reading

Cover
Title Page
Preface
Acknowledgements
Part I
1. 1 Power Systems
  1. 1.1 Three‐phase System of AC Voltages
  2. 1.2 Low Voltage Distribution
  3. 1.3 Examples of Distribution Transformers
  4. 1.4 Practical Magnitude Limits for LV Loads
  5. 1.5 Medium Voltage Network
  6. 1.6 Transmission and Sub‐Transmission Networks
  7. 1.7 Generation of Electrical Energy
  8. 1.8 Sources
  9. Further Reading
2. 2 Review of AC Circuit Theory and Application of Phasor Diagrams
  1. 2.1 Representation of AC Voltages and Currents
  2. 2.2 RMS Measurement of Time Varying AC Quantities
  3. 2.3 Phasor Notation (Phasor Diagram Analysis)
  4. 2.4 Passive Circuit Components: Resistors, Capacitors and Inductors
  5. 2.5 Review of Sign Conventions and Network Theorems
  6. 2.6 AC Circuit Analysis Examples
  7. 2.7 Resonance in AC Circuits
  8. 2.8 Problems
  9. 2.9 Practical Experiment
3. 3 Active Power, Reactive Power and Power Factor
  1. 3.1 Single‐Phase AC Power
  2. 3.2 Active Power
  3. 3.3 Reactive Power
  4. 3.4 Apparent Power or the volt‐amp Product, S
  5. 3.5 Three‐Phase Power
  6. 3.6 Power Factor
  7. 3.7 Power Factor Correction
  8. 3.8 Typical Industrial Load Profiles
  9. 3.9 Directional Power Flows
  10. 3.10 Energy Retailing
  11. 3.11 Problems
4. 4 Magnetic Circuits, Inductors and Transformers
  1. 4.1 Magnetic Circuits
  2. 4.2 Magnetic Circuit Model
  3. 4.3 Gapped Cores and Effective Permeability
  4. 4.4 Inductance Calculations
  5. 4.5 Core Materials
  6. 4.6 Magnetising Characteristics of GOSS
  7. 4.7 Energy Stored in the Air Gap
  8. 4.8 EMF Equation
  9. 4.9 Magnetic Circuit Topologies
  10. 4.10 Magnetising Losses
  11. 4.11 Two‐Winding Transformer Operation
  12. 4.12 Transformer VA Ratings and Efficiency
  13. 4.13 Two‐Winding Transformer Equivalent Circuit
  14. 4.14 The Per‐Unit System
  15. 4.15 Transformer Short‐Circuit and Open‐Circuit Tests
  16. 4.16 Transformer Phasor Diagram
  17. 4.17 Current Transformers
  18. 4.18 Problems
  19. 4.19 Sources
5. 5 Symmetrical Components
  1. 5.1 Symmetrical Component Theory
  2. 5.2 Sequence Networks and Fault Analysis
  3. 5.3 Network Fault Connections
  4. 5.4 Measurement of Zero‐sequence Components (Residual Current and Voltage)
  5. 5.5 Phase‐to‐Ground Fault Currents Reflected from a Star to a Delta Connected Winding
  6. 5.6 Sequence Components Remote from a Fault
  7. 5.7 Problems
  8. 5.8 Sources
6. 6 Power Flows in AC Networks
  1. 6.1 Power Flow Directions
  2. 6.2 Synchronous Condenser
  3. 6.3 Synchronous Motor
  4. 6.4 Generalised Power Flow Analysis
  5. 6.5 Low X/R Networks
  6. 6.6 Steady State Transmission Stability Limit
  7. 6.7 Voltage Collapse in Power Systems
  8. 6.8 Problems
  9. 6.9 Sources
Part II
1. 7 Three‐Phase Transformers
  1. 7.1 Positive and Negative Sequence Impedance
  2. 7.2 Transformer Zero‐Sequence Impedance
  3. 7.3 Transformer Vector Groups
  4. 7.4 Transformer Voltage Regulation
  5. 7.5 Magnetising Current Harmonics
  6. 7.6 Tap‐changing Techniques
  7. 7.7 Parallel Connection of Transformers
  8. 7.8 Transformer Nameplate
  9. 7.9 Step Voltage Regulator
  10. 7.10 Problems
  11. 7.11 Sources
2. 8 Voltage Transformers
  1. 8.1 Inductive and Capacitive Voltage Transformers
  2. 8.2 Voltage Transformer Errors
  3. 8.3 Voltage Transformer Equivalent Circuit
  4. 8.4 Voltage Transformer ‘Error Lines’
  5. 8.5 Re‐rating Voltage Transformers
  6. 8.6 Accuracy Classes for Protective Voltage Transformers
  7. 8.7 Dual‐Wound Voltage Transformers
  8. 8.8 Earthing and Protection of Voltage Transformers
  9. 8.9 Non‐Conventional Voltage Transformers
  10. 8.10 Problems
  11. 8.11 Sources
3. 9 Current Transformers
  1. 9.1 CT Secondary Currents and Ratios
  2. 9.2 Current Transformer Errors and Standards
  3. 9.3 IEEE C57.13 Metering Class Magnitude and Phase Errors
  4. 9.4 Current Transformer Equivalent Circuit
  5. 9.5 Magnetising Admittance Variation and CT Compensation Techniques
  6. 9.6 Composite Error
  7. 9.7 Instrument Security Factor for Metering CTs
  8. 9.8 Protection Current Transformers
  9. 9.9 Inter‐Turn Voltage Ratings
  10. 9.10 Non‐Conventional Current Transformers
  11. 9.11 Problems
  12. 9.12 Sources
4. 10 Energy Metering
  1. 10.1 Metering Intervals
  2. 10.2 General Metering Analysis using Symmetrical Components
  3. 10.3 Metering Errors
  4. 10.4 Ratio Correction Factors
  5. 10.5 Reactive Power Measurement Error
  6. 10.6 Evaluation of the Overall Error for an Installation
  7. 10.7 Commissioning and Auditing of Metering Installations
  8. 10.8 Problems
  9. 10.9 Sources
5. 11 Earthing Systems
  1. 11.1 Effects of Electricity on the Human Body
  2. 11.2 Residual Current Devices
  3. 11.3 LV Earthing Systems
  4. 11.4 LV Earthing Systems used Worldwide
  5. 11.5 Medium Voltage Earthing Systems
  6. 11.6 High Voltage Earthing
  7. 11.7 Exercise
  8. 11.8 Problems (Earthing Grid Design)
  9. 11.9 Sources
6. 12 Introduction to Power System Protection
  1. 12.1 Fundamental Principles of Protection
  2. 12.2 Protection Relays
  3. 12.3 Primary and Backup Protection (Duplicate Protection)
  4. 12.4 Protection Zones
  5. 12.5 Overcurrent Protection
  6. 12.6 Differential Protection
  7. 12.7 Frame Leakage and Arc Flash Busbar Protection
  8. 12.8 Distance Protection (Impedance Protection)
  9. 12.9 Problems
  10. 12.10 Sources
7. 13 Harmonics in Power Systems
  1. 13.1 Measures of Harmonic Distortion
  2. 13.2 Resolving a Non‐linear Current or Voltage into its Harmonic Components (Fourier Series)
  3. 13.3 Harmonic Phase Sequences
  4. 13.4 Triplen Harmonic Currents
  5. 13.5 Harmonic Losses in Transformers
  6. 13.6 Power Factor in the Presence of Harmonics
  7. 13.7 Management of Harmonics
  8. 13.8 Harmonic Standards
  9. 13.9 Measurement of Harmonics
  10. 13.10 Problems
  11. 13.11 Sources
8. 14 Operational Aspects of Power Engineering
  1. 14.1 Device Numbers
  2. 14.2 One Line Diagram (OLD)
  3. 14.3 Switchgear Topologies
  4. 14.4 Switching Plans, Equipment Isolation and Permit to Work Procedures
  5. 14.5 Electrical Safety
  6. 14.6 Measurements with an Incorrectly Configured Multimeter
  7. 14.7 Sources
Index
End User License Agreement

List of Tables

Chapter 01
1. Table 1.1 Voltage definitions.
2. Table 1.2 Typical distribution voltage ranges.
3. Table 1.3 Medium voltage levels.
Chapter 04
1. Table 4.1 Electric–magnetic analogy.
2. Table 4.2 Single‐phase and three‐phase transformer per‐unit comparisons.
3. Table 4.3 Per‐unit parameter evaluation.
4. Table 4.4 Short‐circuit and open‐circuit test results.
Chapter 05
1. Table 5.1 Lumped impedances and their symmetrical component equivalents.
2. Table 5.2 Maximum published fault level and sequence impedance data.
3. Table 5.3 Data for 110 kV:22 kV transformer impedance.
4. Table 5.4 Industrial substation: maximum fault levels (V = 1.1 pu).
5. Table 5.5 Impedance and fault level data.
Chapter 06
1. Table 6.1 Line data.
Chapter 07
1. Table 7.1 Measured phase voltages on an asymmetrically loaded Yy transformer without flux linkage.
2. Table 7.2 Measured phase voltages on a Yy transformer without flux linkage, incorporating a closed delta winding.
3. Table 7.3 Measured phase voltages on an asymmetrically loaded core type Yy transformer.
4. Table 7.4 Measured phase voltages on a core form Yy transformer incorporating a closed delta winding.
5. Table 7.5 Characteristics of different harmonics.
Chapter 08
1. Table 8.1 Voltage Transformer standard secondary voltages.
2. Table 8.2 Accuracy class limits for metering classes 0.1 – 3.0.
3. Table 8.3 Voltage transformer standard burdens as defined in IEC 61869‐3.
4. Table 8.4 Accuracy class limits for metering classes 0.15 to 1.2.
5. Table 8.5 Standard voltage transformer burdens.
6. Table 8.6 Measured error results from a 44 kV Class 0.5, 100 VA VT (graphed in Figures 8.9 and 8.10).
7. Table 8.7 Protective voltage transformer magnitude and phase error limits (IEC 61869‐3).
8. Table 8.8 Rated voltage factors (F_v) for single‐phase inductive VTs.
9. Table 8.9 IEEE Over‐voltage limits.
10. Table 8.10 Ferro‐resonance requirements for effectively earthed CVTs.
11. Table 8.11 Ferro‐resonance requirements for non‐effectively earthed CVTs (isolated neutral).
12. Table 8.12 VT error information.
13. Table 8.13 Impedance information.
14. Table 8.14 VT error information.
Chapter 09
1. Table 9.1 Metering class error limits.
2. Table 9.2 Metering class error limits for class 0.2S and 0.5S CTs.
3. Table 9.3 Accuracy class limits for metering classes 0.3–1.2.
4. Table 9.4 Accuracy class limits for metering classes 0.15 and 0.15S.
5. Table 9.5 Error limits for class P and PR CTs.
6. Table 9.6 Error limits for class PX and PXR CTs as prescribed in IEC 61869‐2.
7. Table 9.7 Error limits for class TPX, TPY and TPZ CTs.
8. Table 9.8 Limits of ratio error for class C and T protection CTs defined by IEEE C57.13.
9. Table 9.9 Standard burdens for relaying.
10. Table 9.10 Characteristics of a C200, 1200:5 multi‐tap CT.
11. Table 9.11 Harmonic error limits for electronic current transformers.
12. Table 9.12 Cable resistance/km.
13. Table 9.13 CT magnetising data.
Chapter 10
1. Table 10.1 CT error limits.
2. Table 10.2 VT error limits.
3. Table 10.3 IEC62053.22 Percentage error limits for polyphase meters with balanced loads.
4. Table 10.4 magnitude and phase errors and corresponding RCFs.
5. Table 10.5 Calculation of overall percentage error.
6. Table 10.6 IEEE C57.13 Transformer correction factors for voltage and current transformers.
7. Table 10.7 TCF limits for class 0.15 and 0.15S instrument transformers.
8. Table 10.8 Comparative data of new and old metering. (You may assume that each set of current transformers share the same errors, as do each set of voltage transformers.)
Chapter 11
1. Table 11.1 RCD sensitivities.
2. Table 11.2 LV earthing systems used worldwide.
3. Table 11.3 Actual transmission substation fault levels in an Australian transmission substation.
4. Table 11.4 MV earthing in some countries.
Chapter 12
1. Table 12.1 Inverse time‐current characteristic equations.
2. Table 12.2 Transformer impedances.
Chapter 13
1. Table 13.1 Harmonic phase sequences.
2. Table 13.2 Typical harmonic planning levels for low‐order, non‐triplen harmonics.
3. Table 13.3 Harmonic Spectrum.
4. Table 13.4 Harmonic calculations.
5. Table 13.5 K‐factor transformer ratings and applications.
6. Table 13.6 Common series resonant frequencies used for voltage support and PFC capacitors.
7. Table 13.7 LV and MV compatibility limits.
8. Table 13.8 MV, HV and EHV indicative planning limits.
9. Table 13.9 IEEE 519 Voltage harmonic distortion limits.
10. Table 13.10 IEEE 519 current distortion limits for system voltages between 120 V and 69 kV.
11. Table 13.11 Harmonic weighting factors for some common MV loads.
12. Table 13.12 Indicative emission limits for stage 2 assessments.
13. Table 13.13 Harmonic summation exponents.
Chapter 14
1. Table 14.1 Common IEEE C37.2 device numbers and their IEC 60617 equivalent symbols.
2. Table 14.2 Common acronyms defined in IEEE C37.2.
3. Table 14.3 Typical Australian limits of approach boundaries for AC shock prevention.

List of Illustrations

Chapter 01
1. Figure 1.1 Three‐phase alternating voltages.
2. Figure 1.2 (a) Typical distribution transformer winding arrangement (b) Low voltage representation.
3. Figure 1.3 Phase and line voltages.
4. Figure 1.4 Typical 230/400 V three‐phase supply.
5. Figure 1.5 Single‐phase transformer using a centre‐tapped winding.
6. Figure 1.6 Three‐phase four‐wire supply from a delta connected secondary winding.
7. Figure 1.7 Open delta configuration from two single‐phase transformers.
8. Figure 1.8 Corner grounded delta, or a grounded b phase system.
9. Figure 1.9 A 500 kVA pole‐mounted distribution transformer (China).
10. Figure 1.10 A 500 kVA ground‐mounted transformer (Australia).
11. Figure 1.11 (a) Transmitted power vs line length (b) Transmitted power vs system voltage.
12. Figure 1.12 Voltage profile of MV feeder trunk and spurs.
13. Figure 1.13 Recloser, bypass switches and isolator switches.
14. Figure 1.14 Radial MV network.
15. Figure 1.15 Sectionaliser or load break switch.
16. Figure 1.16 Three‐phase 22 kV autotransformer regulator.
17. Figure 1.17 Single‐phase 22 kV step regulators (open delta connection).
18. Figure 1.18 Open loop feed. (Extracted from Cahier Technique No. 203, ‘Basic selection of MV public distribution networks’ with kind permission from Schneider Electric).
19. Figure 1.19 11 kV ring main switchboard.
20. Figure 1.20 Circuit breaker and mimic diagram.
21. Figure 1.21 Medium voltage mesh network.
22. Figure 1.22 275 kV single circuit transmission tower (France).
23. Figure 1.23 400 kV dual circuit transmission tower (France).
24. Figure 1.24 Each tower provides a relatively short span, so many towers are required for a long line.
25. Figure 1.25 Fractional voltage drop as a function of the load power factor, for a constant VA load.
26. Figure 1.26 Annual electricity production by country. (Based on IEA data from © OECD/IEA 2016, IEA Energy Atlas, www.iea.org/statistics, Licence: www.iea.org/t&c; modified by the author).
27. Figure 1.27 Operational comparison between a base load machine and a frequency control machine.
28. Figure 1.28 Daily variations in a wind farm generation.
29. Figure 1.29 Typical photovoltaic solar installation performance.
Chapter 02
1. Figure 2.1 Three‐phase 50 Hz alternating voltages (T = 20 ms).
2. Figure 2.2 Definitions of sine and cosine functions.
3. Figure 2.3 Generation of time varying sinusoidal functions from rotary motion.
4. Figure 2.4 Phasor representation of an AC voltage.
5. Figure 2.5 Single phase circuit and its phasor representation.
6. Figure 2.6 (a) Phase voltages (b) Line voltages (c) Summation of voltages V_ab + V_bc.
7. Figure 2.7 Phasor representation of three‐phase balanced voltages and currents.
8. Figure 2.8 Capacitor construction.
9. Figure 2.9 Electric field distribution.
10. Figure 2.10 Polarisation of the dielectric by the applied electric field.
11. Figure 2.11 Capacitor voltage and current phasor diagram.
12. Figure 2.12 Inductor voltage and current phasor diagram.
13. Figure 2.13 Sign conventions.
14. Figure 2.13a Example circuit.
15. Figure 2.14 Thévenin equivalent network.
16. Figure 2.15 Norton equivalent network.
17. Figure 2.16 Circuit defining Millman’s theorem.
18. Figure 2.17 (a) Series circuit (b) Parallel circuit.
19. Figure 2.18 Series LRC phasor diagram.
20. Figure 2.19 Parallel LRC circuit phasor diagram.
21. Figure 2.20 (a) Inductive load equivalent circuit (b) Phasor representation.
22. Figure 2.21 Inductive load with power factor correction.
23. Figure 2.22 (a) Under‐compensated (b) Ideal compensation (c) Over‐compensated.
24. Figure 2.23 (a) AC bus Thévenin equivalent circuit (b) Capacitive loading of an AC bus.
25. Figure 2.24 Capacitive voltage rise. (Note: the voltage drops V_R and V_X have been considerably exaggerated in scale for reasons of clarity).
26. Figure 2.25 Simplified phase sequence indicator.
27. Figure 2.26 Phase sequence indicator phasor diagram.
28. Figure 2.27 I′ phasor diagram.
29. Figure 2.28 I″ phasor diagram.
30. Figure 2.29 Overall phasor diagram.
31. Figure 2.30 Sectional view of an induction furnace showing the arrangement of the furnace transformer. (Ref: ‘Industrial Electric Furnaces and Appliances’ Paschkis & Persson 1960).
32. Figure 2.31 Induction furnace schematic diagram.
33. Figure 2.32 Simplified furnace schematic.
34. Figure 2.33 Furnace, inductor and capacitor currents.
35. Figure 2.34 Phase current summations.
36. Figure 2.35 (a) Series tuned circuit (b) Phase diagram above resonance (c) Phase diagram at resonance.
37. Figure 2.36 (a) Parallel tuned circuit (b) Approximate parallel circuit
38. Figure 2.37 Normalised frequency response of a series resonant circuit with constant excitation.
39. Figure 2.38 Normalised frequency response of a parallel resonant circuit with constant excitation.
40. Figure 2.39 Upper and lower cut‐off frequency definition.
41. Figure 2.40 Parallel tuned circuit phasor diagram.
42. Figure 2.41 Diagram for question 1. (R = 230 Ω, L = 1.267 H, C = 8 μF)
43. Figure 2.42 Diagram for question 2. (R = 230 Ω, L = 1.267 H, C = 8 μF)
44. Figure 2.43 Star and delta connections.
45. Figure 2.44 Diagram for question 5. (R = 10 ohms, X_L = 40 ohms)
46. Figure 2.45 Series and parallel circuit equivalence.
47. Figure 2.46 Two inductor furnace simplified schematic diagram.
48. Figure 2.47 Parallel resonant circuit.
49. Figure 2.48 Improved phase sequence detector.
Chapter 03
1. Figure 3.1 Active power waveform: . (V_RMS = 230 V, I_RMS = 1 A and ϕ = 60°).
2. Figure 3.2 Instantaneous V(t)I(t) product (bottom trace). (V_RMS = 230 V_, I_RMS = 1 A, ϕ = 60° lagging).
3. Figure 3.3 Reactive power waveform: V_RMSI_RMS sin(ϕ)sin(2ωt). (V_RMS = 230 V, I_RMS = 1 A and ϕ = 60°).
4. Figure 3.4 Inductive voltage, current and power waveforms.
5. Figure 3.5 Capacitive voltage, current and power waveforms.
6. Figure 3.6 Resistive voltage, current and power waveforms.
7. Figure 3.7 In‐phase and quadrature current components.
8. Figure 3.8 Power triangle.
9. Figure 3.9 Inductive load with power factor correction.
10. Figure 3.10 Phasor diagram.
11. Figure 3.11 (a) PFC control relay (b) Low voltage PFC cabinet.
12. Figure 3.12 LV customer load profile and power factor.
13. Figure 3.13 Final PF versus the percentage of the original reactive load corrected.
14. Figure 3.14 Small low voltage industrial customer’s load profile.
15. Figure 3.15 Typical large industrial load profile.
16. Figure 3.16 Power flows in the 4th quadrant are defined as positive.
17. Figure 3.17 Power flow definitions from the perspective of the load.
18. Figure 3.18 Highest daily consumption profile.
19. Figure 3.19 Highest weekly consumption profile.
20. Figure 3.20 Unbalanced three‐phase load.
Chapter 04
1. Figure 4.1 Magnetic circuit.
2. Figure 4.2 (a) Non‐laminated core (b) Laminated core.
3. Figure 4.3 Electrical and magnetic circuits.
4. Figure 4.4 A magnetic circuit containing an air gap.
5. Figure 4.5 Air gap fringing flux.
6. Figure 4.6 (a) 22 kV power factor correction de‐tuning reactor (b) Distributed air gaps. (Note that the reactor core in (a) is insulated from the ground and is connected to the midpoint of the inductor winding. Also, the laminated ‘packets’ in (b) provide multiple small gaps throughout the core, minimising the effects of fringing).
7. Figure 4.7 B–H characteristics of grain oriented silicon steel as a function of the peak flux density.
8. Figure 4.8 Magnetising current and voltage for a small current transformer operating at 0.2 tesla.
9. Figure 4.9 Equivalent circuit of an iron‐cored reactor.
10. Figure 4.10 Magnetising current and voltage for a small current transformer operating at 1.7 tesla.
11. Figure 4.11 ‘C’ core and three‐limb ‘E’ core structures containing butt joints.
12. Figure 4.12 Small toroidal power transformer (left) and toroidal 200:5 amp current transformer (right).
13. Figure 4.13 Distributed gap unicores.
14. Figure 4.14 Section of a 500 kVA stacked core three‐phase transformer core (left) Enlarged view (photographed through oil) showing the interleaving of vertical and horizontal laminations (right).
15. Figure 4.15 Typical GOSS active and reactive magnetising loss.
16. Figure 4.16 An unloaded transformer where only magnetising current flows in the primary winding.
17. Figure 4.17 Magnetising phasor diagram.
18. Figure 4.18 Constant flux transformer operation.
19. Figure 4.19 Flux balance phasor diagram. (Note: the magnetising current has been omitted for reasons of clarity).
20. Figure 4.20 Primary phasor diagram (loaded).
21. Figure 4.21 Two‐winding transformer equivalent circuit.
22. Figure 4.22 Leakage flux paths permit a portion of the flux created by one winding to avoid linking the other.
23. Figure 4.23 Transformer equivalent circuit as seen from the primary side. (Component values are usually expressed in terms of per‐unit quantities).
24. Figure 4.24 Phasor diagram of a loaded transformer.
25. Figure 4.25 Busbar mounted 2000:5 metering class current transformers.
26. Figure 4.26 Current transformer configuration.
27. Figure 4.27 Current transformer primary phasor diagram.
28. Figure 4.28 Magna‐bend magnetic bending machine. (1: Magnet body, 2: Clamp bar, 3: Bending beam)
29. Figure 4.29 Magna‐bend ‘U’ type electromagnet construction.
30. Figure 4.30 Magnetisation characteristics mild steel.
31. Figure 4.31 Electrical analogy of the magnetic circuit.
32. Figure 4.32 Measured clamping pressure as a function of sheet thickness.
33. Figure 4.33 Load profile.
34. Figure 4.34 Only a portion of the flux generated by winding 1 links winding 2, and vice versa.
35. Figure 4.35 I₂ definition.
36. Figure 4.36 Transformer equivalent circuit.
37. Figure 4.37 (a) Typical distribution transformer winding arrangement (partially disassembled) (b) The world’s first transformer, Budapest 1885.
38. Figure 4.38 Transformer per‐unit equivalent circuit.
Chapter 05
1. Figure 5.1 Incorrect representation of negative sequence voltages.
2. Figure 5.2 Correct representation and addition of positive and negative phase sequence voltages.
3. Figure 5.3 Zero‐sequence phasors.
4. Figure 5.4 Showing , and therefore .
5. Figure 5.5 (a) Resolution of unbalanced voltages (b) Symmetrical components.
6. Figure 5.6 Resolution of the ‘a’ phase fault voltage and current into symmetrical components.
7. Figure 5.7 Diagram of the ‘a’ phase positive sequence network Thévenin equivalent circuit.
8. Figure 5.8 Diagram of the ‘a’ phase negative sequence network.
9. Figure 5.9 Phase‐to‐ground fault, boundary conditions: V_a = 0, I_c = 0 and I_b = 0.
10. Figure 5.10 Positive sequence network connection for the phase‐to‐ground fault.
11. Figure 5.11 Phase‐to‐ground fault: current phasor diagram.
12. Figure 5.12 Construction of phase ‘b’ and ‘c’ voltages from sequence components.
13. Figure 5.13 Phase‐to‐phase fault.
14. Figure 5.14 Phase‐to‐phase fault sequence network connection.
15. Figure 5.15 Phase‐to‐phase fault, current phasor diagram.
16. Figure 5.16 Phase voltages resulting from the phase‐to‐phase fault.
17. Figure 5.17 Phase‐to‐phase‐to‐ground fault.
18. Figure 5.18 Phase‐to‐phase‐to‐ground fault sequence network connection.
19. Figure 5.19 (a) Phase ‘b’ fault currents (b) Phase ‘c’ fault currents.
20. Figure 5.20 Three‐phase fault. (Note: ).
21. Figure 5.21 (a) Measurement of residual current (b) Measurement of residual voltage.
22. Figure 5.22 Neutral displacement voltage, V_0.
23. Figure 5.23 Star connected phase‐to‐ground fault reflected into a delta connected winding.
24. Figure 5.24 Star connected phase‐to‐phase fault reflected into a delta connected winding.
25. Figure 5.25 Radial Feeder: positive sequence voltage gradient.
26. Figure 5.26 Radial Feeder: negative sequence voltage gradient.
27. Figure 5.27 Simplified bus arrangement.
28. Figure 5.28 Feeder arrangement.
29. Figure 5.29 Negative sequence filter block diagram.
30. Figure 5.30 (a) ‘B’ phase inductive high pass filter (b) ‘C’ phase capacitive low pass filter.
31. Figure 5.31 Gyrator‐based RL filter (Phase B).
32. Figure 5.32 Complete negative sequence filter.
33. Figure 5.33 Zero‐sequence filter.
34. Figure 5.34 Generation of an unbalanced three‐phase supply.
Chapter 06
1. Figure 6.1 Synchronous machine connected to a bus, V_B.
2. Figure 6.2 Phasor diagram of an idling synchronous machine.
3. Figure 6.3 Under‐excited synchronous machine.
4. Figure 6.4 Over‐excited synchronous machine (synchronous condenser operation).
5. Figure 6.5 (a) ASEA synchronous condenser (b) 33 kV static voltage support capacitor.
6. Figure 6.6 Synchronous motor phasor diagram.
7. Figure 6.7 Four‐quadrant operation of a synchronous machine.
8. Figure 6.8 Dual node equivalent network and phasor diagram.
9. Figure 6.9 Line model and phasor diagram.
10. Figure 6.10 Line voltage drop as a function of load PF, for X/R = 8.0, 1.6 and 0.33 (1 pu load).
11. Figure 6.11 Transmission line, phase shifting transformer and associated phasor diagram.
12. Figure 6.12 Composite phase shifting transformer, 132 kV, 200 MVA (Armidale, Australia).
13. Figure 6.13 P–V curve.
14. Figure 6.14 Q–V curve.
15. Figure 6.15 Lossless line phasor diagram.
16. Figure 6.16 Schematic.
Chapter 07
1. Figure 7.1 (a) 110 kV:33 kV, 60 MVA transformer (b) 22 kV:400 V, 100 kVA transformer.
2. Figure 7.2 Core arrangement and leakage flux paths.
3. Figure 7.3 Flux cancellation in the centre limb.
4. Figure 7.4 (a) Very early core form distribution transformer (5 kV:120 V, 150 kVA – the third phase lies behind the other two) (b) A partially dissected core form transformer.
5. Figure 7.5 (Three‐limb core form on the left and five‐limb shell form on the right). Three‐phase core and shell form magnetic circuits.
6. Figure 7.6 Zigzag connected earthing transformer and phasor representation.
7. Figure 7.7 Vector grouping for the Dyn11 connection.
8. Figure 7.8 Zigzag vector group, Dz6.
9. Figure 7.9 Some common vector groupings.
10. Figure 7.10 Transformer regulation as a function of power factor, for a 1 pu load.
11. Figure 7.11 Presence of a zero‐sequence voltage (V₀), shifts the star point from N to N′.
12. Figure 7.12 Magnetising current, flux density and voltage waveforms in a single‐phase transformer.
13. Figure 7.13 Magnetising waveforms for a shell form star connected transformer.
14. Figure 7.14 Presence of a third harmonic voltage in each phase winding causes the star point to oscillate at the third harmonic.
15. Figure 7.15 Magnetising waveforms in shell type transformer incorporating a delta connected winding.
16. Figure 7.16 Magnetising characteristics of a core type transformer with an isolated neutral. (Note that the magnetising current contains significant levels of the 5th and very little 3rd harmonic).
17. Figure 7.17 Magnetising characteristics for a delta connected winding.
18. Figure 7.18 Measured inrush current waveforms.
19. Figure 7.19 Off‐load tap‐change arrangements.
20. Figure 7.20 (a) Resistive tap‐changer (b) Reactive tap‐changer (both shown in the bridging position).
21. Figure 7.21 Tap changer selector and diverter switches.
22. Figure 7.22 Resistive tap‐change flag cycle operating sequence.
23. Figure 7.23 Phasor diagram corresponding to the flag cycle tap‐change sequence.
24. Figure 7.24 Tapping sequence vacuum interrupter based diverter switch.
25. Figure 7.25 Common tap winding connections.
26. Figure 7.26 Typical tapping winding configuration.
27. Figure 7.27 Left: diverter switch drum, Right: transition resistors.
28. Figure 7.28 Diverter switch contacts (open) inside the diverter drum.
29. Figure 7.29 High speed resistive tap‐changers.
30. Figure 7.30 Parallel transformer equivalent circuit.
31. Figure 7.31 Parallel transformer circulating current.
32. Figure 7.32 Voltage set‐point and bandwidth.
33. Figure 7.33 Example of a transformer nameplate.
34. Figure 7.34 (a) Eaton Cooper Power series VR‐32 step voltage regulator.
35. Figure 7.35 Typical pole‐mounted installation (open delta connection). (Note the pole top bypass and isolation switches).
36. Figure 7.36a Type ‘A’ regulator.
37. Figure 7.36b Type ‘B’ regulator.
38. Figure 7.37 (a) Simplified schematic of an Eaton 32 step regulator (b) Single‐phase two‐wire regulator connection.
39. Figure 7.38 Combined diverter‐selector switch.
40. Figure 7.39 Reversing switch.
41. Figure 7.40 Tap changer in non‐bridging and bridging positions.
42. Figure 7.41 The tap‐changer reactor. (The copper strap connects turns interleaved on one leg with those on the other).
43. Figure 7.42 (a) Four‐wire wye connection. (b) Phasor diagram. (Illustrations courtesy of Eaton).
44. Figure 7.43 (a) Two regulator open delta connection (b) Phasor diagram (Illustrations courtesy of Eaton).
45. Figure 7.44 (a) Three regulator, closed delta connection (b) Phasor diagram
46. Figure 7.45 Line drop compensation.
47. Figure 7.46 Phase shift transformer nameplate.
48. Figure 7.47 Phase shift transformer nameplate, continued.
49. Figure 7.48 Quadrature phase shifting.
50. Figure 7.49 Equivalent circuit of phase shifting transformer. (V_L* = Load voltage when I_L = 0, V_S = source voltage and V_q = quadrature voltage).
51. Figure 7.50 Effect of a lagging load current I on the terminal voltage V_L.
52. Figure 7.51 Overall phase shift becomes more lagging as a result of load current, I.
53. Figure 7.52 Single‐phase equivalent circuit.
54. Figure 7.53 Inclusion of the circulating current, i_c.
Chapter 08
1. Figure 8.1 Three‐winding 11 kV VT together with its nameplate.
2. Figure 8.2 (a) A 220 kV capacitive voltage transformer (CVT) (b) CVT equivalent circuit.
3. Figure 8.3 Open delta connection for the detection of residual voltages.
4. Figure 8.4 Magnitude and phase error limits for classes 0.2, 0.5 and 1.0.
5. Figure 8.5 Voltage transformer ratio correction factor and phase error limits.
6. Figure 8.6 Simplified voltage transformer equivalent circuit, including inductive burden.
7. Figure 8.7 VT secondary circuit phasor diagram.
8. Figure 8.8 Class 1.0 voltage transformer magnitude and phase errors (UPF burden).
9. Figure 8.9 Error line corresponding to the VT whose errors appear in Figure 8.8.
10. Figure 8.10 Error lines for the VT whose error results are shown in Table 8.6. (This illustration is also known as a circle diagram or a fan diagram).
11. Figure 8.11 Re‐rating a Class 1 VT to Class 0.5 over a restricted range of burdens.
12. Figure 8.12 Neutral shift voltage resulting from an earth fault.
13. Figure 8.13 Ungrounded network.
14. Figure 8.14 (a) CVT off frequency damping (b) CVT spark gap, saturable inductor damping.
15. Figure 8.15 Capacitive coupling between windings and ground in a voltage transformer.
16. Figure 8.16 VT failure – note the lack of HV fusing, the thermal damage to the left‐hand VT and the carbon condensate damage throughout the cubicle.
17. Figure 8.17 (a) RC voltage divider sensor (b) RC differential voltage sensor.
18. Figure 8.18 Diagram for question 1. (C₁ = 0.0192 μF, C₂ = 0.078 μF, V₁ = 110 kV/√3, f = 50 Hz, the output voltage is 110v/√3 and rated burden of the CVT is 150 VA).
19. Figure 8.19 Variation of magnitude and phase errors with burden power factor.
Chapter 09
1. Figure 9.1 220 kV pedestal CT.
2. Figure 9.2 A 15 VA, Class 1, 600,400,200:5 toroidal bushing CT.
3. Figure 9.3 (a) Four wire connection (b) Residual current connection.
4. Figure 9.4 Busbar mounted multi‐tap metering CTs (3000, 2000, 1000:5, 15 VA).
5. Figure 9.5 Current transformer limits of accuracy as prescribed by IEEE C57.13.
6. Figure 9.6 Comparison of CT specifications (primary circuit pf = 0.6).
7. Figure 9.7 CT equivalent circuit.
8. Figure 9.8 CT phasor diagram. (Note: The magnetising current components have been considerably enlarged for clarity).
9. Figure 9.9 Simplified CT phasor diagram.
10. Figure 9.10 Magnetising admittance of a 200:5 CT (GOSS core).
11. Figure 9.11 Magnetising conductance and susceptance for the composite 200:5 CT shown in Figure 9.12a.
12. Figure 9.12 (a) Composite core construction, 200:5 CT (b) Turns compensated 200:5 CT.
13. Figure 9.13 A 100/50/25:5, 15 VA wound primary metering CT (photographed through oil).
14. Figure 9.14 Typical non‐linear CT current waveforms approaching the knee point.
15. Figure 9.15 In‐phase and quadrature magnetising current components.
16. Figure 9.16 Evaluation of composite error using a reference CT of the same ratio as the DUT.
17. Figure 9.17 Improved composite error test arrangement.
18. Figure 9.18 Security factor as a function of the applied burden for the CT in the example above.
19. Figure 9.19 Knee point voltage definitions according to IEC 61869‐2 (upper) and IEEE C57.13 (lower).
20. Figure 9.20 (a) Transient fault current waveform (b) Flux waveform AC and DC components.
21. Figure 9.21 Typical magnetising characteristics for a multi‐tapped, non‐gapped, class C transformer.
22. Figure 9.22 (a) Class C CT voltage classifications (b) Typical Class T overcurrent ratio curves.
23. Figure 9.23 (a) Series CT connection (b) Parallel CT connection.
24. Figure 9.24 Rogowski coil current measurement.
25. Figure 9.25 Optical sensor applied to a GIS busbar.
26. Figure 9.26 (a) Hall effect (b) Zero flux current measurement.
27. Figure 9.27 Magnetising admittance characteristics.
28. Figure 9.28 Precise measurement of CT turns ratio.
29. Figure 9.29 (a) Primary injection testing of a metering class current transformer. (LHS: CT under test; background transformer: multi‐tapped reference CT. RHS: digital comparators.) (b) Simplified equivalent circuit of the Petch–Elliott current transformer test set.
30. Figure 9.30 In‐phase and quadrature components of spill current.
31. Figure 9.31 Currents in primary and secondary. (Magnitude error at 20 times primary current ≈ 5%).
32. Figure 9.32 (a) Split core current transformer (b) Cable mounted split core CT.
Chapter 10
1. Figure 10.1 Single‐phase electricity meter, circa 1900 (minus its case).
2. Figure 10.2 Meter registers – note the patent dates.
3. Figure 10.3 Four‐wire, three element HV metering connection, including the test block.
4. Figure 10.4 Definition of voltages with respect to the arbitrary node ‘x’.
5. Figure 10.5 Three‐wire metering angle definitions.
6. Figure 10.6 Simplified three‐wire connection phasor diagram.
7. Figure 10.7 Three‐wire (two‐element) metering connection.
8. Figure 10.8 Pole‐mounted current and voltage metering transformer.
9. Figure 10.9 Form 2S Metering Configuration (USA).
10. Figure 10.10 Metering installation for 2½ element metering, and its phasor diagram.
11. Figure 10.11 Balanced voltages and unbalanced phase currents.
12. Figure 10.12 Power flow definitions from the perspective of the load.
13. Figure 10.13 Technique of 90° phase shifting for VAr measurement.
14. Figure 10.14 Two‐element metering, overall error weighting factors.
15. Figure 10.15 Angle definitions.
16. Figure 10.16 IEEE C57.13 metering class accuracy limits: VT (left) and CT (right).
17. Figure 10.17 Typical variations in active overall error with load power factor.
18. Figure 10.18 Typical metering test block, cover removed. (The CT links are on the left, and colour coded voltage terminals are on the right).
19. Figure 10.19 MV/LV distribution transformer.
20. Figure 10.20 Active energy correction factor, k as a function of load power factor.
21. Figure 10.21 Reactive energy correction factor, K as a function of load power factor.
22. Figure 10.22 Negative B phase metering.
23. Figure 10.23 S vectors for a three‐element metering installation.
24. Figure 10.24 S vectors for three‐ and two‐element metering installations for a balanced load.
25. Figure 10.25 S vectors for three‐ and two‐element metering installations with an unbalanced load.
Chapter 11
1. Figure 11.1 Let‐go current distribution (60 Hz) (IEC 40679).
2. Figure 11.2 Electrocardiogram (IEC 60479).
3. Figure 11.3 Ventricular fibrillation and loss of blood pressure.
4. Figure 11.4 AC & DC ventricular fibrillation current threshold vs shock duration.
5. Figure 11.5 Body resistance (ohms) vs touch voltage for hand‐to‐hand or hand‐to‐foot current paths.
6. Figure 11.6 Time–current zones for AC.
7. Figure 11.7 Maximum duration of permissible LV touch voltages. (Curve L: Corresponds to a maximum sustained touch voltage, U_Lt = 50 V, for normal operation, Curve Lp: maximum sustained touch voltage, U_Lt = 25 V, for particular situations; generally wet areas) (Based on Figure C2, IEC TR 61200‐413, Copyright © 1996 IEC Geneva, Switzerland. www.iec.ch.
8. Figure 11.8 Curves Lp and L: maximum duration of permissible touch voltage.
9. Figure 11.9 RCD operating principle. (Extracted and modified from Cahier Technique No 114, Residual Current Devices in LV with kind permission from Schneider Electric).
10. Figure 11.10 RCD trip time vs ground fault current in multiples of I_Δn, for general and type S RCDs.
11. Figure 11.11 A 30 mA RCD used to protect socket outlet circuits.
12. Figure 11.12 TT earthing system.
13. Figure 11.13 Left: An RCD current transformer on an LV circuit breaker; I_Δn = 300 mA. Right: An RCD current transformer on an 11 kV feeder. (Note that since the 11 kV cable sheaths pass through the CT, then in order to remove the effect of any sheath current, the sheath earth conductors must pass back through the CT in the opposite direction).
14. Figure 11.14 TN earthing system.
15. Figure 11.15 Earth fault loop definition.
16. Figure 11.16 (a) TN‐C earthing system (common PEN conductor) (b) TN‐S earthing system (separate neutral and earth conductors) (c) TN‐C‐S earthing system (TN‐C followed by TN‐S).
17. Figure 11.17 MEN switchboard arrangement (AS/NZS 3000:2007)).
18. Figure 11.18 IT earthing system: first fault generates no hazardous touch voltages.
19. Figure 11.19 IT earthing system: phase‐to‐ground fault.
20. Figure 11.20 Second fault on an IT earthed LV network.
21. Figure 11.21 Transferred potential from an MV fault to the LV network.
22. Figure 11.22 MV earthing requirements adopted in France (TT System). (Extracted from Cahier Technique No 172, System Earthing in LV with kind permission from Schneider Electric).
23. Figure 11.23 Capacitive fault currents in an unearthed MV transformer.
24. Figure 11.24 Resonant earthing system and phasor diagram.
25. Figure 11.25 Step and touch potentials.
26. Figure 11.26 Transfer potential developed between a fence and a remote earth.
27. Figure 11.27 Network configuration.
28. Figure 11.28 Earth grid design process.
29. Figure 11.29 Initial grid plan and ground potential profile.
30. Figure 11.30 Revised earth grid design.
Chapter 12
1. Figure 12.1 English Electric electromechanical IDMT overcurrent relay element and plug board from the 1960s.
2. Figure 12.2 X and Y protection: Schneider P546 and Schweitzer 311 L numerical relays.
3. Figure 12.3 Zones of protection.
4. Figure 12.4 Restricted earth fault (REF) unit protection scheme.
5. Figure 12.5 Relay time‐current characteristics.
6. Figure 12.6 Family of standard inverse tripping curves (0.1 ≤ TMS ≤ 1.0).
7. Figure 12.7 (a) Two‐phase overcurrent and earth fault connection (b) Three‐phase overcurrent and earth fault connection.
8. Figure 12.8 Parallel connected feeders.
9. Figure 12.9 Maximum torque angle.
10. Figure 12.10 (a) The 90‐30° connection (b) The 90–45° connection.
11. Figure 12.11 Basic differential protection.
12. Figure 12.12 Transformer differential protection.
13. Figure 12.13 Biased differential protection.
14. Figure 12.14 Bias characteristic for an AREVA KBCH transformer differential protection relay.
15. Figure 12.15 REF comparison of secondary and primary fault currents (impedance earthed system).
16. Figure 12.16 Delta winding REF protection.
17. Figure 12.17 (a) Bus‐zone earth fault protection (b) Bus‐zone phase and earth fault protection.
18. Figure 12.18 Through‐fault operation of high impedance bus‐zone protection.
19. Figure 12.19 Current and position information supplied to a numerical relay.
20. Figure 12.20 (a) Sectionalised frame leakage protected bus (b) Frame leakage CTs.
21. Figure 12.21 Typical two bus frame leakage arrangement.
22. Figure 12.22 (a) Impedance circle (b) Characteristic of a directional impedance relay.
23. Figure 12.23 The ‘mho’ characteristic.
24. Figure 12.24 (a) Zones of protection (b) Lenticular mho characteristic.
25. Figure 12.25 The quadrilateral impedance characteristic.
26. Figure 12.26 (a) Phase‐to‐ground fault (b) Comparison of zero‐sequence networks.
27. Figure 12.27 Faulted cable in a resonant earthed system.
28. Figure 12.28 Discrimination between faulted and un‐faulted feeders.
29. Figure 12.29 One line diagram.
30. Figure 12.30 Primary and secondary CT connections.
31. Figure 12.31 MCAG14 operating characteristic.
Chapter 13
1. Figure 13.1 (a) Personal computer current and voltage waveforms (b) Current harmonic spectrum.
2. Figure 13.2 Square waveform.
3. Figure 13.3 Triangular waveform.
4. Figure 13.4 Half wave rectified current.
5. Figure 13.5 (a) Simplified power triangle in the presence of harmonics (b) Modified power triangle.
6. Figure 13.6 Distortion power factor variation with current THD.
7. Figure 13.7 Three‐phase bridge rectifier and voltage waveforms.
8. Figure 13.8 Star connected three‐phase rectifier line voltages, line current and harmonic spectrum.
9. Figure 13.9 Typical construction of a twelve‐pulse rectifier.
10. Figure 13.10 A 20 kA inter‐phase transformer used in a small electrolytic zinc plant.
11. Figure 13.11 Harmonic cancellation in a twelve pulse rectifier.
12. Figure 13.12 (a) Typical schematic for a harmonic filter (b) Single‐phase equivalent circuit.
13. Figure 13.13 Impedance plot of a 50 Hz single stage HV 5th harmonic filter.
14. Figure 13.14 Frequency response of a 50 Hz four‐stage MV harmonic filter and load.
15. Figure 13.15 Active harmonic filter operation.
16. Figure 13.16 (a) Site disturbance levels (b) Global disturbance levels (IEC/TR 61000‐3‐6 ed.2.0 Copyright © 2008 IEC Geneva, Switzerland. www.iec.ch).
17. Figure 13.17 Pump motor supply.
18. Figure 13.18 Division of harmonic currents.
Chapter 14
1. Figure 14.1 One Line Diagram of a small hydro generating station.
2. Figure 14.2 Part of an urban aerial switchyard.
3. Figure 14.3 (a) 220 kV Dead tank circuit breaker (b) Live‐tank circuit breakers (left) and associated current transformers (right).
4. Figure 14.4 Double bus 145 kV GIS switchgear.
5. Figure 14.5 Left: A single bus 11 kV vacuum circuit breaker, withdrawn from its cubicle. Right: Circuit breaker: busbar contacts (foreground), vacuum interruption canisters (background).
6. Figure 14.6 Single bus arrangement.
7. Figure 14.7 Sectionalised bus.
8. Figure 14.8 (a) MV double bus configuration (b) 11 kV double bus switchboard.
9. Figure 14.9 Double bus 145 kV GIS switchgear.
10. Figure 14.10 Cross‐sectional view of part of an aerial substation and its corresponding OLD.
11. Figure 14.11 Aerial switchyard double bus arrangement.
12. Figure 14.12 Breaker‐and‐a‐half bus configuration.
13. Figure 14.13 MV ring bus.
14. Figure 14.14 Main and transfer bus configuration.
15. Figure 14.15 (a) Sub‐optimal load configuration (b) Improved load configuration.
16. Figure 14.16 (a) Normal bus operation (b) LH feeder OOS, bus sections A and B overloaded.
17. Figure 14.17 A 3500 A LV circuit breaker, withdrawn from its cubicle in the isolated position.
18. Figure 14.18 (a) Resistive 11/22 kV test stick (b) ‘Modiewark’ voltage detector.
19. Figure 14.19 Lock box secured with two personal safety locks.
20. Figure 14.20 Limits of approach boundaries (NFPA 70E®).
21. Figure 14.21 Arc damage, 6″ × 2″ busbar. Fault current: 30 kA for 600 ms.
22. Figure 14.22 (a) Equivalent circuit (b) Phasor diagram (c) Variations in arc voltage and current.
23. Figure 14.23 Category 4 arc flash PPE.
24. Figure 14.24 Low voltage CT chamber.
25. Figure 14.25 Three multimeter configurations (a) correct (b) incorrect (c) potentially dangerous.

AC Circuits and Power Systems in Practice