonding 215
Introduction 215
Design criteria 215
Touch and step voltages 215
Touch and step voltage limits 216
Substation earthing calculations 219
Environmental conditions 219
Earthing materials 222
Earth resistance and earth potential rise 225
Hazard voltage tolerable limits 227
Computer simulation 229
References 232
Insulation Coordination 233
Introduction 233
System voltages 233
Power frequency voltage 233
Overvoltages 234
Clearances 245
Air 245
SF[subscript 6] 248
Procedures for coordination 248
The IEC standard approach 248
Statistical approach 249
Nonstatistical approach 251
Surge protection 251
Rod or spark gaps 251
Surge arresters 253
References 268
Relay Protection 269
Introduction 269
System configurations 270
Faults 270
Unearthed systems 270
Impedance earthed systems 270
Solidly earthed systems 271
Network arrangements 271
Power system protection principles 274
Discrimination by time 274
Discrimination by current magnitude 275
Discrimination by time and fault direction 275
Unit protection 275
Signalling channel assistance 276
Current relays 277
Introduction 277
Inverse definite minimum time lag (IDMTL) relays 277
Alternative characteristic curves 280
Plotting relay curves on log/log graph paper 280
Current relay application examples 281
Differential protection schemes 292
Biased differential protection 292
High impedance protection 295
Transformer protection application examples 296
Pilot wire unit protection 300
Busbar protection 303
Distance relays 306
Introduction 306
Basic principles 307
Relay characteristics 307
Zones of protection 313
Switched relays 314
Typical overhead transmission line protection schemes 315
Auxiliary relays 319
Tripping and auxiliary 319
AC auxiliary relays 323
Timers 323
Undervoltage 325
Underfrequency 325
Computer assisted grading exercise 326
Basic input data 326
Network fault levels 328
CT ratios and protection devices 328
Relay settings 328
Practical distribution network case study 329
Introduction 329
Main substation protection 330
Traction system protection 331
21 kV distribution system and protection philosophy 332
21 kV pilot wire unit protection 334
21 kV system backup protection 335
Use of earth fault indicators 337
Summary 337
Recent advances in control, protection and monitoring 337
Background 337
Developments 338
References 340
Fuses and Miniature Circuit Breakers 341
Introduction 341
Fuses 341
Types and standards 341
Definitions and terminology 345
HRC fuses 345
High voltage fuses 348
Cartridge fuse construction 355
Fuse operation 357
High speed operation 357
Discrimination 357
Cable protection 360
Motor protection 362
Semiconductor protection 363
Miniature circuit breakers 363
Operation 363
Standards 367
Application 368
References 373
Cables 374
Introduction 374
Codes and standards 374
Types of cables and materials 377
General design criteria 377
Cable construction 378
Submarine cables 386
Joints and terminations 388
Cable sizing 389
Introduction 389
Cables laid in air 390
Cables laid direct in ground 390
Cables laid in ducts 395
Earthing and bonding 396
Short circuit ratings 398
Calculation examples 400
Calculation of losses in cables 410
Dielectric losses 410
Screen or sheath losses 411
Fire properties of cables 411
Introduction 411
Toxic and corrosive gases 411
Smoke emission 412
Oxygen index and temperature index 413
Flame retardance/flammability 413
Fire resistance 414
Mechanical properties 415
Control and communication cables 415
Low voltage and multicore control cables 415
Telephone cables 416
Fibre optic cables 417
Cable management systems 423
Standard cable laying arrangements 423
Computer aided cable installation systems 426
Interface definition 429
References 435
Switchgear 436
Introduction 436
Terminology and standards 436
Switching 438
Basic principles 438
Special switching cases 450
Switches and disconnectors 453
Contactors 456
Arc quenching media 460
Introduction 460
Sulphur hexafluoride (SF[subscript 6]) 463
Vacuum 464
Oil 468
Air 470
Operating mechanisms 472
Closing and opening 472
Interlocking 477
Integral earthing 477
Equipment specifications 480
12 kV metalclad indoor switchboard example 480
Open terminal 145 kV switchgear examples 486
Distribution system switchgear example 491
Distribution ring main unit 492
References 498
Power Transformers 499
Introduction 499
Standards and principles 499
Basic transformer action 499
Transformer equivalent circuit 501
Voltage and current distribution 503
Transformer impedance representation 504
Tap changers 506
Useful standards 515
Voltage, impedance and power rating 517
General 517
Voltage drop 517
Impedance 518
Voltage ratio and tappings  general 519
Voltage ratio with offcircuit tappings 519
Voltage ratio and onload tappings 520
Basic insulation levels (BIL) 520
Vector groups and neutral earthing 520
Calculation example to determine impedance and tap range 523
Thermal design 532
General 532
Temperature rise 532
Loss of life expectancy with temperature 533
Ambient temperature 534
Solar heating 535
Transformer cooling classifications 535
Selection of cooling classification 538
Change of cooling classification in the field 539
Capitalization of losses 540
Constructional aspects 541
Cores 541
Windings 542
Tanks and enclosures 544
Cooling plant 546
Low fire risk types 547
Neutral earthing transformers 549
Reactors 549
Accessories 552
General 552
Buchholz relay 552
Sudden pressure relay and gas analyser relay 553
Pressure relief devices 553
Temperature monitoring 553
Breathers 554
Miscellaneous 554
Transformer ordering details 556
References 564
Substation and Overhead Line Foundations 565
Introduction 565
Soil investigations 565
Foundation types 566
Foundation design 575
Site works 576
Setting out 575
Excavation 577
Piling 577
Earthworks 579
Concrete 530
Steelwork fixings 583
Overhead Line Routing 585
Introduction 585
Routing objectives 585
Preliminary routing 587
Survey equipment requirements 587
Aerial survey 587
Ground survey 587
Ground soil conditions 587
Wayleave, access and terrain 588
Optimization 589
Detailed line survey and profile 591
Accuracy requirements 591
Profile requirements 592
Computer aided techniques 593
Structures, Towers and Poles 595
Introduction 595
Environmental conditions 597
Typical parameters 597
Effect on tower or support design 597
Conductor loads 603
Structure design 611
Lattice steel tower design considerations 611
Tower testing 623
Pole and tower types 624
Pole structures 624
Tower structures 625
References 629
Overhead Line Conductor and Technical Specifications 630
Introduction 630
Environmental conditions 630
Conductor selection 631
General 631
Types of conductor 632
Aerial bundled conductor and BLX 633
Conductor breaking strengths 637
Bimetal connectors 639
Corrosion 639
Calculated electrical ratings 641
Heat balance equation 641
Power carrying capacity 642
Corona discharge 645
Overhead line calculation example 649
Design spans, clearances and loadings 651
Design spans 651
Conductor and earth wire spacing and clearances 664
Broken wire conditions 674
Conductor tests/inspections 674
Overhead line fittings 675
Fittings related to aerodynamic phenomena 675
Suspension clamps 677
Sag adjusters 678
Miscellaneous fittings 678
Overhead line impedance 678
Inductive reactance 678
Capacitive reactance 680
Resistance 680
Substation busbar selection  case study 681
Introduction 681
Conductor diameter/current carrying capacity 681
Conductor selection on weight basis 681
Conductor short circuit current capability 684
Conductor support arrangements 687
References 692
Testing and Commissioning 693
Introduction 693
Quality assurance 694
Introduction 694
Inspection release notice 696
Partial acceptance testing 696
System acceptance testing 696
Documentation and record systems 696
Works inspections and testing 698
Objectives 698
Specifications and responsibilities 699
Type tests 699
Routine production tests 700
Site inspection and testing 700
Precommissioning and testing 700
Maintenance inspection 701
Online inspection and testing 701
Testing and commissioning methods 705
Switchgear 705
Transformers 713
Cables 718
Protection 724
Commissioning test procedure requirements 738
Drawings, diagrams and manuals 739
Electromagnetic Compatibility 741
Introduction 741
Standards 742
Compliance 743
Testing 744
Introduction 744
Magnetic field radiated emission measurements 744
Electric field radiated emission measurements 746
Conducted emission measurements 748
Immunity testing 749
Screening 750
Introduction 750
The use of screen wire 750
The use of screen boxes and Faraday enclosures 750
The use of screen floors in rooms 752
Typical useful formulae 755
Decibel reference levels 755
Field strength calculations 755
Mutual inductance between two long parallel pairs of wires 756
Attenuation factors 756
Case studies 757
Screening power cables 757
Measurement of field strengths 761
References 763
Supervisory Control and Data Acquisition 764
Introduction 764
Programmable logic controllers 764
Functions 764
PLC selection 765
Application example 770
Power line carrier communication links 776
Introduction 776
Power line carrier communication principles 777
Supervisory control and data acquisition 780
Introduction 780
Typical characteristics 783
Design issues 785
Example (Channel Tunnel) 786
Software management 788
Software  a special case 789
Software life cycle 790
Software implementation practice 793
Software project management 796
References 798
Project Management 799
Introduction 799
Project evaluation 799
Introduction 799
Financial assessment 800
Economic assessment 807
Financing 811
Responsibilities for funding 811
Cash flow 811
Sources of finance 812
Export credit agencies 812
Funding risk reduction 813
Use of private finance 814
Project phases 816
The project life cycle 816
Cash flow 817
Bonds 819
Advance payments and retentions 820
Insurances 822
Project closeout 822
Terms and conditions of contract 822
Time, cost and quality 822
Basic types of contract 823
Standard terms and conditions of contract 825
Key clauses 829
Tendering 832
Choosing the contractor 832
Estimating 832
Tender evaluation 834
Model forms of contract  exercise 835
Project definition/questionnaire 837
Bidding checklist 863
Distribution Planning 867
Introduction 867
Definitions 867
Demand or average demand 868
Maximum demand (MD) 869
Demand factor 870
Utilization factor (UF) 870
Load factor (LDF) 870
Diversity factor (DF) 871
Coincident factor (CF) 872
Load diversity 873
Loss factor (LSF) 873
Load duration 878
Loss equivalent hours 878
Peak responsibility factor (PRF) 880
Load forecasting 881
Users of load forecasts 881
The preparation of load forecasts 882
The micro load forecast 882
The macro load forecast 885
Nature of the load forecast 886
System parameters 888
Distribution feeder arrangements 888
Voltage drop calculations 889
Positive sequence resistance 891
Inductive reactance 892
Economic loading of distribution feeders and transformers 893
System losses 894
System reliability 896
Introduction 896
Reliability functions 897
Predictability analysis 901
Drawings and materials take off 906
Power Quality  Harmonics in Power Systems 907
Introduction 907
The nature of harmonics 909
Introduction 909
Three phase harmonics 909
The generation of harmonics 910
General 910
Transformers 910
Converters 911
The thyristor bridge 911
Railway and tramway traction systems 913
Static VAr compensators and balancers 915
The effects of harmonics 917
Heating effects of harmonics 917
Harmonic overvoltages 917
Resonances 917
Interference 919
The limitation of harmonics 920
Harmonic filters 920
Capacitor detuning 924
Ferroresonance and subharmonics 924
Introduction 924
A physical description of ferroresonance 925
Subharmonics 928
Interharmonics 928
Harmonic studies 929
The requirement 929
The studies 930
Measurement 931
Case studies 931
References 931
Power Quality  Voltage Fluctuations 933
Introduction 933
The nature and cause of voltage disturbances in power systems 933
Shortterm interruptions and voltage dips and peaks 933
Voltage fluctuations 937
Voltage flicker 937
Slowvoltage fluctuations 938
Voltage unbalance 938
Stepchange events 939
Solutions 939
Energy storage 939
Balancing 940
Static var compensators 940
The STATCOM 942
Case study 942
References 944
Fundamentals 945
Introduction 945
Symbols and nomenclature 945
Symbols 945
Units and conversion tables 946
Alternating quantities 951
Vector representation 954
Vector algebra 959
The j operator 959
Exponential vector format 960
Polar coordinate vector format 961
Algebraic operations on vectors 961
The h operator 962
Sequence components 962
Theoretical background 962
Calculation methodology and approximations 964
Interpretation 965
Network fault analysis 966
Introduction 966
Fundamental formulae 966
Simplified network reduction example 971
Design optimization 977
Introduction 977
Technical problems 978
Loss reduction 982
Communication link gain or attenuation 990
Reactive compensation 991
Power factor correction calculation procedures 994
References 998
Index 1001